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Leya [2.2K]
3 years ago
15

The sum of two numbers is 66. the larger number is 2 more than 3 times the smaller. what are the two numbers?

Mathematics
1 answer:
Montano1993 [528]3 years ago
7 0
The two numbers are 48 and 18.

66 = l + s

l = 2 + 3s

66 = 2 + 3s + s

66 = 2 + 4s

66 - 2 = 64

64 = 4s

64 / 4 = 16

66 = l + 16

66 - 16 = 50

50 - 2 = 48

16 + 2 = 18

66 = 48 + 18
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AnnZ [28]

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Balblair! op opopopopoop

5 0
3 years ago
This question is from the similarity chapter. It would be really kind of you if you would answer this question.
katen-ka-za [31]

Answer:

a) 1650 m

b) 1677.05 m

Step-by-step explanation:

Hi there!

<u>1) Determine what is required for the answers</u>

For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.

For part B, we're asked to solve for the length of the road, or the length of AB.

<u>2) Prove similarity</u>

In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).

How do we know they're similar?

  1. Angles AYX and ACB are corresponding and they both measure 90 degrees
  2. Both triangles share angle A

Therefore, the two triangles are similar because of AA~ (angle-angle similarity).

<u>3) Solve for part A</u>

Recall that we need to find the length of AC.

First, set up a proportion. XY corresponds to BC and AY corresponds to AC:

\frac{XY}{BC}=\frac{AY}{AC}

Plug in known values

\frac{2}{300}=\frac{11}{AC}

Cross-multiply

2AC=11*300\\2AC=3300\\AC=1650

Therefore, the road will rise 300 m over a horizontal distance of 1650 m.

<u>4) Solve for part B</u>

To find the length of AB, we can use the Pythagorean theorem:

a^2+b^2=c^2 where c is the hypotenuse of a right triangle and a and b are the other sides

Plug in 300 and 1650 as the legs (we are solving for the longest side)

300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c

Therefore, the length of the road is approximately 1677.05 m.

I hope this helps!

3 0
3 years ago
Find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=3x+2
Levart [38]

Answer:

the desired equation is y = (-1/3)x + 6

Step-by-step explanation:

Let the given line be A:  y=3x+2

The slope of line A is m = 3.

The slope of any line B which is perpendicular to line A is the negative reciprocal of the slope of A:  m = -(1/3).

The particular perpendicular line that passes through (3, 5) is then

5 = (-1/3)(3) + b, which simplifies to 5 = -1 + b, or b = 6.

Thus, the desired equation is y = (-1/3)x + 6

7 0
2 years ago
a bag contains 5 red m&amp;ms, 4 green m&amp;ms, and 3 blue m&amp;ms. what is the ratio of green to red m&amp;ms? what is the ra
nasty-shy [4]

Answer:

what is the ratio of green to red m&ms

4:5

what is the ratio of green m&ms to the total number m&ms

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Answer:

SSS

Step-by-step explanation:

Given that the sides are equal and no angles are given

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