Explanation
Given the expression
[tex]\frac{z^{2}+3z+1}{z-2}[/tex]We are asked to find the remainder. We can use the remainder theorem. This can be seen below.
According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.
All we need to do is to substitute the value of (a) in the numerator to get the remainder. a is represented in the denominator.
Therefore, we will have;
[tex]\begin{gathered} \text{ Remainder =}2^2+3(2)+1 \\ =4+6+1 \\ =10+1 \\ =11 \end{gathered}[/tex]
A bag has 5 blue marbles and 10 green marbles. Half of the green marbles are made of glass. A marble is selected at random from the bag. What is the probability that it is a green, glass marble
Answer:
1/3Step-by-step explanation:
Total marbles:
5 + 10 = 15Green marbles made of glass:
10/2 = 5Required probability:
P(green glass) = 5/15 = 1/3Does the following graph depict y as a function of x?
in this problem
the graph define a function, because the x-value has only one output (one value of y)
Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF, which intersect at I. If DI = 3, BD = 4, and BI = 8, then find the area of triangle ABC.
The area of a triangle is 1/2 x base x height.
The area of a triangle is 24.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices
The area of a triangle is given by:
Area = 1/2 x base x height
We have,
A triangle ABC.
Angle bisectors are AD, BE, and CF, which intersect at I as shown in the figure below.
DI = 3
DI = AI = 3
Height of the triangle = AD = AI + DI = 3 + 3 = 6
BD = 4 = BC
Base of the triangle = BC = BD + DC = 4 + 4 = 8
The area of a triangle:
= 1/2 x base x height
= 1/2 x 8 x 6
= 1 x 4 x 6
= 24
Thus,
The area of a triangle is 24.
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whats the answer for this question
Answer:
Step-by-step explanation:
12-2=10
9+7-10=6
Only brother: 9-6=3
Only Sister: 7-6=1
Both:6
Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey, 43% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability of the following.
The probability of matching x successes on n further trials in an experiment with two possible outcomes. There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.
Given that,
The probability of matching x successes on n further trials in an experiment with two possible outcomes is known as the binomial probability (commonly called a binomial experiment).
The following formula gives it:
[tex]P=C_{n,x}p^{n}.(1-p)^{n-x}[/tex]
Where is the number of distinct combinations of x items drawn from a set of n elements, as determined by the formula below.
[tex]C_{n,x}=\frac{n!}{x!(n-x)!}[/tex]
And p is the probability that anything will happen.
Being aware that employers are monitoring phone calls is a victory in this issue.
43% of adults fear that their employers are listening to their phone calls,
p=43%=0.43
We must locate Four persons were questioned, and none expressed concern about phone call monitoring by companies.
We count four adults, n=4.
Is there a probability of success of 0? If so, then x = 0.
[tex]P=C_{n,x}p^{n}.(1-p)^{n-x}[/tex]
[tex]P=C_{4,0}(0.43)^{0}.(0.57)^{4}[/tex]
P=0.0488
Therefore, There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.
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Which of the following are geometric sequences?Check all that apply.A.2, -2, 2, -2, 2, -2, 2B.1, 2, 4, 8, 16, 32C.1, 4, 9, 16, 25, 36, 49D.10, 5, 2.5, 1.25, 0.625, 0.3125
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The correct answers are:
CONCLUSION:
The final answers are:
OPTION B and OPTION D
Use synthetic division to solve (x3 + 1) ÷ (x – 1). What is the quotient?
x squared + x + 1 + StartFraction 2 Over x + 1 EndFraction
x squared minus x + 1
x squared + x + 1 + StartFraction 2 Over x minus 1 EndFraction
x cubed minus x squared + x minus 1
The quotient is equal to [tex]x^{2} +x+1[/tex]
Given
The provided equation is as follows:
[tex]\frac{x^{2}+1 }{x-1}[/tex]
What exactly is synthetic division
The synthetic division method is a quick way to divide polynomials.
When divided by the linear factor, it is also known as the polynomial division technique of a specific instance.
Therefore,
The quotient is as follows:
[tex]\frac{x^{2}+1 }{x-1}[/tex]
[tex]\frac{x(x^{2} +x+1)-1(x^{2} +x+1)}{x-1}[/tex]
[tex]\frac{(x-1)(x^{2} +x+1)}{x-1}[/tex]
[tex]x^{2} +x+1[/tex]
As a result, the quotient is
[tex]x^{2} +x+1[/tex]
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Answer: C
Step-by-step explanation:
Using the graph as your guide, complete the following statement.
The discriminant of the function
• A. positive
• B. negative
• C. zero
=======================================================
Reason:
The discriminant is
d = b^2-4ac
which is the stuff under the square root in the quadratic formula.
We have these three cases
d > 0 means we get two different real number solutionsd = 0 means we get exactly one real number solutiond < 0 means there are two nonreal complex solutionsThe graph shows we have 2 solutions. Each solution is an x intercept, aka "root". We go for the case in which d > 0. Therefore, the discriminant is positive.
Simplify the expression.[tex] - 5 {w}^{4} {y}^{ - 2} \div - 15 {w}^{ - 6} {y}^{2} [/tex]w≠0, y≠0
Question:
Simplify the expression
[tex]\frac{-5w^4y^{-2}}{-15w^{-6}y^2},w\ne0,y\ne0[/tex]Step 1:Apply the fraction rule
[tex]\begin{gathered} \frac{-a}{-b}=\frac{a}{b} \\ \frac{-5}{-15}=\frac{1}{3} \end{gathered}[/tex][tex]\frac{-5w^4y^{-2}}{-15w^{-6}y^2}=\frac{w^4y^{-2}}{3w^{-6}y^2}[/tex]Step 2:Apply the law of indices
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex][tex]\frac{w^4y^{-2}}{3w^{-6}y^2}=\frac{w^{4-(-6)}y^{-2-2}}{3}[/tex][tex]\begin{gathered} \frac{w^{4-(-6)}y^{-2-2}}{3} \\ =\frac{w^{4+6}y^{-4}}{3} \\ =\frac{w^{10}y^{-4}}{3} \end{gathered}[/tex]Step 3: Apply the fractional exponent of indices
[tex]a^{-m}=\frac{1}{a^m}[/tex][tex]\begin{gathered} \frac{w^{10}y^{-4}}{3} \\ =\frac{w^{10}}{3}\times\frac{1}{y^4} \\ =\frac{w^{10}}{3y^4} \end{gathered}[/tex]Hence,
The final answer = w¹⁰/3y⁴
2. A line goes through the points (4, 8) and (-4, 6). (a) What is the slope of the line? Show your work (b) Write the equation of the line in point-slope form. Show your work (c) Write the equation of the line in slope-intercept form. Show your work. Answer:
After how many days do only 4/5 of the students recall the important features of the classroom lecture? There are two parts to this questionIt says locate the point on the graph that conveys this information
Given:
[tex]P(x)=90-25log_2x[/tex]Required:
We need to find the value of x when P(x)=80.
Explanation:
[tex]Substitute\text{ P\lparen x\rparen=80 in the equation }P(x)=90-25log_2x.[/tex][tex]80=90-25log_2x[/tex]Solve for x.
[tex]25log_2x=90-80[/tex][tex]25log_2x=10[/tex]Divide both sides by 25.
[tex]\frac{25log_2x}{25}=\frac{10}{25}[/tex][tex]log_2x=\frac{2}{5}[/tex][tex]Use\text{ If }log_bx=y\text{ then }b^y=x.\text{ here b=2 and }y=\frac{2}{5}.[/tex][tex]x=2^{\frac{2}{5}}[/tex][tex]x=2^{0.4}[/tex][tex]x=1.3\text{ days.}[/tex]Final answer:
[tex]x=1.3\text{ days.}[/tex]See a horizontal line from point 80 on the y axis and mark the intersection point on the graph.
One half of a number increased by a second number equals 5. One half of the first number decreased by the second number equals 1. Find the two numbers.
let the first no. is 'a'
second no. is 'b'
so from the statement, One half of a number increased by a second number equals 5.
[tex]\frac{a}{2}+b=5[/tex]and One half of the first number decreased by the second number equals 1.
[tex]\frac{a}{2}-b=1[/tex]add both the equations,
[tex]\begin{gathered} \frac{a}{2}+\frac{a}{2}+b-b=5+1 \\ a=6 \end{gathered}[/tex]put a= 6 in first equation
[tex]\begin{gathered} \frac{6}{2}+b=5 \\ 3+b=5 \\ b=5-3 \\ b=2 \end{gathered}[/tex]so the answer is,
a = 6 & b = 2
lfp 3.1/ 3.2 practice
Divide fractions
3.1/3.2
PART 1,
Pithagorean theorem
x^2 =™9^2 + 12^2 = 81 + 144 = 225
then
x=√225 = 15
PART 2
x^2 = 10^2 + 24^2 = 100 + 576 = 676
then
x= √676 = 26
PART 3
10 ^ 2 = x^2 + 6^2
So then
10^2 - 6^2 = x^2
100 - 36 = x^2
64 = x^2
√64 = 8 = x
PART 4
24^2 = x^2 + 6^2
So then write
24^2 -6^2 = x^2
576 - 36 = x^2
As a result
540 = x^2
Then
√540 = x
The president of the student council wants to survey the student population about parking. She decides to take a random sample of 100 of the 1,020 students at the school. She gets an alphabetical list of the students, and numbers them from 0001 to 1020. Then, using a random number table, and starting at a random line, she selects 100 unique numbers between 0001 and 1020. Is this a simple random sample?
No, because the sample could contain repeating numbers.
No, because the sample could contain numbers other than numbers between 0001 and 1020.
Yes, because each student and sample of 100 has the same chance of being selected.
Yes, because each student is represented by a 4-digit number from 0001 to 1020.
Is this a simple random sample: Yes, because each student and sample of 100 has the same chance of being selected.
What is a simple random sample?A simple random sample can be defined as a subset of items that are selected from a larger data set or statistical population, with each member of the subset having an equal or the same probability (chance) of being selected.
This ultimately implies that, each member of the subset are selected by chance and randomly, and as such a simple random sample is an unbiased representation of a larger data set or a statistical population.
In this context, we can reasonably infer and logically deduce that the data set or statistical population described in this scenario is a simple random sample.
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The nature of a graph which has an odd degree and a negative leading coefficient would be _________.up left; up rightdown left; up rightdown left; down rightup left; down right
Given:
A graph which has an odd degree and a negative leading coefficient.
To find:
The nature of the graph.
Explanation:
Since the has an odd degree and a negative leading coefficient.
So, the end behaviours are,
[tex]\begin{gathered} As\text{ }x\rightarrow-\infty,f(x)\rightarrow\infty \\ As\text{ }x\rightarrow\infty,f(x)\rightarrow-\infty \end{gathered}[/tex]So, the nature of the graph would be, up left and down right
Final answer:
up left; down right.
Given m/8= 86° and m/4= (4x + 2)°, what is the value of x ?
m∠4=m∠8 (Corresponding angles are equal)
[tex]4x+2=86\\4x=86-2\\4x=84\\\frac{4x}{4} =\frac{84}{4} \\x=21[/tex]
x=21°
There are 8 grams of pure drug in 75 milliliters of solution. What is the precent strength of solution? Round tothe nearest hundredth
Step 1: Let's review the information given to us to answer the exercise correctly
Amount of pure drug in the solution = 8 grams
Amount of solution = 75 mL
Step 2: Let's answer the question, as follows:
Percent strength of the solution = Amount of pure drug in the solution/Amount of solution * 100
Replacing with the values we know:
Percent strength of the solution = 8/75 * 100
Percent strength of the solution = 0.10666 * 100
Percent strength of the solution = 10.67% (Rouding to the next hundredth)
Tenth = one decimal place
Hundreth = two decimal places
Thousandth = three decimal places
What should be done to both sides of the equation in order to solve 1/3 x=4? Divide by 4Multiply by 4 Divide by 1/3Multiply by 1/3
The given equation is,
[tex]\frac{1}{3}x=4[/tex]So, from this equation , we have to find the value of x. The left hand side of the equation has x with 1/3 as coefficient, therefore, inorder to make it x, we have to,
[tex]\frac{1}{3}x\times3\rightarrow x[/tex]as the thress get cancelled. If we do some operation on one side of the equal sign, it is to be applied on the other side also so as to maintain the equivalency.
So here we have to multiply by 3.
But in option, there is no as such given , but it is given that divide by 1/3.
[tex]\frac{\frac{1}{3}x}{\frac{1}{3}}\rightarrow\frac{1}{3}x\times3^{}^{}[/tex]which is equuivalent to multiplying by three.
So the option " Divide by 1/3" is correct.
qwdqdqwdwqdqdwqdqwwqdd
Answer:
qwdqdqwdwqdqdwqdqwwqdd
haha lol
Step-by-step explanation:
In ∆XYZ, y =75cm, z=83 cm and
we have:
[tex]undefined[/tex]Rodney opens a savings account with $75 and also deposits $40 each month. Morgan opens an account with $50 and also deposits $40 each month. Will they have the same amount in their account at any point? If so, after how many months? Explain.
FAST RESPONSE ALSO EQUATION AND STEPS
Answer:
Yes, after 3 and a half months, they will both have 215$ in their account.
Step-by-step explanation:
if x is the number of months
Rodney's equation: y=40x+75
Morgan: y = 50x + 40
Equate them together:
50x+40 = 40x+75
10x=35
x=3.5
:]
Yes, after 3 and a half months, they will both have 215$ in their account.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the difference. Write your answer in simplest form.
The expression of the fraction 10¹/₅ - 2¹/₆ as a mixed fraction is; 8¹/₃₀
How to subtract Fractions?We want to subtract two fractions.
Now, fractions could be either proper fraction, improper fraction or mixed fraction.
Now, a proper fraction simply means the numerator is smaller than the denominator, a mixed fraction simply means a whole number and a proper fraction while an improper fraction simply means the numerator is bigger than the denominator
We are given the operation;
10¹/₅ - 2¹/₆
Converting to improper fraction gives;
51/5 - 13/6
Factorizing gives us;
1/30((51 * 6) - (13 * 5))
= 241/30
Converting to mixed fraction gives 8¹/₃₀
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For the following, I have to find where the orthocenter, the centroid, and the circumcenter are within the diagram
Orthocenter
Let
A(2,0)
B(3,2)
C(6,0)
step 1
Find out the slope AB
m=(2-0)/(3-2)
m=2/1
m=2
Remember that
If two lines are perpendicular, then, their slopes are negative reciprocal
so
the slope of the altitude that passes through C is -1/2
Find out the equation of the altitude that passes through C
y=mx+b
we have
m=-1/2
point C(6,0)
substitute
0=-(1/2)(6)+b
solve for b
0=-3+b
b=3
equation is y=-(1/2)x+3 -------> equation 1
step 2
Find out the slope BC
m=(0-2)/(6-3)
m=-2/3
so
the slope of the altitude that passes through A is 3/2
Find out the equation of the altitude that passes through A
y=mx+b
we have
m=3/2
point A(2,0)
0=(3/2)(2)+b
solve for b
0=3+b
b=-3
y=(3/2)x-3 ------> equation 2
step 3
the intersection point equation 1 and equation 2 is the orthocenter
y=-(1/2)x+3 -----> equation 1
y=(3/2)x-3 ------> equation 2
solve the system
solve by graphing
using a graphing tool
the intersection point is (3,1.5)
that means
the orthocenter is (3,1.5)
see the attached figure to better understand the problem
Jessica made 619 cups of punch. Herpunch had two different types of juice init. If the punch had 4 cups of one type ofjuice, how many cups of the other type ofjuice did it have?
