What is the greatest common factor of 3x

The cost of the 4 cartons of grape juice and 8 cartons of apple juice will be $32 and the difference is $12.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3.

The cost of 4 grapes and 8 apples will be,

Cost = 2g + 3a

Cost = ( 2 x 4 ) + ( 3 x 8 )

Cost = 8 + 24

Cost = $32

The difference in the price  Missy and Jared paid is,

Difference = $32 - $ 20

Difference = $12

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Answer: 240 Calories are from Carbohydrates

Step-by-step explanation:

First, we will convert 80% into the decimal 0.8, then we will multiply this by the amount of total calories in the drink to create the following equation:

300 * 0.8 = 240 Calories.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{\frac{23}{25}}{0.07}=t\implies \boxed{16=t}[/tex]

Answer:

5

Step-by-step explanation:

5 x 3 = 15

n x 4 = 4n

3 + 4 = 7

(5 x 3) + (n x 4) = 5(3 + 4)

15 + 4n = 5*7

15 + 4n = 35

4n = 35 - 15

4n = 20

n = 20/4

n = 5

Hence, the value of missing number (n) is 5.

Answer:

[tex]w=\frac{s-2lh}{2(h+l)}[/tex]

Step-by-step explanation:

Given the equation, [tex]S=2(lw+lh+wh)[/tex], solve for w.

[tex]S=2(lw+lh+wh)[/tex], distribute the 2.

=> [tex]S=2lw+2lh+2wh[/tex], subtract [tex]2lh[/tex] from both sides.

=> [tex]S-2lh=2lw+2wh[/tex], factor out a [tex]w[/tex] from the right-hand-side.

=> [tex]S-2lh=w(2l+2h)[/tex], now divide [tex](2l+2h)[/tex] from each side.

=>[tex]\frac{S-2lh}{2l+2h}=w[/tex]

Final answer: [tex]w=\frac{s-2lh}{2(h+l)}[/tex]

Answer:

5.794

Step-by-step explanation:

The seven after the decimal point is the tenth digit, the nine is the hundredth, and the 3 is the thousandth place. Therefore, we look at our neighbor (the number next to the thousandth place) and if its 5 or more we round up, but if its 4 or less we keep it the same.

The angle m∠D of the triangle is 78 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The ΔKDT and ΔKPQ are isosceles triangle.

Isosceles triangle is a triangle that has two sides and angles equal to each other.

Therefore,

∠D + ∠T + ∠k = 180

∠D  = 6x + 6

∠T = 6x + 6

∠K = 2x

Therefore,

6x + 6 + 6x + 6 + 2x = 180

14x + 12  = 180

14x = 180 - 12

14x = 168

divide both side by 14

x = 168 / 14

x = 12

Therefore,

m∠D = 6x + 6 = 6(12) + 6 = 72 + 6 = 78 degrees.

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Answer: Let n be the number of members in the Science Club.

On the first day, the total cost for transportation plus the cost of tickets is 60 + (15n) dollars.

On the second day, the total cost for transportation plus the cost of tickets is 95 + (12n) dollars.

So, the total cost for both days is (60 + 15n) + (95 + 12n) = 155 + 27n dollars.

The expression to represent the total cost for two days for the n members of the club is 155 + 27n dollars.

This equation represents the total cost for the transportation, planetarium and geology museum for 2 days for the n members in the club.

It should be noted that this is the monetary representation and it might vary depending on other factors, such as group discounts.

Step-by-step explanation:

Answer:

(n x 27)+155

Step-by-step explanation:

15 +12 = 27

Each member pays $27 for the tickets so we multiply it by the number of members.

95 + 60 = 155

The members pay $155 in total for transportation.

So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

A. 2+3 × 4 = 22 +12 is not a true statement, because the order of operations is not followed, multiplication should be done before addition.

B. z+zx9 = 9z is not a true statement, because it is not clear what the operation is between z and x, and what the operation is between x and 9

C. -8y + 4.3y + 3.7 = 0 is a true statement because it is a linear equation with one variable y, it represents a straight line.

