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Sholpan [36]
3 years ago
8

What is the length of segment BD? Round your answer to the nearest hundredth. triangles ABC and ABD in which the triangles share

segment AB and angle B is a right angle, the measure of angle CAB is 34 degrees, the measure of angle BDA is 31 degrees, and the measure of segment AB is 3 units 1.8 units 3.5 units 4.99 units 5.82 units

Mathematics
1 answer:
hichkok12 [17]3 years ago
6 0

Answer:

BD = 4.99 units

Step-by-step explanation:

Consider the triangle ABD only.

The angle formed is 31 degrees which occurs between two sides that are AD and BC.

We know that for a right angled triangle, the angle can always be taken as an angle between hypotenuse and base.

Thus, The perpendicular sides is then 3 units, where base is BD and Hypotenuse is AD

Using formula for tanθ

tanθ = Perpendicular/Base

tan31 = 3/BD

0.601 = 3/BD

BD = 3/0.601

BD = 4.99 units

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Car Wash A theater group is having a carwash fundraiser. The liquid soap costs $31 and is enough to wash 40 cars. Each car is ch
zheka24 [161]

Answer:

A) Independent variable is "c"

Dependent variable is "p"

B) Yes, it's a function

C) p = 7c - 31

D)domain of the function: 0 ≤ c ≤ 40

Range of the function: 0 ≤ p ≤ 249

Step-by-step explanation:

A) c is the total number of cars washed and p is the profit. The profit depends on the total number of cars washed. Hence, profit(p) is the dependent variable while "c" is independent variable

B) Yes it's a function because for each number of cars washed, there is a distinct value of profit made.

C) We are told that the liquid soap costs $31 and is enough to wash 40 cars. Each car is charged 7$.

$31 is cost to wash one car. Thus profit made per car is;

p = 7c - 31

D) The cost of $31 liquid soap is enough to only wash a maximum of 40 cars. This means the domain for the cars is from 0 cars to 40 cars

Thus;

domain of the function is 0 ≤ c ≤ 40

The profit function is given in answer C above as p = 7c - 31.

Now, if 0 cars are washed they will make zero profit but if 40 cars are washed then;

p = 7(40) - 31

p = 280 - 31

p = 249

Range of the function: 0 ≤ p ≤ 249

8 0
2 years ago
Solve each word problem using a system of equations. Use substitution or elimination.
nasty-shy [4]

Answer:

Step-by-step explanation:

x + 3y = 24.....multiply by -1

5x + 3y = 36

------------------

-x - 3y = -24 (result of multiplying by -1)

5x + 3y = 36

------------------add

4x = 12

x = 12/4

x = 3 <=======

x + 3y = 24

3 + 3y = 24

3y = 24 - 3

3y = 21

y = 21/3

y = 7 <========

4 0
3 years ago
find the perimeter and diagonal of a square whose area is equal to the area of a rectangle whose length is 9m and breadth is 4m
aalyn [17]
Area\ of\ a\ rectangle:A_{\fbox{ }}=9m\times4m=36m^2\\\\a-side\ of\ a\ square\\\\Area\ of\ a\ square:A_{\fbox{}}=a^2\\\\A_{\fbox{ }}=A_{\fbox{}}\Rightarrow a^2=36m^2\Rightarrow a=\sqrt{36m^2}\Rightarrow a=6m\\\\Perimeter\ of\ the\ square:P=4a\Rightarrow P=4\times6m=\boxed{24m}\\\\Diagonal\ of\ the\ square:d=a\sqrt2\Rightarrow d=\boxed{6\sqrt2\ m}
4 0
3 years ago
Elmer started out with$103 in his bank account .he spent $4 per week at the cafeteria for snacks.what is the slope (m) for this
pochemuha

Answer:

The equation is y=-4x+103

The slope is m=-4

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

y=mx+b

where

y is the amount left in the saving account

x is the number of weeks

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem we have

The slope is equal to

m=-\$4\ per\ week --> is negative because is a decreasing function

The y-intercept or initial value is

b=\$103

substitute

y=-4x+103

5 0
3 years ago
Find the common difference of the sequence shown.
tatyana61 [14]
The common difference is -1/4.
You can figure this out by subtracting each value in the sequence by the value right before it. Ex. 1/4 - 1/2 = -1/4
5 0
3 years ago
Read 2 more answers
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