Melissa’s family is driving out of state to her grandmother’s house. They know that it takes 20 gallons of gas to get there, and the cost of three gallons of gasoline is $10.50. How much should the family budget to make the one-way trip?

In the given scenario regarding a toy sinking in a pool, the constraints related to the depth of the pool and the rate of sinking of the toy could be part of the scenario, which illustrates a system of inequality related to the depth of the toy in the pool over time.

The question requires understanding of the constraints in a scenario that involve a system of inequalities related to the depth of a toy in a pool over time. In this case, the toy is falling, or sinking, into the pool. Therefore, the scenario will involve the depth of the pool and the rate at which the toy is falling.

Firstly, The depth of the pool is important because the toy cannot sink deeper than the pool is. Therefore, both constraints A) The pool is 1 meter deep and B) The pool is 2 meters deep could both be part of the scenario, depending on the actual depth of the pool involved.

Secondly, The rate at which the toy is falling (sinking) is also important. Both constraints C) The toy falls at a rate of at least a 1/2 meter per second and D) The toy sinks at a rate of no more than a 1/2 meter per second could be part of the scenario, depending on the actual sinking rate of the toy.

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The constraint that could be part of the scenario is that the D) toy sinks at a rate of no more than a 1/2 meter per second.

A system of inequalities is a set of two or more inequalities involving the same variables. The solution to the system is the set of values that satisfy all the inequalities simultaneously. Graphically, the solution represents the overlapping region of the individual inequalities on a coordinate plane.

The constraint that could be part of the scenario is that the toy sinks at a rate of no more than a 1/2 meter per second. This constraint ensures that the depth of the toy in the pool does not change too rapidly. If the toy sank at a faster rate than 1/2 meter per second, it would quickly reach the bottom of the pool.

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Answer:

Step-by-step explanation:

The sum of the interior angles of an n gon is found by using the following formula.

(n-2)*180 = sum of the interior angles.

(n - 2) * 180 = 3960                     Divide by 180

(n - 2) 180/180 = 3960/180         Show the division

n - 2 = 22                                     Add 2 to both sides.

n -2+2=22+2                               Combine

n = 24

======================================

To find the size of each angle, use

(n - 2)*180/n

(24 - 2)*180/24

22 * 180/24

3960/24 = 165

===========

another way

===========

You already know there are 24 sides. You are given the sum of the interior angles as 3960

All you really need to do is 3960/24 = 165

Answer:

fff

Step-by-step explanation:

By pythagorean theorum we calculate the height:

[tex]\sqrt{5^2-1^2}[/tex]

=[tex]\sqrt{24}[/tex] = height of triangle

area of triangle = base * height

area = [tex]2*\sqrt{24}[/tex]

There are two triangles so:

[tex]2*2*\sqrt{24}=4\sqrt{24}[/tex]

Multiply this by 13.25 to get total cost:

=$259.65

Answer:

$ 129.82 because it is to the nearest cent

Answer:

[tex]3x^2-2x-6[/tex]

Step-by-step explanation:

[tex](f-g)(x)[/tex]

[tex]f(x)-g(x)[/tex]

So plug in your functions:

[tex][3x^2-2]-[2x+4][/tex]

Distribute:

[tex]3x^2-2-2x-4[/tex]

Combine like terms:

[tex]3x^2-2x-6[/tex]  There was only one pair of like terms -2 and -4.

Answer:

1100 km

Step-by-step explanation:

The problem doesn't clearly state whether the 380,000 km is from the Earth's surface to the moon's center, or to the moon's surface.  Since we'll be rounding to 2 significant figures, it's not enough to make a difference, so I'll assume it's to the moon's center.

Draw circle representing the moon and earth.  Draw tangent lines from the earth's center to the edge of the moon.  The angle between these lines is the subtended angle.  Now draw a line representing the moon's radius from the center of the moon to the point where the tangent line intersects.  Notice this forms a right angle.

(See attached diagram)

Using trigonometry:

sin(θ/2) = r / (R + h)

r = (R + h) sin(θ/2)

Given that R = 6400 km, h = 380,000 km, and θ = 20' = 1/3 degrees:

r = (6400 + 380000) sin(1/6 °)

r = 1100

The moon's radius is 1100 km.

Answer: C≈50.27cm

if u want the solution then here u go

C=2πr=2·π·8≈50.26548cm

The correct answer is [tex]\(\boxed{\frac{1919}{16} - \frac{481\pi}{128}}\)[/tex] cubic inches.

To determine the volume of the empty space in the box, we need to calculate the volume of the box and the volume of the basketball, and then subtract the volume of the basketball from the volume of the box.

