The ratio of students who walk home from school to the students who ride the bus home is 2 : 7. The number of bus riders is how many times the number of students who walk home?

Final answer:

The quadratic expression 3x^2-48 can be completely factored as 3(x-4)(x+4) by first factoring out the common factor and then utilizing the difference of squares.

Explanation:

To factor this expression completely, we first need to look for common factors and any patterns that might help simplify the expression. Both terms in the expression 3x2−48 have a common factor of 3. Factoring out this common factor gives us:

Notice that the expression inside the parenthesis, x2 − 16, is a difference of squares, which can be factored further into (x − 4)(x + 4). Therefore, the fully factored form of the original expression is:

This shows how identifying common factors and utilizing the difference of squares helps in completely factoring the given expression.

Answer:

OPTION B

Step-by-step explanation:

To solve, create a formula.

y= 5(copay)+premium

Using this you get:

Option A: 5(20)+55= $155

Option B: 5(15)+60= $135

Option C: 5(25)+65= $190

Option D: 5(30)+50= $200

Answer:

Option B

Step-by-step explanation:

Option A : 55 + 20(5) = 155

Option B : 60 + 15(5) = 135

Option C : 65 + 25(5) = 190

Option D : 50 + 30(5) = 200

Answer:

The center is (0,0) and the radius is 5

Step-by-step explanation:

To find the center of a circle, you need to look at the equation

In this case this equation could be written as

[tex](x-0)^2+(y-0)^2=5^2[/tex]

The x value is x=0 for the center and the y values is y=0

The radius can be found by looking at the constant that is squared, so r=5

In the case of an equation like this

[tex](x-1)^2+(y+1)^2=3^2[/tex]

The center point would be (1,-1) and r=3

Answer:

61-25=n

Step-by-step explanation:

Answer:

a food container and a bowl

Answer:

  A|  12, 3

Step-by-step explanation:

The polynomial can be factored by looking for factors of 36 that sum to -15. The sum being negative while the product is positive means both factors will be negative. The answer choices suggest ...

  y = (x -12)(x -3)

A quick check shows this product is ...

  y = x^2 -12x -3x +36 = x^2 -15x +36 . . . . as required

The factors are zero when x is either 12 or 3.

The zeros of the equation are 12 and 3.

____

Once you realize the constants in the binomial factors both have a negative sign, you can immediately choose the correct answer (A).

Or, you can use Descartes' rule of signs, which tells you that the two sign changes in the coefficients (+-+) mean there are 2 positive real roots.

Answer:

the numbers are 12, 31

Step-by-step explanation:

Calculate the total wall and ceiling area, then determine the number of gallons of paint needed using the given coverage per gallon.

To calculate the total wall and ceiling area:

Calculate the total wall area: (2 x 12 x 7) + (2 x 15 x 7) = 168 + 210 = 378 square feet.

Add the ceiling area: 12 x 15 = 180 square feet.

Sum the wall and ceiling areas: 378 + 180 = 558 square feet.

To determine how many gallons of paint:

Divide the total area by the coverage of one gallon: 558 ÷ 250 = 2.232 gallons (round up to ensure enough paint).

You would need approximately 2.232 gallons of paint to paint the walls and ceiling of the bedroom.

To find the total area that needs to be painted, we first calculate the area of the walls and the ceiling.

1. Area of the walls:

The bedroom has four walls, two of which are 12 feet by 7 feet and the other two are 15 feet by 7 feet.

Total area of the walls = 2(12 * 7) + 2(15 * 7) = 2(84) + 2(105) = 168 + 210 = 378 square feet

2. Area of the ceiling:

The ceiling is the same size as the floor, which is 12 feet by 15 feet.

Area of the ceiling = 12 * 15 = 180 square feet

3. Total area to be painted:

Total area = Area of walls + Area of ceiling = 378 + 180 = 558 square feet

4. Gallons of paint needed:

Since one gallon of paint covers 250 square feet, we divide the total area by the coverage of one gallon:

Gallons needed = Total area / Coverage per gallon = 558 / 250 ≈ 2.232 gallons

Therefore, you would need approximately 2.232 gallons of paint to paint the walls and ceiling of the bedroom.

Answer: second option.

Step-by-step explanation:

The formula used for calculate the lateral area of a cylinder is this one:

[tex]LA=2\pi rh[/tex]

Where "r" is the radius and "h" is the height

The formula for calculate the area of a circle (which is the base of a cylinder) is:

[tex]A=\pi r^2[/tex]

Knowing the area of the base, you can solve for the radius:

[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]

Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:

[tex]LA=2\pi (6units)(2units)[/tex]

[tex]LA=24\pi\ units^2[/tex]

Answer:

24π square units (edge)

Step-by-step explanation:

Answer:

Option B) 30°

Step-by-step explanation:

Given :  A man on the third floor of a building shouts down to a person on the street. If the man is 25 feet up and the distance between the person on the street and the man in the building is 50 feet.

To find : What is the angle of elevation (in degrees) between the person on the street and the person in the building?

Solution :

According to question, a rough diagram is framed which shows the position of  man on street and man on building.

Refer the attached figure below.

A man on the third floor of a building is 25 feet up i.e. AB=25 feet.

The distance between the person on the street and the man in the building is 50 feet i.e. BC=50 feet.

We have to find the angle of elevation i.e. ∠C.

It form a right angle triangle,

Applying sin property of trigonometric,

[tex]\sin \theta=\frac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]

[tex]\sin \theta=\frac{AB}{BC}[/tex]

[tex]\sin \theta=\frac{25}{50}[/tex]

[tex]\sin \theta=\frac{1}{2}[/tex]

[tex]\sin \theta=\sin 30^\circ[/tex]

[tex]\theta=30^\circ[/tex]

Therefore, Option B is correct.

The angle of elevation is 30°.

Answer:

Its B

Step-by-step explanation:

I just did the test.

Answer:

3.30 for apple and 2.00 for an orange

Step-by-step explanation:

To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. We can then solve this system using the elimination method to find the cost of an apple and an orange.

To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. Let's use x to represent the cost of an apple and y to represent the cost of an orange.

From the given information, we can set up the following equations:

111x + 111y = 5.30

111x + 222y = 7.30

Next, we can solve this system of equations by using substitution or elimination. Let's use the elimination method:

Multiply the first equation by 2, and multiply the second equation by 1:

222x + 222y = 10.60

111x + 222y = 7.30

Subtract the second equation from the first:

111x = 3.30

Divide both sides by 111:

x = 0.03

Substitute this value back into either equation to solve for y:

111(0.03) + 222y = 7.30

3.33 + 222y = 7.30

222y = 3.97

y = 0.01

Therefore, the cost of an apple is $0.03 and the cost of an orange is $0.01 at the fruit stand.

Answer:

C) √5(cos(117°) +i·sin(117°))

Step-by-step explanation:

The rectangular number a+bi can be written in polar form as ...

√(a^2+b^2)×(cos(arctan(b/a)) + i·sin(arctan(b/a)))

Here, we have a=-1, b=2, so the magnitude is ...

√((-1)^2 +2^2) = √(1+4) = √5

and the angle is ...

arctan(2/(-1)) = arctan(-2) ≈ 116.565° . . . . . a 2nd-quadrant angle

Then you have ...

-1 +2i = √5(cos(117°) +i·sin(117°)) . . . . . . customary "polar form"

_____

Comment on the answer

The "polar form" is generally written as ...

(magnitude)·(cos(angle) +i·sin(angle))

You may also see it as ...

(magnitude) cis (angle) . . . . . . . where "cis" is shorthand for "cos + i·sin"

In my engineering courses, we often used the form ...

(magnitude) ∠ (angle)

The form used by my calculator is ...

(magnitude)·e^(i·angle) . . . . . where angle is usually in radians

90 degrees

3 ( square root sign) 10

                 10√2

Then b = ------------ = 5√2

                     Answer:

5√2

Step-by-step explanation:

Notice that the sine function links side b, the hypotenuse (10) and the 45° angle:

                 1

sin 45° = ------ = b/10

                √2

Then b = 10√2 / 2  = 5√2

For this case we have to, by definition:

[tex]tg (B) = \frac {33.2} {a}[/tex]

This means that the tangent of angle B will be equal to the leg opposite the angle on the leg adjacent to the same angle.

Then, clearing to have:

[tex]a = \frac {33.2} {tg (61)}\\a = \frac {33.2} {1.80404776}\\a = 18.403060[/tex]

Rounding out the value of a we have:

[tex]h = 18.4[/tex]

Answer:

Option C

Answer:

The correct answer is option c.  18.4

Step-by-step explanation:

Points to remember:-

Trigonometric ratio

Tan θ = Opposite side/Adjacent side

From the figure we can see a right triangle triangle ABC

To find the value of a

It is given that, b=33.2 and B=61°

Tan 61 = opposite side/Adjacent side

Tan 61 = b/a

a = 33.2/Tan 61 = 18.4

Therefore the correct answer is option c.  18.4

Answer:

the answer is A.

Step-by-step explanation:

Answer:

A) distance, in miles, between the cities

Step-by-step explanation:

correct on edge

Answer:

From the information, we know that Jamal's mother is 28 years older than Jamal, so his mothers age should be:

x + 28 (years)

Also, we know that his uncle's age is twice as much as Jamal's mother age, so we have the following expression:

(x + 28) · 2 = 2x + 56

*Hope this help you

Jamal's uncle's age can be expressed as 2(x + 28), which simplifies to 2x + 56 years.

Jamal is x years old, and his mother is 28 years older than him. Therefore, his mother's age can be represented by x + 28. Jamal's uncle is two times older than Jamal's mother, which means we need to multiply his mother's age by 2 to get the uncle's age. So, the expression for Jamal's uncle's age is 2(x + 28). Simplifying this expression, we get:

2(x + 28)

2x + 2(28)

2x + 56

Thus, Jamal's uncle's age is represented by the expression 2x + 56 years.

Answer:

1

Step-by-step explanation:

We are given a graph, in which x is independent value and y is dependent on the value of x.

f(0) means that x = 0.

so,

we will see in the graph where the x = 0

Obviously it can be anywhere either on origin or on y-axis. The point mark on y-axis is when y = 1

A) The formula for surface area of a sphere is A = 4*PI*r^2

using 3.14 for PI:

Surface area for Earth = 4 * 3.14 x 3960^2 = 196,960,896 miles^2

Surface area of the moon: 4 * 3.14 * 1080^2 = 14,649,984 miles^2

B)Divide the Surface of the Earth by the moon:

196,960,896 / 14,649,984 = 13.44

The Earths surface is 13.4 times larger than the moon.

C) Multiply the surface of the Earth by 70%:

196,960,896 * 0.70 = 137,872,627.2 million square miles of water.

Calculating surface areas of Earth and the moon, comparing them, and determining the amount of water on Earth's surface.

a. Find the surface area of Earth and the moon:

b. Compare the surface areas of Earth and the moon: Earth's surface area is approximately 13.5 times greater than the Moon's surface area.

c. About 70% of Earth's surface is water: There are approximately 137.9 million square miles of water on Earth's surface.

Answer:

g(x), and the maximum is 5

Step-by-step explanation:

for given function f(x), the maximum can be seen from the shown graph i.e. 2

But for the function g(x), maximum needs to be calculated.

Given function :

g (x) = 3 cos 1/4 (x + x/3) + 2

let x=0 (as cosine is a periodic function and has maximum value of 1 at 0 angle)

g(x)= 3 cos1/4(0 + 0) +2

    = 3cos0 +2

     = 3(1) +2

     = 3 +2

     = 5 !

12• (-5)= - 120/2 = -60

ANSWER

The product is

[tex] - 60[/tex]

EXPLANATION

We want to find the product of 12 and -5.

This means that we should find the result of multiplying 12 and -5

Recall that:

[tex]12 \times 5 = 5 \times 12 = 60[/tex]

Therefore,

[tex]12 \times ( - 5) = - 5 \times 12 = 60[/tex]

The product is -60

I'm not sure what to make of the "h" and "i" in your question, so I'll just ignore them (and the 3). Looks like we have

[tex]\vec f(x,y,z)=(x+y,x-y,x^2+y^2-2z)[/tex]

and a surface parameterzied by

[tex]\varphi(u,v)=(u+2v,u-2v,u^2+2v^2)[/tex]

with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. Then

[tex]\varphi_u\times\varphi_v=(4u+4v,4u-4v,-4)[/tex]

so that the flux is given by the integral

[tex]\displaystyle\iint_S\vec f\cdot\mathrm d\vec S=\int_0^1\int_0^1(2u,4v,4v^2)\cdot(4u+4v,4u-4v,-4)\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle8\int_0^1\int_0^1(u^2+3uv-4v^2)\,\mathrm du\,\mathrm dv=\boxed{-2}[/tex]

To calculate the flux of the given vector field through the surface S, you need to calculate the partial derivatives of the parametrization, then find the cross product of these partial derivatives, and finally evaluate the double integral over the surface using the flux formula.

To calculate the flux of the vector field f(x, y, z) = 3hx + y, x − y, x2 + y2 − 2zi through the surface S parametrized by φ(u, v) = u + 2v, u − 2v, u2 + 2v2 with 0 ≤ u, v ≤ 1 and oriented by φu × φv:

Answer: 5/16

Step-by-step explanation:

First, let's calculate the total number of possible outcomes:

4 options in the first bag      and      4 options in the second bag   = 16

Here is the list:

23   24   25    26

33   34    35   36

43   44    45   46

53   54    55   56

Next, calculate the total number of outcomes which result in the product of 12, 13, 14, or 15.

Here are their products:

6    8     10    12

9   12     15    18

12   16     20   24

15   20    25   30

There are 5 outcomes that include a product of 12, 13, 14, & 15.

Probability is:  (# of satisfactory outcomes)/(total outcomes) = 5/16

Answer:

h

Step-by-step explanation:

[(455 + 180 + 324 + 675)/(65 + 36 + 54 + 75)] = 7.10

Answer is D.

Answer:

7.10% is the answer.

according to the picture we have:

x.y=4.7

(7)x(7)y=49xy=(49)(4.7)=230.3

i believe the answer youre looking for is a mile

Answer:

480 = x(6)

Step-by-step explanation:

Given in the question that,

distance travelled by the train = 480 miles

time taken by the train to travel 480 miles = 6 hours

Suppose speed of train = x miles/hour

Formula to use to drive the equation

480 = x(6)

x = 480/6

x = 80 miles/hour

Answer:

The question is incomplete, the complete question is Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 12 ft³ of fluffy material. The base is 3 ft, the height is 2 ft, what is the length of the pillow?

The length of the pillow is 4 feet

Step-by-step explanation:

The formula of the volume of the wedge is [tex]V=\frac{1}{2}bhl[/tex] , where

∵ The pillow in the shape of a wedge

∵ The pillow is filled with 12 ft³ of fluffy material

∴ The volume of the wedge = 12 ft³

∵ The base = 3 feet

∵ The height = 2 feet

- Use the formula of the volume above to find its length

∵ [tex]V=\frac{1}{2}(2)(3)l[/tex]

∴ V = 3 l

∵ V = 12 ft³

- Equate 3 l by 12

∴ 3 l = 12

- Divide both sides by 3

∴ l = 4 feet

∴ The length of the pillow is 4 feet

Answer:

4.06 in.

Step-by-step explanation:

                 4

sin(80)= ----------    multiply by X

                 x

x* sin(80)= 4 divide by sin(80)

         4

X=-------------  simplify

      sin(80)

X= 4.06 in.

Answer:

The length of the hypotenuse is 4.1 in

Step-by-step explanation:

By definition, the sine of an angle is:

[tex]sin(x) = \frac{opposite\ side}{hypotenuse}[/tex]

In this case they tell us that the opposite side measures 4 inches and the angle x measures 80 °.

With this information we can find the length of the hypotenuse h

[tex]sin(80\°) =\frac{4}{h}\\\\h = \frac{4}{sin(80\°)}\\\\h = 4.062\ in[/tex]

Finally the length of the hypotenuse is 4.1 in

Answer:

The scale is 7

Step-by-step explanation:

Divide 12 from 84 to get the answer.

Hope this helps! :)

Answer:

Step-by-step explanation: