I need help understanding these problems.
Answers
Answer: 7. x= 26, 9. x=11/y=3
Step-by-step explanation: Sorry for the terrible photo quality. Comment if you need more help : )
So, for the first examples given set all of the equations as equal to the other angle equation given.For problems like number 9, solve for the x's first (or whichever variable there's more of) you should solve for the x's like you did for the first problem, then set the equation to an A+B=180 format. The reason for this is two angles (in some cases more) on a straight line together will always equal 180 degrees. For 10. set the equations with x in them to that A+B=180 format. Then once you've found x plug it into 6x-7. When you have that answer set 8y+17 equal to the answer you got and solve for y.For 11 and 12. These ones can be a bit more complicated because of their visual appearance, however you just need to combine the earlier steps taken to solve the first couple of equations. Beginning with 12. If you ever see a Z pattern, know that the sides facing > and < ( the inside angles of the Z) are equal to each other. So you set the equations with x equal to each other, and once you get x plug it into the equation inside of the triangle. Since you've already been given 90, set the equation up like this: 43+90+(7y-20)=180. Because all the angles in a triangle are equal to 180 degrees. Then just solve for y. y=9Lastly for number 11. This one is by-far the hardest of all of them. You have to adjust how you look at the problem. You'll see that if you add (3x+49) it's actually congruent to (7x-23). once you figure out x you should then plug x into 3x giving you 54. The set up the equation like this 11y-1=54. That will give you y=5.
Related Questions
Two friends, Andrew and Liz, are playing a game using this spinner. If the spinner lands on region 1, Andrew wins. If it lands on region 2, Liz wins. If it lands on region 3, nobody wins. Is this a fair game?
Answers
Answer:
Based on the information provided, it does not seem like this game is fair. Since region 1 and region 2 are the same size, each player has an equal chance of winning, but since region 3 is significantly larger than the other regions, neither player has a high chance of winning. This means that one player could potentially win multiple times in a row just by luck, without the other player having a chance to catch up. In order for the game to be considered fair, the relative sizes of the regions should be such that each player has a roughly equal chance of winning.
Answer:
yes. they both have ⅓ chance of winning
Step-by-step explanation:
Which of the following is a subspace of R^3? (A) All vectors of the form(0, a, a^2), (B) All vectors of the form(a+2, a, 0), (C) All vectors of the form (a, b, 2), (D) All vectors of the form(a, b, a-2b)
Answers
All vectors of the form(a, b, a - 2b) is a subspace of R³. So, the correct option is option(D).
Subspace:If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if
If u and v are vectors in W, then u + v in W. ku is in W if k is any scalar and u is any vector in W.Now, check the options and find out the option which satisfy the subspace conditions.
A) All the vectors are of form (0, a,a²)
let (0,1,1) = u and v=(0,2,4) and both are belongs to { 0, a,a² : a∈R }, (0,0,0)∈ {0, a,a² : a∈R }.
u + v = (0,1,1) + (0,2,4) = (0,3, 5) not belongs to
{ 0, a,a² : a∈R }. So, this is not correct option.
B) Here, (0,0,0) does not belongs to
{0, a, a+2 : a∈R } because if a= 0 then a+2 =/ 0 .
So, it is also not subspace.
C) All vectors of the form (a, b, 2)
The third tuple is 2 which never be equal to zero. Hence, (0,0,0) does not belongs to (a, b, 2) and it is not form subspace.
D) All vectors of the form (a, b, a - 2b)
When a = 0 , b = 0 => (0,0,0) ∈(a, b, a - 2b)
let u = ( a1, b1 , a1- 2b1) and v = ( a₂, b₂ , a₂ - 2b₂)
and α∈R
u + v = ( a₁, b₁ , a₁- 2b₁ ) + ( a₂, b₂ , a₂ - 2b₂)
= ( a₁ +a₂ , b₁+b₂ , a₁+a₂ -2(b₁ - b₂)) €(a, b, a - 2b)
αu = α(a₁ , b₁ , a₁- 2b₁)
=( αa₁ , αb₁ , α(a₁ - 2b₁))∈(a, b, a - 2b)
both the conditions are satisfied, so it is Subspace of R³.
