when an exponent of a power is an even number and the base is a negative number, the value is always:
A. positive
B. negative
C. 0
D. none of the choices

Weird. A period appears above this... huh.

Answer:

[Th]e cube has a greater value.

Step-by-step explanation:

What the word problem really wants us to get [is ]the question of 'Which is greater, A=6a^2 when 'a' [is] 18 or A=4[tex]\pi[/tex]r^2 when r = 9? And here's how to solve that.

Starting with the[ c]ube we have A=6a^2. A bit t[o]o simple, right?

A=6(18)^2 Substitute numbers.

A=6(324) Solve ex[p]onents.

A=1944 Mult[i]ply.

So w[e] know that the cube is 1944 meters cube[d ] in area. But what about the more [f]ormidable sphere? Fo[r] it we need a slightly m[o]re co[m]plicated formula, A=4[tex]\pi[/tex]r^2. However, instead of using the real pi I will be rounding to 3.14, since we have no calculator so anything more would take way too long and fry your[ bra]in.

A=4(3.14)(9)^2 Subst[i]tute numbers.

A=4(3.14)(81) Solve expone[n]ts.

A=12.56(81) Multip[ly].

A=1017.36 Multiply again[.]

Now, since I'm sure all of us can count, we know that 1944 is greater than 1017.36. Or in other words, the cube is bigger than the sphere.

And PLEASE don't copy this guys. Make your own iteration. Change it up!

Answer:

The missing words

# x ⇒ # y ⇒ # 4 ⇒ # 0

Step-by-step explanation:

* Lets revise how to find the inverse function

- At first write the function as y = f(x)

- Then switch x and y

- Then solve for y

- The domain of f(x) will be the range of f^-1(x)

- The range of f(x) will be the domain of f^-1(x)

* Now lets solve the problem

∵ f(x) = √(x - 4)

∴ y = √(x - 4) ⇒ switch x and y

∴ x = √(y - 4) ⇒ square the two sides

∴ x² = [√(y - 4)]² ⇒ cancel the root by squaring

∴ x² = y - 4 ⇒ add 4 to the both sides

∴ y = x² + 4

∴ f^-1(x) = x² + 4

* To find the domain of the inverse, find the range of the function

∵ The domain of f(x) is ⇒ x - 4 ≥ 0 (no negative value under√)

∴ the domain is x ≥ 4

- Substitute this value in the function to find the range

∵ x = 4

∴ y = √(4 - 4) = 0

∴ y ≥ 0

- The range of f(x) is y ≥ 0

∴ The domain of the inverse f^-1(x) is x ≥ 0

- The missing words

# x

# y

# 4

# 0

Answer:

For the first pic its mode interval and median for the second pic its frequency table.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given a function f(x)

Then at the turning points the derivative of f(x) equals zero, that is

f'(x) = 0 at the turning points

Answer:

Step-by-step explanation:

Any number between 0.390 and 0.400 will work.  For example, 0.391, 0.392, and 0.393.

Answer:

Step-by-step explanation:

just did the question and got it right.

Answer:

2800 cm^3, or 2.8 liters

Step-by-step explanation:

The base of the tank remains 14 cm × 25 cm. The remaining height is 15 -7 = 8 cm, so the remaining volume is ...

(14 cm)(25 cm)(8 cm) = 2800 cm^3 = 2.8 liters

_____

1 liter = 1000 cm^3

Answer:

-65/2

Step-by-step explanation:

I am just a natural genius ;)

Answer:

see explanation

Step-by-step explanation:

Evaluate the parenthesis before multiplication

4² = 4 × 4 = 16 and

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

Thus 16 + [tex]\frac{1}{4}[/tex] = 16 [tex]\frac{1}{4}[/tex] = [tex]\frac{65}{4}[/tex]

Hence

- 2 × [tex]\frac{65}{4}[/tex] = [tex]\frac{-2(65)}{4}[/tex] = - [tex]\frac{65}{2}[/tex] = - 32 [tex]\frac{1}{2}[/tex]

Answer:

D

Step-by-step explanation:

Before the increase, the length is 6 and the width is 5, so the area is 5×6 = 30.

After the increase, the length is x+6, the width is x+5, and the area is tripled: 30×3 = 90.

Therefore:

(x+6) (x+5) = 90

Hey there! :D

f(-3)= 4(2)^x

Just plug in -3 as x and solve.

4(2)^-3

First do the exponent, and then multiply the four on the outside.

4(1/8)

=1/2

I hope this helps!

~kaikers

Final answer:

To calculate f(-3) for the function f(x) = 4(2)ˣ, substitute -3 into the function, yielding f(-3) = 1/2 after simplifying 4 times 2 raised to the power of -3.

