Simplify the following expression (a³b)⁴

Answer:

A (x+3)−1=8open paren x plus 3 close paren minus 1 is equal to 8

C 2(x+3)=182 times open paren x plus 3 close paren is equal to 18

E 2x=122 x is equal to 12

Step-by-step explanation:

Given:

2(x+3) − 2 = 16

2x + 6 - 2 = 16

2x = 16 - 6 + 2

2x = 12

x = 12/2

x = 6

A. (x+3)−1=8

x + 3 - 1 = 8

x = 8 - 3 + 1

x = 6

B (x+3)−2=8

x + 3 - 2 = 8

x = 8 - 3 + 2

x = 7

C 2(x+3)=18

2x + 6 = 18

2x = 18 - 6

2x = 12

x = 12/2

x = 6

D x+3=9x

3 = 9x - x

3 = 8x

x = 3/8

E 2x=12

x = 12/2

x = 6

F 2x=15

x = 15/2

x = 7 1/2

Answer:

D

Step-by-step explanation:

To find the inverse of a function, first replace f(x) with y.

Next, switch all the x's and y's, and then solve for y.

Finally, replace y with f-1(x).

Given:

The dimensions of base are 5 cm and 5cm.

The height of the pyramid is 3 cm.

To find:

The volume of the pyramid.

Solution:

The volume of a pyramid is:

[tex]V=\dfrac{1}{3}Bh[/tex]                ...(i)

Where, B is the base area and h is the height of the pyramid.

The base area of the given pyramid is:

[tex]B=length \times width[/tex]

[tex]B=5 \times 5[/tex]

[tex]B=25[/tex]

Substituting [tex]B=25[/tex] and [tex]h=3[/tex] in (i), we get

[tex]V=\dfrac{1}{3}(25)(3)[/tex]

[tex]V=25[/tex]

Therefore, the volume of the given pyramid is 25 cm³. Hence, the correct option is A.

Answer:

The input for the method is a continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing within the interval). Each iteration performs these steps: Calculate c, the midpoint of the interval, c = a + b2.

Step-by-step explanation:

trust

Answer:

Step-by-step explanation:

2x + 4 + 7x - 13 = 180 degree

9x - 9 = 180

9x = 180 + 9

x = 189/9

x = 21 degree

2x + 4 + 3y + 14 = 180 degree (being linear pair)

2*21 + 4 + 3y + 14 = 180

42 + 18 + 3y = 180

60 + 3y = 180

3y = 180 - 60

y = 120/3

y = 40 degree

Answer:

The area of the image is equal to the area of the pre-image multiplied by the scale factor.

The area of the dilated trapezoid is __54*2/3=36_ square centimeters.

Answer:

P earned $ 718.85.

Step-by-step explanation:

Given that P borrowed $ 16000 from a person at 12% per annum simple interest and lent the whole amount to Q at the same rate of annually compound interest, to determine how much did he gain after 3 years the following calculation must be performed:

16,000 x 0.12 x 3 = X

1,920 x 3 = X

5,760 = X

16,000 x (1 + 0.12 / 1) ^ 3 = X

16,000 x 1.12 ^ 3 = X

16,000 x 1.404928 = X

22,478.85 = X

22,478.85 - 16,000 = 6,478.85

6,478.85 - 5,760 = X

718.85 = X

Therefore, P earned $ 718.85.

Answer:

4 : 3

Step-by-step explanation:

So to answer this, we must find the greatest common factor(GCF) of 18 adn 24 , then divide by that to get the ratio.

So, what are the factors of 18?

Now what are the factors of 24?

All of these work, but we need to GCF, which is the largest factor that goes into both numbers.

Looking at them, it would be 6.

So lets divide both numbers by 6 and see what we get:

18/6

=

3

24/6

=

4

So now there are 3 red crayons and 4 green crayons.

OR

For every 3 red crayons there are 4 green crayons.

This makes the ratio:

3 : 4

Hope this helps!

Ration of red to green crayons is 3:4

Number of red crayons = 18

Number of green crayons = 24

Ration of red to green crayons

Ration of red to green crayons = Number of red crayons / Number of green crayons

Ration of red to green crayons = 18 / 24

Ration of red to green crayons = 3/4

Ration of red to green crayons = 3:4

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Answer:

Step-by-step explanation:

edge 2021

Answer: [tex]20,706\ m^3[/tex]

Step-by-step explanation:

Given

The warehouse has the following dimension

Height is [tex]h=8\frac{1}{2}\ m[/tex]

[tex]h=\dfrac{17}{2}\ m[/tex]

Length is [tex]l=120\ m[/tex]

Width is [tex]w=20\frac{3}{10}\ m[/tex]

[tex]w=\dfrac{203}{10}\ m[/tex]

Volume of the warehouse is the product of height, length and width

[tex]\Rightarrow V=h\times l\times w\\\\\Rightarrow V=\dfrac{17}{2}\times 120\times \dfrac{203}{10}\\\\\Rightarrow V=20,706\ m^3[/tex]

Therefore, the length of the warehouse is [tex]20,706\ m^3[/tex].

Answer:

82.5 = p

Step-by-step explanation:

Q= 4+0.8p

Let q = 70

70= 4+0.8p

Subtract 4 from each side

70-4= 4-4+0.8p

66 = .8p

Divide each side by .8

66/.8 = .8p/.8

82.5 = p

Answer:

Line C.

Step-by-step explanation:

Negatives are supposed to be on the left side of the 0, not the right side, so we can determine that lines B and D are wrong. On line A, -3/5 is on -2 which is wrong, so line C is the correct answer.

Answer:

16.75 Dollars for each Ticket

Step-by-step explanation:

They are three friends so the total money they spent is 75 Dollars so a popcorn costs 8.25 EACH friend so

8.25 x 3

= 24.75

24.75 dollars was spent on the 3 popcorns.

Subtract the total money spent and the total money spent on the 3 popcorns so

75. 00 - 24.75

= 50.25

50.25 dollars were totally spent on the tickets but we're looking for each ticket so divide it by 3.

50.25/3

= 16.75

16.75 dollars each were spent on each ticket.

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Answer:

[tex] \frac{1}{ {a}^{42} } [/tex]

Step-by-step explanation:

[tex] {( {r}^{ - 7}) }^{6} [/tex]

Since,

[tex] {( {a}^{x}) }^{y} = {a}^{xy} [/tex]

Then,

[tex] = {r}^{ (- 7 \times 6)} = {r}^{ - 42} [/tex]

Since,

[tex] {a}^{ - 1} = \frac{1}{a} [/tex]

Then,

[tex] = {r}^{ - 42} = \frac{1}{ {r}^{42} } [/tex]

Therefore,

2nd Option is correct.

Answer:

B

[tex]area = 2\pi \: rh \\ = 2 \times 3 \times 5 \times 1 \\ = 30 \: {cm}^{2} [/tex]

Answer:

the area of the parallelogram = base times the height

For the given parallelogram :

x = 8 units, y = 13 units, and h = 11 units

1) If x is the perpendicular to h

So, the base = 8 and the height = 11

So, the area = 8 * 11 = 88 square units

2) If y is the perpendicular to h

So, the base = 13 and the height = 11

So, the area = 13 * 11 = 143 square units

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Since you want to eliminate y, the y value on the bottom equation has the be the opposite of the y value on the top one. So it's 4y on the top one, so the bottom one has to be -4y to eliminate y. The bottom one is -2y, so -2 times 2 =-4, so multiply the bottom one by 2 omg i miss linear combination

Answer:

£28

Step-by-step explanation:

140 x .2 = 28

28+140 = 168

168/6 = 28

Given the system of equations below:

[tex] \large{ \begin{cases} x + 2y = 12 \\ x = y - 12 \end{cases}}[/tex]

For the second equation, x-term is isolated and can be substituted in the first equation.

[tex] \large{(y - 12) + 2y = 12}[/tex]

The equation above is when we substitute x = y-12 in the first equation. Cancel the brackets.

[tex] \large{y - 12 + 2y = 12}[/tex]

Add up the like term and isolate y-term.

