A construction crew built 514 miles of road in 412 days. What is the unit rate in miles per day? Write your answer as a fraction or a mixed number in simplest form.

Answer:

x=1/2

y=-1/2

Step-by-step explanation:

x = y+1

x = 3y+2

Substitution means that you solve one equation for a variable by plugging it into the other equation. In this case, the first part is already done for you, and all you have to do is plugging in.

As you're given the value of the x in both equations, it does not matter which equation you plug into. You can plug either equation into one another.

For this, I will show you by plugging in the bottom equation for the top equation.

x = y+1

x = 3y+2

As we know x=3y+2, you must SUBSTITUTE that for the "x" in the top equation.

3y+2 = y+1

From there, you must solve it for the "y" value. In order to solve for the "y" value, you must get the "y" by itself onto one side.

So, subtract y from both sides.

(3y-y)+2 = (y-y)+1

Rewrite the equation.

2y+2 = 1

Remember, the goal is to get the "y" BY ITSELF.

There's a "+2" on the side of the y, so that has to be cancelled out. You can cancel it out by doing the OPPOSITE of adding, which is subtracting. So subtract both sides by 2.

2y+(2-2)=(1-2)

When subtracting a bigger number from a smaller number. The pattern is: Keep it, flip it, flip it.

Keep the 1.

Flip the - to a +

Flip the 2 into a -2.

So you get 1+(-2) which is -1. Now, rewrite the equation.

2y=-1

You want the y by itself. Right now, the y is being multiplied by 2, so you have to do the OPPOSITE, which is division. Divide both sides by 2.

y=-1/2

Now, use this value to plug into your ORIGINAL equations (you can pick either)

x = y+1 OR x = 3y+2

x= -1/2 + 1

x=1/2

(1/2, -1/2)

Answer:

x = √324 = 18

Step-by-step explanation:

x shows up only in the second problem, so I'll focus on that problem.

This is a right triangle because one of the three angles is 90 degrees.

Thus, the Pythagorean Theorem applies:  x^2 + 24^2 = 30^2, or

x^2 = 900 - 576 = 324

Then x = √324 = 18

Answer:

75 > x/15

Step-by-step explanation:

Step 1: Mulitply the 15 on both sides in order to get the x by it self.

Step 2: Simplify. 75 x (15) >x/15 x (15)

Step 3: The 15 on the right hand side cancels out leaving the x by itself.

Final Answr: 1125 > x which translates to x < 1125

 The solution to the inequality is: A) (x > 1125)

To solve the inequality 75 > x/15, we need to find the range of values for x that satisfy the inequality.

First, we can start by isolating x on one side of the inequality. To do that, we can multiply both sides of the inequality by 15 (since 15 is a positive number, we don't need to reverse the inequality sign):

75 * 15 > x

Now, simplify the left side of the inequality:

1125 > x

So, the solution to the inequality is x < 1125, which means all values of x that are less than 1125 will satisfy the inequality.

Visually, if we plot the graph of y = x/15 and y = 75, we'll see that y = x/15 is a straight line with a positive slope of 1/15 passing through the origin, and y = 75 is a horizontal line parallel to the x-axis at the y-coordinate of 75. The solution to the inequality is the region below the line y = 75, which corresponds to the values of x that are less than 1125.

In real-world terms, this inequality represents a scenario where 75 is greater than some fraction of x divided by 15. To satisfy the inequality, x must be less than 1125. For example, if x represents the number of items sold in a store, this inequality would indicate that the store must sell fewer than 1125 items to meet the condition. The store's sales would need to be less than 1125 * 15 = 16,875 to maintain the inequality's validity. Beyond this point, if the store sells more items, the inequality would no longer hold true.

To know more about inequality:

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Answer:x=5 or F

Step-by-step explanation:(8x+6)/(5x-2)=2, because it is the midsegment, cross multiply, and you get 2x=10, so x=5

Answer:

2y = x - 3

Step-by-step explanation:

Parallel lines can be defined as lines that do not intersect and as a result of this, parallel lines have the same slope but different intercepts.

Given the following data;

Points (x, y) = (3, 0)

Equation is 8x - 16y = -14

To find the equation of the line?

First of all, we would have to determine the slope of the line;

y = mx + c ......equation 1

8x - 16y = -14

Rearranging the equation, we have

16y = 8x + 14

Dividing through by 16, we have;

y = 8/16(x) + 14/16

y = 1/2(x) + 7/8

Therefore, the slope, m is 1/2

*To find the intercept*

Since the line is parallel we would use, m = 1/2

Substituting the values into equation 1, we have;

y = mx + c for x = 3 and y = 0

0 = 1/2(3) + c

c = -3/2

Re-writing the equation of line;

Slope, m = 1/2

Intercept, c = -3/2

y = 1/2(x) + (-3/2)

Multiplying all through by the lowest common denominator "2"

2y = x - 3

Step-by-step explanation:

: a common multiple of the denominators of a number of fractions. 2 : a common trait or theme.

Answer:

its 2.5 liters of olive oil because .5 times 5 equals 2.5 needed to satisfy ratio.

Answer:

x = 7

y = 10

Step-by-step explanation:

<K and <NLK are marked as being equal.

That means that KN and LN are equal.

So LN = 6

y - 4 = 6

y = 4 + 6 = 10

For the same reason LN = LM

That means that x + 3 = 10

x = 10 - 3

x = 7

Answer: 46 mph

Step-by-step explanation: 15*4=60 so 12*4=46

I hope this helps!

Answer:

2.5

Step-by-step explanation:

2500 ÷ 1000

*Sorry if this is wrong*

Answer:

A. 2000 square inches

B. 53.1 square inches

Answer:

[tex] \huge{ \boxed{ \bold{ \tt{y = - 4}}}}[/tex]

Step-by-step explanation:

[tex] \sf{4y - 9 - 6y = 2(y + 5) - 3}[/tex]

Subtract like terms : 6y from 4y

[tex] \longrightarrow{ \sf{ - 2y - 9 = 2(y + 5) - 3}}[/tex]

Distribute 2 through the parentheses

[tex] \longrightarrow{ \sf{ - 2y - 9 = 2 *y + 2 *5 \: - 3}}[/tex]

[tex] \longrightarrow{ \sf{ - 2y - 9 = 2y + 10 - 3}}[/tex]

Subtract 3 from 10

[tex] \longrightarrow{ \sf{ - 2y - 9 = 2y + 7}}[/tex]

Move 2y to left hand side and change it's sign

[tex] \longrightarrow{ \sf{ - 2y - 2y - 9 = 7}}[/tex]

Move 9 to right hand side and change it's sign

[tex] \longrightarrow{ \sf{ - 2y - 2y = 7 + 9}}[/tex]

Combine like terms

[tex] \longrightarrow{ \sf{ - 4y =7 + 9}}[/tex]

Add the numbers : 7 and 9

[tex] \longrightarrow{ \sf{ - 4y = 16}}[/tex]

Divide both sides by -4

[tex] \longrightarrow{ \sf{ \frac{ - 4y}{ - 4} = \frac{16}{ - 4}}} [/tex]

Remember : Dividing a positive integer by any negative integer gives a negative integer.

[tex] \longrightarrow{ \boxed{ \sf{y = - 4}}}[/tex]

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

Let's check whether the value of y is -4 or not.

L.H.S : [tex] \sf{4y - 9 - 6y}[/tex]

plug the value of y and simplify

[tex] \dashrightarrow{ \sf{4 * (- 4 )- 9 - 6 * (- 4)}}[/tex]

[tex] \dashrightarrow{ \sf{ - 16 - 9 - ( - 24)}}[/tex]

[tex] \dashrightarrow{ \sf{ - 16 - 9 + 24}}[/tex]

[tex] \dashrightarrow{ \sf{ - 16 + 15}}[/tex]

[tex] \dashrightarrow{ \sf{ - 1}}[/tex]

R.H.S :[tex] \sf{2(y + 5) - 3}[/tex]

plug the value of y and simplify

[tex] \dashrightarrow{ \sf{2( - 4 + 5) - 3}}[/tex]

[tex] \dashrightarrow{ \sf{2 *1 - 3}}[/tex]

[tex] \dashrightarrow{ \sf{2 - 3 }}[/tex]

[tex] \dashrightarrow{ \sf{ - 1}}[/tex]

∴ L.H.S = R.H.S

The value of y is -4

And we're done!

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

Hope I helped!

Best regards! :D

~TheAnimeGirl

Answer: red

Step-by-step explanation: that’s mine

Answer:

Pink

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

the value of the expression 5y² + 4x when x = 2.5 and y = 3 will be 55.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression 5y² + 4x

To calculate the value of expression at x = 2.5 and y = 3

Substitute the value of x and y in the expression:

=> 5y² + 4x

=> 5* 9 + 4 * 2.5

=> 45 + 10

=> 55

therefore, 55 is the value of the expression 5y² + 4x when x = 2.5 and y = 3.

Learn more about expression here:

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Answer:

C. 7

Step-by-step explanation:

[tex] In\: \triangle ABC\\

\overline{PQ} \parallel \overline {BC}.. (given) \\[/tex]

Therefore, by Basic Proportionality theorem:

[tex] \frac{AP}{PB} = \frac{AQ}{QC} \\\\

\therefore \frac{x}{x+7} = \frac{x-3}{x+1} \\\\

\therefore \: \frac{x - x - 7}{x + 7} = \frac{x - 3 - x - 1}{x + 1} \\ (by \: dividendo) \\ \\ \frac{ - 7}{x + 7} = \frac{ - 4}{x + 1} \\ \\ \frac{7}{x + 7} = \frac{4}{x + 1} \\ \\ 7x + 7 = 4x + 28 \\ \\ 7x - 4x = 28 - 7 \\ \\ 3x = 21 \\ \\ x = \frac{21}{3} \\ \\ \huge \red{ \boxed{ x = 7}}[/tex]

Answer:

Parker the dog is 76.2 centimeters long.

Step-by-step explanation:

Parker the dog is 2 feet 6 inches long. There are 2.54 centimeters in 1 inch. How many centimeters is Parker the dog?​ 2 feet = 12 inches. 2(12) + 6 = 30

30(2.54) = 76.2.

Please let me know if you have anymore questions.

Good Luck! :)

1 foot = 12 inches

1 inch = 2.54 centimeters

1 foot = 30.48 centimeters

2 x 30.48 =  60.96

6 x 2.54 = 15.24

60.96+15.24=76.20

Parker the Dog is 76.20 centimeters tall.

Answer:

29

Step-by-step explanation:

Start with -39. We need to do inverse operations to figure out the solution. -39 divided by -3 is 13, and 13 plus 16 is 29.

Answer:

29

Step-by-step explanation:

-39=-3(n-16)

13=n-16

29=n

Answer:

7

Step-by-step explanation:

Answer:

it takes 24 days

Answer:

its-5.5°C

explanation

combine it

Answer:

the answer is br-br

Step-by-step explanation:

that is answer bro

Answer:

5 hours

Step-by-step explanation:

276/12= 23

115/23= 5

Answer:

1/2 teaspoon salt

Step-by-step explanation:

We can make this into a ratio of salt:baking soda

1/8:1/4

now, how many 1/4 will we need to make 1?

If we multiply 1/4 by 4, we get one. So, we should do the same to 1/8!

1/8*2=4/8, or 1/2 teaspoon

Answer:

There are 8 girls.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

20 divided by 5 = 4.

4x2=8

Answer:

62-3z ≤ 40

Step-by-step explanation:

62 is the starting point. jasmin's dog can lose 3 lbs per week and z represents the number of possible weeks. then we know it has to be less than or equal to 40. so put that there.

Answer:

okay so the first one can be any of teh five

teh second one is onyl 4 of them bc u've already used one

so we do : 4*5 which is 20

Answer:

WRONG ALL

Step-by-step explanation:

3. Should be:

[tex] - 4 \frac{7}{8} \times \frac{2}{3} \\ \\ - \frac{39}{8} \times \frac{2}{3} \\ \\ \frac{ -13}{4} [/tex]

4. Should be:

[tex] - 3 \frac{1}{5} + - \frac{2}{3} \\ \\ - 3 \frac{3}{15} - \frac{10}{15} \\ \\ - 3 \frac{7}{15} [/tex]

I hope this helps you :)

9514 1404 393

Answer:

  x= 10, corresponding

Step-by-step explanation:

Corresponding angles are in the same direction from their respective intersections. Here, the angles are both northwest of the point where the lines cross. The angles are corresponding.

__

Corresponding angles are congruent, so we have ...

  10x +10 = 110

  10x = 100 . . . . . subtract 10

  x = 10 . . . . . . . . divide by 10

Answer:

12, 43/63

Step-by-step explanation:

Answer: 12 43/63

Step-by-step explanation: it was correct on my test