All categories

3 years ago

Find the value of r.

Mathematics

1 answer:

fgiga [73]3 years ago

6 0

Answer:

r = 10.5

Step-by-step explanation:

using the Pythagorean theorem:

(7 + r)² = 14² + r²

49 + 14r + r² = 196 + r²

subtract r² from both sides of the equation:

14r + 49 = 196

subtract 49 from both sides:

14r = 147

divide both sides by 14:

r = 10.5

You might be interested in

For a school assembly student sit in chairs that are arranged in 53 rows. There are 12 chairs in each row. About how many studen

loris [4]

53x12=636 that is your answer that is the way to estimate it your answer is 636 that is how many students can be seated

6 0

3 years ago

Which difference is about 10?

Helga [31]

Option B is the answer.

70.9 - 58.7

4 0

3 years ago

Jenny and Natalie are selling cheesecakes for a school fundraiser. Customers can buy chocolate cakes and vanilla cakes. Jenny so

IrinaVladis [17]

The cost of 1 chocolate cake is $ 6 and cost of 1 vanilla cake is $ 7

Solution:

Let "c" be the cost of 1 chocolate cake

Let "v" be the cost of 1 vanilla cake

Jenny sold 14 chocolate cakes and 5 vanilla cakes for 119 dollars

Therefore, we can frame a equation as:

14 x cost of 1 chocolate cake + 5 x cost of 1 vanilla cake = 119

$14 \times c + 5 \times v=119$

14c + 5v = 119 ------- eqn 1

Natalie sold 10 chocolate cakes and 10 vanilla cakes for 130 dollars

Therefore, we can frame a equation as:

10 x cost of 1 chocolate cake + 10 x cost of 1 vanilla cake = 130

$10 \times c + 10 \times v = 130$

10c + 10v = 130 -------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

28c + 10v = 238 ------ eqn 3

Subtract eqn 2 from eqn 3

28c + 10v = 238

10c + 10v = 130

( - ) --------------------------

18c = 108

c = 6

Substitute c = 6 in eqn 1

14(6) + 5v = 119

84 + 5v = 119

5v = 119 - 84

5v = 35

v = 7

Thus cost of 1 chocolate cake is $ 6 and cost of 1 vanilla cake is $ 7

8 0

3 years ago

Hey! i’ll give brainliest please help.

S_A_V [24]

Answer:

A is

Step-by-step explanation:

6 0

3 years ago

Can someone tell me if im right? PLEASE DONT JUST SAY YES if you don’t know

tia_tia [17]

Answer: You are incorrect, the slope is correct, but the actual y-intercept is 205 ft.

Then the equation is:

y = (-15 ft/min)*x + 205 ft

Step-by-step explanation:

Ok, let's solve this.

We know that water is drained from a reservoir, let's assume that we can model this situation with a linear relation:

y = a*x + b

Where x is time, y is the height of the water in the reservoir, a is the slope (in this case represents how much changes the height of the water in the reservoir in one unit of time) and b is the initial height of the water in the reservoir.

We know that for a line that passes through the points (x₁, y₁) and (x₂, y₂) the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

For this particular case we know that after 2 minutes the height of the water is 175 ft, then we have the point (2 min, 175 ft)

and after 5 minutes (so 7 minutes in total), the height of the water is 100ft, then: (7 ft, 100ft)

Then the slope of this:

a = (100 ft - 175 ft)/(7 min - 2 min) = (-75ft/5min) = - 15 ft/min

Then our line is something like:

y = (-15ft/min)*x + b

To find the value of b, we can use the fact that when x = 2 min, y = 175 ft

So if we replace these two values in the equation we get:

175ft = (-15 ft/min)*2 min + b

175 ft = -30 ft + b

175 ft + 30 ft = b

(here is your problem, it seems like you subtracted instead of adding in this part)

205 ft = b

Then the equation is:

y = (-15 ft/min)*x + 205 ft

So you are incorrect (but only for a little bit), you computed wrong the y-intercept.

3 0

3 years ago