Starting from the given formula:
[tex]A=\frac{h}{2}(a+b)[/tex]Multiply both sides of the equation by 2:
[tex]\begin{gathered} \Rightarrow2\times A=2\times\frac{h}{2}(a+b) \\ \Rightarrow2A=h(a+b) \end{gathered}[/tex]Divide both sides by h:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}=\frac{h(a+b)}{h} \\ \Rightarrow\frac{2A}{h}=a+b \end{gathered}[/tex]Substract a from both sides of the equation:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}-a=a+b-a \\ \Rightarrow\frac{2A}{h}-a=b \end{gathered}[/tex]Therefore:
[tex]b=\frac{2A}{h}-a[/tex]06 WS Solving Systems of Equations and Inequalities Word Problems
Systems of Equations: Use two equations with two variables to solve each of the following problems.
(1) The sum of two numbers is 51 and their difference is 13. Find the two numbers.
som of
One Saturday the theat
The two numbers are 19 and 32 respectively.
What is equation?
Equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
According to question, let x and y be two numbers
x + y = 51 and
x- y = 13
from equation two,
x = 13+y
put this in equation one,
y+13+y = 51
2y = 51 - 13
2y = 38
y = 38/2 = 19
x = 13+y
x = 13+19
x = 32
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Find the distance between (2, 5) and (-5, 8).
Given:
The two points are,
[tex]\begin{gathered} (2,5) \\ (-5,8) \end{gathered}[/tex]Required:
To find the distance between the given points.
Explanation:
The distance between the two points (x1,y1) and (x2,y2) can be calculated by using the formula,
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]Now the distance between the points (2,5) and (-5,8) is,
[tex]\begin{gathered} \sqrt{(-5-2)^2+(8-5)^2} \\ =\sqrt{(-7)^2+3^2} \\ =\sqrt{49+9} \\ =\sqrt{58} \end{gathered}[/tex]Final Answer:
The distance between two given points is
[tex]\sqrt{58}units[/tex]The solution of a quadratic equation are called it’s ____1- x-intercepts2- zeros 3- roots4- all of the above
ANSWER
All of the above.
EXPLANATION
The solutions to a quadratic equation are the points where the graph of the equation touches the x-axis of the coordinate grid. This is why the solutions are called x-intercepts.
When solving for the solutions of a quadratic equation, the equation is equated to 0. This is why the solutions to a quadratic equation are called zeros of the equation or roots of the equation.
Hence, the correct option is All of the above.
Chloe makes flapjacks.
A pack of flapjacks costs Chloe 60p to make.
She sells the flapjacks for a profit of 30%.
For how much does Chloe sell a pack of flapjacks?
Answer: 78p
Step-by-step explanation:
If she sells them with a profit of 30%, this means she is getting 30% more than they cost to make. They cost 60p, so we will set up an equation. Don't forget that a percent divided by 100 becomes a decimal.
60p * 130% = 60p * 1.3 = 78p
If r is 2 and s is 3 How do I work this problem 2(r s)+4(x)
The value of the expression 2(r+s)+4(x) when r = 2 and s = 3 is 4x + 10.
What is an expression?An expression is written in terms of variables and constants separated by the operation of addition and subtraction. Expressions can be of many types some of them are algebraic expressions, logarithmic expressions, etc.
Given r = 2 and s = 3, we know substitution in which we replace variables with certain numerical values in an expression.
Given 2(r+s)+4(x). ( we'll replace the numerical values of r and s in the
expression).
∴ 2(2+3)+4(x).
2(5)+4x.
10 + 4x, Or
4x + 10.
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Alondra bought a $1,700 television on an installment plan. The installment agreement included a
$170 down payment and 18 monthly payments of $105 each. What is the total finance charge?
The total finance charge is $360.
Given:
Alondra bought a $1,700 television on an installment plan.
The installment agreement included a $170 down payment and 18 monthly payments of $105 each.
Total amount paid = down payment + payment of each month * number of months.
= 170 + 105 * 18
= 170 + 1890
Total amount paid = $2060
Total finance charge = total amount paid - $1700
= $2060 - $1700
= $360.
