Three runners run along a 1.5 mile trail one Saturday morning. The graph shows the runners’ locations starting at 9:00 a.m.
who runs fastest?

Answer:

y = -x + 4

perp: m = 1

y + 4 = x - 3

y = x - 7

Step-by-step explanation:

Answer:

Similar polygon

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

Let the number be x

Then 4 times a number divided by 3 is 5 more than that number divided by 2 gives the equation:

[tex] \frac{4x}{3} = \frac{x}{2} + 5[/tex]

Multiply through by the LCD, which is 6.

[tex] 6 \times \frac{4x}{3} = 6 \times \frac{x}{2} + 5 \times 6[/tex]

Cancel out to obtain:

[tex] 2 \times 4x =3 \times x + 30[/tex]

[tex]8x = 3x + 30[/tex]

Group similar terms

[tex]8x - 3x = 30[/tex]

Simplify the LHS

[tex]5x = 30[/tex]

Divide both sides by 5 to get:

[tex]x = 6[/tex]

Answer:

There are no values of x that make the equation true.

Step-by-step explanation:

3(x-2)=3x+7

3x-6=3x+7

3x-6+6=3x+7+6

3x=3x+13

Dviding 3x by 3x will equal 1, and 1 does not equal 13.

Answer:

There are no value of x

Step-by-step explanation:

3(x-2) = 3x+7

3x-6 = 3x+7

-6= 7

=7 +6

=13

so we can say that,There are no value of x

Answer:$38.39

Step-by-step explanation:

Original price: $

47.99

Discount percentage:

20

%

Results

Discount:

$9.60

Final Price:

$38.39

Answer:

$59.99

Step-by-step explanation:

"20% off" translates into "80% of original price."

Thus, 0.80p = $47.99, where p is the original price.

Dividing both sides by 0.80 yields:

p = $59.99

Answer:6 = 6 represents a true statement because 6 is always equal to 6. When graphed on a coordinate plane, this equation would result in a straight line at y = 6, which means that every point on the line corresponds to a solution of the equation. Since the line extends infinitely in both directions, there are infinitely many solutions to this equation.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

2 times 2 times 2 times 5 = 40

The prime factorization of 40 is 2 times 2 times 2 times 5, which can be written as 2^3 * 5. So, option C, "2 times 2 times 2 times 5," is the correct prime factorization of 40.

The prime factorization of the number 40 is 2^3 * 5. To arrive at this factorization, we break down 40 into its prime factors. We start by dividing 40 by the smallest prime number, 2. Since 40 is even, it can be divided by 2 evenly, resulting in 20. We continue this process until we can no longer divide by 2, which leaves us with 20. Now, we try to divide 20 by the next smallest prime, which is also 2. This division gives us 10. Once again, we divide by 2, and we are left with 5. Since 5 is a prime number, we cannot further divide it. Therefore, we have prime factorized 40 as 2 * 2 * 2 * 5, which can be expressed as 2^3 * 5, where the exponent 3 indicates that we have three 2s multiplied together, and the 5 is the prime factor on its own.

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Answer:

2000 ml

Step-by-step explanation:

Given: Sarai pours all the liquid from a full small beaker into a  larger beaker.

           The liquid fills the large beaker to 15% of its capacity.

            The small beaker holds 300 ml.

Lets assume capacity of large beaker to hold be "x".

As given, Sarai pours all the liquid from a full small beaker into a larger beaker

∴ [tex]15\% \times x= 300\ ml[/tex]

⇒ [tex]0.15x= 300[/tex]

Dividing both side by 0.15

⇒[tex]x= \frac{300}{0.15}[/tex]

∴ [tex]x= 2000\ ml[/tex]

Hence, the large beaker can hold 2000 ml of liquid.

Answer:

rest set option

Step-by-step explanation:

Answer:

The number 1 is not necessary when expressing powers of one. For example, you needn't write "5" as [tex]5^{1}[/tex].

Step-by-step explanation:

The number 1 is written when it is part of a larger number, as it is significant. It is not necessary to write leading zeros. In scientific notation, trailing zeros are excluded, and the number is written in a form where only non-zero digits appear before the decimal.

Understanding when to write the number 1 and when it's not needed depends on the context in mathematics, especially when dealing with significant figures and scientific notation. Generally, all non-zero numbers are considered significant (rule 1), which means that when a value like 1 is part of a larger number, it contributes to the meaning of that number. However, leading zeros do not count as significant (rule 3).

In the case of multiplication by units, like converting from kilograms to grams, we utilize the concept of multiplying by the number 1 to affect the units without changing the value. For example 0.7 kg can be multiplied by 1000/1 (1000 g / 1 kg) to convert to grams. This is because 1000/1 is equal to 1000, indicating multiplication by one does not change the value.

When expressing numbers in scientific notation, it's important to include the non-zero digits only before the decimal point, excluding any trailing zeros. Thus, 1,500,000 would be written as 1.5 x 106, with the power indicating the necessary number of decimal point movements to place it after the first significant digit.

Answer:

A' (-4,0)

Step-by-step explanation:

The complete question is

If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x minus 2, y + 2), what will be the coordinates of A prime? On a coordinate plane, triangle A B C has points A(negative 2, negative 2), B(negative 2, negative 4), C(2, negative 4)

we know that

The rule of the translation is

(x,y) -----> (x-2,y+2)

The coordinates of point A (-2,-2)

Applying the rule of the translation to coordinate A

A (-2,-2) ----- A' (-2-2,-2+2)

A (-2,-2) ----- A' (-4,0)

Answer:

The answer is A on edge

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

If suffices to look at the last term. It must simplify to 4/(3w²), so the exponents of z must match in numerator and denominator, and the ratio of constants must reduce to 4/3.

The exponents of z have the right values in choices B and D, but the ratio of constants only matches in choice D. Looking at the rest of choice D, we see that we can factor 6w²z² from both numerator and denominator, then factor 2 from the remaining numerator to make it match the desired form.

  [tex]\dfrac{(12w^2z^4-24w^2z^2)}{18w^4z^2}=\dfrac{6w^2z^2}{6w^2z^2}\cdot\dfrac{2z^2-4}{3w^2}=\dfrac{2(z^2-2)}{3w^2}[/tex]

Answer: Answer is x = 5, y = -3

(5, -3)

Step-by-step explanation: The instruction is to use the substitution method, and from the first equation,

y = x - 8

This means we replace the value of y in the second equation with x - 8. Hence;

2x + 3y = 1 can now be re-written as

2x + 3(x - 8) = 1

2x + 3x - 24) = 1

5x - 24 = 1

Add 24 to both sides of the equation

5x -24 + 24 = 1 + 24

5x = 25

Divide both sides of the equation by 5

x = 5

Having calculated x as 5, we can now substitute for the value of x in the first equation

y = x - 8 now becomes

y = 5 -8

y = -3

Using the substitution method, we found the solution to be (5, -3), which matches option a.

To solve the system of equations using the substitution method, we'll first solve one equation for one variable and then substitute it into the other equation.

Given:

1. [tex]\( y = x - 8 \)[/tex] (Equation 1)

2. [tex]\( 2x + 3y = 1 \)[/tex] (Equation 2)

From Equation 1, we can solve for y:

[tex]\[ y = x - 8 \][/tex]

[tex]\[ x = y + 8 \][/tex] (Re-arranging)

Now, substitute [tex]\( x = y + 8 \)[/tex] into Equation 2:

[tex]\[ 2(y + 8) + 3y = 1 \][/tex]

Simplify and solve for y:

[tex]\[ 2y + 16 + 3y = 1 \][/tex]

[tex]\[ 5y + 16 = 1 \][/tex]

[tex]\[ 5y = 1 - 16 \][/tex]

[tex]\[ 5y = -15 \][/tex]

[tex]\[ y = -3 \][/tex]

Now, substitute [tex]\( y = -3 \)[/tex] into Equation 1 to find [tex]\( x \)[/tex]:

[tex]\[ x = (-3) + 8 \][/tex]

[tex]\[ x = 5 \][/tex]

So, the solution to the system of equations is [tex]\( (x, y) = (5, -3) \)[/tex].

Answer: n*4512 is less than or equal to 117

Step-by-step explanation: n=number N*45=X X=Number more than 117. X decreased by 12 is less than or equal to 117.

Make an x and y table, and pick any values to plug in for x in the equation.

I will use the numbers from -2 to 2

Now plug in the values you picked for x into the equation to find its y-value

x = -2

y = 3x - 1   Plug in -2 for x

y = 3(-2) - 1

y = -6 - 1

y = -7

x = -1

y = 3x - 1

y = 3(-1) - 1

y = -3 - 1

y = -4                

Do the same for the rest of the numbers, and graph each point and draw a line connecting them.

Answer:-.6666666667x +6

Step-by-step explanation:

I have a school calculator

Answer:

-2/3 is the slope

Step-by-step explanation:

Slope = y2 - y1/x2 - x1

= 10 - 4/-6 - 3

= 6/-9

=-2/3

Answer:

C.x/(x+5)(x-2)

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Complementary angles

Step-by-step explanation:

Complementary angles add up to 90 degrees

Answer: C 25/9

Step-by-step explanation:

Answer:

Algebraic expression in terms of k

     k= T- p

Step-by-step explanation:

As

no of kittens left = k

no of puppies left =p

If total left after giving away kittens  =T

T = p + k

In terms of k the expression will be

k= T- p

Keywords: Algebra

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Final answer:

To write an algebraic expression in terms of k, subtract the number of kittens given away from the initial number of kittens. The algebraic expression in terms of k is (3/5)x.

Explanation:

To write an algebraic expression in terms of k, we need to determine the initial number of kittens before any were given away. Let's call this number 'x'. According to the problem, 2/5 of the kittens were given away. This means that (2/5)x kittens were given away, leaving k kittens remaining.

To find the algebraic expression in terms of k, we subtract the number of kittens given away from the initial number of kittens. So the expression is x - (2/5)x = k.

We can simplify this expression by finding a common denominator for the fractions. In this case, the common denominator is 5. So the expression becomes 5x/5 - (2/5)x = k. Simplifying further, we have (3/5)x = k. Therefore, the algebraic expression in terms of k is (3/5)x.

Answer:

$34

Step-by-step explanation:

So he earns $24 per week (ima just say p/w to make it shorter) meaning he earned around $216 in total. To get to $25 p/w, you have to get $250 in total from the 10 weeks. So $250 - $216 = $34.

⭐ Answered by Foxzy0⭐

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Answer:

(-2,-4),(2,1), and (7,-5)

Step-by-step explanation:

The given triangle has coordinates (6,4), (2,-1), and (-3,5).

When we translate 4 units left, the we obtain:

(6,4)------>(6-4,4)=(2,4)

(2,-1)----->(2-4,-1)=(-2,-1)

(-3,5)----->(-3-4,5)=(-7,5)

When the resulting figure is rotated 180° about the origin, the coordinates of the final figure becomes

(2,4)------>(-2,-4)

(-2,-1)----->(2,1)

(-7,5)------->(7,-5)

NB: The mapping for 180° rotation is:

(x,y)----->(-x,-y)

Answer:

Step-by-step explanation:

First, start off by solving for the slope using this formula:

[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Then, plug in the values: [tex]\frac{0-(-3)}{7.5-0}[/tex]

Solve the equation: [tex]\frac{3}{7.5}[/tex]

That's your slope.

Then plug in one of the coordinates given in the problem for x and y and solve this equation:

y=[tex]\frac{3}{7.5}[/tex]x+b

Hope that helped!!! :)

Answer:

The value of the expression is 4.

Step-by-step explanation:

Consider the provided information.

We have given that:

[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]

Now we need to find the value of:

[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =?[/tex]

Consider the provided fact:

[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]

Multiply [tex]\frac{1}{5}[/tex] both sides.

[tex]\dfrac{1}{5}\times \dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]

[tex]\dfrac{1\times2\dfrac{1}{2} }{5\times\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]

[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =4[/tex]

Hence, the value of the expression is 4.

Answer:

there are 2 groups

Step-by-step explanation: 14 x 2 = 28

Answer:

25 minutes is how long Carter played

Step-by-step explanation:

To find out how many minutes Carter plays, multiply 40 minutes by 5/8, which results in 25 minutes of playtime.

To determine the number of minutes Carter plays in a basketball game, which is 40 minutes long, when he plays 5/8 of the game, we use multiplication. We multiply the total game time by the fraction of the game played:

Steps to calculate:

Therefore, Carter plays for 25 minutes of the basketball game.