Which type of function is represented by the table of values below?





x

y


1

4


2

16


3

64


4

256


5

1,024




exponential

linear

quadratic

square root

The capacity of the gas tank is 20 gallons

.To determine the capacity of the gas tank, we can set up a proportion based on the information given. We know that the tank is 40% full and contains 8 gallons of gas. Let's denote the total capacity of the tank as C gallons.Since 40% of the tank's capacity is equal to the 8 gallons of gas currently in the tank, we can write the following equation: [tex]\[ 0.40 \times C = 8 \[/tex]. To find the total capacity C, we divide both sides of the equation by [tex]0.40:\[ C = \frac{8}{0.40} \[ C = 20 \].[/tex]  Therefore, the capacity of the gas tank is 20 gallons. This means that when the tank is completely full, it can hold 20 gallons of gas.

To find "What fraction of students prefer Mt Rushmore over Grand Canyon ?", we need to take away Grand Canyon [tex] (\frac{8}{28} ) [/tex] from Mt Rushmore [tex] (\frac{14}{28} ) [/tex]

[tex] \frac{14}{28} - \frac{8}{28}\\\\ When \; we \; have\; like\; fractions\; with\; same\; denominator,\; we \; should\; combine \; numerator \\ \\ \frac{14-8}{28} \\ \\ \frac{6}{28} [/tex]

[tex] Divide \; numerator\; and \; denominator\; by \; common\; factor\; 2\\ \\ \frac{6 \div2 }{28 \div 2} = \frac{3}{14} [/tex]

Conclusion:

6/28 fraction of students prefer Mt Rushmore over Grand Canyon.

3/14 is the simplest form of above fraction.

The height of the kite above the ground is approximately 134.82 feet.

To find the height of the kite above the ground, we can use trigonometry. The string of the kite forms a right triangle with the height of the kite as the vertical side and the length of the string as the hypotenuse. We can use the sine function to find the height. sine(64°) = height/150. Rearranging the equation, we get height = 150 * sine(64°).

Using a calculator, we find that sine(64°) ≈ 0.8988. Therefore, height ≈ 150 * 0.8988 ≈ 134.82 feet.

https://brainly.com/question/11016599

#SPJ11

The value of the surface area of this cube is,

⇒ 1536 feet²

A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.

Given that;

One side of a cube = 16 feet

We know that;

the surface area of this cube is,

⇒ 6 × (side)²

Here, Side = 16 feet

Thus, The value of the surface area of this cube is,

⇒ 6 × (side)²

⇒ 6 × (16)²

⇒ 6 × 256

⇒ 1536 feet²

Thus, The value of the surface area of this cube is,

⇒ 1536 feet²

Learn more about the cuboid visit:

https://brainly.com/question/26403859

#SPJ2

Answer:

ummm, ohhh i just realized that i entered in the wrong question and i was so confused lol

Step-by-step explanation:

Answer:

1/3 :)

Step-by-step explanation:

if you do the math it eqals 2/6 but if you simplify it its 1/3 i did this test and got 100% ur welcome

To find the angle supplementary to <COB, we must look for an angle that adds up to 180 degrees with <COB. Assuming <COD is adjacent and forms a straight line with <COB, option 2. COD would be the supplementary angle.

The subject of this question is Mathematics, and it requires an understanding of angle relationships, particularly supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees.

Based on the given theorems and proofs, we must assume that the angles are situated such that finding the angle supplementary to <COB involves identifying an angle that, when combined with <COB, equals 180 degrees.

Given the options provided:

The correct answer to find the angle supplementary to <COB is 2. COD, assuming that <COB and <COD are adjacent angles forming a straight line.

Answer: The angles are 100 degrees, and 80 degrees.

Here's an explanation:

It says that the ratio of the angles are 4:5. In a rhombus, the opposite angles are equal to each other. So, the it would be (4*2)+(5*2) = 360 degrees, since the ratio symbolizes the angle measurements. So, if you calculate that, then 18 units is 360 degrees. 4 units is 80 degrees, and 5 units is 100 degrees.

A rhombus is a quadrilateral. The angles of the rhombus are 80°, 100°, 80°, and 100°.

A rhombus is a quadrilateral such that the pair of opposite sides of the quadrilateral are parallel, and all the sides of the quadrilateral are equal.

As we know that if the ratio of the angles formed by the diagonals and the sides is 4:5, then the ratio of the angles of the rhombus is also 4:5. Also, the pair of opposite angles of a rhombus are equal to each other. Therefore, the angles of the rhombus are 4x, 5x, 4x, and 5x.

