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2 years ago

Find the value of x. Round the answer to the nearest tenth, if needed.

Mathematics

1 answer:

Dafna1 [17]2 years ago

4 0

Let the other 2 unknown sides be y n z

look at the two smaller triangles inside

y^2 = 12^2 + x^2 and

z^2 = 21^2 + x^2

from the biggest triangle

(12+21)^2 = y^2 + z^2

substituting

(12+21)^2 = (12^2 + x^2) + (21^2 + x^2)

33^2 = 12^2 + 21^2 + 2x^2

2x^2 = (33^2 - 12^2 - 21^2)/2 = 504

x^2 = 252

x = 15.9

ans is B

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What is the direct linear variation equation for the relationship?

defon

$\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ K}}&\cdot&x
\\ \\
&& y={{ K }}x
\end{array}
\\ \quad \\

\begin{cases}
y=4\\
x=12
\end{cases}\implies y=Kx\implies 4=K\cdot 12$

solve for "K", to see what "K" is, or the "constant of variation",
once you found K, plug it back in y=Kx, and that's the equation

3 0

2 years ago

At what point will 3y=4x-6 and 8x-6y=-30 intercept

tester [92]

Answer:

The lines don't intercept

Step-by-step explanation:

we have

$3y=4x-6$

isolate the variable y

Divide by 3 both sides

$y=\frac{4}{3}x-\frac{6}{3}$

simplify

$y=\frac{4}{3}x-2$ -----> equation A

$8x-6y=-30$

Isolate the variable y

$6y=8x+30$

Divide by 6 both sides

$y=\frac{8}{6}x-\frac{30}{6}$

simplify

$y=\frac{4}{3}x-5$ -----> equation B

Compare equation A and equation B

The slopes are the same and the y-intercepts are different

Remember that

If two lines has the same slope, then the lines are parallel

therefore

In this problem line A and line B are parallel lines

The system of equations has no solution, because the lines don't intercept

3 0

2 years ago

What is an equation of the line that passes through the points (4, 4) and (8, 1)?

geniusboy [140]

Answer: y = -3/4x + 7

Step-by-step explanation:

first find slope:

y2-y1 / x2 - x1

1-4 / 8-4

-3/4

now just plug the slope (m) into the equation of a line using one of the points to find the y intercept

ill use (8,1)

1 = (-3/4)(8) + b

now solve :)

1 = -6 + b

7 = b

so now plug in the slope and the y intercept into the slope intercept form to find the equation of the line

y = -3/4x + 7

3 0

2 years ago

Sophie can type 128 words in 3 minutes. How many minutes will it take her to type 576 words?

Andrej [43]

Let’s first find the rate that she types at in wok.
128/3 = 42+2/3 words per minute.
Now divide 576 by the rate.
576/42.666= 13.5 minutes

7 0

2 years ago

Write a function number_of_pennies() that returns the total number of pennies given a number of dollars and (optionally) a numbe

seraphim [82]

Ok, first of all, it is important to understand that this function would depend on 2 variables; the number of dollars (x) and the number of pennies (y). Every dollar is equivalent to 100 pennies. So, if we are given x dollars, we have 100*x pennies. If we also have y pennies, we still get y pennies. We need to add these two to get the total amount of pennies. Thus, the correct function is:
f(x,y)=100*x+y

7 0

2 years ago