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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.

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.

Answer:

x = 18, y = 5

Step-by-step explanation:

Because lines L and M are parallel, the corresponding angles 7x - 23 and 49 + 3x are equal.  Thus, 7x - 23 = 49 + 3x, or -72 = 2x.  Thus,

                                  4x = 72 and x = 18.

Check:  Is 7x - 23  =  49 + 3x true when x = 18?

                 7(18) - 23 =  49 + 3(18)?

                       103    =     103?  yes

Also:  If we concentrate on the triangle in the middle of the picture:

49 + (180 - 7x + 23) + (11y - 1) = 180 (sum of the interior angles of a triangle)

Then:  49 + 180 + 23 - 7x + 11y - 1 = 180.  But x = 18, so we have:

125 + 11y = 180, or 11y = 55, and so y = 5

Answer:

y = 2/3x + 4/3

Step-by-step explanation:

you need to know the slope of the line -2x + 3y = -6 because parallel lines have the same slopes

let's put the equation in y=mx+b format (slope-intercept format)

-2x + 3y = -6

add 2x to each side to get:

3y = 2x - 6

divide each side by 3 to get:

y = 2/3x - 2

the equation now shows us the slope is 2/3 and the y-intercept is (0,-2)

now we use y=mx+b again and use the point (-2,0) and the m=2/3 to get the y-intercept ('b' value) of the equation that is parallel:

0 = 2/3(-2) + b

0 = -4/3 + b

b = 4/3

equation would be:

y = 2/3x + 4/3

Answer:

-10i

Step-by-step explanation:

-3-i-9i+3

remove the Opposites

collect like terms

-i-9i

=-10i

Answer:

Step-by-step explanation:

please help me 8x-3+4x+3​

8x - 3 + 4x + 3​ =

8x + 4x  - 3 + 3 =

12x

Answer:

12x

Step-by-step explanation:

1. To simplify this expression, we must group like terms.

Therefore, the answer is 12x.

Answer:

it's 0.24 because if you do 500/120 in the first data table it gives u 0.24 and bc I just took the test

The frequency table is used to find the relative frequency. The value of x is 0.24. Option C is correct.

Relative frequency is the ratio of the considered sub-group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).

The given data from the table as follows;

The subgroup count of the column =  120

The total count = 500

Let x be the relative frequency

The relative frequency is found as;

[tex]x = \dfrac{120}{500} \\\\x = 0.24[/tex]

Therefore, the value of x is 0.24. So, Option C is correct.

To learn more about the frequency table;

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Answer:

4.7kg

Step-by-step explanation:

since when ready it is 7.3

subtract

7.3_2.6

Therefore the answer is4.7kg

Answer:

  a) $560

  b) 80%

  c) $1134

Step-by-step explanation:

The profit is the difference between selling price and cost price:

  profit = $1260 -700 = $560

__

As a fraction of the cost price, the profit is ...

  $560/$700 × 100% = 80% . . . . of the cost price

__

A 10% discount from the selling price makes it ...

  $1260 × (1 -10%) = 0.90×$1260 = $1134

A student will pay $1134 for a calculator.

Answer:

$6 per cat, $10 per car

Step-by-step explanation:

I guess and checked my work.

Answer:

x = -1/3 or x = 6

Step-by-step explanation:

For this equation, you should use the FOIL method or the BOX method. Break it apart to solve it easier. Sites like mathpapa or symbolab can help break these down for you.

Answer:

Step-by-step explanation:

4 magazines, and each magazines has 13 bullets:

4 bullets for each person:

Since we have an even amount of numbers here, the median is going to be the average of the two middle values, in this case:

(2a-1+a+7)/2 = 17

(3a +6)/2 = 17

3a + 6 = 34

3a = 28

a = 9[tex]\frac{1}{3}[/tex]

Answer:

5/6

Step-by-step explanation:

3 hours= 2 1/2 miles

1 hour= 2 1/2 divided by 3

It would take him 5/6 of an hour

Hop this helps!

Answer:

  a) 6

  b) 5

  c) 5

Step-by-step explanation:

In this context, "of" means "times."

a) 1/5 of 30 = 1/5×30 = 30/5 = 6

b) 1/4 of 20 = 1/4×20 = 20/4 = 5

c) 1/3 of 15 = 1/3×15 = 15/3 = 5

Answer:

Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

Answer:

The fundamental idea of calculus is to study change by studying "instantaneous " change, by which we mean changes over tiny intervals of time. And what good is that? It turns out that such changes tend to be lots simpler than changes over finite intervals of time.

Step-by-step explanation:

Answer:

-5+4= -1

Step-by-step explanation:

On a number line, look at -5, then add 4 to that, aka moving it up 4 places. -1 would be where it ends up.

Answer:

  ∠FGH = ∠HGI = 29°

  ∠FGI = 58°

Step-by-step explanation:

GH is marked as an angle bisector, so we have ...

  ∠FGH = ∠HGI

  2x -9 = 3x -28

  19 = x . . . . . . . . . . . . add 28-2x to both sides

Of course, the angle FGH is the sum of its parts. Then the angle measures are  ...

  (2x -9)° = (2·19 -9)° = 29°

  ∠FGH = ∠HGI = 29°

  ∠FGI = 58°

4, 8, 12, 20

10, 20

The least common multiple of 4 and 10

I hoped this helped. :)

Answer:

Step-by-step explanation:

Are the ratios 17:10 and 2:1 equivalent?

17 : 10 = 1.7

2:1      = 2

Answer:

5 2/5 ft

Step-by-step explanation:

2 4/5 + 2 3/5 = 4 7/5 = 4 + 5/5 + 2/5 = 4 + 1 + 2/5 = 5 2/5

Answer:

5 2/5 feet of ribbon

Step-by-step explanation:

   2 4/5

+  2 3/5

    5 2/5

plz mark brainliest

Answer:

B. f(2) = 63

Step-by-step explanation:

f (x) = -3x2 + 180x - 285

For this case, the first thing to do is replace the value of x = 2 in the given function to know the result.

We have to replace:

f (2) = -3 * (2) ^ 2 + 180 * (2) - 285

f (2) = 63

Answer:  

the value of pa for x = 2 is:

f (2) = 63

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

  dilation by a factor of 1/3 about the origin

Step-by-step explanation:

Triangle B has 1/3 the dimensions of triangle A, and it is 1/3 as far from the origin. The transformation of interest is ...

  dilation by a factor of 1/3 about the origin

Answer:

k=28

Step-by-step explanation:

Answer:

140 Minutes

Step-by-step explanation:

Y = 0.125x ---> Corinne every 1 minute

Y = 3.5 + .1x ----> Aretha

0.125x = 3.5 + .1x

-.1x               - .1x

0.025x = 3.5

0.025x/.025 = 3.5/.025

x = 140 minutes

We have a group of 169 students that needs to be seated in a square formation. Then, the number of rows has to be the square root of 169 :-

[tex]r = \sqrt{169} = 13[/tex]

Then, a square of 13 rows and 13 columns will fit the 169 students.

If the number of students is 1024, then the number of rows N can be calculated as :-

[tex] {N}^{2} = 1024[/tex]

[tex]N = \sqrt{1024} [/tex]

[tex]N = 32[/tex]

169 students will seat in a 13×13 formation.

1024 students will seat in a 32×32 formation (N=32)

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Answer:

= .533

Step-by-step explanation:

(−4/3)•(−1/3)= .44

.44•1.2=.533

Answer:

$27

Step-by-step explanation:

You can get the equation 30 - 30 * 1/10 = x, and x is what we are looking for. Simplifying gives 30 - 3, so x is 27. So, the answer is $27.

Answer:

$3

Step-by-step explanation: 10%= 0.10 divide that by 30, 30 ÷ 0.10 = 3

Answer:

Step-by-step explanation: