D=33+31g. Determine the distance the car can travel using 4 gallons

The graph of the quadratic equation is shown in the image attached below.

In accordance with algebra fundamental theorem, we can construct a quadratic equation by knowing the locations of at least three points on Cartesian plane. Herein we find a quadratic equation in vertex form, whose formula is described below:

y - k = C · (x - h)²

Where:

By using this expression, we can find the locations of the vertex and intercepts of the parabola. Now we proceed to find all the required information:

Vertex

y = (x + 5)²

(h, k) = (- 5, 0)

x-Intercepts

(x + 5)² = 0

x = - 5

y-Intercept

y = (0 + 5)²

y = 25

Another point

x = - 1

y = (- 1 + 5)²

y = 4²

y = 16

Finally, we mark the three points on the Cartesian plane and pass a curve through them. The result is shown in the image attached below.

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The surface area of the tank is 7038 square inches

The surface area can be calculated as follows

The diameter is 28 inch

radius= diameter/2

= 28/2

= 14

Height= 66 inch

The surface area can be calculated as follows

2πrh + 2πr²

= 2(3.142)(66) + 2(3.142)(14²)

= 5806+2(616)

= 5806+1232

= 7038 square inches

Hence the surface area of the tank is 7038 square inches

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The three solutions to the linear equation are (0, -2), (1, 1) and (2, 4)

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The linear equation is given as

g(x) = 3x - 2

To determine the solution to the linear equation, we set the value of x to some values

say x = 0, 1 and 2

Substitute x = 0, 1 and 2 in g(x) = 3x - 2

g(0) = 3(0) - 2 = -2

g(1) = 3(1) - 2 = 1

g(2) = 3(2) - 2 = 4

Hence, the three solutions to the linear equation are (0, -2), (1, 1) and (2, 4)

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Answer:

AB and CD are congruent.

Step-by-step explanation:

Given points:

To determine if AB and CD are congruent, calculate the length of the two lines using the distance formula.

[tex]\boxed{\begin{minipage}{7.8 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]

[tex]\begin{aligned}\implies AB & = \sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& = \sqrt{(2-4)^2+(6-1)^2}\\& = \sqrt{(-2)^2+(5)^2}\\& = \sqrt{4+25}\\& = \sqrt{29}\end{aligned}[/tex]

[tex]\begin{aligned}\implies CD & = \sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\& = \sqrt{(-4-(-2))^2+(-3-2)^2\\& = \sqrt{(-2)^2+(-5)^2}\\& = \sqrt{4+25}\\& = \sqrt{29}\end{aligned}[/tex]

Therefore, as AB = CD, we can conclude that AB and CD are congruent.

Simplifying the expression y to the negative seventh power over x to the negative third power using law of exponents gives; x³y⁷

Some of the Laws of Exponents are;

We want to simplify y to the negative seventh power over x to the negative third power. This is expressed as;

y⁷/x⁻³

Now, x⁻³ can also be expressed as 1/x³. Thus, our original equation is now; y⁷/(1/x³) = x³y⁷

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It should be noted that the example of a census is C. The U.S. Population Census.

It should be noted that census simply has to do with knowing the population of the people in a particular place.

Therefore, it should be noted that the example of a census is The U.S. Population Census. It should be noted that this information is important to get the number of people that are living in the United States.

This can also be divided into females and malee. Therefore, the correct option is C.

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When t=0 and t=6s is the time at which the particle have a velocity of 25 m/s and t=3s is the time when acceleration is 0.

a vehicle's capacity to gain speed within a short time

Given s = t^4 − 4t^3 − 36t^2 + 25t

v=d/dt(s)=4t^3-12t^2-72t+25

the particle have a velocity of 25 m/s

So 4t^3-12t^2-72t+25=25

=4t^3-12t^2-72t

=4t(t^2-3t-18)=0

t=0 and

t^2-3t-18=0

(t+3)(t-6)=0

So t=0, t=-3 and t=6

As time>=0, So t=0 and t=6.

Now we required to find acceleration,

Accelaration=d/dt(v)

=d/dt(4t^3-12t^2-72t+25)

=12t^2-12t-72

t=12±√144-4(12)(-72)/24

t=12±60/24

t=12+60/24=3  and 12-60/24=-2

So t=3s

Therefore t=0 and t=6s is the time at which the particle have a velocity of 25 m/s and t=3s is the time when acceleration is 0.

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Answer: 22.5

Step-by-step explanation:

25% is [tex]\frac{1}{4}[/tex] of 100%

So, 90/4 = 22.5

Answer:

22.5

Step-by-step explanation:

10% of 90 is 9

Multiply that by 2 then you get 18.

