Answer:(x+1) (x+8)
Step-by-step explanation:
Answer:
(x + 8)(x + 1)
Step-by-step explanation:
Consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 9)
The factors are + 8 and + 1, since
8 × 1 = 8 and 9 + 1 = 9, hence
x² + 9x + 8 = (x + 8)(x + 1) ← in factored form
If the gcd of 5 and 12 is 1 then
Answer:
The greatest common divisor (gcd) of two or more numbers referst to the largest positive integer that divides each of the integers. Also, two integers are said to be relatively prime, mutually prime, or coprime if the only positive integer that divides both of them is 1. Therefore, If the GCD of 5 and 12 is one, it means that the two numbers are mutually prime.
What is the perimeter of an equilateral triangle if each side is (x+3)?
Answer:
all work is shown and pictured
What is the factored form of the polynomial?
x2 - 12x + 27?
(x + 4)(x+3)
(x - 4)(x + 3)
(x + 9)(x + 3)
(x-9)(x - 3)
Answer:
The answer is option D.
Step-by-step explanation:
Answer:
D: Answer:(x-9)(x-3)
Step-by-step explanation:
f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)?
[tex]f(n+1)=f(n)-8\\f(1)=100\\\\f(2)=100-8=92\\f(3)=92-8=84\\f(4)=84-8=76\\f(5)=76-8=68\\f(6)=68-8=60[/tex]
Select the correct answer.
Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has oil and the test predicts it?
A.
0.09
B.
0.11
C.
0.36
D.
0.44
Reset Next
Answer:
C. 0.36
Step-by-step explanation:
There is already a 45% chance of having oil on the land.
The oil kit has an 80% accuracy rate.
Therefore the kit has an 80% chance, of that 45% chance, of detecting oil. (Assume the owners in the area are correct in their 45% assumption)
This can be expressed as 80%*40% or 0.8*0.45
= 0.36 or 36%
Hope this helps!
Answer:
C. 0.36
Step-by-step explanation:
If f(x)=x-6/x, g(x)=x+4, and h(x)=3x-2, what is (h o f o g)(x)?
A.) x-2/x+4
B.) 3x-8/x
C.) x-14/x+4
D.) 3x-4/x
Answer:
C is correct
Step-by-step explanation:
On edg
match each function to how its graph is related to the graph of the parent function f(x)=^3Гx
a. the graph of the parent function is shifted 7 units down.
b. the graph of the parent function is shifted 7 units right
c. the graph of the parent function is shifted 7 units up
d. the graph of the parent function is shifted 7 units left
Answer:
g(x) = 3 square root of x + 7 is "The graph of the parent function is shifted 7 units up"
j(x) = 3 square root of x + 7 is "The graph of the parent function is shifted 7 units left"
h(x) = 3 square root of x - 7 is "The graph of the parent function is shifted 7 units down"
k(x) = 3 square root of x - 7 is "The graph of the parent function is shifted 7 units right"
Explantion:
Got this right on the test. And for square root of is supposed to mean the symbol for anyone who doesn't know that, I didn't have that thing on my keyboard.
The graph of the parent function f(x)=x^3 can be shifted up, down, left, or right by adding or subtracting constants to the function or its variables. The four variations of the function provided will result in vertical or horizontal shifts.
Explanation:The graph of a parent function f(x)=x3, can be shifted in various ways by altering the function equation. When a positive or negative constant is added to the function, such as f(x)=x3+7 or f(x)=x3-7, it results in vertical shifts. Adding the constant shifts the function upward, while subtracting the constant shifts it downwards. On the other hand, if the constant alters the x-value (inside the parentheses), like in f(x-7)=x3 or f(x+7)=x3, it results in horizontal shifts. Adding the constant shifts the function to the left, while subtracting the constant shifts it to the right.
Match each function to the graph's shift:
The graph of the parent function is shifted 7 units down: f(x) = x3 - 7The graph of the parent function is shifted 7 units right: f(x+7) = (x+7)3The graph of the parent function is shifted 7 units up: f(x) = x3 + 7The graph of the parent function is shifted 7 units left: f(x-7) = (x-7)3Learn more about Function Shifts here:https://brainly.com/question/35952685
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I need help here been stuck here ?!
Answer:
Step-by-step explanation:
Angle 9 = 85 degrees
Angle 9 and < 11 are vertical angles
Vertical angles are equal
<11 = 85 degrees
Which of the following is the maximum value of the equation y=-x^2+2x+5
a. 5
b. 6
c. 2.
d. 1
Answer: b. 6
Step-by-step explanation:
The maximum value is the y-value of the vertex.
Step 1: Find the x-value (aka Axis Of Symmetry) using the formula: [tex]x=\dfrac{-b}{2a}[/tex]
[tex]x=\dfrac{-(2)}{2(-1)}=\dfrac{-2}{-2}=1[/tex]
Step 2: input the x-value (above) into the given equation to solve for y:
[tex]y=-x^2+2x+5\\y=-(1)^2+2(1)+5\\y=-1 + 2 + 5\\y = 6[/tex]
the diagram show a closed structure in the shape of a half cylinder. the diameter of each base is 16 feet. the length of the structure is 50 feet. Find the surface area of the entire structure.
Answer:
The surface area is [tex]SA=(800+464\pi)\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the half cylinder is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the half circle
P is the perimeter of the half circle plus the diameter of circle
L is the length of the structure
Find the area B
The area of the half circle is
[tex]B=\frac{1}{2} \pi r^{2}[/tex]
we have
[tex]r=16/2=8\ ft[/tex] -----> the radius is half the diameter
substitute
[tex]B=\frac{1}{2} \pi (8)^{2}[/tex]
[tex]B=32\pi\ ft^{2}[/tex]
Find the value of P (the perimeter of the half circle plus the diameter of circle)
[tex]P=\pi r+D[/tex]
we have
[tex]D=16\ ft[/tex]
[tex]r=8\ ft[/tex]
substitute
[tex]P=\pi (8)+16[/tex]
[tex]P=(8\pi+16)\ ft[/tex]
Find the surface area
[tex]SA=2B+PL[/tex]
[tex]L=50\ ft[/tex]
substitute
[tex]SA=2(32\pi)+(8\pi+16)(50)[/tex]
[tex]SA=64\pi+400\pi+800[/tex]
[tex]SA=(800+464\pi)\ ft^{2}[/tex]
see the attached figure to better understand the problem
Consider the distribution of exam scores (graded from 0 to 100) for 78 students when 35 students got an A, 25 students got a B, and 18 students got a C. Complete parts (a) through (d) below.
How many peaks would you expect for the distribution?
A.There would probably be many peaks corresponding to the different exam scores that each student had.
B.There would probably be no peaks. The distribution of grades always tends to be uniform.
C.There would probably be three peaks, because even though each exam score could be anywhere between 0 and 100, the only grades received were A, B, and C.
D.There would probably be one peak because there are no obvious reasons why the exam scores would form different groups.
Final answer:
The expected number of peaks in the distribution of exam scores for the described student group would be three, correlating to the clusters of the grades A, B, and C.
Explanation:
The question asks how many peaks we would expect in the distribution of exam scores for a given set of students. Given the information that 35 students got an A, 25 students got a B, and 18 students got a C, it would be reasonable to expect that there would be three peaks in this distribution. This is assuming that the scores that correlate with these grades tend to cluster around a certain range or value, which is common in educational grading systems.
In this scenario, the likely three peaks would correspond to the ranges or average scores that are designated for the grades of A, B, and C. Since these are the only grades mentioned and no other grades such as D, E, or F are indicated, one would not expect additional peaks.
Therefore, the most appropriate answer to the question is Option C: There would probably be three peaks because the only grades received were A, B, and C.
Susan is planting marigolds and impatiens in her garden. Each marigold costs $9, and each impatien costs $7. Susan wants the number of marigolds to be more than twice the number of impatiens. She has a maximum of $125 to spend on the plants. This situation can be modeled by the following system of inequalities.
Which statement describes the system of inequalities?
A.
The system represents the minimum amount that Susan can spend on impatiens, x, and marigolds, y, and the relationship between the number of impatiens and marigolds.
B.
The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.
C.
The system represents the minimum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.
D.
The system represents the maximum amount that Susan can spend on impatiens, x, and marigolds, y, and the relationship between the number of marigolds and impatiens.
Answer:
B.
The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.
Answer:
B.
The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.
The original purchase price of a car is $25,000. Each year, its value
depreciates by 13%. Three years after its purchase, what is the value of the
car?
$16,462.58 (rounded from $16462.575)
Explanation:By subtracting 13%, you leave 87%, because [tex]100-13=87[/tex].
So, the expression we need to simplify is [tex]25000 * 0.87^3[/tex], because you need to multiply 25000 by 87% three times.
Find the exponent with a calculator. [tex]25000 * 0.658503[/tex]Multiply with a calculator. [tex]16462.575[/tex]Round your answer to the nearest cent. [tex]16462.58[/tex]Answer:
$16,462.58
Step-by-step explanation:
100 - 13 = 87
So, then it becomes 87% of its value each year.
25000 * 0.87 = 21,750
21750 * 0.87 = 16,462.575
16,462.575 = $16,462.58 (round up)
Answer is $16,462.58
Write the converse of the following statement:
If the trees have no leaves, then it is fall.
If the trees have no leaves, then it is fall.
The trees have no leaves, therefore it is fall.
It is fall since the trees have no leaves.
If it is fall, then the trees have no leaves.
Answer:
Option 4 (If it is fall, then the trees have no leaves).
Step-by-step explanation:
Conditional Statements are the statements which involve "if" and "then". It contains two sets of statements in it. The statement after the word "if" is the hypothesis, and the statement after the word "then" is the conclusion. Conditional statements are written in the form "If A, then B"; where A is the hypothesis, and B is the conclusion. The converse of a conditional statement is the opposite of the original statement: hypothesis and conclusion replace each other. So the converse of the above statement will be "If B, then A".
In this case, A=The trees have no leaves and B=It is fall. Therefore, the converse will be:
If it is fall, then the tress have no leaves. Option 4 is the right answer!!!
find the slope and y-intercept of each line y=4x+1
Answer:
Step-by-step explanation:
the slope is 4
y int is 1
the distance of point (8,5) from the straight line 3x+4y+1=0 is equal to....
a) 7
b) 9
c)10
d)8
Answer:
9
Step-by-step explanation:
So we need to find the point on 3x+4y+1=0 such that when connecting that point to (8,5) the lines that interest are perpendicular ones.
First step solve 3x+4y+1=0 for y.
subract 3x and 1 on both sides: 4y=-3x-1
divide both sides by 4: y=-3/4x-1/4
So a line that is perpendicular to this one is 4/3
So we have the perpendicular line is in the form of y=4/3 x+ b
now we do want this to go through (8,5)
5=4/3 (8)+b
5=32/3+b
5-32/3=b
(15-32)/3=b
-17/3=b
So the perpendicular line we are looking at is y=4/3 x -17/3 .
Now I can find the point I talked about in my first sentence if I find the intersection of the line I just got and the line we started with. I'm going to just sub one into the other since they are both solve for y now.
-3/4 x-1/4=4/3 x-17/3
add 1/4 on both sides
-3/4 x =4/3 x-65/12
subtract 4/3 x on both sides
-3/4 x-4/3 x=-65/12
simplify
-25/12 x =-65/12
25x=65
x=65/25
x=13/5
Now find y by plugging this into y=-3/4 x-1/4 giving you y=-11/5
So we want to actually just find the distance between (13/5,-11/5) and (8,5)
which is sqrt((27/5)^2+(36/5)^2)=9
Write the following equation in standard form : 8/7x^3 + x^4 + 6x +1
Answer:
x^4 +8/7x^3 + 6x +1
Step-by-step explanation:
8/7x^3 + x^4 + 6x +1
Standard from is from the largest power to the smallest power
x^4 +8/7x^3 + 6x +1
What number should be added to both sides of the equation to complete the square?
x2 + 8x = 4
Answer:
16
Step-by-step explanation:
1/2 the linear term (which in this case is 8x) squared.
The linear term is one which may have a number in front of the x, but there is only 1 x.
x^2 does not qualify as a linear term
So for this question
1/2 8 = 4 leave off the x.
squared = 4^2 = 16
You would add 16 to both sides.
Answer:
Add 16 to each side
Step-by-step explanation:
x^2 + 8x = 4
To complete the square, we take the coefficient of the x term, divide by 2, and then square it
8
8/2 =4
4^2 = 16
Add 16 to both sides of the equation
x^2 +8x +16 = 4+16
(x+4)^2 = 20
What is the volume of the rectangular prism with a length of 8 1/2centimeters, width of 9 1/3 centimeters and a height of 12 2/5 centimeters?
The volume is 90 if you add
Answer:
[tex]V = 983.73\ cm^3[/tex] or [tex]V = 983\ ^{11/15}\ cm^3[/tex]
Step-by-step explanation:
By definition the volume of a rectangular prism is the product of its length (l) by its width (w) by its height (h). This is:
[tex]V = lwh[/tex]
In this case we know that
l = [tex]8\ ^{1/2}[/tex] centimeters
l = [tex]8 + \frac{1}{2}=8.5[/tex] centimeters
w= [tex]9\ ^{1/3}[/tex] centimeters
w = [tex]9 + \frac{1}{3}=9.333[/tex] centimeters
h= [tex]12\ ^{2/5}[/tex] centimeters
h = [tex]12 + \frac{2}{5}=12.4[/tex] centimeters
Then
[tex]V = (8.5)(9.333)(12.4)\ cm^3[/tex]
[tex]V = 983.73\ cm^3[/tex]
[tex]V = 983\ ^{11/15}\ cm^3[/tex]
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Answer:
x = 30
Step-by-step explanation:
The sum of the 3 interior angles of a triangle = 180°, hence
x + x + 10 + 3x + 20 = 180
5x + 30 = 180 ( subtract 30 from both sides )
5x = 150 ( divide both sides by 5 )
x = 30
what is the differnce between (-4)-6
Answer:
24
Step-by-step explanation:
(-4) -6? well it equals 24 because a negative plus a negative equals a positive.
Hope my answer has helped you! If not i'm sorry.
Answer:
The correct answer is -10. 24 isn't correct ^^^^.
Step-by-step explanation:
Write the fraction as a whole or mixed number.
Hong Kong reported approximately 1,500 cellular phones per 1,000 people. Express the number of phones per person as a whole or mixed number.
Answer:
[tex]1\frac{1}{2}[/tex]
Step-by-step explanation:
If there is 1500 cellular phones per 1000 people, then the number of phones per person is:
[tex]\frac{1500}{1000} = \frac{15}{10} = \frac{3}{2}[/tex]
Now we know that [tex]\frac{3}{2} = 1 + \frac{1}{2} = 1\frac{1}{2}[/tex]
5. Which equation is of a circle that has a center at
(3,-2) and a radius of 9?
A (x + 3)2 + (y - 2)2 = 9
B (x + 3)2 + (y - 2)2 = 81
C (x - 3)2 + (y + 2)2 = 9
D (x - 3)2 + (y + 2)2 = 81
Answer:
[tex]\large\boxed{D.\ (x-3)^2+(y+2)^2=81}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center at (3, -2) and the radius r = 9. Substitute:
[tex](x-3)^2+(y-(-2))^2=9^2\\\\(x-3)^2+(y+2)^2=81[/tex]
The volume of a cylinder with a base of radius ris the area of the base times
the length of its height (h). Which of the following is the formula for the
volume of a cylinder?
What is the value of y in the solution to the system of equations?
*x+3y=1
2x – 3y = -30
Answer:
[tex]\large\boxed{y=\dfrac{32}{9}}[/tex]
Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}x+3y=1\\2x-3y=-30\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=-29\qquad\text{divide both sides by 3}\\.\qquad x=-\dfrac{29}{3}\\\\\text{put the value of x to the first equation}\\\\-\dfrac{29}{3}+3y=1\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\left(-\dfrac{29}{3\!\!\!\!\diagup_1}\right)+(3)(3y)=(3)(1)\\\\-29+9y=3\qquad\text{add 29 to both sides}\\\\9y=32\qquad\text{divide both sides by 9}\\\\y=\dfrac{32}{9}[/tex]
By adding the system of equations and solving for x, then substantifying back into the first equation, we find that y in this system of equations is approximately 3.5556.
Explanation:To find the value of y in the given system of equations, you can add the two equations together. The first equation is x+3y=1 and the second equation is 2x – 3y = -30. Here are the steps:
Add the two equations: (x + 3y) + (2x - 3y).The y terms cancel out and you end up with 3x = -29.Divide both sides by 3 to solve for x: x = -29/3 which is about -9.6667.Substitute x = -9.6667 into the first equation: -9.6667 + 3y = 1.Isolate y by adding 9.6667 to both sides and then divide both sides by 3: y = (1 + 9.6667)/3. You will find that y = 3.5556 approx.
This value, 3.5556, is the value of y in the solution for the system of equations.
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Explain how to find the missing exponent given the base and the value
Answer:
To find the value of missing exponent, we have to split the number which is in other side of equal sign (which is not having power) as the multiple of base of the missing exponent.
On both sides, powers have the same base, so their exponents must be equal.
Step-by-step explanation:
Problem 1:Write the missing exponent:
25=5^x
Let x be the missing exponent.
To find the value missing exponent, we have to split the number which is in the left side as the multiple of the base of the missing exponent.
That is,
25=5*5 or 5^2
Now,
5^2=5^x
Powers have the same base so their exponent must be equal.
Hence the missing exponent is 2
the graph of y= sqrtx is translated 4 units left and 1 unit up to create the function h(x). the graph of h(x) is shown on the coordinate grid. what is the range of h(x)?
Answer:
C. [tex]\{y|y\ge 1\}.[/tex]
Step-by-step explanation:
Consider the parent function [tex]f(x)=\sqrt{x}.[/tex]
The domain of this function is [tex]x\ge 0;[/tex]The range of this function is [tex]y\ge 0.[/tex]Now consider given function [tex]h(x)=\sqrt{x+4}+1[/tex] (translated 4 units left and 1 unit up.)
The domain of this function is [tex]x\ge -4;[/tex]The range of this function is [tex]y\ge 1.[/tex]Answer:
The range of the function h(x) is [tex]R=\{y|y\geq 1\}[/tex]
Step-by-step explanation:
Given : The graph of [tex]y=\sqrt{x}[/tex] is translated 4 units left and 1 unit up to create the function h(x).
To find : What is the range of h(x)?
Solution :
When the graph f(x) is translated then
1) f(x)+b shifts the function b units upward.
2) f(x + b) shifts the function b units to the left.
The graph of [tex]y=\sqrt{x}[/tex] is translated 4 units left.
i.e. [tex]y=\sqrt{x+4}[/tex]
The graph of [tex]y=\sqrt{x}[/tex] is translated 1 unit up.
i.e. [tex]y=\sqrt{x+4}+1[/tex]
So, The required function h(x) is [tex]h(x)=\sqrt{x+4}+1[/tex]
The range of a function is set of output values produce by a function.
In the given graph, y value is always greater than and equal to 1.
So, The range of the function h(x) is [tex]R=\{y|y\geq 1\}[/tex]
Rearrange x=3g+2 to make g the suject
please explain this to me well
Answer:
(x-2)/3 = g
Step-by-step explanation:
First you move the 2 over to the same side as the x by subtracting it on both side, because you are trying to make the g "alone". Then you move the 3 by doing the inverse, just like with the 2. Since you are multiplying 3 on one side to move to the other side you have to divide both sides by 3.
Answer:
g= (x-2)/3
Step-by-step explanation:
x=3g+2
Subtract 2 from each side
x-2=3g+2-2
x-2 = 3g
Divide each side by 3
(x-2)/3 = 3g/3
(x-2)/3 =g
g= (x-2)/3
If 132 people attend a concert and tickets for adults cost $3.25 while tickets for children cost $2.25 and total receipts for the concert was $364, how many of each went to the concert?
__adults
__children
Answer:
112 adults
20 children
Step-by-step explanation:
In order to solve this problem, we must create system of equations. By definition, system of equations are two equations which help you find unknown variables.
As for this problem, we need to set two variables for each type of person.
Let x represent adults
Let y represent children
We can break the question apart, and form equations based on the information given.
"tickets for adults cost $3.25 while tickets for children cost $2.25 and total receipts for the concert was $364"
$3.25x + $2.25y = $364
Now, we must form our second equation based on the information given.
"If 132 people attend a concert" "how many of each went to the concert"
x + y = 132
Solve for x, or the total number of adults
x = -y + 132
3.25(-y + 132)+ 2.25y = $364
Distribute 3.25
3.25 * -y = -3.25y
3.25 * 132 = 429
-3.25y + 429 = $364
Subtract 429 from both sides
364 - 429 = -65
-3.25y = -65
Now divide both sides by -3.25 to find the value of y.
y = 20
Therefore, 20 children attended the concert.
In order to find the total amount of adults who attended, subtract 20 from the total number of people that attended.
132 - 20 = 112
So, 112 adults attended as well as 20 children.
To find the number of adults and children who attended the concert, we can set up a system of equations and solve for the variables. Using the given information, we can determine that there were 67 adults and 65 children at the concert.
Explanation:To solve this problem, we can use a system of equations. Let's assume that the number of adults who attended the concert is 'a' and the number of children is 'c'. We can form two equations from the given information:
a + c = 132 (Equation 1)3.25a + 2.25c = 364 (Equation 2)Now, we can solve the system of equations to find the values of 'a' and 'c'.
Solving Equation 1 for 'a', we get a = 132 - c.
Substituting this value of 'a' into Equation 2, we get 3.25(132 - c) + 2.25c = 364.
Expanding and simplifying the equation gives us 429 - 3.25c + 2.25c = 364.
Combining like terms, we get -c = -65.
So, c = 65.
Substituting this value of 'c' into Equation 1, we get a + 65 = 132.
Solving for 'a', we get a = 67.
Therefore, there were 67 adults and 65 children at the concert.
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Linear Equation
Which line represents the linear equation
-3y = 15 - 4x?
The equation -3y = 15 - 4x rewritten in slope-intercept
form is
The y-intercept is and the slope of the line is
Line
v is the graph of the line -3y = 15 - 4x.
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{We have the equation:}\\\\-3y=15-4x\\\\-3y=-4x+15\qquad\text{ivide both sides by (-3)}\\\\\boxed{y=\dfrac{4}{3}x-5}\\\\\boxed{slope=\dfrac{4}{3}}\\\boxed{y-intercept=-5}[/tex]
[tex]\text{To draw a graph we need only two points.}\\\text{We choose any value of x, put it to the equation of the line}\\\text{and calculate the value of y:}\\\\for\ x=0\\\\y=\dfrac{4}{3}(0)-5=0-5=-5\to(0,\ -5)\\\\for\ x=3\\\\y=\dfrac{4}{3}(3)-5=4-5=-1\to(3,\ -1)\\\\\text{The graph is in attachment}.[/tex]
Answer:
answer in picture
Step-by-step explanation: