The admission fee at an amusement park is $12, and each ride costs $3.50. The park also offers an all-day pass with unlimited rides for $33. For what numbers of rides is it cheaper to buy the all-day pass?

Answer:

The quotient is: m^2-10m-6

The remainder is: 0

Step-by-step explanation:

We need to divide m^3-13m^2+24m+18 ÷ m-3 using synthetic division

The division is shown in the figure below.

The quotient is: m^2-10m-6

The remainder is: 0

Answer:

1. (2, -9)

2.  ( 0,-5)

Answer:

All except from point E's y-coordinate (which is -1.5 (found it through the equation y=-1.5 and trying to see if these coordinates are solutions to the above equation) All the others are integers, which you can find through aligning the point on the axis of the chosen (y or x) coordinate.

Step-by-step explanation:

Point C has -2 x-coordinate since it is on the x=-2 line

Similarly, point D has -2 y coordinate,

point E has 2 x-coordinate and -1,5 y-coordinate

and point F , since it's the two axis' common point has coordinates of (0,0).

Hope I helped! Further explanation can be given on request on your behalf.

Answer:

4860 in ^3

Step-by-step explanation:

First we find the volume of the tank

V = l*w*h

V = 30*12*15

V = 5400 in ^3

It is 90% full so we multiply by 90 %

5400 * 90%

5400 * .90

4860 in ^3

Answer:

The number in the square root is 50.

Step-by-step explanation:

Using the pythagorean theorem, we know that c is 10, so we plug in 2a^2=100, since we know that both of the leg lengths are the same.

Simplifying this equation gives a^2=50, which square rooting both sides gives

a = sqrt(50)

Hope this helps!

[tex]\bf x= \begin{cases} 6\\ -4 \end{cases}\implies \begin{cases} x=6\implies &x-6=0\\ x=-4\implies &x+4=0 \end{cases} \\\\\\ (x-6)(x+4)=\stackrel{y}{0}\implies \stackrel{\mathbb{F~O~I~L}}{1x^2-2x-24}=y[/tex]

The taxicab, after all its movements, is about 3.16 blocks away from its starting position. It ends up 3 blocks west and 1 block north from where it initially started.

The question asks us to determine the final position of a taxicab relative to its starting position after following a series of movements. The taxicab's starting position in this case is at the coordinate (1, -2).

Initially, it goes 4 blocks south (downwards in the grid, which we'll regard as negative) and 3 blocks east (to the right on the grid, which we'll regard as positive). Therefore, it moves to a point that is (+3, -4) relative to its starting position.

Next, it goes 6 blocks west (left on the grid, which is negative) and 5 blocks north (up on the grid, which is positive). So, this movement's relative position is (-6, +5).

To find out the final position of the taxicab relative to its starting position, we need to add up these movements' relative positions. The final relative position will be (+3-6, -4+5), which equals (-3, 1).

Hence, in terms of blocks, the taxicab is 3 blocks west and 1 block north of its starting position. The direct distance to the start would then be determined using the Pythagorean theorem, where the total distance is the square root of the sum of the squares of the movements in each direction (x and y coordinates). That forms the equation √((-3)² + 1²) = √10 ≈ 3.16 blocks.

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[tex]1350\sqrt{3}[/tex] square units (approximately 2338.26859)

The formula for finding the area of a regular hexagon when you know its side length is [tex]A=\frac{3\sqrt{3}*s^2}{2}[/tex], where [tex]A[/tex] is the area and [tex]s[/tex] is the side length.

[tex]1350\sqrt{3}[/tex] is as simple as the solution can get without estimating, but you can estimate with a calculator to find that it is approximately 2338.26859.

Answer:

Mia multiplied one side of the equation by 5/3 and the other side by 3/5. This makes the equation unbalanced and untrue. x should be 50

Step-by-step explanation:

Mia made an error when setting up the equation to determine the total time allotted for the math section of the exam. She incorrectly set up the equation as 30 = (1/4) * x, instead of 30 = (1/4) * x. The correct solution is x = 120.

Mia made an error when setting up the equation to determine the total amount of time allotted for the math section of the exam. Since Mia spent 30 minutes answering the math questions, which was 1/4 of the total time, the correct equation should be:

30 = (1/4) * x

To solve for x, we need to multiply both sides of the equation by 4 to undo the division:

4 * 30 = x

x = 120

Therefore, the total amount of time allotted for the math section of the exam is 120 minutes, not 30 minutes as Mia mistakenly calculated.

[tex]x^2 - 25 = 0\\x^2=25\\x=-5 \vee x=5[/tex]

Answer:

x = ± 5

Step-by-step explanation:

Given

x² - 25 = 0

There are 2 possible approaches to solving this equation

Approach 1

add 25 to both sides

x² = 25 ( take the square root of both sides )

x = ± [tex]\sqrt{25}[/tex] = ± 5

Approach 2

x² - 25 ← is a difference of squares and factors as

(x - 5)(x + 5) = 0 ← in standard form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 5 = 0 ⇒ x = 5

Answer:

[tex]y=2x^{2}+1[/tex]

Step-by-step explanation:

we know that

The graph is a vertical parabola open upward

The vertex is the point (0,1)

The equation of a vertical parabola in vertex form is equal to

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

substitute the vertex in the equation

[tex]y=a(x-0)^{2}+1[/tex]

[tex]y=a(x)^{2}+1[/tex]

Find the value of coefficient a

Observing the graph

For x=1, y=3

substitute in the equation

[tex]3=a(1)^{2}+1[/tex]

[tex]a=3-1=2[/tex]

The equation on the graph is equal to

[tex]y=2x^{2}+1[/tex]

Answer:

A' = (- 5, - 1)

Step-by-step explanation:

The coordinates of point A = (- 6, 2)

Under the translation (x + 1, y - 3)

Add 1 to the x- coordinate of A and subtract 3 from the y- coordinate of A

A' = (- 6 + 1, 2 - 3) → A' = (- 5, - 1)

Based on the fact that there are  4 points which are given below, we have to move the trapezoid to the points of A will be (x+1, y-3). The coordinates of A be A(-6,2) =>A'(-5, -1)

A trapezoid is regarded as a  quadrilateral that has only one pair of opposite sides that are said to be parallel.

The points on the graph are:

A(-6,2) =>A'(-5, -1)

B(-5,4) =>B'( -4,1)

C(-2,4)=> C'(-1,1)

D( 1,2) => D'(2,-1)

It is made up of a right angles (called right trapezoid), and it can also contain a congruent sides (isosceles). Note that in the above, the only way the trapezoid  can fit into the translation movement (Point A)is if it is moved to the points of (x+1, y-3) on the graph.

The coordinates of A be A(-6,2) =>A'(-5, -1).

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There are two: -4 and -5/2

Steps

0 = (2x - 5)(x + 4) | FOIL (distribution)

2x = 5 | zero product rule

x = 5/2 <<<

x = -4 <<< | zero product rule again.

[tex](f+g)(x)=-x^2+6x-1+3x^2-4x-1=2x^2+2x-2[/tex]

Answer: [tex](f+g)(x)=2x^2+2x-2[/tex]

Step-by-step explanation:

Given the function f(x), which is:

[tex]f(x)=-x^2 +6x-1[/tex]

And the function g(x), which is:

[tex]g(x) =3x^2-4x-1[/tex]

You can observe that [tex](f+g)(x)[/tex] indicates that you need to add the functions, then you know that:

[tex](f+g) (x)=(-x^2+6 x-1)+(3x^2-4x-1)[/tex]

Finally, to simplify it you must addthe like terms. Therefore, you get that  [tex](f+g)(x)[/tex] is:

[tex](f+g)(x)=-x^2+6 x-1+3x^2-4x-1[/tex]

[tex](f+g)(x)=2x^2+2x-2[/tex]

Answer:

5000 g

Step-by-step explanation:

5000 g = 11.02311 lb

10 lb​ = 4535.92

Answer:

√55x\11x⁸y⁵

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

Answer: C

Explanation:

√55x⁷y⁶/11x¹¹y⁸

→ 55/11 = 5

→ x⁷/x¹¹= x⁷⁻¹¹= x⁻⁴

→ y⁶/y⁸= y⁶⁻⁸= y⁻²

→ √5/x⁴y²

→ √5/x²y

If the exponent is a negative, the base is the reciprocal of itself with a positive exponent.

Ex: 6⁻² = 1/6² = 1/36

The square root of an exponent with a positive, even power is half of that power.

Ex: √x⁴ = x²

Answer:

I(x) = 12x² + 8x + 5

Step-by-step explanation:

* Lets talk about the solution

- P(x) is a quadratic function represented graphically by a parabola

- The general form of the quadratic function is f(x) = ax² + bx + c,

  where a is the coefficient of x² and b is the coefficient of x and c is

  the y-intercept

- To find I(x) from P(x) change each x in P by 2x

∵ P(x) is dilated to I(x) by change x by 2x

∵ I(x) = P(2x)

∵ P(x) = 3x² + 4x + 5

∴ I(x) = 3(2x)² + 4(2x) + 5 ⇒ simplify

∵ (2x)² = (2)² × (x)² = 4 × x² = 4x²

∵ 4(2x) = 8x

∴ I(x) = 3(4x²) + 8x + 5

∵ 3(4x²) = 12x²

∴ I(x) = 12x² + 8x + 5

Answer:

A≈622.04

Step-by-step explanation:

Formula: A=2πrh+2πr²

Answer: A. 622 sq. units

Step-by-step explanation:

The surface area of a cylinder is given by :-

[tex]S.A.=2\pi r(r+h)[/tex], where r is the radius , h is height of the cylinder.

Given : The height of the cylinder : h= 2 units

The radius of the cylinder : r= 9 units

Then , the surface area of a cylinder will be :-

[tex]S.A.=2(3.14159) 9(9+2)\\\\\Rightarrow\ S.A.=622.03482\approx622\text{sq. units}[/tex]

Let x represent Ravi's current age.

Now, Ravi's age fifteen years from now is effectively Ravi's age plus fifteen, therefor we can write this as x + 15.

Four times Ravi's present age is four multiplied by his present age, therefor we can write this as 4x.

If Ravi's age fifteen years from now is equal to four times his present age, then:

x + 15 = 4x

Now all we have to do is solve for x to find Ravi's present age:

x + 15 = 4x

15 = 3x (Subtract x from both sides)

5 = x (Divide both sides by 3)

Therefor, Ravi's present age is 5 years.

Answer:

B.In slope-intercept form, the slope is −79.These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is −AB.

Step-by-step explanation:

A is being moved to the other side of the equation so it has to be negative and is multiplied by B since the y value has to be divided to equal the base of y not 9y but y.

Answer:

A. A number divided by three minus fifteen.

A number is divided by three minus fifteen best describes the given algebraic expression [tex]\frac{x}{3}-15[/tex].

Option A is correct.

An algebraic expression is a variable expression described using its terms, and operations on the terms. For example, x + 3 can be described as "3 more than x".

Given algebraic expression

[tex]\frac{x}{3}-15[/tex]

[tex]\frac{x}{3}[/tex] means a number is divided by three and [tex]\frac{x}{3}-15[/tex] means a number is divided by three minus fifteen.

A number is divided by three minus fifteen best describes the given algebraic expression [tex]\frac{x}{3}-15[/tex].

Option A is correct.

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Answer:

Step-by-step explanation:

The formula of an area of a parallelogram:

A = bh

b - base

h - height

We have A = 140 units², and h = 10 units. Substitute:

140 = 10b           divide both sides by 10

14 = b → b = 14 units

Answer:

A linear function is in the form y = mx + b or f(x) = mx + b, where m is the slope or rate of change and b is the y-intercept or where the graph of the line crosses the y axis. ... if your first diffs are the same it is linear. if not it is not linear.

a LINEar equation is an equation with a polynomial of degree 1 and is the graph of a LINE, let's look at this one, y = x² - 3, notice the exponent of ², meaning is a 2nd degree equation, and is a parabola, so is namely a quadratic, not a linear one.

Answer:

Option A is correct.

Step-by-step explanation:

Given terms,

1 , 4 , 16 , 64 , 256.

If we observe the equation, we can easily say that the terms are getting multiplied by 4 to get the next one.

Since this equation has a common ratio, this can be solved by using the properties of geometric progressions.

From the properties of geometric progressions :

Here,

Common Ratio ( or r ) = any term( except first ) / previous terms = 64 / 16 = 16 / 4 = 4

First terms = 1

Therefore,

= > Next term should be : 1 x ( 4 )^( 6 - 1 ) { Since next term will be 6th term }

= > Next term = 1 x 4^5

= > Next term = 1024

Hence the required next term is 1024.

Option A is correct.

Or

Here we can see that the terms are written in the form of 4^n where n is any whole number.

Since 246 is 4^4 , and terms are increasing in order of 1, next term should be 4^5 i.e. 1024 .

Thus, option A is correct.

Answer:

A

Step-by-step explanation: you times each one by 4

Answer:

0.75 mile(s) per minute

n-6=0.75(t-8)

hope this helps!!

Step-by-step explanation:

Answer:

0.75 miles per minute

Equation: n - 6 = 0.75(t - 8)

Step-by-step explanation:

took the test and got it right

Answer: sorry i meant 7.5 would be incorrect

Step-by-step explanation: she wouldn't be able to do it if it goes over 6 so that is incorrect

Answer:

Teagan is correct.

Step-by-step explanation:

We are given the following information in the question:

Number of friends = 6

Pizza eaten by all friends = [tex]\frac{4}{5}[/tex]

Now, in order to find pizza eaten by each friend, Teagan need to divide pizza eaten by total number of friends.

Formula:

[tex]\text{Pizza eaten by each friend} = \displaystyle\frac{\text{Total pizza eaten}}{\text{Number of friends sharing the pizza}}\\\\= \displaystyle\frac{\frac{4}{5}}{6} = \displasystyle\frac{4}{30} = \displaystyle\frac{2}{15}[/tex]

Thus, each friend had  [tex]\frac{2}{15}[/tex] of a pizza.

Answer:

C

Step-by-step explanation:

note that - (- 19) = + 19

Given

y - (- 19) = 25, that is

y + 19 = 25 ( subtract 19 from both sides )

y = 6 → C

Answer:

Answer is C. 6

Step-by-step explanation:

Because:

y -(-19) = 25 (well i always put a 1 infront of parenthesis) so,

y -1(-19) =25 distribute the 1 in the parenthesis and you would get

19=25 minus 19 on both sides and you get y= 6

Hope my answer has helped you!

Answer:

Sophie has 12.5 cards

Step-by-step explanation:

Let

x -----> number of cards Sophie has

y -----> number of cards Jackie has

we know that

x+y=30 -----> equation A  

y=x+5 -----> equation B

Solve by substitution

Substitute equation B in equation A and solve for x

x+(x+5)=30

2x=30-5

x=12.5 cards

Note I assume the problem was invented without taking into account the result, because the amount of cards should be a whole number

Answer:

a

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Rearrange 3x - y = 4 into this form ( add y to both sides )

3x = y + 4 ( subtract 4 from both sides )

3x - 4 = y OR y = 3x - 4 → a

Final answer:

The equation 3x - y = 4 is rewritten in slope-intercept form as y = 3x - 4, where the slope is 3 and the y-intercept is -4, corresponding to answer option A.

Explanation:

To rewrite the equation 3x - y = 4 in slope-intercept form (y = mx + b), we need to solve the equation for y.

Here are the steps:

Add y to both sides of the equation: 3x = y + 4.

Subtract 4 from both sides of the equation: y = 3x - 4.

Therefore, the equation in slope-intercept form is y = 3x - 4. This represents a line with a slope of 3 and a y-intercept of -4. So the correct answer is option A: y = 3x - 4.

Choice #1 is better

To find the solution to this problem, we have to compute the are in each case, and divide each value by the corresponding cost in order to find the cost per square. The lower the cost, the better the offer because it will give you more pizza for your money Thus:

CHOICE 1:

Here the offer of Big Bob’s Pizza gives one slice of pizza from a pizza with a 22 inches diameter (then the radius is 11 inches) and is cut into 8 slices, so the area for the first entire pizza is:

[tex]A_{1}=\pi r^2=\pi(11)^2 \\ \\ A_{1}=121 \pi in^2[/tex]

Each slice has an area of:

[tex]A_{slice}=\frac{121 \pi}{8} \\ \\ A_{slice}=47.51in^2[/tex]

Finally, the cost per square inch is:

[tex]C=\frac{4.95\$}{47.51in^2}=0.10\$[/tex]

CHOICE 2:

Here the offer of Big Bob’s Pizza gives: An entire personal-size pizza that has a diameter of 6 inches (then the radius is 3 inches), so the area for the entire pizza is:

[tex]A_{2}=\pi r^2=\pi(3)^2 \\ \\ A_{2}=28.27 in^2[/tex]

Finally, the cost per square inch is:

[tex]C=\frac{3.75\$}{28.27in^2}=0.13\$[/tex]

CONCLUSION: Choice #1 gives you more pizza for your money because the cost per square inch is less than the other option.

The special at Big Bob's Pizza which will give you more pizza for your money is Choice #1. Per square inch, Choice #1 will cost less and give more overall pizza at $0.10 a square inch then Choice #2 at $0.13 per square inch. You can find more pizza for your money, by using the area formula for a circle for each pizza and finding the price per square inch of each serving. This is called a unit rate and is the cost per unit.

a. Find the radius of each pizza.

Since a pizza is a circle shape, it has a diameter and radius. The diameter is the distance across the pizza and the radius is half the diameter. We use the radius to find the area.

b. Find the area of each pizza using [tex]A = \pi r^{2}[/tex].

       [tex]A = \pi r^{2} \\A = \pi (11)^{2} \\A = 121\pi \\A= 379.94[/tex]

       The area of one slice is [tex]\frac{379.94}{8} = 47.49.[/tex]

       [tex]A = \pi r^{2} \\A = \pi (3)^{2} \\A = 9\pi \\A= 28.26[/tex]

c. Divide each area by the price.

        [tex]\frac{4.95}{47.49} = 0.10[/tex]

       [tex]\frac{3.75}{28.26} = 0.13[/tex]

Grade: 8th Grade

Subject: Geometry

Chapter: Applications for Area of Shapes

Keywords: circle, area, radius, diameter, cost, unit rate

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