A car uses 3 1/8 gallons of gasoline per hour when driving on the highway, how many gallons will it use after three hours?

Answer:

Slope: 0

Equation : y = 9

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Slope:

-5-9/-3+3

=-14/0

= 0

Equation:

input gradient and pair of x and y valuesin y = mx +c

9= 0(-3)+c

9 = 0 +c

c = 9

input gradient and c:

y = 9

Answer:

d

Step-by-step explanation:

(x+3)/6 = 5/4

butterfly method

4(x+3) = 5×6

4x+12 = 30

4x = 30-12

4x = 18

x = 18/4

x = 9/2

Answer:

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

Step-by-step explanation:

The Quadratic Formula gives us the roots of a quadratic and is defined as: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The discriminant is the part in the square root which is: [tex]b^2-4ac[/tex]

if the discriminant of the quadratic is zero, then the quadratic only has one distinct zero with a multiplicity of 2.

To see why, let's plug in zero for the discriminant: [tex]x=\frac{-b\pm\sqrt{0}}{2a}[/tex]

The square root of zero is just going to be zero: [tex]x=\frac{-b\pm0}{2a}[/tex]

Adding or subtracting zero doesn't change the value: [tex]x=\frac{-b}{2a}[/tex]

As you can see here it doesn't matter if we take the positive or negative solution, we'll get one value.

If the discriminant of the quadratic is positive, then the quadratic will have two distinct real solutions.

Well the solutions are real because the square root has real solutions for positive numbers. The reason we have two distinct solutions is because the square root of a positive number will have a positive and negative solution. These square roots will have a non-zero value and will affect the value of the numerator based on whether you take the negative or positive solution giving you two distinct solutions.

If the discriminant of the quadratic is negative, then the quadratic will have two distinct complex solutions.

To clarify, real numbers are technically complex numbers, since complex numbers are just: [tex]a+bi[/tex], where a=real part, and b=imaginary part. We could use this to represent any real number where b=0.

So when I'm saying "complex solution" I mean a complex solution where b does not equal zero, so there is a non-zero imaginary component to the complex solution.

The reason we have a complex solution in the first place is because we have a negative number in the square root. The square root only has real solutions for positive numbers, since any real number squared will give you a positive number regardless of the sign (positive or negative). The only number that is negative when squared is an imaginary number.

The reason we have two distinct solutions is actually the same reason we have two distinct solutions when the discriminant is positive. Since the square root will yield a non-zero number, so when we add it or subtract it to b, we will get to different values for the numerator, giving us two different values, or two different solutions.

So now let's solve the equation: [tex]3x^2+4x+2=0[/tex]

We have it in standard form where: [tex]ax^2+bx+c=0[/tex]

we want to use the Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Plugging in values we get:

[tex]a=3,\ b=4,\ c=2\\\\x=\frac{-4\pm\sqrt{4^2-4(3)(2)}}{2(3)}\\\\x=\frac{-4\pm\sqrt{16-24}}{6}\\\\x=\frac{-4\pm\sqrt{-8}}{6}[/tex]

From here you'll notice the discriminant is -8, and thus we complex solutions since it's negative. We can first break up this square root into multiple square roots using the fact that: [tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex]

and since -8 can be defined as: -1 * 8, we can split it up like this

[tex]x=\frac{-4\pm\sqrt{-1}*\sqrt{8}}{6}\\\\x=\frac{-4\pm i\sqrt{8}}{6}[/tex]

We can actually simplify the square root a bit more, since we can once more use the identity: [tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex], to simplify the radical. The number 8 can be represented as 4 * 2, and sqrt(4) can be simplified easily.

[tex]x=\frac{-4\pm i *\sqrt{4}*\sqrt{2}}{6}\\\\x=\frac{-4\pm 2i\sqrt{2}}{6}\\\\x=\frac{(-2 * 2)\pm2i\sqrt{2}}{(3*2)}\\\\x=\frac{-2\pm i\sqrt{2}}{3}[/tex]

Now let's take the positive and negative solution to get the two distinct complex solutions. You can start with either but I'll just do the positive first.

Positive Solution:

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

You could leave it like this, but generally whenever we have a complex number we want it in the form: [tex]a+bi[/tex] where the real and imaginary part are separate, so we can just distribute the division of 3

Positive Solution Continued:

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

I also moved the "i" outside the fraction, so it's a bit easier to see the value of "b"

Negative Solution:

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

The equation m/k = x solved for k will be k = m / x.

variable, in algebra, a symbol (usually a letter) that represents an unknown numerical value in an equation. Commonly used variables are x and y (real unknowns), z (complex unknowns), t (time), r (radius), and s (arc length).

