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2 years ago

10q - 30 is equivalent to _____. 3(q - 10) 10(q - 30) 10(q - 3)

Mathematics

2 answers:

shutvik [7]2 years ago

8 0

10q - 30 = 10 · q - 10 · 3 = 10(q - 3)

liubo4ka [24]2 years ago

5 0

Answer:

$10(q-3)$

Last option is correct.

Step-by-step explanation:

We have been given the expression $10q-30$

The greatest common factor or GCF of the given expression is 10.

Hence, we factored out 10. When we factored out 10, we have to divide all the terms by 10.

$10(\frac{10q}{10}-\frac{30}{10})$

On simplifying, we get

$10(q-3)$

Therefore, the expression $10q-30$ is equivalent to $10(q-3)$

Last option is correct.

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Dev has 9 shells. Zoe has 55 shells, Zoe gives some shells to Dev. Now zoe has 3 times as many shells as dev. How many shells do

Goryan [66]

Answer:

number of shells zoe gives to dev = 7

number of shells zoe is left with = 55-7= 48

number of shells dev has = 9+7=16

Step-by-step explanation:

let the initial number of shells that dev has be A, and initial number of shells that zoe has be B.

let the number of shells that zoe gives to dev be x.

after giiving x shells zoe is left with 3 times the number of shell as that of dev.

therefore number of shells with zoe = 3×number of shells with dev.

number of shells with zoe = initial shells - x = 55-x

number of shells with dev = initial shells + number of shells he gets

= 9+x

therefore (55-x)=3×(9+x)

55-x = 27+3x

55-27=3x+x

4x = 28

x= 7

therefore number of shells zoe gives to dev = 7

number of shells zoe is left with = 55-7= 48

number of shells dev has = 9+7=16

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1 year ago

A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to th

solmaris [256]

Answer:

Total number of riders that ride on carpool daily = 2000

Total Cost of one way ticket = $ 5.00

Total Amount earned if 2000 passengers rides daily on carpool = 2000 × 5

= $10,000

If fare increases by $ 1.00

New fare = $5 + $1

= $6

Number of passengers riding on carpool = 2,000 - 100 = 1,900

If 1,900 passengers rides on carpool daily , total amount earned ,if cost of each ticket is $ 6 = 1900 × $6 = $11400

As we have to find the inequality which represents the values of x that would allow the carpool service to have revenue of at least $12,000.

For $ 1 increase in fare = (2,000 - 1 × 100) passengers

For $ x increase in fare, number of passengers = 2,000 - 100·x

= (2,000 - 100·x) passengers

New fare = 5 + x

New Fare × Final Number of passengers ≥ 12,000

(5+x)·(2,000 - 100 x) ≥ 12,000

5 (2,000 - 100 x) + x(2,000 - 100 x) ≥ 12,000

10,000 - 500 x + 2,000 x - 100 x² ≥ 12,000

100 - 5 x + 20 x - x² ≥ 120

- x² + 15 x +100 - 120 ≥ 0

-x² + 15 x -20 ≥ 0

x² - 15 x + 20 ≤ 0

⇒ x = 1.495

x ≥ $ 1.495, that is if we increase the fare by this amount or more than this the revenue will be at least 12,000 or more .

Also, f'(x) = 0 gives x = 7.5

⇒ The price of a one-way ticket that will maximize revenue is $7.50

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1 year ago

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achi

lubasha [3.4K]

Answer:

Shift 2 unit left

Flip the graph about y-axis

Stretch horizontally by factor 2

Shift vertically up by 2 units

Step-by-step explanation:

Given:

Parent function: $f(x)=\log x$

Transformation function: $f(x)=\log(-2x-4)+2$

Take -2 common from transform function f(x)

$f(x)=\log[-2(x+2)]+2$

Now we see the step-by-step translation

$f(x)=\log x$

Shift 2 unit left ( x → x+2 )

$f(x)=\log(x+2)$

Flip the graph about y-axis ( (x+2) → - (x+2) )

$f(x)=\log[-(x+2)]$

Stretch horizontally by factor 2 [ -x(x+2) → -2(x+2) ]

$f(x)=\log[-2(x+2)]$

Shift vertically up by 2 units [ f(x) → f(x) + 2 ]

$f(x)=\log[-2(x+2)]+2$

Simplify the function:

$f(x)=\log(-2x-4)+2$

Hence, Using four step of transformation to get new function $f(x)=\log(-2x-4)+2$

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If the measure of angle 5 equals 102 degrees, then the measure of angle 8 equals what?

kiruha [24]

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1 year ago

We flip a fair coin five times. For every heads you pay me $1 and for every tails I pay you $1. Let X denote the my net winning

TEA [102]

Answer:

The probability mass of X is 0.03

Step-by-step explanation:

If we set the winning requirement of your heads and my tails then the occurring possibility of both is 1/2 or 0.5.

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Where X represents the number of dollars won during the flip of the coin, probability of heads represent the chances of occurrence of the value and of winning the dollars.

The probability of winning start to drop as the winning amount increases.

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1 year ago