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A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?
Answers
following algorithms correctly updates the values, If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.
What is algorithm ?An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially.The game records the highest and lowest scores that were earned. This indicates that the game already has the highest and lowest score stored in its memory.
Now, if a new score, num, is achieved, the game must compare num with the minimum and maximum scores in order to update the minimum and maximum scores. The minimum score is updated to the score, num if the most recent score, num, is lower than the minimum score.
Additionally, the maximum score is updated to the score, num if the most recent score, num, is higher than the maximum score.
Complete Question :
A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?
If num is greater than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num. If num is less than the minimum, set the minimum equal to num. Otherwise, if num is less than the maximum, set the maximum equal to num. If num is greater than the minimum, set the minimum equal to num. Otherwise, if num is less than the maximum, set the maximum equal to num.To learn more about algorithm refer,
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A quiz team of 5 children is to be selected from a class of 25 children. There are 15 girls and 10 boys in the class. (a) How many teams made up of 3 girls and 2 boys can be selected? (b) How many teams can be selected with at least 3 girls?
Answers
Using combination we get 20475 teams can made up of 3 girls and 2 boys and 37128 teams can be selected with at least 3 girls.
Why does combination mean?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.Since this is just a team of 5 children,
we have no of girls = 15
No of boys = 10
teams made up of 3 girls and 2 boys
girls out of 3 girls can be selected in ¹⁵C₃ ways and
2 boys out of 10 boys can be selected in ¹⁰C₂ ways.
[tex]\implies[/tex] ¹⁵C₃ X ¹⁰C₂
= 455*45 =20475 Ways
Teams can be selected with at least 3 girls
It is the probability of at least 3 girls which means P(3 girls,2 boys) or P(4 girls,1 boy) or P(5 girls, 0 boys)
[tex]\implies[/tex] ¹⁵C₃ X ¹⁰C₂ + ¹⁵C₄ X ¹⁰C₁ + ¹⁵C₅ X ¹⁰C₀
= 455 * 45 +1365*10+3003*1
=20475 +13650 +3003
=37128 ways
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Angel wants to invest $4,000.00 in a savings account.
Determine the simple interest rate required for Angel's investment to grow to $13,400.00 in 25 months.
Round your answer to the nearest tenth of a percent and don't forget to include a percent sign, %, in
your answer.
The interest rate required to grow the investment to $13,400.00 is ______
Answers
The interest rate required to grow the investment to $13,400.00 would be = 35%
What is simple interest?Simple interest is the amount of money that is received for a particular period of time due to an investment made to an account.
The principal amount = $4,000.00
The time for investment = 25 months = 2 years
The simple interest = 13,400 - 4000= $9400
The rate (R) = X
The formula for simple interest=
p×t×r/100
9400= 13,400× 2×r/100
Make R the subject of formula;
R = 9400×100/13400×2
R = 940000/ 26800
R= 35%
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Data collected on the discharge of the Colorado River and the speed are given in the table:
Discharge (ft3) Speed
1.3 2.3
2.2 0.99
5.8 3.5
11 5
12 16
14 22
16 27
21 14
49 33
51 35
What is the value of the correlation coefficient and its interpretation?
0.76; There is a strong, positive association between discharge and speed.
0.87; There is a strong, positive association between discharge and speed.
−0.76; There is a strong, negative association between discharge and speed.
−0.87; There is a strong, negative association between discharge and speed.
Answers
Answer:
The value of the correlation coefficient is 0.87, which means there is a strong, positive association between discharge and speed. A positive correlation means that as one variable increases, the other variable also increases. In this case, as the discharge of the Colorado River increases, the speed of the river also increases. The strength of the association is indicated by the magnitude of the correlation coefficient, which ranges from -1 to 1. A value of 0.87 is considered a strong positive correlation, indicating that there is a strong relationship between the two variables.
