Answer:
10.07 meters
Step-by-step explanation:
We are given that the angle of elevation is 40° and the boy is 12 meters from the building.
This means that in order to figure out the height of the building, we must use the tangent function which states that [tex]tan(\theta)=\frac{opposite}{adjacent}[/tex].
The opposite side in this case is the height of the building in relation to the angle and the adjacent side is the distance the boy is away from the building.
Therefore, we can find the height of the building by plugging in our known information and solving for the opposite side:
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
[tex]tan(40^\circ)=\frac{x}{12}[/tex]
[tex]12tan(40^\circ)=x[/tex]
[tex]x=12tan(40^\circ)[/tex]
[tex]x\approx10.07[/tex]
Therefore, the height of the building is approximately 10.07 meters.
Express the following numbers in usual form:
(i) 8.02×10^-5
(ii) 4.5×10^3
(iii) 7×10^-5
(iv) 1.0001×10^8
(v) 4.3×10^12
(vi) 3.61492×10^5
(i) Given number = 8.02×10^-5
⇛ 8.02/100000
⇛ (802/100)/100000
⇛ 802/10000000
⇛ 0.0000802
The usual form of 8.02×10^-5 is 0.0000802
(ii) Given number = 4.5×10³
⇛4.5×1000
⇛ (45/10)×1000
⇛ 45×100
⇛ 4500
The usual form of 4.5×10³ is 4500
(iii) Given number = 7×10^-5
⇛ 7/100000
⇛ 0.00007
The usual form of 7×10^-5 is 0.00007
(iv) Given number = 1.0001×10⁸
⇛ 1.0001×100000000
⇛ (10001/10000)×100000000
⇛ 10001×10000
⇛100010000
The usual form of 1.0001×10⁸ is 100010000
(v) Given number = 4.3×10¹²
⇛ 4.3×1000000000000
⇛ (43/10)×1000000000000
⇛ 43×100000000000
⇛ 4300000000000
The usual form of 4.3×10¹² is 4300000000000
(vi) Given number = 3.61492×10⁵
⇛ 3.61492×100000
⇛ (361492/100000)×100000
⇛ 361492
The usual form of 3.61492×10⁵ is 361492
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the area of the triangle shown.
square units
Reset
Next
Plz help
Step-by-step explanation:
the area of a triangle is baseline × height / 2.
now, we need to count the units : how long is the baseline, he long is the height from the baseline to the top vertex ?
I find the baseline is 14 units long.
the height is 7 units.
so, the area is
14×7/2 = 7×7 = 49 square units.
f(x)=4x+6 g(x)=4x-6 if g(x)=f(x)+k what is the value of k
Answer:
k=-6-6=-12
Im pretty sure that's the answer
Solve the system of equations.
2x-y =7
1x-y = 10
Answer:
(-3, -7)
Step-by-step explanation:
2x - y = 7 multiply by -1 ⇔ -2x + y = -7
1x - y = 10 Do not change ⇔ 1x - y = 10
-x = 3
x = -3
Use the second equation to solve on y when x = -3
-1x - y = 10
-1(-3) - y = 10
3 - y = 10
-y = 10 - 3
-y = 7
y = -7 Solution: (-3, -7)
Rewrite the equation y + 6 = -5(x + 3) into general form (ax + by + c = 0)
Work Shown:
y + 6 = -5(x + 3)
y + 6 = -5x - 15
y + 6 + 5x + 15 = 0
5x + y + 21 = 0
The equation is now in the form ax+by+c = 0 where a = 5, b = 1, c = 21.
Answer:
5x + y = -21
Step-by-step explanation:
y + 6 = -5x - 15
5x + y + 6 = -15
5x + y = -21
6√21 ×√28
please show work :D
Answer:
84√3
Step-by-step explanation:
6√21√28
6√7√3√7√4
(6√7√3√7)(2)
(6*7)(√3)(2)
(42)(√3)(2)
84√3
[tex]6\sqrt{21} \cdot \sqrt{28}\\\\=6 \left(\sqrt{21 \times 28 \right)\\\\=6\left(\sqrt{588}\right)\\\\=6\left(\sqrt{196 \times 3}\right)\\\\=6\left(14\sqrt 3\right)\\\\=84\sqrt{3}[/tex]
a letter is chosen at random from the word 'mathematics'. Fin the probability that letter T is not chosen.
Answer:
2/11 is the answer of your question
a large bottle of juice contains 500 milliliters of juice. a medium bottle contains 70% as much juice as the large bottle. how many milliliters of juice are in the medium bottle.(can you include a number line? thanks!)
Answer:
350 millilitres
Step-by-step explanation:
70/100×500=350
Maya ate breakfast and wanted to leave her waitress a 15% tip. Her meal cost
$7.50. How much money should Maya leave for the TIP?
