Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols. 3x+4y=16 -4x-3y=-19

Answer:

23/10 gallons

Step-by-step explanation:

Alicia uses 3/4 gallon of paint to paint her room.

Alicia use = 3/4 gallon of paint

Becca uses for 4/5 gallon more than Alicia to paint her room.

Becca uses = Alicia (3/4 gallons ) + 4/5

Becca uses = [tex]\frac{3}{4} + \frac{4}{5}[/tex]

Total paint used together = Aliccia used + Becca used

[tex]\frac{3}{4}+\frac{3}{4} + \frac{4}{5}[/tex]

Add like fractions 3/4 + 3/4 becomes 6/4

[tex]\frac{6}{4} + \frac{4}{5}[/tex]

Make the denominators same

[tex]\frac{6*5}{4*5} + \frac{4*4}{5*4}[/tex]

[tex]\frac{30}{20} + \frac{16}{20}[/tex]

[tex]\frac{46}{20}[/tex]

Divide top and bottom by 2

[tex]\frac{23}{10}[/tex] gallons

Final answer:

The percent decrease in the cost of the Barry Bonds baseball card is 40%.

Explanation:

To calculate the percent decrease in the cost of the card, we can use the formula:

Percent decrease = ((original value - new value) / original value) * 100

In this case, the original value of the card was $50 and the new value is $30. Plugging in these values into the formula:

Percent decrease = ((50 - 30) / 50) * 100 = (20 / 50) * 100 = 0.4 * 100 = 40%

Therefore, the percent decrease in the cost of the card is 40%.

Answer:

$210.69

Step-by-step explanation:

Firstly, just calculate how much money you earn:

40 * 10.25 = $410

Your transportation expenses = 5.25 * 5 = $26.25

Your lunch expenses = 3.85 * 5 = $19.25

Expenses for black slacks = $19.95

FICA = 7.65/100 * 410 (money you earned) = $31.365

Federal withholding = 15/100 * 410 = $61.5

State withholding = 10/100 * 410 = $41

Your discretionary income = 410 - (26.25 + 19.25 + 19.95 + 31.365 + 61.5 + 41) = $210.69

Answer:

Putting money into a savings account

Step-by-step explanation:

Answer:

Each year, a law firm gains 20% more clients. This continues on a regular basis. The number of clients that the law firm has will be about 1.2 times the amount from the past year.

Step-by-step explanation:

The system of the inequalities is y ≥ 2x - 2, y ≥ x - 3x. Option B

To determine a system of inequalities graphically, plot each inequality on the same coordinate plane.

Represent each inequality as a boundary line (dashed or solid, depending on the inequality sign) and shade the region that satisfies the inequality. The solution area is the overlapping shaded region where all inequalities intersect.

The points within this shared region satisfy all the given inequalities simultaneously. If there is no intersection or common shaded area, the system has no solution that satisfies all the inequalities simultaneously.

So, we have that;

y ≥ 2x - 2

y ≥ x - 3x

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Final answer:

Brenda will earn $18.75 in simple interest after 18 months on her $500 deposit at a 2.5% annual simple interest rate.

Explanation:

To calculate the simple interest Brenda will earn after 18 months on a $500 deposit at a simple interest rate of 2.5% per year, we can use the simple interest formula:
I = P * r * t, where:

I represents the interest earned,

P is the principal amount (the initial amount of money),

r is the annual interest rate (in decimal form), and

t is the time in years.

First, convert the interest rate from a percentage to a decimal by dividing by 100:

2.5% = 2.5 / 100 = 0.025

Next, since the time is given in months, convert it to years:

18 months = 18 / 12 = 1.5 years

Now, plug the values into the formula:

I = $500 * 0.025 * 1.5

I = $18.75

Therefore, Brenda will earn $18.75 in simple interest after 18 months.

Answer:

9

Step-by-step explanation:

We have been given that dimensions of original photo are 4 inches by 6 inches. We want the photo on the poster to be of dimensions 3 feet by 4 1/2 feet.            

First of all we will convert dimensions of poster from feet to inches.

3ft = 3x12 in = 36ft

4 1/2 ft = 4.5x 12in = 54in

Now let us compare sides of our original photo with corresponding sides of poster.

frac{36}{4}  = 9

Now let us compare the second pair of corresponding sides.

\frac{54}{6} =9

We have seen that sides of poster are 9 times the sides of our original photo, therefore, the scale factor of this dilation is 9.      

To find the scale factor for enlarging a photo from 3 inches by 5 inches to 2 1/2 feet by 4 1/6 feet, first convert feet to inches and then compare the dimensions of both photos. The scale factor is 10, as both width and height are enlarged by a factor of 10.

