Based on the graph below, what are the factors of the quadratic function?

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:

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:

-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:

-7

Step-by-step explanation:

Hope it helped!

Answer:points

Step-by-step explanation:

Answer:

.712

Step-by-step explanation:

Answer:

i think the answer is 722

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:

Find below the calculations of the two areas, each with two methods. The results are:

                     [tex]Area=5000\sqrt{3}units^2[/tex]

                     [tex]Area=14,530m^2[/tex]

Explanation:

A) Method 1

When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:

           [tex]Area=side_1\times side_2\times sin(\alpha)[/tex]

Where, [tex]\alpha[/tex] is the measure of the included angle.

1. Upper triangle:

          [tex]side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2[/tex]

2. Lower triangle:

         [tex]side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2[/tex]

B) Method 2

You can find the height of the triangle using trigonometric properties, and then use the very well known formula:

            [tex]Area=(1/2)\times base\times height[/tex]

Use it for both triangles.

3. Upper triangle:

The trigonometric ratio that you can use is:

                    [tex]sine(\alpha)=opposite\text{ }leg/hypotenuse[/tex]

Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:

         [tex]sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units[/tex]

[tex]Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2[/tex]

3. Lower triangle:

         [tex]sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2[/tex]

[tex]Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\ Area=14,529.96m^2\approx 14,530m^2[/tex]

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:

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:whole numbers

Step-by-step explanation:

Answer:

4.07 is greater

Answer:

4.07

Step-by-step explanation:

Answer:

6 gallons

Step-by-step explanation:

23.00-6.50=16.50

16.50/2.75=6

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]

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

Learn more about inequalities at:

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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:

[tex]x = -1[/tex]

Step-by-step explanation:

To do the last question using the quadratic formula, you first need the equation in standard form.

ax² + bx + c = 0.

To convert 2(x - 2)(x + 1) = x² - 4x - 5 into standard form, simplify by expanding and collecting like terms. Then, have the equation equate to "0" by moving everything to one side.

2(x - 2)(x + 1) = x² - 4x - 5        Expand brackets first using FOIL

2(x² + x - 2x - 2) = x² - 4x - 5        Collect like terms in brackets (x - 2x = -x)

2(x² - x - 2) = x² - 4x - 5        Distribute, multiply bracket numbers by "2"

2x² - 2x - 4 = x² - 4x - 5        Now make the equation equal 0

2x² - 2x - 4 - x² = x² - 4x - 5 - x²        Subtract x² from both sides

x² - 2x - 4 = -4x - 5        "x²" eliminated from the right side. Simplify left side.

x² - 2x - 4 + 4x = -4x - 5 + 4x        Add 4x to both sides.

x² + 2x - 4 = -5        "4x" eliminated from right side. Simplify left side.

x² + 2x - 4 + 5 = -5 + 5        Add 5 to both sides to eliminate it on the right.

x² + 2x + 1 = 0               Simplified left side.

This is now in standard form. State the "a", "b" and "c" values based on the standard form variables.

a = 1; b = 2; c = 1

Substitute into the quadratic formula

[tex]x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}[/tex]      (Please ignore the Â, it's a formatting error)

[tex]x = \frac{-2±\sqrt{2^{2}-4(1)(1)} }{2(1)}[/tex]   Simplify the square root

[tex]x = \frac{-2±\sqrt{0} }{2}[/tex]     The square root of 0 is 0.

[tex]x = \frac{-2}{2}[/tex]      The numerator can only be -2. Simplify the fraction

[tex]x = -1[/tex]         Only one answer for "x".

Whenever the square root equals "0", there will only be one answer for "x".

Answer:

Sams club

Step-by-step explanation:

3.70/5= $.74 per can

6.30/10=$.63 per can

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:

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: $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.

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.

Answer:

6000

Step-by-step explanation:

if you do 200+800=1000 and the if you do 4000+1000=5000+1000=6000

The inequality that represents the amount raised in the second hour of the charity auction is x ≤ 6000.

To represent the amount raised in the second hour of the charity auction, let's use the variable x. According to the information given, the amount raised in the first hour is $4800, which is at most $1200 more than the amount raised in the second hour. This can be represented as the inequality:

x ≤ 4800 + 1200

Simplifying the inequality, we have:

x ≤ 6000

Therefore, the inequality that represents the amount raised in the second hour is x ≤ 6000.

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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

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:

x=2, y=-2. (2, -2).

Step-by-step explanation:

y=x-4

y=4x-10

x-4=4x-10

x-4x-4=-10

-3x-4=-10

-3x=-10+4

-3x=-6

3x=6

x=6/3

x=2

y=2-4=-2

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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