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Posted in Mathematics

Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º. Scarlett's height is 1.65 meters, so the height of the dam is


Make a drawing with a right triangle.

The opposite side, y, is the height of the dam less 1.65 m

The base or adjacent side is 90 m

The angle between the two sides is 90 m.

Then tan (26) = y / 90

y = 90 tan(26) = 90 (0.4877) = 43.90 m

The height of the dam is 43.90m + 1.65m = 45.55 m

Related Questions

Posted in Mathematics

4. Which of the following sets of numbers is a Pythagorean triple? A. 4, 5, 6 B. 8, 15, 17 C. 5, 12, 14 D. 8, 24, 25 Suppose a triangle has side lengths 6, 7, and 10. Which of the following best describes this triangle? A. obtuse B. acute C. right D. Cannot be determined.

Here are the answers to the given questions above:
4. When we say pythagorean triple, this would consists of three positive integers a, b, and c, such that a2 + b2 = c2. So for the given numbers above, the set that is considered a pythagorean triple would be B.  8, 15, 17.
5. The correct answer for this question would be option D. It cannot be determined whether the triangle is obtuse, acute or right if the given values are the side lengths. It should be angles. Hope this answer helps.

Posted in Mathematics

For f(x)=2x+1 and g(x)=x^2-7, find (f-g)(x)

I hope this helps you



(f-g)(x)=2x+1-(x^2-7)



(f-g)(x)=2x+1-x^2+7


(f-g)(x)= -x^2+2x+8

Posted in Mathematics

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm? 4x < h < 10x 10x < h < 4x h = 4x h = 10x

Answer with explanation:

In a triangle sum of two sides , should always be greater than the third side.

Sides of the given triangle are, 3 x cm, 7 x cm and h cm.

1.

3 x + 7 x > h

→ 10 x > h

2.

3 x+ h > 7 x

→h > 7 x -3 x

→h> 4 x

3.

7 x + h > 3 x, which will be always true.

Combining 1, 2 and 3 we get

→4 x < h < 10 x

Option A

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Posted in Mathematics

Drey makes $10 an hour plus $15 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week. Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. Part C: Drey earned $490 in 1 week. How many hours (regular plus overtime) did he work?

For the answer to the question above, let us solve the first for
Part A. $10 x 40 hours= $400 ($10x = W) X= 40 hours a week

Part b. $10 x 40 hours = $400 + $15 x Y=S ($10x=$400 +$15y=S) Y= number of hours overtime. Since he gets $15 for working more than 40 hours you take the number of hours over time and multiply it by 15.

Part c.  Now that he made $490 in 1 week you know that he worked for 40 hours at a rate of $10 an hour. But that's only $400, so we need to figure out 15 times what is equal to 90. 15 times six is equal to 90 which means that Drey worked for 46 hours

Posted in Mathematics

True or false Volume can be measured in liters or cubic meters.

The correct answer of the given statement above would be TRUE. It is true that volume can be measured in liters or cubic meters. Liters and cubic meters are units used to measure volume usually related to liquid volume. Hope this answers your question. 

Posted in Mathematics

What 2-dimensional shape can be rotated about the y-axis to create a cylinder which has a smaller diameter than height?

Based on the given description above, the two dimensional shape that can be rotated about the y-axis to create a cylinder which has a smaller diameter than the height would be a rectangle. Hope this is the answer that you are looking for. 

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Posted in Mathematics

Match Term Definition Line Segment A) a series of points that extend in two directions without end Plane B) two lines that intersect at 90° angles Perpendicular Lines C) lines that lie in the same plane and do not intersect Line D) a flat surface that extends infinitely and has no thickness Parallel Lines E) part of a line that has two endpoints

The correct matches are as follows:

Line Segment 
E) part of a line that has two endpoints

Plane 
D) a flat surface that extends infinitely and has no thickness

Perpendicular Lines 
B) two lines that intersect at 90° angles

Line 
A) a series of points that extend in two directions without end

Parallel Lines 
C) lines that lie in the same plane and do not intersect

Hope this answers the question. Have a nice day.

Posted in Mathematics

A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that best represents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer. Hint: Use the formula, f(x) = P(1 + r)x

For the answer to the question above, I think the formula you is wrong. The x must be in exponential form. It must look like this

f(x) = P(1 + r)^x
Now we can solve.

Given:
P = 2000
r = -0.06

f(x)  =  2000 (1 - 0.06)^x
       =  2000 (0.94)^x


         
2000 (0.94)¹² = 

2000 (0.476)  = 
The answer is 
951.8 square kilometers.
                   

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Posted in Mathematics

If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2% sellers of interest-bearing financial assets _____ interest rates to find willing buyers.

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2% sellers of interest-bearing financial assets greater than interest rates to find willing buyers.

Posted in Mathematics

The sum of the angle measures of any triangle is 180 degrees. Suppose that one angle in a triangle has a degree measure of 7x+3 and another has a degree measure of 3x-6 . Write an expression for the degree measure of the third angle in the triangle.

The sum of the angle measures of any triangle is 180 degrees. It should be that a + b + c = 180. For this problem, we are given the two angles which we assume to be a and b so,

180 = 
7x+3 + 3x-6 + c
c = 180 - (
7x+3 + 3x-6) 
c = 180 - (10x - 3)
c = 177 - 10x

Hope this answers the question. Have a nice day.

Posted in Mathematics

Find the multiplicative inverse of 6 + 2i.

The solution to the problem is as follows:

First thing to do is get rid of the i. Multiplying by 6 - 2i will do this 

( 6 + 2i)(6 - 2i) = 6^2 - (2i)^2 = 36 - 4(-1) = 36 + 4 = 40 

Dividing by 40 gets you 1 

(6 + 2i) (6-2i)/40 = 1 

The answer is (6 - 2i)/40 = (3 - i)/20

I hope my answer has come to your help. God bless and have a nice day ahead!

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Posted in Mathematics

Which one is bigger 60% of 90 or 1/2 pa 100?

60% of 90 = 90 * 0.60 = 54
1/2 of 100 = 100/2 = 50

So, as 54 > 50, 60% of 90 > 1/2 of 100

So, your answer is 60% of 90 is bigger!

Hope this helps!

Posted in Mathematics

The price of a cup of coffee was $2.65 yesterday. today, the price fell to $2.50 . find the percentage decrease. round your answer to the nearest tenth of a percent.

We must find the difference between prices. $2.65 - $2.50 = $0.15. Now we need to calculate what percent $0.15 is of $2.65. It is 5.7%! The price decreased, so it is a 5.7% decrease!

Posted in Mathematics

Convert 1.50 μm² to square meters.

The solution to the problem is as follows:

  1∙5µm² = ? m² 

1m * 1m = 1m² 
But 1m = 1,000,000µm = 1x10^6µm 
1x10^6µm * 1x10^6µm = 1m² 
1x10^12µm² = 1m² (Now, divide both sides by 1x10^12). 
1x10^12µm² /(1x10^12) = 1m² /(1x10^12) 
1µm² = 0∙000 000 000 001 m² (x both sides by by 1∙5). 
1∙5µm² = 0∙000 000 000 0015 m²
 
1∙5µm² = 1∙5x10^-12 m²


I hope my answers has come to your help. God bless and have a nice day ahead!

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Posted in Mathematics

Which of the following is the statement of the triangle inequality theorem? A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle. B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. C. The longest side of a triangle is opposite the largest angle. D. The largest angle of a triangle is between the two longest sides.

we know that

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

Let

a,b,c------> the length sides of a triangle

The theorem states that three conditions must be met

case 1)

 a+b > c

case 2)

 a+c > b

case3)

 c+b > a

therefore

the answer is the option

B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Posted in Mathematics

The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. Which sentence most closely summarizes the data? About 160 people weigh more than 165 pounds. About 320 people weigh more than 165 pounds. About 320 people weigh less than 165 pounds. About 640 people weigh less than 165 pounds.

Z = (X-Mean)/SD 
z1 = (165 - 150)/15 = +1 
z2 = (135 - 150)/15 = - 1 
According to the Empirical Rule 68-95-99.7 
Mean +/- 1SD covers 68% of the values 
100% - 68% = 32% 
The remaining 32% is equally distributed below z = - 1 and z = +1 
32%/2 = 16% 

Therefore, 

a) Number of men weighing more than 165 pounds = 16% of 1000 = 160 
b) Number of men weighing less than 135 pounds = 16% of 1000 = 160

Posted in Mathematics

How many meters are in 7.2 kilometers?

We Know, 1 Km = 1000 m
Then, 7.2 Km = 7.2 * 1000 m = 7200 m

So, your final answer is 7200 m

Hope this helps!

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Posted in Mathematics

A laptop computer sells for $850. the sales tax is 7%. what is the total cost of the laptop?

Answer:

$909.50

Step-by-step explanation:

$850 x 7% = $59.50 (tax amount)

850 x (1+ 0.07) = $909.50

Posted in Mathematics

A car travel 90 Km in 2 1/2 hours. How much time is required to cover 30 Km and find the distance cover in 2 hours

90:2 1/2
90/3 : (2 1/2)/3
30 : (2 1/2)/3
30 : (5/2)/(3/1)
30 : 5/2*1/3
30 : 5/6
30km in 50 mins

90 : 2 1/2
90/(2 1/2) : (2 1/2) / (2 1/2)
90/(2 1/2) : 1
(90/1)/(5/2) : 1
(90/1)*(2/5) : 1
180/5 :1
36:1
Multiply each side by 2:
72:2
72 km in 2 hours

Hope this helps :)

Posted in Mathematics

The price p of an icecream is $3.95 plus $0.85 for each topping t on the ice cream

You can add $3.95 and $0.85 but it mostly depends on how many toppings you put on the ice cream.

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Posted in Mathematics

Sophia is saving money for a new bicycle. The bicycle will cost at least $623. Sophia makes $8.22 per hour. Which inequality could be used find the number of hours Sophia needs to work to make enough money to buy a new bicycle? $8.22h > $623 $8.22h ≤ $623 $8.22h ≥ $623 $8.22h < $623

Answer:

C.8.22 h\geq$ 623

Step-by-step explanation:

We are given that Sophia is saving money for a new bicycle.

The bicycle will  cost atleast $623.

Sophia makes $8.22 per hour.

We have to find the inequality that could be used to find the number of hours Sophia needs to work to make enough money to buy a new bicycle.

Let Sophia works h hours to make enough money to buy a new bicycle.

Sophia makes money per hour =$8.22

Total money made by Sophia in h hours =8.22 h

According to question

8.22 h\geq $623

Hence, option C is true.

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Posted in Mathematics

12 meters into centimeters

We Know, 1 m = 100 cm
hen, 12 m = 100 * 12 = 1200 cm

So, your final answer is 1200 cm

Hope this helps!

Posted in Mathematics

Find the value of 3x + 2 when 7+ x = 5

I hope this helps you




x= 5-7


x= -2


3.(-2)+2


-6+2


-4

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Posted in Mathematics

Find all the zeros of the function y=x^3+6x^2+x+6

Y=X^3+6x^2+X+6 that is your answer
one more thing X= not real solution

Posted in Mathematics

A cone has a diameter of 10 inches. If its height is twice its radius, about what is the volume of the cone in cubic inches? Use 3.14 for π.

Answer with Step-by-step explanation:

The volume of cone is given by:

V=\dfrac{1}{3}\times \pi r^2h

Where r is the radius of cone and h is height

r=d/2 where d is the diameter

Hence, here r=5 in.

height is twice its radius ⇒ h=10 in.

V=\dfrac{1}{3}\times 3.14\times 5^2\times 10

V=261.66 in³

Hence, Volume of cone is:

261.66 in³

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