To factor 4x2-25, you can first rewrite the expression as:

Final answer:

The equation for Function A is x = -5, as it represents a vertical line. The equation for Function B is y = -5, representing a horizontal line. Both cases are special and do not use the slope-intercept form.

Explanation:

To find the equations for Function A and Function B, we will analyze the points given for each function.

Function A

For Function A, we have the points (–5, –2) and (–5, 7). These points share the same x-value but have different y-values, which means the line is vertical. The equation for a vertical line is x = constant. Therefore, the equation of line A is x = -5.

Function B

For Function B, the points are (7, –5) and (–2, –5). These points share the same y-value, indicating a horizontal line. The equation for a horizontal line is y = constant, thus the equation of line B is y = -5.

For both equations, we do not use slope-intercept form as these are special cases of vertical and horizontal lines where slope is undefined (vertical line) and zero (horizontal line)

Final answer:

Function A is a vertical line with the equation x = -5, and Function B is a horizontal line with the equation y = -5.

Explanation:

To find the equations for Linear Functions A and B, we need to consider their points and use them to calculate the slope (m) and y-intercept (b). For Linear Function A, the two points given are (–5, –2) and (–5, 7). Since the x-values are the same and the y-values differ, this indicates a vertical line. For a vertical line, the equation does not have a y-intercept and the slope is undefined because the change in x is zero. The equation for a vertical line is simply x = a constant value. Therefore, Function A has an equation of x = -5.

For Linear Function B, the points provided are (7, –5) and (–2, –5). Here, the y-values are the same, indicating a horizontal line. For a horizontal line, the slope (m) is zero because there is no change in y. The y-value for all points on the line is the same, which is the y-intercept (b). Consequently, Function B has an equation of y = -5.

Answer:

±[tex]12[/tex]

Step-by-step explanation:

We need to find [tex]\sqrt{144}[/tex].

Now, we know that  [tex](12)^{2} = 144[/tex] and [tex](-12)^{2} = 144[/tex]

Therefore: [tex]\sqrt{144}=[/tex]±[tex]12[/tex]

Summarizing, the real square roots of 144 are ±[tex]12[/tex]

[tex]\sqrt{144}=\pm12[/tex]

Answer:

f(x) = 2(x - 5)² - 6

Step-by-step explanation:

Vertex Formula: y = a(x - h) + k; Vertex: [h, k]; there is a vertical stretch at 2 = a. The -h [phase shift (horizontal shift)] in parentheses gives you the OPPOSITE term of what it really is, so really, 5 = h. Now, k [vertical shift] is the ONLY normal term, so -6 = k.

Answer:

x=-16

Step-by-step explanation:

The given equation is:

x = 8a

which was written to find the value of x.

We have to find the value of x when the value of a is inserted as -2

So, putting the value

x = 8(-2)

x= -16

So the value of x when a = -2 is -16 ..

Answer:

x= -16

Step-by-step explanation:

The rewritten equation for x from part A is x = 8a.

Substitute -2 for a in the equation and solve:

x = 8(-2)

x = -16

Easy ₛₕᵢₜ Yo

Answer:

21.66

20.545

20.479

20.15

20.1

Hello There!

From Least To Greatest, The Numbers Would Be

20.1, 20.15, 20.479, 20.545, 21.66

Answer:

Step-by-step explanation:

No c

 as she was initially 300m away from the bridge (distance from bridge=300m)   (time=0) so it was her starting point.

      and after 6 minutes  (time=6min)  she reached the bridge.      (distance from bridge = 0m)

Answer:

C.Katy was initially 300 meters away from the bridge and it tooke her 6 minutes to reach the bridge.

Step-by-step explanation:

As you can see in the table when Katy had been walking for 0 minutes, she was 300 meters away, so initially Katy was 300 meters from the bridge.

When she reaches the bridge is when the distance is reduced to 0, since distances is reduced to 0 at 6 minutes, we can infer that it took her 6 minutes to reach the bridge, and that se was walking at a pace of 50 meters per minute.

