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Lelechka [254]
3 years ago
13

Please can someone help me

Mathematics
1 answer:
Sidana [21]3 years ago
4 0
If the answer is D. the equation to represent the ages of students is:
n + n+1 + n+2 = 45
it is showing that  n is the age of one student and the other student has age one year more than the first one and third students has age of 2 years more than first student and one year greater than the second student. if we solve this equation for the value of n, we get;
3n + 3 = 45
3n = 45 -3
3n = 42
n = 14
so the age of one student is 14, second student 15 and third student 16 years.
and if we add there ages, 14 + 15 + 16 = 45
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One supplementary angle is 15 degrees less than twice the other. Find the measure of the two supplementary angles.
o-na [289]

Hey there!

To find our answer, we need to set up a <u><em>system of equations. </em></u>Remember, <u><em>supplementary angles</em></u> equal 180 degrees when combined. We will call one of our angles A and the other one B. Let's set it up below! :)

A=2B-15 (one angle is 15 degrees less than twice the other)

A+B=180

We need to find one of our variables. To do this, we only put one variable in the equation. But how, there are two variables in both equations! Well, as you can see, we see the A is equal to 2B-15, so we can take 2B-15 and put it into the second equation in place of A because it is equal to A, and then we will only have Bs and we can solve for it. This method is known as solving systems of equations with <u><em>substitution.</em></u>

Let's solve with substitution!

2B-15+B=180

3B-15=180              We combine our Bs.

3B=195              We add 15 to both sides.

B= 65                We divide both sides by three.

Now, we need to find what A is, but this will be really easy to do! If you remember, our angles are supplementary, so when you combine them, we will get 180, as you can see in our second equation in our first system of equations. So, we simply subtract 65 from 180.

180-65=115

Our two angles are 65° and 115°.

We can also check this with the original problem.

If you double 65, we have 130. Then, if we subtract 15, we have 115. Systems of equations are a pretty awesome way to figure this out!

I hope this helps! Have a great day!

5 0
2 years ago
What is the distance between the points (–3, 5) and (2, –6)?
DENIUS [597]

the answer is C.12.1 units
4 0
3 years ago
Read 2 more answers
Find the value of x in a triangle . If the hypotenuse of the triangle is 10 , the opposite is x+2 and the adjacent is x.​
Sauron [17]

Answer:

x = 6

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² + (x + 2)² = 10² ← expand parenthesis on left side and simplify

x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide through by 2 )

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

however, x > 0 , then x = 6

8 0
2 years ago
Find the area of the trapezoid with bases 8 cm and 4 cm and a height of 1/4 cm. (Simplify your answer)
Simora [160]

Answer:

1 1/2 or 1.5

Step-by-step explanation:

trapezoid area formula: a = (a+b/2) x h

bases: 8 + 4 = 12

12/2=6

6 x 1/4 = 1.5 or 1 1/2

4 0
2 years ago
​For the two right triangles above, explain why a/8=x/12 . ​ ​What ​trigonometric ratio is also equal to the two given ratios?
frutty [35]

Answer:

sin trigonometry ratio

Step-by-step explanation:

Given

See attachment for triangles

Required

Explain why \frac{a}{8} = \frac{x}{12}

From the attached diagram, both triangles are similar triangles because

(1) the second triangle is a dilation of the first triangle by a ratio of 1.5

i.e

k = \frac{12}{8}

k = 1.5

(2) They have angle 30 degrees, and have their right angles located at the same point

In the first triangle, the sine of 30 degrees is represented as:

sin(30) = \frac{Opp}{Hyp}

This gives:

sin(30) = \frac{a}{8}

In the second triangle:

sin(30) = \frac{Opp}{Hyp}

So:

sin(30) = \frac{x}{12}

By comparison:

sin(30) = sin(3)

Hence:

\frac{a}{8} = \frac{x}{12}

8 0
3 years ago
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