Graph the inequality.
4x - 4y > 28

The original height of the water level in pool is 5 feet

Given that , A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.  

After the leak is fixed, the height of the water is 4.75 feet.  

The equation 4.75 = x + (- 0.25) can be used to find x, the original height of the water in a pool.

So by solving the given equation and finding value of "x" gives the original height of water in pool

We have to find the original height of the water level in the tank.

So, let us solve the given equation

[tex]\begin{array}{l}{\rightarrow 4.75=x+(-0.25)} \\\\ {\rightarrow 4.75=x-0.25} \\\\ {\rightarrow x=4.75+0.25} \\\\ {\rightarrow x=5}\end{array}[/tex]

Hence, the original height of the water level is 5 feet

Answer5 feet

Step-by-step explanation:

Answer: 2hrs

Step-by-step explanation:

paid 10 dollars at first and then 6 every hour he rode

so let x represent the # of hour rented

6x+10=22

x=2hrs

Answer:

The complete length is 115 cm.

Step-by-step explanation:

Given:

If 20%of a length is 23 cm.

Now, to find the complete length.

Let, the complete length be [tex]x[/tex].

So, according to question:

20% of [tex]x[/tex] = 23 cm

[tex]\frac{20}{100} \times x=23[/tex]

[tex]0.20\times x=23[/tex]

[tex]0.20x=23[/tex]

Dividing both sides by 0.20 we get :

[tex]x=115[/tex]

Therefore, the complete length is 115 cm.

To find the complete length when 20% is 23 cm, divide 23 cm by 0.20 to get 115 cm as the total length.

If 20% of a length is 23 cm, we want to find out what the complete length is. To do so, we recognize that 20% is the same as saying 20 per 100 or 0.20 in decimal form. If 0.20 of the length is 23 cm, it means that 23 cm represents 0.20 of the total length. We can set up the equation like this:

0.20 * Total Length = 23 cm

To find the Total Length, we divide both sides of the equation by 0.20:

Total Length = 23 cm / 0.20

Total Length = 115 cm

Therefore, the complete length is 115 cm.

Answer:

[tex]\large\boxed{\dfrac{1}{10}x-\dfrac{7}{10}=\dfrac{1}{10}(x-7)}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{10}x=\left(\dfrac{1}{10}\right)(x)\\\\\dfrac{7}{10}=\left(\dfrac{1}{10}\right)(7)\\\\\dfrac{1}{10}x-\dfrac{7}{10}=\left(\dfrac{1}{10}\right)(x)-\left(\dfrac{1}{10}\right)(7)=\left(\dfrac{1}{10}\right)(x-7)[/tex]

Answer:

The other 2 angles are 67 and 67 degrees OR 46 and 88 degrees.

Step-by-step explanation:

If the vertex angle is 46 degrees then , as the other 2 angles are congruent, they are  (180 - 46) / 2 =   67 degrees.

The triangle has angles (46, 67 and 67).

If the  2 equal angles are both 46 then the other angles is 180 - 2(46) = 88 degrees.

The other  triangle has angles (46, 46 and 88).

Answer:

Average mark of the semester

EXPLANATION

This is done by adding the total score divided by the number of scores of the semester in that way Matthews average test score would be gotten

Algebra tiles are a useful tool to simplify expressions. Depending on their shape and decoration, they represent different parts of the expression. Review your tiles and match them to the four given expressions carefully.

The question pertains to Algebra and specifically, matching a simplified algebraic expression to a set of tiles. The exact matching algebraic expression cannot be determined as the set of tiles isn't provided in the question but here's how you would approach this kind of problem:

If you're using algebra tiles, squares typically represent x², rectangles portray x, and small squares depict constants like 2. The color or decoration of a tile may indicate a positive or negative value. For example, a square with '- ' could mean '-x²'.

So if you've got a square with '- ', a rectangle without a decoration, and two small plain squares, your expression should be '-x² - x + 2'. If the rectangle had a '-', your expression would be '-x² + x + 2' instead.

