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4 years ago

Write a function rule for the input output table input x -2, -1, 0, 1 output y 13, 14, 15, 16

Mathematics

1 answer:

mojhsa [17]4 years ago

4 0

Answer:

y = x+15

Step-by-step explanation:

x-values increase by 1, as do y-values. The ratio of increases is Δy/Δx = 1/1 = 1. This is the slope (m) that is needed in the function rule.

The y-value is 15 for an x-value of 0, so we can use 15 as the y-intercept (b) in the function rule.

In slope-intercept form, the function rule is ...

y = mx +b

y = x +15

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mark is 11 years older than his sister. In 8 years he will be twice as old as she will be then. How old are they now

Whitepunk [10]

Answer: 14 years old and his sister is 3 years old

Step-by-step explanation:

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4 years ago

Arrange the cones in order from lease volume to greatest volume

bearhunter [10]

Answer:

Volume of the cone in ascending order.

$V_{2}=270\pi\ units^{3}$

cone with DIAMETER of 18 & height of 10

cone with RADIUS of 10 & height of 9

cone with RADIUS of 11 & height of 9

cone with DIAMETER of 20 & height of 12

Step-by-step explanation:

Let $V_{2}. V_{3}. and\ V_{4}.$ be the volume of the cone.

Let d, r and h be the diameter, radius and height of the cone.

Given:

$d_{1} = 20\ and\ h_{1}=12$

$d_{2} = 18\ and\ h_{2}=10$

$r_{3} = 10\ and\ h_{3}=9$

$r_{4} = 11\ and\ h_{14}=9$

Arrange the cones in order from lease volume to greatest volume.

Solution:

The volume of the cone is given below.

$V=\pi r^{2} \frac{h}{3}$ ----------------(1)

where: r is radius of the base of cone.

and h is height of the cone.

The volume of the cone for $d_{1} = 20\ and\ h_{1}=12$

$r_{1} = \frac{d_{1}}{2}$

$r_{1} = \frac{20}{2}=10\ units$

$V_{1}=\pi (r_{1})^{2} \frac{h_{1}}{3}$

$V_{1}=\pi (10)^{2} \frac{12}{3}$

$V_{1}=\pi\times 100\times 4$

$V_{1}=400\pi\ units^{3}$

Similarly, for volume of the cone for $d_{2} = 18\ and\ h_{2}=10$

$r_{2} = \frac{d_{2}}{2}$

$r_{2} = \frac{18}{2}=9\ units$

$V_{2}=\pi (r_{2})^{2} \frac{h_{2}}{3}$

$V_{2}=\pi (9)^{2} \frac{10}{3}$

$V_{2}=\pi\times 81\times \frac{10}{3}$

$V_{2}=\pi\times 27\times 10$

$V_{2}=270\pi\ units^{3}$

Similarly, for volume of the cone for $r_{3} = 10\ and\ h_{3}=9$

$V_{3}=\pi (r_{3})^{2} \frac{h_{3}}{3}$

$V_{3}=\pi (10)^{2} \frac{9}{3}$

$V_{3}=\pi\times 100\times 3$

$V_{3}=\pi\times 300$

$V_{3}=300\pi\ units^{3}$

Similarly, for volume of the cone for $r_{4} = 11\ and\ h_{4}=9$

$V_{4}=\pi (r_{4})^{2} \frac{h_{4}}{3}$

$V_{4}=\pi (11)^{2} \frac{9}{3}$

$V_{4}=\pi\times 121\times 3$

$V_{4}=\pi\times 363$

$V_{4}=363\pi\ units^{3}$

So, the volume of the cone in ascending order.

$V_{2}=270\pi\ units^{3}$

7 0

3 years ago

What is the y -value of the vertex of 4x^2 + 8X -8?

Aleksandr-060686 [28]

Answer:

-12

Step-by-step explanation:

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3 years ago

What is a sector of a circle? What is the area for the sector's formula?

tatyana61 [14]

A sector of a circle is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector.
The area A of a circle with radius r is given by A = πr2. The circumference C of that same circle is given by C = 2πr. But these are the formulas for the entire circle. Sometimes you will need to work with just a portion of a circle's revolution, or with many revolutions of the circle.

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3 years ago

One base of a trapezoid is 8 cm longer than the other. The height of the trapezoid is 2 cm longer than the shortest base. If the

Hitman42 [59]

Answer:

Step-by-step explanation:

Let's call the shortest side a. The longest base, b, is 8cm longer than a. The height, h, is 2cm longer than a.

b = a + 8

h = a + 2

A = (a + b)h/2

48 = (a + (a+8))(a+2)/2

= (2a+8)(a+2)/2

= (2a^2+12a+16)/2

48 = a^2+6a+8

a^2+6a-40=0

Now, we factor this:

(a + 4)(a - 10)=0

a = -4, 10

a (length) cannot be a negative no. so the only possible answer is a = 10.

b = 10 + 8 = 18

h = 10 + 2 = 12

The answer is B

Hope this helps!

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3 years ago

Write a function rule for the input output table input x -2, -1, 0, 1 output y 13, 14, 15, 16​

Write a function rule for the input output table input x -2, -1, 0, 1 output y 13, 14, 15, 16