The amount of money spent at the gas station varies directly with the number of gallons of gas purchased. 12 gallons of gas costs $36.00. How much would 8 gallons of gas cost?

Answer:

The correct option is;

The variable x has a coefficient

Step-by-step explanation:

The given vertex form of a quadratic function and the quadratic function can be written as follows;

Vertex form of a quadratic function, f(x) = (3·x + 1/3)² + 8/9

The quadratic function, f(x) = 9·x² + 2·x + 1

The vertex form of a quadratic function f(x) = a·x² + b·x + c is f(x) = a·(x - h)² + k

Where;

h = -b/(2·a) = -2/(2×9) = -1/9

k = f(h) = f(-1/9) = 9 × (-1/9)² + 2 × (-1/9) + 1 = 8/9

Which gives the vertex form a s f(x) = 9·(x - (-1/9))² + 8/9

f(x) = 9·(x + 1/9)² + 8/9

Therefore,  f(x) = (3·x + 1/3)² + 8/9 is not the vertex form of f(x) = 9·x² + 2·x + 1 because the variable x has a coefficient.

Answer:

height = 2m at t = 0s

height = 22.1m at t = 1s

height = 32.4m at t = 2s

height = 32.9m at t = 3s

height = 23.6m at t = 4s

height = 4.5m at t = 5s

Step-by-step explanation:

Given equation:

H(t) = -4.9t² + 25t + 2           ----------------(i)

The height of the ball is a function of time. Therefore;

(i) At the 0th second. i.e t = 0, we get the height by substituting the value of t = 0 into equation (i). i.e

H(0) = -4.9(0)² + 25(0) + 2

H(0) = 2

∴ At t = 0, the height is 2 meters. This is also obvious in the first statement of the question.

(ii) 1st second. i.e t = 1, we get the height by substituting the value of t = 1 into equation (i). i.e

H(1) = -4.9(1)² + 25(1) + 2

H(1) = 22.1

∴ At t = 1, the height is 22.1 meters.

(iii) 2nd second. i.e t = 2, we get the height by substituting the value of t = 2 into equation (i). i.e

H(2) = -4.9(2)² + 25(2) + 2

H(2) = 32.4

∴ At t = 2, the height is 32.4 meters.

(iv) 3rd second. i.e t = 3, we get the height by substituting the value of t = 3 into equation (i). i.e

H(3) = -4.9(3)² + 25(3) + 2

H(3) = 32.9

∴ At t = 3, the height is 32.9 meters.

(v) 4th second. i.e t = 4, we get the height by substituting the value of t = 4 into equation (i). i.e

H(4) = -4.9(4)² + 25(4) + 2

H(4) = 23.6

∴ At t = 4, the height is 23.6 meters.

(vi) 5th second. i.e t = 5, we get the height by substituting the value of t = 5 into equation (i). i.e

H(5) = -4.9(5)² + 25(5) + 2

H(5) = 4.5

∴ At t = 5, the height is 4.5 meters.

Answer:

the answer is (0,2) ball thrown from an initial height of two feet Jeremys change jar that started with a 2$ deposit

Step-by-step explanation:

Step-by-step explanation:

According to the question:

(x+4) : = 3:4

or, (x+4) / (3x+1) = 3 / 4

or, (x+4) * 4 = (3x+1) * 3

or, 4x + 16 = 9x + 3

or, 16 - 3 = 9x - 4x

or, 13 = 5x

or, 13/5 = x

•

• • x = 2.6

Answer:

x = [tex]\frac{13}{5}[/tex]

Step-by-step explanation:

Express the ratios as equivalent fractions, that is

[tex]\frac{x+4}{3x+1}[/tex] = [tex]\frac{3}{4}[/tex] ( cross- multiply )

3(3x + 1) = 4(x + 4) ← distribute parenthesis on both sides

9x + 3 = 4x + 16 ( subtract 4x from both sides )

5x + 3 = 16 ( subtract 3 from both sides )

5x = 13 ( divide both sides by 5 )

x = [tex]\frac{13}{5}[/tex]

Answer:

Greatest prime factor of [tex]nt[/tex] is 7.

Step-by-step explanation:

Given that

Two positive integers are [tex]n[/tex] and [tex]t[/tex].

(1) Greatest Common Factor or HCF of [tex]n[/tex] and [tex]t[/tex] is 5.

(2) Least Common Multiple or LCM of [tex]n[/tex] and [tex]t[/tex] is 105.

To find:

The greatest prime factor of the product [tex]nt[/tex] = ?

Solution:

First of all, let us learn about a property of HCF and LCM of two numbers.

The product of two numbers [tex]p[/tex] and [tex]q[/tex] is equal to the product of their HCF and LCM.

[tex]p \times q =LCM\times HCF[/tex]

Using this property for the given numbers:

[tex]n\times t =5\times 105\\OR\\nt =5\times105[/tex]

Now, let us make prime factors of [tex]5 \times 105[/tex] to find the greatest of the prime factors.

[tex]5\times 105 = 5\times 5 \times 21 =5\times 5 \times 3 \times \bold{7}[/tex]

So, the prime factors of [tex]5 \times 105[/tex] are 5, 5, 3 and 7.

Greatest prime factor of [tex]nt[/tex] is 7.

Answer: 6

Step-by-step explanation:

The factors of 6 are 1, 2, and 3.

1 + 2 + 3 = 6

Answer:

[tex]26x^2+22x+25[/tex]

Step-by-step explanation:

We remove the brackets, getting [tex]19x^2+12x+12+7x^2+10x+13[/tex].

We then combine like terms, getting [tex](19+7)x^2+(12+10)x+(12+13)[/tex].

As a result, we get [tex]26x^2+22x+25[/tex].

Answer:

Step-by-step explanation:

[tex] \sf{(19 {x}^{2} + 12x + 12) + ( {7x}^{2} + 10x + 13)}[/tex]

Remove the unnecessary Parentheses

⇒[tex] \sf{19 {x}^{2} + 12x + 12 + (7 {x}^{2} + 10x + 13)}[/tex]

When there is a ( + ) in front of an expression in parentheses , the expression remains the same

⇒[tex] \sf{19 {x}^{2} + 12x + 12 + 7 {x}^{2} + 10x + 13} [/tex]

Collect like terms

⇒[tex] \sf{26 {x}^{2} + 22x + 12 + 13}[/tex]

Add the numbers

⇒[tex] \sf{26 {x}^{2} + 22x + 25}[/tex]

Hope I helped!

Best regards!

Answer:

n

Step-by-step explanation:

4n-3n=1n

1n=n

Answer:

A

Step-by-step explanation:

Your answer is 5670 m

1km=1000m

5.67km=5.67×1000

=5670m

hope this helps

Answer:

5670

Step-by-step explanation:

Answer:

[tex]slope = m = 2[/tex]

Answer:

2

Step-by-step explanation:

The slope intercept form is

y = mx+b where m is the slope

Solve for y

12x - 6y = 30

Subtract 12x from each side

-6y =-12x+30

Divide by -6

y = -12x/-6 +30/-6

y = 2x -5

The slope is 2

Answer:

-2n + 6

Step-by-step explanation:

To combine this expression, we simply put the like terms, the coefficient with the same variables, and constants together.

5n + 6 + (-7n)

So we can reorganize this:

(5n + -7n) + 6

==> (-2n) + 6

==> -2n + 6

So that is the equivalent expression with the combination of like terms.

Cheers.

Answer:

-2n +6

Step-by-step explanation:

The expression we are given is:

5n + 6 + (-7n)

We want to combine like terms. First, let's analyze each term.

5n ⇒ has a variable, "n"

5 ⇒ does not have a variable

-7n ⇒ also has a variable, "n"

The like terms in this case are 5n and -7n, since they both include a variable. Let's combine the like terms.

5n + 6 + (-7n)

(5n - 7n) +6

Subtract 7n from 5n.

(5-7) *n +6

(-2)*n +6

(-2n)+6

-2n + 6

There are no more like terms, so this is simplified as much as possible.

The expression 5n+6+(-7n) after combining the like terms is -2n+6.

Answer:

A is in  length dimensions

Step-by-step explanation:

The expression:

x  =  A sin (2πft)

has in the second member two factors   A   and sin (2πft); a sine is a relation between two sides with the same dimension that means a sine is a number ( with minimum and maximum values of 0 for zero degrees and 1 for 90 degrees ). As t is in units of time ( seconds, minutes or hours) frequency "f", which is the number of cycles per unit of time       ( seconds, minutes or hours), t  and f should be both in the same unit, in order to get just a number for sin2πf.

Therefore A should be in units of length and x will get its units from A

For instance

x = A sin(2πft)  

t in seconds          f  in 1/seconds        A in meters

By substitution, we can see that

x[ m ]  = A [m] * sin[ 2π*sec* 1/sec ]

x[ m ]  = A [m] * number

Answer:

area = 385 cm²

Step-by-step explanation:

area = 5cm * 77cm

area = 385 cm²

Answer:

x => y

-6 => 9

3 => 5

15 => -3

-12 => 15

Step-by-step explanation:

Given the domain function, {-12, -6, 3, 15}, and the equation of the function, [tex] y = -\frac{2}{3}x + 7 [/tex], we can complete the given table by simply plugging in the value of either x to find y, or y to find x in the table given. The domain values are all x-values you have in the table.