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The set of tiles shown represents the expression x² - x + 2.

The set of tiles shown represents the expression x² - x + 2.

To match the tiles to the simplified expression, look at the coefficient and exponent of x on each tile. The first tile has an exponent of 2 and a coefficient of 1. The second tile has an exponent of 1 and a coefficient of -1. The third tile has an exponent of 0 and a coefficient of 2. Therefore, the simplified expression that matches the set of tiles is x² - x + 2.

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Answer:

$21.75

Step-by-step explanation:

Add 25% then subtract to get back to $17.40

Answer:

-5

Step-by-step explanation:

A negative number divided by a positive number will be negative.

20/4 is 5.

(5x4=20)

Therefore (-20)/4 = (-5)

Answer: 5 faces

Step-by-step explanation:

The Euler's polyhedron formula states that:

number vertices - number of edges + number of faces = 2

That is :

6 - 9 + F = 2

-3 + f = 2

f = 2 + 3

f = 5

Therefore , it has 5 faces

Chloe made 4 three-point shots and 5 two-point shots.

Let's solve this problem using a system of equations.

Let x be the number of three-point shots Chloe made and y be the number of two-point shots she made.

We have the following equations:

x + y = 9 (equation 1)

3x + 2y = 22 (equation 2)

From equation 1, we can solve it for x:

x = 9 - y

Substitute this value of x into equation 2:

3(9 - y) + 2y = 22

27 - 3y + 2y = 22

-y = -5

y = 5

Substitute this value of y back into equation 1:

x + 5 = 9

x = 4

Therefore, Chloe made 4 three-point shots and 5 two-point shots.

83.78% students turned in their homework and 16.22 percent students did not turn in their homework

Step-by-step explanation:

Percentage formula will be used for this problem

Given

Total students = 74

Students who turned their homework = 62

So the percentage of students who turned in their homework will be:

[tex]Percentage\ of\ students\ who\ turned\ in\ their\ hw = \frac{62}{74} *100\\=0.8378*100\\=83.78\%[/tex]

So the students who did not turn in their homework = 100-83.78

=16.22%

Hence,

83.78% students turned in their homework and 16.22 percent students did not turn in their homework

Keywords: Percent, percentage

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Answer:

First side: 12 feet, second side: 16 feet

Step-by-step explanation:

We know that the second side is 4 feet longer than the first side. If the first side is x, then the second side is x+4

b) The total amount of the border is 28 feet, so we can say that first side+second side=28, or

x+(x+4)=28

2x+4=28

2x=24

x=12 feet is the first side

x+4 = 16 feet is the second side

We can check that 12 feet + 16 feet = 28 feet as stated by the problem

Answer:

Yes

Step-by-step explanation:

3 and 9 are both divisible by 3. Divide 3 and 9 by 3. You would get the fraction 1/3. You cannot simplify this fraction anymore.

~Stay golden~  :)

Answer:

$969.3

Step-by-step explanation:

The DVDs are sold in packages of 50

Divide the total number you need by 50, therefore 2700/50 = 54 packages are needed

The packages are sold at $17.95 for one, hence amount needed is 54 * 17.95 = $969.3

For this case we must find an expression equivalent to:

[tex]36y-18x-108y + 54[/tex]

We add similar terms:

[tex]36y-108y-18x + 54 =[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]-72y-18x + 54[/tex]

Thus, an equivalent expression is:

[tex]-72y-18x + 54\\-18x-72y + 54[/tex]

Answer:

[tex]-18x-72y + 54[/tex]

Final answer:

To find equivalent expressions, we combine like terms in the given expression 36y - 18x - 108y + 54.

Explanation:

To find expressions equivalent to 36y - 18x - 108y + 54, we can combine like terms.

First, combine the y terms: 36y - 108y = -72y.

Next, combine the x terms: -18x.

Combining the constants, we have: 54.

Putting it all together, the equivalent expression is: -18x - 72y + 54.

