A train travels 750 miles in 15 hours. which unit rate describes the speed of the train?
a. 50 miles per hour
b. 75 miles per hour
c. 150 miles per hour
d. 350 miles per hour

Answer:

IF the other line is parallel you use the same slope (m) as the line given then find the y intercept (b) by plugging in the (x,y) and m into y = mx + b

Step-by-step explanation:

 all the coordinates of the original triangle have been multiplied by 1/2

A (-4,-6) x 1/2 = -2,-3

B (-8,2) * 1/2 = -4,1

C (-2,4)  *1/2 = -1,2

 so the scale factor is 1/2

 Answer is B

Answer: b. 300 feet

Step-by-step explanation:

We know that 1 yard = 3 feet

Given : The length of a football playing field is 100 yards between the opposing goal lines.

Then, the length of the football field in feet will be :-

[tex]100\times3=300[/tex]

Therefore, the length of the football field in feet = 300 feet

Hence b is the correct option.

An equation is formed of two equal expressions. The number is 1,011.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the unknown number be represented by x.

Given that if you add one-third of a number to itself, you get 1348. Therefore, we can write the given statement in the form of an equation as,

(1/3)x + x = 1348

(x/3) + (3x/3) = 1348

(x + 3x)/3 = 1348

4x / 3 = 1348

4x = 1348 × 3

x = (1348×3)/4

x = 1011

Hence, the number is 1,011.

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The expression sin(2x) − sinx is equivalent to 2sin (3x/2) sin(x/2) therefore option (D) is correct.

Recall the formula of sine

[tex]\sin x-\sin y=2 \sin (\frac{x+y}{2}) \sin (\frac{x-y}{2})[/tex]

The given expression is sin (2x) − sin x.

Apply the formula

[tex]\sin (2x) - \sin x =2 \sin (\frac{2x+x}{2}) \sin (\frac{2x-x}{2})[/tex]

                      [tex]=2 \sin (\frac{3x}{2}) \sin (\frac{x}{2})[/tex]

Hence the expression is equivalent to 2sin (3x/2) sin(x/2)

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To solve the linear system given by -14x + 11y = 23 and 7x - 3y = 37, we used the elimination method, which resulted in finding the solution x = 13.6 and y = 19.4.

To solve the system of linear equations given by -14x + 11y = 23 and 7x - 3y = 37, you can use the method of substitution or elimination. Here, I'll demonstrate the elimination method:

Therefore, the solution to the system of equations is x = 13.6 and y = 19.4.

He needs 15 weeks to pay back his brother completely.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Hugo decided to pay $2 a week to his brother to buy a bicycle.

The equation y - 10 = - 2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.

To pay back to the brother he must owe no money which is y = 0.

∴ The weeks needed is,

0 - 10 = -2(x - 10).

- 10 = -2x + 20.

2x = 30.

x = 15.

He needs 15 weeks to pay back completely.

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Answer:

Thus, she has enough pizza left for the meeting.

Step-by-step explanation:

It is given that, Cyndi cut pizza in 12 pieces.

Also, She ate 1/6 of pizza yesterday afternoon.

⇒ She ate = [tex]12\times\frac{1}{6} = 2\ \text{pieces}[/tex]

Her Brother ate 1/5 of left pizza

⇒ Her Brother ate = [tex]10\times\frac{1}{5} = 2\ \text{pieces}[/tex]

Then she has left pieces of pizza = 12 - (2 + 2) = 8 pieces

And also that much pieces she wants for the club meeting.

Thus, she has enough pizza left for the meeting.

So the other guy has the right work but at the end he messed up. The real answer is 10 miles.

By establishing the relationship between Ted's uphill and downhill travel times, we can set up an equation to solve for the one-way distance D of the hike. We find that the one-way distance D is 5 miles, making the total length of the hike 10 miles.

On an uphill hike, Ted climbs at a rate of 3 miles an hour. Going down, he runs at a rate of 5 miles an hour. If it takes him 40 minutes longer to climb up than run-down, we need to figure out the total length of Ted's hike.

First, let's establish the relationship between the times it takes Ted to hike up and run down the hill. If T is the time it takes to run down, then the time to hike up is T + 40/60 hours (since 40 minutes is two-thirds of an hour).

Let D be the distance of the hike one way. As Ted climbs up at a rate of 3 miles per hour, the uphill time is D/3. Running down at a rate of 5 miles per hour, the downhill time is D/5. We can set up the following equation:

D/3 = D/5 + 40/60

Multiplying through by 15 to eliminate fractions, we get:

5D = 3D + 10

This simplifies to:

2D = 10

Dividing by 2:

D = 5 miles

Since the total hike involves going up and then down the same distance, the total length of the hike is:

Total Length = 5 miles + 5 miles = 10 miles.

The woman's average speed is 49 miles per hour, so in 7 hours she will travel 343 miles.

To solve how far a woman will drive in 7 hours at the same rate as she did for 245 miles in 5 hours, we need to calculate her average speed and then use that to find the distance for 7 hours. The average speed is calculated by dividing the total distance by the total time of travel. So in this case, the average speed is 245 miles divided by 5 hours, which is 49 miles per hour.

Next, to find out how far she will travel in 7 hours, we multiply her average speed by the total time of travel. Therefore, 49 miles per hour multiplied by 7 hours equals 343 miles.

The area of rectangle is 60 yd²

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of a rectangle is 4 yd longer than its width.

Let, the length = x

And, width = y

Now,

Perimeter of rectangle = 2(x+y)

the area of rectangle = xy

x = y+ 4

2(x+y) = 32

Subtract x by equation (1) in (2), we get;

2(y+4+y) = 32

2y+8 +2y = 32

4y = 24

y= 24\4

y  =6yd

And, x = 6+4

x  = 10yd

Thus, Area of rectangle = xy

                                   = 10 × 6

                                   = 60yd²

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The triangle's base measures 82 in length.

What is the Permeter of a traingle?

According to our question,

IF (3X+2) & (5X-14) ARE THE EQUAL SIDES THEN

3X+2=5X-14

-2X=-16

X=-16/-2

X=8

THUS THE EQUAL SIDES ARE

3*8+2=24+2=26

5*8-14=40-14=26

SO

82=BASE+26+26

BASE=82-52

B=30 CM.

30+26+26=82

82=82

Hence we can say that the triangle's base measures 82 in length.

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Final answer:

The lengths of the two legs of the isosceles triangle are equal, and by setting the expressions for these lengths equal to each other and solving for 'x', we find that the length of the base of the triangle is 30 cm.

Explanation:

The perimeter of an isosceles triangle is given as 82 cm. The two legs are represented by the expressions (3x + 2) and (5x - 14). Since it is isosceles, these two expressions must be equal because the lengths of the legs are equal, as stated by the theorem.

First, set the expressions equal to each other to find the value of 'x':

3x + 2 = 5x - 14

We then solve for 'x' by subtracting 3x from both sides and adding 14 to both sides:

16 = 2x
x = 8

After finding 'x', we can determine the length of one of the equal sides by substituting 'x' back into either of the original expressions:

Length of one side = 3x + 2 = 3(8) + 2 = 26 cm

Since we have two sides of the same length, we multiply by 2 to find the total length of the two legs:

Total length of two legs = 26 cm  imes 2 = 52 cm

To find the length of the base, subtract the total length of the two legs from the perimeter:

Length of the base = 82 cm - 52 cm = 30 cm.

Therefore, the length of the base of the isosceles triangle is 30 cm.