A motorcycle can travel 70 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 60 km?
[1 mile = 1.6 km]
a- 0.2
b- 0.5
c- 0.8
d- 1.4

Answer: Choice C) line L is parallel to line M by the converse of the same side interior angle theorem

The same side interior angle theorem says that if two lines are parallel (such as L and M) then the same side interior angles that form are supplementary, meaning they add to 180 degrees.

Flip this in reverse, and you'll get the converse which says that if the same side interior angles add to 180, then the lines must be parallel.

note: if line Q is making things more complicated and confusing, then I suggest covering it up or drawing out the diagram again but leaving out line Q

Answer:

Step-by-step explanation:

In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of 3 + 4i is 3 − 4i. In polar form, the conjugate of is.

A complex conjugate is the element of a complex number that has the same real part but an opposite-sign imaginary part, and multiplying a complex number by its conjugate yields a real number.

A complex conjugate in mathematics is a paired element of a complex number that has the same real part but an opposite-sign imaginary part. When you have a complex number, let's call it A, which can be expressed in the form (a + ib) where 'a' is the real part and 'b' is the imaginary part, the complex conjugate of A, denoted as A*, would be (a - ib). One important property of complex conjugates is that when you multiply a complex number by its conjugate, you get a real number. This is because the product A* A = (a + ib) (a - ib) = a² + b².

For example, if a complex number is a = 3 + 4i, its complex conjugate would be a* = 3 - 4i. Multiplying a by its conjugate, we get a* a = (3 + 4i) (3 - 4i) = 9 + 16 = 25, which is a real number. This property is very useful, especially in fields such as quantum mechanics, where physical measurements must yield real numbers.

Answer:

The first step is to add 7 to each side

Step-by-step explanation:

2x-7 = 18

To solve this equation, the first step is to add 7 to each side

2x-7+7 = 18+7

2x = 25

Answer:

the first step is to add 7 to both sides.

Step-by-step explanation:

           2x-7 = 18

               +7    +7

              2x = 25

divide by 2

              25/2 = 12.5

so x= 12.5

Answer:

x = 9 and x = −15

Step-by-step explanation:

|2x + 6| − 4 = 20

Add 4 to each side

|2x + 6| − 4+4 = 20+4

|2x + 6|  = 24

Now we have an absolute value equation that has the absolute value isolated.  We can separate them, have two equations, one positive and one negative.

2x+6 =24   and 2x+6=-24

Subtract 6 from each side

2x+6-6=24 -6    2x+6-6 = -24-6

2x = 18                   2x =-30

Divide by 2

2x/2 = 18/2          2x/2 = -30/2

x =9                        x=-15

Answer:

C.  -5x − 3y = 0

Step-by-step explanation:

A(-3, 0) and B(-6, 5)

First we find the slope of line AB

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{5-0}{-6+3} =\frac{-5}{3}[/tex]

Slope of the line parallel to AB =  slope of line AB

When the lines are parallel then their slope are equal

So the slope of line parallel to AB = [tex]\frac{-5}{3}[/tex]

The line passes through the origin (0,0)

Use equation y-y1= m (x-x1)

m = -5/3 , x1=0 and y1=0

[tex]y-0 = \frac{-5}{3}(x-0)[/tex]

[tex]y= \frac{-5}{3}(x)[/tex]

multiply the whole equation by 3

3y = -5x

Subtract 3x from both sides

0=-5x-3y

-5x - 3y =0

Final answer:

Kendra's original allowance was $10.

Explanation:

To find out how much Kendra's allowance was, we can use algebraic equations. Let 'x' represent Kendra's original allowance.

Kendra lost half of her allowance, which means she had x/2 left.

Then her mother gave her four more dollars, so now she has x/2 + 4.

Given that Kendra has $9, we can set up the equation x/2 + 4 = 9 and solve for x.

x/2 + 4 = 9

x/2 = 9 - 4

x/2 = 5

Multiplying both sides of the equation by 2, we get x = 10.

Therefore, Kendra's allowance was $10.

