Yesterday, the price of a gallon of gas at five gas stations was $3.56, $3.71,
$3.62, $3.93, and $3.83, respectively, but today each gas station raised it:
price by $0.08. What is today's mean price of a gallon of gas at the five
stations?
O A. $3.81
O B. $3.65
O C. $3.89
O D. $3.73

Answer:

[tex]p(x)=-5(x-12)^2+405[/tex]

Step-by-step explanation:

Hi there!

Vertex form: [tex]f(x)=a(x-h)^2+k[/tex]

[tex]p(x)=-5x^2+120x-315[/tex]

Factor out -5 from the first two terms

[tex]p(x)=-5(x^2-24x)-315[/tex]

Complete the square by adding [tex](\frac{24}{2} )^2[/tex] (the square of half of the x-coefficient)

[tex]p(x)=-5(x^2-24x+(\frac{24}{2} )^2)-315-(-5)(\frac{24}{2} )^2[/tex]

We're subtracting [tex](-5)(\frac{24}{2} )^2[/tex] because we need to keep the equation balanced and we can't just add new values.

Complete the square

[tex]p(x)=-5(x-(\frac{24}{2} ))^2-315-(-5)(\frac{24}{2} )^2[/tex]

Simplify

[tex]p(x)=-5(x-12)^2-315+720\\p(x)=-5(x-12)^2+405[/tex]

Summary:

I hope this helps!

Roller coaster B has greater top speed than roller coaster A.

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.

Given,

speed of roller coaster A = 110ft./s

speed of roller coaster B = 85mph

1 mile = 5280 feet

⇒ 85 mile = 5280 × 85 = 448800 feet

1 hour = 3600 seconds

speed of roller coaster  B = 448800/3600 ft/s = 124.67 ft/s

comparing speed of both

Speed of roller coaster B > speed of roller coaster A

Hence roller coaster B has greater top speed.

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Answer:

$25.22

Step-by-step explanation:

26 x .03= 0.78

26-0.78= $25.22

i hope this helps :)

The total length of the two boards put together is 5ft 11in.

Length is a measure of distance. It is typically measured in units such as inches, feet, yards, miles, millimeters, centimeters, and meters. Length can also be measured in other units, such as the amount of time it takes to travel a certain distance. Length is an important concept in mathematics and is used in many different topics and applications.

To simplify this answer in feet, we can convert the 10 inches and 9 inches to feet, giving us a total of 5 feet. Therefore, the total length of the two boards put together is 5ft.

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Answer:

y=(7)^x represents the exponential growth

Answer:y=(7)^x exponential growth, and do you use monarch aop? cause i do and i was wondering

Step-by-step explanation:

The number of months Mark can have the phone is given by the equation

A = 11.4 months

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of months be represented as = A

Now , the equation is

Now , the total amount with Mark = $ 146.43

The initial amount for the smartphone = $ 33

The amount per month for 2GB is = $ 9.95

So , the amount for A months = $ 9.95 ( A )

So , the equation will be

Initial amount for the smartphone + the amount for A months = total amount with Mark

Substituting the values in the equation , we get

33 + 9.95 ( A ) = 146.43   be equation (1)

On simplifying the equation , we get

Subtracting 33 on both sides of the equation , we get

9.95 ( A ) = 113.43

Divide by 9.95 on both sides of the equation , we get

A = 11.4 months

Therefore , the value of A is 11.4 months

Hence , the number of months is 11.4 months

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By adding the weight of the triangle, the weight of the circle heavier than that of the square.

The linear equation that results from examining the weights will contain the following parameters.

Let t stand for the triangle.

Let c stand for the circle.

Let's use the shape square.

left side of the equation = 6s + 3t

right side of the equation = 3s + 3c

equating both sides

6s + 3t = 3s + 3c

6s - 3s + 3t = 3s + 3c

3s + 3t = 3c

3(s + t) = 3c

dividing all through by 3

s + t = c

10 + t = c

Because of the resulting equation, we can conclude that the the circle is weightier than the square by the weight of the triangle

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Let the numbers be x and 4x. So, according to the question,

x + 4x = 100

=> 5x = 100

=> x = 100/5

=> x = 20

So, the number are,

x = 20

and

4x = 4×20 = 80

So, the two numbers are 20 and 80.

Answer:

it answer is 180

Step-by-step explanation:

plz mark me as brainlist

Answer:

[tex]\huge\boxed{\fcolorbox{green}{violet}{Answer}}[/tex]

[tex]144(x - 36) \\ = 144 \times x - 144 \times 36 \\ = 144x - 5184 \\ x = \frac{5184}{144} \\ x = 36[/tex]

Answer:

A) 1 line of symmetry

Step-by-step explanation:

The exponential expression is (√4×√2)².

Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.

The given number is √8.

Now, 8=(√4×√2)²

=(2×√2)²

= 4×2

= 8

Therefore, the exponential expression is (√4×√2)².

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"Your question is incomplete, probably the complete question/missing part is:"

Rewrite the exponential expression using factors of √8 so that the base of the equation is a product of two factors, with one factor being a perfect square.

Answer:

[tex] ln \: {x}^{ \sqrt{3} } = \sqrt{3} \: ln(x) [/tex]

We can write by power property of logarithm that [tex]logx^{\sqrt{3}}=\sqrt{3} logx[/tex]

A logarithm is the power to which a number must be raised in order to get some other number

We need to use the Property of Logarithms to write the logarithm as a product[tex]logx^{\sqrt{3}}[/tex]

We have a power property of logarithm that [tex]loga^{b} =bloga[/tex]

So Given logx to the power of root three

Here consider x as a and b as root 3.

[tex]logx^{\sqrt{3}}=\sqrt{3} logx[/tex]

Hence, We can write by power property of logarithm that [tex]logx^{\sqrt{3}}=\sqrt{3} logx[/tex]

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Answer:

26

Step-by-step explanation:

if she is 8 years older, then is just 34-8 which is 26

Answer:

The temp. started at -20. If it rose +8 degrees, then it would be -20+8=-12, because since the -20 and +8 are opposites, you would subtract them and the answer would have the sign of the larger number which is -. so -12 is the answer.

Step-by-step explanation:

since the -20 and +8 are opposites, you have to subtract them and you get -12

the temperature at midnight is -12 get it?

Answer:

It would be B.

Step-by-step explanation:

This is because adding a negative exponent onto a number is telling you how many times you have to divide it by. So in this case, it would be the equation 1 / 2^4 to solve it.

Answer:

answer is b friend

Step-by-step explanation:

Answer:

[tex] \frac{5}{6} * 20 = \frac{5 * 20}{6} = \frac{100}{6} = \frac{50}{3} = 16\frac{2}{3} [/tex]

Step-by-step explanation:

[tex] \frac{5}{6} * 20 [/tex]

Multiply

[tex] = \frac{5 * 20}{6} [/tex]

[tex] = \frac{100}{6} [/tex]

Simplicity by reducing the fraction. Divide the numerator and denominator by 2, respectively.

[tex] = \frac{50}{3} [/tex]

Divide 50 by 3 to get a mixed number

[tex] = 16\frac{2}{3} [/tex]

for an inequality graph, if the line is dashed, that means that the border line is not part of the shaded region, so any points on it are not a solution of it, any points inside the shaded region or "true" region are solutions to it, only if the border line is solid then the border is part of the "true" region, Check the picture below.

Answer:

B. 1

Step-by-step explanation:

I calculated it logically

Answer:

The correct answer bbbbb B. 1

Answer:

The answer is 28

Step-by-step explanation:

B×h ÷ 2

8×7 ÷ 2

Answer: W'' = (2, -3)Step-by-step explanation:Reflection over the x-axis negates the y-coordinate ...

Step-by-step explanation:

Answer:

About $982.

Step-by-step explanation:

The average cost is:

[tex]y = 1.182x + 19.096[/tex]

When the cost of a one-bedroom apartment is 815, we have [tex]x = 815[/tex], so we should expect the cost to be:

[tex]y = 1.182(815) + 19.066 = 982.4[/tex]

So:

About $982.

The given equation is a second order differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

Isaac Newton listed three kinds of differential equations given -

[tex]${\displaystyle {\begin{aligned}{\frac {dy}{dx}}&=f(x)\\[4pt]{\frac {dy}{dx}}&=f(x,y)\\[4pt]x_{1}{\frac {\partial y}{\partial x_{1}}}&+x_{2}{\frac {\partial y}{\partial x_{2}}}=y\end{aligned}}}[/tex]

Given is a differential equation as follows -

d²a/db² + a = 4b + 10sin(b)

The given equation is -

d²a/db² + a = 4b + 10sin(b)

Let y = a and x = b, then we can write -

d²y/dx² + y = 4x + 10sin(x)

A second order differential equation is one that expresses the second derivative of the dependent variable as a function of the variable and its first derivative. It is of the form -

d²y/dx² + P(x) dy/dx + Q(x) y = f(x)

For the equation given -

d²y/dx² + y = 4x + 10sin(x)

On comparing, we get -

P(x) = 0

Q(x) = 1

f(x) = {4x + 10sin(x)}

Therefore, the given equation is a second order differential equation.

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Step-by-step explanation:

Set the origin of the coordinate system at the top of the tower.

Given:

y = -234 ft (when the ball hits the ground)

v0 = +19ft/a

g = 32 ft/s^2

a) The equation of motion. for this freely-falling body is

y = v0t - (1/2)gt^2

When the ball hits the ground, t = T (time of flight)

----> -234 ft = (19 ft/s)T - (1/2)(32 ft/s^2)T^2

Rearranging the terms and dropping the units momentarily for brevity, we get

(16)T^2 - 19T - 234 = 0

This is a quadratic equation whose solution is

T = (1/32)[19 +- {(-19)^2 - 4(16)(-234)}]^(1/2)

= 4.46 s. or -2.68 s

Therefore, the time of flight T = 4.46 s

b) To find the velocity upon impact, we use

v = v0 - gt, where t = T = 4.46 s

= (19 ft/s) - (32 ft/s^2)(4.46 s)

= -123.7 ft/s

The negative sign means that its velocity is pointing down.

Answer:

Step-by-step explanation:

You want to know if the standard form quadratic equation ax² +bx +c = 0 can be factored when c=0.

When the constant is zero, the equation becomes ...

  ax² +bx = 0

Factoring out x, we have a factored form as ...

  x(ax +b) = 0

showing that the equation can always be factored.

Answer:

Too much money

Step-by-step explanation:

Answer:

y = -3x + 1

Step-by-step explanation:

Plug in your x (2) and y (-5) values into your slope-intercept formula (y=mx+b).

-5 = -3(2) +b

Solve for b:

-5 = -3(2) + b

-5 = -6 + b

1 = b

Plug in the value of b, and the slope (-3) for the formula:

y = -3x + 1

Answer:

102200

Step-by-step explanation:

564+458= 1022

1 decagram=100 decigram

So multiply the sum by 100

1022*100=102200