Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.


Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′.

The slope of is
.

Answer:

[tex]\large\boxed{V=\dfrac{32}{3}\pi\ cm^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{A diameter}\ D=2R\Rightarrow R=\dfrac{D}{2}.\\\\\text{We have}\ D=4\ cm\to R=\dfrac{4}{2}\ cm=2\ cm\\\\\text{Substitute:}\\\\V=\dfrac{4}{3}\pi(2)^3=\dfrac{4}{3}\pi(8)=\dfrac{32}{3}\pi\ cm^3[/tex]

Answer:

maybe number 2

Step-by-step explanation:

because if 2+k=18 then there is no other k there and where did the additional 2 come from ?and 2k=18 then value of k is 9 + there is balance.I may be wrong correct me but i think it is no.2

Answer:

2k = 18

k = 9

Step-by-step explanation:

First we have to look at each side of the hanger.

There are 2 k's, which can be represented as "2 times the value of k" or 2k.

On the other side, we have the value of 18. The question states that the two sides are balanced. Therefore, the correct equation that represents the image is:

2k = 18.

To find the value of k that makes the equation true, we must isolate the variable k. To do this, we divide 2 from each side of the equation.

2k ÷ 2 = 18 ÷ 2

k = 9.

The value of k that makes the equation true is 9.

The calculated value of y in this linear system is 18

How to determine the value of y in this linear system?

From the question, we have the following parameters that can be used in our computation:

x + y + z = 62

x - y = 12

2x + y + z = 92

Subtracting the equations 1 and 2, we have

2x - x = 92 - 62

x = 30

In equation (2), we have

x - y = 12

This gives

y = x - 12

Substitute the known values into the equation

y = 30 - 12

Evaluate

y = 18

Hence, the value of y is 18

The best name for the part of the figure identified by the arrow is line of symmetry.

The best name for the part of the figure identified by the arrow is line of symmetry. It refers to a line that divides a figure into two equal halves, which are mirror images of each other.

The line of symmetry can be identified by the arrow in the figure where the reflection occurs.

For example, in the letter 'A', the line through the middle vertically is the line of symmetry, as both sides of the letter are identical when folded along that line.

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Word Problem #1:

You are in a submarine at a depth of some unknown value x. The submarine rises 15 feet. After this point, you are able to record the depth to be 18 feet below sea level.

x = original depth

15 = height you rise up

-18 = final depth

x+15 = final depth

x+15 = -18 is the equation we solve to find the value of x

=========================================================

Word Problem #2:

You are in debt to your friend. Debt is represented by negative numbers. For example, writing -2 means you are 2 dollars in debt. If you start off being x dollars in debt, but pay off $15, then you will have a balance of x+15 dollars. If this new final balance is -18, then we can say x+15 = -18

So in short: you go from x dollars in debt to 18 dollars in debt after paying off $15 to your friend.

Answer:

A. Buying socks and buying shoes are dependent events.

Step-by-step explanation:

We are given that

The probability that a customer buys socks ,P(A)=0.15

The probability that a customer socks given that the customer buys shoes P(A\B)=0.20

The probability that a customer buys shoes,P(B)=1-0.15=0.85

By using formula P(E')=1-P(E)

Where P(E)= Probability of an event that is happened

P(E')=Probability of an event that is not happened

We have to find [tex]P(A\capB)[/tex]  for two events

[tex]P(A)\cdot P(B)[/tex]

[tex]=0.85\times 0.15=0.1275[/tex]

We know that conditional probability of an event when given that the probability of an event B is given

[tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}[/tex]

[tex] 0.20=\frac{P(A\cap B)}{0.85}[/tex]

[tex]P(A\cap B)=0.20\times 0.85=0.17[/tex]

[tex]P(A\cap B)\neq P(A)\cdot P(B)[/tex].

Therefore, the two events are dependent .Hence, Buying socks and buying shoes are dependent events.

Therefore, option A is true.

