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padilas [110]
2 years ago
6

5 Exam-style ABCD is a kite.

Mathematics
1 answer:
Mnenie [13.5K]2 years ago
5 0

let's recall that in a Kite the diagonals meet each other at 90° angles, Check the picture below, so we're looking for the equation of a line that's perpendicular to BD and that passes through (-1 , 3).

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of BD

y = \stackrel{\stackrel{m}{\downarrow }}{3}x-1\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}

\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{3\implies \cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}

so we're really looking for the equation of a line whose slope is -1/3 and passes through point A

(\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{1}{3}}[x-\stackrel{x_1}{(-1)}]\implies y-3=-\cfrac{1}{3}(x+1) \\\\\\ y-3=-\cfrac{1}{3}x-\cfrac{1}{3}\implies y=-\cfrac{1}{3}x-\cfrac{1}{3}+3\implies y=-\cfrac{1}{3}x+\cfrac{8}{3}

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svlad2 [7]

Answer:

6000

Step-by-step explanation:

3 0
3 years ago
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ACCTUALLY HELP ME??!!!!!!! NEEDED FOR TOMORROW AND 50 POINTS! will award brainliest for first answer!!
drek231 [11]

Answer:

a:c = 35:24

a:c = 20:27

a:c = 35:22

a:c = 28:27

Step-by-step explanation:

a:b = 7:3

Using cross products

3a = 7b

Divide by 7

3a/7 = b

Now we want

8b = 5c

Substitute in 3a/7 for b

8 (3a/7) = 5c

24/7a = 5c

Multiply by 7

24/7a *7 = 5*7c

24a = 35c

Divide by c

24 a/c = 35

Divide by 24

a/c = 35/24

a:c = 35:24

a:b = 4:9

Using cross products

9a = 4b

Divide by 4

9a/4 = b

Now we want

3b = 5c

Substitute in 9a/4 for b

3 (9a/4) = 5c

27/4a = 5c

Multiply by 4

27/4a *4 = 5*4c

27a = 20c

Divide by c

27 a/c = 20

Divide by 27

a/c = 20/27

a:c = 20:27

b:c = 5:11

Using cross products

11b = 5c

Divide by 11

b = 5c/11

Now we want

2a = 7b

Substitute in 5c/11 for b

2a = 7(5c/11)

2a = 35c/11

Multiply by 11

2a*11 = 35c

22a = 35c

Divide by c

22 a/c = 35

Divide by 22

a/c = 35/22

a:c = 35:22

b:c = 14:3

Using cross products

3b = 14c

Divide by 3

b = 14c/3

Now we want

9a = 2b

Substitute in 14c/3 for b

9a = 2(14c/3)

9a = 28c/3

Multiply by 3

9a*3 = 28c

27a = 28c

Divide by c

27 a/c = 28

Divide by 27

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a:c = 28:27

7 0
3 years ago
estamos construyendo una carretera que enlace los puntos a = 12 ,21 y b =(17,23) otro punto se encuentra en c =(3,9) es posible
Nadusha1986 [10]

Answer:

is not possible

Step-by-step explanation:

<u><em>The question in English is</em></u>

we are building a road that links the points a = (12 ,21) and b =(17,23) another point is in c =(3,9) it is possible that a single road allows to join these three points?

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

step 1

Find the slope ab

we have

a = (12 ,21) and b =(17,23)

substitute

m=\frac{23-21}{17-12}

m=\frac{2}{5}

step 2

Find the slope ac

we have

a = (12 ,21) and c =(3,9)

substitute

m=\frac{9-21}{3-12}

m=\frac{-12}{-9}

simplify

m=\frac{4}{3}

step 3

Compare slopes ab and ac

The slopes are different

That means ----> is not possible that a single road allows to join these three points

7 0
3 years ago
25-3x=2x help what’s x
Stolb23 [73]

Answer:

x=5

Step-by-step explanation:

add 3x to 2x

25=5x

then divide 25 by 5x

5=x

and flip

x=5

3 0
3 years ago
A factory makes 750 cakes every day. The cakes are orange cakes or lemon cakes. Each day Aadil takes a sample of 25 cakes to che
pochemuha
<h2><em><u>Answer:</u></em></h2>

<em><u></u></em>

A) 210

B) 0.18

<h2><u><em>Step-by-step explanation:</em></u></h2>

A) On Monday, 7/25 of the 750 are orange cakes. 7/25 x 750 = 210

B) If the proportion of orange cakes is 5/25 where 5 is correct to the nearest whole number, then the 4.5 would be the lowest number that would still be rounded up to 5. 4.5/25 = 0.18

8 0
3 years ago
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