Simplify 3.5m(3m + 1.8) using the distributive property.

10.5m + 6.3m
10.5m + 1.8
10.5m2 + 6.3m
10.5m2 + 1.8

The polynomial that represents the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate is;

p(x) = x(1 + 6/100)

g(x) = (1500 - x)(1 + 3.8/100)

The compound interest is defined as a form of interest whereby the rate of interest is applied on the amount obtained after every given interval of time.

We are given that;

The total amount invested in the two mutual funds = $1500.

The growth rate of the first mutual fund = 6%.

The growth rate of the second mutual fund = 3.8%.

If the amount invested in the first mutual fund is x, then the amount invested in second mutual fund is 1500 - x.

The growth for both mutual funds can then be represented by;

First mutual fund; p(x) = x(1 + 6/100)

The second mutual fund; g(x) = (1500 - x)(1 + 3.8/100)

Thus, the polynomial expression for both the mutual funds are;

p(x) = x(1 + 6/100) and g(x) = (1500 - x)(1 + 3.8/100) respectively.

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Answer:

x=-1 and y=4

Step-by-step explanation:

When you draw a graph you will see point of intersection which is solution

Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2

A mathematical depiction of two equal variables, one on either side of a "equals" sign, is called an equation. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.

Here,

Given : synthetic division for

x³ + 3x² + 8x + 14

------------------------

x + 2

Write the problem in synthetic division format

-2  | 1 3 8 14

         -2 -2  

------------------------

     1   1  6

Carry down the leading coefficient, unchanged, to below the division symbol

-2  |    1 3 8 14

           -2 -2

---------------------------

         1  1   6

Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:

1(-2)=-2

-2 |  1 3 8 14

        -2 - 2

------------------

     1    1   6

=> We get:

As

x² +x+6+ [tex]\frac{2}{x+2}[/tex]

and remainder is 2

Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2.

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The graph of an inequality in two variables is the set of points that represents all solutions to the inequality.

The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half. For > and, the border line is solid, and for and, it is dashed.

To determine the equation governing the inequality line, enter your slope and a point into the formula y = mx + B, where "m" denotes the slope, "x, y" denotes a point on the line, and "b" is the y-intercept. By inserting (0, 0), you get 0 = 0 + b, which equals 0.

When you rewrite the equation, you get y = x/2. The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilised in this inequality, the LHS is clearly greater than the RHS.

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Answer:

The manager is not correct in her calculation.

Step-by-step explanation:

There are 244 males and n females who entered the mall as the manager at the shopping mall counts.

If 25% of all males are children, then the number of male children are .

Again, the 25% of all female are children, then the number of female chilfren are .

Therefore, the total number of children will be (60 + 0.25n).

But the manager gives the number of children to be 0.25n + 61 who entered the mall.

So, the manager is not correct in that calculation. (Answer)

Step-by-step explanation:

The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.

A stew recipe uses 3 teaspoons of salt for every 4 cups of water.

There is a ratio issue here.

As X is to three, 3 is to 4.

3 : 4 :: X : 3

To eliminate the fractions, multiply each integer in the ratio by 12.

9 : 12 :: 9X : 12

This is a portion of what is

9 / 12 = 9X / 12

to obtain, cross-multiply.

9 / 12 = 3 teaspoons of salt,

Check: 3 cup of flour yields 3 cups, which is a 4x increase.

The amount of salt in 9/12 tablespoons is four times that of 3 tablespoons.

The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.

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Using the Algebraic tile method we get x=2 solution for equation model

The algebra tile method is a method of solving equations by using visual models, such as tiles with different values on them, to represent the unknowns and constants in the equation. It is often used to help students understand the process of solving equations and to see how the operations of addition and subtraction correspond to the process of combining or separating algebraic expressions.

In the question, we have 3 kinds of tile

Equation will be :

⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1

⇒ 3x - 2 = 4

⇒ 3x = 6

⇒ x = 2

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Therefore, $52.25 is the answer to the inquiry about what percentage of a person's income is withheld each week for federal income tax.

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here,

The Federal Insurance Contribution Act is the American legislative framework in use here, and it contains the criteria and guidelines that are utilized to determine payroll taxes on an employee's paychecks. The social security and Medicare programs are funded through taxation, which is paid by both employers and employees.

The amount of federal income tax deducted from the weekly cheque is:

6.2% from Social Security plus 1.45% from Medicare.

= 7.5 percent of the weekly gross salary.

The amount of federal income tax withheld each week from Beverly Hibbs's $683.00 weekly salary is:

= 0.0765 × 683

= $52.25

Therefore, $52.25 is the answer to the inquiry about what proportion of a person's income is withheld each week for federal income tax.

