a utility worker is 5.5 feet tall and is casting a shadow 4 feet long at the same time a nearby utility pole casts a shadow 20 feet long write and solve a proportion to find the height of the utility pole
Answers
So this is essentially a proportion problem. They want you to be able to recognize a relationship between the two. The easiest way to go about this is to draw a picture (I have included one). What you want to do is notice that you are given both shadow lengths. This is essentially going to be your first step to creating the proportion.
Understanding that we know the shadow lengths, we can turn these into a fraction such as so:
4ft/20ft.
Now that we know that, we need to look at are unknown. Our unknown is the height of the utility pole. We can solve this by substituting for X since we know the utility worker is 5.5 ft tall.
Your fraction for that would look like:
5.5ft/X
Make sure to always make your top to top match, such as since I put the utility worker's shadow on top, I need to put his height on top.
Now we can solve.
4ft/20ft =5.5ft/X
We need to cross multiply to get an equation we can work with. If we cross multiply, Your equation will look like:
4x = 110ft
This is a simple one step equation. Divide both sides by 4 to get your answer.
x= 27.5ft.
This means your Utility pole's height is 27.5ft.
To find the height of the utility pole, set up a proportion with the utility worker's height and shadow length as one ratio, and the utility pole's height and shadow length as the other ratio. Solve the proportion by cross-multiplying and simplifying the equation. The height of the utility pole is 27.5 feet.
Explanation:To find the height of the utility pole, we can set up a proportion with the utility worker's height and shadow length as one ratio, and the utility pole's height and shadow length as the other ratio. Let's call the height of the utility pole 'x'. The proportion can be written as:
(5.5 ft) / (4 ft) = x / (20 ft)
Cross-multiplying, we get:
(5.5 ft) * (20 ft) = 4 ft * x
Simplifying, we find:
x = (5.5 ft * 20 ft) / 4 ft = 27.5 ft
Therefore, the height of the utility pole is 27.5 feet.
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Related Questions
What’s the product of -2(-3.4)
Answers
i dont get this question can someone explain???
Answers
The inequality based on the information will be 0.8x + 8 ≤ 15.
What's the inequality?Let x be the number of rides you can go on.
The total amount of money you will spend on rides is 0.8x dollars.
The total amount of money you will spend on admission, lunch, and a snack is $4 + $3 + $1 = $8.
The total amount of money you have to spend is $15.
Therefore, the inequality based on the information will be 0.8x + 8 ≤ 15.
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1.Hannah walked the same number of miles each day for 5 days. Let m represent the total number of miles Hannah walked. Write a linear expression for the total number of miles she walked.
2.Jimmy brought 2 books per day to the book drive. Peter brought 4 books per day to the book drive. Let d represent the number of days of the book drive. Write a linear expression to represent the total number of books they brought.
3.Patricia buys clothes that are on sale with a 30% discount. Let c represent the cost of the clothes. Write a linear expression for the cost of the clothes.
4.A family of four had dinner together at a restaurant. Write two expressions for calculating their total bill if they leave a 15% tip. Let c represent the cost of their meal before tipping.
5.Tommy has $40 in his pocket. He sees a pair of pants that cost $37 and wants to buy them. If there's 10% sales tax where Tommy lives, can he afford to buy the pants? Write a linear expression and use it to solve the problem.
6.Add the expressions x + 18 and 3x − 12.
7.Subtract 3x − 4 from 5x + 7.
8.Subtract −4x + 1 from x − 2.
Answers
1) Given m represent the total number of miles Hannah walked.
Let us assume Hannah walked x miles each day.
So total number of miles Hannah walked in 5 days is m=5x.
2)Given Jimmy brought 2 books per day and Peter brought 4 books per day.
If d is the number of days the book drive, total number of books they brought
=total number books brought by Jimmy+ total number of books brought by Peter
= 2d+4d = 6d
3) Given that c represent cost of the clothes.
Then 30% discount = 0.3c
Hence cost of the clothes = c-0.3c = 0.7c
4) Given c represent the cost of their meal before tipping.
And tip is 15% of the cost.
Hence tip = 0.15c
Hence total bill = c+0.15c=1.15c
5) Given that Tommy had 40$ in his pocket.