Answer: A. Buying socks and buying shoes are dependent events.

Step-by-step explanation:

Answer:

1/(x+3)+7/(x+2)

Step-by-step explanation:

I'm assuming the full numerator is (8x+23)... and by making that assumption I'm assumed the fraction was (8x+23)/[(x+3)(x+2)].

(8x+23)/[(x+3)(x+2)]=A/(x+3)+B/(x+2)

8x+23=A(x+2)+B(x+3)                   I multiply both sides by (x+3)(x+2)

Set x to -2 that gives -16+23=B          so this means B=7

Set x to -3 instead that gives -24+23=A(-1)   so this means A=1

So (8x+23)/[(x+3)(x+2)]=1/(x+3)+7/(x+2)

Answer:

3^2=x+1 is the equivalent

Step-by-step explanation:

3^2=(x+1)  is equivalent to log_3(x+1)=2

where x+1 is positive

Answer:

1/32768

Step-by-step explanation:

First, solve the parenthesis:

2^3 = 2 * 2 * 2 = (2 * 2) * 2 = (4) * 2 = 8

Next, solve the outer power. Note that it has a negative sign, which means that after you solve for the power sign, you have to put the number under 1.

(8)^-5 = 1/(8 * 8 * 8 * 8 * 8) = 1/32768

1/32768 is your answer.

~

Answer:

A) 1/2^15

Step-by-step explanation:

edge2021

Answer:

f(x) = -(x-4)^2 + 5

Step-by-step explanation:

The function [tex]f(x) = -(x-4)^2 + 5[/tex] is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.

Proving that [tex]f(x) = -(x-4)^2 + 5 \le 5[/tex] for all x:

[tex]x^2 \ge 0 \Rightarrow (x-4)^2 \ge 0 \Rightarrow -(x-4)^2 \le 0 \Rightarrow -(x-4)^2 + 5 \le 5.[/tex]

The function which has a range of {y | y < 5} is f(x) = -(x – 5)² + 4​.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given a range of the function, {y | y < 5}.

We want to find the corresponding function.

The range of the function contains all the values less than 5.

For the first two functions, when we substitute x = 4,

The value of the function, f(x) = 5

So this is not possible.

For the third function also, when we substitute any integers other than 5, the value of function is greater than 5.

Hence the correct option is D.

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[tex]\bf \begin{cases} f(x)=3x^2\\ g(x)=4x^3+1 \end{cases}\qquad (f\cdot g)(x)\implies f(x)\cdot g(x)\implies [3x^2]\cdot [4x^3+1] \\\\\\ 12x^2x^3+3x^2\implies 12x^{2+3}3x^2\implies \stackrel{\textit{5th degree}}{12x^{\stackrel{\downarrow }{5}}+3x^2}[/tex]

Answer:

15

Step-by-step explanation:

Substitute x = - 5 into f(x)

f(- 5) = 5(- 5) + 40 = - 25 + 40 = 15

Answer:

[tex]\large\boxed{B)\ \dfrac{3V}{3.14r^2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{3}\cdot3.14\cdot r^2h=V\\\\\dfrac{3.14}{3}r^2h=V\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{3.14}{3\!\!\!\!\diagup_1}r^2h=3V\\\\3.14r^2h=3V\qquad\text{divide both sides by}\ 3.14r^2\\\\h=\dfrac{3V}{3.14r^2}[/tex]

Answer:5x2+12x-14

Step-by-step explanation:

(5x2+11x-9)-(2x-3x+5)

5x2+11x-9-2x+3x-5

5x2+12x-14

[tex](5x^2 + 11x - 9) - (2x - 3x + 5)=5x^2+11x-9-2x+3x-5=5x^2+12x-14[/tex]

-------------------------------------------------

[tex](5x^2 + 11x - 9) - (2x^2 - 3x + 5)=5x^2+11x-9-2x^2+3x-5=3x^2+14x-14[/tex]

Answer: 20

Step-by-step explanation:

Given: Point [tex]\text{G}[/tex] is on line segment [tex]\text{FH}[/tex]. Given [tex]\text{FH}[/tex] is [tex]4\text{x}+8[/tex] , [tex]\text{FG}[/tex]. is [tex]\text{x}[/tex], and [tex]\text{GH}[/tex] is [tex]5\text{x}[/tex].

