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klemol [59]
3 years ago
11

Two triangular roofs are similar. The ratio of the corresponding sides of these roofs is 2:3. If the altitude of the smaller roo

f is 4.5 feet, find the corresponding altitude of the larger roof. Round to the nearest hundredth.

Mathematics
1 answer:
schepotkina [342]3 years ago
5 0

Answer:  6.75 feet

Step-by-step explanation:

Since, the ratio of the side of the similar triangle = 2 : 3

Thus, by the property of similar triangle,

The ratio of the altitudes of the triangle = 2 : 3

Let the altitude of smaller triangle = 2 x

And, the altitude of larger triangle = 3 x

Where x is any number.

According to the question,

2 x = 4.5

x = 2.25

Therefore, the altitude of larger triangle = 3 × 2.25 = 6.75 feet

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A cube has a volume of 512 mm^3. If all sides of the cube are divided by 4, what will the resulting volume be?
pshichka [43]
\bf \textit{volume of a cube}\\\\
V=s^3\qquad \boxed{s=\frac{s}{4}}\implies V=\left( \cfrac{s}{4} \right)^3\implies V=\cfrac{s^3}{4^3}\implies V=s^3\cdot \cfrac{1}{4^3}
\\\\\\
V=s^3\cdot \cfrac{1}{64}\impliedby \frac{1}{64}\textit{ of the original volume, if the original was 512}
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512\cdot \cfrac{1}{64}\implies \cfrac{512}{64}
3 0
3 years ago
X +5+11x=12x+Y It says find the value of y that makes each equation true for all values of
sladkih [1.3K]
X + 5 + 11x = 12x + y

Simplify: 12x + 5 = 12x + y (We are adding x and 11x on the left side)

Subtract 12x from each side makes each zero.

5 = y

So we can plug in and test. I'm picking two random numbers to plug in for x. 10, and 82

x = 10, y = 5
10 + 5 + 11(10) = 12(10) + 5
125 = 125

x = 82, y = 5
82 + 5 + 11(82) = 12(82) + 5
989 = 989

So we verified y = 5
3 0
3 years ago
Simplify -3(2x-4)+8x-8
ryzh [129]
-3(2x-4)+8x-8
-6x+12+8x-8
2x+4
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3 0
3 years ago
Read 2 more answers
Which expresses 1050 : 2000 in decimal form
MatroZZZ [7]

Answer: 10.5 : 20.2

Step-by-step explanation:

5 0
3 years ago
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Write the quadratic equation whose roots are -2 and 1, and whose leading coefficient is 4 .
Kaylis [27]

Answer: the equation is

4x^2 + 4x - 12

Step-by-step explanation:

A quadratic equation is an equation in which the highest power of the unknown is 2.

The general form of a quadratic equation is expressed as

ax^2 + bx + c

Where

a is the leading coefficient

c is a constant

Assuming we want to write the quadratic equation in x, from the information given, the roots which are given are -2 and 1 and the leading coefficient is 4.

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the equation becomes

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= x^2 - x +2x - 3

= x^2 + x - 3

Given a leading coefficient of 4, we will multiply the quadratic expression by 4. It becomes

4(x^2 + x - 3)

= 4x^2 + 4x - 12

7 0
3 years ago
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