Solve the equation for the given variable. Select the answer that best
describes your solution.
4(2x + 7) + 3 = 8x +31

Infinitely many solutions
No solution
One solution

the answer is 12pi

just took the quiz :)

The period of the function is 12π, the correct option is B.

The period of a function is the distance in which the graph repeats itself.

For a trigonometric function, the length of one complete cycle is called the periodic function.

For the function

y = a sin (bx + c)

Here,

a is the amplitude,

b is the period of the sine curve, and

c is the phase shift of the sine curve

The amplitude is the height of the curve.

The coefficient of b = 1, for a period of 2π

To find the period of the sine curve for any coefficient b,

Divide 2π by the coefficient of b to get the new period of the curve.

The coefficient b and the period of the sine curve have an inverse relationship,

As b gets smaller, the length of one cycle of the curve gets bigger.  Similarly, on increasing the value of b, the period will decrease.

The function is y = sin1/6x

The period of the function is,

= 2π / ( 1/6)

= 12π

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Answer:

Part a) Wayne's savings before he spent $28 was $31.08

Part b) Stef's savings after she spent $28 was $9.29

Step-by-step explanation:

Part a)

Let

x ----> original amount of Wayne's savings

y ----> original amount of Stef's savings

we know that

Original ratio

[tex]\frac{x}{y}=\frac{5}{6}[/tex]

[tex]x=\frac{5}{6}y[/tex] ----> equation A

After spending $28 each

[tex]\frac{x-28}{y-28}=\frac{1}{4}[/tex]

Multiply in cross

[tex]4x-112=y-25\\y=4x-112+25[/tex]

[tex]y=4x-87[/tex] ----> equation B

substitute equation A in equation B

[tex]y=4(\frac{5}{6}y)-87[/tex]

solve for y

[tex]\frac{20}{6}y-y=87[/tex]

[tex]\frac{7}{3}y=87[/tex]

[tex]y=37.29[/tex]

Find the value of x

[tex]x=\frac{5}{6}(37.29)=31.08[/tex]

so

The original amount of Wayne's savings was $31.08 and the original amount of Stef's savings was $37.29

therefore

Wayne's savings before he spent $28 was $31.08

Part b) Find  Stef's savings after she spent $28

Subtract $28 from the original savings

so

$37.29-$28=$9.29

therefore

Stef's savings after she spent $28 was $9.29

Answer:

AROUND 6-7 HOURS

Step-by-step explanation:

Answer:

Step-by-step explanation:

When x equals to 4

4-4 = 0

   -------------

4-6 = -2

0/-2 = 0

The rational expression X-4/x-6 equals zero when X equals 4, as long as the denominator is not zero, which avoids division by zero.

The question asks: For what value of x is the rational expression below equal to zero? The expression given is X-4/x-6. To find when this expression is equal to zero, we need to understand that a rational expression equals zero when its numerator is zero (and the denominator is not zero, to avoid division by zero).

To solve X-4 = 0, we simply add 4 to both sides of the equation, getting X = 4. This means that the rational expression is equal to zero when X equals 4, given that X is not equal to 6 to avoid making the denominator zero, which would be undefined. Hence, the value of X that satisfies the condition is 4.

Answer:points

Step-by-step explanation:

6 inches taller

Step-by-step explanation:

There’s 12 inches in a foot. So 12•6 is 72 then plus another 2 then you get 74. Then subtract 74 by 68 and you get 6

Answer:

Step-by-step explanation: since 1 foot =12 inches then we multiply 12*6=72 inches +2 inches =74 inches therefore Donato is 74 inches which is obviously bigger than 64 inches so we subtract 74-64=10

As a result ,Donato is 10 inches taller than his sister

29+x+41 = 90

x+70 = 90 ..... combine like terms

x+70-70 = 90-70 .... subtract 70 from both sides

---------------------------------------

113 - y = 90

113 - y = 90 - 113 ... subtract 113 from both sides

-y = -23

Answer:

10(7-4p)

Step-by-step explanation:

Answer:

The length of the shaded part is [tex]\frac{9}{4}[/tex]

Step-by-step explanation:

The original figure, which you may have unintentionally missed to add, is attached below.

