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Roman55 [17]
3 years ago
14

One number is 33 times a first number. a third number is 100 more than the first number. if the sum of the three numbers is 3103

10​, find the numbers.
Mathematics
1 answer:
kherson [118]3 years ago
7 0
Create some expressions.

1# number: x

2# number: 33x

3# number: 100 + x


this all equals to 310310 when added so

x+33x+(x+100) = 310310

Solve what you know first then rearrange it.

34x + x + 100 = 310310

35x = 310310-100

35x = 310210

x = 310210/35

x = 8863.142857

Substitute the x into the expressions made and you'll find the 2# and 3# number. You've already found the 1# number since it's only x.
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A triangle is dilated by a scale factor of 1/5 and then rotated 90 degree clockwise about the origin. Why is the image similar t
yan [13]
<u><em>Answers:</em></u>
The corresponding angles of the triangles are congruent
The image is a reduction of the pre-image
Neither the dilation nor the rotation change the shape of the triangle

<u><em>Explanation:</em></u>
<u>For shapes to be similar:</u>
1- there should be a ratio between the sides
2- angles in first shape should be congruent to angles in second shape

Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

<u>Let's check the choices:</u>
<u>1- </u><span><u>The corresponding sides of the triangles are congruent:</u>
This option is incorrect as dilation changes the lengths of the sides

<u>2- </u></span><span><u>The corresponding angles of the triangles are congruent:</u>
This option is correct as neither dilation nor rotation alters the measures of the angles

<u>3- </u></span><span><u>The corresponding sides of the image are 5 times as long as those of the pre-image:</u>
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image

<u>4- </u></span><span><u>The image is a reduction of the pre-image:</u>
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced

<u>5- </u></span><span><u>Neither the dilation nor the rotation change the shape of the triangle:</u>
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)

<u>6- </u></span><u>The rotation reduces the size of the triangle:</u>
This option is incorrect as rotation does not alter the size of the shape. It only changes its position

Hope this helps :)

3 0
3 years ago
Read 2 more answers
Estimate the sum of 487 and 310
Ronch [10]
487 + 310 ≈ 500 + 300 ≈ 800
3 0
3 years ago
Read 2 more answers
Find the rate of change of total​ revenue, cost, and profit with respect to time. Assume that​ R(x) and​ C(x) are in dollars. ​R
tresset_1 [31]

Answer:

Step-by-step explanation:

Given the Total revenue R(x) = 2x

Cost C(x) = 0.01x²+0.3x+30 where;

x = 30 and dx/dt = 9units per day.

Rate of change of revenue dR/dt = dR/dx • dx/dt

dR/dt = 2dx/dt

dR/dt = 2(9) = $18

Rate of change of revenue with respect to time is 18dollars/day.

Rate of change of cost dC/dt = dC/dx • dx/dt

dC/dt = (0.02x+0.3)dx/dt

dC/dt at x = 30 and dx/dt = 9 will give;

dC/dt = {0.02(30)+0.3}×9

dC/dt = (0.6+0.3) × 9

dC/dt = 0.9×9

dC/dt = $8.1

Rate of change of cost with respect to time is 8.1dollars/day

Profit = Revenue - Cost

Profit = 18-8.1

Daily Profit = $9.9

4 0
3 years ago
I need the last two please help I need it by 11
stich3 [128]

Answer:

Rectangle - Diamond

Oval - doughnut

Step-by-step explanation:

Takes some visualisation.

7 0
3 years ago
Read 2 more answers
A jet travels 530 miles in 5 hours. What is the speed (unit rate) at which the jet traveled? How far can the jet go in 12 hours?
Citrus2011 [14]

Answer:

unit rate is 106 miles per hour and it can go 1272 miles in 12 hours

Step-by-step explanation:

-divide 530 by 5 and you get 106 miles an hour.

-then multiply 106 by 12 to get 1272 miles an hour.

7 0
3 years ago
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