Now, as the sum of adjacent angles of a rhombus is 180. Therefore, we can write the sum as,

[tex]4x+5x=180\\\\ 9x=180\\\\x=20[/tex]

Further, the measure of the angles can be written as,

[tex]4x = 4(20) =80^o\\\\5x = 5(20) =100^o\\\\4x = 4(20) =80^o\\\\5x = 5(20) =100^o\\[/tex]

Hence, the angles of the rhombus are 80°, 100°, 80°, and 100°.

Learn more about Rhombus:

https://brainly.com/question/4165249

Answer: The correct options are A and D.

Explanation:

If we want to find the average rate of change from the beginning of the slide to when the slide has covered a horizontal distance of 15 feet, the we have to find the initial point and point where horizontal distance is 15 feet.

In the given graph x axis represents the horizontal distance and y axis represents the height of the slide.

From the figure it is crealy noticed that the coordinates of the points are (0,80), (5,40), (10,20), (15,10) and (20,5).

Since at the initial point the horizontal distance is 0, so the coordinates of initial point is (0,80).

The coordinates of the point where horizontal distance is 15, are (15,10).

Therefore to find the slope or average rate of from the beginning of the slide to when the slide has covered a horizontal distance of 15 feet the required points are (0,80)and (15,10). So option A and D are correct.

Answer:

A and D

Step-by-step explanation:

Just took it. Edg 2020. Hope this helps :)

This should get you a hundred on the 4.11 quiz. :)

Answer:

The original graph will shift 6 units down.

Step-by-step explanation:

Given : If the equation y = x + 4 is changed to y = x - 2.

To find : How will the graph of the equation change.

Solution : We have given

Original graph equation : y =  x + 4.

Transformed equation : y = x -2.

y =  x + 4 →→ y = x - 2.

If we subtract the 6 from 4 it become - 2

We can see x + 4 -6 = x -2 .

So , y = x +4 -6  →→ y = x - 2.

By the transformation rule : f(x) →→  f(x) - k it mean graph shifted down by k units.

Then the original graph will shift 6 units down.

Therefore, The original graph will shift 6 units down.

To have $400,000 for retirement in 25 years with an annual interest rate of 6% compounded annually, Thurston must invest $93,171.77 today.

Thurston must calculate how much he needs to invest today to have $400,000 when he is 80 years old, given that he is currently 55 years old and the investment will yield 6% interest compounded annually. To find this amount, we use the formula for the present value of a lump sum, which takes into account the future value desired, the interest rate, and the number of compounding periods. The formula is:

PV = FV / (1+r)n

Where PV is the present value, FV is the future value, r is the annual interest rate, and n is the number of years until retirement.

In Thurston's case:

Plugging these values into the formula gives us:

PV = $400,000 / (1+0.06)25

PV = $400,000 / (1.06)25

PV = $400,000 / 4.29187072

PV = $93,171.77 (rounded to two decimal places)

Thus, Thurston must invest $93,171.77 today to retire with $400,000 in 25 years at an annual interest rate of 6% compounded annually.

Total money earned by Juan = 3w-6

Now Juan saved 1/3 of the money.

So money Juan spent will be 2/3 of what he earned.

Money Juan spent :

[tex] \frac{2}{3} (3w-6) [/tex]

Simplifying we get :

2w-4

Emma wrote the expression as 2(3w-6) which is not equal to 2w-4.

So we can say that the expression found by Emma was incorrect .

9(x ∙ y), the distributive property is not used because (x ∙ y) = xy which means that only one term can be multiplied by the term outside the parenthesis. 

 (7 ∙ a)(b), the distributive property is not used because (7 ∙ a) = 7a which means that only one term can be multiplied by the term outside the parenthesis. 

Cornell's class took 2 field trips last year. This is determined by setting up and solving the equation based on the given information.

To solve this problem, we need to set up an equation. Given in the problem that Cornell's class took one more than three times as many field trips as last year's class, we can represent this as 3x + 1 = y, where x is the number of field trips last year and y is the number of field trips this year. We know that y is 7 so we can substitute this into our equation getting 3x + 1 = 7.

To find x, you would subtract 1 from both sides of the equation giving 3x = 7 - 1, which simplifies to 3x = 6. Finally, dividing both sides of the equation by 3 gives us x = 2, so Cornell's class took 2 field trips last year.

https://brainly.com/question/1184396

#SPJ2