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Choices that is equivalent to the expression √5. √20 is 5.2

In mathematics, the word "equivalent" designates two quantities, numbers, or meanings that are the same. A bar across an equivalent sign or Equivalent Sign shall be used to indicate the equivalence of two such quantities. Additionally, it denotes the logical equivalent of two values or a group of quantities.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

x= (5)^1/2*(20)^1/2

x= (5)^1/2*(2.2.5)^1/2

x=5.2

So B is the correct option.

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Answer:100

Step-by-step explanation:

If Raj was getting a 5% commission, he would make 24000 * 5% = $<<240005.01=1200>>1200 on $24,000 of sales.

If he is now getting a 6.5% commission, he will make 24000 * 6.5% = $<<240006.5.01=1560>>1560 on $24,000 of sales.

Thus, Raj will make 1560 - 1200 = $<<1560-1200=360>>360 more on $24,000 of sales with his new commission rate of 6.5% than he did with his old commission rate of 5%.

a) The total cost of buying the car with HST is given as follows: $36,160.

b) The amount of money saved by the customer leasing the car instead of buying is given as follows: $14,760.

c) The customer should lease a new car, as according to the two options in this problem, leasing is more economic than purchasing a new car.

The costs are obtained applying the proportions in the context of this problem.

The HST tax is the Ontario Sales Tax, which means that an additional 13% of taxes has to be paid when purchasing the car.

Hence the total cost of buying the car, considering the HST tax, is given as follows:

1.13 x 32000 = $36,160.

The costs for leasing the car are given as follows:

Hence the total cost for leasing the car is given as follows:

1000 + 48 x 425 = $21,400.

Then the amount saved by the customers when he/she decides to lease the car instead of purchase is given as follows:

36160 - 21400 = $14,760.

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Answer:

x = -5

y = 2

Step-by-step explanation:

1)  -5x-4y = 17

2) 3x-4y = -23

subtract equation 2 from equation 1:

-8x + 0 = 40

-8x = 40

x = -5

substitute x = -5 into equation 1 and solve for y:

-5(-5) - 4y = 17

-4y = -8

y = 2

test answers by substituting x and y values into eqation 2:

3(-5) - 4(2) = -23   Answers are correct!

The cost function is a function that describes the total cost of producing x number of books. The fixed cost of 25000 is a constant cost that does not depend on the number of books produced, so it is not included in the cost function. The cost function is therefore:

Cost function: C(x) = 30x

The profit function is a function that describes the profit made from selling x number of books. The profit is equal to the revenue from selling the books minus the cost of producing the books. The revenue from selling x number of books at a price of 50 each is 50x, so the profit function is:

Profit function: P(x) = 50x - 30x = 20x

This profit function tells you that for every book you sell, you will make a profit of 20.

Answer:

54°

Step-by-step explanation:

Angles corresponding in parallel lines are the same

The function f(x) = -x-3.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given function:

f(x)+3f(-x) = 2x+6.

Let the function is an even function.

So, f(-x) = f(x)

To solve for f(x):

Substituting the property of an even function,

f(x) - 3f(x) = 2x + 6

-2f(x) = 2x + 6

f(x) = -x-3

Therefore, f(x) = -x-3 is the function.

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Answer: -14

Step-by-step explanation:

By sing the following conversions between metric and US systems 26.794 yard = 0.024500 .

What is the value of 1meter in terms of centimeter ?

1 meter can be equal to 100 centimeters and suppose for x meters , then it could be around 100x centimeters .

Given,

1 meter= 3.28 feet

1 Liter= 0.26 gallons

1 kilogram = 2.20 pounds

we know that ,

1yard = 0.0009144 km

so ,

26.794 yard = 26.794*0.0009144 km

= 0.024500

Hence by sing the following conversions between metric and US systems 26.794 yard = 0.024500 .

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The average speed in laps per minute of Ryan is 2.5 laps per minute

From the question, we have the following parameters that can be used in our computation:

The above can be expressed as

(x, y) = (1, 5) and (3, 10)

The average speed in laps per minute can be calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Rewrite as

Average speed = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (1, 5) and (3, 10)

Substitute the known values in the above equation

So, we have the following equation

Average speed = (10 - 5)/(3 - 1)

Evaluate

Average speed = 2.5

Hence, the average speed is 2.5

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Answer:16

Step-by-step explanation: If henry hits 80% of pitches, then the easiest way is to make 80% of 10, which is half of 20, is 8. So if it is 20 times he is up to bat, then 8*2, 2*8 is 16, so he hits the ball 16 times.

Tasha, because she has the lowest ratio since 0.7 < 0.625

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The ratio of hits compared to total attempts is their batting average

Each player on the team wants to have the highest batting average to help their team the most.

Jana has hit the ball 7 times out of 10 attempts.

Average is 7/10=0.7

Tasha has hit the ball 10 times out of 16 attempts.