Suppose we roll a fair die four time. What is the probability that a 6 occurs on exactly one of the rolls?
Answers
The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.
What are the 3 types of probability?The Three Kinds of Probability
Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).
Subjective Probability. Definition of Relative Frequency.
What is the formula to find out probability?Formula used to find probability
The probability is often defined as the proportion of positive outcomes to all outcomes in the sample space. It is written as, the likelihood of an event
P(E) = (Number of favorable outcomes) ÷ (Sample space).
As die is rolled 4 times ,
X≈ binomial(4, 1/6)
P(X=r) = nCr (p)^r (q)^(n-r)
P(X = 1) = 4C1 × (1/6)^1 × (5/6)^3
= 4 × 1/6 × (5/6)^3
∴P(X = 1) = 0.257
The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.
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In Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. In Game 3, Emerson struck out 42 times in 140 times at bat.
What percentage of times at bat did Emerson actually hit the ball?
%
Answers
Emerson actually hit the ball 32% of times at bat.
What is percentage ?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Since in Game 1, Emerson struck out 30 times in 90 times at bat;
in Game 2, he struck out 40 times in 120 times at bat;
in Game 3, Emerson struck out 42 times in 140 times at bat;
To determine what percentage of times at bat did Emerson actually hit the ball, the following calculation must be performed:
(30 + 40 + 42) / (90 + 120 + 140) = X
112/350 = X
0.32 = X
Therefore, Emerson actually hit the ball 32% of times at bat.
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Last week Scott ran 43 miles less than James. Scott ran 5 miles. How many miles did James run?
A. 35
B. 44
C. 38
D. 48
Answers
Answer:
D) 48
Step-by-step explanation:
Let s = Scott
Let j - James
s = 5
s + 43 = j Substitute 5 for s
5 + 43 = j
48 = j
A hospital director is told that 54% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 120 patients found that 60 were insured. Find the value of the test statistic. Round your answer to two decimal places.
Answers
According to question,
Given data,
A hospital director is told that 54% of the emergency room visitors are insured.
A sample of 120 patients found that 60 were insured.
We know that,
To determine the percentage,
we have to divide the value by the total value and then multiply the resultant by 100,
Percentage formula
Is /of=%?100
Or
Part/whole=%/100
With the help of formula,
Part/sample of patient=%/100
60×100/120=50%
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Given the graph of f(x), determine the range of f−1(x).
Rational function with one piece decreasing from the left in quadrant 2 asymptotic to the line y equals 3 and passing through the point 0 comma 2 and asymptotic to the line x equals 2 and another piece decreasing from the left in quadrant 1 asymptotic to the line x equals 2 passing through the point 4 comma 4 asymptotic to the line y equals 3.
ℝ
(2, ∞)
(−∞, 2) ∪ (2, ∞)
(−∞, 3) ∪ (3, ∞)
Answers
Given the graph of f(x), the range of f⁻¹(x) is; (−∞, 2) ∪ (2, ∞)
How to find the range of the function?The range of a function is defined as the set that is composed by all the output values on a function. Thus, on the graph, the range of a function is composed by the values of y of the function.
For the inverse function, the input and the output are exchanged, and as such given the graph of a function, we can say that the range of the inverse function is given by the domain of the initial function, which is, the values of x of the graph of the original function.
From the description of the rational function, we are told that the asymptote is given as: x = 2
Thus, the domain of the graphed function, would be the same as the range of the inverse function, will be given by the interval:
(−∞, 2) ∪ (2, ∞).
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Neglecting air resistance and the weight of the propellant, determine the work done in propelling a 10-ton satellite to a height of 200 miles above Earth. Assume that the Earth has a radius of 4000 miles. O 4.190.48 mi-ton 1,142.86 mi-ton O 1,904.76 mi-ton 2,857.14 mi-ton 1,523.81 mi-ton
Answers
Therefore ,the the the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.