Explanation:

To find f(-3) for the function f(x) = 4(2)ˣ, simply substitute -3 for x in the equation. Here's How:

Start with the original function f(x) = 4(2)ˣ.

Replace every x with -3 to get f(-3) = 4(2)⁻³.

Calculate 2⁻³, which equals 1/8 because negative exponents represent the reciprocal of the base raised to the positive exponent.

Now, multiply 4 by 1/8 to get f(-3) = 4 * 1/8 = 1/2.

Therefore, f(3) for the given function equals 1/2.

Hello wendywagor!

Let x = the original price of the sneakers

x - .60x = 22.40

.40x = 22.40

x = $56

Thanks For Using Brainly.com

Have A Great rest of Your Day!

Answer:

w=18 minutes per mile, r=12 minutes per mile

Step-by-step explanation:

Let w and r represent the rates, in minutes per mile, that Carly walked and ran on the treadmill, respectively.

1. On Monday, Carly walked 3 miles and spent 3w minutes, ran 2 miles and spent 2r minutes. In total Carly spent 78 minutes, so

3w+2r=78

2. On Thursday, Carly walked 2 miles and spent 2w minutes, ran 3 miles and spent 3r minutes. In total Carly spent 72 minutes, so

2w+3r=72

Solve the system of two equations:

[tex]\left \{ {{3w+2r=78} \atop {2w+3r=72}} \right.[/tex]

Multiply the first equation by 2, the second equation by 3 and subtract them:

[tex]2(3w+2r)-3(2w+3r)=2\cdot 78-3\cdot 72\\ \\6w+4r-6w-9r=156-216\\ \\-5r=-60\\ \\r=12[/tex]

Substitute it into the first equation:

[tex]3w+2\cdot 12=78\\ \\3w=78-24\\ \\3w=54\\ \\w=18[/tex]

Answer:

[tex]\boxed{\sqrt{65}}[/tex]

Step-by-step explanation:

The radius of circle D is the distance from the origin to (-4, -7).

In math, the distance formula gives us the distance between two points, (x₁, y₁) and x₂, y₂):

[tex]d = \sqrt{(x _{2}-x_{1})^{2} +(y _{2}-y_{1})^{2}}[/tex]

You are really using Pythagoras' Theorem to find the distance. You are building a right triangle whose hypotenuse connects two given points.  

For example, in the blue triangle below, the distance between the points (0,0) and (-4, -7) is

[tex]d = \sqrt{(0 - (-4))^{2} +(0 -(- 7))^{2}}\\\\ = \sqrt{4^{2} +7^{2}}\\ = \sqrt{16 + 49}\\=\sqrt{65}[/tex]

[tex]\text{The radius of the circle is }\boxed{\mathbf{\sqrt{65}}}[/tex]

Answer:

Vertex ( 5 ,8) .

Step-by-step explanation:

Given  : f(x) = 2(x − 5)² + 8.

To find : Determine the vertex of the function .

Solution : We have given

f(x) = 2(x − 5)² + 8.

Vertex form of parabola  : f (x) = a(x - h)² + k, where (h, k) is the vertex.

On comparing f(x) = 2(x − 5)² + 8. with vertex form of parabola.

a = 2 , h = 5 , k = 8 .

Vertex ( 5 ,8) .

Therefore, Vertex ( 5 ,8) .

Answer: (5,8)

Step-by-step explanation:

The given function :[tex]f(x) = 2(x - 5)^2 + 8.[/tex]

We know that the vertex form of a quadratic equation is given by :

[tex]f (x) = m(x - a)^2+ b[/tex]   (1)

, where (a,b)= Vertex of the function f(x).

When we compare the given function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] to equation (1) , we conclude that the given function is already in its vertex form.

with a= 5 and b= 8

Therefore , the vertex of the function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] = (5,8)

To solve the equation Z + mx = yx for x, we first move 'mx' to the right side to get 'yx - mx = Z'. We then factor out 'x' to get 'x(y - m) = Z'. Finally, we divide by '(y - m)' to get 'x = Z / (y - m)'. This solution holds as long as y ≠ m.

Here, we're going to solve the equation for x: Z + mx = yx.

We can start by grouping the terms with 'x' together. This gives us: yx - mx = Z. Now, we can factor x out of the left side of the equation. This results in: x(y - m) = Z. Finally, to solve for x, we divide both sides of the equation by (y - m). This gives us the solution: x = Z / (y - m).

Note: This solution is under the assumption that y ≠ m because division by zero is undefined.

https://brainly.com/question/24875240

#SPJ3

Answer:

7.782352941

Step-by-step explanation:

4.2 divided by 1.02 the multiply the out come of that by 1.89 to get 7.782352941

Answer:

13. 90

14. 43

15. 146

Answer:

(x + 6)²

Step-by-step explanation:

This is a perfect square of the form

(x + a)² = x² + 2ax + a²

here a² = 36 ⇒ a = 6 and 2ax = 2 × 6x = 12x

Hence

x² + 12x + 36 = (x + 6)²

Answer:

(x+6)(x+6)

Step-by-step explanation:

Answer: the range is 209

Step-by-step explanation: the biggest number minus the smallest will give you the range

The answer is 209. Hope this helps

Answer:

17

Step-by-step explanation:

Use the distance equation.

d² = (x₁−x₂)² + (y₁−y₂)²

The order doesn't matter.  If I choose (x₁, y₁) to be (8, 4) and (x₂, y₂) to be (-7, -4), then:

d² = (8−(-7))² + (4−(-4))²

d² = 15² + 8²

d² = 289

d = 17

Final answer:

The distance between the points (8,4) and (-7,-4) on a coordinate plane is 17 units.

Explanation:

In order to find the distance between two points on a coordinate plane, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the points (8,4) and (-7,-4), we can substitute the x and y values into the formula:

d = √((-7 - 8)^2 + (-4 - 4)^2)

d = √(225 + 64)

d = √289

d = 17

Therefore, the distance of the segment formed by joining the two given points is 17 units.

17) 5:6

18) 3:4

19) 4:5

20) 2:3

21) 3:4

22) 2:3

23) 3:5

24) 9:10

These answers are all simplified ratios

Final answer:

The questions involve finding the ratio of two quantities and simplifying them by dividing both numbers by their greatest common divisor. Each ratio gives a comparative relationship between two different counts of items or scores in different subjects.

Explanation:

The questions provided all relate to finding the ratio of two quantities.

In each case, the ratio is found by comparing two quantities and simplifying by dividing both numbers by their greatest common divisor (GCD).

ANSWER

[tex](-8, - 3)[/tex]

EXPLANATION

Given that: (-8,-8) is on f(x).

Then we can write (-8,f(-8)) is on f(x).

The corresponding point on

[tex]f(x) + 5[/tex]

will be

[tex](-8,f(-8)+5)[/tex]

We substitute f(-8)=-8 to obtain;

[tex](-8, - 8+5)[/tex]

This simplifies to

[tex](-8, - 3)[/tex]

Therefore the corresponding point on f(x)+5 is (-8,-3).

Answer:

see explanation

Step-by-step explanation:

Given

4x - 8x ÷ 2

Under the rules of PEMDAS , division must be performed before subtraction.

Hence

4x - 8x ÷ 2 = 4x - 4x ← dividing - 8x by 2, then

4x - 4x = 0 ← correct answer

Answer:

The answer would be A. 1.25

Answer:

35/5 = 7 Minutes per Window thus: 12*7 = 84 Minutes

Step-by-step explanation:

Answer:

84 minutes or 1 hour and 24minutes

Step-by-step explanation:

12*35=420

420/5=84

Answer:

$142500

Step-by-step explanation:

We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.

Assuming [tex]x[/tex] to be the salary of the department head, if the total of the two salaries is $190000, we are to find the salary of the president of the University.

We can write an equation in terms of [tex]x[/tex]:

[tex]3x+x=190000[/tex]

[tex]4x=190000[/tex]

[tex]x=47500[/tex]

Salary of the president of the University = [tex]3(47500)[/tex] = $142500

Answer:

15. Option A is correct

16. Option B is correct.

Step-by-step explanation:

Question 5:

sin2Ф = 2sinФcosФ

We are given sinФ = 9/13

and we need to find cosФ in order to find sin2Ф

We know that sin^2Ф + cos^2Ф= 1

so, cos^2Ф = 1- sin^2Ф

cos^2Ф = 1- (9/13)^2

cos^2Ф = 88/169

taking √ on both sides:

√cos^2Ф = √88/169

cosФ = (2√22)/13

Now

sin2Ф = 2sinФcosФ

          = 2 (9/13) (( 2√22)/13)

sin 2Ф = 36√22 / 169

Now we find cos2Ф

The formula for cos2Ф = cos^2Ф - sin^2Ф

cos2Ф = ((2√22)/13)^2 - (9/13)^2

cos2Ф = 4*22 /169 - 81/169

cos2Ф = 7/169

So, Option A is correct

Question No 6

We need to find sin2Ф and cos2Ф where cosФ = 6/13

We are given cosФ = 6/13

and we need to find sinФ in order to find sin2Ф and cos2Ф

We know that sin^2Ф + cos^2Ф= 1

so, sin^2Ф = 1- cos^2Ф

sin^2Ф = 1- (6/13)^2

sin^2Ф = 133/169

taking √ on both sides:

√sin^2Ф = √133/169

sinФ = √133/13

Now

sin2Ф = 2sinФcosФ

          = 2 (√133/13) (6/13)

sin2Ф  = 12√133 / 169

Now we find cos2Ф

The formula for cos2Ф = cos^2Ф - sin^2Ф

cos2Ф =  (6/13)^2 - (√133/13)^2

cos2Ф = 36/169 - (133/169)

cos2Ф = -97/169

Since the quadrant is 1st so, cos2Ф will be Positive i.e. 97/169

cos2Ф = 97/169

So, Option B is correct.