And pair of pants cost 37$ with 10% sales tax.
Hence cost of pants including sales tax = 37+37*0.1 = 40.1$ >40$
Hence Tommy cannot afford the pants with 40$ in his pocket.
For following problems, we should group the like terms together and then simplify.
6) (x+8)+(3x-12) = (x+3x)+8-12 = 4x-4
7) 5x+7-(3x-4) = 5x+7-3x+4 = (5x-3x)+7+4 = 2x+11
8) (x-2)-(-4x+1)=x-2+4x-1 = (x+4x)-2-1 = 5x-3
PICKING BRIANLIEST ANSWER NOW!!!!!!! Which graph shows a dilation? LOOK AT PICTURES
Answers
The answer is D the last graph.
The required graph shows a dilation in graph D. Option D is correct.
Following the given case, 4 graphs are shown we have to determine the graph showing the dilation of concentric triangles.
Dilation of a triangle refers to the transformation that changes the size of the triangle while preserving its shape. It involves scaling the triangle by a factor, either enlarging or reducing its dimensions. The dilation is centered at a fixed point called the center of dilation.
While going through the figure, graphs A, B, and C are none dilated triangles because the triangles show dissimilarities. But D shows the dilation of the triangle because the two triangles are similar.
Thus, the required graph shows a dilation in graph D. Option D is correct.
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A designer wants to make a circular fountain inside a square of grass as shown at the right. What is a rule for the area A of the grass as a function if r
Answers
Answer:
[tex]A=4r^{2}-r^{2}\pi[/tex]
Step-by-step explanation:
1. To calculate the area of the grass you must substract the area of the square and the area of the circle.
2. The area of the square is:
[tex]A1=L^2[/tex]
Where [tex]L[/tex] is one side of the square.
3. You have that:
[tex]L=2r[/tex]
4. Therefore:
[tex]A1=(2r)^{2} =4r^{2}[/tex]
5. The area of the circle is:
[tex]A2=r^{2}\pi[/tex]
6. The are of the grass is:
[tex]A=4r^{2}-r^{2}\pi[/tex]
Angle (<) E and <F are vertical angles. If m<E = 17x+1 and m<F =20x-14, find m<F.
Answers
The vertical angles theorem states that vertical angles are congruent to each other. Since angles E and F are vertical angles, this means you can make them equal to each other in an equation.
m∠E = m∠F
17x + 1 = 20x - 14
Subtract 20x from both sides.
-3x + 1 = -14
Subtract 1 from both sides.
-3x = -15
Divide both sides by -3.
x = 5
Substitute 5 for x in m∠F (20x - 14).
20(5) - 14 = 86
m∠F = 86°
a perfectly spherical orange is split into four equal sections of the radius of the Orange is 4 centimeters what is the total surface area of a
Answers
Answer: 32π cm2
Step-by-step explanation:
Answer:
B: 32π cm2
Step-by-step explanation:
On edg
1+2g=-7 how do you do this?
Answers
Answer:
you would - 1 to -7 and get -8 then divide -8 by -2 than it would be 4
Step-by-step explanation:
I like my equations to have the variable before the constant.
2g+1=-7
Subtract 1 from the left side. Remember, whatever you do on one side, you MUST do it on the other.
2g=-8
Divide 2 from BOTH sides.
g=-4
Hope this helps!
:)
If 2x=8 what does "x" equal?
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Can’t remember what I learned in class,I need some help!
Answers
Answer:
1. ∠9 = 115°
2. ∠10 = 65°
3. ∠8 = 70°
4. ∠3 = 70°
5. ∠4 = 110°
6. ∠11 = 70°
7. ∠5 = 65°
8. ∠14 = 115°
Step-by-step explanation:
Given that, two parallel lines and two transversal lines.
also given that, ∠1 = 115° & ∠12 = 110°
We know that, straight angle = 180°
∠1 + ∠2 = 180°
∠2 = 180 - 115
∠2 = 65°
∠2 & ∠5 are vertical angles. So, they are same
∠2 = ∠5
∠5 = 65°
Similarly, ∠1 = ∠6 (vertical angles)
∠6 = 110°
Now given that, ∠12 = 110°
∠11 + ∠12 = 180°
∠11 = 180 -110
∠11 = 70°
∠11 & ∠16 are vertical angles.