D. 12-1.8b+ 1.8b = 1.8b is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.

E. m8+7(8) = m is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.

So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0

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Answer:

x

)

=

2

x

4

−

3

x

+

3

f(x)=2x

4

−3x+3, then what is the remainder when

f

(

x

)

f(x) is divided by

x

−

1

x−1?

The function p(x) = (x + 3)² is transformed 3 units left along the x-axis.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over the x-axis, (x, -y).

Given, A function f(x) = x².

Now, p(x) = f(x + 3).

p(x) = (x + 3)² and it is a transformed function to the parent function f(x).

Now, The function p(x) = (x + 3)² is transformed 3 units to the left along the x-axis.

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If you have $82 in your bank account and you write checks for $54, $35, and $15, then the total amount you have written in checks is $54 + $35 + $15 = $104.

So the remaining balance is $82 - $104 = -$22, which means you are now overdrawn.

After you deposit $35 and $42, the new balance will be $82 - $22 + $35 + $42 = $155

So after the deposit, the account balance is $155

It is important to keep track of your bank account balance, if you do not have enough funds in the account and the check you wrote is cashed the bank will bounce the check and incur additional fees.

Answer:y=

Step-by-step explanation:Firstly let's find the slope which is (7-7)/(4-(-3))=0. Using the point slope formula y-y1=m(x-x1) we plug in one of the points and simplify y-7=0(x-4). Simplifying and solving for y gives us y=

Answer:

37.04%

Step-by-step explanation:

To find the percentage increase in the value of Tessa's stock, we need to calculate the difference between the original price and the current price, and then divide that difference by the original price, and multiply by 100 to express the result as a percentage.

Here is the calculation:

percentage increase = ((284.96 - 208.00) / 208.00) * 100

= (76.96 / 208.00) * 100

= 37.04 * 100

= 37.04%

So Tessa's stock has increased in value by 37.04%.

Answer:

37 % increase

Step-by-step explanation:

To find the percentage increase, take the new amount and subtract the original amount

284.96 -208 =76.96

Divide this by the original amount

76.96/208=.37

Change the decimal form to a percent

.37 * 100% = 37 %

Answer:

Step-by-step explanation:

20)63(3

    -60

   -------

        3

so every children gets 3 toys but 3 toys are left which can be distributed among 3 children.

so 3 children get 1 toy more.

Hence 3 children get 3+1=4 toys (each)

Answer:

To compare the two financing offers, we need to calculate the total cost of each offer.

Part A: What is the total cost of offer 1?

To calculate the total cost of offer 1, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 24.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2490/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,534.89.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,534.89 = $4,509.89.

Therefore, the total cost of offer 1 is $4,509.89.

Part B: What is the total cost of offer 2?

To calculate the total cost of offer 2, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,

To continue the calculation of the total cost of offer 2, we need to calculate the total interest using the formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,405.70.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,405.70 = $4,381.70.

Therefore, the total cost of offer 2 is $4,381.70.

Part C: Which financing offer should the new homeowner choose?

Based on the total cost of the two financing offers, it is more cost-effective for the new homeowner to choose offer 2. Offer 2 has a lower total cost ($4,381.70) compared to offer 1 ($4,509.89), so it would be the better choice for the new homeowner.

Step-by-step explanation:

Answer: To model the problem with a division equation, we can write 46 ÷ 7 = x, where x represents the number of swimmers that each lane will have.

To solve the equation using repeated subtraction, we can subtract 7 from 46 several times until we reach a number that is less than 7. The number of times we subtract 7 will give us the number of swimmers each lane will have. Here's one way to do it:

46 - 7 = 39

39 - 7 = 32

32 - 7 = 25

25 - 7 = 18

18 - 7 = 11

11 - 7 = 4

As you can see, we are able to subtract 7 from 46 a total of 6 times before we get a number less than 7. This means that each lane will have 6 swimmers, and the remaining 4 swimmers will practice diving. So each lane will have 6 swimmers.

So the equation 46 ÷ 7 = 6, and also by repeated subtraction method it shows the same result of 6 swimmers each lane.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

[tex]x=1-sin(a)\\y=1+cos(a)[/tex]

Solve for [tex]a[/tex] in the second equation.

[tex]y=1+cos(a)[/tex]

[tex]y-1=cos(a)[/tex]

[tex]a=cos^{-1}( y-1)[/tex]

Insert our answer for [tex]a[/tex] into the first equation.

[tex]x=1-sin(a)[/tex]

[tex]x=1-sin(cos^{-1}( y-1))[/tex]

[tex]cos^{-1}=arccos[/tex]

[tex]x=1-sin(arccos( y-1))[/tex]

Lets simplify [tex]1-sin(arccos( y-1))[/tex]

A piece of graph paper would be helpful in my opinion.

Here is how I would go about doing so

Draw a triangle in the plane with vertices [tex](y-1,\sqrt{1^2-(y-1)^2}),(y-1,0)[/tex] and the origin.

[tex]arccos(y-1)[/tex] is is the angle between the positive x-axis and the ray beginning at the origin and passing through [tex](y-1,\sqrt{1^2-(y-1)^2})[/tex]. Therefore [tex]sin(arccos(y-1))[/tex] is [tex]\sqrt{1-(y-1)^2}[/tex]

Now we have

[tex]x-1-\sqrt{1-(y-1)^2}\\a=arccos(y-1)[/tex]

We can write [tex]1[/tex] as [tex]1^2[/tex]. Since both terms are now perfect squares, we can factor using the difference of squares formula.

[tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=1[/tex] and [tex]b=y-1[/tex]

[tex]x=1-\sqrt{(1+y-1)(1-(y-1))}[/tex]

After simplifying we get

[tex]x=-\sqrt{y(-y+2)}+1[/tex]

[tex]x=-\sqrt{y(-y+2)}+1[/tex]

[tex]a=arccos(y-1)[/tex]

I think this is what your question was. If not let me know.

The least amount of money that was originally put in the savings account is $426.

The amount of money in the savings account is a function of the money that was originally in the account and the amount by which the account was increased by.

The inequality that represents the total amount of money in the savings account is:

amount originally in the account + amount deposited > 500

x + $75 > $500

x > $500 - $75

x > $425

The least amount would be $426 because this is the smallest number that is greater than $425 that would make the total amount more than $500.

To check:

$75 + $426 = $501

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the answer is right there

Answer:

a. Their down payment is 25% of the purchase price.

Calculation:

Down payment ÷ Purchase price = Percentage

$35,000 ÷ $140,000 = 0.25 = 25%

b. A $7,000 down payment would be 5% of the purchase price.

Calculation:

Down payment ÷ Purchase price = Percentage

$7,000 ÷ $140,000 = 0.05 = 5%

The number of hours does each group member work on the project is 4 hours. Therefore, the correct answer is option B.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x+45/4=4x.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

4x-x=45/4

3x=45/4

x=15/4

x=3.75

x≈4 hours

Therefore, option B is the correct answer.

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The reason why the cousin's procedure for getting the x and y intercepts work is because they represent the definition of those points on a graph.

The x-intercept of a graph or function simply refers to the point at which the graph crosses the graph crosses the x-axis or the point at which y = 0. In a similar manner, the y-intercept simply refers to the point at which the graph crosses the y-axis or simply the point at which x = 0.

Now, we are given the equation of the line as;

5x + 4y = 14

The general form of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Rewriting the equation of the line in slope intercept form is;

y = -⁵/₄x + ⁷/₂

Now, the reason why we plug in 0 for x to get the y-intercept is because when x = 0, that is only where we can get the y-intercept as the corresponding value of x will be traced to 0.

Similarly,  the reason why we plug in 0 for y to get the x-intercept is because when y = 0, that is only where we can get the x-intercept as the corresponding value of y will be traced to 0.

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40% of an hour is 24 minutes = 2/5 hours.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Given that,

there are 60 minutes in an hour,

we can multiply this by 0.4 to find that 24 minutes constitutes 40% of an hour.

i.e. 60*40%= 24 minutes

Hence, 40% of an hour is 24 minutes = 2/5 hours.

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The number of times 5×10³ greater than 15×10⁹ is 3×10⁶.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Given that, 15×10⁹ and 5×10³.

Number of times 5×10³ greater than 15×10⁹ is

Now, 15×10⁹/5×10³

= 3×10⁶

Therefore, 3×10⁶ times 5×10³ greater than 15×10⁹.

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