A parking garage charges $22.50 for the first hour and $2.50 for each additional hour. Write and solve an equation to find how many hours you can park in the garage for $30. Use "x" to represent the number of hours.​

f(x) = x² - 6x - 1

To find the axis of symmetry, use the axis of symmetry formula: -b\2a, according to the Quadratic Equation y = Ax² + Bx + C. You understand?

Answer:

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

Step-by-step explanation:

To find axis of symmetry we use formula

[tex]x=\frac{-b}{2a}[/tex]

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

a=1, b=3

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

[tex]f(x) = x^2 -3x - 3[/tex]

a=1, b=-3

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

[tex]f(x) = x^2 + 6x + 3[/tex]

a=1, b=6

[tex]x=\frac{-6}{2}=-3[/tex]

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

a=1, b=-6

[tex]x=\frac{6}{2}=3[/tex]

Answer:

y=4x+27

Step-by-step explanation:

y+5=4(x+8)= (5-)y+5=4x+32(-5)

y=4x+27

Step-by-step answer:

Let's attack the left side:

log_8 12 = log (base 8) 12 = log(12)/log(8) = 1.1949875 (approx.)

Next solve

log_8 12 = x-2

log(12)/log(8) = x-2

x = 2 + log(12)/log(8)

= 3.195 (to one thousandth)

For this case we have the following expression:

[tex]log_ {8} (12) = x-2[/tex]

We rewrite how:

[tex]x-2 = log_ {8} (12)[/tex]

We add 2 to both sides of the equation:

[tex]x = log_ {8} (12) +2[/tex]

We rewrite [tex]log_ {8} (12)[/tex] as[tex]log_ {8} (2 ^ 2 * 3):[/tex]

[tex]x = log_ {8} (2 ^ 2 * 3) +2[/tex]

We apply logarithm properties:

[tex]x = log_ {8} (2 ^ 2) + log_ {8} (3) +2[/tex]

We apply logarithm properties:

[tex]x = 2log_ {8} (2) + log_ {8} (3) +2[/tex]

The logarithmic base 8 of 2 is [tex]\frac {1} {3}:[/tex]

[tex]x = 2 (\frac {1} {3}) + log_ {8} (3) +2\\x = \frac {2} {3} + log_ {8} (3) +2[/tex]

We simplify:

[tex]x = \frac {2} {3} + 2 + log_ {8} (3)\\x = \frac {2 + 6} {3} + log_ {8} (3)\\x = \frac {8} {3} + log_ {8} (3)[/tex]

Decimal form:

3,195

Answer:

[tex]x = \frac {8} {3} + log_ {8} (3) = 3,195[/tex]

Answer:

y - 12 = - 5(x + 2)

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

Given f(x) = - 5x + 2 ← in slope- intercept form with slope m = - 5

using m = - 5 and (a, b) = (- 2, 12), then

y - 12 = - 5(x - (- 2)), that is

y - 12 = - 5(x + 2) ← on point- slope form

Answer:

a                        y – 12 = –5(x + 2)

Step-by-step explanation:

Answer:

The radius of the base is [tex]r=6.3\ in[/tex]

Step-by-step explanation:

we know that

The volume of a cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]V=288\ in^{3}[/tex]

[tex]h=7\ in[/tex]

[tex]\pi=3.14[/tex]

substitute and solve for r

[tex]288=\frac{1}{3}(3.14)r^{2} (7)[/tex]

[tex]864=(3.14)r^{2} (7)[/tex]

[tex]r^{2}=864/[(3.14)(7)][/tex]

[tex]r=6.3\ in[/tex]

Answer:

d = 28 cm

r = 14 cm

Step-by-step explanation:

Circumference = Pi × Diameter

( Divide both sides by Pi )

Circumference ÷ Pi = Diameter

28 ÷ π = Diameter

Diameter = 28

Radius = Half the diameter

28 ÷ 2 = 14

Answer:

true

Step-by-step explanation:

1/10=0.1

0.1*2=0.2

By property of fraction, 0.2 is 1/10 of 2 is true.

By the property of fraction we know that 1/x times of a is a/x where a and x are two non-zero real numbers.

Given statement is 1/10 of 2

Thus we have, 1/10*2 = 2/10

And, 2/10 = 0.2 .

Therefore, by property of fraction, 0.2 is 1/10 of 2 is true.

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Answer:

Step-by-step explanation:

To create a system of inequalities, write an inequality to model each condition that must be satisfied in the given situation.

It is given that x represents the area of the base of the barrel in square feet and y represents the volume of the pump in cubic feet.