Half of 10% will give you the remaining 5% which is 4.5

Then add 18 and 4.5 you 22.5

Using the calorie count C for a serving of food C =5h + 8f + 5​p, the formula for f is derived to be; f = (C - 5h  - 5​p) / 8

An equation is an expression that shows the relationship between two or more numbers and variables.

WE have been Given data that C =5h + 8f + 5​p

Where C is the calorie count, h is the number of grams of carbohydrate, f is the number of grams of fat and p is the number of grams of protein

Now solving for f in the given equation;

C = 5h + 8f + 5​p

Then f the subject of formula;

C - 5h  - 5​p = + 8f

8f = C - 5h  - 5​p

Now dividing through by 8

f = (C - 5h  - 5​p) / 8

Hence, The number of grams of fat, f, contained in a serving of food is; f = (C - 5h  - 5​p) / 8

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These are our two tables of values for the following functions using the integers from -4 to 4.

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The given functions using the integers from -4 to 4 are

a. F(x)=6/x-2b.

r(x)=6x+12/x²-4

According to given question we have

f(x) = 6/x - 2

Now we just need to evaluate the function in all the given points:

a) f(x) = 6/x - 2

Now we can put the value

f(-4) = 6/(-4) - 2 =  -3/2 - 4/2 = -7/2

f(-3) = 6/-3 - 2 = -4

f(-2) = 6/-2 - 2 = -5

f(-1) = 6/-1 - 2 = -8

f(0) is undefined

f(1) = 6/1 - 2 = 4

f(2) = 6/2 - 2 = 1

f(3) = 6/3 - 2 = 0

f(4) = 6/4 - 2 = -1/2

b. r(x)=6x+12/x²-4

Now we can put the value

r(-4) = 6(-4)+12/(-4)²-4=-27.25

r(-3) = 6(-3)+12/(-3)²-4=-20.66

r(-2) = 6(-2)+12/(-2)²-4=-13

r(-1) = 6(-1)+12/(-1)²-4= 2

r(0) = 6(0)+12/(0)²-4= ∞

r(1) = 6(1)+12/(1)²-4 =14

r(2) = 6(2)+12/(2)²-4=11

r(3) = 6(3)+12/(3)²-4 =15.33

r(4) = 6(4)+12/(4)²-4=20.75

Therefore, these are our two tables of values for the following functions using the integers from -4 to 4.

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Answer:

10

Step-by-step explanation:

50.75 = 50

0.18 = 0.2

50x 0.2 = 50/5

50/5 = 10

Step-by-step explanation:

2 cups of sugar mix with 7 cups of water.

so, 2/2 = 1 cup of sugar mixes therefore with 7/2 = 3.5 cups of water.

and 5 cups of sugar (= 5×1 cups) mix with 5×3.5 = 17.5 cups of water.

not 21. not 28. it is 17.5 cups of water !

The solution to the equation is x = 38

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

1/3|x - 8| = 10

Multiply through by 3

So, we have

|x - 8| = 30

Remove the absolute bracket

So, we have

x - 8 = 30

Add 8 to both sides of the equation

So, we have

x = 38

Hence, the solution to the equation is x = 38

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Answer:

1. 7/2

Hope this helps a little. :)

The amount that would be in th IRA when he retires at age 65 is $21,932.15.

An annuity is a series of payment that is made over a period of time. In this question, the annuity is monthly which lasts for 47 years (65 - 18). An ordinary annuity is when the payments are made at the end of the period. An annuity due is when the payment is made at the beginning of the period.

The amount deposited increases by the amount you put in it every month and by the interest rate the account accrues. The account earns an APR, this means that interest would be compounded yearly.  

Total amount of deposits = amount deposited monthly x number of months in a year x number of years

$60 x 12 x 47 = 33,840

The formula that can be used to determine the future value of the account in 47 years is:

Monthly deposit x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$60 x [{(1.00583)^564 - 1} / 0.07] = $21,932.15

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Answer:

f(1/x)=5+3x/6+7x ; 9(x-2)=[tex]\sqrt{x} ^2-8x+12[/tex] the [tex]\sqrt{x}[/tex] goes over the -8x+12

Step-by-step explanation:

number of hamburgers for x pounds of ground meat is

h(x) = x/0.5

x = 3.23

h(3.23) = 3.23/0.5 = 6.46

so, he could make 6 hamburgers and had some meat (0.23 pound) left.

Antonio will save $113.4 after calculating using mensuration and buying from Pets Galore instead of Healthy pets.

As per the question statement, Antonio needs to buy 150 pounds of dog food for the local dog shelter. Healthy Pets, sells dog food in 50-pound bags for $85.95 per bag and Pets Galore sells one bag for $48.15

We are supposed to calculate the amount of money saved by Antonio if he buys 150 pounds of dog food from Pets Galore instead of from Healthy Pets.

Using concept of mensuration,

Quantity of dog food in one bag = 50 pounds

Quantity required of dog food = 150 pounds

Therefore number of bags required = 150/50 = 3

Price of dog food at Pets Galore per bag = $48.15

Total money to be paid to Pets Galore for 3 bags = $48.15*3  = $144.45

Total money to be paid to Healthy Pets for 3 bags = $85.95*3 = $275.85

Therefore money saved = $275.85 - $144.45  = $113.4

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A) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ exactly​ three is;

P(X = 3) = 0.2397

B) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ at least​ four is;

P(x ≥ 4) = 0.50748

C) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ less than eight is;

P(x < 8) = 0.99051

The formula for binomial Probability distribution is;

P(X = x) = ⁿCₓ * p^(x) * (1 - p)^(n - x)

We are told that 36​% adults favor the use of unmanned drones by police agencies. Thus;

p = 30% = 0.3

sample size; n = 12

A) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ exactly​ three is;

P(X = 3) = ¹²C₃ * 0.3³ * (1 - 0.3)^(12 - 3)

P(X = 3) =  ¹²C₃ * 0.3³ * 0.7⁹

P(X = 3) = 0.2397

B) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ at least​ four is;

P(x ≥ 4) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12)

P(x ≥ 4) = 0.50748

C) Probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ less than eight is;

P(x < 8) = 1 - (P(8) + P(9) + P(10) + P(11) + P(12))

P(x < 8) = 1 - 0.00949

P(x < 8) = 0.99051

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Answer:

to solve for X, first remember that Y=mx+b

Step-by-step explanation:

1 Add 77 to both sides.

4x=3+7

4x=3+7

2 Simplify  3+73+7  to  1010.

4x=10

4x=10

3 Divide both sides by 44.

x={10}{4} x=10/4x = 4 10

​

4 Simplify  10/4

4

10

​

  to  \5/2

2

5

​

.

x= 5/2

x=

2

5

​

Done

Decimal Form: 2.5

Answer: Yes it is proportional

Step-by-step explanation: First I used two points on paper and used the formula y2-y1/x2-x1 and used these two points (20,100) and (15,175) and got -15, And finally it is proportional at a negative rate!

Hope This helps owo

Answer:

4x+8=3x-6

4x-3x=-6-8

x= -14 answer

hope you understand

Answer:

[tex]x=-14[/tex]

Step-by-step explanation:

Given coefficients: a = 4, b = x, c = 2

[tex]4\left(x+2\right)\\=4x+(4\cdot \:2)\\=4x+8\\3\left(x-2\right)\\=3x-(3\cdot \:2)\\=3x-6\\4x+8=3x-6\\4x+8-8=3x-6-8\\4x=3x-14\\4x-3x=3x-14-3x\\=-14[/tex]

Answer: (5, -6)

Step-by-step explanation:

I'm not really 100% sure if i can put in detail but this is the correct answer

The words related to the mathematical operation of division are:

A division between two numbers tells us how many times the denominator can be fit into the numerator (the numerator is the number being divided by the denominator).

The "math word" used for divisions is "quotient"

The quotient between two numbers is equivalent to say the "outcome of the division between two numbers"

So that is one of the correct options.

Other correct option is "separate"

Like in the word problem example "3 friends separate evenly 9 candy between them". Here we have a division.

Similar, "cut" is also related to divisions.

The word problem "A piece of wire of 1 meter is cut into 3 pieces, how long is each one?"

Again, this is a division problem.

The last correct option is renumber, which is mostly a way of rewritting a number, but it uses divisions to do it.

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7 is greater than 21 times by 147 (7x21).

Greater than denotes that a variable or number exceeds a specified upper limit. Conversely, greater than or equal to indicates that the value is greater than or equal to the specified limit. The greater-than symbol is denoted by the prefix >, while the greater-than or equal-to sign is denoted by the prefix.

The symbols greater than and less than signify a disparity between two values. ">" and "" are used to indicate greater than and less than, respectively. Find more mathematical symbols right here.

The number 2 is 5 more than the number -3. Detailed explanation: Any natural number, including zero and both positive and negative numbers, is an integer.

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Answer: A. 5.19$

Step-by-step explanation: divide 25.95 by 5

160?

Step-by-step explanation: