A 12 foot fence on the property line casts a 25 foot shadow on the shortest day of the year, and the north side of the house is set back 60 feet from the property line.
Using similar triangles formed by the fence, and the house, the top of which the property line passes, the height of the house can be determined.
The height of the house is 28.8 feet.Reasons:
The given parameters are;
Height of the fence = 12 foot
Length of the shadow cast by the fence = 25 foot
Distance of the house from the property line = 60 feet
The maximum allowable height for the house.
Solution:
Using similar triangles, we have;
[tex]\displaystyle \frac{Height \ of \, fence}{Length \ of \ fence \ shadow} = \mathbf{\frac{Height \ of \, house}{Distance \ of \ house\ from \ property \ line}}[/tex]
Which gives;
[tex]\displaystyle \frac{12}{25} = \mathbf{\frac{Height \ of \, house}{60}}[/tex]
[tex]\displaystyle Height \ of \ house = \frac{12}{25} \times 60 = 28.8[/tex]
The height of the house = 28.8 feet
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Please find attached the drawing of the question created with MS Visio, obtained from a similar question online.
which of the following values are solutions to the inequality 9≤3x+4
Answer:
x≤5/3
So any number at 5/3 or above is a solution
Step-by-step explanation:
Subtract 4 on both sides:
5≤3x
Divide 3 on both sides
x≤5/3
So any number at 5/3 or above is a solution
Hope this helps!
plz help look at the pic below
Answer:
You can use the exponential rule where
[tex](n^x)^y=n^{xy}[/tex]
Therefore,
[tex](a^3)^{-2}=a^{3*(-2)}=a^{-6}[/tex]
[tex]\\ \rm\leadsto (a^3)^{-2}[/tex]
(a^m)^n=a^mn[tex]\\ \rm\leadsto a^{-6}[/tex]
[tex]\\ \rm\leadsto \dfrac{1}{a^6}[/tex]
35,000 is invested at 5% compound interest.What is the interest at the end of three years
Answer:
$40,516.86
Step-by-step explanation:
start by taking 35,000 and multiplying it by 0.05 to get 5% of the number. then add that number (1,750) to the original 35,000 and you should get 36,750. this would be the first year. Then multiply 36,750 by 0.05 again and add that number (1837.5) to the original 36,750 and you should get 38,587.5. Finally multiply that by 0.05 and add that number (1,929.375) to the original 38,587.5 and you should get 40516.875. Round to the hundredths since it is money.
Given $P(10,12)$ and $Q(20,36)$, find the coordinates of a point whose distance from both $P$ and $Q$ is exactly $13.$
The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)
The distance between points, P and Q can be evaluated by the Pythagoras theorem as follows;
Distance, PQ = √(20-10)² + (36-12)²PQ = √(100+576)PQ = √676PQ = 26.Therefore, a point whose distance from both P and Q is exactly 13 is the midpoint of PQ.
Therefore,
x = (20 + 10)/2x = 15y = (36 + 12)/2y = 24.The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)
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An ice cream shop serves about 60 customers in one day. About how many customers does the ice cream shop serve in 40 days?
Answer:
2400
Step-by-step explanation:
60(customers/day) x40(days) = 2400 customers in 40 days
solve x. 24-8x=-16 and have a bless day
Answer:
x = 5
Step-by-step explanation:
24 - 8x = -16
Subtract 24 from both sides.
-8x = -40
Divide both sides by -8.
x = 5
Answer:
5
Step-by-step explanation:
24 - 8x = -16
24 + 16 = 8x
8x = 40
x = 40/8
= 10/2
= 5
HELP ME PLEASE
A newly made car will have a model number, a parts number, and a serial number. A model number is assigned by the manufacturer to identify each type of car. A parts number identifies one part of the smaller parts that make up the car. A serial number is unique to each car produced and identifies it.
Which relation is a function? (2 points)
(parts number, serial number)
(model number, parts number)
(serial number, model number)
(serial number, part number)
Answer:
(serial number, model number)Step-by-step explanation:
(X-2)(x+1)
Expand and siplify
[tex]\\ \sf\longmapsto (x-2)(x+1)[/tex]
[tex]\\ \sf\longmapsto x(x+1)-2(x+1)[/tex]
[tex]\\ \sf\longmapsto x^2+x-2x-2[/tex]
[tex]\\ \sf\longmapsto x^2-x-2[/tex]
How many brownies can you make in an 8x8 inch pan?