You are making a poster and need to determine the scale factor for resizing a photo from 3 inches by 5 inches to 2 1/2 feet by 4 1/6 feet. To find the scale factor, you compare the dimensions of the enlarged photo to the original photo.

First, convert the measurements of the larger photo from feet to inches, since the original photo is in inches (1 foot = 12 inches):
2 1/2 feet = 2.5 * 12 inches = 30 inches
4 1/6 feet = (4 + 1/6) * 12 inches = (4 * 12) + (1/6 * 12) inches = 48 + 2 inches = 50 inches.

Next, calculate the scale factor for each dimension separately and check that they are consistent:
Scale factor for width = 30 inches / 3 inches = 10
Scale factor for height = 50 inches / 5 inches = 10

Since both width and height have the same scale factor of 10, the overall scale factor for the dilation is 10.

Substitute y = 2x + 5 to the second equation 6x - 3y = 6:

6x - 3(2x + 5) = 6             use distributive property

6x - (3)(2x) - (3)(5) = 6

6x - 6x - 15 = 6

-15 = 6    FALSE

Answer: NO SOLUTION

The total cost for the magazine and 4 paperback books is $23.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

Given that,

The cost of a magazine is $3.

And, the cost of each of 4 paperback books is $5.

Then, the cost of 4 paperback books is 4 × 5 = 20

Thus, the expression for the total cost is given as,

3 + 4 × 5

= 23

Hence, the total cost is given as $23 and the terms in the expression 3 + 4 × 5 represent the cost of magazine and that of 4 books respectively.

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Answer:

degree 5

Step-by-step explanation:

the degree of a polynomial is determined by the term with the largest exponent and is the value of the exponent.

[tex]x^{5}[/tex] is the term with the largest exponent of 5

degree of polynomial is 5

Answer:

22.5% = 9/40 as a fraction

Step by Step Solution

To convert 22.5 percent to a fraction follow these steps:

Step 1: Write down the percent divided by 100 like this:

22.5% = 22.5/100

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,

22.5/100 = (22.5 x 10)/(100 x 10) = 225/1000.

Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(225,1000) = 25. So,

(225÷25)/(1000÷25) = 9/40 when reduced to the simplest form.

Step-by-step explanation:

Answer:

9/4, or 2 1/4 is your answer

Step-by-step explanation:

Note that 22 is a whole number, and that 5 is a decimal.

Change the decimal into a fraction. To do so, move the decimal point to the right two place values and set the number over 100

22.5 = 225/100

Simplify.

(225/100)/(25/25) = 9/4

9/4, or 2 1/4 is your answer

~

Answer:

A) D + Q = 50

B) .10D + .25Q = 7.10

We multiply A) by -.10

A) -.10D - .10Q = -5 then adding this to B)

B) .10D + .25Q = 7.10

.15Q = 2.10

Quarters = 14 = 3.50

Dimes = 36 = 3.60

Step-by-step explanation:

Answer:

The play lasted 1 hour and 12 minutes.

Step-by-step explanation:

Start: 2:10 pm. End: 3:22 pm.

3 hours - 2 hours = 1 hour

Start: 2:10 pm. End: 3:22 pm.

22 minutes - 10 minutes = 12 minutes

The play lasted 1 hour and 12 minutes.

Answer:

D

Step-by-step explanation:

Let's find unit rate of each (number of miles traveled in 1 hour). For that we will divide the distance by time to get the unit rate.

Note: [tex]rate=\frac{Distance}{Time}[/tex]

(A)

rate = [tex]\frac{300}{4}=75[/tex] mph (miles per hour)

(B)

rate = [tex]\frac{450}{6}=75[/tex] mph

(C)

rate = [tex]\frac{750}{10}=75[/tex] mph

(D)

rate = [tex]\frac{800}{12}=66\frac{2}{3}[/tex] mph

As we can see, the first 3 rates are same, 75 mph, and the last one is [tex]66\frac{2}{3}[/tex] mph. So clearly, the last rate is the slowest.

D is the right answer.

Answer:

D) 800 miles in 12 hours

Step-by-step explanation:

300/4=75

450/6=75

750/10=75

800/12=66.6666667

Answer:

The perimeter of the larger sign : 144*1,25= 180 inches

Side of the triangle= 180/3= 60 inches

square of the height= 60^(2) - 30^(2)= 2700 ( Pythagoras' theorem)

height= square root ( 2700)= 51,96

Step-by-step explanation:

To find the height of the larger sign, determine the scale factor between the two signs and use the formula for the height of an equilateral triangle.

To find the height of the larger sign, we need to determine the scale factor between the two signs. The perimeter of the original sign is 144 inches, and the new sign has a perimeter that is 1.25 times the original. This means the perimeter of the new sign is 144 x 1.25 = 180 inches.

Since the original sign is an equilateral triangle, each side has a length of 144/3 = 48 inches. The larger sign will have sides that are 180/3 = 60 inches in length.

Since the larger sign is also an equilateral triangle, we can use the formula h = (√3/2) x s, where h is the height and s is the length of a side. Therefore, the height of the larger sign is h = (√3/2) x 60 = 51.96 inches (rounded to two decimal places).

Each person in the group could have either bought a regular bag of popcorn for $6 or a super size bag for $8. The total costs would be $240 and $320 respectively.

In this scenario, we have a group of 40 people each buying popcorn at a theme park. The prices available were the regular bag for $6 each or the super size for $8 each. Depending on their choice, the total amount spent will vary. For example, if every person in the group purchased a regular bag, the total would be 40 * $6 = $240. And if everyone decided to get a super size bag, it would end up being 40 * $8 = $320

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Answer:

dive below = 5 1/4 ft

Step-by-step explanation:

Dive above water + dive below water = total dive

We know the dive above water is 3 1/2 ft

The total length of the dive is  8 3/4 ft

Substitute in what we know

3 1/2 + dive below = 8 3/4

get a common denominator of 4

3 1/2*2/2 +dive below = 8 3/4

3 2/4 +dive below = 8 3/4

Subtract 3 2/4 from each side

3 2/4 - 3 2/4 +dive below = 8 3/4 - 3 2/4

dive below = 5 1/4 ft

Final answer:

To find out how far below the surface of the water Mya is at the end of her dive, subtract the diving board's height from the total dive length. Convert mixed numbers to improper fractions for easy subtraction, and after calculation, you find that Mya is 5 1/4 feet below the water's surface.

Explanation:

To determine how far below the surface of the water Mya is at the end of the dive, we need to subtract the height of the diving board from the total length of the dive. Mya's dive board is 3 1/2 feet above the water, and the total length of her dive is 8 3/4 feet.

First, convert the mixed numbers to improper fractions to make the subtraction easier. For 3 1/2, multiply 3 (the whole number) by 2 (the denominator) and add 1 (the numerator) to get 7/2. For 8 3/4, multiply 8 by 4 and add 3 to get 35/4.

The fractions are now 7/2 and 35/4. Before subtracting, find a common denominator, which is 4 in this case.

Convert 7/2 to 14/4, so we can subtract it from 35/4.

Subtract 14/4 from 35/4 to find the distance below the water's surface: 35/4 - 14/4 = 21/4.

Finally, convert the improper fraction back to a mixed number. The mixed number for 21/4 is 5 1/4, which means Mya is 5 1/4 feet below the surface of the water at the end of her dive.

Answer:

- 1 and 1

Step-by-step explanation:

using the rule of exponents

• [tex]a^{0}[/tex] = 1

- ([tex]2^{0}[/tex]) = - 1

( - [tex]\frac{4}{9}[/tex])^0 = 1

For this case we have that by definition, any number raised to zero gives 1.

Knowing that:

[tex]\frac {a ^ 2} {a ^ 2} = 1[/tex] and by power properties of the same base we have that: [tex]\frac {a ^ 2} {a ^ 2} = a ^ {2-2} = a ^ 0[/tex]

So:

[tex]a ^ 0 = 1[/tex]

So, if we have:

[tex]- (2) ^ 0 = - (1) = - 1\\(- \frac {4} {9}) ^ 0 = 1[/tex]

Answer:

[tex]- (2) ^ 0 = - (1) = - 1\\(- \frac {4} {9}) ^ 0 = 1[/tex]

Jaden can build a dance floor measuring 48 square yards with his budget of $526.50, based on the cost of $3.25 per wooden plank.

To calculate the size of the dance floor Jaden can build with his budget, we first need to determine how many wooden planks he can purchase. Each plank costs $3.25 and he has $526.50 to spend.

Number of planks = Total budget / Cost per plank
= $526.50 / $3.25
= 162 planks

Next, we need to find out the area that each plank covers. Since each plank is 8 feet long and 4 inches (or 1/3 feet) wide, its area in square feet is:

Area per plank = Length * Width
= 8 feet * 1/3 feet
= 8/3 square feet

Now, let's calculate the total area covered by 162 planks:

Total area in square feet = 162 planks * [tex]\frac{8}{3}[/tex] square feet/plank
= 432 square feet

Since 1 square yard is equivalent to 9 square feet, we convert the total area to square yards:

Total area in square yards = Total area in square feet / 9
= 432 square feet / 9
= 48 square yards

Therefore, Jaden can build a dance floor measuring 48 square yards within his budget.

