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3 years ago

Line a is parallel to line b. Which statement about lines a and b is true?

Mathematics

2 answers:

GalinKa [24]3 years ago

8 0

They both have the same slope.

ivann1987 [24]3 years ago

4 0

They both have the same slope

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On a coordinate plane, triangles R S T and L M N are shown. Triangle R S T has points (5, 5), (2, 1), and (1, 3). Triangle L M N

ivolga24 [154]

Answer:

LMN has a larger area

Step-by-step explanation:

Given

RST

$R =(5,5)$

$S= (2,1)$

$T = (1,3)$

LMN

$L = (0,-1)$

$M= (2,-4)$

$N= (-2,-3)$

Required

Compare both areas

The area of triangle is:

$Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|$

For RST, we have:

$Area = \frac{1}{2}|5*1 - 2*5 + 2*3 - 1*1 + 1*5 - 5*3|$

$Area = \frac{1}{2}|-10|$

Remove absolute signs

$Area = \frac{1}{2}*10$

$Area = 10$

For LMN, we have:

$Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|$

$Area = \frac{1}{2}|0*-4-2*-1+2*-3--2*-4--2*-1-0*-3|$

$Area = \frac{1}{2}|-14|$

Remove absolute signs

$Area = \frac{1}{2}*14$

$Area = 7$

<em>By comparing both areas, we can conclude that LMN has a larger area</em>

3 0

3 years ago

Apples are sold in bags of four that cost $5, or bags of six that costs $7 per bag. What is the smallest cost at which you can b

babunello [35]

STEP 1:
BAGS OF FOUR
find number of bags needed to total 74 apples

= 74 ÷ 4 apples/bag
= 18.5 bags

*must round up to 19 bags because we cannot buy a partial bag

STEP 2:
BAGS OF FOUR
calculate price of 19 bags of 4 apples per bag

= 19 bags * $5/bag
= $95 for 19 bags of 4 apples/bag

STEP 3:
BAGS OF SIX
find number of bags needed to total 74 apples

= 74 ÷ 6 apples per bag
= 12.3333 bags needed

*must round up to 13 bags because we cannot buy a partial bag

STEP 4:
BAGS OF SIX

calculate price of 13 bags of 6 apples per bag

= 13 bags * $7 per bag
= $91 for 13 bags of 6 apples/bag

ANSWER: The smallest cost to buy 74 apples is $91.

Hope this helps! :)

3 0

3 years ago

Helpppppppppppppppppppppppppppppp

Alexxx [7]

The answer would be c

7 0

3 years ago

Read 2 more answers

1. Whats the exact value of Y?<br> 2. Whats the exact value of X?

Alexxx [7]

Answer:

Hello! The answer is in this link.

Step-by-step explanation:

8518-06-04-10-15-instructional.mp4. I hope this helps! Have a great rest of your day!

4 0

2 years ago

Bill and George go target shooting together. Both shoot at atarget at the same time. Suppose Bill hits the target withprobabilit

german

Answer: (a) $\frac{2}{9}$ (b) $\frac{6}{41}$

Step-by-step explanation:

(a) P( Bill hitting the target) = 0.7 P( Bill not hitting the target) = 0.3

P( George hitting the target) = 0.4 P(George not hitting the target) = 0.6

Now the chances that exactly one shot hit the target is = 0.7 x 0.6 + 0.4 x 0.3

= 0.54

Chances that George hit the target is = 0.4 x 0.3 = 0.12

So given that exactly one shot hit the target, probability that it was George's shot = $\frac{0.12}{0.54}$ = $\frac{2}{9}$ .

(b) The numerator in the second part would be the same as of (a) part which is 0.12.

The change in the denominator will be that now we know that the target is hit so now in denominator we include the chance of both hitting the target at same time that is 0.4 x 0.7 and the rest of the equation is same as above i.e.

Given that the target is hit,probability that George hit it = $\frac{0.4\times 0.3}{0.7\times 0.6 +0.4\times 0.3+0.4\times 0.7}$ = = $\frac{6}{41}$

6 0

3 years ago