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3 years ago

Independent Practice

Mathematics

1 answer:

gladu [14]3 years ago

4 0

Answer:

d = 3t; 90 mi

Step-by-step explanation:

Bicycling A bicyclist traveled at a constant speed during a timed practice period. Write a proportion to find the distance the cyclist traveled in 30 min.

elapsed time distance

10 min 3 mi

25 min 7.5 mi

Graph it. :)

Start at (0,0), then at 10 min. on the x-axis, go 3 spaces up on the y-axis and plot a point. Do the same for 25 min. and 7.5 miles. Draw a line through all of those points, and see where the line hits on the y-axis when the x-axis is at 30 min. :)

If two things vary directly it means their ratio is a constant. Therefore from the formula rt=d. r=d/t, r=3/10 or 7.5/25 which reduces to 3/10. This is the constant speed,the lable is mi/min. Now use (d/30)=(3/10) and solve for d. Cross multiply and 10d=90, or d=9 mi

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Two sides of an acute triangle meaure 5 inches and 8 inches. The length of the longest side is unknown. What is the greatest pos

gladu [14]

The greatest whole possible whole number length of the unknown side is 9 inches.

<h3>How to identify if a triangle is acute?</h3>

Let us have:

H = biggest side of the triangle

And let we get A and B as rest of the two sides.

Then we get:

$A^2 + B^2 < C^2$

then the triangle is acute

Two sides of an acute triangle measure as 5 inches and 8 inches

The length of the longest side is unknown.

We have to find the length of the unknown side

WE know that the longest side of any triangle is a hypotenuse

For an acute triangle we know:

$A^2 + B^2 < C^2$

Here in this sum,

a = 5 inches

b = 8 inches

c = ?

Substituting we get,

$A^2 + B^2 < C^2\\\\5^2 + 8^2 < C^2\\\\25 + 64= C^2$

c < 9

Hence, The greatest whole possible whole number length of the unknown side is 9 inches.

Learn more about angles;

brainly.com/question/14489478

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2 years ago

Use the laws of Sines and law of cosines to find missing dimensions

Andrei [34K]

Answer:

A) ERROR

B) ∠C = 26°

Step-by-step explanation:

Houston, We have a problem!!! too much information

If we had a legit triangle, the law of sines would hold

19/sin138 = 8/sin20

28.395 = 23.390

as this is NOT an equality, the triangle does not exist as described.

IF it did, we'd get different results depending on which set we used

∠F = 180 - 138 - 20 = 22°

Law of sines

19/sin138 = DE/sin22 ⇒ DE = 19sin22/sin138 = <u>10.63697...</u>

8/sin20 = DE/sin22 ⇒ DE = 8sin22/sin20 = <u>8.762211...</u>

If we attempt to use Law of cosines

DE² = 19² + 8² - 2(19)(8)cos22 = <u>11.9639...</u>

so really none is correct because we attempt to use trig calculations to a non-triangle.

12) AC² = 15² + 19² - 2(15)(19)cos120

AC = 29.51270...

29.51270 / sin120 = 15/sinC

C = arcsin(15sin120/29.51270) = 26.1142... <u>26°</u>

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