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2 years ago

Find two consecutive even integers whors sum is 86. Which of the following could be used to solve the problem?

Mathematics

1 answer:

Yuliya22 [10]2 years ago

5 0

Answer:

42 and 44

Step-by-step explanation:

The even numbers are numbers which can be written as 2n where n is any integer number.

Therefore, two consecutive numbers would be "2n" and "2n + 2"

We then have that

2n + (2n+2) = 86

4n + 2 = 86

4n = 84

n = 21

And the even number 2n is 2(21) = 42.

(We can verify this answer by doing 42 + 44 = 86)

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A woodworking artist makes two types of carvings: type X and type Y. He

ivolga24 [154]

Answer:

part C. 3x + 2y < 30, 5x + 7y < 105

Step-by-step explanation:

Part 1:

spends 3 hours making each type X (3x)-each type x will take 3 hours so as the number of type x increases, the hours will increase by 3.

spends 2 hours making each type Y (2y)-each type y will take 2 hours so as the number of type y increases, the hours will increase by 2.

Part 2:

he can spend up to 30 hours each week making carvings. (<30)-because he cannot spend more than 30 hours

Therefore, He has to spend 30 hours or less to make type X and type Y.

3x + 2y < 30

Part 3:

His materials cost him $5 for each type X carving. (5x)-each type x will take $5 so as the number of type x increases, the cost will increase by 5.

His materials cost him $7 for each type Y carving, (7y)-each type y will take $7 so as the number of type y increases, the cost will increase by 7.

Part 4:

he must keep his weekly cost for materials to $105 or less (<105)-total cost cannot be more than $105.

Therefore, the total cost of making x and y should be $105 or less.

5x + 7y < 105

6 0

2 years ago

at a local restaurant the health inspector visits every 7 Days and the fire inspector visits every 12 days make a table for the

seraphim [82]

Day Inspector

7 H

12 F

14 H

21 H

24 F

28 H

35 H

36 F

42 H

48 F

49 H

56 H

60 F

63 H

70 H

72 F

77 H

84 H, F

6 0

2 years ago

find x if the distance between points L and M is 15 and point M is located in the first quadrant. L=(-6,2) M=(x,2)

aivan3 [116]

Answer:

Therefore,

$x = 9$

Step-by-step explanation:

Given:

Let,

point L( x₁ , y₁) ≡ ( -6 , 2)

point M( x₂ , y₂ )≡ (x , 2)

l(AB) = 15 units (distance between points L and M)

To Find:

x = ?

Solution:

Distance formula between Two points is given as

$l(LM)^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$

Substituting the values we get

$15^{2}=(x--6)^{2}+(2-2)^{2}\\\\225=(x+6)^{2}$

Square Rooting we get

$(x+6)=\pm \sqrt{225}=\pm 15\\\\x+6 = 15\ or\ x+6 = -15\\\\x= 9\ or\ x = -21$

As point M is located in the first quadrant

x coordinate and y coordinate are positive

So x = -21 DISCARDED

Hence,

$x = 9$

Therefore,

$x = 9$

3 0

3 years ago

Nicole has 17 nickels n and dimes d. If the value of her coins is $1.30, how many of each coin does she have?

denis-greek [22]

Answer:

8 nickels and 9 dimes

Step-by-step explanation:

If all were dimes, the value would be $1.70. It is $0.40 less than that. Changing a dime for a nickel reduces the value by $0.05, so there must have been $0.40/$0.05 = 8 such changes.

There are 8 nickels and 9 dimes.

_____

Check

8 · 0.05 + 9 · 0.10 = 0.40 + 0.90 = 1.30 . . . the answer checks OK

7 0

3 years ago

Please find the question

melisa1 [442]

Answer:

By distance formula ,

AB² = (5+1)² + (3-6)²

AB² = 36 + 9

AB = 6.71 units

6 0

3 years ago