All categories

3 years ago

This equation shows how the distance Tess runs depends on the number of track practices she attends.

Mathematics

1 answer:

nikdorinn [45]3 years ago

4 0

Answer:

$3\ track\ practices$

Step-by-step explanation:

Let

d ----> distance Tess runs in miles

p ---> the number of track practices she attends

we have

$d=p+8$

This is a linear equation in slope intercept form

where

The slope or unit rate is

$m=1\ mile/track$

The y-intercept (value of d when the value of p is equal to zero) is

$b=8\ miles$

For d=11 miles

substitute in the linear equation and solve for p

$11=p+8$

solve for p

$p=11-8\\p=3\ track\ practices$

You might be interested in

Sin B =

Vika [28.1K]

Answer:

12/13

Step-by-step explanation:

sin can be remembered by opposite over hypotenuse.

the length of the side opposite to angle B is 12, and the hypotenuse is 13. therefore, sin B will be 12/13.

4 0

3 years ago

Find the slope of a line that is perpendicular to the line y= - 1/3x+7

adell [148]

the slope of the line is 3

7 0

3 years ago

Find the probability of each event. Answer IN FRACTION form.

IrinaK [193]

Answer:

So the idea is that we want to find the total number of ways that we can pick 7 diamonds (real or fake) from the 12 diamonds.

So as you said, 12 choose 7 = 792

Now we need the total number of ways that we can satisfy that of the 7 we picked, exactly three are real, but this also means that four are fake.

So to choose 3 real from 5 is 5 choose 3 = 10

And to choose 4 fake from 7 is 7 choose 4 = 35

3x10/792= 350/792= 175/396

5 0

4 years ago

Find the Value of Sin A rounded to the nearest hundredth, if necessary.

leonid [27]

Step-by-step explanation:

In trigonometry, the law of sines is an equation that relates the length of the sides of a triangle (any type of triangle) to the sines of its angles. This is expressed mathematically as

$\displaystyle\frac{a}{\sin \alpha} \ = \ \displaystyle\frac{b}{\sin \beta} \ = \ \displaystyle\frac{c}{\sin \gamma}$ ,

where $a$ , $b$ , and $c$ are the lengths of the sides of the triangle and $\alpha$ , $\beta$ , and $\gamma$ are the opposite angles (as shown in the figure below). Likewise, the law is sometimes written as it reciprocals,

$\displaystyle\frac{\sin \alpha}{a} \ = \ \displaystyle\frac{\sin \beta}{b} \ = \ \displaystyle\frac{\sin \gamma}{c}$ .

Therefore,

$\displaystyle\frac{\sin A}{BC} \ = \ \displaystyle\frac{\sin B}{AC} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sin B \ \times \ BC}{AC} \\ \\ \\\sin A \ = \ \displaystyle\frac{\sin \left(90^{\circ}\right) \ \times \ \sqrt{\left(10\right)^{2} \ - \ \left(\sqrt{78}\right)^{2}}}{10} \\ \\ \\ \sin A \ = \ \dsiplaystyle\frac{\sqrt{22}}{10} \\ \\ \\ \sin A \ = \ 0.47 \ \ \ \ (\text{nearest hundredth})$

Alternatively, you can solve this question using the definition of the trigonometric function sine. For the angle $\theta$ in the figure below,

$\sin \theta \ = \ \displaystyle\frac{\text{opposite}}{\text{hypothenuse}}$ .

Therefore,

$\sin A \ = \ \displaystyle\frac{BC}{AC} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sqrt{\left(10\right)^{2} \ - \ \left(\sqrt{78}\right)^{2}}}{10} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sqrt{22}}{10} \\ \\ \\ \sin A \ = \ 0.47 \ \ \ \ (\text{nearest hundredth})$

8 0

3 years ago

A rectangular prism has a volume of 540, if the length, width and height are all reduced 1/3 the size of the original. What is t

katrin2010 [14]

Answer:

20 units³

Step-by-step explanation:

Since<em> all dimensions are being reduced by 1/3</em>, that means that the total volume will decrease by <em>1/3 * 1/3 * 1/3 = 1/27</em> the size of its original.

That means that the new volume is 1/27 * 540 = 20 units³

8 0

3 years ago