MATHEMATICS HIGH SCHOOL

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 1

Answer:

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

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

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

$7x+3x=12-2$

$10x=10$

$x=1$

Answer 2

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

The third one is 3x+4=5x

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B. A rectangle has a length of 6 centimeters.
C. For every 2 red candies in a bag, there are 3 green candies.
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Answers

Answer:

C. For every 2 red candies in a bag, there are 3 green candies.

Step-by-step explanation:

Ratios are comparing two things in an order so having 2 red and 3 green would then move to 4 red and 6 green and so on.

Answer:

c is for cool, cause that what you are ;)

Step-by-step explanation:

2x-y ;x=5,y=1 evaluating algebraic expressions

Answers

Answer:

Step-by-step explanation:

2(5)-(1)

10-1

Mentally estimate the total cost of items that have the following prices: $1.85, $.98, $3.49, $9.78, and $6.18. Round off your answers to the nearest half-dollar.

Answers

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Dorothea is making friendship bracelets. She has 260cm of string. She needs 20 cm for each bracelet. How many bracelets can she make?

Answers

Answer:

13 bracelets

Step-by-step explanation:

If you have 260 cm of string and you need 20 cm for each bracelet, you have to divide 260 by 20. Which gives you 13

Answer: Dorothea can make 13 bracelets.

Step-by-step explanation: If Dorothea has 260cm of strings, she should cut the string accordingly to set aside the strings. Cutting 260cm of 20cm length each would be the same as doing 260 divided by 20. If you do the math (mentally or using a calculator), you would get 13 pieces of strings, meaning Dorothea can make 13 bracelets. Hope this helped!

What is the value of the Y coordinate of the solution to the system of equations x-2y=1 and x+4y=7?

Answers

$\left\{\begin{array}{ccc}x-2y=1\nx+4y=7&/\cdot(-1)\end{array}\right\n\n+\left\{\begin{array}{ccc}x-2y=1\n-x-4y=-7\end{array}\right\n-----------\n.\ \ \ \ \ \ \ \ \ -6y=-6\ \ \ \ \ /:(-6)\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ y=1\n\nx-2\cdot1=1\nx-2=1\nx=1+2\nx=3\n\nAnswer:\n\left\{\begin{array}{ccc}x=3\ny=1\end{array}\right$