MATHEMATICS MIDDLE SCHOOL

Select the pair of equations whose graphs are perpendicular.  A.2y = –3x + 5    2x + 3y = 4  

B.5x – 8y = 9    12x – 5y = 7 

 C.y = 2x – 7     x + 2y = 3 

 D.x + 6y = 8     y = 2x – 8

Answers

Answer 1
Answer: k:\ y=m_1x+b_1\ \ \ \ and\ \ \ \ l:\ y=m_2x+b_2\n \nthe\ line\k\ is\ perpendicular\ to\ the\ line\ l\ \ \ \Leftrightarrow\ \ \ m_1\cdot m_2=-1\n----------------------------\n\nA.\n2y=-3x+5\ \ \Rightarrow\ \ \ y=- (3)/(2) x+2.5\ \ \Rightarrow\ \ m_1=- (3)/(2) \n\n2x+3y=4\ \ \Rightarrow\ \ 3y=-2x+4\ \ \Rightarrow\ \ y=- (2)/(3)x+1 (1)/(3) \ \ \Rightarrow\ \ m_2=- (2)/(3) \n\nm_1\cdot m_2=- (3)/(2) \cdot (- (2)/(3))=1 \neq -1

B.\n5x-8y=9\ \ \Rightarrow\ \ -8y=-5x+9\ \ \Rightarrow\ \ \ y= (5)/(8) x-1 (1)/(8) \ \Rightarrow\ \ m_1= (5)/(8) \n\n12x-5y=7\ \Rightarrow\ \ -5y=-12x+7\ \ \Rightarrow\ \ y= (12)/(5)x-1 (2)/(5) \ \ \Rightarrow\ \ m_2= (12)/(5) \n\nm_1\cdot m_2= (5)/(8) \cdot (12)/(5)= (3)/(2) \neq -1

C.\ny=2x-7\ \ \Rightarrow\ \ m_1=2 \n\nx+2y=3\ \Rightarrow\ \ 2y=-x+3\ \ \Rightarrow\ \ y= -(1)/(2)x+1 (1)/(2)\ \ \Rightarrow\ \ m_2=- (1)/(2) \n\nm_1\cdot m_2= 2 \cdot (- (1)/(2))= -1\ \ \Rightarrow\ \ y=2x-7\ \ \ \ \perp\ \ \ \ x+2y=3

D.\nx+6y=8\ \ \Rightarrow\ \ 6y=-x+8\ \ \Rightarrow\ \ \ y=- (1)/(6) x+1 (1)/(3)\ \ \Rightarrow\ \ m_1= -(1)/(6) \n\ny=2x-8\ \Rightarrow\ \ m_2= 2 \n\nm_1\cdot m_2= -(1)/(6) \cdot2=- (1)/(3) \neq -1

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Anna, Elisa and Tiara are selling candy bars to raise money for the track team. The ratio of candy bars sold by Anna, Elisa and Tiara are 2 to 4 to 7.Elisa has sold 28 candy bars. How many candy bars do the girls sold altogether?

Answers

Number of candy bars sold by girls altogether is 91

Solution:

Given that The ratio of candy bars sold by Anna, Elisa and Tiara are 2 to 4 to 7

So ratio of candy bars sold by Anna, Elisa and Tiara = 2 : 4 : 7

Let the candy bars sold by Anna be 2a

Let the candy bars sold by Elisa be 4a

Let the candy bars sold by Tiara be 7a

Given that Elisa has sold 28 candy bars

Number of candy bars sold by Elisa = 28

4a = 28

a = 7

So we have found "a" as 7

Thus we get,

candy bars sold by Anna = 2a = 2(7) = 14

candy bars sold by Elisa = 4a = 4(7) = 28

candy bars sold by Tiara = 7a = 7(7) = 49

We have to find the number of candy bars sold by girls altogether

number of candy bars sold by girls altogether = candy bars sold by Anna + candy bars sold by Elisa + candy bars sold by Tiara

number of candy bars sold by girls altogether = 14 + 28 + 49 = 91

So altogether girls sold 91 candies

A markdown that is less than 1%

Answers

Then mark it down by less then 1%, of by whatever the number would be. 

The possible outcomes for rolling a pair of fair dice are shown.What is the probability of rolling a sum that is a multiple of two? PLEASE HELP FAST

A) 4/9
B) 1/3
C) 1/2
D) 1/4

Answers

1/4
Because......
Dice=6
From 1-6, only 2,4,6 are even numbers( or multiple of 2 )
So 3 ( numbers of even numbers ) /6
There are two dices we need to roll..
So 3/6 X 3/6
We simplify 3/6 by 2 :
1/2 X 1/2

Which equals 1/4

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Answers

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Use the Segment tool to draw a rectangle with a length of 4 units and a height of 2 units. One of the sides of the rectangle falls on line EF
, and the rectangle has a vertex of E.
 
Each segment on the grid represents 1 unit.

Answers

See attached image.

Starting from point E, count 4 units, and you reach the point F. This is the length of the rectangle.

From F, count 2 units towards the right, and you reach the point G. Draw a line. This is the height of the rectangle.

Complete the rectangle by going 4 units upward from G to H and then 2 units to the left to reach E.

EFGH is a rectangle with length = 4 units and height = 2 units with a vertex at E

Answer:

From e point count down to f  and then count 2 units to g

Step-by-step explanation:

Hope that helps

Frieda drove 20 miles in 24 minutes. At this rate how many miles did she drive in 6 minutes?

Answers

The number of miles that she drives in 6 minutes will be 5 miles.

What is speed?

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

Frieda drove 20 miles in 24 minutes. The speed is calculated as,

S = 20 / 24

S = 5/6 miles per minute

The number of miles that she drives in 6 minutes is calculated as,

D = 5/6 x 6

D = 5 miles

More about the speed link is given below.

brainly.com/question/7359669

#SPJ2
20/24 = x/6
Cross multiply
24x = 20*6
24x = 120
divide by 24
x = 5
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