First, let's calculate the volume of the cubic box. Since the edge of the cube is given as 9.5 inches, the volume of the cube [tex]\( V_{box} \)[/tex] is the edge length cubed:

[tex]\[ V_{box} = 9.5^3 \][/tex]

[tex]\[ V_{box} = \left(\frac{95}{10}\right)^3 \][/tex]

[tex]\[ V_{box} = \frac{95^3}{10^3} \][/tex]

[tex]\[ V_{box} = \frac{95^3}{1000} \][/tex]

[tex]\[ V_{box} = \frac{857375}{1000} \][/tex]

[tex]\[ V_{box} = \frac{1919}{4} \][/tex] cubic inches.

 Next, we calculate the volume of the basketball. The basketball is a sphere with a diameter of 9.5 inches, so its radius [tex]\( r \)[/tex] is half of that:

[tex]\[ r = \frac{9.5}{2} \][/tex]

[tex]\[ r = \frac{95}{20} \][/tex]

[tex]\[ r = \frac{19}{4} \] inches.[/tex]

The volume of a sphere [tex]\( V_{sphere} \)[/tex] is given by the formula:

[tex]\[ V_{sphere} = \frac{4}{3}\pi r^3 \][/tex]

[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{19}{4}\right)^3 \][/tex]

[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{19^3}{4^3}\right) \][/tex]

[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{6859}{64}\right) \][/tex]

[tex]\[ V_{sphere} = \frac{481\pi}{128} \] cubic inches.[/tex]

Now, we subtract the volume of the basketball from the volume of the box to find the volume of the empty space [tex]\( V_{empty} \):[/tex]

[tex]\[ V_{empty} = V_{box} - V_{sphere} \][/tex]

[tex]\[ V_{empty} = \frac{1919}{4} - \frac{481\pi}{128} \] cubic inches.[/tex]

 To simplify the expression, we can multiply the terms by a common denominator of 128 to combine them:

[tex]\[ V_{empty} = \frac{1919 \times 32}{128} - \frac{481\pi}{128} \][/tex]

[tex]\[ V_{empty} = \frac{61408}{128} - \frac{481\pi}{128} \][/tex]

[tex]\[ V_{empty} = \frac{61408 - 481\pi}{128} \] cubic inches.[/tex]

 However, we notice that the denominator of 128 can be simplified by dividing both numerator and denominator by 4, which gives us the final

[tex]\[ V_{empty} = \frac{1919}{16} - \frac{481\pi}{128} \][/tex] cubic inches.

Therefore, the volume of the empty space in the box is [tex]\(\boxed{\frac{1919}{16} - \frac{481\pi}{128}}\)[/tex] cubic inches.

Answer: 88

Step-by-step explanation:

(8x2)=16/2=8

8x6=48

8x4=32

48+32+8=88

Answer:

112

Step-by-step explanation:

Answer:

You need to draw a horizontal line that goes through the point (0,4).

Step-by-step explanation:

Slope of zero means it does not go up or down. It looks like this ↔, but stretched out to the two sides of the graph.

A line with a slope of zero is flat and does not rise or fall. To graph this line, draw a horizontal line through the given y-coordinate.

A line with a slope of zero means that the line is flat and has no rise or fall. To graph a line with a slope of zero passing through the point (0,4), you would draw a horizontal line through the y-coordinate 4. Since the slope is zero, the line will not change in the vertical direction.

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Answer:

A 15

Step-by-step explanation:

In an isosceles trapezoid, each pair of base angles is congruent.

In this isosceles trapezoid, angles B and C are congruent, so their measures are equal.

m<B = m<C

60 = 3x + 15

Subtract 15 from both sides.

45 = 3x

Divide both sides by 3.

15 = x

x = 15

Answer:  The correct option is (A) 15.

Step-by-step explanation:  As shown in the attached figure below, ABCD is an isosceles trapezoid with AD parallel to BC.

Also, m∠B = 60°  and  ∠C = (3x +15)°.

We are to find the value of x.

Since ABCD is an isosceles trapezoid with AB and CD as the two legs, so we have

[tex]AB=CD\\\\\Rightarrow m\angle C=m\angle B~~~~~~~~~~~~~~~~~~~[\textup{Angles opposite to equal legs are equal}]\\\\\Rightarrow (3x+15)^\circ=60^\circ\\\\\Rightarrow 3x+15=60\\\\\Rightarrow 3x=60-15\\\\\Rightarrow 3x=45\\\\\Rightarrow x=\dfrac{45}{3}\\\\\Rightarrow x=15.[/tex]

Thus, the required value of x is 15.

Option (A) is CORRECT.

Answer:

40 combinations

Step-by-step explanation:

We just multiply the outcomes.

4*2*5=40

There are 40 different ways to redecorate.

4 colors of paint * 2 kinds of curtains * 5 colors of carpet

= 40 outcomes.

In the possibility principle, an outcome is a probable result of a test or trial. every possible final result of a selected experiment is precise, and one-of-a-kind results are together one of a kind (most effective final results will occur on each trial of the experiment).

To locate the total wide variety of consequences for two or greater occasions, multiply the variety of effects for every occasion collectively. that is referred to as the product rule for counting because it involves multiplying to discover a product.

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Answer:

5.

Step-by-step explanation:

There are a total of  21 items so the median is the mean of the 10th and 11th .

This lies on the highest column so the median is  5.

Answer:

C

Step-by-step explanation:

The surface area (A) of a sphere is calculated as

A = 4πr² ← r is the radius, here r = 12, hence

A = 4π × 12²

  = 4π × 144 = 576π units² → C

The surface area of the sphere is  576 square units. The correct option is B.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called as the surface area.

The surface area (A) of a sphere is calculated as

A = 4πr² ← r is the radius, here r = 12, hence

A = 4π × 12²

A= 4π × 144

A = 576π units²

Hence, the correct option is B.

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Answer:

Option A 50-page photo album holds 400 photographs.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

step 1

Find the value of k

For the point (3,24)

x=3,y=24

k=y/x

k=24/3=8

The equation is equal to

y=8x

step 2

Verify each statement

case A) 50-page photo album holds 400 photographs.

For x=50

substitute in the equation

y=8(50)=400 -----> is correct

case B) 80-page photo album holds 560 photographs.

For x=80

substitute in the equation

y=8(80)=640 -----> is not correct

case C) 100-page photo album holds 8,000 photographs.

For x=100

substitute in the equation

y=8(100)=800 -----> is not correct

case D) 900-page photo album holds 8,400 photographs.

For x=900

substitute in the equation

y=8(900)=7,200 -----> is not correct

Answer:

Yes ! The correct answer is A.) 50-page photo album holds 400 photographs.

Step-by-step explanation:

I did the Unit Test and i got it correct.

Answer:

See picture.

In the picture I graphed (0,1) and then graphed (1,3).

I connected the points with a straight-edge.

Step-by-step explanation:

This question is asking us to use slope-intercept form of a line to answer it.

Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

Your equation is y=2x+1 so our m=2 and b=1.

So our y-intercept is 1.  This is the first point we graph.

The slope is 2 or as a fraction 2/1. Recall that slope=rise/run.  So this tells us after we plot (0,1) we need to go up 2 units and right 1 unit to get one more point to graph.  This point will be (0+1,1+2) or just (1,3).

I will draw a graph also to show you this:

Answer:

Graph Attached Below

Step-by-step explanation:

Hello!

To graph a line, we just need any two points that belong to that line.

We know the y-intercept, (0,1), given in the equation itself. We can plot that point as our first point.

The second point can be found by using the slope. The slope is 2/1, and we can go up 2 units and to the right 1 unit to find the second point.

The second point is (1,3).

we use divsion, 10 divided by 5 is 2, everyone get 2 yumy cupcakes.

Answer:

[tex]f^{-1}[/tex](x) = [tex]\frac{x-3}{2}[/tex]

Step-by-step explanation:

Let y = f(x) and rearrange making x the subject

y = 2x + 3 ( subtract 3 from both sides )

y - 3 = 2x ( divide both sides by 2 )

[tex]\frac{y-3}{2}[/tex] = x

Change y back into terms of x, hence

[tex]f^{-1}[/tex](x ) = [tex]\frac{x-3}{2}[/tex]

Keep in mind that f(x) means the same thing as y so...

y = 2x + 3

To find the inverse operation you switch the places of x and y like so...

x = 2y + 3

Now you must solve for y. To start off you must subtract 3 to both sides.

x - 3 = 2y + 3 - 3

x - 3 = 2y

Now divide 2 to both sides to completely isolate y

(x - 3) / 2 = 2y / 2

[tex]\frac{1}{2} x - \frac{3}{2}[/tex] = y

OR

[tex]\frac{x}{2} -\frac{3}{2}[/tex] = y

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

$102.29 is the original price of the suit.

Explanation:

$x ------- 100% price (full price)

$35.80 --------------- 35% of the original price (100%-65%=35%).

To find x, use cross-products.

x=(35.80×100)/35 =3580/35 = approximately $102.29.

Answer:

The original price of the suit was $102.29.

Step-by-step explanation:

Alex purchased a new suit discounted by 65%.

He paid $35.80 for the suit.

Let the original price (100% price) be x.

After discount the price is given = 100% - 65% = 35%

35% of x = 35.80

0.35x = 35.80

x = [tex]\frac{35.80}{0.35}[/tex]

x = 102.2857 rounded to $102.29

The original price of the suit was $102.29.

Answer:

I have to assume that the 24, the 72, and the 18 are feet.

If those are the dimensions of a rectangular prism, like a box, a crate,

or a humongous block of ice, then

           Volume = (length) x (width) x (height) =

                            (24-ft) x (72-ft) x (18-ft) =  31,104 cubic ft

If those numbers are inches, then here's the easy way to handle it:

      24 inches  =  2 ft

      72 inches  =  6 ft

      18 inches  =  1.5 ft

              Volume  =  (length) x (width) x (height) =

                                    (2ft) x (6ft) x (1.5ft)  =  18 cubic feet

The transformation which do not describe a rigid motion transformation is:

           Option: C

   C. dilating a figure by a scale factor of 1/4

Rigid motion transformation is a transformation in which the shape and size of the figure is preserved i.e. it remains the same.

A)

Translating a figure 5 units right.

We know that in the translation transformation the shape and size of the figure remains the same only the location of points are changed.

B)

Rotating a figure 90 degrees.

In rotation the shape and size is preserved.

Hence it is a rigid transformation.

C)

dilating a figure by a scale factor of 1/4

This is not a rigid transformation because the size of the figure is changed.

since the scale factor is less than 1.

Hence, the transformation is a reduction of the original figure.

D)

reflecting a figure across the x-axis.

The reflection is also a rigid transformation.

since it preserves the shape and size of the object.

Answer:

The correct answer is C.

Answer:

Step-by-step explanation:

His chances of getting the purple one are 1/6

His chances of getting the blue one after drawing the purple one and not replacing are 1/5

The probability of both happening are 1/6 * 1/5 = 1/30

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables, and then solve for "y".

[tex]\bf y = 4x^2-8\implies \stackrel{\textit{quick switcheroo}}{\underline{x} = 4\underline{y}^2-8}\implies x+8=4y^2\implies \cfrac{x+8}{4}=y^2 \\\\\\ \sqrt{\cfrac{x+8}{4}}=y\implies \cfrac{\sqrt{x+8}}{\sqrt{4}}=y\implies \cfrac{\sqrt{x+8}}{2}=\stackrel{f^{-1}(x)}{y}[/tex]

Answer:

the required answer is 125/24.

Answer:

The cost price of one calculator is Rs.750.

The cost price of other calculator is Rs.500.        

Step-by-step explanation:

Cost price of 1'st calculator = x

Cost price of 2'nd calculator = 1250-x

He sold one at a profit of 2%.

The selling price of one calculator is

[tex]SP_1=CP(1+\frac{P\%}{100})[/tex]

[tex]SP_1=x(1+\frac{2}{100})[/tex]          

[tex]SP_1=x(1+0.02)[/tex]      

[tex]SP_1=1.02x[/tex]    

He sold other at a loss of 3%.

The selling price of other calculator is

[tex]SP_2=CP(1-\frac{L\%}{100})[/tex]

[tex]SP_2=(1250-x)(1-\frac{3}{100})[/tex]          

[tex]SP_2=(1250-x)(1-0.03)[/tex]      

[tex]SP_2=(1250-x)(0.97)[/tex]

[tex]SP_2=1212.5-0.97x[/tex]  

According to given condition,

[tex]SP_1+SP_2=1250[/tex]

[tex]1.02x+1212.5-0.97x=1250[/tex]

[tex]0.05x=1250-1212.5[/tex]

[tex]0.05x=37.5[/tex]

[tex]x=\frac{37.5}{0.05}[/tex]

[tex]x=750[/tex]

The cost price of one calculator is Rs.750.

The cost price of other calculator is 1250-750=Rs.500.

Answer:

-8

Step-by-step explanation:

If you want to find the fourth term in the sequence, or b(4), then you just plug in the value 4 for n, resulting in

b(4)=1(-2)^(4-1).

Simplifying, we get

b(4)=1(-2)^3

     =1(-2*-2*-2)

     =1(-8)

     =-8

Answer:

$11,700

Step-by-step explanation:

If Cary earns $975 each month on his part-time job, he would earn $11,700 in a year.

1 year = 12 months

$975 per month

975 x 12 = 11700

In this question, we're going to need to find out how much Cary earns in a year.

To do this, we need to go back to the problem to see if we can get some valuable information.

We know that Cary earns $975 each month.

With the information above, we can solve the problem.

There are 12 months in a year, so that means we're going to multiply 975 by 12 in order to find out how much Cary earns in a year.

975 × 12 = 11,700

When you multiply, you would end up with the answer "11,700"

This means that Cary earns $11,700 in a year

Answer:

y=3x+5

Step-by-step explanation:

To determine the slant asymptote you must perform polynomial division and also the degree of the numerator must be one greater than degree of the denominator for it to even exist.  (We do have that here by the way since degree of the top is 2 and the degree of the bottom is 1).

Let's begin the division process:

I'm using synthetic. You can also use long.

3 goes on the outside because we are dividing by x-3

3 |   3     -4      5

  |           9      15

    ----------------------

      3       5       20

So [tex]\frac{3x^2-4x+5}{x-3}=3x+5+\frac{20}{x-3}[/tex]

So the slant aymptote is y=3x-5 since 20/(x-3) approaches 0 as x approaches  infinity.

To find the slant asymptote of the given function, perform long division to divide the numerator by the denominator. As x approaches infinity, the slant asymptote is 3x + 5.

To find the slant asymptote of the function f(x) = (3x^2 - 4x + 5) / (x - 3), we need to determine what happens as x approaches positive or negative infinity. We can do this by dividing the numerator polynomial by the denominator polynomial using long division.

Performing long division, we get:

3x^2 - 4x + 5 / (x - 3) = 3x + 5 + (8 / (x - 3))

As x approaches infinity, the 8 / (x - 3) term becomes negligible and we are left with the slant asymptote:

f(x) = 3x + 5

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Answers: Ten millions

Answer:

18 and 19

Step-by-step explanation:

Consecutive positive integers have a difference of 1 between them

let n and n + 1 be the 2 integers, then

n(n + 1) = 342, that is

n² + n = 342 ( subtract 342 from both sides )

n² + n - 342 = 0 ← quadratic equation in standard form

(n + 19)(n - 18) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 19 = 0 ⇒ n = - 19

n - 18 = 0 ⇒ n = 18

However, n > 0 ⇒ n = 18 and n + 1 = 18 + 1 = 19

The 2 integers are 18 and 19

Answer:

The average rate of change is -6

Step-by-step explanation:

The formula for average rate of change is

[tex]=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

where

x₁=-1 and x₂=2

In this case we replace f(x) with z(x)

Substitute values of x₁ and x₂ in the formula given the function as

[tex]z(x)=-6x+2+3\\z(x)=-6x+5\\\\\\=\frac{z(x_2)-z(x_1)}{x_2-x_1} \\\\\\z(x_1)=z(-1)=-6*-1+5=6+5=11\\\\\\z(x_2)=z(2)=-6*2+5=-12+5=-7\\\\\\x_2-x_1=2--1=3\\\\Rateofchange=\frac{-7-11}{3} =\frac{-18}{3} =-6[/tex]

Answer:

a = 12

b = 22

c = 25.96186

Angle A = 27.417°

Angle B = 57.583°

Angle C = 95°

Area = 131.4977

Perimeter = 59.96186

a = 12,b = 22,c = 25.96186

∠A = 27.417°,∠B = 57.583°,∠C = 95°

Law of sine states that the ratio sine of an angle and its opposite side in a triangle is same for all 3 angles and their corresponding sides.

sinA/a=sinB/b=sinC/c

Law of cosine is the generalized Pythagoras theorem is applied. It is applied for measuring one side where the opposite angle and other two sides are given.

c²=a²+b²-2abcosC

here given,

a = 12

b = 22

∠C = 95°

Applying law of cosine,

c²=a²+b²-2abcosC

=12²+22²-2.12.22.cos95°

=674.018

⇒c=√674.018

⇒c=25.96

Applying law of sine

sinA/a=sinC/c

⇒sinA=(a/c)sinC

⇒sinA=(12/25.96)sin95°=0.46

⇒A=sin⁻¹(0.46)

⇒A=27.417°

As we know sum of the 3 angles in a triangles are 180°.

∠B=180°-(∠A+∠C)=180°-(27.417°+95°)=180°-(122.42)

⇒∠B=57.583°

Therefore a = 12,b = 22,c = 25.96186

∠A = 27.417°,∠B = 57.583°,∠C = 95°

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