Therefore the total finance charge is $360.
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Work out a)4/5-1/5 b)9/11+5/11 c)3/4+1/8
The solutions are:
a) 3/5
b) 14/11
c) 7/8
What are the steps of adding and subtracting fractions?The steps for adding and subtracting fractions are as follows:
Step 1: Match the denominators.
Step 2: Add and subtract the numerators.
Step 3: Make the fraction simpler.
Fractions with different denominators can be added or subtracted by using Least Common Multiple(LCM) to convert them to like fractions.
a) 4/5 - 1/5
The denominators of the fractions are the same so we have to just subtract the numerators.
= (4 - 1)/5
= 3/5
b) 9/11 + 5/11
Similarly, the denominators of these fractions are also equal so we have to just add the numerators.
= (9 + 5)/11
= 14/11
c) 3/4 + 1/8
First, we find the Least Common Multiple (LCM) of the denominators to convert them into like denominators and then add the respective numerators.
LCM of 4 and 8 = 8
= [tex]\frac{6+1}{8}[/tex] = 7/8
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An insurance agent estimates that it takes 2/3 of an hour to
process a customer's claim. If the agent spends 22 hours per
week processing claims, about how many claims does he
process in a week?
You deposit $3000 each year into an account earning 8% interest compounded annually. How much will youhave in the account in 20 years?
The rule of the compounded interest is
[tex]A=P\frac{\lbrack(1+\frac{r}{n})^{nt}-1\rbrack}{\frac{r}{n}}[/tex]A is the final amount
P is the amount each year
r is the interest rate in decimal
t is the time
n is the number of periods per year
Since you deposit $3000 each year, then
P = 3000
Since the annual rate is 8%, then
r = 8/100 = 0.08
n = 1
Since the time is 20 years, then
t = 20
Substitute them in the rule above to find A
[tex]\begin{gathered} A=\frac{3000\lbrack(1+\frac{0.08}{1})^{1(20)}-1\rbrack}{\frac{0.08}{1}} \\ A=\frac{3000\lbrack(1.08)^{20}-1\rbrack}{0.08} \\ A=137285.8929 \end{gathered}[/tex]You will earn $137 285.8929 after 20 years
(Type an integer or decimal rounded to the nearest tenth as needed.)
The slope of the wooden beam is 39.8 ft
STEP - BY -STEP EXPLANATION
What to find?
The slope of the wooden beam.
Let y be the slope length.
To determine the slope length of the wooden beam we will follow the steps below.
Step 1
Write down the formula in calculating the sloping beam.
rise² + run² = slope length²
Step 2
Observe from the given diagram;
The value of the rise =12
The value of the run =76/2 = 38
Step 3
Substitute the values into the formula.
12²+ 38² = y²
Step 4
Simplify the above.
144 + 1444 = y²
1588 = y²
Step 5
Take the square root of both-side of the equation.
y = 39.8 ft
Therefore, the length of the sloping beam is 39.8 ft
12 feet to how many meters
EXPLANATION
1 feet is equal to 0.3048 meters.
So, 12 feets will be equal to ---> 12*0.3048 = 3.6576 meters.
Answer: 12 feets are equal to 3.65
This is the problem I am having.
Answer:
Can you send a better picture please thanks.
Step-by-step explanation:
This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeАBсDFFrequency 5101532Using the frequencies given, find theprobability that a student earns a grade of A.p = [?]
Probability is expressed as
number of favourable outcomes/total number of possible outcomes
Looking at the given scenario, the number os students that earned a grade of A is 5. Since we are concerned with these students, then, the number of favourable outcomes is 5.
The total number of students for all grades is 35. This means that the total number of possible outcomes is 35
Thus, the probability that a student earns a grade of A is
5/35
= 0.14
Susana is enrolled in a photography class and has been Complete each statement.
pricing entry-level DSLR cameras. The prices are
Normally distributed.
Use the z-table to answer the question.
w
88%
-2 -1
Z-score
1 2 3
The Z-score of about
tells us that 88% of
the observations in the distribution are at or below
standard deviations above the mean.
The Z-score of about
tells us that 12%
of the observations in the distribution are at or below
standard deviations below the mean.
Answer:
Step-by-step explanation:
1.175
1.175
-1.175
1.175
First find the closest values possible to 0.88 (88%) on the z-score table. Once found we can see that it is located at positive 1.1 and directly in-between .07 and .08. Therefore we take the half of the two, .075, and get the answer of 1.175. The positive z-score, 1.175, tells us that we are 1.175 standard deviations above the mean.
Second find the closest values possible to 0.12 (12%) on the z-score table. We find it at -1.1 and perfectly in-between .07 and .08. We repeat the same steps as before and get -1.175. The negative z-score, -1.175, tells us the we are 1.175 standard deviations below the mean.
Answer:
The z-score of about
✔ 1.175
tells us that 88% of the observations in the distribution are at or below
✔ 1.175
standard deviations above the mean.
The z-score of about
✔ –1.175
tells us that 12% of the observations in the distribution are at or below
✔ 1.175
standard deviations below the mean.
Step-by-step explanation:
edge 2023
What matrix results from B+ A?
Enter your answer by filling in the boxes.
Answer:
[tex]\begin{bmatrix}6 & -5\\-5 & 1\\13 & 6\\-15 & -9\\\end{bmatrix}[/tex]
======================================================
Explanation:
In the top left corner of matrix B is the value 7
For matrix A, the top left corner is -1
The values add to 7+(-1) = 6 which is the result in the top left corner box of the answer matrix.
Add the other corresponding values the same way.
As you can see, the two matrices must be the same size in order to add them. They must have the same number of rows, and the same number of columns.
Matrix addition is commutative allowing us to write B+A = A+B
what is y = -5/2 - 4 in standard form?
The slope-intercept form of the equation of a line is:
y = mx + c
where m is the slope
and c is the y-intercept
The given equation is:
[tex]y\text{ = -}\frac{5}{2}x\text{ - 4}[/tex]Comparing the given equation with y = mx + c:
The slope, m = -5/2
The equation perpendicular to y = mx + c and passing through the point (x₁, y₁) is given by the equation:
[tex]\text{y - y}_1=\frac{-1}{m}(x-x_1)[/tex]Since m = -5/2
-1/m = 2/5
The line passes through the point (5, 4)
x₁ = 5, y₁ = 4
The equation becomes:
[tex]\begin{gathered} y\text{ - 4 = }\frac{2}{5}(x\text{ - 5)} \\ y\text{ - 4 = }\frac{2}{5}x\text{ - 2} \\ \text{y = }\frac{2}{5}x\text{ - 2 + 4} \\ y=\frac{2}{5}x\text{ + 2} \end{gathered}[/tex](1) In the 1970’s the popular advice columnist Ann Landers published a letter from a young couple about to be married. The letter said, “so many of our friends seem to resent their children. They envy us and our freedom to go and come as we please. Then there’s the matter of money. They say their kids keep them broke. Will you please ask your readers the question: 'If you had it to do over again – would you have children?' ” Nearly 10,000 of her readers responded. 70% said “no.” (2) The Good Housekeeping magazine published the results of the poll with a sidebar that said, “All of us at Good Housekeeping know that no mother will be able to read Ann Landers’ report without passionately agreeing or disagreeing. We would like to know what your reaction is. Won’t you therefore, take a minute or two to let us know how you would answer the question: 'If you had it to do over again, would you have children?' ” The results for the Good Housekeeping poll were 95% “yes.” These two polls gave opposite results! What i
Now that the poll has been published in magazines and newspapers, it is up to the readers to decide whether they want to participate. Consequently, the findings are biased by D. volunteer responses.
How to illustrate the information?Option A is incorrect since the estimate need not be underrepresented.
Option B is incorrect since it omits mentioning the good housekeeping magazine.
Option C is incorrect since the discrepancy isn't the result of sampling variance. Both resources' audiences are distinct and do not accurately reflect the general population.
Therefore, this is a voluntary answer, Option D is accurate.
Note that the complete question is attached.
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I need to know the answer quick because I have to go somewhere
First, we need to remember to rules when working with exponents:
[tex]\begin{gathered} \frac{1}{b^a}=b^{-a} \\ \text{and} \\ b^a\cdot b^c=b^{a+c} \end{gathered}[/tex]So, going back to our problem
[tex]\begin{gathered} \frac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}} \\ =2^{\frac{3}{4}}\cdot2^{-\frac{1}{2}}=2^{\frac{3}{4}-\frac{1}{2}}=2^{\frac{1}{4}} \end{gathered}[/tex]And this last result is equal to
[tex]\begin{gathered} 2^{\frac{1}{4}}=\sqrt[4]{2} \\ \Rightarrow\frac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}}=\sqrt[4]{2} \end{gathered}[/tex]Out of Retries Correct Answer Show Enter an estimate. Round each mixed number to the nearest whole in your estimate. 1 WIN Estimate: 0 Find the difference and enter it in simplest form. 3
The mixed fraction are simplify as :
[tex]a\frac{b}{c}=\frac{(a\times c)+b}{c}[/tex]The given expression is :
[tex]5\frac{1}{4}-3\frac{8}{9}[/tex]Simplify the mixed fraction:
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9} \\ 5\frac{1}{4}-3\frac{8}{9}=\frac{(5\times4)+1}{4}-\frac{(3\times9)+8}{9} \\ 5\frac{1}{4}-3\frac{8}{9}=\frac{21}{4}-\frac{35}{3} \end{gathered}[/tex]LCM of ( 4 & 3 ) is 12 So,
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9}=\frac{21}{4}-\frac{35}{3} \\ 5\frac{1}{4}-3\frac{8}{9}=5.25-11.6667 \\ 5\frac{1}{4}-3\frac{8}{9}=5-11 \\ 5\frac{1}{4}-3\frac{8}{9}=-6 \end{gathered}[/tex]Answer :
a)
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9}\text{ can be express as :} \\ \text{Estimate : 5 - 11 =- 6} \end{gathered}[/tex]b)
Diffreence is :
[tex]\text{ 5}\frac{1}{4}\text{ - 3}\frac{8}{9}\text{ = }-6[/tex]
DeAndre is coding a program for a school project. He uses pre-built Python modules to save himself some time. But when he runs his program, he receives an error. What has he most likely done wrong?
A.
He has not saved his code before running it.
B.
He forgot to put the names of the modules in all uppercase letters.
C.
He forgot to import the library that the modules came from.
D.
He forgot to print the results of the modules.
The thing that he.has done regarding the program is A. He has not saved his code before running.
What is coding?The act of writing computer code using programming languages is referred to as coding. The websites, apps, and other technology we use on a daily basis are programmed using coding.
A series of instructions written in a programming language for a computer to follow is referred to as a computer program. Software, which also contains documentation and other intangible components, comprises computer programs as one of its components. Source code is a computer program's human-readable form.
It should be noted that the fact that he didn't save will lead to the error that was faced.
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Graph the line that has an z-intercept at (1,0) and a y-intercept at (0, - 4). What is the slope of this line? And what is m=
Answer: m= -5
Step-by-step explanation:
Answer:
m = 4
Step-by-step explanation:
Change in y over change in x
[tex]\frac{-4-0}{0-1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4
From the ordered pairs are in the form (x,y)
so your y's are -4 and 0
your x's are 0 and 1
Given rectangle ABCD, solve for x and y.
Answer:
x=20, y=10
Step-by-step explanation:
50=2x+y
3x+3y = 90
x+y = 30
x=30-y,
substitute x:
50=2(30-y)+y
50=60-y
y=10, x=20
:]
4. How many integers are in the solution set of the inequality x² - 10 ≤ 0?
(a)1
(b) 2
(c) 3
(d) 6
(e) 7
Answer: 7
Step-by-step explanation: There are an infinite number of integers that satisfy the inequality. There are only seven integers that don't satisfy the inequality which are -3, -2, -1, 0, 1, 2 and 3.
Evaluate the expression when c=4 and x=-4.-C+2x
ok
c = 4 x = 4
-c + 2x
Substitution
-4 + 2(4)
-4 + 8
Result
4
The answer for the second question is 2v + 15
Find a quadratic equation in standard form given its roots are 2+/- i square root of 3/2
We want to find a quadratic equation with the following roots:
[tex]\begin{gathered} x_+=2+i\sqrt{\frac{3}{2}} \\ x_-=2-i\sqrt{\frac{3}{2}} \end{gathered}[/tex]Then we have:
[tex]\begin{gathered} y=(x-x_+)\cdot(x-x_-) \\ y=(x-2-i\sqrt{\frac{3}{2}})\cdot(x-2+i\sqrt{\frac{3}{2}}) \\ y=x^2-2x+i\sqrt{\frac{3}{2}}x-2x+4-i2\sqrt{\frac{3}{2}}-i\sqrt{\frac{3}{2}}x+i2\sqrt{\frac{3}{2}}+\frac{3}{2} \\ y=x^2-4x+\frac{11}{2} \end{gathered}[/tex]For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.
Given the function (f + g) (x) as
[tex]4x^2+x-7[/tex]The domain of the function above is the set of x values except the for x- values that will make the function undefined
For the function above, the domain is defined at all set of real numbers and the interval notation is given as
[tex]-\inftyHence, the correct option is BJacqueline took out a personal line of credit in her senior year of college with an annual simple interest rate of 4%.she takes 51 months to pay off the loan in full and pays 1530 in interest. A. How much was the original line of credit amount.B. How much did Jacqueline pay in total.
Given data:
The given annual interest is r=4%.
The given time is t=51 months= 4 year+3 months=4.25 years.
The interest ammount is i=1530.
A)
The expression for the simple innterest is,
i=(Prt)/100
Substitute the given values in the above expression.
1530=P(4)(4.25)/100
P=9000.
Thus, the original amount credit is 9000.
B)
The expression for the total amount is,
A=P+i
Substitute the above calculated values.
A=9000+1530
=10530
Thus, the total amount is 10530.
Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y-intercept to the nearest integer.
X: 0 1 2 3 4 5 6 7
Y:-8 -5 -2 -1 -1 2 5 8
The Equation of line is 3x - y + 24 =0.
Given:
The table is given by:
X: 0 1 2 3 4 5 6 7
Y:-8 -5 -2 -1 -1 2 5 8
To find the equation of line by using the above data.
Now, According to the question:
From the table, We have
We know that,
Slope (m) = [tex]\frac{y_{2}-y_{1} }{x_{2} - x_{1} }[/tex]
and, slope (m) = [tex]\frac{-5-(-8)}{1-0}[/tex]
m = (-5 + 8)/ 1 = 3
So, [tex]y - y_{1} = m (x - x_{1} )[/tex]
y - 0 = 3 (x - (-8))
y = 3(x + 8)
y = 3x + 24
Hence, The Equation of line is 3x - y + 24 =0.
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The history museum charges a $10 fee plus $15 per student for a field trip.
The aquarium charges a $20 fee plus $10 per student. The lines in the graph
represent the cost of each field trip,
For what number of students will the total cost of each field trip be the same,
and what will that cost be?
O A. 120 students: $10
O B. 2 students: $40
O G. 40 students: $2
OD. 10 students: $120
Need help fast
Method 1
Write an equation for the total cost for each trip.
The history museum
Let the number of students = n
Total cost = 10 + 15n
The aquarium
Let the number of students = n
Total cost = 20 + 10n
Next, equate the two equations to find what number of students will the total cost of each field trip be the same.
[tex]\begin{gathered} 10\text{ + 15n = 20 + 10n} \\ 15n\text{ - 10n = 20 - 10} \\ 5n\text{ = 10} \\ n\text{ = }\frac{10}{5} \\ n\text{ = 2} \end{gathered}[/tex]The number of students = 2
The cost = 20 + 10(2) = 20 + 20 = $40
Answer
2 studnets; $40
Method 2:
To find number of students will the total cost of each field trip be the same.
From the graph, look for the point where the two graphs intercept.
Read the number of students as 2 and the cost as $40
Final answer
2 studnets; $40 Option B
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