∠11 = 16
∠16 = 70°
∠12 = ∠15 (vertical angle)
∠15 = 110°
∠4 & 12 are Corresponding Angles
∠12 = ∠4
∠4 = 110°
∠3 = 180 - ∠4 = 180 - 110
∠3 = 70°
∠7 = ∠4 (vertical angle)
∠7 = 110°
∠3 = ∠8 (vertical angle)
∠8 = 70°
∠1 = ∠9 (Corresponding Angles )
∠9 = 115°
∠10 = ∠2 (Corresponding Angles )
∠10 = 65°
∠13 = ∠10 (vertical angle)
∠13 = 65°
∠14 = ∠9 (vertical angle)
∠14 = 115°
9. ∠7 and ∠2 no relation between them.
10. ∠6 and ∠14 are corresponding angles.
11. ∠13 and ∠12 no relation.
12. ∠7 and ∠11 are Consecutive Interior Angles
13. ∠1 and ∠8 no relation.
Kelly is reading an 858-page book. During the past 6 days she has read 468 pages. At this rate, how many more days will it take her to complete
Answers
5 days because she reads 78 pages a day and she has 390 pages left, 78 goes into 390 5 times
My favorite songstress gives away 25% of the sales of the signature fragrance collection to her charity. Last month her sales were $1,200. How many much of her total sales did she donate
Answers
She donated
$
300
to her charity.
Explanation:
The amount
(
x
)
given in charity on
$
1200
sales at
25
%
is:
x
=
1200
×
25
100
x
=
12
00
×
25
1
00
x
=
12
×
25
x
=
300
the graph of a quadratic function has a vertex ar (3,-6). One point of the graph is (7,10). What is another point on the graph?
Answers
Answer:
y + 6 = (x -3)^2
Step-by-step explanation:
Let's use the general form of the vertex equation of a quadratic: y - k = a(x - h)^2.
Subst. 10 for y, 7 for x, -6 for k and 3 for h. Then, 10 + 6 = a(7 - 3)^2, or
16 = a(4)^2, or 16 = a(16). Thus, a = 1, and the equation of this particular parabola is:
y + 6 = (x -3)^2
Given a quadratic function with a vertex at (3,-6) and a point (7,10), by substituting the values into the equation, we find that another point on the graph is (4,-5).
The vertex form of a quadratic function is [tex]\(y = a(x - h)^2 + k\)[/tex], where (h, k) is the vertex of the parabola. In this case, the vertex is (3, -6), so the equation is [tex]\(y = a(x - 3)^2 - 6\).[/tex]
You're also given a point on the graph, which is (7, 10). You can use this point to find the value of a.
Substitute the point's coordinates into the equation and solve for a:
[tex]\(10 = a(7 - 3)^2 - 6\)[/tex]
[tex]\(10 = a(4^2) - 6\)[/tex]
10 = 16a - 6
Now, isolate a:
16a = 10 + 6
16a = 16
a = 1
Now that you know a = 1, you can use this information to find another point on the graph. Simply plug in a different value for x into the equation. Let's choose x = 4 for example:
[tex]\(y = 1(4 - 3)^2 - 6\)[/tex]
y = 1(1) - 6
y = 1 - 6
y = -5
So, another point on the graph is (4, -5).
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Not really getting this can someone plz explain.
Answers
your answer would be b becuase that is 3/6 so thats half and ou would simply it and 1/4 do the same
The floor of a room is being covered with tile. An area of 3/4 of the length and 3/5 of the width is covered. Find the fraction of the floor that has been covered.
Answers
To determine the fraction of the floor covered, we multiply the fraction of the length covered (3/4) by the fraction of the width covered (3/5), resulting in a covered area of 9/20 of the floor space.
To find the fraction of the floor that has been covered by tile, we need to multiply the fraction of the length covered by the fraction of the width covered. If an area of 3/4 of the length and 3/5 of the width is covered, then we perform the multiplication: (3/4) x (3/5) = 9/20.
