Solve the system of linear equations bus graphing
y=1/2x+3
y= -2/3x-5
(1,3)

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.

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

Answer:

4 [tex]\frac{8}{9}[/tex]

Step-by-step explanation:

2 [tex]\frac{1}{5}[/tex] × 2 [tex]\frac{2}{9}[/tex]

[tex]\frac{11}{5}[/tex] × [tex]\frac{20}{9}[/tex] = [tex]\frac{220}{45}[/tex] = 4 [tex]\frac{8}{9}[/tex]

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:

The answer is 118

Step-by-step explanation:

In order to solve this you need to subtract this weeks, to last weeks.

361 - 243 = 118.

Hope this helps :)

Bryan unloaded 118 more crates this week than last week.

To find out how many more crates Bryan unloaded this week than last week, we can subtract the number of crates unloaded last week from the number of crates unloaded this week.

So, to find the difference, we subtract 243 from 361:

= 361 - 243

= 118

Therefore, Bryan unloaded 118 more crates this week than last week.

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Answer:

Not equivalent

Step-by-step explanation:

Let,

3(x-2) + 5 = 3x + 1

By Multiplying

3x - 6 + 5 = 3x + 1

3x - 1 = 3x + 1

So, the expressions are not equal

Answer:

Sams club

Step-by-step explanation:

3.70/5= $.74 per can

6.30/10=$.63 per can

Answer:

-7

Step-by-step explanation:

Hope it helped!

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.

Manuela works at least 22 hours in a week.

Step-by-step explanation:

Given,

Per hour salary of Manuela = $15

Amount deducted = $125

Amount received = $205

Let,

x be the number of hours per week.

Per hour salary * Number of weeks - Amount deducted ≥ Amount received

[tex]15x-125\geq 205\\15x\geq 205+125\\15x\geq 330[/tex]

Dividing both sides by 15

[tex]\frac{15x}{15}\geq \frac{330}{15}\\x\geq 22[/tex]

Manuela works at least 22 hours in a week.

Keywords: inequality, division

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2x + 3y + 4 = 15

2(1) + 3(3) + 4 = 15

2 + 9 + 4 = 15

11 + 4 = 15

15 = 15

x = 1 and y = 3

Hope this helps! ;)

Answer: The correct answer choice is D.

Step-by-step explanation: I will show all the work done for each answer choice so it is more clear.

First Answer Choice's Work:

2(6) + 3(3) + 4

12 + 9 + 4

12 + 9

21

21 + 4

25.

Second Answer Choice's Work:

2(3) + 3(5) + 4

6 + 15 + 4

21 + 4

25.

Third Answer Choice's Work:

2(6) + 3(4) + 4

12 + 12 + 4

24

24 + 4

28.

Fourth Answer Choice's Work:

2(1) + 3(3) + 4

2 + 9 + 4

11

11 + 4

15.

Therefore, the correct answer choice is D.

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

To know more about Period of a function

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Answer:

10(7-4p)

Step-by-step explanation:

Answer:

lenght= 60 inches

width = 18 inches

Step-by-step explanation:

parameter = 2(L+B)

let lenght be x

width be y

so

x = 3y+6

let's put this in formula

156 = 2( x+y )

156 = 2( 3y+6 + y )

156 = 2 ( 4y + 6 )

156/2 = 4y + 6

78 = 4y + 6

4y = 78-6

4y = 72

y = 72/4

y = 18

so width is 18 inches

and lenght is 3*18+6 = 60 inches

The width of the rectangle is 18 inches, and the length is 54 inches.

Let's denote the width of the rectangle as 'w'. According to the problem, the length of the rectangle can be expressed as 3w + 6. The problem also states that the perimeter of the rectangle is 156 inches. Remember that the formula for the perimeter of a rectangle is 2(length + width). Given that the length is expressed as 3w + 6 and the width as w, we can plug these values into the perimeter formula: 2(3w + 6 + w) = 156. Simplifying, we get 8w + 12 = 156. Isolating w, we have w = 18 inches. We also need to find the length, which is  3w + 6 = 54 inches. This gives us a width of 18 inches and a length of 54 inches.

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Answer:points

Step-by-step explanation:

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.

Answer:

The sales tax rate is 5%

Given:

Sales price = 5.00

Total amount paid = 5.25

Sales tax value = Total amount paid - sales price

                         = $5.25 - $5.00 

Sales tax value = $0.25

Sales tax rate = Sales tax / Sales price

                       = 0.25/5 

Sales tax rate  = 0.05 or 5%

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Thanks to taskmasters.

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:

6 gallons

Step-by-step explanation:

23.00-6.50=16.50

16.50/2.75=6

Answer:

314 square feet

Step-by-step explanation:

we know that

The area that will be covered by the spray of the quarter-circle sprinkler head, is equal to the area of a quarter circle with radius of 20 feet

so

The area of a quarter circle is

[tex]A=\frac{1}{4}\pi r^{2}[/tex]

we have

[tex]r=20\ ft[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]A=\frac{1}{4}(3.14)(20)^{2}=314\ ft^2[/tex]

The area covered by the quarter-circle sprinkler head to the nearest square foot is 314 square feet.

To find the area covered by the quarter-circle sprinkler head, we need to calculate the area of a quarter circle with a radius of 20 feet. The formula for the area of a circle is [tex]\( A = \pi r^2 \), where \( r \)[/tex] is the radius. Since we are dealing with a quarter circle, we will take [tex]\( \frac{1}{4} \)[/tex] of the full circle's area.

Given that the radius [tex]\( r \)[/tex] is 20 feet, the area of the full circle would be:

[tex]\[ A_{\text{full circle}} = \pi \times (20 \text{ feet})^2 \] \[ A_{\text{full circle}} = \pi \times 400 \text{ square feet} \] \[ A_{\text{full circle}} = 400\pi \text{ square feet} \][/tex]

Now, to find the area of the quarter circle, we divide the full circle's area by 4:

[tex]\[ A_{\text{quarter circle}} = \frac{1}{4} \times 400\pi \text{ square feet} \] \[ A_{\text{quarter circle}} = 100\pi \text{ square feet} \][/tex]

Using the value of [tex]\( \pi \)[/tex] as approximately 3.14159, we get:

[tex]\[ A_{\text{quarter circle}} \approx 100 \times 3.14159 \text{ square feet} \] \[ A_{\text{quarter circle}} \approx 314.159 \text{ square feet} \][/tex]

Rounding to the nearest square foot, the area covered by the quarter-circle sprinkler head is 314 square feet.

Answer:whole numbers

Step-by-step explanation:

Answer:

The needle palm tree is growing faster.

Step-by-step explanation:

The rate of growth of needle palm tree = 4.35 cm / day

The rate of growth of cabbage palm tree = 1.26 cm /day

From the given data we can clearly see ,

                 4.35  > 1.26

So the needle palm tree is growing faster.

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:

-6

Step-by-step explanation:

12, 10, 8, 6, 4, 2, 0, -2, -4, -6

Subtracting two each time

Answer:

-6

Step-by-step explanation:

It subtracts 2 each time in the sequence.

The first term is 12.

You subtract 2 ten times to get to the tenth number in this sequence. 10*2 = 20. 12-20 = -6

Answer:

4x² - 20x + 26

Step-by-step explanation:

To evaluate g(f(x)), substitute x = f(x) into g(x), that is

g(2x - 5 )

= (2x - 5)² + 1 ← expand factor using FOIL

= 4x² - 20x + 25 + 1

= 4x² - 20x + 26

Answer:

.712

Step-by-step explanation:

Answer:

i think the answer is 722

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.