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shtirl [24]
3 years ago
15

If the sin of angle x is 4 over 5 and the triangle was dilated to be two times as big as the original, what would be the value o

f the sin of x for the dilated triangle? Hint—Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces. (4 points)
Mathematics
1 answer:
beks73 [17]3 years ago
4 0

Answer:

Sin of x does not change

Step-by-step explanation:

Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.

From trigonometry,

Sin(x)=opposite/hypotenose

Where x=4/5

Sin(4/5)= opposite/hypotenose

But we were given the scale factor of 2 which means the dilation is to two times big.

Then we have

Sin(x)=(2×opposite)/(2×hypotenose)

Then,if we divide by 2 the numerator and denominator we still have

Sin(x)=opposite/hypotenose

Which means the two in numerator and denominator is cancelled out.

Then we still have the same sin of x. as sin(4/5)

Hence,Sin of x does not change

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What is the value of r?
finlep [7]

Answer:

A.12

Step-by-step explanation:

2×r-13 = 11

r + 2 = 14

11 + 14 = 25

3 0
3 years ago
Suppose you are asked to find the area of a rectangle that is 2.1-cm wide by 5.6-cm long. Your calculator answer would be 11.76
IRINA_888 [86]

Answer:

The area of the rectangle is 12 cm² (to two significant figures)

Step-by-step explanation:

To determine the area of a rectangle that is 2.1-cm wide by 5.6-cm long,

The area of a rectangle is given by

Area = l × w

where l is the length

and w is the width

From the question,

l = 5.6 cm

and w = 2.1 cm

Hence, Area of the given rectangle will be

Area = 5.6 cm × 2.1 cm

Area = 11.76 cm²

Now, we will convert the answer to two significant figures

Then,

Area = 12 cm²

Hence, the area of the rectangle is 12 cm² (to two significant figures)

3 0
3 years ago
PLEASE HELP!!!<br> Find the common difference for the arithmetic sequence. -55, -50, -45, -40.....
Fed [463]

Answer:

5

Step-by-step explanation:

Just grap any two consecutive terms in the sequence. lets say -55 and -50

-50-(-55) = 5

you can check this by picking two other terms

7 0
2 years ago
What is the solution set of this inequality?
Gnoma [55]

Answer:

A.

x\ge \:4

Step-by-step explanation:

8(x-5) -3x\geq -20\\\\\mathrm{Expand\:}8\left(x-5\right)-3x:\quad 5x-40\\\\5x-40\ge \:-20\\\\\mathrm{Add\:}40\mathrm{\:to\:both\:sides}\\\\5x-40+40\ge \:-20+40\\\\Simplify\\\\5x\ge \:20\\\\\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5x}{5}\ge \frac{20}{5}\\\\Simplify\\\\x\ge \:4

8 0
3 years ago
A box has a volume of 308 cm cubed. Its height is 4 cm greater than its length. Its length is 3 cm greater than its width. What
kifflom [539]

Answer:

4 cm.

Step-by-step explanation:

Given:

A box has a volume of 308 cm cubed.

Its height is 4 cm greater than its length.

Its length is 3 cm greater than its width.

Question asked:

What is the width of the box?

<u>Solution</u>:

Let width  = x\ cm

Length = x+3\ cm

Height = x+3+4=x+7\ cm

<u>As we know:</u>

<u />Volume\ of\ box=length\times width\times height

308=(x+3)\times x\times(x+7)\\ \\ 308=(x^{2} +3x)(x+7)\\ \\ 308=x^{2} (x+7)+ 3x(x+7)\\ \\ 308=x^{3} +7x^{2} +3x^{2} +21x\\ \\ 308=x^{3} +10x^{2} +21x\\ \\ Subtract\ 308\ from\ both\ sides\\ \\ x^{3} +10x^{2} +21x-308=0\\ \\ factor\ left\ side\ of\ equation\\ \\ (x-4)(x^{2} +14x+77)=0\\ \\  Set\ factors\ equal\ to\ 0.\\ \\ x-4=0 \ or\  x^{2} +14x+77=0\\ \\ \\

As width can never be in negative, x= 4\ cm

By substituting the value:-

Width  = x\ cm = 4 cm

Thus, width of the box is 4 cm.

4 0
3 years ago
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