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Masteriza [31]
2 years ago
15

Find the area of ABCHelp

Mathematics
1 answer:
Katarina [22]2 years ago
6 0

The value of the scale factor is 3. Then the height and area of the triangle ΔABC will be 9 ft and 54 square ft.

<h3>What is dilation?</h3>

Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.

The area of the triangle ΔDEF is 6 square ft. And the base length of the triangle ΔDEF is 4 ft.

The area of the triangle is given as

\rm Area = \dfrac{1}{2} \times bh\\\\

Then the height of the triangle ΔDEF will be

\rm 6 = \dfrac{1}{2} \times 4 \times h\\\\h = \dfrac{12}{4}\\\\h  = 3

Then the scale factor will be

\rm SF = \dfrac{12}{4} = 3

Then the height of the triangle ΔABC will be

\rm \dfrac{H}{3} = 3\\\\H \ = 9

Then the area of the dilated triangle ΔABC will be

\rm Dilated \ Area = \dfrac{1}{2} \times 12 \times 9\\\\Dilated \ Area = 54 \ ft^2

More about the dilation link is given below.

brainly.com/question/2856466

#SPJ1

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Natasha2012 [34]
(a)
The inverse is when you swap the variables and solve for y.
g(t) = 2t - 1 (Note: g(t) represents y)
rewrite as: y = 2t - 1
swap the variables: t = 2y - 1
solve for y: t + 1 = 2y
                   \frac{t + 1}{2} = y
Answer for (a): g^{-1}(t) =  \frac{t + 1}{2}

(b)
Same steps as part (a) above:
h(t) = 4t + 3
rewrite as: y = 4t + 3
swap the variables: t = 4y + 3
solve for y: y =\frac{t - 3}{4}

Answer for (b): h^{-1}(t) = \frac{t - 3}{4}

(c)
g^{-1} ( h^{-1}(t)) =  g^{-1} (\frac{t - 3}{4})
replace all t's in the g^{-1}(t) equation with \frac{t - 3}{4}
 g^{-1} (\frac{t - 3}{4}) = \frac{ \frac{t-3}{4} + 1}{2}
= \frac{ \frac{t-3}{4} +  \frac{4}{4}}{2} = \frac{ \frac{t - 3 + 4}{4}}{2} = \frac{ \frac{t + 1}{4}}{2} =  \frac{t + 1}{8}
Answer for (c): g^{-1} ( h^{-1}(t)) = \frac{t + 1}{8}

 (d)
h(g(t)) = h(2t - 1) = 4(2t - 1) + 3 = 8t - 4 + 3 = 8t - 1
Answer for (d): h(g(t)) = 8t - 1

(e)
h(g(t)) = 8t - 1
   y = 8 t - 1
   t = 8y - 1
  t + 1 = 8y
\frac{t + 1}{8} = y
Answer for (e): inverse of h(g(t)) = \frac{t + 1}{8}
 
























8 0
3 years ago
A college student completed some courses worth 3 credits and some
-BARSIC- [3]

Answer:

  • A. 13

Step-by-step explanation:

<u><em>Note:</em></u><em> It seems typo in the question. 5% should read 59.</em>

Let 3 credit courses = x, 4 credit courses = y

<u>As per  given we have following equations:</u>

  • x + y = 18
  • 3x + 4y = 59

<u>Solve the system by elimination. Multiply the first equation by 4 and subtract the second one:</u>

  • 4(x + y) - (3x + 4y) = 4(18) - 59
  • 4x + 4y - 3x - 4y = 72 - 59
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The answer is 13

Correct choice is A

4 0
3 years ago
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Answer:

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Vertical lines do not have a horizontal change; the line goes straight up and down. In other words, the change in the x values between any points on the graph is always 0, which would make the denominator of the slope 0. Since anything divided by 0 is undefined, the slope of a vertical line is <u>undefined</u>.

Source: https://www.brightstorm.com/math/algebra/linear-equations-and-their-graphs/finding-the-slope-of-a-line-from-a-graph-problem-3/

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2 years ago
Please help asap!!! 19 pts
wlad13 [49]
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