Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each does he have . SHow your work

Answers

Answer 1
Answer: x-\ nickels\ny-\ quarters\n\n0,05x+0,25y=8,85\nx+y=49\ \ \ \ x=49-y\n\n\0,05(49-y)+0,25y=8,85\n2,45-0,05y+0,25y=8,85\n0,2y+2,45=8,85\ \ \ | subtract\ 2,45\n0,2y=6,4\ \ \ | divide\ by\ 0,2\ny=32\n\nx=49-32=17\n\nHe\ had\ 17\ nickels\ and\ 32\ quarters.

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Mike works h hours in a week. To find his weekly pay he multiplies his hours by his pay of $30 per hour and adds $5 for his sales bonus. He's decided that he wanted to take one-fifth of his weekly pay and place it in his savings. Which simplified expression represents the amount that will go into his savings each week?

How do I solve for x in the two equations below using substitution.
4x-2y=4
8x+2y=20

Answers

4x-2y=4 \n8x+2y=20 \n \n\hbox{from the 1st equation:} \n4x-2y=4 \n-2y=-4x+4 \ny=2x-2 \n \n\hbox{substitute 2x-2 for y in the 2nd equation:} \n8x+2(2x-2)=20 \n8x+4x-4=20 \n12x=24 \nx=2 \n \ny=2 \cdot 2-2 \n\y=4-2 \ny=2 \n \n \hbox{the answer:} \nx=2 \n y=2
4x-2y=4
8x+2y=20

12x=24
x=24/12
x=2

sub x into 8x+2y=20
8(2)+2y=20
16+2y=20
2y=20-16
2y=4
y=4/2
y=2

solution (2,2)

check
4x-2y=4(2)-2(2)=4
8x+2y=8(2)+2(2)=16

hope this helps

If the sale tax in your city is 5.4% and an item costs $5 before tax how much tax would you pay on that item round up to the nearest cent

Answers

5.4% is 0.054
Multiply by 1.054 because it is being added to $5

5 × 1.054
$5.27

Final answer:

The sales tax on an item costing $5 with a tax rate of 5.4% will be $0.27. This is calculated by converting the percentage to a decimal (0.054) and multiplying by the original cost ($5).

Explanation:

The subject of this question is mathematics, specifically, it's a problem of calculating the sales tax. In this scenario, if the tax rate is 5.4% and the initial price of the item is $5, you can calculate the amount of tax to pay by multiplying the original price of the item by the tax rate in decimal form.

So, step 1 is converting the percentage into a decimal by dividing by 100. That gives us 5.4 / 100 = 0.054.

Step 2 is multiplying this tax rate by the original price of the item:  $5 * 0.054 = $0.27.

Therefore, the tax you would pay on an item that costs $5 before sales tax is approximately $0.27, rounding up to the nearest cent.

Learn more about Sales Tax Calculation here:

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Factor the four-term polynomial. mn - 15 + 3m - 5nmn-15+3m-5n Let's rearrange the terms mn + 3m - 15 - 5n = m*(n + 3) - 5(n + 3) = (m - 5)(n + 3)

Answers

I think the answer is 

(m-5)(n+3)

Compare and contrast the perpendicular bisectors and angle bisectors of a triangle. How are they alike? How are they different?

Answers

They are alike because they both divide something.. They are different because one perpendicular bisector divides one side of the triangle into two equal lengths at a 90 degree angle. So if there's is three perpendicular bisectors, then it splits all three sides the triangles into equal lengths. Angle bisectors splits an angle of a triangle into two even degrees.

Answer:

Step-by-step explanation:

The perpendicular bisectors and angle bisectors are alike in one manners that they both divide the entities they are drawn at.

Perpendicular bisector bisect the sides of triangle in two equal halves and angle bisectors divides the angles to which they are drawn in two equal halves.

The difference is that ,

the point at which perpendicular bisectors meet, is the center of circumcircle which is drawn through the vertices of triangle

the point at which angle bisectors are met, is called the incenter , and is the center of incircle inscribed in a triangle touching its three sides.

Simplify {n - 1 - [n - 1 - (n - 1)]}.

Answers

{n-1-[n-1-(n-1)]} | Given
{n-1-[n-1-n+1]} | Distribute most inner negative
{n-1-n+1+n-1]} | Distribute next inner negative
n-1 | Simplify like terms

Answer: the correct answer is n-1

Liam has a bag of b beads. He gives 20 beads to his sister. He then makes 4 necklaces with the same number of beads on each necklace using all of the remaining beads. Write an expression that represents the number of beads on each necklace. Show your work.

Answers

The expression in one variable b that shows the number of beads on each necklace is (b-20)/4

What is an expression in one variable?

An expression in one variable is a statement formed by the using constants and an unknown variables and mathematical operators but sign is equal to is not used. Expression in one variable is linear if the power of the unknown variable is equal to one .

Standard form of linear expression in one variable x is  ax +b , where a and b are constants .

Given that Liam has a bag of b beads

He gave 20 beads to his sister

Then, remaining beads = b -20

Remaining beads are used to make 4 necklaces

Let the beads on each necklace be x

Then beads in four necklaces = 4x

As, Remaining beads = beads in four necklaces

⇒4  x = b - 20

Dividing the equation by 4 on both sides

⇒ x = (b-20)/4

∴ The expression that shows the number of beads on each necklace is (b-20)/4

Also, Learn more about the expressions in one variable from the link below:

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Answer:

5

Step-by-step explanation:

just do 20 divided by 4 and you will get 5. Also, do 5x4 to make sure you let your teacher know that you got the right answer.