Tasha Average is 10/16=0.625

We need to find the player who has better batting average

Tasha, because she has the lowest ratio since 0.7 < 0.625

Hence, Tasha, because she has the lowest ratio since 0.7 < 0.625

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A) [tex]$x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i$[/tex]

B) [tex]$y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i$[/tex]

c) [tex]$y-z=(\sqrt{3}-1)-\sqrt{3} i$[/tex]

are the value of given algebraic expression.

The numbers which can be expressed in the form of [tex]$x+iy[/tex] where, [tex]$x, y$[/tex] are real numbers and 'i' is an imaginary number called "iota".

here [tex]$\mathrm{i}$[/tex] is iota whose value is: [tex]$\mathrm{i}=\sqrt{-1}[/tex]

Given .

[tex]$$\begin{aligned}& x=1+\sqrt{3}+2 i \\& y=\sqrt{3}-(1+\sqrt{3}) i \\& z=1-i\end{aligned}$$[/tex]

upon solving two complex number we solve coefficient of iota together and real number together.

A) to find [tex]$(x+y)$[/tex]

[tex]$$\begin{aligned}& x+y=(1+\sqrt{3}+2 i)+(\sqrt{3}-i-\sqrt{3} i) \\& x+y=(1+2 \sqrt{3})+(2-1-\sqrt{3}) i \\& x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i\end{aligned}[/tex]

B) [tex]$\mathbf{y}+\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y+z=(\sqrt{3}-i-\sqrt{3} i)+(1-i) \\& y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i\end{aligned}[/tex]

c) [tex]$\mathbf{y}-\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y-z=(\sqrt{3}-i-\sqrt{3} i)-(1-i) \\& y-z=(\sqrt{3}-1)-\sqrt{3} i\end{aligned}[/tex]

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The sum of the solutions of the equation 4x(x - 3) = 23 is 3.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, An equation 4x(x - 3) = 23.

Now, Distributing the terms in the LHS we have,

4x² - 12x = 23.

4x² - 12x - 23 = 0.

By applying Sridhar acharya's formula we have,

[tex]x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\left(-23\right)}}{2\cdot \:4}[/tex].

[tex]x=\frac{3+4\sqrt{2}}{2},\:x=\frac{3-4\sqrt{2}}{2}[/tex].

Therefore, The sum of the solutions of the equation is,

x + x = (3 + 4√2)/2 + (3 - 4√2)/2.

= (3 + 4√2 + 3 - 4√2)/2.

= 6/2.

= 3.

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Answer:

39

Step-by-step explanation:

6a - b = 6 x 8 - 9 = 48 - 9 = 39

Answer: 39

Step-by-step explanation:

Given that a=8 and b=9

The expression is 6a-b

That is; we have to find 6 times a and then subtract b from it.

6a = 6*8=48

b=9

6a-b=48-9=39

Therefore the answer to the question is 39.

Answer:

1/3

Step-by-step explanation:

2÷2=1

6÷2=3

Solution: 1/3

[tex]8-2z+3(x+y)[/tex] when x is 4, y is 9, and z is 3

Substitute:

[tex]8-2(3)+3(4+9)[/tex]

[tex]8-6+39[/tex]

Solve:

[tex]8-6+39\\=\fbox{23}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{8 - 2z + 3(x + y)}[/tex]

[tex]\mathsf{= 8 - 2(3) + 3(4 + 9)}[/tex]

[tex]\mathsf{= 8 - 6 + 3(4) + 3(9)}[/tex]

[tex]\mathsf{= 8 - 6 + 12 + 27}[/tex]

[tex]\mathsf{= 2 + 12 + 27}[/tex]

[tex]\mathsf{= 14 + 27}[/tex]

[tex]\mathsf{= 41}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{41}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

h(x) = (x+1)²

h(-2) = 1

h(-1) = 0

h(3) = 8

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

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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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Using mathematical operations, the construction worker requires C. 2 pounds of cement to mix 3 pounds of sand.

The basic mathematical operations are subtraction, addition, division, and multiplication.

These mathematical operations combine numbers, variables, mathematical operands, and the equation symbol to solve mathematical problems.

In this situation, we can apply the mathematical operation of multiplication to determine the quantity of cement required for 5 pounds of gravel.

The quantity of gravel per pound of sand = 1²/₃ = 1.667 pounds

For 3 pounds of sand, the quantity of gravel required = 5 pounds (1²/₃ x 3)

The quantity of cement per pound of gravel = ²/₅ pounds or 0.4

For 3 pounds of sand and 5 pounds of gravel, the quantity of cement required = 2 (5 x 0.4) or (5 x ²/₅)

Thus, 2 pounds of cement are needed to mix with 3 pounds of sand and 5 pounds of gravel.

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