Answer:
You can make as many as you want, infinitely smaller but you need to specify the size of the brownies
Step-by-step explanation:
How would I graph this equation: 3x + 9y = −18
Find the unit rate for each problem
Answer:
1. 3 tacos per person
2. 8 chairs per table
3. 6 avocados per bag
Step-by-step explanation:
1. Divide 45 by 15 to get the unit rate: # of taco per person.
45 = 15x
45/15 = 15x/15
3 = x
3 tacos per person
2. Divide 72 by 9 to get the unit rate: # of chairs per table.
72 = 9x
72/9 = 9x/9
8 = x
8 chairs per table
3. Divide 42 by 7 to get the unit rate: # of avocados per bag.
42 = 7x
42/7 = 7x/7
6 = x
6 avocados per bag
Find the quotient. 1,329 ÷ 4
Answer:
Quotient is basically division.
Step-by-step explanation:
1329/4 is basically
332.25 is the answer
A car accelerates
at a rate of 7 m/s2. If its
original speed is 13 m/s, how many seconds will it take the car to reach a
final speed of 62 m/s?
PLEASE SHOW WORK
Answer:
7 Seconds
Step-by-step explanation:
This is kinematics
Vf=Vi+at
t=[tex]\frac{Vf-Vi}{a}[/tex]
t=[tex]\frac{62-13}{7}[/tex]
t=[tex]\frac{49}{7} =7[/tex]
please help, this is due today:
Answer:
x = 17
Step-by-step explanation:
∠ DCE = ∠ ACE ( vertically opposite angles )
The sum of the 3 angles in a triangle = 180° , then
∠ DCE = 180° - (100 +x) = 180 - 100 - x = 80 - x
∠ ACE = 180 - (49 + 4x) = 180 - 49 - 4x = 131 - 4x
Equating the 2 angles
80 - x = 131 - 4x ( add 4x to both sides )
80 + 3x = 131 ( subtract 80 from both sides )
3x = 51 ( divide both sides by 3 )
x = 17
HELP PLSSSSS TY
Health Club Fees You are choosing between two health clubs. Club A offers membership for a fee of $14 plus a monthly fee of $29. Club B offers membership for a fee of $28 plus a monthly fee of $22. After how many months will the total cost of each health club be the same?
Answer:
2 months
Step-by-step explanation:
To solve this equation create an expression for the cost of each club. Use the slope-intercept form of y=mx+b where m is the monthly fee and b is the flat fee. So the 2 expressions would be A) 29x+14 and B) 22x+28. Since we want to find when these are equal, set the expressions equal to each other. This gives the equation 29x+14=22x+28. Then, solve for x.
29x+14=22x+287x+14=287x=14x=2When solved, x=2. This means that after 2 months the cost of each will be the same.
Which statements about the function fare true? Check
all that apply.
The domain of f(x) is {all real numbers).
Answer:
see explanation
Step-by-step explanation:
The following statements are true
The domain of f(x) is all real numbers
The range of f(x) is all real numbers
f(2) = 4
locate x = 2 on the x- axis, go vertically up to meet the line at (2, 4 ) , then
f(2) = 4
Please help me please help me
Answer:
C=66, C=25 1/7
Step-by-step explanation:
i
C=pi(d)
C=22/7*21
C=66
ii
C=pi(d)
C=22/7*16
C=25 1/7
solve: 9x-7≤28+4x;x€W
we have 9x - 7 ≤ 28 + 4x
⇔9x - 4x ≤ 28 +7
⇔5x ≤ 35
⇔x ≤ 7
ok done. Thank to me :>
The temperature of a pan of water on the stove increases steadily from 22°C to 100°C at a rate of 8°C per minute. The temperature after 5 minutes is what.
Answer:
ui100
Step-by-step explanation:
125
The temperature of a pan of water on the stove after 5 minutes would be 40°C.
What is temperature?Temperature is the measure of the degree of hotness and coldness which is expressed in different scales.
The temperature of a pan of water increases steadily from 22°C to 100°C at a rate of 8°C per minute.
We need to find the temperature after 5 minutes.
