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erma4kov [3.2K]
3 years ago
11

In the figure shown, ABC is a right triangle with side lengths a, b, and c, and CD is an altitude to side AB. The side lengths o

f triangle ACD are b, h, and r, and the side lengths of triangle CBD are a, s, and h.
Which proportions are true?


A) c/a = a/s and c/b = b/r


B) c/a = s/a and c/b = r/b


C) c/b = a/s and c/a = b/r


D) c/b = s/a and c/a = r/b

Mathematics
1 answer:
ycow [4]3 years ago
5 0

Answer:

A

Step-by-step explanation:

In the figure shown, ABC is a right triangle with side lengths a, b, and c, and CD is an altitude to side AB. This altitude divides the triangle into two right triangles ADC and BDC. In these triangles,

  • \angle CBD\cong \angle ACD\cong \angle CBA
  • \angle DCB\cong \angle DAC\cong \angle BAC

So,

\triangle ABC\sim \triangle CBD\sim \triangle ACD

1. From the similarity \triangle ABC\sim \triangle CBD, you have

\dfrac{AB}{BC}=\dfrac{BC}{BD}\\ \\\dfrac{c}{a}=\dfrac{a}{s}

2. From the similarity \triangle ABC\sim \triangle ACD, you have

\dfrac{AB}{AC}=\dfrac{AC}{AD}\\ \\\dfrac{c}{b}=\dfrac{b}{r}

Hence, option A is true

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A garden is rectangular with an area of 6/7 square miles. If the length of the garden is 3/5 miles, what is its width?
Dafna11 [192]

Answer:

Step-by-step explanation:

Area= length x width

area=6/7, length=3/5, width=?

6/7=3/5 x width

6/7 divided by 3/5= 6/7 x 5/3 (you have to multiply by the recipricol, or flip the fraction.)

6/7 x 5/3=30/21= 1 3/7=width

7 0
3 years ago
What is the equation of a line passing through (-3,7) and having a slope of -1/5<br> PLEASE HELP
OLEGan [10]

Answer:

y = -1/5x +32/5

Step-by-step explanation:

The slope intercept form of the equation of a line is

y = mx+b

we know m = -1/5

y = -1/5x+b

We know a x and y on the line

7 = -1/5(-3) +b

7 = 3/5 +b

Subtract 3/5 from each side

35/5 -3/5 = b

32/5 =b

So the equation is

y = -1/5x +32/5

8 0
3 years ago
Please help me with the below question.
tresset_1 [31]

We have the following three conclusions about the <em>piecewise</em> function evaluated at x = 14.75:

  1. \lim_{t \to 14.75^{-}} f(t) = 66.
  2. \lim_{t \to 14.75^{+}} f(t) = 10.
  3. \lim_{t \to 14.75} f(t) does not exist as \lim_{t \to 14.75^{-}} f(t) \ne  \lim_{t \to 14.75^{+}} f(t).

<h3>How to determinate the limit in a piecewise function</h3>

In a <em>piecewise</em> function, the limit for a given value exists when the two <em>lateral</em> limits are the same and, thus, continuity is guaranteed. Otherwise, the limit does not exist.  

According to the definition of <em>lateral</em> limit and by observing carefully the figure, we have the following conclusions:

  1. \lim_{t \to 14.75^{-}} f(t) = 66.
  2. \lim_{t \to 14.75^{+}} f(t) = 10.
  3. \lim_{t \to 14.75} f(t) does not exist as \lim_{t \to 14.75^{-}} f(t) \ne  \lim_{t \to 14.75^{+}} f(t).

To learn more on piecewise function: brainly.com/question/12561612

#SPJ1

8 0
2 years ago
2 (4x - 8) + 16t = 48
Effectus [21]
Distributive property first so you wanna do 2•4 then you will get 8x then you have to do 2•8 Wich is 16 then you will end up with 8x-16+16t=48 move the expression to the right 8x=48+16-16t 8x=64-16t x=8-2t?
8 0
3 years ago
4 x equals negative 2x + negative 6
erastovalidia [21]
So x equals two if it is an exponent.9
7 0
3 years ago
Read 2 more answers
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