Answer:

Can you put a picture?

Step-by-step explanation:

Answer:

i need a picture

Step-by-step explanation:

Answer: D) 4/5

================================================

Explanation:

There are a few ways to see how this is the answer.

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The first is to notice how 16/20 = 0.80 when using long division or a calculator. At the same time, 4/5 = 0.80 as well. So that means 16/20 = 4/5.

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Another way to see how this works is to multiply top and bottom of 4/5 by 4. So we have 4*4 = 16 as the new numerator and 5*4 = 20 as the new denominator. Going in reverse, you can divide each piece of 16/20 by the GCF 4 to reduce this fraction into 4/5.

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

Finally, we can equate the two fractions and cross multiply

16/20 = 4/5

16*5 = 20*4

80 = 80

Both sides are the same value, so that confirms the original equation is true as well.

Answer:

Step-by-step explanation:

The absolute value of x is x.

y = 2x

Use the rise over run method.

2 is the same as 2/1. So, you rise 2 square up from the origin and then go over one, repeating the process. To do it in the negative zone, you just work backwards. Down two and left one.

You should have a diagonal line going from left to right that goes through the origin. Linear equations never end. They continue on forever, so your domain would be (-infinity, infinity) and your range would be (-infinity, infinity). Be sure to use the symbol for infinity instead of the word. The symbol, in case you do not know, looks like an 8 rotated 90 degrees.

The answer is:

The probability that both John and Ted will be on time is 48%.

Since we are dealing with percentages, in order to make it easy to understand, let's remember that percentages are used to simplify the way we refer to something, talking in numeric terms. For example, meaning 100% it's equal to say that somethinh is complete, or absolute. Also, we can see the percentage as a ratio that is expressed as a fraction of the number 100 or [tex]\frac{1}{100}[/tex]

From the statement the know that John is late 20% of the time, making it easy to understand, it's equal to say that from 100 times, John is late 20 times.

So, calculating we have:

For John:

[tex]Probability=TotalTimes(percent)-LateTimes(Percent)\\\\Probability=100-20=80[/tex]

So, we have that the probability that John will be on time is 80%.

For Ted:

[tex]Probability=TotalTimes(percent)-LateTimes(Percent)\\\\Probability=100-40=60[/tex]

So, we have that the probability that Ted will be on time is 60%.

Now, to calculate the probability that both John and Ted will be on time, we need to calculate the combined probability. It can be calculated using the following equation:

[tex]CombinedProbability=Probability_{1}*Probability_{2}[/tex]

Let be:

[tex]Probability_{1}=80(percent)=\frac{80}{100}=0.8\\\\Probability_{2}=60(percent)=\frac{60}{100}=0.6[/tex]

So, substituting and calculating we have:

[tex]CombinedProbability=Probability_{1}*Probability_{2}[/tex]

[tex]CombinedProbability=0.8*0.6=0.48=48(percent)[/tex]

Hence, we have that the probability that both John and Ted will be on time is 48%.

Have a nice day!

The x-intercept of the equation y = -2.65x + 25 is approximately 9.43. The x-intercept generally represents the value of x at which y is zero or the point where correlation between x and y starts.

The x-intercept of a graph is the point at which the line crosses the x-axis. In terms of your equation y = -2.65x + 25, the x-intercept is found when y equals 0. By setting y equal to 0 and solving for x, we get: 0 = -2.65x + 25. Isolate x by dividing both sides by -2.65 and adding 25. This calculates to x ≈ 9.43. In terms of real life situations, the x-intercept often represents the value of x where y is nil or where the correlation between x and y begins. However, the real-world interpretation of this value depends on the context of the problem.

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You will have the points: (0,0) and (1,10) and (2,20) and (3,30) etc etc

Plot at least 2 of these points. Then draw a line through them.

Each point has an x,y pair such that the y value is ten times the x value

For example, if x = 2, then

y = 10*x = 10*2 = 20

so that shows how (2,20) is one of the points.

