A 7-foot tall stop sign creates a shadow that is 2 feet long. At the same time, a utility pole creates a shadow that is 11 feet long. How tall, in feet, is the utility pole?
Answers
11/2
5.5
Multiply that by 7
5.5x7
38.5 feet tall
Answer:
The height of the pole is 38.5 m.
Step-by-step explanation:
Given information:
The height of stop sign is [tex]h=7\rm \; ft[/tex]
Length of shadow of stop sign is [tex]l=2\rm \; ft[/tex].
The length of shadow of pole is [tex]L=11\rm \; ft[/tex].
Now, the shadow is measured at the same time for both the cases. So, the triangles formed by stop sign and its shadow, and pole and its shadow will be similar.
For similar triangles, the sides are always in same proportion.
Solve for the length of pole as,
[tex]\dfrac{H}{h}=\dfrac{L}{l}\\\dfrac{H}{7}=\dfrac{11}{2}\\H=7\times 5.5\\H=38.5[/tex]
Therefore, the height of the pole is 38.5 m.
Refer the diagram for more clarity.
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Related Questions
How many times larger is 9 x 10-8 than 3 x 10-12?
Answers
First solve the equations
9*10-8
90-8
(82)
3*10-12
30-12
(18)
Divide 82/18= 4.5
[tex]9\times10^{-8}[/tex] is [tex]3\times10^{4}[/tex] times larger than [tex]3\times10^{-12}[/tex].
The given number is [tex]9\times10^{-8}[/tex] and [tex]3\times10^{-12}[/tex].
We need to find how many times larger is [tex]9\times10^{-8}[/tex] than [tex]3\times10^{-12}[/tex].
What is scientific notation?To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.
If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive.If the given number is smaller than 1, then the decimal point has to move to the right, so the power of 10 will be negative.Now, [tex]\frac{9\times10^{-8}}{3\times10^{-12}}[/tex]
[tex]=3\times\frac{10^{-8}}{10^{-12}}[/tex]
[tex]=3\times10^{-8+12}[/tex] (∵[tex]\frac{a^{m}}{a^{n}} =a^{m-n}[/tex])
[tex]=3\times10^{4}[/tex]
Therefore, [tex]9\times10^{-8}[/tex] is [tex]3\times10^{4}[/tex] times larger than [tex]3\times10^{-12}[/tex].
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Ericka observed the total variation in the water level over 6.2 years to be −13.64 mm. She compared this to the average annual trend, which shows the water level rising 1.8 mm/year. Remember, she used 6.2 years as her time period. What is the difference between how much average water levels rose and how much the water level fell in the part of the river she observed?
Answers
-13.64 ÷ 6.2 = -2.2 mm/ year.
The difference between how much average water levels rose and how much water levels in her part of the river fell is:
1.8 -(-2.2) = 4 mm/year
During the 6.2 year period:
4 mm/year * 6.2 = 24.8 mm
Answer:
24.8
Step-by-step explanation:
12x+28y=84 how do I graph it
Answers
12x+28y=84
-12x -12x
28y=84-12x
÷28 ÷28
y= 2/5x+3
the +3 is your y-intercept (the point which your line touches the y-intercept
then the 2/5x is the slope (slope: rise over run)
so starting from your y intercept go up 2 to the right 5, then if you need to go down from the y-intercept do the opposite (down 2 to the left 5) now just draw the line to connect the points
hope this helps!!
what is the midpoint of FB
Answers
Answer:d
Step-by-step explanation:
−p(d+z)=−2z+59. solve for z.
Answers
we have
[tex]-p(d+z)=-2z+59[/tex]
Solve for z
[tex]-p(d+z)=-2z+59\\-pd-pz=-2z+59[/tex]
Group terms that contain the variable z, and move the other terms to the opposite side of the equation
[tex]-pz+2z=59+pd\\z(2-p)=59+pd[/tex]
Divide by [tex](2-p)[/tex] both sides
[tex]z=\frac{(59+pd)}{(2-p)}[/tex]
therefore
the answer is
[tex]z=\frac{(59+pd)}{(2-p)}[/tex]
Final answer:
The equation −p(d+z)=−2z+59 was solved for z by distributing the negative sign, combining like terms, and dividing by the coefficient of z, resulting in z = (59 + pd)/(2 - p).
Explanation:
The student asked to solve the equation −p(d+z)=−2z+59 for z. To solve for z, we need to isolate z on one side of the equation, following these steps:
Distribute the negative sign through the parentheses on the left side of the equation: −pd − pz = −2z + 59.
Move the terms containing z to one side of the equation: −pz + 2z = 59 + pd.
Combine like terms by adding pz to both sides: 2z + pz = 59 + pd or z(2 - p) = 59 + pd.
Divide both sides by (2 - p) to solve for z: z = (59 + pd)/(2 - p).
Now, z is isolated and the solution is given in terms of p and d.
15/16 is 1 sixteenth group of what size?
Answers
15/16 is 1 sixteenth group of size 1.0667.
15/16 represents a fraction where the numerator (15) is smaller than the denominator (16), indicating that it is less than a whole. When we express 15/16 as a mixed number, we get 15/16 = 0.9375, which means it is almost a whole.
In terms of groups, 15/16 can be thought of as 15 groups of a certain size out of 16. To find out the size of each group, we divide the total (16) by the number of groups (15), which gives us 16 ÷ 15 = 1.0667. Therefore, 15/16 is 1 sixteenth group of size 1.0667.
In other words, if we divide the whole into 16 equal parts, each part would be approximately 1.0667 units in size, and taking 15 of these parts would give us 15/16 of the whole.
This demonstrates that fractions can be interpreted as division problems and can be represented in various ways to understand the concept more deeply.
Write each mixed number as a percent 2 1/2
Answers
_____________________________________
Which equation represents a line that passes through the two points in the table
Answers
All of the answers are in point-slope form btw.
Answer:
[tex]y-1=\frac{5}{4}(x-1)[/tex]
Step-by-step explanation:
we know that
The equation of the line into point slope for, is equal to
[tex]y-y1=m(x-x1)[/tex]
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
In this problem we have
[tex]A(1,1), B(5,6)[/tex]
Substitute the values
[tex]m=\frac{6-1}{5-1}[/tex]
[tex]m=\frac{5}{4}[/tex]
with the point A and the slope m find the equation of the line
substitute the values
[tex]y-1=\frac{5}{4}(x-1)[/tex]
Which of the following measurements could be the side lengths of a right triangle? A. 66 in, 88 in, 110 in
B. 66 in, 88 in, 132 in
C. 66 in, 99 in, 110 in
D. 55 in, 88 in, 110 in
please dont answer if not 100 % sure.
Answers
A^2 + B^2 = C^2
Letter A is the only one that would work, because the first number squared (times itself), added to the second number squared, would equal the third number squared. This is a basic principle of the pythagorean theorem, which I can explain in more detail if you'd like. :)
Answer:
Step-by-step explanation:
The cable is 50 yards long, viewing post is 40 yard high , how far is the bottom cable from the base of the viewing post
Which statements about opposites are true?
Select each correct answer.
A.The product of a number and its opposite is always 1.
B.A number and its opposite are located the same distance from zero on a number line.
C.The opposite of zero is zero.
The opposite of a negative number is always a positive number.
D.
Answers
B is true
D as well
Given that ∠A≅∠B , Gavin conjectured that ∠A and ∠B are complementary angles.
Which statement is a counterexample to Gavin 's conjecture?
m∠A=30° and m∠B=60°
m∠A=25° and m∠B=25°
m∠A=10° and m∠B=15°
m∠A=45° and m∠B=45°
Answers
Given that ∠A is congruent to ∠B, this means that the measure of angle A is equal to the measure of angle B.
Two angles are said to be complementary if their sum is 90 degrees.
Consider, m∠A=25° and m∠B=25°, clearly, ∠A≅∠B, but m∠A + m∠B = 25° + 25° = 50°.
Thus, ∠A≅∠B , but ∠A and ∠B are not complementary angles.
i just took the test answer is B hope that helped!
Evaluate c-2 when c =7
Answers
Answer:
The value of given expression c-2 is 5 when c=7.
Step-by-step explanation:
The given expression
[tex]c-2[/tex]
We have to find the value of given expression c-2 when c=7.
Substitute c=7 in the given expression.
[tex]c-2=7-2[/tex]
[tex]c-2=5[/tex]
Therefore the value of given expression c-2 is 5 when c=7.
Factor 5x2 - 7x + 2.
Answers
The factored form of the given expression 5x² - 7x + 2 is equal to (5x - 2)(x - 1).
To factor the quadratic expression 5x² - 7x + 2,
find two binomials in the form (ax + b)(cx + d) whose product gives us the original expression.
The general form of a quadratic expression is ax² + bx + c, where:
a = 5
b = -7
c = 2
To factor the expression, look for two numbers whose product is ac (5× 2 = 10) and whose sum is b (-7).
The two numbers are -5 and -2 because:
-5 × -2 = 10
-5 + (-2) = -7
Now, rewrite the middle term (-7x) using these two numbers:
5x² - 5x - 2x + 2
Next, we group the terms and factor them by grouping:
(5x² - 5x) + (-2x + 2)
Factor out the greatest common factor from each group:
5x(x - 1) - 2(x - 1)
Now, factor out the common binomial factor (x - 1):
(5x - 2)(x - 1)
Therefore, the factored form of 5x² - 7x + 2 is (5x - 2)(x - 1).
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a football team gains 8 yards in one play, then loses 5 yards in the next.How many yards did the team gain in these two plays
Answers
cause if they move up 8 and take away 5 then they only moved up 3 yards
8-5=3
Nadeen is at an arcade. She started out with 18 tokens, and each game costs 3 tokens to play. Suppose x is the number of games Nadeen has already played.
Answers
Answer:
The expression [tex]18-3x[/tex] describe the number of tokens Nadeen has left.
Step-by-step explanation:
Consider the provided information
Nadeen is at an arcade. She started with 18 tokens. Each game costs 3 tokens.
The cost of each game is 3 tokens
Suppose x is the number of games played by Nadeen
Thus, the cost of x games is 3x tokens
it is given that Nadeen started with 18 tokens.
So, token left = [tex]18-3x[/tex]
Therefore, the expressions [tex]18-3x[/tex] can be used to describe the number of tokens Nadeen has left.
Show how 10 - 4 helps you solve 30 - 4
Answers
[tex]\boxed{ \ 30 - 4 = \ ? \ }[/tex]
30 - 4 = ...
/ \
20 + 10
[tex]\boxed{ \ 10 - 4 = 6 \ }[/tex]
[tex]\boxed{ \ 20 + 6 = 26 \ }[/tex]
[tex]\boxed{ \ \boxed{ 30 - 4 = 26} \ }[/tex]
Further explanation
This material is part of the common core mathematics curriculum.
Show how 10 - 4 helps you solve 30 - 4.
We know 10 - 6 = 4.
Furthermore, we can take out 10 from 30 and subtract 6 from 10.
[tex]\boxed{ \ 10 - 4 = 6 \ }[/tex]
Then we can add what is left, which is 20 to add to 6.
20 + 6 = 26
So, results from 30 - 4 are 26.
Let's review the steps again.
[tex]\boxed{ \ 10 - 4 = 6 \ }[/tex]
[tex]\boxed{ \ 20 + 6 = 26 \ }[/tex]
[tex]\boxed{ \ \boxed{ 30 - 4 = 26} \ }[/tex]
Learn more4 times as much as 3 is ... https://brainly.com/question/5737299 ten thousands divided by ten https://brainly.com/question/545132²/₇m - ¹/₇ = ³/₁₄ solve step by step https://brainly.com/question/4853649Keywords: show how, 10 - 4, helps you, solve, 30 - 4, subtracts, add, waht is left, the common core mathematics curriculum
With the help of 10 - 4, the solution of 30 - 4 is 26.
Using 30 - 4 to solve 10 - 4
Since the subtracted value from 30 and 10 are the same (4) ;
Therefore,
The sum of the difference between :
(10 and 4) and (30 and 10)
(10 - 4) + (30 - 10)
6 + 20 = 26
Hence, from 10 - 4; 30 - 4 gives 26
Subtracting directly also gives :
30 - 4 = 6.
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Write a problem involving how much more Than and solve it. Explain how drawing a diagram helped you solve the problem
Answers
"John has 8 apples and 17 oranges. How much more oranges does John has than apple?"
To answer this item, one needs to subtract the number of apples from the number of oranges. This is as shown below,
D = 17 - 8 = 9
The concept of "how much more than" is linked to finding the difference between the numbers.
a school has a goal of getting at least 2000 boxtops. they have 872 so far.
they have 8 days left to get it.at least how many do they need to collect each day to meet or exceed their goal.
Answers
what is volume of a sphere with radius of 9 inches. Need to know the steps also.
Answers
The work is provided in the image attached.
The flagpole in Mario's yard is 3,000 centimeters tall. How many meters tall is the flagpole?
Answers
Use a bar model to find the unknown value: 3/6 = ?/7
Answers
I can't figure this out... Can someone please help me?
Answers
[tex]j(x)=-5[/tex]
[tex]x=15[/tex]
Hope I helped!
The next plane will arrive in 22 minutes and 30 seconds. In how many seconds will the next train arrive?
Answers
So you just want to multiply 60 seconds by 22 groups of 60.
22 * 60 = 1320 seconds
And then add the previous seconds;
1320 + 30 = 1350 seconds
mrs.dryson divided her collection of 52 glass bears into equal groups. she had one bear left over.how many groups did Mrs.dryson make how many bears are in each group
Answers
That means she was able to divide 51 bears evenly.
51 can be divided by only 2 numbers (other than 1 and 51), NAMELY, 3 and 17, both of which are prime.
She either made 17 groups of 3 or 3 groups of 17.
Either way, she'd use 51 bears and have 1 left over.
The total number of groups Mrs. Dryson made is 17 so that an equal amount of glass bear is in each group and this can be determined by using the arithmetic operations.
Given :
Mrs. Dryson divided her collection of 52 glass bears into equal groups. She had one bear left over.The following steps can be used in order to determine the total number of Mrs. Dryson make:
Step 1 - Arithmetic operations can be used in order to determine the total number of Mrs. Dryson make.
Step 2 - Remember according to the given data, there are 52 glass bears and she divided these bears into equal groups and after dividing she had one bear left.
Step 3 - So the total number of bears to divide into groups of equal quantity is given by:
= 52 - 1
= 51
Step 4 - Now, the number from which 51 is divided so that the answer comes is an integer is 3.
Step 5 - So, the total number of groups made by Mrs. Dryson is:
[tex]=\dfrac{51}{3}=17[/tex]
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A cold front moved in last weekend.In 8 hours overnight,the temperature outside dropped 24 degrees. what was the average temperature change for each hour?
Answers
24/8= 3
The average temperature change was 3.
A delivery truck made 8 stops in one neighborhood. By stop 5, there were 11 packages delivered. This graph shows this information.
How many stops did it take to have 5 packages delivered?
12
8
3
2
Answers
Find the point that hits 5 on the "packaging delivery".
Then look down to find the 'x'
your x is 2
hope this helps
How many planes can two distinct lines have in common?
Answers
3x+y-1=0 What does y=
Answers
[tex]3x + y -1=0 Add 1 to both sides 3x + y -1+1=0+1 3x + y = 1 Transfer 3x on the other side y = 1 - 3x Thus, Y = -3x + 1[/tex]
Good luck with your studies!
Hii pleaseeeeee helpppppp meeeee understand how to do this I want to understand.
Answers
The value given is 3 23/66
23/66 = 0.34848
3 + 0.34848 = 3.34848
Thus, 3 23/66 = 3.348.
A bar line is placed on the top of the '48' portion of the answer to show that 48 is a repeating number in the decimal, that is, there are still a lot of 48 infront of the decimal point which we have not written as part of the answer.
can some one please help with this PLEASE
Answers
The diameter if the circle is given to be 32. That means the radius is 16.
The distance around the shape is then the circumference of the circle plus the side distance which is the total length 54 minus 16 on both sides.
p = 2(pi)16 + 2(54 - 32)
p = 32(pi) + 44
p = 32(3.14) + 44
p = 100.48 + 44
p = 144.48