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Basile [38]
3 years ago
7

A board is leaning against a vertical wall. One end of the board rests on the ground at a point eight feet from the wall. The ot

her end of the board touches the wall at a point that is six feet above the ground.
35 POINTS!Use a trigonometric function to determine the angle that the board creates with the ground (m∠A). In at least four sentences, explain why you chose your specific function and how it applies to the measure of angle A. Be sure to include the key vocabulary words "tangent", "ratio", "opposite side", "adjacent side" and "angle measure" in your response. Describe each computational step in complete sentences.

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
3 0

Answer:

36.87°

Step-by-step explanation:

Since ABC is a right-angle triangle, we can use trigonometric ratios to solve for unknown angles and sides.

For Angle at A, we have lengths of opposite and adjacent sides so we can use tangent at A.

tan(A) = opposite/adjacent

tan(A) = CB/AB

tan(A) = 6/8

A = (tan^-1)(0.75)

A = 36.86989765°

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Tapiwa raked 5% more leaves than Adam raked. Together, they raked 697 liters of leaves. How many liters of leaves did Adam rake?
EleoNora [17]
Assume that the number of leaves raked by Adam is x.
Tapiwa raked 5% more leaves than Adam, this means that:
Leaves raked by Tapiwa = x + 0.05x = 1.05x liters
We are given that the total number of raked leaves is 697 liters.
This means that:
Total raked = raked by Adam + raked by Tapiwa
697 = x + 1.05x
697 = 2.05x
x = 697 / 2.05 
x = 340
Based on the above calculations:
Adam raked 340 liters of leaves
Tapiwa raked 1.05(340) = 357 liters of leaves
7 0
3 years ago
Your mother takes you to your grandparents’ house for dinner. She drives 60 minutes at a constant speed of 40 miles per hour. Sh
Tomtit [17]

Answer:

a) 75 miles

b) 90 minutes

c) His constant speed was higher for a longer period of time

Step-by-step explanation:

a) 70 / 2 = 35

40 + 35 = 75

b) 60 + 30 = 90

4 0
2 years ago
Identify whether or not each pair of terms can be combined to so oily the expression (3x + 1) + (2x -5)
eimsori [14]

Answer:

3x and 2x can be combined bc it has ex at the end.

1 and 2x cannot be combined bc 1 doesn't have an x.

1 and -5 can be combined

6 0
2 years ago
The sum of two numbers is 59 and the difference is 15 . what are the numbers?
UkoKoshka [18]
Write a system of equation based on the number
For an instance, the two numbers are a and b.
"The sum of two numbers is 59" can be written as follows.
⇒ a + b = 59  <em>(first equation)
</em>"The difference is 15" can be written as follows.
⇒ a - b = 15  <em>(second equation)</em>

Solve the system of equation by elimination/substitution method.
First, eliminate b to find the value of a.
a + b = 59
a -  b = 15
--------------- + (add)
2a     = 74
  a     = 74/2
  a     = 37

Second, substitute 37 as a in one of the equations
a + b = 59
37 + b = 59
b = 59 - 37
b = 22

The numbers are 37 and 22
5 0
3 years ago
A linear regression was conducted on the number of cigarettes a person smokes in a day versus the number of times they cough in
makvit [3.9K]

Answer:

a) response variable

Step-by-step explanation:

The response variable is the variable that depends on other variables such as the independent or explanatory variable, it is the variable that is being tested. The response variable is also called the dependent variable.

In linear regression, the y variable is referred to as the response variable while the x variable is referred to as the explanatory or independent variable.

In this case the y variable is "the number of times they cough in a day" and this variation depends on the x variable "number of cigarettes a person smokes in a day".

8 0
3 years ago
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