Write an inequality to represent the amount of water that the barrel needs to hold after the pump is inserted. To find the volume of the barrel, multiply the area of the base by the height of the barrel. Then subtract the volume that will be taken up by the pump from that amount.

x(x-4) - y ≤ 90

To find the cost of the supplies for the barrel, find the surface area by multiplying the perimeter of the base by the height of the barrel and then adding the area of the base. Since there is no top, the area of the base only needs to be added once. Then, multiply the cost per square foot by the surface area.

To find the cost of the pump, multiply the cost per square foot of the pump by its volume.

Write an inequality representing the total cost. The cost must be less than or equal to $1,100.

8(x(x-4)+x) + 50y ≤ 1,100

Combining both of the inequalities gives the following system of inequalities.

x(x-4) - y ≤ 90

8(x(x-4)+x) + 50y ≤ 1,100

Answer:

The answer is

x(x-4) - y GREATER THAN OR EQUAL TO 90

8(x(x-4) + x) +50y LESS THAN OR EQUAL TO 1,100

Step-by-step explanation:

Answer:

i believe its positive

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

Answer:

360 and 60.

Step-by-step explanation:

Let Christopher earns x amount of money and y be money earned by Michael.

Firstly, Christopher has six times as much money as Michael so,

x=6y........ (i)

If Michael earns $80 and Christopher earns $60, Christopher will then have three times as much money as Michael so,

x+60=3(y+80)

From (i),

6y +60= 3(y+80)

3(2y+20)=3(y+80)

2y+20=y+80

2y-y=80-20

y=60

Substituting value of y in equation (i),

x=6×60=360.

Therefore, Christopher earned 360 and Michael earned 60.

Final answer:

Initially, Michael has $60, and Christopher has $360. After Michael earns $80 and Christopher earns $60, Michael will have $140, and Christopher will have $420.

Explanation:

Let's denote Christopher's initial amount of money as C and Michael's initial amount of money as M.

According to the given information, Christopher has six times as much money as Michael: C = 6M.

When Michael earns $80, and Christopher earns $60, Christopher will then have three times as much money as Michael: C + $60 = 3(M + $80).

Now we can solve these two equations together:

C = 6M

C + $60 = 3(M + $80)

Substitute the expression from the first equation into the second equation:

6M + $60 = 3(M + $80)

6M + $60 = 3M + $240

Combine like terms:

6M - 3M = $240 - $60

3M = $180

Divide both sides by 3:

M = $60

Use the value of M to find C:

C = 6M = 6 × $60

C = $360

Now, adding their respective earnings:

Michael's new total: $60 + $80 = $140

Christopher's new total: $360 + $60 = $420

Answer:

QR

Step-by-step explanation:

KLMN is in the same spot as PQRS

Answer:

QR corresponds to LM

Step-by-step explanation:

Two figures are said to be similar if they have same shape but not necessarily same size.

Two polygons are said to be similar if their corresponding angles are equal and corresponding sides are proportional .

A trapezoid is a polygon in which a pair of sides is parallel .

Here, two trapezoids are given i.e KLMN, PQRS.

As KLMN and PQRS are similar, so their angles are equal i.e

[tex]\angle K=\angle P\,,\,\angle L=\angle Q\,,\,\angle M=\angle R\,,\,\angle N=\angle S[/tex]

Also, corresponding sides are proportional i.e

[tex]\frac{KL}{PQ}=\frac{LM}{QR}=\frac{MN}{RS}=\frac{KN}{PS}[/tex]

Therefore, side QR corresponds to LM.

Check the picture below.

clearly the angle at vertex C isn't the right angle, so let's check if AB ⟂ BC.

[tex]\bf A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad B(\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-3}{0-(-4)}\implies \cfrac{-4}{0+4}\implies \cfrac{-4}{4}\implies -1 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf B(\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-1)}{2-0}\implies \cfrac{1+1}{2}\implies \cfrac{2}{2}\implies 1 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{-1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{1}\implies 1}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{so is a right triangle}}{AB\perp BC}~\hfill[/tex]

Answer:

7

Step-by-step explanation:

Average value of a function F(t) on interval [a,b]

is [tex] \frac{1}{b-a} \int_a^b F(x)dx[/tex]

So let's plug it in!

a=0

b=9

F(x)=(x-4)^2

To integrate (x-4)^2 just use power rule for integration.

So this what we get

[tex] \frac{1}{9-0} \frac{(x-4)^3}{3}|_0^9 [/tex]

[tex] \frac{1}{9-0} [\frac{(9-4)^3}{3}-\frac{(0-4)^3}{3}] [/tex]

[tex] \frac{1}{9} [\frac{5^3}{3}-\frac{(-4)^3}{3}] [/tex]

[tex] \frac{1}{9} \cdot \frac{125+64}{3} [/tex]

[tex] \frac{1}{9} \cdot \frac{189}{3} [/tex]

7

Answer:

Using digits it would look like 5,000,900

A rectangle is the shape with parallel opposite sides, combined with all the 90 degree angles. As the type of the parallelogram, it has the opposite parallel sides. In the rectangle, 1 set of parallel sides is longer than the other, making it look like an elongated square

The rectangle field is 400 meters long and 300 meters wide. What is the area in square kilometers?

1km=1000m

Secondly the area of the rectangle is defined as the product of the width or the height:

A= w∗h

We could now approach the problem in 2 ways, we convert the sides of the rectangle to kilometers 1st and we convert the area from square meters to the square kilometers.

Let w = width, h = height and A = area

w=300m=300/1000m=0.3km

h=400m=400/1000m=0.4km

A=0.3∗0.4km2=0.12km2

Let's first calculate the area in square meters:

Am=300∗400=120000m2

We know from above that 1km=1000m

That gives 1km2=1000∗1000m2=1000000m2

So Ak=Am/1000000=0.12km2

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the area of the rectangular field is 0.12 square kilometers.

To calculate the area of a rectangular field in square kilometers, you need to multiply the length and width of the field and then convert the result from square meters to square kilometers. Given that the rectangular field is 400 meters long and 300 meters wide, the area in square meters is calculated as follows:

Area = length × width = 400 m × 300 m = 120,000 m2

Since 1 square kilometer (km2) is equal to 1,000,000 square meters (m2), you convert square meters to square kilometers by dividing by 1,000,000:

Area in square kilometers = Area in square meters / 1,000,000 = 120,000 m2 / 1,000,000 = 0.12 km2

Therefore, the area of the rectangular field is 0.12 square kilometers.

If a function is even, it gives the same result for positive and negative inputs such as 8 and -8.

From the choices, the even functions are D and A.

D because the absolute value thing makes any input positive, and A because any number raised to an even power gives a positive result.

A function assigns the value of each element of one set to the other specific element of another set. The correct options are A and D.

A function assigns the value of each element of one set to the other specific element of another set.

A function is an even function if f of x is equal to f of −x for all the values of x.

A.)

f(x) = x⁴ - x²

f(-x) = (-x)⁴ - (-x)²

      = x⁴ - x²

Since f(x) and f(-x) are equal, therefore, the given function is a function.

B.)

f(x) = x² - 3x + 2

f(-x) = (-x)² - 3(-x) + 2

      = x² + 3x + 2

Since f(x) and f(-x) are not equal, therefore, the given function is a function.

C.)

f(-x) = √[(-x)- 2]

      = √(-x- 2)

Since f(x) and f(-x) are not equal, therefore, the given function is a function.

D.)

f(x) = |x| = x

f(-x) = |-x| = x

Since f(x) and f(-x) are equal, therefore, the given function is a function.

Hence, the correct options are A and D.

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Answer:

A. Multiplicative Inverse Property

X=1

Step-by-step explanation:

First, you do is multiply fractions from left to right.

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

Then, you can cancel the fraction out.

Common factor term of 2.

[tex]=\frac{3}{3}[/tex]

Divide the numbers.

[tex]\frac{3\div3=1}{3\div3=1}=1[/tex]

[tex]x*1=1[/tex]

X=1 is the correct answer.

Multiplicative Inverse Property is the correct answer.

The number of the sides of the polygon will be 15. Then the correct option is A.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Each exterior angle of a regular polygon measures 24°.

Then the number of the sides of the polygon will be

Let n be the number of the sides. Then we have

360° / n = 24°

          n = 360° / 24°

          n = 15

Then the number of the sides of the polygon will be 15.

Then the correct option is A.

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Answer:

2

Step-by-step explanation:

The median is the middle. The middle of 5 numbers is the third number. the list goes through 12235 so the median is 2

Answer:

f(-2) = 1/9

Step-by-step explanation:

Plug in -2 to x in the equation:

f(x) = 3^x

f(-2) = 3^(-2)

Solve. Note that if there is a negative in the power, you must flip the "fraction" and set it over 1. The answer itself does not become negative:

f(-2) = 1/(3^2)

f(-2) = 1/(9)

f(-2) = 1/9 is your answer.

~

[tex]\frac{1}{9}[/tex]

Answer:

the answer is the second one

Answer:

The correct answer is "Sandwiches and salads are almost equally preferred."  

Step-by-step explanation:

From the survey, we get

122 students prefers Sandwich

15 students prefers Hot Dog

123  students prefers Salad

We are going to analyse every option

A sandwich is the most preferred lunch.  FALSE

Most preferred lunch is Salad (123) ,  sandwich is 122

Sandwiches and salads are almost equally preferred.  TRUE

A hot dog is two times more popular than sandwich. FALSE

No,  hot dog is 15 ,  and sandwich is 122,  sandwich is more popular than hot dog

A salad is almost two times more popular than a hot dog. FALSE

No,  hot dog is just 15 , and salad 123 more than 8 times hot dog

Answer:  see graph

Step-by-step explanation:

Set each equation equal to y, then graph each equation.

y = -x² + x + 6      (parabola)

y = 2x + 8            (line)

Notice that the system has NO SOLUTION because the parabola and the line never intersect.

The given equation represents the inconsistent system (It has no solution).

The graphs of a system that does not have any point of intersection are said to be inconsistent system. Which means the system has no solution.

The given system of equations as

[tex]y=-x^2+x+6[/tex] and [tex]y=2x+8[/tex]

So, plotting these equations in the graph,

We get a curve and a line that do not have any intersections.

So, the given system has no solution.

Therefore, the given system is an inconsistent system.

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Answer:

(3)(-16)(-7)(-14) = (-48)(-7)(-14) = (+336)(-14) = - 4704;

Step-by-step explanation:

Answer:

There are 52 such numbers that have even divisors.

Step-by-step explanation:

All the  numbers between 2 and 59 have an EVEN number of positive divisors.

Except the Perfect Squares..

or 4, 9, 16, 25, 36 and 49, which have 3 divisors each.

So:

59 - 2 + 1 =58

Now subtract 58 from 6 (perfect squares)

58- 6=52

Therefore,it means that there are 52 such numbers that have EVEN divisors....

Answer:

52

Step-by-step explanation:

Answer:

Scalene

Step-by-step explanation:

Note the definition of each triangle:

Equilateral: For a triangle to be an Equilateral, all sides must have the same measurements.

Isosceles: For a triangle to be an Isosceles, the two leg sides must be congruent. The base can vary, but cannot equal the leg sides.

Scalene: For a triangle to be an Scalene, none of the sides can be congruent.

~

Answer:

scalene

Step-by-step explanation:

an scalene triangle has sides of all different lengths

Answer:

The value for c is B. 49

Answer:

7

Step-by-step explanation:

-|-7|=

-1 (|-7) =

|-7| = absolute value of |-7| is 7 because an absolute number is always positive.

the minus symbol should be -1.

so the sum is -1(7) = -7

the opposite of -7 is 7

Answer:

Step-by-step explanation:

the opposite of -|-7| is : - (-|-7|) = 1+7l

Answer:

c=−35

Step-by-step explanation:

Let's solve your equation step-by-step.

−5=

c

7

Step 1: Simplify both sides of the equation.

−5=

1

7

c

Step 2: Flip the equation.

1

7

c=−5

Step 3: Multiply both sides by 7.

7*(

1

7

c)=(7)*(−5)

[tex]\frac{c}{7} = -5[/tex]

***I switched the order of c/7 and -5. It means the same thing, but I just find it easier this way

To solve for c you must isolate this by bringing 7 to the other side. To do this you must multiply 7 to both sides. This will cancel 7 from the left side (the right side in the way the equation is written in the question) and bring it over to the right side

[tex]7(\frac{c}{7} ) = -5 * 7[/tex]

c = -35

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

–3, –9.6, –22.8

Step-by-step explanation:

Given rule is:

[tex]A(n) =-3+(n-1)(-2.2)[/tex]

So,

For first term:

[tex]A(1) =-3+(1-1)(-2.2)\\A(1) = -3 +0\\= 0[/tex]

For fourth term:

[tex]A(4) =-3+(4-1)(-2.2)\\=-3+(3)(-2.2)\\=-3+ (-6.6)\\=-3-6.6\\= -9.6[/tex]

For tenth term:

[tex]A(10) =-3+(10-1)(-2.2)\\=-3+(9)(-2.2)\\=-3+ (-19.8)\\=-3-19.8\\= -22.8[/tex]

The first, fourth and tenth terms are -3, -9.6 and -22.8 respectively.

So, third option is correct ..