Analyze the equation.An expression is composed of a number, a variable, both, or neither, and specific operation symbols. An equation is made up of two expressions, which are separated by an equal sign.
Here,
Use F(x) = C/[tex]x^{2}[/tex]
Where c is a constant and x is the radius of the earth
F(x) is satellite weight
We have to find c.
thus,
=> 10 = c /[tex]4000^{2}[/tex]
=> c =160000000
Therefore,
=> F(x) = 160000000/ [tex]x^{2}[/tex]
Workdone ,
=> W = [tex]\int\limits^{4200}_{4000} {F(x)} \, dx[/tex]
=>W = [tex]\int\limits^{4200}_{4000} {160000000 /x^{2} } \, dx[/tex]
=>W =[tex]\left \{ {{4200} \atop {4000}} \right. \frac{-160000000 }{x}[/tex]
=> W =1904.7619 million ton
Therefore ,the the the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.
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what is a acute angle
Answers
Answer: Measure less 90 degrees
Step-by-step explanation: Less than 90 degrees measure acute angle. 90 degrees in right corner. Obtuse corners are larger than 90 degrees
A fast food chain decides to decrease the size of its soft drink cups by 10%. If the new soft drink
cup holds 27 oz, how much did the original cup hold?
Answers
Answer:
30 oz
Step-by-step explanation:
x = size of original cup
x - (0.10)x = 27 oz
(0.90)x = 27 oz
x = 27 / 0.90 = 30 oz
2. The width, w, of a rectangular garden is x-2. The area of the garden is ³-2x-4. What is
an expression for the length of the garden?
Ox²-2x-2
Ox²+2x-2
Ox²-2x+2
Ox²+2x+2
Answers
Consequently, the rectangular garden's length is [tex]x^{2} +2x+2[/tex]
option D is correct
what is area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. Surface area refers to an open surface or the perimeter of a three-dimensional object, whereas plane region or plane area refers to a shape or planar lamina.
given
the width(w) of the rectangular garden= [tex]x[/tex][tex]-2[/tex]
area of the rectangular garden = [tex]x^{3} -2x-4[/tex]
The area of a rectangle is,
area = length × width(w) ,
If l is the rectangle's length,
w is the width of the rectangle,
By substituting values,
[tex]x^{3}-2x-4[/tex] = ([tex]x-2[/tex]) * length ( l )
[tex]l=\frac{x^{3}-2x-4 }{x-2}[/tex] = [tex]x^{2} +2x+2[/tex] (by long division method)
Consequently, the rectangular garden's length is [tex]x^{2} +2x+2[/tex]
option D is correct
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Complete the following.
(a) Consider the following statement.
The water temperature is 70.
Check all the statements below that are negations of this statement.
The water temperature is less than 80.
It is not the case that the water temperature is 70.
The water temperature is not 70.
(b) Consider the following conditional statement.
If the dress is red, then Keisha likes the dress.
What is the conclusion of this statement?
It is not true that Keisha owns a dress.
Keisha likes the dress.
The dress is red.
Keisha loves the dress.
The dress likes Keisha.
Answers
a) The option that is a negation of the given statement is; The water temperature is not 70.
b) The conclusion of the given conditional statement is; Keisha likes the dress.
How to Interpret Conditional Statements?In mathematics, a conditional statement is defined as a statement that can be written in the form “If P then Q,” where P and Q are sentences.
a) We are given the statement as;
The water temperature is 70.
Now, negation is a false/opposite form of the given statement and as such among the options, the only one that is a negation is that
"The water temperature is not 70."
b) We are given the conditional statement as;
If the dress is red, then Keisha likes the dress.
Thus, the conclusion of this is that likes the dress.
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Solve:(6x^2+5x+1)÷(x+2)
Answers
Answer:
6x+6x2+3
Step-by-step explanation:
6x2+5x+1+x+2
Combine 5x and x to get 6x.
6x2+6x+1+2
Add 1 and 2 to get 3.
6x2+6x+3
I need help these problems
Answers
Step-by-step explanation:
she made shots = 34%of 54
=50*34/100
=17
he made 17 shots
Construct a cumulative frequency distribution
765-799| 22
Answers
The steps to construct a cumulative frequency distribution table are mentioned above.
What is cumulative frequency distribution? What is a mathematical function, equation and expression? cumulative frequency : A cumulative frequency is defined as the total of frequencies, that are distributed over different class intervals. function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is to construct a cumulative frequency distribution table.
Since the data is not given, we can write the steps to construct a frequency distribution table. The steps to create a cumulative frequency distribution table are mentioned below -
find the individual frequencies for each distinct value or category.arrange the obtained data in ascending order.the cumulative frequency of a distinct category is calculated by finding the sum of a category’s frequency and the total frequencies of all categories below it. the cumulative frequency of the first category equals the category’s individual frequency.Therefore, the steps to construct a cumulative frequency distribution table are mentioned above.
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An account executive receives a base salary plus a commission. On $50,000 in monthly sales, the account executive receives $6500. On $60,000 in monthly sales, the account executive receives $6800.
(a) Determine a linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x.
(b) Use this model to determine the account executive's compensation for $90,000 in monthly sales.
$
Answers
A) A linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x is;
B) The account executive's compensation for $90,000 in monthly sales is; $300
How to model a linear equation?
The general equation of a line in slope intercept form is;
y = mx + b
where;
m is slope
b is y-intercept
x and y are provided in the problem: x = monthly sales and y = compensation
We will have to find m (Slope), which represents the commission percentage, and b (y-intercept), which represents the the base salary.
x₁ y₁ x₂ y₂
(50000, 6500) (60000, 6800)
Slope;
m = (y₂ - y₁) / (x₂ - x₁)
m = (6800 - 6500) / (60000 - 50000)
m = 300/10000
m = 3/100 = 0.03 = 3%
To find b, we have to take one of our ordered pairs [ (50000, 6500) or (60000, 6800) ] and plug it into the equation, y=mx+b.
Let's use (60000, 6800)
6800 = 0.03(60000) + b
6800 = 1200 + b
b = 6800 - 1200
b = $5600
The base salary = $5600
The equation is y = 0.03x + 5600
b) For $90000 in monthly sales, the executive's compensation is;
y = 0.03(90000) + 5600
y = 2700 + 5600
y = $300
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when conducting a study comparing more than two groups of parametric (normally distributed) data, which of the following statistical tests should be used? g
Answers
Answer:
.
Step-by-step explanation:
sorry i hit my daily limit and i need more answers
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Find the sum of the finite arithmetic sequence.
Sum of the first 150 positive integers
Answers
Answer:
11325
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[a+l]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $l$ is the last term.\\\phantom{ww}$\bullet$ $n$ is the number of terms.\\\end{minipage}}[/tex]
A positive integer is a whole number that is greater than zero.
Therefore:
The first term, a, of the first 150 positive integers is 1.The last term, l, of the first 150 positive integers is 150.The number of terms, n, is 150.Substitute the values into the formula to find the sum of the first 150 positive integers:
[tex]\implies S_{150}=\dfrac{1}{2}(150)\left[1+150\right][/tex]
[tex]\implies S_{150}=75 \cdot 151[/tex]
[tex]\implies S_{150}=11325[/tex]
It is known that 25 % percent of Americans identify themselves as republican . In a random sample of n=20 Americans , what is the expected number of republicans ? It is known that 25 % percent of Americans identify themselves as republican . In a random sample of n=20 Americans , what is the standard deviation of the number of republicans ? ( Round to 2 decimal places )
Answers
Using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
So, we have a random sample of 20 people.
n = 20
And we also know that 25% of Americans identify themselves as republicans.
Then the number of republicans in 20 people would be:
20/100 * 25
.2 * 25
5
Therefore, using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.
