What are three consecutive integers whoose sum of 138? Write and solve an equation with one variable.

Answers

Answer 1

Answer: Consecutive integers are 1 more than the other.

If one of them is x.

The three would be x, x + 1, x + 2

Since the sum are 138

x + (x + 1) + (x +2) = 138

x + x + 1 + x +2 = 138

x + x + x + 1 + 2 = 138

3x + 3 = 138

3x = 138 - 3

3x = 135

x = 135/3

x = 47.

So the numbers are, x, x + 1, x + 2, = 47, 47 + 1 = 48, 47 + 2 = 49

The integers are 47, 48, and 49.

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Henry rolls 2 number cubes numbered 1 through 6 while playing his favorite board game. He will get a second turn if he rolls a sum that is an even number less than 10. What are Henry's chances of getting a second turn when he rolls the number cubes? 7/18 11/18 5/36 17/36 I got 5/18. I added up the amount of different ways to get 2-8. I found 10. Either the test is wrong or I'm really bad at counting, and I'm not confident enough to count either of them out.

Answers

Answer: $(7)/(18)$

Step-by-step explanation:

The sample size n ( total pairs )= $6*6=$ 36

Pairs having the even sum less than 10 area

(1,3), (3,1), (1,5), (5,1),(3,5),(5,3),

(2,4), (4,2), (2,6),(6,2),

(1,1),(3,3),(2,2),(4,4)

The number of ways to get a sum that is an even number less than 10= 14

The chances of getting a second turn when he rolls the number cubes= $=\frac{\text{favourable outcomes}}{\text{Total outcomes}}(14)/(36)=(7)/(18)$

Hence, The chances of getting a second turn when he rolls the number cubes= $(7)/(18)$

First of all, we know that each cube can land in 6 different ways,
so two cubes can land in (6x 6) = 36 different ways.

Now let's check your count. How many ways can you roll a 2, 4, 6, or 8 ?

Cube-A Cube-B
1 1 2
1    3 4
3    1 4
2    2 4
1    5     6
      5    1 6
      2    4 6
      4    2 6
      3 3 6
      2    6 8
      6    2       8
3 5 8
    5 3 8
4    4    8

I get 14 ways.

So the probability of success is

   (number of successful ways) / (total possible ways) =

   (14) / (36) = 7/18 .

Prove that if AC=DF and AB=DE then BC=EF

Answers

in triangle ABC and DEF
AC =DF, [ given ]
AB =DE, [ given ]
angle A = angle D
by SAS
ABC congruent to triangle DFE
so
BC = EF, [ CPCTC]
hence proved

Jesse drives to work. The distance Jesse’s car travels (d) on a number of gallons of gas (g) is given by the equation d = 15g. The constant of proportionality in terms of distance traveled per gallon of gas is?

Answers

I can only half answer this question, as it doesn't tell what form of distance is used

the equation is...

d=15g

Now lets solve for 1 gallon of gas

d=15g
d=15(1)
d=15

This means that for every 1 gallon of gas, 15 (insert missing unit of distance here) can be driven.

15/1=15

Answer:The constant of proportionality is 15.

3. Please help. Are lines ℓ and k parallel? Justify your response.

Answers

Answer:

No, lines ℓ and k are not parallell because their slopes are not equal

No lines L and K are not parallel because they’re slope isn’t the same

Which is the opposite of -12?

Answers

Answer: The opposite of -12 would be 12. You simply just turn the negative number, into a positive. Hope this helped you.

Step-by-step explanation:

Is sec (11 pi/6) equal to (2 sqrt 3/3)?

Answers

$sec (11 \pi )/(6)= (1)/(cos (11 \pi )/(6) )$
Than: $cos (11 \pi )/(6)= ( √(3) )/(2)$
$(1)/( ( √(3) )/(2) ) = (2)/( √(3) ) = (2 √(3) )/(3)$
Answer:Yes, it is equal.

Yeap. sec (11pi/6) = 1/cos(11pi/6), verifying by calculator, you will get 1.1547, which is the value of 2 sqrt3/3

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