If f(x)=x/2-2and g(x)=2x^2+x-3 find (f+g) (x)

Answer:607.81

Step-by-step explanation:that’s what I got believe me on this one guys

The value of the collector's item after 4 years is $607.75.

Given :

Item is purchased for $500.

Value increases at a rate of 5% per year.

Solution :

We know that the exponential growth function is

[tex]y = a(1+r)^x[/tex]

where,

a = $500

r = 0.05

x = 4

The value of the item after 4 years is,

[tex]= 500(1+0.05)^4[/tex]

[tex]= 500\times(1.05)^4[/tex]

[tex]= 607.75[/tex]

The value of the item after 4 years is $607.75.

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Answer: 1.25

Step-by-step explanation:

x=2/1.6

x=1.25

Answer:

x = 1.25

Step-by-step explanation:

Divide 1.6 on both sides to isolate x. 2 ÷ 1.6 = 1.25, so x = 1.25

Answer:

[tex]6\sqrt{3}[/tex]

Step-by-step explanation:

We need to find the product of [tex]3\sqrt{4} \sqrt{3}[/tex]

We know that:

[tex]3\sqrt{4} \sqrt{3}[/tex] ⇒ [tex]3\sqrt{12}[/tex] ⇒[tex]6\sqrt{3}[/tex]

Therefore, the product is [tex]6\sqrt{3}[/tex]

The product of 3sqrt4 and sqrt3 can be calculated as 6sqrt3. This result is obtained by multiplying 3 by the square root of 4, which is 2, giving you 6, and then multiplying that by the square root of 3.

The product of 3sqrt4 and sqrt3 can be calculated following the rules of multiplication for square roots. Firstly, sqrt4 is 2. Therefore, 3sqrt4 is 3*2, which equals 6. Secondly, you multiply this result by sqrt3 to get the final product:

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Answer:

8000

Step-by-step explanation:

The value of 8 in this number is 80, so you multiply that by to get 8000.

I am joyous to assist you.

Answer:

C (X,Y)->(X-4,×-5) I would say bro

Answer:

b) [tex]12x^2-48x+21[/tex] ; all real numbers

Step-by-step explanation:

f and g are polynomials and polynomials have domain all real numbers.

This is because when you input any number there will always be a existing output. There are no restrictions on what you can plug into a polynomial.

So the answer is either b or c.

[tex](f \times g)(x)=f(x) \times g(x)[/tex]

[tex](f \times g)(x)=(-2x+7) \times (-6x+3)[/tex]

[tex]f \times g)(x)=(-2x+7)(-6x+3)[/tex]

Let's use foil!

First: [tex]-2x(-6x)=12x^2[/tex]

Outer: [tex]-2x(3)=-6x[/tex]

Inner:  [tex]7(-6x)=-42x[/tex]

Last:  [tex]7(3)=21[/tex]

-----------------------------Add like terms:

[tex]12x^2-48x+21[/tex]

The answer is b.

The system of equation will have one solution.

The correct answer is an option (B)

It is a collection of one or more linear equation involving the same variable.

For given question,

Two equations have negative reciprocal slope .

Which means if one equation have slope = m

then slope of other equation will be = -1/m

This means, both the lines are perpendicular to each other , hence both the lines must be intersecting each other at one point.

In system of equation , the solution of the two equation is the point where they intersect .

Since, both the lines are intersecting at one point . Hence, it will have only one solution.

Therefore, the correct answer is an option b) the system will have one solution

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Answer:

A standard deck of 52 playing cards contains four of each numbered card 2–10 and four each of aces, kings, queens, and jacks. Two cards are chosen from the deck at random.

Which expression represents the probability of drawing a king and a queen?

StartFraction (4 P 1) (3 P 1) Over 52 P 2 EndFraction

StartFraction (4 C 1) (3 C 1) Over 52 C 2 EndFraction

StartFraction (4 P 1) (4 P 1) Over 52 P 2 EndFraction

StartFraction (4 C 1) (4 C 1) Over 52 C 2 EndFraction

it is D

Step-by-step explanation:

The probability of drawing a king and a queen is 1/169.