[tex] \large{3y - 12= 12} \\ \large{3y - 12 + 12 = 12 + 12}[/tex]

Add both sides by 12 to get rid of 12 from the left side to isolate y-term.

[tex] \large{3y = 24}[/tex]

Divide both sides by 3 so we can finally isolate the term.

[tex] \large{ \frac{3y}{3} = \frac{24}{3} } \\ \large{ \frac{ \cancel{3}y}{ \cancel{3}} = \frac{ \cancel{24}}{ \cancel{3}} } \\ \large{y = 8}[/tex]

Next, find the x-value because in system of equations - we have to answer as in an ordered pairs or coordinate point. We know y-value now but we don't know x-value yet. To find x-value, we substitute the y-value in one of two equations that are given. You can substitute in both equation but it's not necessary to substitute in both equations at one. I will choose to substitute in x = y-12.

[tex] \large{x = y - 12}[/tex]

Substitute y = 8 in the equation.

[tex] \large{x = 8 - 12} \\ \large{x = - 4}[/tex]

Now that we know the both values. We finally have an answer to this problem. Hence.

Answer

The second answer is in ordered pair form. Let me know if you have any doubts!

Answer:

Line m

Step-by-step explanation:

The line is labeled with an m.

Answer:

Step-by-step explanation:

11:30-9:30=2

so Danielle starts 2 hrs late.

let Danielle catches them after x hrs.

x×60=(x+2)×20

divide by 20

3x=x+2

3x-x=2

2x=2

x=1

so Danielle takes 1 hour to catches them.

Answer:

[tex]g(-3)=42[/tex]

Step-by-step explanation:

Given:

[tex]g(x)=4x^2+6[/tex]

Let's substitute -3 for [tex]x[/tex]

[tex]g(-3)=4(-3)^2+6[/tex]

Now, let's solve

[tex]g(-3)=4(9)+6[/tex]

[tex]g(-3)=36+6[/tex]

[tex]g(-3)=42[/tex]

Hope this helps

Answer:

You get 6 dollars per car

Step-by-step explanation:

I divided 30 by 5

Answer: $6 per car

Step-by-step explanation:

If it's 30 dollars for 5 cars and we want to know how much it is for 1 car we need to divide both by 5

[tex]\frac{30}{5} =6\\\frac{5}{5} =1[/tex]

$6 per one car

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❀ [tex]\huge\underline{ \underline{ \text{Answer :-}}}[/tex]

➺ It's likely to be option D.

[tex]\underbrace{ \overbrace{ \mathfrak{Explanation}}}[/tex]

➺ The first figure has a line which divides the circle ⭕ into 2 parts. The 2nd figure divides the circle ⭕ into 3 parts while the 3th figure divides the circle ⭕ into 4 parts. Obviously, the 4th figure then should divide the circle ⭕ into 5 parts. Checking all the given options,

⟹ So, option D. is the correct answer.

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꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

The coordinates of the point on the unit circle at the given angle. 135° is (-√2 / 2, √2 / 2).

A circle on the Cartesian Plane with a radius of one unit and a center position is referred to as a unit circle (0, 0). When working with angles and trigonometric functions, the unit circle is a useful tool that makes reference much simpler. The Pythagorean Theorem can be used with the unit circle.

Given:

The unit circle at the given angle 135°,

Calculate the value of sin45 as shown below,

sin (180 - 135) = 1 / √2

sin 45 = 1 / √2

cos(180 - 135) =  1 / √2

cos45 = 1 / √2

Write the coordinates as shown below,

Coordinates = (1 / √2 × √2 / √2, 1 / √2 × √2 / √2 )  (Second quadrant is (-x, y))

Coordinates = (-√2 / 2, √2 / 2)

Thus, the coordinates are  (-√2 / 2, √2 / 2).

To know more about unit circle:

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Answer:

c = 12

Step-by-step explanation:

If c is one side you would need to multiply that side times 4 because that's the way you find the perimeter. In this case, you need to divide 48 by 4 so that you get the centimeters for each side. The answer is 12

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Answer:

21

Step-by-step explanation:

75÷100×28=21

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