MATHEMATICS HIGH SCHOOL

The ratio of Ed's toy cars to Pete's toy cars was initially 5:2. After Ed gave 30 toy cars to Pete, they each had an equal number of cars. How many toy cars did they have altogether?

Answers

Answer 1

Answer:

140 toy cars

Step-by-step explanation:

The ratio of Ed's toy car to Pete's toy car is initially given as 5:2

Ed gave Pete a total number of 30 cars

Let x represent the greatest common factor that exists between both number

Number of Ed's car is represented as 5x

Number of Pete car is represented as 2x

Since they each have an equal number of cars which is 30 then we can solve for x as follows

5x-30=2x+30

Collect the like terms

5x-2x= 30+30

3x= 60

Divide both sides by the coefficient of x which is 3

3x/3=60/3

x=20

Ed's car is 5x, we substitute 20 for x

5(20)

= 100 cars

Pete car is 2x,we substitute 20 for x

2(20)

= 40 cars

Therefore, the total number of cars can be calculated as follows

= 100+40

= 140 toy cars

Hence they have 140 toy cars altogether

Answer 2

Answer:

Answer:

140

Step-by-step explanation:

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Five times a number decreased by nine is equal to twice the number increased by 23. Which equation could be used to solve the problem?Rachna has nickels, dimes, and quarters in her piggy bank. She has $4.65 altogether. She has three more quarters than dimes and twice as many nickels as quarters. How many quarters does Rachna have?

Three times a number, x, increased by four is equal to five times the number, x. Which equation can be used to solve for x?

What is the value of x in the equation 0.2(x + 1) + 0.5x = –0.3(x – 4)?

Answers

Answer:

Part 1) $5x-9=2x+23$

Part 2) $11\ quarters$

Part 3) $3x+4=5x$

Part 4) $x=1$

Step-by-step explanation:

Part 1)

Let

x-----> the number

The expression" Five times a number decreased by nine is equal to twice the number increased by $23$ ", is equal to the algebraic expression

$5x-9=2x+23$

Part 2) we have that

$1\ nickel=\$0.05$

$1\ dime=\$0.10$

$1\ quarter=\$0.25$

Let

x------> the number of nickels

y-------> the number of dimes

z-------> the number of quarters

$0.05x+0.10y+0.25z=4.65$

Multiply by $100$ both sides

$5x+10y+25z=465$ ------> equation A

$z=3+y$ -----> isolate the variable y

$y=z-3$ ------> equation B

$x=2z$ ------> equation C

substitute equation B and equation C in equation A

$5(2z)+10(z-3)+25z=465$

$10z+10z-30+25z=465$

$45z=465+30$

$45z=495$

$z=11\ quarters$

Part 3) we know that

Let

x------> the number

The equation that represent the expression is equal to

$3x+4=5x$

Part 4) we have

$0.2(x+1)+0.5x=-0.3(x-4)$

Multiply by $10$ both sides

$2(x+1)+5x=-3(x-4)$

$2x+2+5x=-3x+12$

$7x+3x=12-2$

$10x=10$

$x=1$

The first one is 5x-9=2x+23

The third one is 3x+4=5x

Write 22.056 in an expanded form

Answers

We know the first place after decimal is tenths

The second place after decimal is hundredths

The third place after decimal is the thousandths place

So for 0.056

0 is at the tenths place

5 is at the hundredths place

and 6 is at the thousandths place

Expanding 22.056 we get

22.056 = 20 + 2 + 0.05 + 0.006

22.056 = $20+2+(5)/(100)+(6)/(1000)$

20.000 + 2.000 + .050 +.006

Can somebody explain y=2x+3 and y intercept please

Answers

Answer:

see below

Step-by-step explanation:

y=2x+3

This is the slope intercept form of a line

y = mx+b where m is the slope and b is the y intercept

y = 2x+3

The slope is 2 and the y intercept is 3

The y intercept is where it crosses the y axis ( where x =0)

If 1 lb = 454g, how many pounds would you have if you measured 285 g of Lead?

Answers

Answer:

approx. 0.628g of lead

Step-by-step explanation:

285 ÷ 454 = 0.62775...

Compare and order the numbers below from least to
greatest.
4.6,2.8,,17,7

Answers

2.8, 4.6, 7, 17

The first number is less than the second number by 1.8, second number is less than the third number by 2.4, third number is less than the forth number by 10.

Find the area of the circle. Round your answer to two decimal places, if necessary.

Answers

Final answer:

To find the area of a circle, use the formula A = πr^2. Identify the radius and substitute it into the formula to calculate the area. Round the answer to two decimal places if necessary.

Explanation:

To find the area of a circle, you can use the formula A = πr^2, where A represents the area and r represents the radius of the circle. Start by identifying the radius of the circle, which is the distance from the center to any point on the circumference. Once you have the radius, substitute its value into the formula and calculate the area. Make sure to round your answer to two decimal places if necessary. For example, if the radius of the circle is 5 units, the area would be A = 3.14 * 5^2 = 3.14 * 25 = 78.5 square units.