Answer:

Step-by-step explanation: The answer to your question is 15 pretzels.To figure this out, you first multiply 8.99 by 4 since he did buy 4 pizzas and each pizza is 8.99. Then once you do that, you should come up with 35.96. Then subtract 50.81 from 35.96,which should give you 14.85. Then just divide 14.85 by 0.99 to figure out the amount of pretzels he bought.It should give you 15.Hope this helps!!!!

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Answer:

15

Step-by-step explanation:

Danny buys 4 pizzas and some pretzels for his baseball team.

The cost of each pizza is $8.99

Total cost of 4 pizza = 4 × 8.99

                                  = $35.96

Let buy p numbers of pretzels whose cost $0.99 each.

Total cost for p pretzels = 0.99p

Total  spend by Danny on pizzas and pretzels = $50.81

                               35.96 + 0.99p = 50.81

                                             0.99p = 50.81 - 35.96

                                             0.99p = 14.85

                                                     p = 15

Hence, Danny bought 15 pretzels for baseball team.

The inequality that represents x is [tex]$x \geq 6$[/tex]. This means that the total length of all the sides of the shape must be at least 6 feet.

Let's say the total length of all the sides of the shape is represented by the variable x. We are given that the perimeter is at least 18 feet.  This can be written as an inequality: [tex]$x \geq 18$[/tex]

Since the sides of the triangle measure 3 feet, 5 feet and x-2 feet, we can express the perimeter inequality in terms of x as: [tex]$x+ 3 + 5 +x-2 \geq 18$[/tex]

Simplifying the left side of the inequality, we get: [tex]$2x + 6 \geq 18$[/tex]

Subtracting 6 from both sides, we obtain: [tex]$2x \geq 12$[/tex]

Dividing both sides by 2, we get: [tex]x \geq 6$.[/tex]

Answer:

The correct answer is 904.1 pounds per square foot

Step-by-step explanation:

(mcgraw)

Simply just subtract 5 from 15 to get 14^10, or D.

Answer:

1563.2

Step-by-step explanation:

If you just multiply 0.3 by 10 you will get 3

Now all you need to do is write 3 or have a number which has unit place value of 3

Answer: The number in which the value of the 3 is 10 times the value of the digit 3 in 156.32 = 3

Step-by-step explanation:

The given number = 156.32

The place value of 3 in 156.32 is 3 tenth [since it the left most number after the decimal].

3 tenth can be written as [tex]\frac{3}{10}[/tex]

The number 10 times [tex]\frac{3}{10}[/tex]= [tex]10\times\frac{3}{10}[/tex]

Therefore, The number 10 times [tex]\frac{3}{10}[/tex]=3

Hence, the number in which the value of the 3 is 10 times the value of the digit 3 in 156.32 = 3

Final answer:

To determine Joshua's earnings after mowing lawns for 5 weeks, multiply the total number of lawns mowed in 5 weeks by the rate of $25 per lawn.

Explanation:

To calculate the money Joshua will earn after mowing lawns for 5 weeks:

Therefore, Joshua will earn $X after mowing lawns for 5 weeks.

Answer:

D. y > or = 3x - 4

Step-by-step explanation:

Looking at the graph, we know the y intercept, or where the graph crosses the y axis, is -4.

We can find the slope of the line from 2 points (0,-4) and (2,2)

The slope is  given by

m = (y2-y1)/(x2-x1)

   = (2--4)/(2-0)

  = (2+4)/(2-0)

   =6/2

   =3

Using the slope intercept form for the line, y=mx+b

y = 3x+-4

y = 3x-4

The graph is shaded above the line so y is greater than the line, and the line is solid so y is also equal to the line

y ≥3x-4

Answer: Translation

More specifically, it is a translation shifting every point 5 units to the right and 7 units down.

In geometry, "translation" is a special term to basically mean "shift the point left, right, up or down". You can think of the point sliding across the page in some manner.

Answer:

translation

Step-by-step explanation:

the point is moved 5 units to the right and 7 units up

Answer:

10)C 18,000

11) B 130.83

12)B or C not for sure

13) D the domain is 1 < f<7 the range is 24 < c(f)<168

Step-by-step explanation:

-72, I don't see any of that over there

Answer:

The solution set is (6,3)

Step-by-step explanation:

Begin by multiplying equation 1 by 2. You'll see why in a moment

2y = 2*(1/2) x

2y = x

Substitute this value into equation 2.

2y + 4y = 18                  Combine like terms on the left

6y = 18                          Divide both sides by 6

6y/6 = 18/6                    Do the division

y = 3

To solve for x just use the top equation

y = 1/2x

3 = 1/2x                          Multiply by 2

3*2 = x

x = 6