There are two types of variables in math:

In mathematics, a variable is an alphabet or term that represents an unknown number or an unknown value or an unknown quantity. Variables are  used especially in algebraic expression or algebra. For example, x 9=. is a linear equation where x is a variable, where 9 and  are constants.

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Answer: 6a³ + a² - 7

Step-by-step explanation:

(5a³ + 4a² − 3a + 2) + (a³ − 3a² + 3a − 9)=

5a³ + a³ + 4a² − 3a² - 3a + 3a + 2 - 9=

6a³ + a² - 0 - 7 = 6a³ + a² - 7

Answer:

6a³ + a²-7

Step-by-step explanation:

1. Get rid of the parentheses by distributing them.

(5a³ + 4a² − 3a + 2) + (a³ − 3a² + 3a − 9) = 5a³ + 4a² − 3a + 2 + a³ − 3a² + 3a − 9

2. Add like-terms.

5a³ + 4a² − 3a + 2 + a³ − 3a² + 3a − 9 = 6a³ + a²-7

Answer: Yes, the point (-1, 3) makes the equation true.

Step-by-step explanation:

You would need to plug in the coordinates to the following places in the equation.

y=-3x

(3) = -3(-1)

3 = 3

Hope this helps!

Have a great day! :)

Answer: 0.187

Step-by-step explanation:

I just did the question

The equation of the line parallel to 2x + 3y = 18 and passing through point ( 6, 4) is 3y + 2x = 24.

Consider the line 2x + 3y = 18,

The equation of the line in slope-intercept form can be written in the form y = mx + b, where m is the slope of the line.

Therefore,

2x + 3y = 18

Subtracting 2x from each side

2x + 3y - 2x = 18 - 2x

3y = 18 - 2x

Dividing each side by 3.

y = 6 - ( 2/3 )x

y = - (2/3)x + 6

Hence, the slope of the line is - 2/3.

Now, if two lines are parallel then they have the same slope.

Now, the line parallel to 2x + 3y = 18 passes through ( 6,4).

Therefore, using the slope-intercept form:

y = mx + b

4 = ( -2/3 ) × 6 + b

4 = - 4 + b

b = 8

Therefore, the equation of the line parallel to 2x + 3y = 18 is:

y = ( - 2/3 )x + 8

3y = - 2x + 24

3y + 2x = 24

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The evaluation of the expression, if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2 | 16 + 4 ( 3 q + p ) is 46.

the given expression is  t = − 2 | 16 + 4 ( 3 q + p )

Then since we are given  m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5

Then, we can substitute all the given values of the terms into the given expression as :

t = − 2 | 16 + 4 ( 3 q + p )

t= -2 I 16+4(-18+2)

t= -2 I 16+4(-16)

t= -2 I 16 -64

t= -2 I -48

t =46

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No, the divisor 0.03 is not a whole number, we should multiply by 10² to get a divisor a whole number.

As given in the question,

Given expression:

13.5 divided by 0.03

Dividend of the given expression = 13.5

Divisor of the given expression = 0.03

No, the divisor 0.03 is not a whole number.

Power of 10 which should be multiply by 0.03 to get a whole number

0.03 = 3 /100

(3/100) should get multiply by 100

100 = 10²

0.03 ×10² =3 whole number

Therefore, the divisor 0.03 is not a whole number, we should multiply by 10² to get a divisor a whole number.

The complete question is:

Is our divisor a whole number? 13.5 divided by 0.03 . By what powers of 10  should you multiply by to get a whole number?

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Answer:

25

Step-by-step explanation:

the tens cancle each other out

Answer:

-8°

Step-by-step explanation:

-24+16=-8

Answer:

Step-by-step explanation: do 193.75 divided by 15

Answer:

c 6√5 - 4√5

Step-by-step explanation:

your answer is correct

Answer:

B is bigger

Step-by-step explanation:

a) 3^2 / 2^3

3*3 / 2*2*2

9/8

b) 9^4 / 4^6

9*9*9*9/4*4*4*4*4

6561 / 4096

1.601807

The arity typically assumed to be limited. The "typical" operations of finite dimensionality are referred to as the finiteary operations when infinitary operations are taken into consideration. The mean of the five numbers is 8.2, four of numbers are 8, 10, 12 and 10. The fifth number is 1.025.

An operation, often known as a "operand" or "argument," is the function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by number of operands.

Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are operations that are most frequently studied. A constant is operation with arity zero, often known as a nullary operation. An example of operation of arity 3, sometimes known as a ternary operation, is the mixed product.

The arity typically assumed to be limited. The "typical" operations of finite dimensionality are referred to as the finiteary operations when infinitary operations are taken into consideration.

Similar to an operation, but with partial function in place of a function, is the definition of a partial operation.

The mean of five numbers is 8.2. Four numbers are 8, 10, 12 and 10.

