A fmaily wants to rent a van for a four day camping trip. The rental cost is $32.00 per day plu s$0.15 per miles driven. Their vacation budget allows them to spend $225.00 to rent the van. Which expression represents the number of miles that they can drive without going over their budget?

Answer:

The equation which reveals the minimum value for the equation is  2·x² + 12·x - 14 = 0 is the option;

2·(x + 3)² = 32

Step-by-step explanation:

The given function can be presented as follows;

2·x² + 12·x - 14 = 0

The quadratic equation in standard form is a·(x - h)² + k

Where;

(h, k) is the vertex of the parabola

Given that the coefficient of the x² is positive, the graph is U-shaped and the lowest point is given by the vertex of the graph as follows;

2·x² + 12·x - 14 = 2·x² + 12·x - 14 = 2·(x² + 6·x - 7) = 0

2·(x² + 6·x - 7) = 2·(x² + 6·x + 9 - 7 - 9) = 2·((x + 3)² - 16)

2·((x + 3)² - 16) = 2·(x + 3)² - 32 = 0

∴ 2·x² + 12·x - 14 = 2·(x + 3)² - 32 in vertex form

The minimum value (vertex, (h, k)) for the equation = (-3, -32)

Therefore, the equation which reveals the minimum value for the equation is 2·(x + 3)² = 32

Answer:

2(x + 3)2 = 32

Step-by-step explanation:

I took the test.

Answer:

x = -8

Step-by-step explanation:

Answer:

583 student tickets

Step-by-step explanation:

This question is likely asking us to set up a system of equations. Let us say that:

x represents the number of student tickets  

y represents the number of non-student tickets

We know that there were a total of 874 tickets sold, so:

x + y = 874

We also know that every student ticket was sold for $3 and every non-student ticket was sold for $7. We also know the total sales, so:

3x + 7y = 3786

These are our two equations. We can use substitution to solve for the number of student tickets, x:

x + y = 874

y = 874 - x

3x + 7y = 3786

3x + 7(874 - x) = 3786

3x + 6118 - 7x = 3786

-4x = -2332

x = 583 student tickets

Answer:

204 ft^2

Step-by-step explanation:

triangle on the left:

A= l x w x 1/2

A = 12 x 5 x 1/2

A = 30 ft^2

triangle on the right:

Same thing

A = 30 ft^2

square in the middle:

A = l x w

A = 12 x 12

A = 144 ft^2

Add them up:

30 + 30 + 144 = 204 ft^2

Answer: $119

Step-by-step explanation:

Let's take this equation

85(n)

n will equal 1.40 as the price mark up is 140%

85(1.40)

$119

Answer:

4 a + 2 a^2 - 8 a^3 + 3 a^2 b - 12

Step-by-step explanation:

Simplify the following:

3 (b a^2 - 4) + a (-8 a^2 + 2 a + 4)

Hint: | Distribute a over -8 a^2 + 2 a + 4.

a (-8 a^2 + 2 a + 4) = -8 a^3 + 2 a^2 + 4 a:

-8 a^3 + 2 a^2 + 4 a + 3 (b a^2 - 4)

Hint: | Distribute 3 over a^2 b - 4.

3 (a^2 b - 4) = 3 a^2 b - 12:

Answer: 4 a + 2 a^2 - 8 a^3 + 3 a^2 b - 12

Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

2x+3y=16

3x+4y=22

---------------

3(2x+3y)=3(16)

-2(3x+4y)=-2(22)

--------------------------

6x+9y=48

-6x-8y=-44

------------------

y=4

2x+3(4)=16

2x+12=16

2x=16-12

2x=4

x=4/2

x=2

Answer: 4,5

Step-by-step explanation:

The actual length of the Olympic-size swimming pool which is drawn by Christina on the scale model is 50 meters.

Scale factor is the factor which is used to enlarge or smaller the original figure.

Scale factor is the ratio of representation measurement of the figure to the original figures.

Christina drew a scale model of an Olympic-size swimming pool using a scale in which 3 centimeters represents 10 meters.

Thus, the scale factor is for cm to m,

[tex]r=\dfrac{3}{10}\rm[/tex]

The length of the pool in her drawing is 15 centimeters. Let the length of the actual pool is x cm. Thus,

[tex]\dfrac{15}{x}=\dfrac{3}{10}\\x=50\rm \; m[/tex]

Thus, the actual length of the Olympic-size swimming pool which is drawn by Christina on the scale model is 50 meters.

Learn more about the scale factor here;

https://brainly.com/question/10253650

Answer:

Its C

Step-by-step explanation:

:D

Answer:

B

Step-by-step explanation:

To test a circuit he does not need to gather opinions

Answer:

b

Step-by-step explanation:

Answer:

JM = 20

Step-by-step explanation:

Find the value of JM

Using similar triangles;

MJ/HN = GJ/HK

GJ+JM/HN = GJ/HK

15+JM/12+16 = 15/12

15+JM/28 = 15/12

Cross multiply

12(15+JM) = 15*28

180+12JM = 420

12JM = 420 - 180

12JM = 240

JM = 240/12

JM = 20

Hence the length of JM is 20

Answer:

$136

Step-by-step explanation:

$42.50 divided by 5= 8.5 per pizza

So you do 8.5x16 pizzas to get $136 for 16 pizzas.

Answer:

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4

Answer:

Step-by-step explanation:

so common factors are 1, 3,9 and 27

Answer:

p+37 = 2p-50

87

m<I=124

Step-by-step explanation:

Answer:

$804

Step-by-step explanation:

33%=0.33----Covert the percentage as a decimal.

0.33*1200=396----Multiply the decimal by the price of budget. This is the cost of equipment.

$1200-$396=$804----Subtract the cost of equipment ($396) by the cost of budget($1200). You get $804!

Hope this helped.

Answer:

804

Step-by-step explanation:

what the other person said

Answer: y= 2/5 * x - 6

Step-by-step explanation:

y intercept

y= 2/5 x+b putting in the point 5,4

y=2/5 5+ b

4=10+b

b= -6

Answers:

1. D po

Step-by-step explanation:

i hope its hepl

Answer:

40.64 feet

Step-by-step explanation:

Answer:

The height of the bridge is 71.47 m.

Step-by-step explanation:

Since the eye of the surveyor is 1.45m creating the horizontal distance, we must add the 1.45 m to the 70.02 m to determine the total height of the bridge.

70.02 m + 1.45 m = 71.47 m

The height of the bridge is 71.47 m.

Answer:

see explanation

Step-by-step explanation:

∠ 1 + ∠ 2 = 90, that is

x + x - 8 = 90

2x - 8 = 90 ( add 8 to both sides )

2x = 98 ( divide both sides by 2 )

x = 49

Answer:

18 miles

Step-by-step explanation:

6% of 300 miles is 18 miles

Answer:

Step-by-step explanation:

y

=

4

−

2

x