Answer:

A (7^6)

Step-by-step explanation:

Step 1: Find the property of 7^13/7^7

b^m/b^n=b^m-n

Therefore, when the numerator and denominator are the same number, the powers can be subtracted to simplify the answer.

Step 2: Apply the property to the question

7^13/7^7 = 7^13-7

=7^6

Hence, option A is the correct answer.

!!

Answer:

The equivalent expression is [tex]7^{6}[/tex] ⇒ answer A

Step-by-step explanation:

* Lets revise some rules of the exponents

- In the exponential functions we have some rules

# In multiplication if we have same base then add the power

  b^m  ×  b^n  =  b^(m + n)  

- Ex: [tex]5^{11}*5^{4}=5^{11+4}=5^{15}[/tex]

# In division if we have same base we subtract the power

  b^m  ÷  b^n =  b^(m – n)

- Ex: [tex]\frac{3^{10}}{3^{4}}=3^{10-4}=3^{6}[/tex]

* Now lets solve the problem

- There is the expression [tex]\frac{7^{13}}{7^{7}}[/tex]

- We have base 7 up and down

∵ In division if we have same base we subtract the power

∵ The base up is 7 and the base down is 7

- We will subtract the powers

∴ [tex]\frac{7^{13}}{7^{7}}=7^{13-7}=7^{6}[/tex]

∴ The answer is [tex]7^{6}[/tex]

* The equivalent expression is [tex]7^{6}[/tex]

Answer:

Answer:

The area of the triangle is [tex]A=4\ units^{2}[/tex]

Step-by-step explanation:

Let

A(0, −2),B​ (0, −3) and ​ C(8, -3)

Plot the vertices

see the attached figure

Triangle ABC is a righ triangle

The area of the triangle ABC is equal to

[tex]A=\frac{1}{2}(BC)(AB)[/tex]

[tex]BC=8-0=8\ units[/tex]

[tex]AB=-2-(-3)=1\ units[/tex]

substitute

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

[tex]A=4\ units^{2}[/tex]

Final answer:

To find the unit rate of a 16oz soda bottle that costs $3.49, divide the price by the ounces, resulting in $0.218125 per ounce, which rounds to $0.22 per ounce.

Explanation:

The question is about calculating the unit rate of a 16oz bottle of soda that costs $3.49. To find the unit rate, we divide the total cost by the number of ounces. Thus, the unit rate is $3.49 ÷ 16 oz, which equals approximately $0.218125 per ounce. Rounding to the nearest tenth of a cent, the unit rate is $0.22 per ounce.

Answer:

B'C'D'

Step-by-step explanation:

The figure was just translated, without any deformation, these are similar figures... so their corresponding angles are the same.

Since it was just moved down by 4 units, none of the angles were changed, and none of the side lengths were changed.

Since vertex C' corresponds to vertex C, the angle B'C'D' corresponds to original angle BCD.

Answer:2321

Step-by-step explanation:

The answer is:

The correct option is:

C. 18 inches.

To calculate the volume of a cylinder we need to use the formula:

[tex]Volume=\pi *radius^{2}*height[/tex]

We are given a cylinder that has a volume of 288 π cubic inches and we know that its radius is equal to 4 inches, so, to calculate the height of the cylinder, we need to isolate it from the equation of volume, so, isolating we have:

[tex]Volume=\pi radius^{2} height[/tex]

[tex]\frac{Volume}{\pi radius^{2} }=height[/tex]

Now, substituting the given information, we have:

[tex]height=\frac{288\pi in^{3}}{\pi (4in)^{2} }=\frac{288\pi in^{3}}{16\pi in^{2} }=18in[/tex]

Hence, we have that the correct answer is:

C. 18 inches.

Have a nice day!

Answer:

The correct answer is option c 18 inches

Step-by-step explanation:

Points to remember

Volume of cylinder =  πr²h

Where r - Radius of cylinder and

h - Height of cylinder

To find the height of cylinder

Here volume = 288π cubic inches and radius = 4 inches

Volume = πr²h

288π = π* 4² * h

288 = 16h

h = 288/16 = 18 inches

Therefore height of cylinder = 18 inches

The correct answer is option c 18 inches

Answer:

Step-by-step explanation:

Subtracting a number means the same as adding the opposite number.

(-)(-) = (+)

6 - (-4) - (-3)

opposite number to -4 is 4

opposite number to -3 is 3

6 - (-4) - (-3) = 6 + 4 + 3 = 13

Answer:

the correct answer is 13.

Step-by-step explanation:

Answer:

She spent 25%

Hello There!

The girl spent 1/4 of her money. 12 is divisible by 3 and when we divide, we get a quotient of 3

If the girl spent $3, we subtract 3 from 12 and we see that 3 = 1/4 6=2/4 and 9=3/4 but if she spent $3 it would be 1/4

The Girl Spent 1/4 of her money. This is also known as 25%

Answer:

The length of side BC is 20.5 in

Step-by-step explanation:

we know that

In the right triangle ABC

The function cosine of angle of 35 degrees is equal to divide the adjacent side to angle of 35 degrees by the hypotenuse of the right triangle

so

cos(35°)=a/25

Solve for a

Multiply by 25 both sides

a=(25)*cos(35°)=20.5 in

therefore

The length of side BC is 20.5 in

The answer is:

The length of BC is equal to 20.5 inches.

Since we are working with a right triangle and we already know some of its dimensions, we can calculate the length of PC using the following equation:

[tex]Cos\alpha =\frac{a}{Hypotenuse}[/tex]

Where,

a is equal to BC

hypotenuse is equal to 25 inches.

alpha is equal to 35°

So, we will have the following equation and we can isolate "a" from it, so substituting we have:

[tex]Cos(35\°)=\frac{a}{25in}[/tex]

[tex]a=25in*Cos(35\°)=20.47inches[/tex]

Hence, the length of BC is equal to 20.5 inches (rounded to the nearest tenth)

Have a nice day!

Answer:

Option A. 54.008 cubic feet

Step-by-step explanation:

we know that

The volume of the barrel is equal to

[tex]V=\pi r^{2}h[/tex] ----> volume of the cylinder

we have

[tex]r=4/2=2\ ft[/tex] ----> the radius is half the diameter

[tex]h=4.3\ ft[/tex] ---> is the depth

[tex]\pi =3.14[/tex]

substitute

[tex]V=(3.14)(2)^{2}(4.3)[/tex]

[tex]V=54.008\ ft^{3}[/tex]

[tex]C=ad\\\\a=\dfrac{C}{d}[/tex]

Answer:

Step-by-step explanation:

C.  878 and D.  1 are the only whole numbers.  The rest are either mixed numbers or fractions.

Answer:

Angle GBH:

Angle ECD: 34

Angle HGB: 20

Angle FGH:

Step-by-step explanation:

Find all of the angles, some are needed to find others. Use the given angles...

FEC is 124, so the other side of it, CED must be 180-124 which is 56

Now we know CED is 56 and CDE is 90, and a triangles angles add up to 180, therefore angle ECD is 180-56+90, which is 34

Now we can find HCE, 180-90+34, which is 56

Angle CBG is 70 because 180-110 is 70

You can find angle HGB by looking at angle BCG which is 90 and angle CBG which is 70 and subtracting them from 180. 180-90+70=20

Answer:

The answer is 72

Step-by-step explanation:

In order to resolve the expression, we have to know the factorial function.

The factorial function (with a symbol: !) says to multiply all whole numbers from our chosen number down to 1.

For example:

5!=5*4*3*2*1=120

When the exercise has a fraction with factorial functions, we usually try to simplify it, that is, we have to expand the factorial value until to get the same factorial value in the denominator or numerator:

5!/3!=[tex]\frac{5*4*3!}{3!} =5*4=20[/tex]

In this case:

9!/(9-2)!=9!/7!=[tex]\frac{9*8*7!}{7!} =9*8=72[/tex]

The final value is 72.

The value of the factorial 9!/(9-2)! is 72

To find the value of 9!/(9-2)!, we first need to evaluate the factorial expressions.

9! means the factorial of 9, which is calculated by multiplying all positive integers from 1 to 9:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Similarly, (9-2)! means the factorial of (9-2), which simplifies to 7!:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1

Now, let's substitute the factorial expressions back into the original equation:

9!/(9-2)! = (9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(7 x 6 x 5 x 4 x 3 x 2 x 1)

Now we can simplify the expression:

9!/(9-2)! = (9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(7 x 6 x 5 x 4 x 3 x 2 x 1)

= 9 x 8

= 72

Therefore, the value of 9!/(9-2)! is 72.

To learn more on Factorial click:

https://brainly.com/question/29364177

#SPJ6

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=12\\ h=45 \end{cases}\implies V=\cfrac{\pi (12)^2(45)}{3}\implies V=2160\pi[/tex]

Answer:

The correct answer is 15.

Answer:

∠2 and ∠3 are complementary

Step-by-step explanation:

Complementary angles add up to 90°. Angles 1 and 3 are complementary, so the formula is ∠1 + ∠3 = 90°. Given that Angle 1 equals to angle 2, we substitute angle 2 for angle one in the equation stated before. Now we have ∠2 + ∠3 = 90°, so angles 2 and 3 are complementary

Answer:

-¼x + y = -2

Step-by-step explanation:

First, convert to Slope-Intercept Form by moving "1" to the other side of the equivalence symbol to get y = ¼x - 2, then finally convert to Standard Form by moving "-¼x" to the other side of the equivalence symbol to end up with -¼x + y = -2. Do you understand?

Answer:

[tex]\large\boxed{(3-2i)(3+2i)=13}[/tex]

Step-by-step explanation:

[tex](3-2i)(3+2i)\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=3^2-(2i)^2=9-4i^2\qquad i=\sqrt{-1}\to i^2=-1\\\\=9-4(-1)=9+4=13[/tex]

Answer: 6, 8, 10

Step-by-step explanation:

We can write the three numbers as: x, x+2, and x+4

(x+2)(x+4) = 10x + 20

x² + 6x + 8 = 10x + 20

x² - 4x - 12 = 0

(x-6)(x+2) = 0

x = -2,6

We will focus on x = 6 and ignore -2

To check our answer: (6+2)(6+4) = 10(6) + 20?

                                     8*10 = 60 + 20?

                              Yes, 80 = 80

Answer:

y = (1/3)x

Step-by-step explanation:

If this is truly a line, then we can find its equation using any two of the three given points.  If we go from (3, 1) to (27, 9), x increases by 24 and y increases by 8.  Thus, the slope of this line is m = rise / run = 8 / 24, or m = 1/3.

Using the point (3, 1) and the slope m = 1/3, the slope-intercept form y = mx + b becomes 1 = (1/3)(3) + b.  Thus, b = 0, and the line is y = (1/3)x.

Answer:

y=[tex]\frac{1}{3}[/tex]x ~apex

Step-by-step explanation:

Final answer:

The given relation is not a function because there are multiple output values for one input value.

Explanation:

The given relation, xy1−21−3213−2, is not a function. In order for a relation to be a function, each input value (x) must have only one corresponding output value (y).

Let's examine the relation:

x = 1, y = 2

x = 2, y = -3

x = 3, y = 2

As you can see, for x = 1, there are two different corresponding values of y (2 and -3). Therefore, the given relation is not a function.

[tex](g\cdot f)(x)=\dfrac{1}{x}-4[/tex]

[tex]D_{g(f(x))}:x\not =0[/tex]

No, since 0 doesn't belong to the domain.