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2 years ago

What is the value of x in the equation 2.5 x + 10 = x- 0.5?

Mathematics

2 answers:

blsea [12.9K]2 years ago

7 0

Answer:

$=-7$

Step-by-step explanation:

$2.5x+10=x-0.5\\\mathrm{Multiply\:both\:sides\:by\:}10\\2.5x\cdot \:10+10\cdot \:10=x\cdot \:10-0.5\cdot \:10\\Refine\\25x+100=10x-5\\\mathrm{Subtract\:}100\mathrm{\:from\:both\:sides}\\25x+100-100=10x-5-100\\Simplify\\25x=10x-105\\\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}\\25x-10x=10x-105-10x\\Simplify\\15x=-105\\\mathrm{Divide\:both\:sides\:by\:}15\\\frac{15x}{15}=\frac{-105}{15}\\Simplify\\\frac{15x}{15}=\frac{-105}{15}\\\mathrm{Simplify\:}\frac{15x}{15}:\quad x\\\frac{15x}{15}$

$\mathrm{Divide\:the\:numbers:}\:\frac{15}{15}=1\\=x\\\mathrm{Simplify\:}\frac{-105}{15}:\quad -7\\\frac{-105}{15}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}\\=-\frac{105}{15}\\\mathrm{Divide\:the\:numbers:}\:\frac{105}{15}=7\\=-7$

yanalaym [24]2 years ago

6 0

Answer:

-7

Step-by-step explanation:

2.5x+10=x−0.5

Step 1: Subtract x from both sides.

2.5x+10−x=x−0.5−x

1.5x+10=−0.5

Step 2: Subtract 10 from both sides.

1.5x+10−10=−0.5−10

1.5x=−10.5

Step 3: Divide both sides by 1.5.

1.5x

1.5

−10.5

1.5

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maria [59]

Answer:

The answer is 40 degrees.

Step-by-step explanation:

Since the two triangles are congruent, which means they are the same shape and size, they share the same angle measures. Since angle B is the same as angle F, it equals 40 degrees.

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2 years ago

1. Kim works as a book keeper and creates invoices for a variety of companies. Help Kim find the total

Zanzabum

This is about calculation of invoice.

1) Total for the invoice = $2641.25

2) Total for the invoice = $30

3) Total for the invoice = $1925

1) 12 cameras for $200 each

Amount for cameras = 12 × 200 = $2400

25 cables with length of 10 ft each cost $1.25

Amount for 10 ft cables = 25 × 1.25 = $31.25

12 ft specialty cables cost $1.75 per foot

10 of these cables will have length =12 × 10 = 120 ft

Amount for 10 of these cables = 1.75 × 120 = $210

Total for the Invoice = $2400 + $31.25 + $210

Total for the invoice = $2641.25

2) 250 yards of rope costs $500.

Thus, price per yard = 500/250 = $2 per yard

For a customer that wants 15 yard;

Total for the invoice = 15 × $2 = $30

3) Dump truck is rented for $275 per hour. And the minimum is 2 hours per day. This means that anything less than 1 hour, the money paid must be money for 2 hours.

Thus;

On monday; 1 hour will cost; 2 × $275 = $550

On Tuesday; 3 hours will cost; 3 × $275 = $825

On wednesday; 2hours will cost; 2 × $275 = $550

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1 year ago

Suppose you roll a pair of honest dice. If you roll a total of 7 you win $22, if you roll a total of 11 you win $66, if you roll

JulijaS [17]

Answer:

The expected payoff for this game is -$1.22.

Step-by-step explanation:

It is given that a pair of honest dice is rolled.

Possible outcomes for a dice = 1,2,3,4,5,6

Two dices are rolled then the total number of outcomes = 6 × 6 = 36.

$\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$

The possible ways of getting a total of 7,

{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }

Number of favorable outcomes = 7

Formula for probability:

$Probability=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}$

So, the possibility of getting a total of 7 = $\frac{6}{36}=\frac{1}{6}$

The possible ways of getting a total of 11,

{(5,6), (6,5)}

So, the probability of getting a total of 11 = $\frac{2}{36}$ = $\frac{1}{18}$

Now, other possible rolls = 36 - 6 - 2 = 36 - 8 = 28,

So, the probability of getting the sum of numbers other than 7 or 11 = $\frac{28}{36}$ = $\frac{7}{9}$

Since, for the sum of 7, $ 22 will earn, for the sum of 11, $ 66 will earn while for any other total loss is $11,

Hence, the expected value for this game is

$\frac{1}{6}\times 22+\frac{1}{18}\times 66-\frac{7}{9}\times 11$

$\frac{11}{3}+\frac{11}{3}-\frac{77}{9}$

$\frac{22}{3}-\frac{77}{9}$

$\frac{66-77}{9}$

$-\frac{11}{9}$

$-1.22$

Therefore the expected payoff for this game is -$1.22.

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2 years ago

What is not a pair of equivalent fractions for 5/8 and 1/2

n200080 [17]

Two fractions equivalent to each: Just divide or multiply both top AND bottom by the same number.
5/6: 10/12 OR 15/18
15/30: 5/10 OR 1/2
45/60: 8/12 OR 4/6

Rewrite each pair or fractions with common denominator: Find the difference between the two bottom numbers, and multiply top and bottom number.

5/8 and 3/4: 4X2=8, 3X2=6. So, 5/8 and 6/8.
2/5 and 1/2: 2/5 and 2.5/5
9/9 and 5/7: 9/9 and ~5.7/9

Rewrite each in simple form: Find greatest common factor and divide.

9/54: 1/6
20/40: 1/2
100/110: 10/11

Are these fractions equivalent?
No. 5/1 and 5/5 are, because they are both 5 wholes. 1/5 is not because it is a fifth of a whole.

In what situation can you use multiplication to find equivalent fractions?
I'm sorry but I do not understand this question.
Source(s):I hope I helped, seeing as I have graduated with a math degree.

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2 years ago