Rate of temperature per minute = 8°C
Rate of temperature after 5 minutes = 8°C × 5
= 40°C
Therefore, the temperature after 5 minutes would be 40°C.
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722000
= ×10
its scientific notation help please
Answer:
7.22 x 10^5
Step-by-step explanation:
Remember that the decimal is always to the right of the ones place.
1. Move it one place to the left and multiply by 10 to compensate.
2. Move it two places to left and multiply by 10^2.
3. Move the decimal point three times and multiply 10^3 to compensate, and the pattern continues until you reach the very last digit, the 7.
4. Numbers after the 7 that are not zeros will be after the decimal point.
so, 7.22 x 10^5
complete the pattern 1,2,4,8___and __and __
Answer:
16, 32, and 64
Step-by-step explanation:
The number is being doubled every time.
The diagram below shows two triangles.
Based on the diagram, which statements are true?
Select three that apply.
(Select all that apply.)
The two triangles are congruent since all isosceles right
triangles are congruent.
The two triangles are congruent since the corresponding
sides and angles are congruent.
The two triangles are congruent since a rotation can carry one
triangle onto the other triangle.
The two triangles are congruent since a reflection can carry
one triangle onto the other triangle.
Answer:
1st , 2nd , and 4th
Step-by-step explanation:
Amy buys 16 envelopes for 14p each and pays with a £5 note.
How much change does she get?
Give your answer in pounds, £.
Answer:
£2.76
Step-by-step explanation:
The cost of Amy's purchase is ...
16×(£0.14) = £2.24
Her change from £5.00 is ...
£5.00 -2.24 = £2.76 . . . . Amy's change
Please help
??
:$):’jfidifkvk
Answer:
For the question a i think its b
Step-by-step explanation:
PLS HELP NEED THIS IN 1 HOUR 25 POINTS!!!!
The function below represents the annual interest Alexander earns on a savings account. Identify the term that represents the amount of time that the money is accruing interest.
f(x) = 500(1 + 0.02)x
500
1
0.02
x
Answer:
500: starting amount
(1 + 0.02): interest/growth rate
x: time
Step-by-step explanation:
Solve the equation for x.
x + 13 = 22
x + -13 = 22
Reorder the terms:
-13 + x = 22
Solving
-13 + x = 22
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '13' to each side of the equation.
-13 + 13 + x = 22 + 13
Combine like terms: -13 + 13 = 0
0 + x = 22 + 13
x = 22 + 13
Combine like terms: 22 + 13 = 35
x = 35
Simplifying
x = 35
Solve the equation. Plz help.
Answer:
x=5
Step-by-step explanation:
Find the slope of the line that passes through (10, 9) and (6, 18).
Answer:
M = -2 1/4
Step-by-step explanation:
You can use the formula y2 - y1 / x2 - x1 to get your answer.
y2 is 18 and y1 is 9. x2 is 6 and x1 is 10 so plugging that into the formula above you will get 18 - 9 / 6 - 10.
18 - 9 is 9 and 6 - 10 is -4
9/-4 = M (M is short for slope)
M = -2 1/4
Hope this worked for you.
y=1/2x+4
y=-2x+9
elmantion or substutuion method
Answer:
(2;5)
Step-by-step explanation:
Elimination:
Let's first multiply the first by 2 to clear fractions and write them both in standard form:
[tex]\left\{ {x-2y=-8} \atop {2x+y=9}} \right. \\[/tex]
Eliminate x: Multiply the first by 2, then subtract the equations:
[tex]2I-II: 2x-4y-2x-y=-16-9\\-5y=-25 \rightarrow y= 5[/tex]
Eliminate y: Multiply the second by 2, then add equations:
[tex]I+2II: x-2y +4x+2y = -8+18\\5x=10 \rightarrow x=2[/tex]
Subtsitution
Solve the first for y (oh, what a coincidence, it's done already!) and replace the value in the second.
[tex]\frac12x +4 = -2x+9 \rightarrow \ x+8=-4x+18\\x+4x = 18-8 \rightarrow 5x=10 \rightarrow x=2[/tex]
Then let's plug this value into a convenient one - let's say, the first - and find y from there:
[tex]y=\frac12\cdot 2 +4\rightarrow y =1+4 \rightarrow y=5[/tex]
If anyone tries saying it's not substitution, bring the system in standard form, as you did for the elimination method, then solve again for y.