Given,

A standard deck of 52 playing cards contains four of each numbered card 2–10 and four each of aces, kings, queens, and jacks.

Two cards are chosen from the deck at random.

We need to find which expression represents the probability of drawing a king and a queen.

A combination is used when we want to determine the number of possible arrangements in a collection of items where the order of the selection does not matter.

The formula is given by:

[tex]^nC_r[/tex] = n! / r! ( n-r)!

We have,

52 playing cards

4 kings and 4 queens.

This means we have

The probability of drawing a king and a queen is:

= probability of drawing a king x probability of drawing a queen

= ^4C_1 / ^52C_1 x  ^4C_1 / ^52C_1

= 4 / 52 x 4 / 52

= 1/13 x 1/13

= 1/169

Thus the probability of drawing a king and a queen is 1/169.

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We found the values of the function f(x) at points 1 and 3 and compared them. It's found that the value of f(1) is significantly larger than the value of f(3), hence the third statement is true.

To answer your question, we need to substitute 1 and 3 into the function f(x)=-2x^2+3x+10, respectively. So:

For f(1), we get -2*1^2 + 3*1 + 10 = -2 + 3 + 10 = 11.

For f(3), we get -2*3^2 + 3*3 + 10 = -18 + 9 + 10 = 1.

Therefore, we can clearly see that the value of f(1) is larger than the value of f(3), meaning the third statement is true.

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Answer:

Step-by-step explanation:

x +  y = 22

22 cards = 26

5(4) +y(2) = 26

20+2y = 26

20-20 +2y = 26-20

2y =6

2y/2 = 6/2

y = 3

andy bought 3 cards

David bought 5 of the $4 cards and 17 of the $2 cards. By setting up and solving the equations, we determined the number of each type of card he purchased.

To solve this problem, we set up two key equations based on the given information.

Let x be the number of $4 cards and y be the number of $2 cards.

The equations are:

We know that David bought 5 of the $4 cards.

Therefore, x = 5.

Substituting x into the first equation:

5 + y = 22

y = 22 - 5

y = 17

So, David bought 17 of the $2 cards.

Answer:

[tex]4\sqrt{2}.\sqrt{2} = 8\\3\sqrt{7}-2\sqrt{7} =\sqrt{7}\\\frac{\sqrt{7}}{2\sqrt{7}} = \frac{1}{2}\\2\sqrt{5}.2\sqrt{5} = 20[/tex]

Step-by-step explanation:

[tex]4\sqrt{2}.\sqrt{2}\\=4 . (\sqrt{2})^2\\=4*2\\=8\\\\3\sqrt{7}-2\sqrt{7}\\As\ the\ square\ root\ is\ same\ in\ both\ terms\\= (3-2)\sqrt{7}\\=\sqrt{7}\\\\\frac{\sqrt{7}}{2\sqrt{7}} \\The\ square\ roots\ will\ be\ cancelled\\= \frac{1}{2}\\ \\2\sqrt{5}.2\sqrt{5}\\=(2*2)(\sqrt{5})^2\\=4*5\\=20[/tex]

Answer:

Below we present each expression with its simplest form.

[tex]4\sqrt{2} \sqrt{2}=4(2)=8[/tex]

[tex]3\sqrt{7} -2\sqrt{7}=(3-2)\sqrt{7} = \sqrt{7}[/tex]

[tex]\frac{\sqrt{7} }{2\sqrt{7} } =\frac{1}{2}[/tex]

[tex]2\sqrt{5} 2\sqrt{5}=4(5)=20[/tex]

So, the first expression matches with 8.

The second expression matches with the square root of seven.

The third expression matches with one-half.

The fourth expression matches with 20.

