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3 years ago

AD= DC= Angle a= Angle b= Angle c=

Mathematics

1 answer:

Nadya [2.5K]3 years ago

4 0

9514 1404 393

Answer:

AD= 8

DC= 15

Angle a= 112°

Angle b= 68°

Angle c= 112°

Step-by-step explanation:

We have to assume the figure is a parallelogram.

Opposite sides of a parallelogram are congruent, so ...

BC = AD = 8

AB = DC = 15

Opposite angles are congruent, and adjacent angles are supplementary.

180° - ∠D = Angle a = Angle c = 112°

∠D = Angle b = 68°

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You and your friend each collect rocks and fossils. Your friend collects three times as many rocks and half as many fossils as y

pochemuha

Answer:

I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.

Step-by-step explanation:

The number of total objects collected by me = 20

The number of objects collected by my friend = 20

Let us assume:

The number of rocks collected by me = m

The number of fossils collected by me = 2 k

⇒ m + 2 k = 20 .... (1)

So, according to the question:

The number of rocks collected by my friend = 3 x (rocks collected by me)

= 3 x (m) = 3 m

The number of fossils collected by my friend = 1/2 x (fossils collected by me) = 1/2 x (2k ) = k

⇒ 3 m + k = 20 .... (2)

Solving (1)and (2) for the value of m and k, we get:

m + 2 k = 20 ⇒ m = 20 - 2 k ... Put this in (2)

3 m + k = 20 ⇒ 3 (20 - 2 k) + k = 20

⇒ 60 - 6 k + k = 20

or, - 5k = -40

or, k = 40/5 = 8

⇒ k= 8

m + 2(8) = 20

or, m = 4

Hence, the number of rocks collected by me = m = 4

The number of fossils collected by me = 2 k = 2 (4) = 16

Hence, the number of rocks collected by my friend = 3 m = 3 x 4 = 12

The number of fossils collected by my friend = k = 8

Hence, I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.

4 0

3 years ago

Find the missing side of each triangle. i need help!!!

Nezavi [6.7K]

Answer:

√161 yd

Step-by-step explanation:

Hi there!

We're given a right triangle (notice the right angle), the measure of one of the legs (one of the sides that make up the right angle) as 8 yd, and the hypotenuse (the side opposite to the right angle) as 15 yd.

We need to find x, which is the other leg in the triangle

If we are given 2 sides and need to find a third, we can use Pythagorean Theorem, which states that a²+b²=c² if a and b are legs and c is the hypotenuse

In this case, a=8, b=x, and c=15

So let's substitute those values into the formula

(8)²+x²=(15)²

raise everything to the second power

64+x²=225

subtract 64 from both sides

x²=161

take the square root of both x and 161

x=√161, x=-√161

-√161 cannot work in this case, as distance cannot be negative.

The question asks for the answer to be in simplified radical form, but √161 cannot be simplified down further

so the answer is <u>√161 yd</u>

Hope this helps! :)

3 0

3 years ago

What would you multiply by to decrease<br> an amount by 95%?

Crazy boy [7]

Answer:

-0.95

Step-by-step explanation:

Divide the percent by 100 and since you are decreasing it would be a negative.

4 0

3 years ago

The difference between a number and four is multiplied by negative five. The result is twenty. What is the number?

spayn [35]

(n-4)*-5=20 Answer is n= 8

4 0

3 years ago

Read 2 more answers

Ariana plans to use $260 less than three-fourths of savings to buy a car. If the purchase price of the car is 9,340, how much do

tangare [24]

She has $12,488 in savings

Step-by-step explanation:

Ariana plans to use $260 less than three-fourths of savings to buy a car.

If the purchase price of the car is 9,340, we need to find how much

she has in savings

To find the savings

Assume that she has $x in savings
Write an equation of x
Solve the equation to find x

∵ She has $x in savings

∵ She plans to use $260 less than three-fourths of savings

- Three-fourths means $\frac{3}{4}$ and less than means subtract

∴ She plans to use $\frac{3}{4}$ x - 26

∵ The purchase price of the car is 9,340

- Equate the expression of x by 9,340

∴ $\frac{3}{4}$ x - 26 = 9,340

Now let us solve the equation

∵ $\frac{3}{4}$ x - 26 = 9,340

- Add 26 to both sides

∴ $\frac{3}{4}$ x = 9,366

- Divide both sides by $\frac{3}{4}$

∴ x = $12,488

She has $12,488 in savings

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7 0

3 years ago