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3 years ago

The rectangle shown is dilated by a scale factor of 3

Mathematics

1 answer:

dsp733 years ago

5 0

120 cm by 24 cm

A dilation is getting larger, so multiply each side by 3.

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Which of the following numbers could be the sides of a right triangle. A)8,15,17. B)6,8,12 C)9,11,21 D)4,13,16

ArbitrLikvidat [17]

Answer:

A) 8, 15, 17.

Step-by-step explanation:

Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option (the hypotenuse) that means that those numbers could be the sides of a right triangle.

The Pythagorean theorem states that: $a^2+b^2=c^2$

Thus:

$\sqrt{a^2+b^2}=c$

Option A:

$\sqrt{8^2+15^2}=17$ → 17 = 17 OK!

Option B:

$\sqrt{6^2+8^2} = 10$ → 10 ≠ 12 NO

Option C:

$\sqrt{9^2+11^2} = [tex]\sqrt{202}$ [/tex] → $\sqrt{202}$ ≠ 21 NO

Option D:

$\sqrt{4^2+13^2} = \sqrt{185}$ → $\sqrt{185}$ ≠ 16 NO

3 0

3 years ago

What is the solution to the inequality below x2>25

4vir4ik [10]

Answer:

Ans: (-5, 5)

-5 < x < 5

Step-by-step explanation:

Standard form: f(x) = x^2 - 25 < 0.

First solve x^2 - 25 = 0 --> x = +- 5

Use the algebraic method to solve f(x) < 0. Between the 2 real roots (-5) and (5), f(x) < 0, as opposite in sign to a = 1.

Answer by open interval: (-5, 5)

3 0

3 years ago

Read 2 more answers

Lucas' mom is eight years older than twice his age. The sum of their ages is 77. How old are Lucas and his mom?

Rudiy27

Answer:

Age of Lucas = 23 years

Age of Lucas Mom = 54 Years

Step-by-step explanation:

In this question we have to find the age of Lucas and his Mom

Let the age of Lucas be x

According to given condition

Twice of his age 2 * x =2x

Eight years older means age + 8x

Age of his mom = Twice of his age + 8

= 2x + 8 .................(ii)

now according to second condition

Age of Lucas + Age of his mom = 77

Put the values in the condition above

x + (2x + 8) = 77

x + 2x + 8 =77

3x + 8 = 77

subtracting 8 from both sides

3x + 8 - 8 = 77 -8

3x = 69

Dividing both sides by 3

x = 69 / 3

x = 23 years

Age of Lucas = 23 years

Now from equation (i)

Age of Lucas Mom = 2(x) + 8

putting in the value we get

Age of Lucas Mom = 2 ( 23) + 8

=46 + 8

=54 Years

Age of Lucas Mom = 54 Years

3 0

3 years ago

An electric motor uses 6kw at an efficiency of 63%. How much power does it deliver?

r-ruslan [8.4K]

The delivered power is:
$6\times0.63=3.78$
The answer is 3.78kW.

7 0

3 years ago

Read 2 more answers

Find the missing side length of m.

zysi [14]

Answer:

m=4

Step-by-step explanation:

Since we know that quadrilateral ABCD is similar to QRST, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of m.

$\frac{ST}{CD}=\frac{RS}{BC}\\\\\frac{6}{15} =\frac{m}{10}\\$

$\frac{6*10}{15} =m\\m=60/15=4$

m=4

6 0

3 years ago