Answer:

Step-by-step explanation:

The input-output table can be made by putting value of x and finding the value of f(x)

f(x) = 3x^2-x+4

f(0) = 3(0)^2-0+4 = 0-0+4 = 4

f(1) = 3(1)^2-1+4 = 3-1+4 = 2+4 =6

f(2) = 3(2)^2-2+4 = 3(4)-2+4 = 12-2+4 = 10+4 = 14

f(3) = 3(3)^2-3+4 = 3(9)-3+4 = 27-3+4 = 24+4 = 28

So put value of x and find f(x) and fill the input-output table.

x  f(x)

0   4

1    6

2   14

3    28

Answer:

x^2

Step-by-step explanation:

given:

x^3-1/x+2

As the denominator is linear function and the highest power in numerator is x^3

So the first term in quotient is going to be x^2 to cancel first term of numerator i.e x^3!

Answer:

x^2

Step-by-step explanation:

given:

x^3-1/x+2

As the denominator is linear function and the highest power in numerator is x^3

So the first term in quotient is going to be x^2 to cancel first term of numerator i.e x^3!

Step-by-step explanation:

hvvvbgdddtunnfdyjvhjk

Answer: There were 7 groups.

Step-by-step explanation:

43 + 13 = 56

56/8 = 7

Answer: 7 groups.

Step-by-step explanation: Add the new and the only players.

43+13=56

Divide this number by 8.

56/8=7

There are 7 groups.

Answer:

1 3/4 meters

Step-by-step explanation:

1.75 = 1 3/4 [think of it as since 3 quarters equals 75 cents, and 4 quarters equals 100 cents or a dollar.]

So, 1 3/4 meters

[tex](g\circ f)(x)=-4(-2x-7)+6=8x+28+6=8x+34\\\\(g\circ f)(-5)=8\cdot(-5)+34=-6[/tex]

For this case we must indicate an expression equivalent to:

[tex]\sqrt {10x ^ 7}[/tex]

By definition of properties of powers and roots we have that:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, we can rewrite the expression as:

[tex]10 ^ {\frac {1} {2}} * x ^ {\frac {7} {2}}[/tex]

Answer:

OPTION A

Answer:

A parallelogram is a quadrilateral whose opposite sides are parallel and equal, opposite angles are equal, the sum of the interior angles is 360 degrees. Therefore, the parallelogram EFGH might be a rhombus.

Step-by-step explanation:

Answer:

then it might be a rhombus

Step-by-step explanation:

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=2(3)^{x}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value (y-intercept)

b is the base

r is the rate of change

b=(1+r)

In this problem

a=2

b=3

1+r=3

r=3-1=2

r=200%

using a graphing tool

The graph in the attached figure

Answer:

the two expressions are equivalent.

Step-by-step explanation:

We know that f(x)= 3x-7 and g(x)= -2x+5, therefore:

f(x) - (-g(x)) = 3x-7 - ( +2x-5) = 3x - 7 - 2x + 5 = x -2

f(x) + g(x) = 3x-7 -2x + 5 = x - 2

Therefore,  f(x) - (-g(x)) is equivalent to f(x) + g(x).

Another way to check that the two expressions are equivalent is by solving the parenthesis:

f(x) - (-g(x)) →  f(x) + g(x)

Therefore, the two expressions are equivalent.

Answer:

735,130.

Step-by-step explanation:

The order of election of the 3 representatives does not matter so it is a combination.

The number of possible combinations

= 165! / 162! 3!

=  (165 * 164 * 163) / (3*2*1)

= 735,130.

Final answer:

The scenario of electing 3 representatives from a student body of 165 students involves combinations since the order of selection does not matter. Using the combination formula, there are 4,598,340 possible ways to choose the representatives.

Explanation:

The scenario described involves electing 3 representatives from a student body of 165 students. In this context, we are dealing with combinations, not permutations, because the order of selection does not matter; it only matters who is chosen, not in which order they are elected.

To calculate the number of possible combinations of 165 students taken 3 at a time, we can use the combination formula:

C(n, k) = n! / [k!(n - k)!]

where:

Therefore, the number of possibilities is:

C(165, 3) = 165! / [3!(165 - 3)!]

Calculating this gives us:

165! / (3! * 162!) = (165 * 164 * 163) / (3 * 2 * 1) = 4,598,340 combinations.

Answer:

The correct answer is option B.  11√2

Step-by-step explanation:

From the figure we can see two isosceles right angled triangle.

Therefore the sides are in the ratio 1 : 1 : √2

It is given that equal sides of the triangle is 11 units

So we can write, 11 : 11 : x = 1 : 1 : √2

x = 11√2

Therefore the value of x = 11√2

The correct answer is option B.  11√2

Answer:

10.2 kilograms

Step-by-step explanation:

You do the equation,  1.4kg+5kg+3.8kg​ and that is = to 10.2 kg

Hope that helped you :)

Good luck :))

Answer: 11.2 kg

Step-by-step explanation: Add the weights.

1.4+5+3.8=11.2

The total weight is 11.2 kg.

Answer:

[tex]y'=\frac{y^2-xy\ln(y)}{x^2-xy\ln(x)}[/tex]

Step-by-step explanation:

Take natural log of both sides first.

[tex]x^y=y^x[/tex]

[tex]\ln(x^y)=\ln(y^x)[/tex]

Taking the natural log of both sides allows you to bring down the powers.

[tex]y\ln(x)=x\ln(y)[/tex]

I'm going to differentiate both sides using the power rule.

[tex](y)'(\ln(x))+(\ln(x))'y=(x)'(\ln(y))+(\ln(y))'x[/tex]

Now recall (ln(x))'=(x)'/x=1/x while (ln(y))'=(y)'/y=y'/y.

[tex]y'(\ln(x))+\frac{1}{x}y=1(\ln(y))+\frac{y'}{y}x[/tex]

Simplifying a bit:

[tex]y' \ln(x)+\frac{y}{x}=\ln(y)+\frac{y'}{y}x[/tex]

Now going to gather my terms with y' on one side while gathering other terms without y' on the opposing side.

Subtracting y'ln(x) and ln(y) on both sides gives:

[tex]\frac{y}{x}-\ln(y)=-y'\ln(x)+\frac{y'}{y}x[/tex]

Now I'm going to factor out the y' on the right hand side:

[tex]\frac{y}{x}-\ln(y)=(-\ln(x)+\frac{x}{y})y'[/tex]

Now we get to get y' by itself by dividing both sides by (-ln(x)+x/y):

[tex]\frac{\frac{y}{x}-\ln(y)}{-\ln(x)+\frac{x}{y}}=y'[/tex]

Now this looks nasty to write mini-fractions inside a bigger fraction.

So we are going to multiply top and bottom by xy giving us:

[tex]\frac{y^2-yx\ln(y)}{-xy\ln(x)+x^2}=y'[/tex]

[tex]y'=\frac{y^2-xy\ln(y)}{x^2-xy\ln(x)}[/tex]

The derivative of the implicit function [tex]x^y = y^x[/tex] is [tex]\[\frac{dy}{dx} = \frac{\ln(y) - \frac{y}{x}}{\ln(x) - \frac{x}{y}}\][/tex].

To find the derivative of the implicit function defined by [tex]\( x^y = y^x \),[/tex] follow these steps:

        [tex]\ln(x^y) = \ln(y^x)[/tex]

        y ln(x) = x ln(y)

Differentiate both sides with respect to x. Use implicit differentiation where y is considered a function of x:

        [tex]\[ \frac{d}{dx}[y \ln(x)] = \frac{dy}{dx} \ln(x) + y \cdot \frac{1}{x} \][/tex]

        [tex]\[ \frac{d}{dx}[x \ln(y)] = \ln(y) + x \cdot \frac{1}{y} \cdot \frac{dy}{dx} \][/tex]

        [tex]\[ \frac{dy}{dx} \ln(x) + \frac{y}{x} = \ln(y) + \frac{x}{y} \cdot \frac{dy}{dx} \][/tex]

Solve for [tex]\( \frac{dy}{dx} \):[/tex]

        [tex]\[ \frac{dy}{dx} \ln(x) - \frac{x}{y} \cdot \frac{dy}{dx} = \ln(y) - \frac{y}{x} \][/tex]

        [tex]\[ \frac{dy}{dx} \left(\ln(x) - \frac{x}{y}\right) = \ln(y) - \frac{y}{x} \][/tex]