Answer:

[tex]\frac{31548}{7} x[/tex]

Step-by-step explanation:

Answer:

31548/7 x

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Since 30%/3 is 10%, 6 is 10% of the total number of garden beds, since 18/3 is 6.

And 10% times 10 is 100%, or all of it, so 60 is the total amount of garden beds, since 6 times 10 is 60.

60 garden beds in the students plans.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Present flower bed= 18

This is 30% of the total number of garden beds.

let the total flower bed be x.

So, 30% of x= 18

30/100 x = 18

x= 1800/ 30

x= 60

Hence, 60 garden beds in the students plans.

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Answer:

7 + n

Step-by-step explanation:

Answer:

-6(2b-c-3)

Step-by-step explanation:

Collect like terms

-12b+6c+12+6

Add the 2 numbers on right

-12b+6c+18

Factor -6 out of expression

-6(2b-c-3)

Answer:

2.03

Step-by-step explanation:

Answer:

The cups of other type of juice is 615

Step-by-step explanation:

Given as :

The total cups of punch made by Jessica = 619

The two different types of juice is x and y

Let The one type of juice = x = 4

And According to question

x + y = 619

So, 4 + y = 619

Or, y = 619 - 4

∴ y = 615

Hence The cups of other type of juice is 615 . Answer

Answer:

The money he will save if he earns $120.00 is $90.00.

Step-by-step explanation:

Given:

In the figure is the ratio of the savings and the earnings.

Now, to find out that how much savings will be if Miguel earns $120.00.

We need to get the percentage of the ratio of the earning and saving.

So, according to the table:

If he earns $10.00 then he saves $7.50.

[tex]\frac{7.50}{10}\times 100[/tex]

[tex]=0.75\times 100[/tex]

[tex]=75[/tex]

So, if Miguel earns $10.00 he save the 75% of it.

If he earns $50.00 then he saves $37.50.

As we calculate the percentage as the above process then the saving is 75% of the earning.

And, if he earns  $150.00 and save $112.50 then it is also the 75% of the earning as mentioned above.

Now, to find the saving of the earning $120.00.

So, it will be 75% of the earning as we observe in the above case:

75% of $120.00

[tex]\frac{75}{100}\times 120[/tex]

[tex]=0.75\times 120[/tex]

[tex]=90[/tex]

Therefore, the money he will save if he earns $120.00 is $90.00.

Answer:

7^-12 or 1/7^12

Step-by-step explanation:

To divide exponents with the same base, subtract the second exponent from the first.

So:

7^-5/7^7 = 7^-5-7 = 7^-12

You can also write 7^-12 as 1/7^12.

She planted [tex]\frac{3}{4}[/tex] arcs of each type

Step-by-step explanation:

The given is:

We need to find how many acres of each type she planted

∵ The farmer planted [tex]4\frac{1}{2}[/tex] arcs of land

∵ She planted 6 types of wheat

∵ She planted an equal amount of each type of wheat

- Divide the total number of arcs by 6 to find the number of arcs

  for each type

To divide the total number of arcs change it from the mixed number

[tex]4\frac{1}{2}[/tex] to improper fraction

∵ [tex]4\frac{1}{2}=\frac{(4*2)+1}{2}=\frac{9}{2}[/tex]

∴ The total number of arcs = [tex]\frac{9}{2}[/tex]

∴ The number of arcs of each type = [tex]\frac{9}{2}[/tex] ÷ 6

- Change the division sign to multiplication sign and reciprocal

   the number after the division sign

∴ The number of arcs of each type = [tex]\frac{9}{2}[/tex] × [tex]\frac{1}{6}[/tex]

∴ The number of arcs of each type = [tex]\frac{9*1}{2*6}[/tex]

∴ The number of arcs of each type = [tex]\frac{9}{12}[/tex]

- Reduce the fraction by dividing up and down by 3

∴ The number of arcs of each type = [tex]\frac{3}{4}[/tex]

She planted [tex]\frac{3}{4}[/tex] arcs of each type

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Answer:

B.) Open circle on 3 and all numbers to the left shaded

It will take 7.30 years until Dale can by his mask

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

[tex]A=Pe^{rt}[/tex] , where

Dale invests $6000 in an account at 9.5% interest compounded continuously. The mask costs $12000. We need to find how long will it take Dale until can buy this mask

∵ Dale invests $6000

∴ P = 6000

∵ The interest rate is 9.5% ⇒ compounded continuously

∴ r = 9.5% = 9.5 ÷ 100 = 0.095

∵ The mask costs $12000

∴ A = 12000

Substitute these values in the formula above

∵ [tex]12000=6000e^{0.095t}[/tex]

- Divide both sides by 6000

∴ [tex]2=e^{0.095t}[/tex]

- Insert ㏑ for both sides

∴ [tex]ln(2)=ln(e^{0.095t}[/tex])

- Remember that [tex]ln(e^{n})=n[/tex]

∴ [tex]ln(2)=0.095t[/tex]

- Divide both sides by 0.095

∴ t = 7.29628611

∴ t = 7.30 ⇒ to the nearest hundredth year

It will take 7.30 years until Dale can by his mask

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It will take Dale 7.64 years to save enough money to buy the mask we can use the method of compound interest.

To find how long it will take Dale to save enough money to buy the mask, we can use the following formula for compound interest:

A = P * e^(rt)

where:

A is the final amount

P is the principal amount

r is the interest rate

t is the time in years

We know that A = $12000, P = $6000, and r = 9.5%. We need to solve for t.

12000 = 6000 * e^(0.095t)

e^(0.095t) = 2

ln(2) = 0.095t

t = ln(2) / 0.095

t = 7.64

Therefore, it will take Dale 7.64 years to save enough money to buy the mask.

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The number is -40

Step-by-step explanation:

Let x be the number that we have to find

Then according to the given statement

the square of the sum of the number and 5 is equal to 1225.

[tex](x+5)^2 = 1225[/tex]

Taking square root on both sides

[tex]\sqrt{(x+5)^2} = \sqrt{1225}\\x+5 = -35 and x+5 = -35\\[/tex]

Subtracting 4 from both sides

[tex]x+5-5 = 35-5\ and\\ x+5 = -35-5\\x = 30\ and\ x = -40[/tex]

As it is mentioned in the equation, that the number is a negative number

So,

x = -40

Keywords: Radicals, Linear equations

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The unit rate, expressed in price per pound is $0.80​.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is constant.

The slope of the line running through coordinates (0,0) and coordinates (30,24) is,

m= (24-0)/(30-0) = 0.8

Hence, the unit rate, expressed in price per pound is $0.80​.

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Answer:

13

Step-by-step explanation:

26 * 50/100 = 26 * 1/2 = 13

Answer:

13

Step-by-step explanation:

50% = 50/100 = 1/2

That means that 1/2 of the children have blue eyes.

26*(1/2) or 26/2 = 13

To make a minimum profit of $100 with each snack priced at $4.00, a total of 47 snacks need to be sold at the concession stand. This includes 22 snacks to cover the total cost of $86.56 and an additional 25 snacks to achieve the profit goal.

The question is about finding out how many snacks need to be sold at a concession stand to achieve a minimum profit. To get the answer, we first need to determine how many snacks would make up the total cost, and then calculate how many additional snacks would be necessary to attain the profit goal.

Given that each snack at the concession stand costs $4.00 and that the total cost of the snacks is $86.56, we can find out how many snacks were initially purchased by dividing the total cost by the price of each snack: $86.56 ÷ $4.00 = 21.64 snacks. Since we can't sell a fraction of snack, we round up to 22 snacks to cover the total cost.

To calculate the number of additional snacks needed to attain a $100 profit, we divide the profit goal by the price of each snack: $100 ÷ $4 = 25 snacks.

Therefore, to cover the total cost and also make a minimum profit of $100, the concession stand needs to sell 22 snacks for the cost and additional 25 snacks for the profit, totaling 47 snacks altogether.

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