From the figure, it is easy to figure out that:

So, the ratio of shaded parts to total parts will be: [tex]\frac{3}{4}[/tex]

In order to determine length of the shaded part, just multiply the ratio of the shaded parts to total parts by the total length of the bar.

So,

         [tex]\frac{3}{4} \times3=\frac{9}{4}[/tex]

Therefore, the length of the shaded part is [tex]\frac{9}{4}[/tex]

Keywords: ratio, length

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Answer:

see the explanation

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The fraction of the shaded part is equal to divide the number of shaded parts divided by the total number of parts

so

Let

x ----> the number of shaded parts

y ----> the total number of parts

we have

x=3, y=4

so

[tex]\frac{3}{4}[/tex]

To find out the length of the shaded part, multiply the fraction of the shaded parts by the total length of the bar

so

[tex]\frac{3}{4}(3)=\frac{9}{4}=2.25\ units[/tex]

Answer:

15 degrees

Step-by-step explanation:

It went from -6 to 0 which is 6 degrees of change then from 0 to 9 degrees which is 9 degrees of change 9+6=15

The amount of temperature that has been increased from midnight to midday is 15°C.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Midnight temperature = -6°C

Midday temperature = 9°C

The difference between the temperature.

= 9 - (-6)

= 9 + 6

= 15°C.

Thus,

The temperature is raised by 15°C.

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Answer:

17%

Step-by-step explanation:

3/17.95 = 0.167

0.167 × 100 = 16.7 *rounding to 17

12.95 × 0.17 = 3.0515

The answer is 10 because 45-9 is 36, so 46-x must be 36, which would result in 10

Answer:

y=0.7

Step-by-step explanation:

-1.2y-4.2y=-3.78

Simplify:

-5.4y=-3.78

5.4y=3.78

3.78/5.4=0.7

y=0.7

Answer:

Step-by-step explanation:

-4y + X  = 2

-4y = 2 - x

y = 2 - x/ -4

hope this helps!!

The value of y in terms of x is -1/2 + x/4.

To solve for y, we start with the equation 2(-4y + x) = 4.

Distribute the 2 inside the parentheses: -8y + 2x = 4.

Move the term with x over to the other side by subtracting 2x from both sides: -8y = 4 - 2x.

Isolate the y by dividing both sides by -8: y = (4 - 2x) / -8.

Simplify the right side by dividing both terms by -8: y = -1/2 + x/4.

Answer:

Sams club

Step-by-step explanation:

3.70/5= $.74 per can

6.30/10=$.63 per can

Final answer:

An elephant that eats about 2500 pounds of food in 10 days would eat approximately 250,000 pounds in 1000 days. You find this by dividing 2500 pounds by 10 to get a daily consumption rate and then multiply that rate by 1000 days.

Explanation:

If an elephant eats about 2500 pounds of food in 10 days, to find out how much food it eats in 1000 days, you should first calculate how much it eats per day and then multiply that number by the total number of days (1000). To find the daily food consumption, you divide the total food consumed in 10 days by the number of days:

2500 pounds ÷ 10 days = 250 pounds per day.

Now multiply the daily consumption by 1000 days to find the total amount for that period:

250 pounds per day × 1000 days = 250,000 pounds.

So the elephant would eat approximately 250,000 pounds of food in 1000 days.

Step-by-step explanation:

Given , the total price of a bag of peaches varies directly with the cost per pound. If 3 pound of peaches cost $3.60.

Therefore,

[tex]{\textrm{beg of peaches}}\propto{\textrm{cost}}[/tex]

[tex]\Leftrightarrow {\textrm{beg of peaches}}= {\textrm{k cost}}[/tex].......(1)      [ k is a constant]

cost = $3.60 when beg of peaches = 3 pounds

[tex]3 = 3.60 k[/tex]

[tex]\Leftrightarrow k = \frac{3}{3.60}[/tex]

[tex]\Leftrightarrow k = \frac{1}{1.20}[/tex]

Therefore the equation (1) becomes

[tex]{\textrm{beg of peaches}}=\frac {cost}{1.20}[/tex]

[tex]\Leftrightarrow {\textrm{beg of peaches}}\times 1.20={cost}[/tex]

When beg of peaches = 5.5 pound

[tex]cost = 5.5 \times 1.20[/tex]

[tex]\Leftrightarrow cost = 6.60[/tex]

Therefore the cost of 5.5 pound of peaches is $ 6.60.

Answer:

2 x 14 = 28

28 - 18 = 10

He needs to study for 10 hours that week or, about one and half hours per day.

Answer:

14 & 16

Step-by-step explanation:

30÷2=15

15+15=30, so we can make the conclusion...

14+16=30

Answer: $7.20

Step-by-step explanation:

20% equals 1/5 and 35.99 divided by 1/5 is 7.198 now round to the nearest tenth and you got 7.20.

Answer:

The dimensions of the largest enlargement are

[tex]8\frac{1}{2}\ in\\10\frac{1}{5}\ in[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the scale factor is the ratio of its corresponding sides

step 1

Divide 8 1/2 by 5

[tex]8\frac{1}{2}=\frac{8*2+1}{2}=\frac{17}{2}\ in[/tex]

so

[tex]\frac{17}{2}/5=1.7[/tex]

step 2

Divide 11 by 6

so

[tex]\frac{11}{6}=1.83[/tex]

step 3

Find the largest complete enlargement

The scale factor is the smaller of the two previous values

so

The scale factor is 1.7

The dimensions are

[tex]5(1.7)=8.5=8\frac{1}{2}\ in[/tex]

[tex]6(1.7)=10.2=10\frac{1}{5} \ in[/tex]

The largest complete enlargement of the original 5 in by 6 in design that can be made on an 8.5 in by 11 in paper has dimensions of 8.5 in by 10.2 in, determined by the limiting width dimension and maintaining the aspect ratio.

The question involves finding the dimensions of the largest complete enlargement of a design with an original size of 5 in. by 6 in. onto a piece of paper that is 8.5 in. by 11 in. To determine the largest complete enlargement, we must consider the scale factor that will allow the design to fit within the dimensions of the larger paper while maintaining the aspect ratio of the original design.

To maintain the aspect ratio, the scale factor for width and height must be the same. We compare the ratio of the widths and the heights of the original and target sizes to find the limiting dimension:

Since the scale factor for the width (1.7) is less than the scale factor for height, the width is the limiting factor. Thus, we can enlarge the original design by a factor of 1.7 to fit the paper. Now, we calculate the enlarged dimensions:

The largest complete enlargement of the design that can be made on an 8.5 in by 11 in paper will have dimensions of 8.5 in by 10.2 in.

Answer:

Yes!

Step-by-step explanation:

Besides 15 and one, 3 and 5 are the greatest common factors of 15. Those numbers are therefore divisible by any product of 15.

Example:

45

45/3 = 15

45/5 = 9

45/15 = 3

Answer:

Yes it is

Step-by-step explanation:

Since the multiplication of 3 and 5 will give 15

I.e 3 × 5 = 15

Then any number that can be divided by 3 and 5, can also be divided by 15.

Answer:

her weekly allowance would be 7

Step-by-step explanation:

Answer:

$24

Step-by-step explanation:

12 is 1/2 of 24.

So, when she weeds the garden, she will have $17.

If she gets her weekly allowance and the $5, she will have $41, assuming she doesn't spend any of the money she already has.

Answer:

6:35

Step-by-step explanation:

Answer: 6:35

Step-by-step explanation:

7:10 take 10 from 35 and you get down to 7:00 and then subtract 25 from 7:00 and get your answer

Answer:

8x^2+64

Step-by-step explanation:

Answer:

.712

Step-by-step explanation:

Answer:

i think the answer is 722