Which graph does NOT represent y as a function of ?<br> PLEASE HELP ME<br> 20 points!!!!!

Write the inequality for the graphs

Irina18 [472]

A. -3 < x < 1
b. x < = 4 or x > = 6

4 0

3 years ago

Does anyone know how to solve this?

Lilit [14]

The pattern is that the numbers in the right-most and left-most squares of the diamond add to the bottom square and multiply to reach the number in the top square.

For example, in the first given example, we see that the numbers 5 and 2 add to the number 7 in the bottom square and multiply to the number 10 in the top square.

Another example is how the numbers 2 and 3 in the left-most and right-most squares add up to the number 5 in the bottom square and multiply to the number 6 in the top square.

Using this information, we can solve the five problems on the bottom of the paper.

a) We are given the numbers 3 and 4 in the left-most and right-most squares. We must figure out what they add to and what they multiply to:

3 + 4 = 7

3 x 4 = 12

Using this, we can fill in the top square with the number 12 and the bottom square with the number 7.

b) We are given the numbers -2 and -3 in the left-most and right-most squares, which again means that we must figure out what the numbers add and multiply to.

(-2) + (-3) = -5

(-2) x (-3) = 6

Using this, we can fill the top square in with the number 6 and the bottom square with the number -5.

c) This time, we are given the numbers which we typically find by adding and multiplying. We will have to use trial and error to find the numbers in the left-most and right-most squares.

We know that 12 has the positive factors of (1, 12), (2,6), and (3,4). Using trial and error we can figure out that 3 and 4 are the numbers that go in the left-most and right-most squares.

d) This time, we are given the number we find by multiplying and a number in the right-most square. First, we can find the number in the left-most square, which we will call $x$ . We know that $\frac{1}{2}x = 4$ , so we can find that $x$ , or the number in the left-most square, is 8. Now we can find the bottom square, which is the sum of the two numbers in the left-most and right-most squares. This would be $8 + \frac{1}{2} = \frac{17}{2}$ . The number in the bottom square is $\boxed{\frac{17}{2}}$ .

e) Similar to problem c, we are given the numbers in the top and bottom squares. We know that the positive factors of 8 are (1, 8) and (2, 4). However, none of these numbers add to -6, which means we must explore the negative factors of 8, which are (-1, -8), and (-2, -4). We can see that -2 and -4 add to -6. The numbers in the left-most and right-most squares are -2 and -4.

4 0

3 years ago

A 13?-foot board is cut into two pieces. The longer piece is 7.5 feet longer than the shorter piece. What is the length of each?

chubhunter [2.5K]

Answer:

The smaller board would be 2.75 feet and the longer one would be 10.25 feet.

Step-by-step explanation:

In order to find this, assume the shorter board is equal to x. Next, we would know that the longer board would be equal to x + 7.5. Using these two assumptions, we can add the lengths together, set equal to 13 and then solve for x.

x + (x + 7.5) = 13

2x + 7.5 = 13

2x = 5.5

x = 2.75

Now that we have the length of the shorter board, we can add 7.5 to it to get the larger one.

2.75 + 7.5 = 10.25

6 0

3 years ago

Find unit rate. The tub fills with 12 gallons of water in 5 minutes?

Varvara68 [4.7K]

2.4 gallons in 1 minute.

7 0

3 years ago

A sphere of radius r is cut by a plane h units above the equator, where

Anika [276]

Consider the top half of a sphere centered at the origin with radius $r$ , which can be described by the equation

$z=\sqrt{r^2-x^2-y^2}$

and consider a plane

$z=h$

with $0$ . Call the region between the two surfaces $R$ . The volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx$

Converting to polar coordinates will help make this computation easier. Set

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\var\phi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

Now, the volume can be computed with the integral

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

You should get

$\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)$

5 0

3 years ago

Which graph does NOT represent y as a function of ? PLEASE HELP ME 20 points!!!!!