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3 years ago

How many quarts are there in 12 gallons and 3 quarts? enter the number only. Do not include units

Mathematics

1 answer:

lidiya [134]3 years ago

5 0

Answer:

Step-by-step explanation:

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In order to tell if a graph is a function it must

nikitadnepr [17]

You can use the vertical line test (the blue lines on the drawing) and if the other end or if any part of the line touches the blue line, then it isn’t a function.

5 0

3 years ago

1 Solve - (8x – 12) = 2x – 3 4 218x - pleaseee help!!

Alex Ar [27]

Answer:

1/4.(-96)=2x-3

-1/4.96=2x-3

-24=2x-3

-2x-24=-3

-2x=-3+24

-2x=21

x=-21/2

Step-by-step explanation:

8 0

2 years ago

I need help. Someone help please. (photo)

gayaneshka [121]

Answer:

Step-by-step explanation:

In order to solve all of these problems, you have to first create an equation. The typical format for an equation looks like this: y = mx + b

m is the slope and b is the y-intercept.

In order to create an equation, you have to find the slope and y-intercept of the function. You can find the slope using this expression: $\frac{y2-y1}{x2-x1}$ To find the y-intercept, you use a known point and the slope in the equation to solve for b.

Now that we know this, we can solve the problems.

1a.

To create the equation, let's find the slope using points (1, 15) and (2, 30)

$\frac{30 - 15}{2 - 1}$ = 15/1 = 15

The equation now looks like this: h = 15w + b

Let's use the point (1, 15) from the table to find b

15 = 15(1) + b

15 = 15 + b

subtract 15 from both sides the isolate the b

0 = b

There is no y-intercept for this equation, so the equation looks like this:

h = 15w

1b. We know the equation is h = 15w, so all we have to do is input the 9 into the equation.

h = 15(9)

h = 135

2a. We'll use the points (1, 8) and (2, 16) to find the slope

$\frac{16 - 8}{2-1}$ = 8/1 = 8

The slope is 8.

Since it's impossible to sell any houses in 0 months, we already know that there is no y-intercept, so the equation looks like this:

h = 8m

2b. Put the value of 15 inside the equation and solve.

h = 8(15)

h = 120

3a. We'll use the points (1, 35) and (2, 70) to find the slope.

$\frac{70 - 35}{2 - 1}$ = 35/1 = 35

The slope is 35.

It's impossible to see any movies in 0 months, so there is no y-intercept. The equation looks like this:

c = 35m

3b. We know that there are 12 months in a year, so put 12 into the equation and solve.

c = 35(12)

c = 420

4a. We'll use the points (1, 8) and (2, 16) to find the slope

$\frac{16 - 8}{2 - 1}$ = 8/1 = 8

The slope is 8.

It's impossible for there to be a cost if there are no hats, so the y-intercept must be 0. The equation looks like this:

c = 8h

4b. Put the 30 hats into the equation and solve.

c = 8(30)

c = 240

4 0

3 years ago

In the diagram below,AB is the diameter of the circle with centre P.Point C lies on the y-axis.Given the coordinates of A and B

Step2247 [10]

Answer:

The coordinates of P are (-2,0)

The radius of the circle is 5.

Step-by-step explanation:

Analytic geometry

The diagram shows a circle with center P, and two points A(-6,3) and B(2,-3) that form the diameter of the circle.

The center of the circle lies at the midpoint of A and B. The midpoint (xm,ym) can be calculated by:

$\displaystyle x_m=\frac{x_1+x_2}{2}$

$\displaystyle y_m=\frac{y_1+y_2}{2}$

Substituting x1=-6, x2=2, y1=3, y2=-3:

$\displaystyle x_m=\frac{-6+2}{2}=\frac{-4}{2}=-2$

$\displaystyle y_m=\frac{3-3}{2}=0$

Thus, the coordinates of P are (-2,0)

b) The radius of the circle is the distance from the center to any point in its circumference. We can use the distance from P to A or B indistinctly.

Given two points A(x1,y1) and P(x2,y2), the distance between them is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substituting x1=-6, x2=-2, y1=3, y2=0:

$r=\sqrt{(-2+6)^2+(0-3)^2}$

$r=\sqrt{4^2+(-3)^2}$

$r=\sqrt{16+9}=\sqrt{25}=5$

The radius of the circle is 5.

4 0

3 years ago

1. Let f(x, y) be a differentiable function in the variables x and y. Let r and θ the polar coordinates,and set g(r, θ) = f(r co

Olenka [21]

Answer:

$g_{r}(\sqrt{2},\frac{\pi}{4})=\frac{\sqrt{2}}{2}\\$

Step-by-step explanation:

First, notice that:

$g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}cos(\frac{\pi}{4}),\sqrt{2}sin(\frac{\pi}{4}))\\$

$g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}(\frac{1}{\sqrt{2}}),\sqrt{2}(\frac{1}{\sqrt{2}}))\\$

$g(\sqrt{2},\frac{\pi}{4})=f(1,1)\\$

We proceed to use the chain rule to find $g_{r}(\sqrt{2},\frac{\pi}{4})$ using the fact that $X(r,\theta)=rcos(\theta)\ and\ Y(r,\theta)=rsin(\theta)$ to find their derivatives:

$g_{r}(r,\theta)=f_{r}(rcos(\theta),rsin(\theta))=f_{x}( rcos(\theta),rsin(\theta))\frac{\delta x}{\delta r}(r,\theta)+f_{y}(rcos(\theta),rsin(\theta))\frac{\delta y}{\delta r}(r,\theta)\\$

Because we know $X(r,\theta)=rcos(\theta)\ and\ Y(r,\theta)=rsin(\theta)$ then:

$\frac{\delta x}{\delta r}=cos(\theta)\ and\ \frac{\delta y}{\delta r}=sin(\theta)$

We substitute in what we had:

$g_{r}(r,\theta)=f_{x}( rcos(\theta),rsin(\theta))cos(\theta)+f_{y}(rcos(\theta),rsin(\theta))sin(\theta)$

Now we put in the values $r=\sqrt{2}\ and\ \theta=\frac{\pi}{4}$ in the formula:

$g_{r}(\sqrt{2},\frac{\pi}{4})=f_{r}(1,1)=f_{x}(1,1)cos(\frac{\pi}{4})+f_{y}(1,1)sin(\frac{\pi}{4})$

Because of what we supposed:

$g_{r}(\sqrt{2},\frac{\pi}{4})=f_{r}(1,1)=-2cos(\frac{\pi}{4})+3sin(\frac{\pi}{4})$

And we operate to discover that:

$g_{r}(\sqrt{2},\frac{\pi}{4})=-2\frac{\sqrt{2}}{2}+3\frac{\sqrt{2}}{2}$

$g_{r}(\sqrt{2},\frac{\pi}{4})=\frac{\sqrt{2}}{2}$

and this will be our answer

3 0

3 years ago