Answer:
$1.13
Step-by-step explanation:
You multiply 0.15*7.5, and you get 1.125, which you add up to $1.13
Which table is y a function of x?
Answer:
The first chart
Step-by-step explanation:
I NEED THIS ANSWERED ASAP
Which point is a solution to the system of equations?y=2x+2y=3x
A: (0,2)
B: (0,0)
C: (2,6)
D: (6,2)
Answer: B
Step-by-step explanation:
David has a loyalty card good for a 19% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $32? Round to the nearest cent.
Discounts are used to reduce the original price of an item.
David will pay $25 and 92 cents for an item of $32, before tax
The discount (d) is given as:
[tex]d =19\%[/tex]
The price (p) of the item is given as:
[tex]p = \$32[/tex]
So, the amount (A) paid before tax is calculated using:
[tex]A = p \times (1 - d)[/tex]
Substitute known values
[tex]A = \$32 \times (1 - 19\%)[/tex]
Express percentage as decimal
[tex]A = \$32 \times (1 - 0.19)[/tex]
Subtract 0.19 from 1
[tex]A = \$32 \times 0.81[/tex]
Multiply 32 and 0.81
[tex]A = \$25.92[/tex]
Hence, David will pay $25 and 92 cents for an item of $32, before tax
Read more about discounts at:
https://brainly.com/question/11538623
The supplement of the complement of an angle is 132 degrees. What is the supplement of that angle
Based on the information given, it should be noted that the supplement will be 48°.
It should be noted that two angles are called supplementary angles when the values that are added together will be equal to 180°.
In this case, we've been informed that one of the angles is 132°. Therefore, the value of the second angle will be:
= 180° - 132°
= 48°
The second angle is 48°.
Learn more about angles on:
https://brainly.com/question/23991796
Hi, let me help you out!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
In this problem, we're trying to find the supplement of [tex]\tt{132\textdegree}[/tex].
Supplementary angles add up to [tex]\tt{180\textdegree}[/tex].
So, let's find its supplement:
[tex]\tt{\angle x+132=180}[/tex], where x is the unknown angle.
Subtract 132 from both sides of the equal sign:
[tex]\boxed{\tt{\angle x=48\textdegree}}[/tex] [tex]\longleftarrow\tt{We\:conclude\:that\:this\:is\:the\:answer.}[/tex]
I hope it helps you! Have an awesome day!
If you need any explanation or clarification, feel free to comment and ask me, and I'll respond asap and do my best to help you out! :D
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
At time t= 0, a storage tank is empty and begins filling with water. For t > 0 hours, the depth of the water in the tank is increasing at a rate of W (t) feet per hour. Which of the following is the best interpretation of the statement W' (2) > 3?
a. Two hours after the tank begins filling with water, the depth of the water is increasing at a rate greater than 33 feet per hour.
b. Over the first two hours after the tank begins filling with water, the depth of the water is always increasing at a rate greater than 3 feet per hour.
c. Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.
d. Over the first two hours after the tank begins filling with water, the rate at which the depth of the water is rising is always increasing at a rate greater than 33 feet per hour per hour.
The given function is the rate of change of the water depth. therefore,
W'(t) is the second derivative.
The correct option is; d. Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.Reasons:
The volume of water in the tank is 0 at time t = 0 (the tank is empty)
The function that gives the rate at which the depth of water in the tank is
increasing at time t > 0 is W(t).
Where;
t = The time in hours
Therefore;
W'(t), the derivative of the function of the rate at which the water in the
tank is increasing in feet per hour is the rate of increase of W(t).
Which gives;
W'(2) = The rate of change of the rate at which the water level is rising (second derivative) two hours after begins to fill with water, per hour per hour.
Therefore;
W'(2) > 3 = Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.Learn more about second derivative here:
https://brainly.com/question/10305010
How does a plastic fork, whale, hospital and chocolate bar relate with each other?
Answer:
They all include the letter A
Step-by-step explanation:
I need help and I can’t find any sadly. Help!!
Answer:
Step-by-step explanation:
for 1. The addition property of equality esssentially means that if you were to add/subtract the same value to both sides of the equation, the equation would remain equal. this would be associated with 3. since adding 12 to both sides would give x on one side and 16 on the other which is equal to x=16
for 2. "given" just means the problem, so it is the 1st option. it just means "given the problem..."
for 3. collectiing like terms is the addition of -5x +6x. since they are on the same side eof the equation, and are in the same measurements (of x) they can be combined to eqaul positive x, this is represented by option 2
if I was 14 in 1947 then how old am I?
To join the tennis club, there is a $18.50 initial fee and a $1.10 yearly fee. What would be the value of the y-intercept in this situation?
