Find the value of t.

Mathematics

2 answers:

zaharov [31]3 years ago

5 0

Answer:

t =12 m

Step-by-step explanation:

We can use similar triangles and proportions to solve this problem.

Put the smaller triangle on top and the larger triangle on bottom

12 9

------ = -------

16 t

Solve by using cross products

12 t = 9*16

12 t =144

Divide by 12

12t/12 = 144/12

t = 12

Dmitriy789 [7]3 years ago

5 0

$\text{We have similar right triangles (Acute Angle Similarity)}$ $\triangle BAC\sim\triangle BED\\\\\dfrac{BA}{AC}=\dfrac{BE}{ED}\\\\\text{We have}\\\\BA=12m,\ AC=9m,\ BE=16m,\ ED=t.\\\\\text{Substitute:}\\\\\dfrac{12}{9}=\dfrac{16}{t}\qquad\text{cross multiply}\\\\12t=(9)(16)\\\\12t=144\qquad\text{divide both sides by 12}\\\\\boxed{\boxed{t=12\ m}}$ . Therefore the legs make proportions.

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Alexa pays 7/20 of a dollar for each minute she uses her pay-as-you-go phone for a call, and 2/5 of a dollar for each minute of

9966 [12]

Answer:

The system of equations is x + y = 85 and 7/20x+2/5y=31
To eliminate the x-variable from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7.
B-She used 60 minutes for calling and 25 minutes for data.

Step-by-step explanation:

It is always a good idea to start by defining variables in such a problem. Here, we can let x represent the number of calling minutes, and y represent the number of data minutes. The the total number of minutes used is ...

x + y = 85

The total of charges is the sum of the products of charge per minute and minutes used:

7/20x + 2/5y = 31.00

We can eliminate the x-variable in these equations by multiplying the first by -7 and the second by 20, then adding the result.

-7(x +y) +20(7/20x +2/5y) = -7(85) +20(31)

-7x -7y +7x +8y = -595 +620 . . . . eliminate parentheses

y = 25 . . . . . . . . simplify

Then the value of x is

x = 85 -y = 85 -25

x = 60

7 0

3 years ago