This means that the fraction of the floor covered with tile is 9/20. This fraction represents the percentage of the entire floor that is tiled, which in this case indicates that less than half of the room is covered because 9/20 is less than 1/2.
show work please or explain.
Answers
1340 units²
There are 2 rectangles 25 × 12, 2 rectangles 25 × 10 and 2 rectangles 12 × 10
SA = 2(25 × 12) + 2(25 × 10) +2(12 × 10)
= 600 + 500 + 240 = 1340 units²
Two hikers stopped for a snack. They shared 2/3 of a pound of trail mix. If the hikers shared the trail mix equally, how much trail mix did each hiker get?
Answers
each hiker gets 1 1/2
i hope this helped
Answer:
1/3 is the answer
How do I use distributive property to simplify 1/5( 30-1/3 )
Answers
A student's cost for last semester at her community college was $2300. She spent $276 of that on books. What percent of last semester's college costs was spent on books?
Answers
Answer: There is 12% of last semester's college costs was spent on books.
Step-by-step explanation:
Since we have given that
Amount spent at her community college = $2300
Amount spent of that on books = $276
We need to find the percent of last semester's college costs was spent on books is given by
[tex]\dfrac{276}{2300}\times 100\\\\=\dfrac{27600}{23}\\\\=12\%[/tex]
Hence, there is 12% of last semester's college costs was spent on books.
The student spent 12% of last semester's college costs on books.
How to solve the percentageTo find the percentage of last semester's college costs that was spent on books, you can use the following formula:
Percentage = (Part / Whole) * 100
In this case:
The "Part" is the amount spent on books, which is $276.
The "Whole" is the total college cost for last semester, which is $2300.
Percentage = ($276 / $2300) * 100
Percentage = (0.12) * 100
Percentage = 12%
So, the student spent 12% of last semester's college costs on books.
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hi, I am a sub for Glenridge and I need the answer to the question as soon as possible please here is the question Carl is boarding a plane. He has 2 checked bags of equal weight and a backpack that weights 4 kg. The total weight of Carl's baggage is 35 kg.
Write an equation that illustrates the problem and can be used to determine the weight, w, of each of Carl's checked bags.
Answers
The equation to determine the weight of each of Carl's checked bags is 2w + 4 = 35. After solving, we find that each checked bag weighs 15.5 kg.
To solve the problem regarding Carl's baggage weight, we set up an equation. Carl has two checked bags of equal weight, let's call the weight of each bag w kilograms. He also has a backpack weighing 4 kg. According to the problem, the total weight of all his baggage is 35 kg. We can represent this situation with the following equation:
2w + 4 = 35
This equation adds the weight of the two checked bags (2w since there are two of them and they are equal in weight) and the 4 kg backpack to get the total weight of 35 kg. To find the weight of each checked bag, we can simply subtract the weight of the backpack from the total weight and then divide by two:
Subtract the weight of the backpack from the total weight: 35 - 4 = 31 kgDivide the remaining weight by two to find the weight of each checked bag: 31 / 2 = 15.5 kgTherefore, the weight of each of Carl's checked bags is 15.5 kg.
Tony is writing a fraction equivalent to 2/7 using the formula 2*m/7*n. Which statement about m and n must be true so that tony fraction has the same value as 2/7
A. M/n has to be greater than 1
B. M/n has to equal 7
C. M/n has to be greater than 2
D. M/n has to equal 1
Answers
the answer is A i think
hope it helps
Answer:
Step-by-step explanation:
Given that Tony is writing a fraction equivalent to [tex]\frac{2}{7}[/tex] using the formula [tex]\frac{2}{7} *\frac{m}{n}[/tex]
Since this is equal to 2/7
we must have the value of [tex]\frac{m}{n} =1[/tex]
Hence option D is right.
Katarina wrote the standard form of a linear equation as 4x – 2/3 y = 8. Sofiya told her that the equation was not yet in standard form and gave her the right advice for how to fix it. What advice did Sofiya give to Katarina?
A. Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 24.
B.Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12.
C.Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 8.
D.Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 4.