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The domain would be the set of positive whole numbers assuming Tyler can only work a whole number of hours. If partial time values are accepted, then the domain would be the set of positive real numbers. Negative x values are not allowed as Tyler can't work negative 3 hours for instance.

In a similar fashion, the range is the set {0, 10, 20, 30, 40, ...} incrementing by multiples of 10 if x is the set of positive whole numbers. If x is the set of positive real numbers, then y can be 0 or larger which sets up the range of y being the set of positive real numbers as well.

Answer:

99 yd

Step-by-step explanation:

When I add these, I line them up vertically

  29 yd. 2ft. 11 in.

+ 55 yd. 1 ft. 10 in.

+ 13 yd. 1 ft.  3 in.

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

97 yd  4ft   24 in

We know that 12 in = 1 ft

so 24 in = 2ft

Subtract 24 in and add 2 ft

97 yd  4ft   24 in

           +2ft  -24 in

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

97  yd   6ft

We know 3 ft = 1yd

so 6ft = 2yd

Subtract 6ft and add 2 yd

97  yd   6ft

+2yd   - 6ft

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99 yd

Answer:

c = 7

Step-by-step explanation:

given 2c = c + 7 ( subtract c from both sides )

c = 7

Answer:

80 spaces

Step-by-step explanation:

Answer:

{-3, 1, 6 }

Step-by-step explanation:

the domain is the values of x ( input) from the relation in ascending order.

Values are not repeated.

domain {- 3, 1, 6 }

Answer:

{- 3, 1, 6 }

Step-by-step explanation:

The domain is the values of x inputs from the relation in ascending order.  Values cannot be repeated.

Answer:

[tex]tan(\frac{5\pi}{3})=\sqrt{3}[/tex]

Step-by-step explanation:

we are given

[tex]tan(\frac{5\pi}{3})[/tex]

we know that

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

so, we can write our expression as

[tex]tan(\frac{5\pi}{3})=\frac{sin(\frac{5\pi}{3})}{cos(\frac{5\pi}{3})}[/tex]

now, we can use unit circle

[tex]sin(\frac{5\pi}{3})=-\frac{\sqrt{3} }{2}[/tex]

[tex]cos(\frac{5\pi}{3})=-\frac{1}{2}[/tex]

now, we can plug values

[tex]tan(\frac{5\pi}{3})=\frac{-\frac{\sqrt{3} }{2}}{-\frac{1}{2}}[/tex]

[tex]tan(\frac{5\pi}{3})=\sqrt{3}[/tex]

Answer:

Rounding to the whole number or an estimation.

Step-by-step explanation: Pretty sure there isn't really a name for this

Rounding a number to its first digit is known as rounding to the nearest whole number. This method simplifies calculations while maintaining a number's approximate value.

The process of rounding a number to its first digit is often referred to as rounding to the nearest whole number. For example, if you have a number like 4.58, rounded to the nearest whole number it's 5, because the number next to 4 is 5 which is equal or higher than 5. But if the number was 4.42, rounded to the nearest whole number it's 4, because the number next to 4 is 2 which is less than 5. This rounding method applies when you want to make calculations simpler, while still keeping the number's value close to what it was.

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Answer:

(5/9)(v – 1)  

Step-by-step explanation:

(2/9)v - ((-1/3)v +5/9)     Remove parentheses

= (2/9)v + (1/3)v - 5/9    Multiply each term by 9/9

= (2/9)v + (3/9)v - 5/9   Combine like terms

= (2v + 3v)/9 -5/9         Combine like terms

=  5v/9 - 5/9                 Factor out 5/9

= (5/9)(v – 1)

Answer: 169.7

Step-by-step explanation:

Answer:

There are 1,014 kilograms of rice in 6 stacks of rice. 5 kilograms of rice remain.

Step-by-step explanation:

7 ÷ 1188 = 169

169 × 6 = 1,014

Answer:

$5

Step-by-step explanation:

So we know that altogether Michael paid $12 right?

So if his brother's price is x  then his price is x+2

so 2x+2=12 x=5

Michael's brother's price was $5

and his was $7

In this mathematics problem, Michael's brother's movie ticket cost $10, arrived at by subtracting $2 from the total cost of $12.

This is a simple subtraction problem. According to the problem, Michael paid $12 total, with his brother's ticket costing $2 less. Therefore, if we subtract $2 from Michael's ticket, we will have the cost of his brother's ticket.

Here are the steps:

Therefore, his brother's ticket cost $10.

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Answer:

184

Step-by-step explanation:

We are rounding at the 3, so we need to look at the next digit 9.

9>=5 so we will round the 3 up to 4

183.92 rounds to 184

Answer:

184

Step-by-step explanation:

183.92

Look at the digit directly to the right of the given digit. It is a 9. Because 9 is greater than 3, round up.

183.92 rounded to the nearest one place is 184.

184 is your answer

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[tex]a\cdot a\cdot a=216\\\\a^3=216\to a=\sqrt[3]{216}\\\\\boxed{a=6}\\\\\text{Substitute}\ b\cdot c=52\ \text{to the second expression}\ a\cdot b\cdot c=96:\\\\abc96\ \wedge\ bc=52\to a(52)=96\qquad\text{divide both sides by 52}\\\\a=\dfrac{96}{52}\to a=\dfrac{24}{13}\neq6[/tex]

a = 6 and a = 24/13  FALSE!!!

Answer:

–6 or 6

Step-by-step explanation:

7|x| = 42

We need to isolate the absolute value, so we will divide each side by 7

7|x|/7 = 42/7

 |x| = 6

Now we remove the absolute values and set what is inside the absolute value equal to plus and minus what is on the right hand side

x = + 6 and x = -6

Answer:

Solve for x over the integers:

7 abs(x) = 42

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by 7:

abs(x) = 6

Hint: | Eliminate the absolute value.

Split the equation into two possible cases:

Answer:  x = 6 or x = -6

Step-by-step explanation:

Answer:

communicative property of addition

Step-by-step explanation:

associative property of addition   is   (EX)     x + (a + 4) = (x + a) + 4

associative property of multiplication   is   (EX) 5(ab) = (5a)b

communicative property of multiplication   is  (EX) (2)(a) = (a)(2)

Final answer:

The equation 6+4=4+6 is an example of the commutative property of addition, stating that the order of addition does not affect the sum.

Explanation:

The equation 6+4=4+6 illustrates the commutative property of addition, which states that the order in which two numbers are added does not affect the sum. This is expressed mathematically as A+B=B+A. For ordinary numbers, if you add 2 + 3 or 3 + 2, for example, both expressions will equal to the same result - 5. The commutative property is also applicable to the addition of vectors, where the order of vectors being added together does not change the resultant vector.

Answer:

Any graph which passes through the origin(0,0)

Step-by-step explanation:

To check a graph if it  represents direct variation or not, one needs to check whether it passes through the origin or not .

So any graph which passes through the origin is of direct variation.

And in equation form : [tex]y=kx\\ y=mx +b\\[/tex]

                                      ⇒b=0 , m=k

So it is of direct variation if it passes through the origin (0,0)

Answer: its c

Step-by-step explanation: i just got it right

Answer:

-5 + 6i

Step-by-step explanation:

(-3)+(-2)+(3i)+(3i) = -5 + 6i

Answer: Infinitely many solutions

The second equation is equivalent to y = 2x - 5 when we subtract 5 from both sides, but this is the exact same as the first equation given to us. So we effectively have 2 copies of the same thing. One is just written in a different format.

Graphing these equations leads to the straight line. One line will be right on top of the other one. The two lines intersect an infinite number of times leading to infinitely many solutions. Any solution point is simply a point on the line y = 2x-5. The solution ordered pair is of the form (x,y) = (x, 2x-5). Two example points on this line are (0,-5) and (1,-3)

side note: We can say that this system is consistent (because it has at least one solution) and it's also dependent (because one equation depends on the other; or it is basically a copy)