To Find: the numerical length for [tex]\text{GH}[/tex].

Solution:

Point [tex]\text{G}[/tex] is on the line segment [tex]\text{FH}[/tex]

therefore,

[tex]\text{FH}=\text{FG}+\text{GH}[/tex]

putting the values

[tex]4\text{x}+8=\text{x}+5\text{x}[/tex]

[tex]4\text{x}+8=6\text{x}[/tex]

[tex]8=2\text{x}[/tex]

[tex]\text{x}=4[/tex]

Now,

[tex]\text{GH}=5\text{x}[/tex]

[tex]\text{GH}=5\times4[/tex]

[tex]\text{GH}=20[/tex]

Hence numerical length of line segment [tex]\text{GH}[/tex] is [tex]20[/tex]

The numerical length of GH is 20

If Point G is on the line segment FH, this means that:

Given the following parameters:

FH=4x+8

FG=x

GH=5x

Substitute the given values into the formula as shown:

x + 5x = 4x + 8

6x = 4x + 8

6x - 4x = 8

2x = 8

Divide both sides by 2

2x/2 = 8/2

x = 4

Get the length of GH

GH = 5x

GH = 5(4)

GH = 20

Hence the numerical length of GH is 20

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Answer:

C. 40°

Step-by-step explanation:

From the diagram, in triangle XYZ, XY=XZ=6 units. This means triangle XYZ is isosceles triangle with base YZ.

In isoscels triangle angles adjacent to the base are congruent, so

∠ZYX=∠YZX=70°

The sum of all interior angles in triangle is always 180°, so

∠ZYX+∠YZX+∠ZXY=180°

∠ZXY=180°-70°-70°

∠ZXY=40°

∠ZXY is ∠X, so ∠X=40°

Answer:

2nd choice B.

Step-by-step explanation:

You can use the options A-D to help you eliminate pretty quickly without actually graphing

So first chose says you have the graph on the left when x<1 But you should see our visual actually says we want to include what happens at 1 (the filled dot) so this isn't the answer

Second choice Possible

Third choice... I'm just going to look at one of the parts... x^2+4 for x<=1 says we should have part of a parabola to the left of x=1 (inclusive) but there is not parabola in our visual

Fourth choice: same reason as third choice

Answer is the 2nd

Answer:

Q1. The solution for the quadratic equation on a graph is same as the value of x-intercept(zeros)

Q2. discriminant(b^2-4ac) when y=ax^2 + bx + c

there are 3 situations:

1. discriminant > 0 → 2 real solutions(2 x-intercepts/zeros)

2. discriminant = 0 → 1 real solution(1 x-intercept/zero)

3. discriminant < 0 → 0 real solution(0 x-intercept/zero) → also 2 imaginary solution

Hope it helped!

Step-by-step explanation:

Answer:

1) You find the solution by identifying the x-intercepts.

2) Possible real solutions:

- One real solution.

- Two distinct real solutions.

Step-by-step explanation:

1) The graph of a quadratic equation is a parabola.

By definition, the x-intercepts (Where [tex]y=0[/tex]) are the solutions of the quadratic equation .

2) Given a quadratic equation [tex]ax^2+bx+c=0[/tex], you can know the number of real solutions by using this formula to find the Discriminant :

[tex]D=b^2-4ac[/tex]

If  [tex]D=0[/tex], then there is one real solution with multiplicity two.

If  [tex]D>0[/tex], then there are two distinct real solutions.

On a graph:

-If the graph has two x-intercepts, then the quadratic equation has two real solutions.

 -If the graph has one x-intercept , then the quadratic equation has one real solution.

Answer:

Step-by-step explanation:

First, factor the denominator: (x-5)(x+4)

Since the denominator already has the two values, you only need to multiply it by (x+3), which means you need to multiply the numerator by (x+3):

(x-1)(x+3)/(x-5)(x+4)(x+3)

(x-1)(x+3) then simplifies to [tex]x^2+2x-3[/tex]

Answer:

Step-by-step explanation:

Slope = y/x

y1-y2/x1-x2=slope of 2 points

8-3/-6-2 = 5/-8 which equals -5/8 or -.625.

The slope of line for the points is -5/8.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

given:

We have the Points (–6, 8), (2, 3).

So, the slope is

m = (3- 8)/ (2- (-6))

m = -5 / (2+6)

m = -5 / 8

Thus, the Slope is -5/8.

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Answer:

[5, 0]

Step-by-step explanation:

x-intercept is where 0 = y. Just simply plug in 0 for y, then your x is given to you in your face.

Answer:

it is 2

Step-by-step explanation:

Hello There!

The slope of this line would be 3.

The slope is gradually increasing so starting from the Y intercept value, its consistently going up 3 on the Y axis and going over 1 on the X axis

ANSWER

[tex]k = 17[/tex]

EXPLANATION

The given function is

[tex]f(x) = 2x + 3[/tex]

The translation that shifts this function 10 units to the right is

[tex]f(x - 10)[/tex]

This implies that

[tex]f(x - 10) = 2(x - 10) + 3[/tex]

We expand the parenthesis to get:

[tex]f(x - 10) = 2x -20+ 3[/tex]

[tex]f(x - 10) = 2x - 17[/tex]

Comparing this equation with

[tex]f(x) = 2x - k[/tex]

we have

[tex]k = 17[/tex]

k=17

The new function would be f(x)=2x-17

In the previous function when u put x=0 you got 3.

Now when the function moves 10 units to the right you still have to get y=3 for x=10. So

2x-k=3 substitute 10 for x

20-k=3 solve for k

K=17.

Answer:

The value of 8m is 2

Step-by-step explanation:

step 1

Find the value of m

we know that

[tex]m^{-3} =64[/tex]

so

[tex]\frac{1}{m^{3}}=64\\ \\m^{3}=\frac{1}{64}\\ \\ m=\frac{1}{\sqrt[3]{64}}\\ \\m=\frac{1}{4}[/tex]

step 2

Find the value of 8m

[tex]8m=8(\frac{1}{4})=2[/tex]

Answer:7

Step-by-step explanation:since it has the rule f(n) =2n+1

Third term is when n=3

Therefore 2(3) +1=7

Answer:

The y-intercept is the point (0,5)

Step-by-step explanation:

step 1

Find the slope of the line perpendicular to the line y=(3/4)x+3

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

we have

m1=3/4 -----> the slope of the line y=(3/4)x+3

Find m2

substitute

(3/4)*m2=-1

m2=-4/3

step 2

Find the equation of the line into point slope form

The equation is equal to

y-y1=m(x-x1)

we have

m=-4/3

(x1,y1)=(3,1)

substitute

y-1=-(4/3)(x-3) ----> equation of the line into point slope form

step 3

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation of the line and solve for y

y-1=-(4/3)(0-3)

y-1=4

y=4+1=5

The y-intercept is the point (0,5)

Final answer:

The y-intercept of the line perpendicular to y = 3/4x+3 that includes the point (3, 1) is 5.

Explanation:

To find the y-intercept of the line perpendicular to the line y = 3/4x+3 that includes the point (3, 1), we first need to determine the slope of the perpendicular line. Since the given line has a slope of 3/4, the slope of the perpendicular line will be the negative reciprocal, which is -4/3. We then use the point-slope form of a line equation, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope.

Substituting the point (3, 1) and the slope -4/3 into the equation gives us y - 1 = -4/3(x - 3). Simplifying, we get y = -4/3x + 5. The y-intercept of this line is the y-value when x is zero, which in this case is 5.

Answer:

The vertical distance from the ground to the bird's eyes is 47.67 m

Step-by-step explanation:

* Lets explain the situation of the problem

- There is a bird on the top of  a tree

- The bird looks down on a field mouse at an angle of depression of 50°

- The field mouse is 40 meters from the base of the tree

* Consider that the vertical distance from the ground to the bird's eyes,

 the distance from the field mouse to the base of the tree distance

 from the bird eyes to the field mouse formed a right triangle

- The hypotenuse is the distance from the bird eyes to the field mouse

- The horizontal side is the distance from the field mouse to the base

 of the tree

- The angle between the hypotenuse and the horizontal side is the

 angle of depression which = 50°

- The opposite side to the angle of measure 50° is the vertical distance

 from the ground to the bird's eyes

* Lets use trigonometry functions to find the vertical distance

∵ The length of the adjacent side to the angle of measure 50° is 40 m

∵ The length of the opposite side to the angle of measure 50° is h m

∵ tan Ф = opposite side to Ф ÷ adjacent side to Ф

∵ Ф = 50°

∴ tan 50° = h/40 ⇒ by using cross multiplication

∴ 40 tan 50° = h

∴ h = 47.67 m

* The vertical distance from the ground to the bird's eyes is 47.67 m

Answer:

2957

Step-by-step explanation:

Instead of just giving you a formula.. I want to show you how to understand the formula

So 2200 is the initial population

After 1st year, we are going to have an increase of 3% so 1st yr gives us 2200(1.03)=2266

After 2nd year, we are going to have increase of 3% from previous year so we could do 2266(1.03) or realize this is the same as 2200(1.03)^2 .

so you are going to keep multiplying factors of 1.03 to that per year.

So at 10 years we have 2200(1.03)^10

The formula I mentioned was really this initial population times (1.03)^(number of yrs)

So answer is 2956.616

To the nearest whole number is 2957

The correct option is:

C. [tex]2(y+1)+y=7[/tex]

To find which of the given options are not the result of a substitution in the given system, we need to isolate the variable in function of the other variable, and then substitute it.

So, substituting and discarding, we have:

- First equation:

[tex]2x+y=7[/tex]

Isolating "y", we have:

[tex]y=7-2x[/tex]

Then, substituting it into the second equation, we have:

[tex]y-x=1[/tex]

[tex]7-2x-x=1[/tex]

We have that it's a result of a substitutiong in the following system (option A)

- Second equation:

[tex]y-x=1[/tex]

Isolating "y", we have:

[tex]y=x+1[/tex]

Then, substituting it into the first equation, we have:

[tex]2x+y=7[/tex]

[tex]2x+(x+1)=7[/tex

[tex]2x+x+=7[/tex

We have that it's a result of a substitution in the following system (option B)

Hence, we have that the option C is not a result of a substitution in the given system of equations since there is not a possible value of the variable "x" that is equal "y+1".

So, the correct option is:

C. [tex]2(y+1)+y=7[/tex]

Have a nice day!

Answer:

C. 2(y + 1) + y = 7​

Step-by-step explanation:

The correct answer is D. (2x^2+4-7)(x)+(2x^2+4x-7)(x-2).

To use the distributive property, we need to distribute the first factor,

(2x^2 +4−7), over the two factors in the second set of parentheses, (x) and  (x−2).

This means we multiply each term in the first factor by each term in the second set of parentheses, and then add the products together.

Here is the correct distribution:

(2x^2+4-7)(x) + (2x^2+4-7)(x-2)

= (2x^3+4x-7x) + (2x^3-4x+14x-14)

= 4x^3-3x+7 + 10x-14

= 4x^3+7x-7

Therefore, the correct answer is D. (2x^2+4-7)(x)+(2x^2+4x-7)(x-2).

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