Given:
Total cups of punch made = 619
The punch contains tw different types of juice
If f(x) = -4x-5, what is f(1)?
Given that f(x) is defined as the function below:'
[tex]f(x)=-4x-5[/tex]To determine the value of f(1), we substitute the x with 1. Therefore:
[tex]\begin{gathered} f(1)=-4(1)-5 \\ =-4-5 \\ f(1)=-9 \end{gathered}[/tex]The value of f(1) is -9.
Eric had $197 in his savings account before he was paid his weekly salary. His current savings balance is $429. How much money does Eric earn each week? (Form an equation.)
Answer:
[tex]197+\text{ n= 429}[/tex]Explanation:
Here, we want to get the amount of money Eric earns per week
Let the amount earned be n
Now, to get the value earned, we have to subtract the value he had before from what he has now or simply add what he had before to what he earned now and equate to his total balance now
Mathematically, we have that as:
[tex]197\text{ + n = 429}[/tex]
Melissa will only drink a cup of coffee if she has slept less than 8 hours or she had to wake up before 6
am.
In which of the following cases does Melissa not drink a cup of coffee?
Melissa sleeps for 8 hours and wakes up at 7 am
Melissa sleeps for 7 hours and wakes up at 8 am
Melissa sleeps for 9 hours and wakes up at 5:30 am
Melissa sleeps for 7 hours and wakes up at 6 am
Check
W
Answer: Melissa sleeps for 8 hours and wakes up at 7 am.
Step-by-step explanation: For this i was able to do just eliminate some answer. "Melissa sleeps for 7 hours and wakes up at 8 am," in this case Melissa would drink coffee because she slept less than 8 hours. "Melissa sleeps for 9 hours and wakes up at 5:30 am," in this case Melissa would drink coffee since she had woke up at 5:30 am. "Melissa sleeps for 7 hours and wakes up at 6 am," in this case Melissa would drink coffee since she had less than 8 hours of sleep. In conclusion, The only time Melissa wouldn't had drank coffee is when she had slept for 8 hours and woke up at 7 am. That is because had slept more than 8 hours and had woke up after 7 am.
Find x and the measure of angle 1
The measure of angle 1 is 42° . Angles Central angles can be expressed as Central angle = (Arc length 360o)/(2r) degrees or Central angle = Arc length/r radians, where r is the radius of the circle.
What is meant by angle?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex exists as the familiar point of contact. Angle is derived from the Latin word angelus, which means "corner." An angle is formed when two line segments are joined at a single point, or when two line segments meet at a common endpoint. This common point is known as the angle's vertex, and the two line segments are known as the angle's sides or arms. Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation are the names of basic angles. An angle is a geometrical shape formed by connecting the ends of two rays.∴ The measure of angle 1 is 42°
180 - 48 - 90 = 42
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Answer the questions below.
Answer:21
Step-by-step explanation:
A woman borrows #20 000 for 4 weeks. She agrees to pay #25 000 back at the end of the 4 weeks. How much interest does she pay over the a 4 weeks? b How much interest does she pay per week?how to solve
The interest she pays over 4 weeks is #5000 and the interest she pays per week is #1250.
According to the question,
We have the following information:
A woman borrows #20 000 for 4 weeks.
She agrees to pay #25 000 back at the end of the 4 weeks.
Now, we will subtract the borrowed amount from the amount paid after 4 weeks to find the interest paid after 4 weeks.
(a) Interest paid over 4 weeks = #(25000-20000)
Interest paid over 4 weeks = #5000
(b) Now, we can easily find the interest paid per week by the interest paid over 4 weeks by the total number of weeks.
Interest paid per week = Interest paid in 4 weeks/4
Interest paid per week = 5000/4
Interest paid per week = #1250
Hence, the answers to part a is #5000 and the answer to part b is #1250.
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