Let the number be x,

[tex]\frac{8+10+12+10+x}{5} = 8.2[/tex]

x= 1.025

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I WILL USE CROSS MULTIPLICATION

[tex]63(4x) = 84(12) \\ 63(4x) = 1008 \\ \frac{63(4x)}{63} = \frac{1008}{63} \\ 4x = 16 \\ \frac{4x}{4} = \frac{16}{4} \\ x = 4[/tex]

ATTACHED IS THE SOLUTION

The time period that Riko would be behind is going to be the inequality 0 ≤ t < 52.5 minutes .

How to solve for the period t that Riko would be behind her brother

The question says that at the time he left the house, Yuto was 5.25 miles ahead of her.

The amount of miles that she would have gained on Yuto within this period would be 0.35 - 0.25 = 0.1 miles on Yuto

Therefore at every mile she would be closing in on 0.1 miles

For her to close the gap that is made here, it would be 5.25 / 0.1

= 52.5 minutes

Therefore we would say that The time that Riko would be behind is going to be  0 ≤ t < 52.5 minutes .

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Answer:

As a fraction, it would be 10/7 or as a number, 1 and 3/7.

Note that the rational numbers represented on points- P, Q, R, and S are given as follows:  7/3, 8/3, -4/3, -5/3 respectively. See the explanation below.

A rational number is defined in mathematics as the proportion or fraction p/q of two integers, a numerator p, and a non-zero denominator q. 3/7, for example, is a rational number, as is every integer.

For the solution above:
Each section in between two numbers is broken into three sections.

Thus, we have a = (6/3), P = (7/3), Q = (8/3) and B = (9/3)

In the same way,

T = = -3/3,

R = -4/3

S = -5/3 and

U = -6/3

Therefore, the rational numbers represented - P, Q, R, and S are given as follows:  7/3, 8/3, -4/3, -5/3.

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11975 is value of multiplication .

What does multiplication mean in math?

5×395=5×(400×-5)

1975 = 5 * ( - 2000 )

1975 = - 10000

= 10000 + 1975

= 11975

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Answer:

a=1/30

Step-by-step explanation:

6a+4a=1/3

10a=1/3

30a=1

a=1/30

1/30

is the anwser i think.i might be wront tho

   First, we need to know the units they used. For every hectare, there are 2.47105 acres.

   Next, we can set up a proportion to solve.

        [tex]\displaystyle \frac{\text{\$8,963}}{1 \;acre} =\frac{\text{\$x}}{2.47105 \;acres}[/tex]

   Now, we will cross-multiply:

       $8,963 * 2.47105 = x

       x ≈ $22,148

   I was $10 from the answer they ended up with, so I most likely used a different conversion unit factor than they did. However, the steps are still the same.

the coodrinates of JKLM is,

J(1,3) , K(3,1), L(-1,-3) and M(-3,-1)

the length JK is ,

length KL is,

Length LM is,

length MJ

so, the perimeter = sum of sides,

= JK + KL + LM + MJ

= 2 root 2 + 4root2 + 2root2 + 4root2

= 12 root 2

thus, the perimeter is 12 root 2

The interquartile range for the given set of numbers {0,2,4,6,8,10,12,14,16,18,20} is 12 .

The interquartile range(IQR) can be calculated by the formula

IQR = Q₃ - Q₁

where Q₃ is the third quartile

and Q₁ is the first quartile

In the question,

the set of numbers is ascending order is given as

0,2,4,6,8,10,12,14,16,18,20

Q₃ means median of the upper half

the upper half of the data is 12,14,16,18,20

the median of the upper half is 16 ,

So Q₃ = 16 .

Q₁ means median of the lower half

the lower half of the data is 0,2,4,6,8

the median of the lower half is 4 ,

So Q₁ = 4 .

Hence , the IQR = Q₃ - Q₁ = 16-4 = 12  .

So, IQR for given set of numbers is 12.

Therefore , the interquartile range for {0,2,4,6,8,10,12,14,16,18,20}  is 12 .

The given question is incomplete , the complete question is

Find the Interquartile range for the given set of numbers 0,2,4,6,8,10,12,14,16,18,20  .

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Step-by-step explanation:

-13x < 65

-13x * -1 < 65 * -1

13x > -65

13x/13 > -65/13

x > -5

Hope this helps! :)

Answer:

[tex]-2 < a < 1[/tex]

Step-by-step explanation:

-15 < 9a + 3 < 12 (Combine like terms)

-18 < 9a < 9 (Subtraction Property)

-2 < a < 1 (Division Property)

Note that just like solving a linear equation, instead of having two sides, you have three. And, whatever you carry out on one side, you have to carry out on all three.

Although, unlike linear equations, if you are dividing/multiplying all sides with a negative integer, then you have to flip the signs.