If f(x) = 3x + 10 and g(x) = 2x – 4, find (f + g)(x).
A. (f + g)(x) = 3x – 2x + 14

B. (f + g)(x) = 3x + 2x + 6

C. (f + g)(x) = 5x + 6

D. (f + g)(x) = –3x – 2x – 14

Answer:

D on edge 2020 :)

Step-by-step explanation:

⇒Polar Coordinate of point (x,y)=(r,Ф)

The Point (x,y) lies in First Quadrant.

r=Distance from Origin to point (x,y)

[tex]r=\sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{y}{x}\\\\ \theta=A[/tex]

⇒The Point (-x,y) lies in Second Quadrant.

[tex]r=\sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{y}{-x}\\\\ \theta=\pi-A[/tex]

Polar Coordinate of point (-x,y)=(r,π-Ф)

⇒The Point (-2x,-2y) lies in Third Quadrant.

[tex]r=\sqrt{(-2x)^2+(-2y)^2}\\\\r=\sqrt{4x^2+4y^2}\\\\r=2\times \sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{-2y}{-2x}\\\\=\tan^{-1}\frac{y}{x}\\\\ \theta=\pi+A[/tex]

Polar Coordinate of point (-2x,-2y)=(2r,π+Ф)

⇒The Point (3x,-3y) lies in Fourth Quadrant.

[tex]r=\sqrt{(3x)^2+(-3y)^2}\\\\r=\sqrt{9x^2+9y^2}\\\\r=3\times \sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{-3y}{3x}\\\\=\tan^{-1}\frac{-y}{x}\\\\ \theta=-A[/tex]

Polar Coordinate of point (3x,-3y)=(3r,-Ф)

The simplified form of 2√3 - 2√3 is 0, which is a rational number.

In order to determine if the simplified form of 2√3 - 2√3 is rational, we first need to simplify the expression. Since we have the same terms being subtracted from each other, the expression will simplify to 0. Therefore, the simplified form is 0, and 0 is considered to be a rational number since it can be written as 0/1.

Answer:

he answer is D.)y = 400(1/2)X-1

Step-by-step explanation:

Option D is correct, y=400(1/2)ˣ⁻¹ is the equation  that models the sequence 400, 200, 100, 50, ..

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The sequence 400, 200, 100, 50, ... is a geometric sequence with a common ratio of 1/2, since each term is half the previous term.

To write an equation that models this sequence, we can use the general formula for a geometric sequence:

aₙ = a.rⁿ⁻¹

where aₙ is the nth term of the sequence, a is the first term of the sequence, r is the common ratio of the sequence and n is the number of the term we want to find

Since the first term is 400 and the common ratio is 1/2, we have:

a= 400

r = 1/2

aₙ=400(1/2)ˣ⁻¹

y=400(1/2)ˣ⁻¹

Hence, option D is correct, y=400(1/2)ˣ⁻¹ is the equation  that models the sequence 400, 200, 100, 50, ..

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The answer is B.) $210

Answer:

degree of the polynomial is 11.

C is the correct option.

Step-by-step explanation:

We have been given the polynomial

[tex]7x^7+10x^4+4x^3-5x^{11}-10x^6-6x^7[/tex]

Rewrite this polynomial in standard form i.e from descending exponents

[tex]-5x^{11}-6x^7+7x^7-10x^6+10x^4+4x^3[/tex]

On simplifying, we get

[tex]-5x^{11}+x^7-10x^6+10x^4+4x^3[/tex]

Now, we know that the degree of the polynomial is the highest exponent.

Here, the highest exponent is 11.

Therefore, the degree of the polynomial is 11.

C is the correct option.

Answer: The answer is (c) - 5, (e) 0 and (f) - 200.

Step-by-step explanation:  We are to select the correct numbers from the given options that cannot represent the area of a polygon.

We know that the area of any figure cannot be a negative number or zero.

So, the numbers which cannot represent the area of a polygon are - 5, 0 and - 200.

Thus, (c), (e) and (f) are the correct options.

If the point (8,4) is on the graph of an even function, the point (-8,4) must also be on the graph.

An even function is a function that satisfies the property f(x) = f(-x) for all values of x in the domain of the function. If the point (8,4) is on the graph of an even function, then the point (-8,4) must also be on the graph. This is because substituting x = -8 into the function would give the same y-value as when x = 8.

To find the purchase price at which the $5 off coupon and the 20% off coupon have the same value, solve the equation x - $5 = 0.8x by isolating x.

To find the purchase price at which the $5 off coupon and the 20% off coupon have the same value, we need to set up an equation and solve for the purchase price.

Let's assume the purchase price is x dollars. The $5 off coupon would give us a discount of $5, so the price after the discount would be x - $5. The 20% off coupon would give us a discount of 20% of x, so the price after the discount would be 0.8x.

We can set up the equation:

x - $5 = 0.8x

Now we can solve for x:

x - 0.8x = $5

0.2x = $5

x = $25

Therefore, the coupons will have the same value at a purchase price of $25.

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To multiply the complex numbers (2 - 7i) and (9 + 5i), we use the distributive property to get the result of 53 - 53i.

To multiply the complex numbers (2 - 7i) and (9 + 5i), we use the distributive property, also known as the FOIL method in this context (First, Outer, Inner, Last). Applying this method, we get:

First: 2 × 9 = 18

Outer: 2 × 5i = 10i

Inner: (-7i) × 9 = -63i

Last: (-7i) ×5i = -35i²

Recall that i² = -1, so -35i² = -35(-1) = 35. Combine like terms (the real numbers with real numbers, and the imaginary numbers with imaginary numbers):

18 + 35 (real parts) + 10i - 63i (imaginary parts) equals to 53 - 53i.

Thus, the product of (2 - 7i) and (9 + 5i) is 53 - 53i.

Answer:

[tex]\frac{1}{64}[/tex]  makes the statement true.

Step-by-step explanation:

Given expression,

[tex]8^{-2}[/tex]

By using the property of exponent, i.e. [tex]a^m=\frac{1}{a^{-m}}[/tex]

[tex]\implies 8^{-2}=\frac{1}{8^{2}}[/tex]

[tex]=\frac{1}{64}[/tex]

Hence, the true statement would be,

[tex]8^{-2}=\frac{1}{64}[/tex]

Answer:  The circumference of the patio is 21.98 meters.

Step-by-step explanation:  Given that there is a circular patio with a diameter of 7 meters. Greg is going to put a titled edge around the patio.

We are to find the circumference of the patio.

If 'r' units is the radius of a circle, then the circumference of the circle is given by

[tex]C=2\pi r.[/tex]

Since the diameter of the circular patio is 7 meters, so the radius 'r' will be given by

[tex]\textup{radius}=\dfrac{1}{2}\textup{ of the diameter}\\\\\Rightarrow r=\dfrac{1}{2}\times 7\\\\\Rightarrow r=3.5~\textup{meters.}[/tex]

Therefore, the circumference of the patio is given by

[tex]C=2\pi r=2\times 3.14\times 3.5=21.98~\textup{meters}.[/tex]

Thus, the circumference of the patio is 21.98 meters.

The required 3 5/8 as a decimal is 3.625, as of the given mixed fraction.

Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,

Here,

To convert 3 5/8 to a decimal, we can first convert the mixed number to an improper fraction and then divide the numerator by the denominator using a long division or a calculator. Here are the steps,

3 5/8 = (3 x 8 + 5)/8 = 29/8

Dividing 29 by 8 using long division, we get:

3 5/8 =  3.625

Therefore, 3 5/8 as a decimal is 3.625.

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[tex]\( C' \cap A' \)[/tex] contains only the element [tex]\( r \).[/tex]

To find [tex]\( C' \cap A' \)[/tex], we first need to determine the complement of sets ( A ) and ( C ) with respect to the universal set ( U ).

The complement of set ( A ), denoted as ( A' ), consists of all elements in ( U ) that are not in (A). So, [tex]\( A' = \{r, t, v, x, z\} \).[/tex]

Similarly, the complement of set [tex]\( C \),[/tex] denoted as [tex]\( C' \)[/tex], contains all elements in (U) that are not in (C). Hence, [tex]\( C' = \{q, r, s, t, u\} \).[/tex]

Now, to find the intersection of [tex]\( C' \) and \( A' \)[/tex], we list the elements that are common to both sets:

[tex]\[ C' \cap A' = \{r\} \][/tex]

Therefore,[tex]\( C' \cap A' \)[/tex] contains only the element [tex]\( r \).[/tex]

To calculate the proceeds from discounting a note, subtract the bank discount from the face value.

To calculate the proceeds from discounting a note, we need to use the formula:

Proceeds = Face Value - Bank Discount

First, let's calculate the bank discount using the formula:

Bank Discount = Face Value * Discount Rate * Time

For the given note:

Face Value = $15,000

Discount Rate = 9%

Time = 120 days / 365 days/year (assuming a 365-day year)

Plugging in the values, we get:

Bank Discount = $15,000 * 0.09 * (120/365)

Next, we can calculate the proceeds by subtracting the bank discount from the face value:

Proceeds = $15,000 - Bank Discount

Answer:

C

Step-by-step explanation:

You have to subtract the 11% that you are putting into your 401k to find out how much you are earning and that you're not putting into retirement.

67,200*0.11 = 7,392

67,200 - 7,392 = 59,808

Mustafa's pretax income after contributing 11% to his 401(k) plan is 59808 dollars.

A percentage is a value per hundredth.

Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given Mustafa contributes 11% of his $67,200 annual salary to his 401(k) plan.

∴ 11% of $67200 is = (11/100)×67200 dollars.

= 7392 dollars.

So, his pretax income is (67200 - 7392) dollars.

= 59808 dollars.

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Step-by-step explanation:

Arrangement according to her priorities are as follow:

1) Finish homework which is due the next day (Tuesday).

2) Prepare for a French test that is due on Thursday.

3) Prepare  a science project that is due on the following Monday.

4) Prepare for the algebra test that is on the next friday.

5) Complete her essay that is due in two weeks.

6) Plan a surprise party for her best friend's birthday that is on weekend after next.

To solve the system of equations, rewrite them in standard form, eliminate x, solve for y, and substitute the value of y into the equations to solve for x. The solution to the system of equations is x = 4 and y = 2.

To solve the system of equations:

The solution to the system of equations is x = 4 and y = 2.

To solve the provided system of linear equations, the elimination method can be used. The solution to the equations 3x - 2y = 14 and 5x + 6y = 42 is x = 6 and y = 2.

The student has provided two linear equations which form a system of equations:

To solve this system, we can use either the substitution method, the elimination method, or graphical method. In this case, the elimination method may be more straightforward. Here's a step-by-step explanation:

Therefore, the solution to the system of equations is x = 6, y = 2.