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Use the properties to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive)
1. ln((xy)^5)
2. ln (seventh root(t))
3. ln (√x²/y^5)
Answers
Properties of log:
[tex]log\ ab=log\ a + log\ b[/tex][tex]log\ a/b =log\ a-log\ b[/tex][tex]log\ a^b=b\ log\ a[/tex]Evaluate given using the properties above:
Q1
[tex]ln((xy)^5) = 5ln(xy) = 5(ln x + ln y) = 5\ ln\ x + 5\ ln\ y[/tex]Q2
[tex]ln(\sqrt[7]{t} ) = ln(t^{1/7})=1/7\ ln\ t[/tex]Q3
[tex]ln(\sqrt{x^2}/y^5)=ln(x/y^5)= ln\ x - ln\ y^5 = ln\ x - 5\ ln\ y[/tex]Answer:
[tex]\textsf{1.} \quad 5 \ln x + 5 \ln y[/tex]
[tex]\textsf{2.} \quad \dfrac{1}{7} \ln t[/tex]
[tex]\textsf{3.} \quad \ln x - \dfrac{5}{2}\ln y \;\; \;\;\textsf{or} \;\;\;\; \ln x - 5\ln y[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Natural log laws}\\\\Product law: \;$\ln xy=\ln x + \ln y$\\\\Quotient law: $\ln \left(\dfrac{x}{y}\right) = \ln x - \ln y$\\\\Power law: \;\;\;\;$\ln x^n=n \ln x$\\\end{minipage}}[/tex]
Question 1Apply the power law followed by the product law:
[tex]\begin{aligned}\ln (xy)^5 & = 5 \ln (xy)\\ & = 5\left( \ln x + \ln y \right) \\ & = 5 \ln x + 5 \ln y\end{aligned}[/tex]
Question 2[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}[/tex]
then apply the power law:
[tex]\begin{aligned}\ln \sqrt[7]{t} & = \ln t^{\frac{1}{7}} \\ & = \dfrac{1}{7} \ln t\end{aligned}[/tex]
Question 3It is not completely clear where the square root sign begins and ends, so I have provided answers for both permutations:
[tex]\begin{aligned}\ln \left(\sqrt{\dfrac{x^2}{y^5}}\right) & = \ln \left(\dfrac{\sqrt{x^2}}{\sqrt{y^5}}\right) \\\\& = \ln \left(\dfrac{x}{y^{\frac{5}{2}}}\right) \\\\&=\ln x - \ln y^{\frac{5}{2}}\\\\&=\ln x - \dfrac{5}{2}\ln y\end{aligned}[/tex]
[tex]\begin{aligned}\ln \left(\dfrac{\sqrt{x^2}}{y^5}\right)& = \ln \left(\dfrac{x}{y^5}\right) \\\\&=\ln x - \ln y^5\\\\&=\ln x - 5\ln y\end{aligned}[/tex]
if the circumference of a circle is 5cm, then the diameter is ____cm.
a. 5 cm
b. 31.4 cm
c. 15.7 cm
d. 1.57 cm
Answers
C=2πr
The circumference, “C,” is 5cm
5=2πr
Let’s rewrite the formula using the commutative property of multiplication so we can solve for “d:”
5=π2r
The order in which numbers are multiplied does not affect the product. Since the diameter is double the radius, 2r will equal the diameter since 2r equals r+r. So, we can substitute “d” in for 2r:
5=πd
Now, let’s solve for d
Divide both sides by pi:
5/π=d
1.591=d
We can check this back into the formula:
C=π(1.591)
C=4.998
So, your answer is 1.57 since it is the closest.
Question 1-28
What is the range of possible values for x?
