For a project in her Geometry class, Chloe uses a mirror on the ground to measure
the height of her school's football goalpost. She walks a distance of 10.65 meters from
the goalpost, then places a mirror on flat on the ground, marked with an X at the
center. She then steps 1.2 meters to the other side of the mirror, until she can see the
top of the goalpost clearly marked in the X. Her partner measures the distance from
her eyes to the ground to be 1.75 meters. How tall is the goalpost? Round your answer
to the nearest hundredth of a meter.

For A Project In Her Geometry Class, Chloe Uses A Mirror On The Ground To Measurethe Height Of Her School's

Answers

Answer 1

Answer: 15.53

Step-by-step explanation:

Let the height of the goalpost be y. Then,

[tex]\frac{y}{10.65}=\frac{1.75}{1.2}\\\\y \approx 15.53[/tex]


Related Questions

If f(x) = 3x + 1 and f^-1 = x-1/3 , then the ordered pair of f(3) =

Answers

Answer:

10

Step-by-step explanation:

f(x) = 3x + 1

f^-1 = x-1/3 , it is known as inverse function.

f(3)= 3*3 +1

=9+1

=10

To find inverse,

x=3x + 1

y=3x+1

Exchanging the position or x and y

x=3y+1

x-1=3y

.•. y=x-1/3

A system of equations is shown:
4x = -3y + 17
3x - 4y = -6
What is the solution to this system of equations? (5 points)
(3,2)
(-3,-2)
(-2,-3)
(2,3)

Answers

(3, 2) false

(-3, 2) false

(-2, -3) false

(2, 3) true

Answer: (2;3).

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{4x=-3y+17} \atop {3x-4y=-6}} \right. \ \ \ \ \left \{ {{4x+3y=17\ |*4} \atop {3x-4y=-6\ |*3}} \right. \ \ \ \ \left \{ {{16x+12y=68} \atop {9x-12y=-18}} \right. \\Let's\ sum \ up\ these\ equations:\\25x=50\ |:25\\x=2.\\4*2=-3y+17\\8+3y=17\\3y=9\ |:3\\y=3.[/tex]

what do I check off

Answers

A and F are the right answer
Answer is A, E and F.

Reason.

364 ____ 225

A = not equal sign
E = greater than or equal to sign
F = greater than sign

Harvey is analyzing the production cost of a new product launched by his company. The initial production cost was $1,050. The production cost is at its lowest amount, $250, for 200 items, and thereafter increases as the number of items increases. Which of the following graphs represents the production cost of the product?

Answers

It would be the bottom left graph

Initial production: 1050

so the graph will be started at 1050 which makes top right graph incorrect

Next, the money at the lowest was 250 which makes the top left and bottom right incorrect.

leaving only the bottom right graph to be correct

Answer:

Graph Y

Step-by-step explanation:

Given information:

Initial production cost = $1,050Lowest production cost = $250 for 200 itemsProduction cost increases after 200 items.The x-axis shows number of items in hundreds.The y-axis shows the cost in dollars.

The initial production cost is when the number of items is zero.

Therefore, the y-intercept of the graph will be (0, 1050).

The lowest production cost is the minimum point of the curve.

Therefore, the vertex of the graph will be (2, 250).

The only graph that satisfies these conditions is graph Y (attached).

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A radioactive material has a half life of 10 years. What is the fraction of the initial isotope is left after 60 years

Answers

Answer:

1/2^6 = 1/64

Step-by-step explanation:

Half life = 10 years

Time = 60 years

No of half life = T/t

= 60 / 10 = 6

Remaining fraction = 1/2^(no of half life)

= 1/2^6

= 1/64

If a=3x^3, b=4x^4, and c=ab^2, then what is the value of bc?

Answers

[tex]a=3x^3\hspace{5em}b=4x^4 \\\\[-0.35em] ~\dotfill\\\\ c=ab^2\implies c=(\underset{a}{3x^3})(\underset{b}{4x^4})^2\implies c=(3x^3)(4^2x^{4\cdot 2}) \\\\\\ c=3x^3\cdot 16x^8\implies c=(3\cdot 16)x^{3+8}\implies c=48x^{11} \\\\[-0.35em] ~\dotfill\\\\ \boxed{bc}\implies (\underset{b}{4x^4})(\underset{c}{48x^{11}})\implies (4\cdot 48)x^{4+11}\implies \boxed{192x^{15}}[/tex]

Answer:

  bc = 192x^15

Step-by-step explanation:

Perform substitution as required, then simplify.

Evaluation

  bc = b(ab^2) = ab^3 = (3x^3)(4x^4)^3 = (3·4^3)(x^3)(x^(4·3))

  = 192x^(3+12)

  bc = 192x^15

__

Additional comment

The relevant rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

Which number line shows the solution to the inequality? y minus 2 less-than negative 5 A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. A closed circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 7. Everything to the left of the circle is shaded.

Answers

The number line which represents the solution bro the inequality y -2 < -5 is;

An open circle is at negative 3. Everything to the left of the circle is shaded.

First, we must solve the inequality so that it looks it's simplest form in order to be represented on a number line.

Solving the inequality is as follows;

y - 2 < -5

y < -5 +2

y < -3.

In essence, representation of the inequality, y < -3 on the number line is as follows;

An open circle is at negative 3. Everything to the left of the circle is shaded.

PS: It is only a closed circle if the inequality includes an equal to sign.

Can someone help me out please

Answers

By just adding the given areas, we conclude that the definite integral is equal to 3.026

How to calculate the definite integral?

The integral will be equal to the sum of the four areas between points a and c.

The areas above the horizontal axis are positive areas, these are A and C.

While the areas below the horizontal axis are negative areas, these are B and D.

Then the definite integral will be:

I = A - B + C - D

Here we know that:

A = 1.311

B = 2.229

C =  5.545

D = 1.601

Replacing that, we conclude that the definite integral is

I =  1.311 - 2.229 +5.545 - 1.601 = 3.026

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What is the value of x?
90 degrees
170 degrees
X
Z

Answers

Answer:

x =  45 degrees.

Step-by-step explanation:

The arc of 90 degrees  an angle of 1/2 its value on  the circumference.

1/2 * 90

= 45 degrees.

45 degrees is the correct answer

Find the area of the irregular figure.
6 in.
13 in.
12 in.
5 in.
4 in.
4 in.
A = [? ]in.² please explain why or how you got the answer for future questions I only have so many points

Answers

Answer:

153 in²

Step-by-step explanation:

Area of irregular figure

[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]

[tex]\sf \boxed{\text{\bf Area of square = side *side}}[/tex]

Figure I:

   length = 12 in

   width = 6 in

Area of figure I = 12 * 6

                         = 72 in²

Figure II:

      length = 13 in

      width = 5 in

Area of figure II = 13 * 5

                          = 65 in²

Figure III:

       side = 4 in

Area of figure III = 4 * 4

                           = 16 in²

Area of irregular shape = 72 + 65 + 16

                                      = 153 in²

Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

Answer:

9 or 16... but I'm leaning more to 9

Step-by-step explanation:

Since the graph seems to be going up and down, it seems like its at its highest point and should go down now so it could be 9. But if not and its still going to go higher 16 is possible.

Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

Answer:

C (Third option)

Step-by-step explanation:

The prime factorization of 675 is 5*5*3*3*3 or 5^2*3^3. With the square root, we take out all square integers, leaving (5*3)(sqrt3). The answer is 15(sqrt3) or C.

√675

Break

√225×3√225√3√15²√315√3

Option C

Can anyone help me with this?

Putting the question into an online calculator gives me 4 Rad x. but what are the steps to solve it?

Simplify the following expression:
(x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6

Show all work to recive full credit.

Answers

The simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)

How to simplify the expression?

The algebraic statement is given as:

(x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6

Rewrite the algebraic statement as:

[(x^0 y^2/3 z^-2y)^2/3]/[(x^2 z^1/2)^-6]

Evaluate the like factors

[(x^0 y^(2/3+1) z^-2)^2/3]/[(x^2 z^1/2)^-6]

Evaluate the sum

[(x^0 y^5/3 z^-2)^2/3]/[(x^2 z^1/2)^-6]

Expand the exponents

[(x^(0*2/3) y^(5/3 * 2/3)z^(-2*2/3)]/[(x^(2*-6) z^(1/2*-6)]

Evaluate the products

[(x^0 y^(10/9) z^(-4/3)]/[(x^(-12) z^(-3)]

Apply the quotient law of indices

x^(0+12) y^(10/9) z^(-4/3+3)

Evaluate the sum of exponents

x^(12) y^(10/9) z^(-1/3)

Hence, the simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)

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20 pts !!! Please give a detailed answer thanks :)

How do you construct the inscribed and circumscribed circles of a triangle?

Answers

Answer:

inscribed: centered at the intersection of angle bisectors, radius = distance to one sidecircumscribed: centered at the intersection of perpendicular bisectors, radius = distance to one vertex

Step-by-step explanation:

The steps to constructing either circle start with finding the relevant center and radius. The required construction techniques are ...

bisect an angleperpendicular to a line through an external pointperpendicular bisector

Inscribed circleSummary

The incenter (center of the inscribed circle) is located at the coincidence of the angle bisectors. The radius is the perpendicular distance to any side, so will lie on the line through the incenter and perpendicular to one side.

Angle bisectors

Reference the first attachment. We have elected to bisect the largest two angles of triangle ABC. In each case, we used these steps:

Centered at a vertex (B for example), draw an arc through the two sides of that angle (arc HI for example).Centered at the points of intersection with the sides, draw two intersecting arcs with the same radius (arcs HQ and IQ).Draw the angle bisector through this point of intersection and the original vertex (green line BQ).

After this process is repeated for another angle, the point of intersection of the two angle bisectors is the incenter (R).

Radius

Finding the radius requires finding the perpendicular distance to one side of the triangle. That is done by constructing a perpendicular to the side through the incenter.

Centered at the incenter (R), draw an arc that intersects one side in two places (arc UV).Centered at the points of intersection with the side, draw two intersecting arcs with the same radius (arcs UZ and VZ. Z is the unlabeled point at upper right).Draw perpendicular RZ intersecting the midpoint of UV at X.

Incircle

The inscribed circle is centered at R and has radius RX.

__

Circumscribed CircleSummary

The circumcenter (center of the circumscribed circle) is located at the coincidence of the bisectors of the sides of the triangle. The radius is the distance from the circumcenter to any vertex.

Perpendicular bisector

Reference the second attachment. We have elected to bisect the longest and shortest of the triangle's sides. The purpose of this choice is to make the perpendicular bisectors intersect at a large angle, so the point is as accurately located as possible.

Choose one side of the triangle and set the radius to more than half its length.Using that radius, draw intersecting arcs using each end of the side as a center (side AB and arcs FG, for example).Draw the perpendicular bisector through the points where the arcs intersect (line FG).

Repeat this process for another side (BC to create bisector JK). The intersection of the two bisectors (L) is the circumcenter.

Circumcircle

The circumscribed circle is centered at L and has radius LA.

__

Additional comments

In general, arcs that are required to intersect each other will be drawn with the same radius. An arc that is required to intersect two lines, or one line in two places, may have any convenient radius.

As with any geometric construction, the tools required are a marking tool, a compass, and a straightedge. Usually, the preferred marking tool is a sharp pencil.

If the triangle is obtuse, the circumcenter will be outside the triangle (adjacent to the long side). If the triangle is a right triangle, the circumcenter is the midpoint of the hypotenuse.

Suppose you have a right triangle with congruent legs and a hypotenuse that measure (12sqrt(5))/5 What is the length of the smaller leg? Round to the nearest hundredth

Answers

The length of the smaller leg is 3.79

How to determine the length of the smaller leg?

Represent the smaller leg with x.

So, we have:

[tex]x^2 + x^2 = ((12\sqrt5)/5)^2[/tex] -- Pythagoras theorem

This gives

2x^2 = 144/5

Divide by 2

x^2 = 72/5

This gives

x^2 = 14.4

Take the square root

x = 3.79

Hence, the length of the smaller leg is 3.79

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The sum of five consecutive positive integers is 2020. Find the largets of these numbers.

Answers

Answer:

406

Step-by-step explanation:

let the 5 consecutive positive integers be

n , n + 1 , n + 2 , n + 3 , n + 4 , then

n + n + 1 + n + 2 + n + 3 + n + 4 = 2020

5n + 10 = 2020 ( subtract 10 from both sides )

5n = 2010 ( divide both sides by 5 )

n = 402

then

largest integer = n + 4 = 402 + 4 = 406

"i see that your new product is available for $412.50 on the website. how much is it if i buy it in the store?" employee: "buying through the website gets you a 25% discount. if you buy the product in the store, it will cost you __________."

Answers

The online product is 75% of the store product

412.50 / 0.75 = $550

Check
550 * 0.75 = $412.50

The cost of new product on the website is $309.375.

Given that, the cost of product = $412.50 and discount percentage = 25%.

What is discount?

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Discount = 25% of 412.50

= 25/100 × 412.50

= 0.25 × 412.50

= 103.125

So, cost = 412.50-103.125

= $309.375

Therefore, the cost of new product on the website is $309.375.

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find the average rate of change of the function in the interval 6,13

Answers

Using it's concept, the average rate of change of the function on the interval [6,13] is given by:

[tex]r = \frac{f(13) - f(6)}{7}[/tex]

What is the average rate of change of a function?

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this problem, we want to find the rate in the interval [6, 13], which is given as follows:

[tex]r = \frac{f(13) - f(6)}{13 - 6} = \frac{f(13) - f(6)}{7}[/tex]

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Find the area of the surface the part of the plane y=x^2 y^2 cylinder x^2 z^2=16

Answers

The area of the surface is 144.708

The equation of the given surface is,

z=g(x,y)=xy

Solving the partial derivatives,

∂g∂x=y,∂g∂y=x

Substituting to the formula

S=∬√1+( ∂g∂x)2+(∂g∂y)2dA

Thus,

S=∬√1+(y)2+(x)2dAS=∬√1+x2+y2dA

The region in the XY-plane is defined by the intervals  0≤θ≤2π,0≤r≤4

Converting the integral into polar coordinates,

S=∫2π0∫40√1+r2rdrdθ

Integrating with respect to r

S=∫2π0[13(1+r2)32]40dθ

S=∫2π0(17√173−13)dθ

Integrating with respect to θ

S=(17√173−13)[θ]2π0

S≈144.708

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Salah is building a brick walkway around his garden, which is 17 feet wide and 40 feet long. he wants the walkway to be 18 inches wide on all sides. if the bricks are 6 inches wide and 8 inches long, what is the minimum number of bricks Salah will have to buy?

Answers

The minimum number of bricks Salah will have to buy is 4050 bricks

How to find the minimum number of bricks Salah will have to buy?

Given that the

width of the garden is w = 17 feet and length l = 40 feet. Also, the walkway iis 18 feet wide.

So, the length of walkway plus garden, L = 40 ft + 18 ft = 58 ft. The width of walkway plus garden, W = 17 ft + 18 ft = 35 ft.

The area of the walkway

We now need to find the area of the walkway.

Area of walkway, A" = area of walkway plus garden - area of garden

= LW - lw

= 58 ft × 35 ft - 40 ft × 17 ft

= 2030 ft² - 680 ft²

= 1350 ft²

Now, since each brick is 6 inches wide and 8 inches long, the area of each brick is A' = 6 in × 8 in  = 48 in²

So, the number of bricks required, n = area of walkway/area of brick

= 1350 ft²/48 in²

= 1350 × 144 in²/48 in²

= 194400 in²/48 in²

= 4050 bricks

So, the minimum number of bricks Salah will have to buy is 4050 bricks

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A boat took 4 hours to make a downstream
trip with a current of 6 km/h. The return trip
against the same current took 6 hours. Find
the speed of the boat in still water.

Answers

Answer:

30 km/h

Step-by-step explanation:

Let X km/h be the speed of the boat in still water

Let the distance covered each way be D km

Relative speed of boat downstream = X + 6

Relative speed of boat upstream = X - 6

Distance covered by boat when going downstream

D = 4(X + 6) = 4X + 24

Distance covered by boat upstream is the same as distance covered downstream
D = 6(X-6) = 6X -36

Setting the two X equations equal to each other gives us

6X - 36 = 4X + 24

Collecting like terms

6X - 4X = 24-(-36)

2X = 60

X = 30 km/hr which is the speed of boat in still water

Check

Downstream speed is 30+6 = 36 km/h and distance traveled downstream in 4 hours = 36 x 4 = 144km

Upstream speed is 30-6 = 24 km/h and it travels for 6 hours. Distance covered = 24 x 6 = 144 miles

So distance covered is same and hence check succeeds

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.

Which best describes the range of possible values for the third side of the triangle?

x < 12.5, x > 18.9
12.5 < x < 18.9
x < 6, x > 26
6 < x < 26

Answers

Answer:

12.5< × < 18.9

Step-by-step explanation:

because you would use the pythagoras theorem which a² + b² = c² in this case c is the third side the unknown so to work this out do square root of ( 10² + 16²) which is 100 + 256 = 356 and the square root of 356 is 18.86 which rounds to 18.9 so the second answer is correct :)

i hope this helps pls ask if you need any more help :)

Bob's favorite restaurant were salmon filet and filet mignon. The restaurant served 70 specials in all, 80% of which were salmon filets. How many salmon filets did the restaurant serve?

Answers

By working with percentages, we will see that they served 56 salmon filets.

How many salmon filets did the restaurant serve?

Here we know that the restaurant served 70 specials in total, such that 80% of these were salmon filets.

So we just need to calculate what is the 80% of 70.

This is just given by:

70*(80%/100%) = 70*0.8 = 56

This means that they served 56 salmons filet.

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Simplify the expression 120x^3/18xy

Answers

120 / 18 = 20/3
x^3 / xy = x^2 / y

20x^2 / 3y

find the size of each of the angles marked with letter​

Answers

Answer:

f = 78 , g = 32 , h = 74

Step-by-step explanation:

f and 78° are alternate angles and are congruent , then

f = 78

---------------------------

h and 74° are alternate angles and are congruent , so

h = 74

--------------------------

the sum of the 3 angles in the triangle = 180°

sum the 3 angles and equate to 180

78 + g + h = 180

78 + g + 74 = 180

152 + g = 180 ( subtract 152 from both sides )

g = 28

What is the simplest form of this expression? (x − 4)(x^2 + 3x − 5)

Answers

Answer:[tex]x^3-x^2-17x+20[/tex]

Step-by-step explanation:

What number has to fill in the blank to make this a perfect square trinomial: 9x^2 + ___+ 144

Answers

The number that has to fill the blank to make the trinomial a perfect square is 72x

Perfect square trinomial

From the question, we are to determine the number that makes the given trinomial a perfect square

The given trinomial is

9x² + ___+ 144

For any given trinomial ax² + bx + c, the trinomial is a perfect square if

b² = 4ac

In given trinomial,

a = 9, c = 144, b = ?

Now, we will determine the value of b

Putting the values into the equation,

b² = 4ac

b² = 4×9×144

b² = 5184

b = √5184

b = 72

Thus,

The trinomial will become 9x² + 72x+ 144

Hence, the number that has to fill the blank to make the trinomial a perfect square is 72x

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If AB = 55, and BC = 49, find the length of the radius to the nearest tenth. Assume BC is tangent to Circle A.

Answers

Answer:

25.0

Step-by-step explanation:

Notice that points A, B, and C form a right triangle. This allows us to use the Pythagorean theorem, a^2 + b^2 = c^2, to find the missing side. AB is the hypotenuse, so substitute 55 for c, and BC is the leg, so substitute 49 into either a or b in the formula.

a^2 + b^2 = c^2

49^2 + b^2 = 55^2

b^2 = 3025 - 2401

b^2 = 624

b = sqrt (624)

b = 24.9799919936

A choir has 3 spots open for altos, and 8 altos are interested in them. in how many ways can the open spots be filled? 24 56 112 336

Answers

Answer:

56

Step-by-step explanation:

combinations

C(8,3)

What is the congruence correspondence, if any, that will prove the given triangles congruent?

Answers

Answer:

The answer is option A SAS.We have a side,an angle and the last side.If this helps please mark me BRAINLIEST

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