A rectangles length is 6 units greater than its width. Which type of polynomial function would be most appropriate for modeling the area of the rectangle?

Answer:

2

Step-by-step explanation:

The constant of proportionality In the equation y=2x is 2.  For every unit by which x increases, y increases twice as much.

The constant of proportionality In the equation y=2x is 2.

Given that,

Based on the above information, the information is as follows:

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Answer:

Step-by-step explanation:

Six times a number is greater than 2 less than 4 times the same number.​

n - the number

six times a number: 6n

is greater than: >

2 less than 4 times the same number: 4n - 2

6n > 4n - 2             subtract 4n from both sides

6n - 4n > 4n - 4n - 2

2n > -2         divide both sides by 2

2n : 2 > - 2 : 2

n > -1

Answer:

64 : 343

Step-by-step explanation:

First use the radii to find the volume

1) Radius of first sphere is 4 (taken from 4:7 ratio)

   Insert it into the equation for volume of a sphere: V=4 /3πr^3

   V = (4/3)(π)(4^3)

   V = (4/3)(π)(64)

   V = 256/3 π

   Volume of the first sphere = 256/3 π

2) Radius of the second sphere is 7 (also taken from 4:7 ratio)

   Insert it into the equation for volume of a sphere: V=4 /3πr^3

   V = (4/3)(π)(7^3)

   V = (4/3)(π)(343)

   V = 1372/3 π

   Volume of the second sphere = 1372/3 π

Next, calculate the ratio by dividing the two numbers

256/3 π ÷ 1372/3 π

Answer should be 64 : 343

The simple way to do this problem is to just cube the numbers:  

4:7 becomes 4^3 : 7^3 = 64 : 343

Either way works.

Answer:

x = 8

3rd choice

Step-by-step explanation:

8x - 18 + 5x + 4 = 90

13x - 14 = 90

13x = 104

x = 8

https://mathbitsnotebook.com/Geometry/Trigonometry/TGTrigSineCosine.html

Answer:

a) [tex]A=224.55\ ft^2[/tex]

b) [tex]P = 58.85\ ft[/tex]

Step-by-step explanation:

a) The area of a rectangle is calculated as the product of its length by its width.

[tex]A = lw[/tex]

Then the area of the rectangular room is:

[tex]A = 14 * 12\\\\A = 168\ ft ^ 2[/tex]

The area of a semicircle is[tex]A = \frac{1}{2}\pi r ^ 2[/tex]

We know that the diameter is 12 feet, then the radius is:

[tex]r = \frac{12}{2} = 6\\\\r = 6\ ft[/tex]

[tex]A = \frac{1}{2}\pi(6) ^ 2\\\\A = 56. 55 ft ^ 2[/tex]

Finally, the total area is:

[tex]A=56. 55\ ft ^ 2+168\ ft ^ 2[/tex]

[tex]A=224.55\ ft^2[/tex]

b) The perimeter of a rectangle is:

[tex]P = 2l + 2w[/tex]

The perimeter of a semi-circle is:

[tex]P = 0.5 * 2\pi r[/tex]

In this case r = 6

Since the semi-circle is attached to one of the sides of the room and its diameter is 12 feet, you cannot add one of the sides of rectangle that measures 12 feet to the perimeter (Observe the figure attached, which is not drawn to scale).Then the perimeter is:

[tex]P = (12 + 2 * 14)+(0.5 * 2\pi (6))\\\\P = 58.85\ ft[/tex]

Answer:

6 book for $32.16

Step-by-step explanation:

Divide 21.80 by 4 and you will get 5.45

5.45 is the price for each book

Divide 32.16 by 6 and you will get 5.36

5.36 is the price for each book

Answer:

The answer would be the 6 books

Step-by-step explanation:

If you do 21.80 divied by 4 you get 5.45.If you go the same with the 6 books and the number of money you get 5.36.