B
A
8.2
11.7
(11x-4)
D
84°
C
Answers
The range of possible values for x is 4/11 < x < 8
How to determine the range of possible values for x?From the question, we have the following parameters that can be used in our computation:
Triangles = 2
On these triangles, we have the following angles
Angle 1 = 11x - 4
Angle 2 = 84
Angle 1 cannot exceed angle 2
So, we have
11x - 4 < 84
Add 4 to both sides
11x < 88
Divide
x < 8
Angle 1 cannot exceed be negative or 0
So, we have
11x - 4 > 0
Add 4 to both sides
11x > 4
Divide
x > 4/11
Hence, the range is 4/11 < x < 8
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Rory is an independent filmmaker and has great ideas for several movies. For each short film or full-length movie she makes, she has to raise money. She figures that it will take 7 months to raise money for each short film and 7 months to raise money for each full-length movie. She has given herself at most 49 months to raise money for the films before she abandons the project.
1
While Rory is raising money, she also has to write the scripts. It will take her of a month to write each short film script and 2 months to write each full-length movie script. She is committed to spending at most 13 months on writing scripts.
a. What is the system of inequalities that models this scenario?
b. What is the graph of the solutions?
continued
Answers
The required inequality expressions are 7x + 7y ≤ 49 and x + 2y ≤ 13 an the graph has been plotted with clarity.
How to write an expression for linear inequality?The expression for inequality can be written by taking the suitable sign for the given problem and then relating the variable part to the constant terms.
(a) Suppose the number of short film and full movie are x and y respectively.
Then, the inequality expression for the given case can be written as follows,
The inequality for money raised is,
7x + 7y ≤ 49
And, the inequality for script writing is,
x + 2y ≤ 13
(b) These inequalities can be graphed as follows,
Hence, for the given case the required system of inequalities is 7x + 7y ≤ 49 and x + 2y ≤ 13 and the graph for the solution is drawn properly.
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Please help!!!!!!!!!!!!
Answers
The value of variable x in the equation is x = -3y + 5/ 2
How to solve an equation for a variable?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Therefore, the equation 2x + 3y = 5 can be solved for x as follows:
We have to make x the subject of the formula in the equation.
Subject of the formula is the variable which is expressed in terms of other variables involved in the formula.
Hence,
2x + 3y = 5
subtract 3y from both sides of the equation
2x + 3y = 5
2x + 3y - 3y = 5 - 3y
2x = 5 - 3y
divide both sides by 2
Therefore,
x = 5 - 3y / 2
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I need help that's all if you cN helpe please do I'm beginning you
Answers
The slope of y = 7x - 10 is 7 while the y-intercept is -10 thus it has a high slope but a lower y-intercept so option (D) is correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear function with slope m and y-intercept c is given as y = mx + c.
Compare the given function y = 7x - 10
Slope m = 10
y-intercept = -10
Hence "Y = 7x - 10 has a slope of 7 and a y-intercept of -10, meaning it has a high slope but a low y-intercept".
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For each diagram below, work out whether AB is a tangent to the circle, is not a
tangent to the circle, or if it is not possible to tell.
Justify your answers.
13 cm
5 cm
12 cm
10 cm
4 cm
11 cm
18 cm
18 cm
25 cm
Not drawn accurately
Answers
The tangent AB is for circle in figure (a).The correct option is (a).
What is the relation between the tangent and a circle?For a given circle there can only be one tangent at one point.
The tangent and the circle has only one point in common.
The tangent to a circle is always perpendicular to the radius at that point.
The tangent drawn to a circle is always at right angle to the radius at that point.
The given figures are examined one by one as follows,
(a) The sides of the triangle are given as 5, 12 and 13.
And, 13² = 5² + 12²
Which implies it is a right triangle by Pythagoras theorem.
(b) The sides of the triangle are given as 4, 10 and 11.
And, 11² ≠ 10² + 4²
Which implies it is not a right triangle by Pythagoras theorem.
(c) The sides of the triangle are given as 18, 25 and 18.
And, 25² ≠ 18² + 18²
Which implies it is not a right triangle by Pythagoras theorem.
Thus, only for figure (a) the criteria for the tangent satisfies.
Hence, the line segment AB is tangent to the circle given in figure (a).
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