Tony is 1/2 of a mile ahead of Laura on a jogging path. If Tony is running at 5 miles per hour, and Laura is running at 7 miles per hour, how long will it take Laura to catch up with Tony?

Answer:

[tex]XZ=146[/tex]

Step-by-step explanation:

Since [tex]M[/tex] is the midpoint of segment [tex]XZ[/tex]:

[tex]XM+MZ=XZ[/tex]

[tex]XM=MZ[/tex]

Identify your known values:

[tex]XM=2x+35\\MZ=5x-22\\[/tex]

Solve for [tex]x[/tex]:

[tex]2x+35=5x-22[/tex]

Subtract [tex]35[/tex] from both sides of the equation:

[tex]2x=5x-57[/tex]

Subtract [tex]5x[/tex] from both sides of the equation:

[tex]-3x=-57[/tex]

Divide by the coefficient of [tex]x[/tex], which is [tex]-3[/tex]:

[tex]x=19[/tex]

Substitute:

[tex]XM=2(19)+35\\MZ=5(19)-22[/tex]

Solve:

[tex]XM=73\\MZ=73[/tex]

Again, we know:

[tex]XM+MZ=XZ[/tex]

Therefore:

[tex]XZ=73+73[/tex]

Solve:

[tex]XZ=146[/tex]

Answer:

7x+y, when x+4 and y+5

7(4) + 5=

28+5=

33

Step-by-step explanation:

Hope this helps. :)

Answer:

1/2 and 5/10 are equivalent because when you reduce 5/10, you get 1/2. Also, whenever we speak, we always say half of 10 is 5. Finally, the factor of 5 made them have an equal value. Therefore, 5/10 and 1/2 are equivalent.

Hope this helps!

Multiply the fraction by 5/5 makes them equivalent fraction.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

1/2 and 5/10

Now, to make fraction equivalent we have to find the factorizing factor.

As, 1/2 x 5/5= 5/10

Hence, multiply the fraction by 5/5 makes them equivalent fraction.

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Since , the relation is linear .

Let equation is y = mx + c .

Putting , x = 0 and y = 32 .

32 = c  .......( 1 )

Also , putting x = 100 and y = 212 .

We get :

212 = 100m + c .......( 2 )

Comparing equation 1 and 2 .

100m = 212 - 32

x = 1.8

Therefore , y = 1.8x + 32 .

Hence , this is the required solution .

[tex]y=\dfrac{9}{5}x+32[/tex]  represents degrees Fahrenheit in terms of degrees Celsius. where  x represent the temperature in degrees Celsius and y represents the temperature in degrees Fahrenheit.

Temperature can be expressed in different units like degrees Celsius and degrees Fahrenheit.

Let us consider two variables x and y as following:

x represent the temperature in degrees Celsius

y represent the temperature in degrees Fahrenheit

Equation depicting relation between variable x and y is

[tex]y-y_1=m(x-x_1)[/tex]...........................1

where,  [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using the given conditions:

[tex](x_1,y_1)=(0,32) \text{\ and\ }(x_2,y_2)=(100,212)[/tex]

Substituting to calculate the value of m,

[tex]m=\dfrac{212-32}{100-0}\\\\m=\dfrac{180}{100}\\\\m=9/5[/tex]

From equation 1

[tex]y-32=\dfrac{9}{5}(x-0)\\y-32=\dfrac{9}{5}x\\y=\dfrac{9}{5}x+32[/tex]

Thus, an equation that representing degrees Fahrenheit in terms of degrees Celsius is  [tex]y=\dfrac{9}{5}x+32[/tex].

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Answer:

7x-15=20

Step-by-step explanation:

7x-15=20

7x=35

x=5

Answer:

it would be 11:07

Step-by-step explanation:

what grade are u in???

Answer:

2.80×50

Step-by-step explanation:

2.80×50 step by step

Answer:

In math :The objective function is a mathematical term that describes how different variables contribute to a certain value that is being sought to be optimized.

In science: Scientific objectivity is a characteristic of scientific claims, methods and results. It expresses the idea that the claims, methods and results of science are not, or should not be influenced by particular perspectives, value commitments, community bias or personal interests, to name a few relevant factors.

In ela: Being the object or goal of one's efforts or actions. not influenced by personal feelings, interpretations, or prejudice; based on facts; unbiased: an objective opinion. ... being the object of perception or thought; belonging to the object of thought rather than to the thinking subject (opposed to subjective).

Step-by-step explanation:

The system of equation should be C) 250x+150y=550 ; 180x+120y=420

250x+150y=550 ; 180x+120y=420

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Answer: The Answer is C

I just took the test

Step-by-step explanation:

The scale factor of the dilation is 3. The correct option is C.

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

From the given image:-

The initial size in the image is calculated as 11 - 2 = 9

The dilated size in the image is calculated as 5 - 2 = 3

The scale factor will be given as:-

Scale factor  = ratio of the initial size to the dilated size

Scale factor  = Initial size / Dilated size

Scale factor = 9 / 3 = 3

Therefore, the scale factor of the dilation is 3. The correct option is C.

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Answer:

56

Step-by-step explanation:

(7/20)=(x/160)

160(7/20)=x

x=56

Answer:

x = -28/11

Step-by-step explanation:

-2(4x + -4) - 3x - 2 =34

Distribute

-8x+8 -3x-2 =34

Combine like terms

-11x +6 = 34

Subtract 6 from each side

-11x+6-6 = 34-6

-11x = 28

Divide each side by -11

-11x/-11 = 28/-11

x = -28/11

Answer:

x= -28/11

Step-by-step explanation:

Multiply -2 by 4x +4

That equals -8x+8

So the equation is now

-8x+8+3x -2 = 34

Now combine  like terms

11x+6=34

Subtract 6 from both sides

11x=28

divide by 11 on both sides

x =  -28/11

Answer:

d

Step-by-step explanation:

Answer:

  C.  It is just right.

Step-by-step explanation:

We want to compare the ratios ...

  bags : liters = 15 : 2

and

  bags : liters = 90 : 12

If we multiply the numbers of the first ratio by 6, we see they are identical to those in the second ratio:

  (15)(6) : (2)(6) = 90 : 12

The ratio of bags to liters for Peggy's tea matches the ratio Kermit likes. He will think it is just right.

Answer:

C its just right

Step-by-step explanation:

Answer:

30 minutes

Step-by-step explanation:

Think of it as a fractions. Player 1: 6 min./1 lap, Player 2: 10 min./1 lap. So in order to do this you have to find the greatest common factor. The GCF is 30. [learned this 2 yrs ago, im not entirely sure]

Answer:

D -$7.20

Step-by-step explanation:

so your answer is -$7.20

I hope this helps

$7.20 will be Jennys total allowance.

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

Jenny has $2.40 deducted from her monthly allowance every time she forgets to do a chore.

If she forgets three times in a month.

Thus, Jennys total allowance will be

=2.40 x 3

=$7.20

Hence, $7.20 will be Jennys total allowance.

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Answer:

≈ 7.28

Step-by-step explanation:

Calculate the length using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A(- 5, - 4) and (x₂, y₂ ) = B(- 3, 3)

AB = [tex]\sqrt{(-3+5)^2+(3+4)^2}[/tex]

     = [tex]\sqrt{2^2+7^2}[/tex]

     = [tex]\sqrt{4+49}[/tex]

     = [tex]\sqrt{53}[/tex] ≈ 7.28 ( to the nearest hundredth )

Answer:

0.51764705

Step-by-step explanation:

Answer:

254c = 333

Step-by-step explanation:

254c = 333

Answer:

Step-by-step explanation:

Given P to be the point that divides the coordinates J and K in the ratio 1:3

then the coordinate of point P will be xpressed as;

P(X, Y) = [tex](\frac{bx_1+ax_2}{b+a}, \frac{by_1+ay_2}{b+a})[/tex]

Given J = (-4, 11) and K = (8, -1)

[tex]x_1 = -4, y_1 = 11, x_2 = 8 \ and \ y_2 = -1, a = 1, b = 3[/tex]

substituting the given parameters into the line division formula

[tex]P(X, Y) = (\frac{3(-4)+1(8)}{3+1}, \frac{3(11)+(1)(-1)}{3+1})\\\\P(X, Y) = (\frac{-12+8}{4}, \frac{33-1}{4})\\\\P(X, Y) = (\frac{-4}{4}, \frac{32}{4})\\\\P(X, Y) = (-1, 8)[/tex]

Hence the coordinates of P is (-1, 8)

Answer:

Step-by-step explanation:

Length of fence = Perimeter of triangle

                          = 10 + 20 + 15

Length of the fence = 45 m

Cost of fencing per meter = Rs. 25

Cost of fencing 45 m = 25 * 45

                                  = Rs. 1125

[tex]\huge{\fbox{\fbox{Given:}}}[/tex]

Lengths of the three sides of triangle are 10m,20m and 15m.

Perimeter of the ∆

[tex]\large{\fbox{\gray{Cost \: of \: fencing \: the \: field=}}}[/tex]

[tex]45 \times 25 = Rs1125[/tex]

Answer: Inequality Form:

n > 4

Interval Notation:

4, (infinite)



Answer:

8

Step-by-step explanation:

2 (2)(2)

2 times itself 3 times.

Answer: 8

Step-by-step explanation: Since 2 is to the power of 3 that means multiply by itself 3 times, so 2 x 2 x 2 = 8.

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Answer:

Step-by-step explanation:

Let us take this one by one. One color can pair with three colors.

Green = Maroon, Blue, Wheat = GM, GB, GW

Maroon = Green, Blue, Wheat = MG, MB, MW

Blue = Green, Maroon, Wheat = BG, BM, BW

Wheat = Green, Maroon, Blue = WG, WM, WB

So the combinations are:

GM, GB, GW, MG, MB, MW, BG, BM, BW, WG, WM, WB

Which is letter B.

Answer:

A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Put (-6,0) and (0,3) into a table of values

form of the equation: mx+b

x -6 0

y 0 3

3/-6=-0.5 (m)

3=b (the value of y when x=0)

equation: y=0.5x+3

Answer:

C

Step-by-step explanation:

[tex]15x^{\frac{1}{3} }y^{\frac{1}{5} }\\\\=15x^{\frac{5*1}{5*3} }y^{\frac{3*1}{3*5} }\\\\=15x^{\frac{5}{15} }y^{\frac{3}{15} }\\\\=15\sqrt[15]{x^{5}y^{3} } \\\\[/tex]

The expression 15x^(1/3) y^(1/5) can be written as 15 * ∛x * ∜y

To express 15x^(1/3) y^(1/5) using a radical, we will start by writing each term with a common base.

Now express x^(1/3) as a radical. We know x^(1/3) is the cube root of x, this is rewritten as ∛x.

Now, we express y^(1/5) as a radical. We know that y^(1/5) is the fifth root of y, so we is rewritten it as ∜y.

Putting it all together, we have:

15x^(1/3) y^(1/5) = 15 * ∛x * ∜y.

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