Solve the inequality and graph its solution: x - 7>-20
A x>-13
-12
6
0
6
12
18
24
30
-30 -24 -18
B. x>-13
-6
0
6
12
18
24
30
-30 -24 -18 -12
cx<-27
6
0
6
12
18
24
30
-3024 -18 -12
X<-27
D.
+
+ +
--3026 -18
1
-12
6
0
6
12
18
24
30

Answer:

Step-by-step explanation:

The question is asking for a system of equations, which make explanations easy. :)

Define the variables. Setting [tex]x[/tex] to the number of clubhouse seats sold and [tex]y[/tex] to the number of grandstand seats sold will be sufficient. The "let statement[s]" will be:

The number of equations shall be no less than the number of variables for the solution to be unique. There are two variables. It will take at least two equations to find a unique solution.

Everyone at the race need a seat. The number clubhouse seats plus the number of grandstand seats shall be the same as the number people at the race. There were 36,000 people. Therefore the first equation shall be:

[tex]x + y = 36000[/tex].

Every clubhouse seat will add $12.00 to the receipt. [tex]x[/tex] clubhouse seats will add $[tex]12\;x[/tex] to the receipt. Similarly, [tex]y[/tex] grandstand seats will add $[tex]5\;y[/tex] to the receipt. The two values shall add up to $250,000.

Drop the dollar sign to get the second equation:

[tex]12\;x +5\;y =250000[/tex].

Hence the system:

[tex]\displaystyle \left\{\begin{aligned}& x + y = 36000 && \textcircled{\raisebox{-0.9pt}1}\\ & 12\;x + 5\;y = 250000 && \textcircled{\raisebox{-0.9pt}2}\end{aligned} \phantom{\small credit for the raisebox hack: tex[dot]stackexchange[dot]com/questions/7032/good-way-to-make-textcircled-numbers}[/tex].

Solve this system.

The first non-zero coefficient in equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is already one. That's the coefficient for [tex]x[/tex]. Use multiples of equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get rid of [tex]x[/tex] in other equations (equation [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] in this case.)

[tex]-12[/tex] times equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is

[tex]-12 \;x - 12\;y = -432000[/tex].

Add [tex]-12\times \textcircled{\raisebox{-0.9pt}1}[/tex] to [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] to get:

[tex]0\;x + -7\;y = -182000[/tex].

Divide both sides by -7 to get:

[tex]y = 26000[/tex].

Add -1 times this equation to equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get:

[tex]x = 10000[/tex].

That is:

[tex]\displaystyle \left\{\begin{aligned}&x = 10000\\&y = 26000\end{aligned}[/tex].

In other words,

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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Answer:

25% Increase

Step-by-step explanation:

[(350 - 280) / 280] × 100% = 0.25 × 100% = 25%

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!

Answer:

5000 g

Step-by-step explanation:

5000 g = 11.02311 lb

10 lb​ = 4535.92

[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]

Step-by-step answer:

Given:

5% annual interest (APR)

compounded daily

Principal = 500

Solution:

Since it is compounded daily, we first calculate the

daily rate =  5% / 365 = 0.05/365

After one year,

future value

= 500 ( 1 + 0.05/365)^365

= 525.634 (to the tenth of a cent)

note: sometimes a year is considered to be rounded to 360 days, or 366 days for a leap year, but there is practically no difference in the results for this problem.

Final answer:

To calculate the future value of a $500 deposit with a 5% annual interest rate compounded daily for one year, we use the compound interest formula. The resulting amount is approximately $525.64.

Explanation:

To calculate the value of a $500 deposit in a credit union that pays 5% annual interest compounded daily, we will use the formula for compound interest:

A = P(1 + (r/n))^(nt)

Where:

A = the amount of money accumulated after n years, including interest.

P = the principal amount (the initial amount of money).

r = the annual interest rate (decimal).

n = the number of times that interest is compounded per year.

t = the time the money is invested or borrowed for, in years.

Using the given information:

P = $500

r = 5% or 0.05 (as a decimal)

n = 365 (since the interest is compounded daily)

t = 1 year

Substituting the values into the formula:

A = 500(1 + (0.05/365))^(365*1)

After calculating, we get:

A ≈ $525.64

Therefore, the value of the $500 deposit at the end of one year with daily compounding at a 5% annual interest rate is approximately $525.64.

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.

[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]

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:

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:

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:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}10x+2y=64&\text{multiply both sides by 2}\\3x-4y=-36\end{array}\right\\\underline{+\left\{\begin{array}{ccc}20x+4y=128\\3x-4y=-36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad23x=92\qquad\text{divide both sides by 2}\\.\qquad x=4\\\\\text{put the value of x to the first equation:}\\\\10(4)+2y=64\\40+2y=64\qquad\text{subtract 40 from both sides}\\2y=24\qquad\text{divide both sides by 2}\\y=12[/tex]

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

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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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.

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:

The approximate value of angle theta is [tex]57.8\°[/tex]

Step-by-step explanation:

we have that

[tex]cos(\theta)=8/15[/tex]

so

using a calculator

[tex]\theta=arccos(8/15)=57.8\°[/tex]

Answer:

for plato or edmentum its option A 50 degrees

Step-by-step explanation:

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:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = [tex]\frac{1}{2}[/tex] and (a, b) = (5, 1), so

y - 1 = [tex]\frac{1}{2}[/tex](x - 5)

The equation that represents a line that passes through (5, 1) and has a slope of 1/2 is; C: y - 1 = ¹/₂(x - 5)

The formula for equation of a line in point- slope form is expressed as;

y - b = m(x - a)

where;

m is the slope of line

(a, b) is a coordinate point on the line

In this question, we are given;

m = 1/2  and (a, b) = (5, 1)

Thus equation of the line is;

y - 1 = ¹/₂(x - 5)

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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:

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:

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.

Answer:

-0.41 radians

Step-by-step explanation

(Credit goes to calculista)

let

A---> the angle

if sin A=-0.4

then 

A=sin-1(-0.4)

using a calculator

A=-23.578°----> the angle A belong to the IV quadrant

convert to radians

if pi radians--]----> 180°

x--------> -23.578°

x=-23.578*pi/180----> x=-0.41 radians

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Answer:

C. –0.41

Step-by-step explanation:

Answer:

The surface area increases by 4 times

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the surface area of the new rectangular prism

y ---> the surface area of the original rectangular prism

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=2[/tex] ----> because is doubled

[tex]y=254\ in^{2}[/tex]

substitute and solve for x

[tex]2^{2}=\frac{x}{254}[/tex]

[tex]x=(4)254=1,016\ in^{2}[/tex] ----> surface area increases by 4 times.

Answer:

The surface area increases by four times.

Step-by-step explanation:

Answer:

The third quartile is:

[tex]Q_3=29[/tex]

Step-by-step explanation:

First organize the data from lowest to highest

4, 5, 10, 12, 14, 16, 18, 20, 21, 21, 22, 22, 24, 26, 29, 29, 33, 34, 43, 44

Notice that we have a quantity of n = 20 data

Use the following formula to calculate the third quartile [tex]Q_3[/tex]

For a set of n data organized in the form:

[tex]x_1, x_2, x_3, ..., x_n[/tex]

The third quartile is  [tex]Q_3[/tex]:

[tex]Q_3=x_{\frac{3}{4}(n+1)}[/tex]

With n=20

[tex]Q_3=x_{\frac{3}{4}(20+1)}[/tex]

[tex]Q_3=x_{15.75}[/tex]

The third quartile is between [tex]x_{15}=29[/tex] and [tex]x_{16}=29[/tex]

Then

[tex]Q_3 =x_{15} + 0.75*(x_{16}- x_{15})[/tex]

[tex]Q_3 =29 + 0.75*(29- 29)\\\\Q_3 =29[/tex]

Answer:

29

Step-by-step explanation:

[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:

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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Answer:

x = 2.

Step-by-step explanation:

8(4-x) = 7x + 2​

32 - 8x = 7x + 2

32 - 2 =  7x + 8x

15x = 30

x =2.