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3 years ago

Find the quotient and remainder

Mathematics

1 answer:

statuscvo [17]3 years ago

7 0

Answer:

quotient = x^2 + 2x + 10

remainder = 35

Step-by-step explanation:

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The length of each side of an equilateral triangle is increased by 20%, resulting in triangle ABC. If the length of each side of

kompoz [17]

Answer: Area of ΔABC is 2.25x the area of ΔDEF.

Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

$A=\frac{\sqrt{3} }{4} a^{2}$

with a as side of the triangle.

Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:

a₁ = 1.2a

Then, its area is

$A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}$

$A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}$

Triangle DEF is 20% smaller than the original, which means its side is:

a₂ = 0.8a

So, area is

$A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}$

$A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}$

Now, comparing areas:

$\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )$

$\frac{A_{1}}{A_{2}} =$ 2.25

The area of ΔABC is 2.25x greater than the area of ΔDEF.

7 0

3 years ago

For the right triangles below, find the exact values of the side lengths a and d.

VashaNatasha [74]

Answer:

$a = \frac{4\sqrt3}3$ ; $d= 2\sqrt 2$

Step-by-step explanation:

First one is half an equilateral triangle. It means the hypotenuse is twice the shorter side, so 2a. Then let's apply the Pythagorean theorem:

$(2a)^2 = a^2 + 4^2\\4a^2 = a^2 + 16\\3a^2 = 16$

At this point is simply take the square root, use the positive value since they're lengths, and rearrange the fraction to have things look nice:

$a^2 = \frac{16}3\\a= {4\over \sqrt3}\\a = {4\sqrt3\over \sqrt3 \sqrt3}}\\ a = \frac{4\sqrt3}3$

Second one is half a square - or if you prefer, it's an isosceles right triangle, both side lengths are 2. Then its Pythagoras again:

$d^2 = 2^2 + 2^2\\d^2= 4+4 = 8\\$

Again, we just have to pick the square roots, and rearrange in a better looking way.

$d= \sqrt 8 = \sqrt{4\cdot2} = 2\sqrt 2$

6 0

3 years ago

1. What complex fraction is equal to 2/3?

mariarad [96]

The answer would be D.

GoodLuck!

5 0

3 years ago

Read 2 more answers

Pls help pls pls pls pls

dimaraw [331]

Step-by-step explanation:

f(x)=(x-5)(5x +2)=0

=> x=5 or, x=-2/5

smaller x = -2/5

larger x=5

3 0

4 years ago

Read 2 more answers

Calculate the standard deviation of the volume of water at a temperature of 25°C.

vaieri [72.5K]

Answer:

0.01

Step-by-step explanation:

Water is non viscous liquid and it has less density. The measure volume of water is 10.03 ml at 25 degree Celsius which is used to identify the standard deviation of the water.

Average volume of water 10.03ml.

Standard deviation is 0.0001 + 0.0001

Standard deviation is $\sqrt{0.0002}$ = 0.01.

5 0

3 years ago