Answers
The standard form of a linear equation in general is given by:
[tex]ax+by=c[/tex]
Now we are given the equation :
[tex]4x-\frac{2}{3}y=8[/tex]
In order to convert this into standard equation, we have to eliminate the 3 in the second term on the left side of equation.
Here 3 is in division ,so we have to perform opposite operation of division that is multiplication.
So multiplying both sides by 3 , we have
[tex]12x-2y=24[/tex]
So that means option A.Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 24. is the correct advice given by Sofiya.
Answer:
a
Step-by-step explanation:
I took test on edge
How do I round 24 and 80 percent to the nearest whole?
Answers
24 rounds to 25 and 80 stays the same
Can you tell me
what is 2 4/5 x 3
Answers
4 1/5
hope this helped, im better at algebra tho :)
Which expressions are equivalent to x+x+x + 2 ?
Choose 2 answers:
A
3x + 2
B
3 + 2x
C
3(x+2)
D
2(x+1)+x
E
5x
Answers
Answer:
A and D
Step-by-step explanation:
Only Answers A and D are equivalent to the given expression.
In A we see the variable 'x' show up three times, and so we write 3x + 2.
In D, after performing the indicated multiplication, we have 2x + 2 + x, which condenses to 3x + 2.
A mathematical expression is a finite arrangement of symbols and variables following a rule relating to the set of the finite variables.
From the given information:
x +x + x + 2= 3x + 2Also, we can have it has: 2(x+1) +x.
This is because if we simplify the above expression, we will arrive at 3x +2.
Let's solve:
The first thing we will want to do is to open the brackets
= 2(x+1) + x = 2x + 2 + xBy rearrangement of like terms, we have:
= 2x + x + 2= 3x +2Therefore, we can conclude that the mathematical expressions that are equivalent to x + x + x +2 are in Option A and D.
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DaMontre is at basketball practice, where he takes 30 shots a minute. He also took an extra 70 shots before practice. If DaMontre took 1,870 shots, how long did he practice for?
Answers
DaMontre practiced for 60 minutes after taking a total of 1,870 shots, with an initial 70 shots before practice and 30 shots per minute during practice.
Explanation:The question asks how long DaMontre practiced basketball if he took a total of 1,870 shots, with a pre-practice session of 70 shots, and during practice, he takes 30 shots a minute.
Step-by-step solution:
First, subtract the extra shots DaMontre took before practice from the total number of shots to find out how many shots were taken during practice. So, 1,870 - 70 = 1,800 shots during practice.
Next, to find out how long he practiced for, divide the number of shots taken during practice by the rate at which he takes shots per minute. Therefore, 1,800 shots divided by 30 shots/minute = 60 minutes.Thus, DaMontre practiced for 60 minutes, which is the answer to the question.
The table displays the total cost, y, of purchasing x tickets for the carnival. Which conclusions can you draw from the data shown in the table? Select all that apply. Twelve tickets cost $30.00. Thirty tickets cost $12.00. Each additional ticket costs $2.50. The table is a partial representation. (27.50, 11), (30, 12) and (32.50, 13) are the ordered pairs represented in the table.
Answers
Answer:
Twelve tickets cost $30.00.
Each additional ticket costs $2.50.
The table is a partial representation.
Answer:
A C D
Step-by-step explanation:
Lauren is tutoring students at the library on Saturday. If she is at the library for a total of 6 hours and she helps each student, one at a time, for 3/4 of an hour, how many students does she tutor?
Answers
24/3 = 8
She tutors 8 people.
Answer:
She tutors 8 students
Step-by-step explanation:
She is at the library for 6 hours. One hour has 60 minutes so she is at the library for [tex]6*60=360[/tex] minutes.
She helps each student for [tex]3/4[/tex] of an hour, that means [tex]3/4*60=45[/tex] minutes.
So now we have to calculate how many times does 45 minutes fits in 360 minutes (how many students she can help in 6 hours). That is [tex]360/45=8[/tex] students.
Vertex of f(x)=x^2+12x+8
Answers
the vertex is (-6,-28). let me know if i'm wrong
Why did the scientist create an exact duplicate of himself
Answers
To do his work that he didn't want to do.