Find y when x = -6:

[tex] y = -\frac{2}{3}(-6) + 7 [/tex]

[tex] y = -\frac{2}{1}(-2) + 7 [/tex]

[tex] y = 2 + 7 [/tex]

[tex] y = 9 [/tex]

Find x when y = 5:

[tex] 5 = -\frac{2}{3}x + 7 [/tex]

[tex] 5 - 7 = -\frac{2}{3}x + 7 - 7 [/tex]

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

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

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

[tex] -6 = -2x [/tex]

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

[tex] 3 = x [/tex]

[tex] x = 3 [/tex]

Find y when x = 15:

[tex] y = -\frac{2}{3}(15) + 7 [/tex]

[tex] y = -\frac{2}{1}(5) + 7 [/tex]

[tex] y = -10 + 7 [/tex]

[tex] y = -3 [/tex]

Find x when y = 15:

[tex] 15 = -\frac{2}{3}x + 7 [/tex]

[tex] 15 - 7 = -\frac{2}{3}x + 7 - 7 [/tex]

[tex] 8 = -\frac{2}{3}x [/tex]

[tex] 8 = \frac{-2x}{3} [/tex]

[tex] 8*3 = \frac{-2x}{3}*3 [/tex]

[tex] 24 = -2x [/tex]

[tex] \frac{24}{-2} = \frac{-2x}{-2} [/tex]

[tex] -12 = x [/tex]

[tex] x = -12 [/tex]

Answer:  x²−9

Step-by-step explanation:

A square number is obtained ehen we multiply a number to itself.

For example: 5 × 5 = 5² = 25 [It is a square number]

We can do this in expression too, For example: z×z =z²

From all the given options, only x²−9 has both terms as square.

∵ x² = x × x

and 9 = 3×3= 3²

So that,  x²−9  =(x)²-(3)²

Hence, the correct option is x²−9.

Answer:

2 ( n + 2 ) ( n + 1 2 )

Step-by-step explanation:

coefficient of the first term:  

2 = 2 × 1

coefficient of the last term:  

2 = 2 × 1

coefficient of the middle term (using only the factors above):  

5 = 2 × 2 + 1 × 1

2 n 2 + 5 n + 2 = ( 2 n + 1 ) ( n + 2 )

Alternative method:

Treat the given expression as a quadratic set equal to zero, with the form

a n 2 + b n + c

and use the quadratic formula

− b ± √ b 2 − 4 a c 2 a

This will given solutions

n = − 2  and  n = − 1 2

for a factoring

2 ( n + 2 ) ( n + 1 2 )

Hope this helped

Answer:

He will have 334 Euros

Step-by-step explanation:

Hello.

Here is a currency conversion problem.

The man in this question seeks to convert his Canadian dollars to Euro as he is in France for a trip.

The exchange rate is given as;

1.28 canadian dollar = 1 euro

He has 427 CAD , and we want to know the amount in euro.

let the equivalent amount in Euro be x

Thus;

if

1.28 CAD = 1 EUR

427 CAD = X EUR

By cross multiplying, we have

1.28 * x = 427 * 1

x = 427/1.28

x = 333.59 Euros which is approximately 334 Euros

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

The multiplicative inverse of 4 is 1/4.

Answer:

1/4

Step-by-step explanation:

Multiplicative inverse is another meaning for reciprocal. The reciprocal of 4 is 1/4

Answer:

6 candies

Step-by-step explanation:

The sentences "Ethan and his guests spent the first half...time for the guests to go home at 4:30 pm" are extra information because they don't relate to the problem, therefore, we can ignore them. We know that Ethan had 48 pieces of candy and that 8 guests came to his party. Since each guest got an equal amount of candy, to find the answer, we can do 48 / 8 = 6 candies.

Answer: The inverse relation is { (-1, -8), (-1, -8), (-8, -2), (8, 2) }

The inverse is effectively the opposite of the original relation. It undoes what the original relation does. So we'll swap the x and y values for each given point in the form (x,y). Something like (8,-1) becomes (-1,8). The other points follow the same pattern as well.

Answer:

3

Step-by-step explanation:

so if he buys 2 packs of soda and three packs of cupcakes they will be even

cause it's gonna be 12-12

Answer:

Step-by-step explanation:

14+5*3-3²=14+15-9=29-9=20

14-5*3+3^2=14-15+9=23-15=8

Answer:

12,500= £25

Step-by-step explanation:

Because every 1000 it makes £2 from ad venue, we must: (we can do two methods)

1.Divide £25 by £2 then multiply it by 1000. By doing this, we will know how many times 1000 are made when there is £25.

1000= £2

? = £25

So:

£25 ÷ £2= 12.5

12.5 × 1000= 12,500

2. Find how much it made for £1 by dividing 1000 by £2, then multiplying it by £25.

So:

1000 ÷ £2= 500

500 × £25= 12,500

I hope this helps! I'm sorry if it's wrong and too complicated.

Answer:

A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived.

Step-by-step explanation:

The Addition Postulate: If you have one apple and Sally has one apple, when you both add the same quantity to your existing number of apples, you'll still have the same number of apples. Using algebra, the postulate states:

If x = y, then x + 4 = y + 4

The Subtraction Postulate: If you have ten apples and Sally has ten apples, when you both subtract the same quantity of apples from your existing number of apples, you'll still have the same number of apples.

If x = y, then x - 3 = y - 3

Without being repetitive, these same principles apply to both multiplication and division.

The Multiplication Postulate: If x = y, then x * 3 = y * 3

The Division Postulate: If x = y, then x / 7 = y / 7

Answer:

suggest or assume the existence, fact, or truth of (something) as a basis for reasoning, discussion, or belief.

Step-by-step explanation:

Answer:

Hi! You already have the percentage of the nickel to the nearest hundredth, you just need to move to the left once to get to the tenth. That would mean the answer is 8.3%! Easy as that.

Answer:

8.3%

I just took the test

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]x(t)=sin(t)\\\\dx=cos(t)dt\\\\\text{For x = }\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{2} \text{ we have } t = \dfrac{\pi}{4}[/tex]

So, we can write.

[tex]\displaystyle \int\limits^{\dfrac{1}{\sqrt{2}}}_0 {\dfrac{1}{\sqrt{1-x^2}}} \, dx =\int\limits^{\dfrac{\pi}{4}}_0 {\dfrac{cos(t)}{\sqrt{1-sin^2(t)}}} \, dt\\\\=\int\limits^{\dfrac{\pi}{4}}_0 {\dfrac{cos(t)}{\sqrt{cos^2(t)}}} \, dt\\\\=\int\limits^{\dfrac{\pi}{4}}_0 {\dfrac{cos(t)}{cos(t)}} \, dt \\\\=\int\limits^{\dfrac{\pi}{4}}_0 {1} \, dt\\\\=\large \boxed{\sf \bf \dfrac{\pi}{4}}[/tex]

Thank you

Answer:  [tex]\bold{\dfrac{\pi}{4}}[/tex]

Step-by-step explanation:

Note the following integral formula:   [tex]\int\limits^a_b {\dfrac{1}{\sqrt{1-x^2}}} \, dx =\sin^{-1}(x)\bigg|^a_b[/tex]

We can rationalize the denominator to get: [tex]\dfrac{1}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)=\dfrac{\sqrt2}{2}[/tex]

*************************************************************************************

[tex]\int\limits^{\frac{\sqrt2}{2}}_0 {\dfrac{1}{\sqrt{1-x^2}}} \, dx \\\\\\=\sin^{-1}(x)\bigg|^{\frac{\sqrt2}{2}}_0\\\\\\= \sin^{-1}\bigg(\dfrac{\sqrt2}{2}\bigg)-\sin^{-1}(0)\\\\\\=\dfrac{\pi}{4}-0\pi\\\\\\=\large\boxed{\dfrac{\pi}{4}}[/tex]

Answer:

54kg

Step-by-step explanation:

Body weight = B

Tail weight = T

Head weight = H

Total weight = F

Use equation = B + T + H = F

We are told that T = 9kg, H = T + (1/3) x B, B = H + T

We have 3 equations and 3 unknowns, solve the system of equations to find W.  

B = H + 9

H = 9 + 1/3 x (H+9)=9+H/3+3 --> 2/3 x H = 12  --> H = 18

B = 18 + 9 = 27

F = 18 + 27 + 9 = 54kg

Explanation:

It's probably not obvious, but the squiggly portion through the x intercept x = -1 is a triple root. This is because this portion resembles a cubic graph. If instead it was a more straightish line through this root, then we'd have a single root.

So because x = -1 is a triple root, this means the factor (x+1) has the exponent 3. We have the factor (x+1)^3

The other factor is (x-2) from x = 2 being the other root.

All together we have (x+1)^3*(x-2) as the complete factorization. The leading coefficient is 1 to have this graph open upward. Or put another way, since the end behavior is going to positive infinity for both endpoints, the leading coefficient must be positive.

Answer:

C.) 7√2/2

Step-by-step explanation:

tan¤ = opp/adj

tan 45° = y/7√2/2

1 = y/7√2/2

1 = 2y/7√2

7√2 = 2y

2y = 7√2

y = 7√2/2

NOTE: ¤ = Theta

Answer:

A= -1 B=10

Step-by-step explanation:

Answer:

a: -1

b: 10

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