        [tex]\[ \frac{dy}{dx} = \frac{\ln(y) - \frac{y}{x}}{\ln(x) - \frac{x}{y}} \][/tex]

Answer:

(x + 1) (3 x^2 + 1)

Step-by-step explanation:

Factor the following:

3 x^3 + 3 x^2 + x + 1

Factor terms by grouping. 3 x^3 + 3 x^2 + x + 1 = (3 x^3 + 3 x^2) + (x + 1) = 3 x^2 (x + 1) + (x + 1):

3 x^2 (x + 1) + (x + 1)

Factor x + 1 from 3 x^2 (x + 1) + (x + 1):

Answer:  (x + 1) (3 x^2 + 1)

Answer:

(x + 1) (3 x^2 + 1)

Step-by-step explanation:

For this case we must find the solutions of the following equation:

[tex]4x ^ 2-x + 9 = 0[/tex]

We apply the cudratic formula:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 4\\b = -1\\c = 9[/tex]

Substituting:

[tex]x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (4) (9)}} {2 (4)}\\x = \frac {1 \pm \sqrt {1-144}} {8}\\x = \frac {1 \pm \sqrt {-143}} {8}[/tex]

Thus, the complex roots are:

[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]

Answer:

[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]

Answer: OPTION A.

Step-by-step explanation:

You know that the rule that will be used for the translation of the figure ABC is:

[tex](x,y)[/tex]→[tex](x-3,\ y+4)[/tex]

You can observe in the figure that the coordinates of the point A is this:

[tex]A(1,1)[/tex]

Then, in order to find the coordinates that will best represent point A', you need to subtract 3 from the x-coordinate of the point A and add 4 to the y-coordinate of the point A:

[tex]A'(1-3,\ 1+4)\\\\A'(-2,5)[/tex]

Answer:

A. (-2,5)

Step-by-step explanation:

The figure ABC is translated to A'B'C' by the rule (x-3, y+4)

The Image of the triangle will therefore be as follows:

A' (1-3,1+4)

B'(2-3,5+5)

C'(3-3,2+5)

The vertices will thus be A'(-2,5), B'(-1,10) and C'(0,7)

Thus the correct answer will be A. (-2,5)

Equivalent expressions are expressions of equal values.

[tex]\mathbf{x^2 - 50x + 9}[/tex] and [tex]\mathbf{ -(-x^2 + 50x - 9)}[/tex] are equivalent expressions for the opposite of [tex]\mathbf{-x^2 + 50x - 9}[/tex]

The expression is given as:

[tex]\mathbf{f(x) = -x^2 + 50x - 9}[/tex]

To calculate the opposite, we simply negate the signs of the expression.

So, we have:

[tex]\mathbf{-f(x) = -(-x^2 + 50x - 9)}[/tex]

Expand

[tex]\mathbf{-f(x) = x^2 - 50x + 9}[/tex]

The above highlights mean that:

[tex]\mathbf{x^2 - 50x + 9}[/tex] and [tex]\mathbf{ -(-x^2 + 50x - 9)}[/tex] are equivalent expressions for the opposite of [tex]\mathbf{-x^2 + 50x - 9}[/tex]

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Final answer:

To find equivalent expressions for the opposite of the polynomial [tex]-x^2+50x-9[/tex], we change the signs of all terms to get [tex]x^2-50x+9[/tex]. Equivalent expressions may be generated by distributing a factor such as [tex](-1)(-x^2+50x-9)[/tex], but the polynomial does not factor nicely over the integers for other simplifications.

Explanation:

To find two equivalent expressions for the opposite of the polynomial [tex]-x^2+50x-9[/tex], we start by taking the opposite of the given polynomial. The opposite (or negative) of a polynomial consists of changing the sign of each term. Therefore, the opposite of the given polynomial is [tex]x^2 - 50x + 9.[/tex]

An equivalent expression can be obtained by factoring, if possible, or by using other algebraic manipulations. However, in this case, [tex]x^2 - 50x + 9[/tex] does not factor nicely over the integers. To get an equivalent expression, we can express it in different forms, such as:

Another way to express an equivalent polynomial is to add and subtract the same value within the expression, which maintains its equality.