Answer:

The friends will each have passed _33_ scales in _7_ weeks.

Step-by-step explanation:

We must write an equation for the number of scales that Nick approves and an equation for the number of scales that Mary approves.

For Nick we have:

5 initial scales

Nick has committed to approve 4 scales per week. Let's call x the number of weeks.

So the number of scales and for Nick is:

[tex]y = 5 + 4x[/tex]

For Mary we have:

12 initial scales

Mary has committed to approve 3 scales per week. Let's call x the number of weeks.

So the number of scales and for Mary is:

[tex]y = 12 + 3x[/tex]

To know when the two friends have passed the same number of scales we must equal both equations and solve for x:

[tex]12 + 3x = 5 + 4x[/tex]

[tex]12-5= 4x-3x[/tex]

[tex]x= 7\ weeks[/tex]

And

[tex]y=12+3*7\\\\y=33\ scales[/tex]

Final answer:

Nick and Mary will both have passed 33 scales in 7 weeks. This is determined by setting the equation for the number of scales Nick will pass equal to the number for Mary and solving for the number of weeks.

Explanation:

To determine when Nick and Mary will have passed the same number of scales, we can set up an equation based on the given information. Nick has currently passed 5 scales and will pass 4 scales each week. Mary has passed 12 scales and will pass 3 scales each week. The point at which they will have passed the same number of scales is when their total passed scales are equal.

Let's denote the number of weeks it will take to reach this point as w. For Nick, the total number of scales passed after w weeks will be 5 + 4w (his current count plus 4 times the number of weeks). For Mary, it will be 12 + 3w (her current count plus 3 times the number of weeks). Setting these two expressions equal to each other:

5 + 4w = 12 + 3w

Subtract 3w from both sides:

5 + w = 12

Subtract 5 from both sides:

w = 7

So, it will take 7 weeks for Nick and Mary to have passed the same number of scales. At that point, to find the total number of scales:

Nick: 5 + 4 x 7 = 33 scales

Mary: 12 + 3 x 7 = 33 scales

The friends will each have passed 33 scales in 7 weeks.

Answer:

The domain of the graph is all real number ⇒ the last answer

Step-by-step explanation:

* Remember that our original exponential formula was y = ab^x

- The b value is the growth factor

* Lets revise how to find the domain of this function

- The domain is all values of x that make the function defined

* Lets revise the composite function

- A composite function is a function that depends on another function.

- A composite function is created when one function is substituted

 into another function.

- For example, f(g(x)) is the composite function that is formed when

 g(x) is substituted for x in f(x).

∵ f(x) = 2^x

∵ g(x) = x - 2

∴ (f · g)(x) = f(x - 2)

∵ f(x) = 2^x

∴ (f · g)(x) = f(x - 2) = 2^(x - 2)

- For this function there is no values of x make the function undefined

∴ The Domain is all real numbers

- Look to the graph, the values of x go from -∞ to ∞

* The domain of the graph is all real number

Answer:

4 Dimes

9 Nickels

Step-by-step explanation:

I did guess and check (if you have an equation leave a comment or answer!)

So I did kept playing with the numbers making them go down until I could subtract the number of coins and divide to get the rest:

85-40 (4 dimes)=45

45/5=9 nickels

4+9=13

I hope this helps!

To solve for the number of nickels and dimes amounting to $0.85 in 13 coins, we set up and solve a system of equations. We found that there are 9 nickels and 4 dimes in the wallet.

To find out how many nickels you have when you have 13 coins composed of nickels and dimes amounting to $0.85, we can set up a system of equations where the number of nickels is represented by n and the number of dimes by d.

The first equation comes from the total number of coins: n + d = 13.

The second is derived from the total amount of money: 0.05n + 0.10d = 0.85.

We have two equations:

n + d = 13

0.05n + 0.10d = 0.85

Now, let's multiply the second equation by 20 to get rid of the decimals:

n + 2d = 17

By subtracting the first equation from this new equation:

d = 4

Substitute d back into the first equation:

n + 4 = 13

Thus:

n = 9

So you have 9 nickels and 4 dimes.