Answer:

238

Step-by-step explanation:

let the number of marbles Sam has be x, then

Jim has x + 92 ← 92 more than Sam

After swap of 18 marbles

Sam has x - 18 and sam has x + 92 + 18 = x + 110

Jim now has twice as many as Sam, that is

x + 110 = 2(x - 18)

x + 110 = 2x - 36 ( subtract x from both sides )

110 = x - 36 ( add 36 to both sides )

146 = x

At first Jim had 146 + 92 = 238 marbles

Answer is 27.5

= 92+18

=110 divided by 2

=55

Haha this is wrong

Answer:

[tex]m=\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

we know that

The tangent of angle theta is equal to divide the opposite side angle theta by the adjacent side angle theta

[tex]tan(\theta)=\frac{m}{(1/2)}=2m[/tex]

[tex]tan(\theta)=\sqrt{3}[/tex]

so

[tex]2m=\sqrt{3}[/tex]

[tex]m=\frac{\sqrt{3}}{2}[/tex]

Answer:

9.3 feet

Step-by-step explanation:

See attachment for the picture.

Let f represent how high up the bird is in the tree.

This side length of the right triangle is opposite the given angle which is 25 degrees.

The side length adjacent to the given angle is 20 ft.

We use the tangent ratio to obtain:

[tex]\tan 25\degree=\frac{opposite}{adjacent}[/tex]

We substitute the values to obtain:

[tex]\tan 25\degree=\frac{f}{20}[/tex]

[tex]f=20\tan 25\degree[/tex]

f=9.3 ft

Therefore the bird is 9.3 feet high up in the tree.

choice B is the correct answer

Answer: the second option is correct

Step-by-step explanation:

Answer:

Anna needs 12 cups.

Anna needs twice as many cups of milk as pints, so for 6 pints she needs 12 cups of milk.

The student is asking how many cups of milk are needed if Anna needs 6 pints to make yogurt. To answer this, we need to use the conversion that 1 pint is equal to 2 cups. Therefore, if Anna needs 6 pints of milk, we calculate the number of cups needed by multiplying 6 by 2.

Step-by-step conversion

Understand the conversion ratio: 1 pint = 2 cups.

Multiply the number of pints Anna needs by the conversion ratio: 6 pints × 2 cups/pint.

Calculate the total number of cups: 12 cups of milk.

So, Anna will need 12 cups of milk to make her yogurt.

Answer:

222 ft/sec

Step-by-step explanation:

Essentially you're being asked to find the unit speed (that is, distance per sec).

1000 ft

------------ = 222 feet/sec is the approx. average speed / unit speed

4.5 sec

Answer:

Final answer in standard form of the line is [tex]4x+y=5[/tex].

Step-by-step explanation:

Given that slope of the lime m = -4

Now we need to find the equation of a line that has a slope of -4 and passes through the point (0,5). Write the equation of this line in standard form.

So plug the given slope m=-4 and the point (0,5) into point slope formula:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-5=-4\left(x-0\right)[/tex]

[tex]y-5=-4\left(x\right)[/tex]

[tex]y-5=-4x[/tex]

[tex]y=-4x+5[/tex]

[tex]4x+y=5[/tex]

Hence final answer in standard form of the line is [tex]4x+y=5[/tex].

Answer:

The equation of this line in standard form is

[tex]4x + y = 5[/tex]

Step-by-step explanation:

To find the equation of a line we need to know two points by which the line passes. You can also find the equation if you know a point through which the line passes and its slope.

For the equation of the line:

[tex]y = mx + b[/tex]

m is the slope and b is the section.

Sane that

[tex]m = -4[/tex]

To find b we substitute the point (0,5) in the equation and solve for b[tex](5) = -4 (0) + b[/tex]

[tex]b = 5[/tex]

The equation is

[tex]y = -4x +5.[/tex]

We rewrite the equation as:

4x + y = 5

87.96+30x<200

Subtract 87.96 from both sides

30x= 112.04

X=3.73

She can buy 3 t shirts

Answer:

3 shirts

Step-by-step explanation:

1. Subtract the cost of tickets (87.96) from the total (200)

    200-87.96 = 112.07

2. Divide 112.07 by the cost per shirt (30)

    112.07 / 30 = 3.74

Since you cannot purchase part of a shirt - she can buy 3 shirts.

Answer:

C. 30 / 6 =5

hope this helps

Answer: Option C

Step-by-step explanation:

 You know that when you multiply 5 and 6, the product is 30:

[tex]5*6=30[/tex]

Let's check all the options:

Option A shows us that [tex]30*6=5[/tex], this is not true, because:

[tex]30*6=180[/tex]

 Option B shows us that [tex]5\div6=30[/tex], this is not true, because:

[tex]5\div6=0.833[/tex]

Option C shows us that [tex]30\div6=5[/tex], this is true.

Option D shows us that [tex]30*5=6[/tex], this is not true, because:

[tex]30*5=150[/tex]

Therefore, the option that shows one one way to check the answer to  [tex]5*6=30[/tex] is the Option C.

ANSWER

$1,413.81

EXPLANATION

The compound interest formula is given by:

[tex]A=P(1+r\%)^t[/tex]

Where P=900 is the balance in the account, t=10 is the number of years and r=0.0462 is the rate.

We substitute the values in to the formula to get:

[tex]A=900(1+4.62\%)^{10} [/tex]

[tex]A=900(1.0462)^{10} [/tex]

This simplifies to:

[tex]A=1413.81[/tex]

Therefore $1413.81 will be in the account after 10 years.

Answer:

Correct choice is $1413.81.

Step-by-step explanation:

Initial amount P = $900

Rate of interest = r = 4.62% = 0.0462

Number of compounding periods per year n = 1 {Compounded annually}

Time = 10 years

Then balance that is future value after 10 years in the account is given by formula :

[tex]A=P\left(1+\frac{r}{n}\right)^{\left(n\right)\left(t\right)}[/tex]

[tex]A=900\left(1+\frac{0.0462}{1}\right)^{\left(1\right)\left(10\right)}[/tex]

[tex]A=900\left(1+0.0462\right)^{\left(10\right)}[/tex]

[tex]A=900\left(1.0462\right)^{\left(10\right)}[/tex]

[tex]A=900\left(1.57089499829\right)[/tex]

[tex]A=1413.80549846[/tex]

Hence correct choice is $1413.81.

The variable x represents the total number of days in the total fees equation of “pay upfront” y = 33 + 8x, and “drive now pay later” Y = 18 + 11x.

In other terms, an equation is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given:

The “pay upfront” car rental company charges an insurance and gas fee of $33,

Daily rental fee = $8 per day,

The “drive now pay later” car rental company charges an insurance and gas fee of $18,

Daily rental fee = $11 per day,

Write the equation for the total fees by “pay upfront” as shown below,

y = 33 + 8x

Here, y is the total fees and x is the number of days,

Write the equation for the total fees by “drive now pay later” as shown below,

Y = 18 + 11x

Here, Y is the total fees and x is the number of days,

Thus, x represents the number of days.

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Final answer:

The variable x represents the number of days a car is rented at two different car rental companies. Calculations can be made to compare total costs based on this variable, determining which company offers the better deal for a given rental period.

Explanation:

Comparing Car Rental Company Costs

The question asks us to interpret the role of the variable x in the context of comparing costs between two different car rental companies, one with the option to pay upfront and the other with the option to drive now pay later. The "pay upfront" company charges a flat fee for insurance and gas at $33, with an additional daily rental fee of $8. On the other hand, the "drive now pay later" company has a lower initial fee for insurance and gas at $18, but a higher daily rental fee of $11. The variable x represents the number of days the car is rented.

To determine which option is more cost-effective, one can set up equations for each company's rental costs in terms of x (the number of days) and compare the total costs. For the "pay upfront" company, the cost equation is C = $33 + $8x. For the "drive now pay later" company, it is C = $18 + $11x. By analyzing these equations, one can determine the breakeven point or compare costs for a specific rental period.

Answer:

Answer C is correct.

Step-by-step explanation:

f(x) clearly has a maximum:  y = +10 at x = 0.

Analyzing g(x) = -(x + 1)^2 - 10, we see that the vertex is at (-1, -10), and that the graph opens down.  Thus, -10 is the maximum value; it occurs at x = -1.

Answer A is false.  Both functions have max values.

Answer B is false.  One max is y = 10 and the other is y = -10.

Answer C is correct.  The max value of f(x), which is 10, is greater than the max value of g(x), which is -10.

Answer D is false.  See Answer B, above.

The top is 1 unit.

The bottom is 9 units.

Use the distance formula to find the length of the side.

Give the end points coordinates

(2,2) and (6,5)

Length = √((6-2)^2 +(5-2)^2) = 5 units.

The total perimeter is the top + the bottom + 2 sides.

Perimeter = 1 + 9 + 5 + 5 = 20 units.

The perimeter of a figure is the distance around the figure.

To find the perimeter of the trapezoid shown, we can simply add all the sides. Since there are no numbers we can count each block as 1 unit.

Let's identify our values:

Top of trapezoid = 1 unit

Bottom of trapezoid = 9 units

Left and right side of trapezoid = 10 units "added together"

Now, we can add these numbers up and we will get the perimeter of the figure.

1 + 9 + 10 = 20

Therefore, the perimeter of the trapezoid is 20 units.

Answer:

A = 11, B = 25/3, C = -1

Step-by-step explanation:

A linear function has the form:

f(x) = ax + b

(1)

f(3) = 8a + b = 8

f(5) = 5a + b = 9

Using the last 2 equations we can solve for 'a' and 'b'.

8a + b = 8 | 5a + b = 9

We multiply the second one by -1:

8a + b = 8 | -5a -b = -9

And then we add them together:

3a = -1

a = [tex]\frac{-1}{3}[/tex]

We then solve for 'b':

5a + b = 9

5(-1/3) + b = 9

b = 9 + 5/3

b = 32/3 = [tex]11\frac{1}{3}[/tex].

We then use this to find A, B, C.

f(x) = (-1/3)x + 32/3

(2)

f(A) = -A/3 + 32/3 = 7

[tex]\frac{-A}{3} + \frac{32}{3} = 7\\A - 32 = -21\\A = 11[/tex]

(3)

f(7) = -7/3 + 32/3 = B

25/3 = B

(4)

f(C) = -C/3 + 32/3 = 11

[tex]\frac{-C}{3} + \frac{32}{3} = 11\\C - 32 = -33\\C = -1[/tex]

(15 games) is the minimum number of games the team must have played

Answer:

5

Step-by-step explanation:

We are given that a soccer team has played  = 25 games

The team won the games =60% of games that has played

We have to find the minimum number of additional games the team must win in order to finish the season winning 80% of the games it has played.

60% of the games=[tex]\frac{60}{100}\times 25=15[/tex]

A soccer team won games that has played =15

if the team won 80% of the games

Then,80% of 25= [tex] \frac{80}{100}\times 25=20[/tex] games

Number of games added to win 80% of the games =20-15=5

Hence, the minimum number of additional games that the team must win 80 % of the games it has played=5

The triangular prism with a side of 16.8 cm and a height of 20.4 cm will be similar to the triangular prism with a side of 8.4 cm and a height of 10.2 cm.

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

As we know for similar figures, the ratio of their corresponding sides is in ratio, therefore, if multiply the dimension of the given prism by 2, we will get the similar triangular prism that we need.

[tex]\text{Side of the triangle} = 8.4\rm\ cm \times 2 = 16.8\ cm[/tex]

[tex]\text{Height of the prism} = 10.2\rm\ cm \times 2 = 20.4\ cm[/tex]

Thus, the triangular prism with a side of 16.8 cm and a height of 20.4 cm will be similar to the triangular prism with a side of 8.4 cm and a height of 10.2 cm.

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Answer:

Step-by-step explanation:

x: 2    5     8

y: 2 0.8 0.5

Simply by looking at what happens to y as x increases, we can see that y decreases, and that we therefore have inverse variation.

The appropriate model is y = k/x.

If x = 5, y = 0.8, and so     0.8 = k/5

Solving for the constant of proportionality, we get 4 = k.

Then y = 4/x models this data.

The data in the table reflect an inverse variation, characteristic of the y-values decreasing as x-values increase. The constant of variation k is 4, yielding the model equation of the data as y = 4/x.

The data in the table appears to represent an inverse variation rather than a direct one. This is because as the x-values are increasing, the y-values are decreasing. This is indicative of an inverse relationship between the two variables.

To model the inverse variation, recall the general form of the equation for inverse variation which is y = k/x, where k is the constant of variation. We derive the value of k by multiplying the corresponding x and y values. For instance, 2(2)=4.

Assuming the constant stays the same across the data, we can test the other pairs. Indeed, for x=5, y=0.8, we have 5*0.8=4 and for x=8, y=0.5, we also have 8*0.5=4.

Hence, k=4 and, therefore, the model equation for this data is y = 4/x.

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Answer:

She omitted the y- intercept

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept)

To calculate m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 7.5) and (x₂, y₂ ) = (2, - 5)

m = [tex]\frac{-5+7.5}{2+3}[/tex] = [tex]\frac{2.5}{5}[/tex] = 0.5, thus

y = 0.5x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, - 5), then

- 5 = 1 + c ⇒ c = - 5- 1 = - 6

y = 0.5x - 6 ← equation if line

You forgot to DISTRIBUTE THE NEGATIVE, giving you this: -8 + 11x = -x - 8; 0⃣ = x.

Answer:

Step-by-step explanation:

From 6:05 to 7:00 there are 55 minutes.

From 7:00 to 9:00 there are two hours.

From 9:00 to 9:17 there are 17 minutes.

Therefore we have

2h + 55min + 17min = 2h + 72min = 2h + 60min + 12min = 2h + 1h + 12min

= 3h + 12min = 3h + 12/60h = 3h + 1/5h = 3h + 0.2h = 3.2h

1h = 60min → 1min = 1/60h

well, let's take a peek, "m" is drawn on the x-axis most likely and H(m) is drawn on the y-axis, making a straight line.

so at m = -5, namely 5 minutes before he was told to go home, the kite was 375 meters up.

then he was told to go home, when m = 0, and the kite was 300 meters up.

now, as far as the other numbers, m = 5, 5 minutes after he was told, the kite was 225 m up, then 10 minutes later, then 15 minutes later then 20 minutes later m = 20, the kite was at 0, namely on the ground, he already had rolled up all the kite string that he was coiling up, so he can pack it in his carriage bag and go home.

Answer:

144°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 10, hence

sum = 180° × 8 = 1440°, thus

each angle measure = 1440° ÷ 10 = 144°

Answer:

1470 students do not have a full-time or part-time job

Step-by-step explanation:

We have a relationship between students who have a part-time job and those who do not. The ratio is 7 out of 10 students.

Then we use this relationship as a conversion factor.

If of 10 students, 7 of them have a job, then of 4900 students, how many of them have a job?

[tex]4900 * \frac{7}{10}=3430[/tex] students

Finally, those who do not have a job are:

[tex]4900- 3430 = 1470[/tex]

Answer:

[tex](x-6)^{2}+(y+16)^{2}=6,400[/tex]

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

In this problem we have

The center of the radio tower (position) is the point [tex](6,-16)[/tex]

The radius of the radio tower (range) is [tex]r=80\ miles[/tex]

substitute

[tex](x-6)^{2}+(y+16)^{2}=80^{2}[/tex]

[tex](x-6)^{2}+(y+16)^{2}=6,400[/tex]

The standard equation for the radio tower's signal range is (x - 6)² + (y + 16)² = 6400, representing a circle with a center at (6, -16) and a radius of 80 miles.

The student is asking for the equation of a circle that represents a radio tower's signal range on a coordinate grid. Since the radio tower is centered at (6, -16) and has a range of 80 miles, the equation of the circle can be written using the standard form of a circle's equation, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Substituting the given values, the equation becomes (x - 6)² + (y + 16)² = 80².