Use the image to answer the question.
An illustration shows two similar right trapezoids.
For trapezoid A B C D, base C D measures 10, and side A D measures 20. Right angle symbols are indicated at vertices A and D. For trapezoid M N O P, base O P measures 8, and side P M measures 16. Right angle symbols are indicated at vertices M and P. Between the two trapezoids, the angle at vertex A is congruent with the angle at vertex M. The angle at vertex D is congruent with the angle at vertex P. The angle at vertex C is congruent with the angle at vertex O, and the angle at vertex B is congruent with the angle at vertex N.
Trapezoid ABCD is similar to trapezoid MNOP . Find the ratio between trapezoid ABCD and trapezoid MNOP . Express the answer in simplest form.
(1 point)
Responses
21
Start Fraction 2 over 1 End Fraction
45
Start Fraction 4 over 5 End Fraction
12
Start Fraction 1 over 2 End Fraction
54
Start Fraction 5 over 4 End Fraction
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The ratio between trapezoid ABCD and trapezoid MNOP is 2:1.
Solve the following problem involving income tax. Show all your work. Priya had $52.50 deducted from their paycheck. If Priya’s income tax rate is 12%, find Priya’s total income before tax. (4 points)
Let x be Priya's total income before tax.
According to the problem, $52.50 is deducted from x for income tax.
Since the income tax rate is 12%, we can set up the equation:
12% * x = $52.50
To find x, we divide both sides of the equation by 12% (or 0.12):
x = $52.50 / 0.12
Calculating this, we find:
x = $437.50
Therefore, Priya's total income before tax is $437.50.
To find the ratio between trapezoid ABCD and trapezoid MNOP, we need to compare corresponding sides of the two trapezoids. Looking at the given information, we can see that side AD of trapezoid ABCD is congruent to side PM of trapezoid MNOP.
Given that AD = 20 and PM = 16, we can set up a ratio:
Start Fraction AD over PM End Fraction
Start Fraction 20 over 16 End Fraction
To simplify this ratio, we can divide both the numerator and denominator by their greatest common divisor, which is 4:
Start Fraction 20 divided by 4 over 16 divided by 4 End Fraction
Start Fraction 5 over 4 End Fraction
So, the ratio between trapezoid ABCD and trapezoid MNOP is 5/4.