486x <img src="https://tex.z-dn.net/?f=486x" id="TexFormula1" title="486x" alt="486x" align="absmiddle" class="latex-formula"

an architect wants to build three similar triangles such that the ratio of the middle triangle. The smallest one has side length

vampirchik [111]

Answer: 15

Step-by-step explanation:

small: 5 12 13

middle: __ 36 39

large: 45 108 117

Notice that to get from the small to the large, multiplied by 9

5(9) = 45 12(9) = 108 13(9) = 117

That is because the sides are proportional $\dfrac{5}{45}=\dfrac{12}{108}=\dfrac{13}{117}\rightarrow\dfrac{1}{9}$

To get from small to middle, multiply by 3

5(3) = 15 12(3) = 36 13(3) = 39

To solve it using proportions:

$\dfrac{5}{x}=\dfrac{12}{36}\\\\\\\text{Cross Multiply and solve for x:}\\5(36)=12x\\\\\dfrac{5(36)}{12}=x\\\\5(3)=x\\\\\large\boxed{15}=x$

7 0

2 years ago

Which system of equations represents the matrix shown below?

weqwewe [10]

Answer:

I don't know how to do it...

7 0

1 year ago

Read 2 more answers

(8 -2i)^2 a:60 b:68-32i c:60-32i d:64-32i+4i^2

AURORKA [14]

Answer:

60-32i

Step-by-step explanation:

(8-2i)^2=8^2-2.8.2i+(2i)^2

=64-32i+4i^2

=64-32i-4

=60-32i

8 0

2 years ago

A copy machine makes 28 copies per minute. How many copies does it make in 3 minutes and 45 seconds?

lina2011 [118]

Convert minutes and seconds to minutes:
$\text{3 mins 45 seconds} \longrightarrow 3 \dfrac{3}{4} \text{mins}$

FInd 3 3/4 mins:
$\text{1 min} \longrightarrow 28 \text{ copies}$

$3 \dfrac{3}{4} \text{ min} \longrightarrow 28 \times 3\dfrac{3}{4} \text{ copies}$

$3 \dfrac{3}{4} \text{ min} \longrightarrow 28 \times \dfrac{15}{4} \text{ copies}$

$3 \dfrac{3}{4} \text{ min} \longrightarrow 105 \text{ copies}$

Answer: It can make 105 copies.

4 0

3 years ago

Two sides of a right triangle measure 6 cm and 8 cm what is the length of the hypotenuse

andrew-mc [135]

Answer:

10 cm

Step-by-step explanation:

a^2 + b^2 =c^2

6^2 + 8^2 = c^2

36 + 64 = 100

then find the square root of 100 which equals 10

5 0

2 years ago