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
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
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.
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.
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.
3 x + 7 x > h
→ 10 x > h
3 x+ h > 7 x
→h > 7 x -3 x
→h> 4 x
7 x + h > 3 x, which will be always true.
Combining 1, 2 and 3 we get
→4 x < h < 10 x
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?
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
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
E) part of a line that has two endpoints
D) a flat surface that extends infinitely and has no thickness
B) two lines that intersect at 90° angles
A) a series of points that extend in two directions without end
C) lines that lie in the same plane and do not intersect
Hope this answers the question. Have a nice day.
Which of the following are properties of the incenter of a triangle? Choose all that apply. A. The incenter is where all of the bisectors of the angles of the triangle meet. B. The incenter of an obtuse triangle lies on the outside of the triangle. C. The incenter is equidistant from each vertex of the triangle. D. The incenter of a triangle is always inside it.
The real answers are A and D, but not C
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
f(x) = P(1 + r)^x
Now we can solve.
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.
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.
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.
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.
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!
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!
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!
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
a,b,c------> the length sides of a triangle
The theorem states that three conditions must be met
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.
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.
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%
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
Then, 7.2 Km = 7.2 * 1000 m = 7200 m
So, your final answer is 7200 m
Hope this helps!
$850 x 7% = $59.50 (tax amount)
850 x (1+ 0.07) = $909.50
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
Multiply each side by 2:
72 km in 2 hours
Hope this helps :)
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
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 =
According to question
Hence, option C is true.
Marcus finds that (3x^2-2y^2+5x)+(4x^2+12y-7x)= 7x^2-10y^2-2x What error did Marcus make? A: He combined the terms 5x and –7x incorrectly. B: He combined the terms 3x^2 and 4x^2 incorrectly. C: He combined the terms –2y^2 and 12y^2 incorrectly. D: He subtracted the polynomials instead of adding.
Combine like terms
the answer is the option C
He combined the terms and incorrectly
Katie ordered candles that cost $3 each from a website. She was charged a flat shipping fee of $6 and no sales tax. If she spent a total of $54, which equation can be used to find c, the number of candles she ordered? 3c = 54 6c = 54 3c + 6 = 54 3c – 6 = 54
hen, 12 m = 100 * 12 = 1200 cm
So, your final answer is 1200 cm
Hope this helps!
one more thing X= not real solution
Answer with Step-by-step explanation:
The volume of cone is given by:
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.
Hence, Volume of cone is: