Answer:
B
Step-by-step explanation:
According to the Factor Theorem, if (x - a) is a factor (where a is a zero) of the polynomial P(x), then P(a) must equal zero.
Our zeros are 4, √7, and - √7. Hence, when evaluating P(4), P(√7), and P(-√7), all must evaluate to zero.
Testing each choice, we can see that only choice B is true. That is:
[tex]\displaystyle \displaystyle \begin{aligned} f(4)&= (4)^3 - 4(4)^2 - 7(4) + 28 \\ &= (64) - (64) - (28) + 28 \\ &= 0 \stackrel{\checkmark}{=}0 \\f(\sqrt{7}) &= (\sqrt{7})^3 - 4(\sqrt{7})^2 - 7(\sqrt{7}) + 28 \\ &= (7\sqrt{7}) - (28) - (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0\\ f(-\sqrt{7}) &= (-\sqrt{7})^3 - 4(-\sqrt{7})^2 - 7(-\sqrt{7}) + 28 \\ &= (-7\sqrt{7}) - (28) + (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0 \end{aligned}[/tex]
In conclusion, our answer is B.
what does X equal? giving 50 points
Write a proof. Given x - 2 = 3(x - 4) Prove x = 5
x=5
Step-by-step explanation:
x-2=3(x-4)
x-2=3x-12
12-2=3x-x
10=2x
x=10/2
x=5
Answer:
x = 5
Step-by-step explanation:
x - 2 = 3(x - 4)
x - 2 = 3x - 12
-2x - 2 = -12
-2x = -10
x = 5
evaluate the following 1340five minus 242five
Answer:
10980 is the correct answer
friends??
disc; misti.#7628
tt; mistis.wishes
You start a travelling car wash service. You spend $30 on supplies and plan to charge
$6 for each car you wash. Which of the following equations could be used to find your
profit based on the number of cars you wash?
O y = 6x - 30
O y = 6x
O y = 6x + 30
Answer:
y= 6x - 30
Step-by-step explanation:
First yu would take the 30 dollars you spent then you will subtract 6 times how many cars you have done.
23. What is the value of 3.2/0.8
Answer:
When you divide 3.2 by 0.8 you get 4.
please help me for this question....
Answer:
the answer is 3. but the workings are so long
please help me please
answer:
sorry i don't know the answer but are you an army ?
The typing speeds for the students in a typing class is normally distributed with mean 44 words per minute and standard deviation 6 words per minute. What is the probability that a randomly selected student has a typing speed of less than 38 words per minute
Answer:
15.87%
Step-by-step explanation:
*Probability-Below 15.87%
Z1=-1
*x-1 38
*µ 44
*σ 6
The probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.
What is z-score?The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.
Formula for z-scorez = (x -μ)/σ
Where,
Z is standard score.
x is observed value.
μ is mean of the sample.
σ is standard deviation of the sample.
What is probability?The area under the normal distribution curve represents probability.
According to the given question.
Mean, μ = 44
Standard deviation, σ = 6
Observed value, x = 38
Therefore, z-score = [tex]\frac{38-44}{6}= -1[/tex]
So, the are P(z > -1) = 15.87%
Hence, the probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.
Find out more information about z-score and probability here:
https://brainly.com/question/25638875
#SPJ2
FURTHER MATHEMATICS Use determinants to solve the systems of equation:
2x + y + 2z = 13
X + y - 2z = 8
X + 2y + z = 11
Answer:
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+1y+2z&=&13\\1x+1y-2z&=&8\\1x+2y+1z&=&11\\\end{array}\right.\\\\\\\Delta=\left| \begin{array}{ccc}2&1&2\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\0&\frac{1}{2}&-3\\0&1&3\end{array}\right| =2*(\frac{3}{2}+3)=9\\\\[/tex]
[tex]\Delta_1=\left| \begin{array}{ccc}13&1&2\\8&1&-2\\11&2&1\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\8&1&-2\\\frac{11}{2}& 1&\frac{1}{2}\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\-5&0&-4\\\frac{-5}{2}& 0&\frac{5}{2}\end{array}\right| \\\\=2*(-1)*(\frac{-25}{2}-\frac{20}{2}) =45\\[/tex]
[tex]\Delta_2=\left| \begin{array}{ccc}2&13&2\\1&8&-2\\1&11&1\end{array}\right| \\\\\\=\left| \begin{array}{ccc}3&21&0\\3&30&0\\1&11&1\end{array}\right| \\\\\\=1*(90-63) =27\\[/tex]
[tex]\Delta_3=\left| \begin{array}{ccc}2&1&13\\1&1&8\\1&2&11\end{array}\right| \\\\\\=\left| \begin{array}{ccc}0&-1&-3\\0&-1&-3\\1&2&11\end{array}\right| \\\\\\=0\\[/tex]
[tex]\left\{\begin{array}{ccc}x=\dfrac{\Delta_1}{\Delta}=\dfrac{45}{9}=5\\\\y=\dfrac{\Delta_2}{\Delta}=\dfrac{27}{9}=3\\\\z=\dfrac{\Delta_3}{\Delta}=\dfrac{0}{9}=0\\\end{array}\right.[/tex]
blake and josh are both saving money for a new bike. the ratio of blake,s saving to josh saving is 3:1 if they have saved 400$, how much has each boy saved
Answer:
200 each.
Step-by-step explanation:
400 divided by 2 is 200
Can anyone solve numbers 60 through 65?
Answer:
[tex]4a + 9a \\ \\ = (4 + 9).a \\ \\ = 13a \\ \\ 9y + 3y - 5x \\ \\ (9y + 3y) - 5x \\ \\ (9 + 3).y - 5x \\ \\ 12y - 5x[/tex]
Dad is getting food ready for my birthday party! Including me, there will be 16 people at the party. Dad is baking cookies for us! He can bake 20 cookies per batch.
How many batches should I tell Dad to make so we can each have 3 cookies?
Answer:
3 batches but you will have some left over
Step-by-step explanation:
Read the image below
NCERT Portion, grade 8, Lesson 1. Rational numbers
Answer:
[tex]-\frac{43}{70}[/tex]
Step-by-step explanation:
One is given the following equation,
[tex]\frac{2}{3}*\frac{-3}{7}-\frac{1}{14}-\frac{3}{7}*\frac{3}{5}[/tex]
Simplify, use the order of operations. The order of operations is a sequence by which one must simplify an equation. This sequence is the following,
1. Parehtensis
2. Exponents
3. Mutliplcaiton or Division
4. Addition or subtraction
Simplify the given expression. Remember, when multiplying fractions, one must cancel out like terms or factors that can be found in both the numerator and denominator,
[tex]\frac{2}{3}*\frac{-3}{7}-\frac{1}{14}-\frac{3}{7}*\frac{3}{5}[/tex]
[tex]\frac{-2}{7}-\frac{1}{14}-\frac{3}{7}*\frac{3}{5}[/tex]
[tex]\frac{-2}{7}-\frac{1}{14}-\frac{9}{35}[/tex]
Convert to the least common denominator. In this case, the least common denominator is (70). Remember to multiply both the numerator (number over the fraction bar) and denominator (number beneath the fraction bar) to convert the denominator.
[tex]\frac{-2}{7}-\frac{1}{14}-\frac{9}{35}[/tex]
[tex]\frac{-2}{7}*\frac{10}{10}-\frac{1}{14}*\frac{5}{5}-\frac{9}{35}*\frac{2}{2}[/tex]
Simplify,
[tex]\frac{-2}{7}*\frac{10}{10}-\frac{1}{14}*\frac{5}{5}-\frac{9}{35}*\frac{2}{2}[/tex]
[tex]\frac{-20}{70}-\frac{5}{70}-\frac{18}{70}[/tex]
[tex]-\frac{25}{70}-\frac{18}{70}[/tex]
[tex]-\frac{43}{70}[/tex]
Line R is represented by the equation `y=-2x+7`and Line Z is represented by the equation `y=3x-3`. At what point will line R and line Z intersect?
2/5 (z+ 1) = y for z
Answer:
z = 5y/2 - 1
Step-by-step explanation:
Solve for z
by simplifying both sides of the equation, then isolating the variable.
the perimeter of a triangle is 14x - 4. if two sides measure 3x - 2 and 5x + 3, then how long is the third side?
Answer:
6x-5
Step-by-step explanation:
14x-4- (3x-2)-(5x+3)= 14x-4-3x+2-5x-3= 6x-5
Please help ill mark brainliest dont forget explanation too please
please help me with this math is for my math homework
Answer:
that answer is (1)
hope that helps you
9514 1404 393
Answer:
1
Step-by-step explanation:
You can put either number in the form of the other to see they are equal. A number divided by itself gives a quotient of 1.
-1 1/10 = -(10·1 +1)/10 = -11/10 . . . . . matches the denominator
or
-11/10 = -1 1/10 . . . . . matches the numerator
__
(-11/10)/(-11/10) = 1 . . . . your quotient
_____
Additional comment
Here, we see that both numbers in the problem are negative, so we have an even number of minus signs. That means the quotient will be positive. Knowing this lets us eliminate the minus signs from the problem.
As you may know, there are a couple of (fully equivalent) ways to divide fractions.
1) "invert and multiply" or "dot swap"
(11/10) ÷ (11/10) = (11/10) · (10/11) . . . . . . . the denominator has been inverted
= (11·10)/(10·11) = 110/110 = 1
2) use the numerators when the denominators are equal.
(11/10) / (11/10) = 11/11 = 1 . . . . denominators of the fractions are both 10
How many solutions does this equation have?
–3h = 1 − 3h
100 POINTS
PLEASE DO THESE FOUR QUESTIONS (even if it’s just one)
1. write a number sentence expressing the value of the missing angle in the diagram below
2. write a number sentence expressing the value of r in the diagram
3. label the diagram below so that one pair of parallel lines, and one pair of equal lines
4. use the index laws to simplify the expression below, giving your answer with positive indices. SHOW ALL WORKING OUT.
Step-by-step explanation:
1. k = 76°
2. r = 25cm
3. as the drawing attached
one pair of parallel lines : AB and DC
one pair of equal angles : L A and L D
4. (7²× 3`¹)⁴×7^5 / (3² × 7^(-6))³
= (7^8 × 3`⁴)×7^5/ (3² × 7^(-6))³
= (7^13 × 3`⁴)/ (3^6 × 7^(-18))
= (7^(31) × 3^(-10))
= 7^31 / 3^10
what is the value of x when the distance between the points (-2,-3) (-3,x) is equal to 5
Answer:
(-3,-4)
Step-by-step explanation:
These are AP statistics multiple choice questions. I don’t know if I got them correct but can double you check for me?
Answer:
first question
mean = 5.11
median = 6
mean = sum of the terms
number of terms
= 271
53
= 5.11
median is the 27th (arrange lowest to highest number)
conclusion, the median is higher than mean, the answer is B.
sec question
a is the answer
third question
a is the answer
last question
mean = 60838
median = 60000
the answer is B
Marco surveyed the first 10 people
who arrived at the pool. He asked
them what they thought was the
best time to close the pool.
The best time to close the pool is the evening from 4 to 7 pm.
This is called the taking of average among all possible samples.
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.This can also be solved using mean, mode or median is data is given.
Learn more about mean here:-https://brainly.com/question/1136789
#SPJ2
if U = {1,2,3,10},A={2,4,6,8,10}and B={3,6,9}
,find AUB
Answer:
AUB = {2,3,4,6,8,9,10,12}
Solve the equation for y. Then find the value of Y for each value of X.
y+7x=9;x=-1,0,2
y=?
x=?
(help i hate this math hw)
Answer:
y=9-7x
If x= -1, y=16
If x= 0, y=9
If x=2, y= -5
Step-by-step explanation:
Because you are solving the equation for y, you want to have y by itself on one side. The only way to do that in this problem is by subtracting the 7x on both sides.
y+7x=9
-7x -7x ---> y=9-7x
The next part of the question says to find the value of Y for each value of X. Using the given X values, we plug them into the equation we just got in order to find Y.
y=9-7(-1) ----> y=16
y=9-7(0) ----> y=9
y=9-7(2) ----> y=-5
How does this work please explain clearly :) also 25 points
Compare and order the numbers below from least to greatest.
4.6, 2.8, V7, V17,
Answer:
2.8, 4.6, V7, V17
i hope it help n im sorry i can't explain
XY=32, YZ=7d, and XZ=74
The value of d = 6 and the value of YZ = 42
Since XY=32, YZ=7d, and XZ=74
Based on this question, it should be noted that the addition of XY and YZ will equal to the value of XZ. Therefore,
XY + YZ = XZ
32 + 7d = 74
Collect like terms
7d = 74 - 32
7d = 42
Divide through by 7
7d/7 = 42/7
d = 6
Since d is 6, the value of YZ will be:
= 7d = 7 × 6 = 42
In conclusion, the value of d = 6 and the value of YZ = 42.
Read related link on:
https://brainly.com/question/24475076