4x-3y=12. solve for Y
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The number of cheese sticks you can buy for $1 has decreased by 20%, and the price per cheese stick has increased by 25%.

To find the percent change in quantity and price for the cheese sticks, we need to compare the old and new situations. Let's calculate both parts of the question:

a) Previously, you could buy 5 cheese sticks for $1, but now you can only buy 4 for the same amount. To find the percent decrease, we subtract the new quantity from the old quantity, divide by the old quantity, and then multiply by 100 to get a percentage.

Percent decrease = [(New - Old) / Old] × 100%

Percent decrease = [(4 - 5) / 5] × 100%

Percent decrease = [-1 / 5] × 100% = -20%

There is a 20% decrease in the number of cheese sticks you can buy for $1.

b) To find the price per stick before, we divide the total price by the number of sticks, which is ($1) / 5 = $0.20 per stick.

After the change, it's ($1) / 4 = $0.25 per stick. Now find the percent increase:

Percent increase = [(New - Old) / Old] × 100%

Percent increase = [(0.25 - 0.20) / 0.20] × 100%

Percent increase = [0.05 / $0.20] × 100%

Percent increase = 0.25 × 100% = 25%

There is a 25% increase in the price per cheese stick.

Hence, there's a 20% decrease in quantity and a 25% increase in the price per cheese stick.

The scale of the map is found by dividing the actual length of the river by the length of the river on the map. In this case, the scale of the map is approximately 52 miles per inch.

To find the scale of the map, we need to divide the actual length of the river by the length of the river on the map. In this case, the actual length of the river is 247 miles and the length of the river on the map is 4.75 inches. So, the scale of the map is 247 miles / 4.75 inches.

Doing the division, we find that the scale of the map is approximately 52 miles per inch. This means that every inch on the map represents 52 miles in real life.

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To solve the equation -2b + 7 = -13, subtract 7 from both sides and then divide by -2.

To solve the equation -2b + 7 = -13 using the properties of equality, you would subtract 7 from both sides first to isolate the variable. This gives you -2b = -20. Then, divide both sides by -2 to solve for b. This gives you b = 10. To write the sentence 'the product of a number and 5 is 11' as an algebraic expression, you would use the equation X * 5 = 11. This represents the multiplication property of equality, where the number (X) is being multiplied by 5. The property of equality you could use to solve -3x = 348 is the division property. To isolate x, divide both sides by -3. This gives you x = -116.

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To express and evaluate given expressions in exponential form: (3/5)^2 = 9/25, (-1/6)^4 = 1/1296, (1.2)^3 = 1.728, and (-1/4)^4 = 1/256. The exponential form indicates the base number is being multiplied by itself a certain number of times.

To write each expression in exponential form and find its value, follow these steps:

For the expression 3/5 imes 3/5, since the same base (3/5) is multiplied by itself, it is written in exponential form as (3/5)^2.

To find the value, (3/5)^2 = 3/5 × 3/5 = 9/25.

The expression -1/6 × -1/6 × -1/6 × -1/6 is written as (-1/6)^4 in exponential form.

The value is (-1/6)^4 = -1/6 × -1/6 × -1/6 × -1/6 = 1/1296.

The value of (1.2)^3 is found by cubing the base: (1.2)^3 = 1.2 × 1.2 × 1.2 = 1.728.

The expression (-1/4)^4 is raising -1/4 to the 4th power, resulting in a positive value due to the even exponent: (-1/4)^4 = (-1/4) × (-1/4) × (-1/4) × (-1/4) = 1/256.

To solve for the value of x where f(x) = -22 for the function f(x) = -2x + 9, we set up the equation -2x + 9 = -22, subtract 9 from both sides, and then divide by -2, resulting in x = 15.5.

To find the value of x that makes f(x) = -2x + 9 equal to -22, we need to set the function equal to -22 and solve for x.

-2x + 9 = -22

First, subtract 9 from both sides:

-2x = -22 - 9

-2x = -31

Next, divide both sides by -2 to solve for x:

x = 31 / 2

x = 15.5

The value of x that makes f(x) equal to -22 is 15.5.

The product of smallest two digit number gives the three digit number.

In mathematics, a product is the outcome of multiplying two or more numbers together.

The multiplication of two or more numbers results in the product.

As, we know that the product means the multiplication of two numbers.

Now, if we multiply two dight number with a two digit number.

As, the greatest two digit number is 10.

So, 10 x 10 = 100

Thus, the product of smallest two digit number gives the three digit number.

Learn more about product here:

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By calculating the cost per ticket at $7.75 and then multiplying by 12, the total comes to $93.00. Therefore, the Suarez family can use their $100 gift certificate to buy 12 movie tickets.

The Suarez family wants to find out if they can buy 12 movie tickets with a $100 gift certificate, given they paid $23.25 for 3 tickets. First, calculate the cost per ticket by dividing the total cost by the number of tickets purchased:

Now, multiply the cost per ticket by the number of desired tickets to get the total cost:

Since $93.00 is less than the $100 gift certificate, the family can indeed use their gift certificate to purchase 12 movie tickets.

Final answer:

By dividing the total number of muffins (252) by the number of batches (7), we find that there were 36 muffins in each batch.

Explanation:

The student asked how many muffins were in a batch if a baker made 7 batches of muffins with a total of 252 muffins, and there was the same number of muffins in each batch. To find the answer, we need to divide the total number of muffins by the number of batches.

Divide 252 by 7 to find how many muffins were in each batch:

252 muffins ÷ 7 batches = 36 muffins per batch

Therefore, there were 36 muffins in each batch.

Answer:

The value of the expression [tex]0.9 \cdot (\frac{1}{2}-2)+0.6[/tex]  is  -0.75.

Explanation:

Given: the expression [tex]0.9 \cdot (\frac{1}{2}-2)+0.6[/tex]

BODMAS acronym is;

B - Bracket

O - Orders

D -Division

M - Multiplication

A - Addition

S - Subtraction  

Using BODMAS rule in the given expression, first solve the bracket terms;

[tex]\frac{1}{2} -2 = \frac{1-4}{2} = \frac{-3}{2}[/tex]

Then we have;

[tex]0.9 \cdot \frac{-3}{2} - 9[/tex]

next, multiply the terms 0.9 and [tex]\frac{-3}{2}[/tex] we get

[tex]-1.35 +0.6[/tex]

then, Add the above numbers;

[tex]-1.35 +0.6[/tex] = -0.75

Therefore, the value of given expression is, -0.75

Answer:

When we want solve expression mentally, that is, without writing down anything, a nice way is to separate number in simpler expressions, like tens for example.

So, in first place we could multiply 7 x 50, which involves a number expressed in tens, this product would be 350, then we multiply 7 x 3, which is 21, at the end, we sum both results 350 + 21 = 371. Therefore, the product is 371.

7 x 50 + 7 x 3 = 350 + 21 = 371

To determine how many days the birdseed will last, divide the total amount (3 cups) by the daily usage (2/3 cup), resulting in 4.5 days of birdseed.

To calculate how many days the birdseed will last, you can set up a conversion factor or use division to find the answer.

Steps to Determine the Duration of Birdseed:

First, identify the total amount of birdseed you have, which is 3 cups.

Next, determine the daily usage, which is 2/3 cup per day.

Then, divide the total amount of birdseed by the daily usage: 3 / (2/3).

To divide by a fraction, multiply by its reciprocal: 3 * (3/2).

Perform the multiplication: 3 * (3/2) = 9/2.

Finally, 9/2 breaks down to 4.5, so the birdseed will last for 4.5 days.

Thus, the birdseed will sustain for approximately 4 and a half days before running out.

Answer:

30.60

Step-by-step explanation:

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