Y = 18.50
Please tell me if it is right XD <3
Mikayla designed a survey to determine the number of people expected at opening night of a community theater. The community has about 5,000 members. She selected a sample of the first 25 parents dropping off actors during theater rehearsal. Which best explains Mikayla’s sample? random and biased random and unbiased nonrandom and biased nonrandom and unbiased.
The sample is based on the first 25 parents dropping off actors during theater rehearsal hence the sampling method is non random and biased.
A non random sample refers to a sampling method that is not based on chance alone. A biased sampling is one in which some members of the population are more likely to be selected thereby excluding the others.
Since the sample is based on the first 25 parents dropping off actors during theater rehearsal, the sampling method is non random and biased.
Learn more: https://brainly.com/question/24842573
Answer:
its nonrandom and biased
Step-by-step explanation:
so you don't have to read the other guys answer
The graph represents the fees in thousands of dollars, y, depending on the amount invested in millions, x, with one financial investment firm.
Over what interval is the change constant?
[0, 5)
[1, 5)
[0, 20)
[1, 20)
What is the domain and range .
A youth group earns $600 for charity and decides to put it in a bank. Calculate the amount of money the group will have for each scenario.
Part A chase bank pays simple interest at 5% and the group leaves the money for 5 years
part B witney bank pays an interest rate of 4% compounded annually and the group leaves the money for 6 years
Based on the types of compounding and the interest rates, the following are true:
Part A - The group will have $750Part B - The group will have $759.19When using simple interest, the amount the group will have is:
= Amount x ( 1 + rate x number of years )
= 600 x ( 1 + 5% x 5)
= $750
When using compound interest, the group will have:
= Amount x ( 1 + rate) ^ Number of years
= 600 x ( 1 + 4%)⁶
= $759.19
In conclusion, compound interest yields more.
Find out more about compound interest at https://brainly.com/question/25263325.
Check image for question
Answer:
a. 18
Step-by-step explanation:
a= 2
b= 3
[tex]ab^{2} =(2)(3)^{2} =2(9)=18[/tex]
Hope this helps
a=2
b=3
Now
a*b=ab²2*3=2(3)²2*3=2(9)2*3=18help! provide the missing statement and reasons for the following proof:
Theorem: opposite sides of parallelograms are congruent
Given: Parallelogram ABCD with diagonal AC
Prove: AB ≅ CD and AD ≅ BC
Answer:
So I figured it would be easier if I sent the pics instead. Hope it helps
. What is the second step in solving the following equation: 3(2x - 1) = 15, if the
Distributive property is used as the first step.
Help please. I dont know how to do this :((
Answer:
You need the distance of all four sides so that is:
2 * (5y +1) + 2 * (2y -3) which equals
10y + 2 + 4y -6 and that equals
14y -4
Step-by-step explanation:
For any parallelogram what is not always true
Answer:
The diagonals are congruent.
Step-by-step explanation:
Answer:
1) The diagonals are congruent.
3) The opposite angles are congruent.
4) The opposite sides are parallel.
Step-by-step explanation:Two pairs of opposite sides are congruent. The diagonals are perpendicular to each other. 4 In parallelogram QRST, diagonal is drawn. Which statement must always be true?
if it does not work sorry
In 2019, the average full-time worker in the U.S. spent `8.5` hours working each workday. This is an increase on the average of `8.1` hours per workday in 2014. What is the percent change from 2014 to 2019? Round to the nearest tenth of a percent.
Answer 2019 /0.0047 /2014/ 0.493
Step-by-step explanation:
The percent change in average full-time worker in the U.S from 2014 to 2019 is 4.93%.
What is Percent Change?A percentage is a portion of a whole that is stated as a number between 0 and 100 as opposed to being expressed as a fraction.
The percentages of everything are 100%, nothing is 0%, 50% of something is 50%, and nothing is 0%.
Given:
In 2019, the average full-time worker in the U.S. spent `8.5` hours working each workday.
This is an increase on the average of `8.1` hours per workday in 2014.
So, Percent change = (Final value - initial value) / initial value x 100
Percent change = 8.5 - 8.1 / 8.1 x 100
Percent change = 4.93%
Thus, the percent change in average full-time worker in the U.S from 2014 to 2019 is 4.93%.
Learn more about the percent change here:
brainly.com/question/809966
#SPJ2
A book sold 35,100 copies in its first month of release. Suppose this represents 8.8% of the number of copies sold to date. How many copies have been sold to date?
Answer:
561,972 copies
Step-by-step explanation:
MATH-
Look at the translation of the shape. Describe the translation that moves EFGH to E'F'G'H'.
3 boxes left 4 boxes up
4 boxes right 3 boxes up
4 boxes left 3 boxes up
Answer:
4 boxes left 3 boxes up.
Step-by-step explanation: