Let f(x) = x^2 + 2 and g(x) = -3. Find f(x) • g(x).

A. X^3-6x^2+12x-6

B. X^3-5x^2+8x-6

C. X^3-3x^2+6x-6

D. X^3-2x^2+5x-6

In the context of the issue, the letter D represents the meaning of the y-intercept.

The value of the investment at the outset is determined to be $600.

Based on the data, the growth of the savings plan over the course of one year, denoted by the variable x, may be modeled using the exponential function f(x) = 600 * (1.04)x.

In this instance, the significance of the y-intercept in relation to the situation at hand is that the beginning value of the investment is equal to $600.

In conclusion, the choice D is the one that should be made.

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Answer:

(A)  The initial value of the investment is $400.

Step-by-step explanation:

Got it right on my quiz.

The closest y-intercept is in function 1 so in option (A), the Greatest y-intercept is +4 in function 3 so in option (C), Functions 1 and 2 will have a slope less than 3 option (A) and (B).

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

Given four functions,

The y-intercept is a point on the y-axis where the graph intersects therefore coordinate of x will be 0.

In function 1 ⇒ y-intercept = -1 in rest, all it is far from 1 therefore it is close to 0.

The y-intercept of function 3 is →

y = x + 4 ⇒ y = 0 + 4 = 4 which is greatest positive value among all.

The slope of any function associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

The slope of function 1 has points (0,-1) and (1,-5)

(-5 + 1)/(1 - 0) = -4 < 3

The slope of function 2 →

(5 - 8)/(-1 + 2) = -3 < 3 rest all function have slope as > 3.

Hence "The closest y-intercept is in function 1, the Greatest y-intercept is +4 in function 3 , Functions 1 and 2 will have a slope less than 3".

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

According to given information,

when, x is not equal to -2, that means g(x) = 4 for all values of x except " - 2 "

Therefore,

[tex]\qquad \sf  \dashrightarrow \: g( - 5) = 4[/tex]

and

[tex]\qquad \sf  \dashrightarrow \: g(3) = 4[/tex]

And, when x = -2, it's value is 2, hence :

[tex]\qquad \sf  \dashrightarrow \: g( - 2) = 2[/tex]

The sets represents L ∪ (M ∩ N) is {0 , 10 , 20 , 40 , 80 , 100}.

What is domain and range ?

The bis the set of possible input values, and the range is the set of all possible output values of the graph.

In the sets:

Union (∪) of two sets means all the elements in the two sets without repeating the same elements

Intersection (∩) of two sets means the common elements in the two sets

∵ Set L = {0 , 20 , 40 , 80 , 100}

∵ Set M = {5 , 10 , 15 , 20 , 25}

∵ Set N = {10 , 20 , 30 , 40 , 50}

We need to find L ∪ (M ∩ N)

At first find (M ∩ N)

M ∩ N means find the common elements of M and N

10 and 20 are common elements in M and N

M ∩ N = {10 , 20}

Now find the union of L and {10 , 20}

L ∪ {10 , 20} means all elements in L and {10 , 20} without repeating the same elements

L ∪ {10 , 20} = {0 , 10 , 20 , 40 , 80 , 100}

L ∪ (M ∩ N) = {0 , 10 , 20 , 40 , 80 , 100}

The sets represents L ∪ (M ∩ N) is {0 , 10 , 20 , 40 , 80 , 100}

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Answer:The answer would be the second

Step-by-step explanation:The square root of 97 to the third power is 955.3. 78/9 is 8.6 and the square root of 45 is 6.7.

The polynomial that added to [tex]-3c^{2}+3-6c[/tex] in order to get a sum of [tex]2c^{2}-c+5[/tex] is [tex]5c^{2}+5c+2[/tex]

Given,

The first polynomial =  [tex]-3c^{2}+3-6c[/tex]

The result =  [tex]2c^{2}-c+5[/tex]

Then,

[tex]-3c^{2}+3-6c[/tex] + second polynomial =  [tex]2c^{2}-c+5[/tex]

The second polynomial =   [tex]2c^{2}-c+5[/tex] -( [tex]-3c^{2}+3-6c[/tex] )

[tex]=2c^{2}-c+5+3c^{2}+6c-3\\ =(2+3)c^{2}+(-1+6)c+(5-3)\\ =5c^{2}+5c+2[/tex]

Hence, the polynomial that added to [tex]-3c^{2}+3-6c[/tex] in order to get a sum of [tex]2c^{2}-c+5[/tex] is [tex]5c^{2}+5c+2[/tex]

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Answer: C, F

Step-by-step explanation: this is a form of distribution meaning you have to distribute -10 to the numbers inside the parenthesis. -10x4= -40x and -10 x -5= 50 therefor it is -40x+50. This answer can work as commutative meaning -40x+50 can also be written as 50-40x

Answer:

  12 1/2 pounds

Step-by-step explanation:

You want to know the total weight of 50 hamburger patties that weigh 1/4 pound each.

The weight of 50 patties will be the sum of their weights. That sum is most easily figured using multiplication.

  (1/4 lb) +(1/4 lb) +(1/4 lb) +... +(1/4 lb) . . . . 50 repetitions

  = 50 × (1/4 lb)

  = (50/4) lb = 12.5 lb

Rita bought 12 1/2 pounds of hamburgers.

Amount of sludge dispose per minutes is 100 lb.

What is Rate of change?

A rate is anything that can be measured over time. Common rates include velocity (which is the rate of distance traveled), power (rate of work being done), etc. All these have one thing in common which is that they are all divided by the amount of time it took to obtain a certain measurement.

Here it is given that :

A pump can dispose of sludge at the rate of 6,000 lb/h, that is in one hour pump dispose 6000 lb of sludge.

it is known that 1 hour = 60 minutes

Therefore, to find the amount of sludge dispose by pump in ome minute we divide 6000 with 60 :

amount of sludge dispose in one hour = 6000 lb

amount of sludge dispose in 60 minutes = 6000 lb

amount of sludge dispose in 1 minutes = 6000 lb/60 = 100 lb

Therefore, amount of sludge dispose per minutes is 100 lb

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Answer:I think it's 8.702 L

Step-by-step explanation:

The intercepts of the graph (0, 6) (0, -6) is symmetry on x-axis, y-axis and it is graphically shown.

A symmetry of a function is a transformation that leaves the graph unchanged. Symmetric function is a function having several variables which remain unchanged for any type of permutation of the variable.

For the given situation, Symmetry with respect to x-axis

The point becomes (x, -y) as the point flips by itself up or down which changes its y coordinate to negative of whatever it was. And there is no motion is done horizontally so no change in x coordinate.

The interecpets are; (0, 6) (0, -6)

Thus this intercepts is symmetric to y-axis. this intercepts is not symmetric about origin.

Hence we can conclude that the intercepts is symmetric about x - axis.

Therefore, The intercepts of the graph (0, 6) (0, -6) is symmetry on x-axis and it is graphically shown.

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Answer:

C. 32 - 4x = 12

Step-by-step explanation:

An equation that represents Tamara's net pay, where x represents her gross pay per pay period is: D. f(x) = 0.11x - 200

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

Mathematically, net pay can be calculated by using this formula:

Net pay = Gross pay - Deductions.

In order to solve this word problem, we would assign variables to the gross pay and then translate the word problem into algebraic equation as follows:

Let x represent the gross pay.

Translating the word problem into an equation, we have;

f(x) = 0.11x - 200

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3 is a whole number, as it is a regular number, on the other hand decimals and negatives are a diffrent story! Have fun on Brainly!

Student t distribution

A measurement of a data set's deviation from the mean is referred to as "standard deviation". While a high standard deviation indicates that the data are more spread, a low standard deviation suggests that the data are clustered around the mean.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

We have,

Claim : μ = 83

Sample data : s = 15.1, n = 24, and x = 103

The hypothesis test uses the student t distribution because we are evaluating the mean in this situation, the sample standard deviation of a normal distribution is estimated or supplied, and the population's standard deviation is unknown.

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Step-by-step explanation:

x= 14 and x = -4 these are the answers

Answer:

$3900

Step-by-step explanation:

100*30=$3000

10%=0.1 ---> 3*0.1=0.3

3000*1.3=$3900

Answer:

1 inch per hour.

Step-by-step explanation:

If a candle burns 6 inches in 6 hours, this means 1 inch of the candle melted every hour. Therefore, the candle burned/melted at a rate of 1 inch per hour.

Hope this helps!

Answer: the candle burns down at about 1 inch per hour

Step-by-step explanation: since if it is burning the whole time the equation you can do is 6 hours divided by 6 inches which is 1 hour by 1 inch

Answer:

x = -20

Step-by-step explanation:

Solve for x:

(3 x)/4 + 7 = -8

Put each term in (3 x)/4 + 7 over the common denominator 4: (3 x)/4 + 7 = (3 x)/4 + 28/4:

((3 x)/4 + 28/4) = -8

(3 x)/4 + 28/4 = (3 x + 28)/4:

(1/4 (3 x + 28)) = -8

Multiply both sides of (3 x + 28)/4 = -8 by 4:

(4 (3 x + 28))/4 = -8×4

(4 (3 x + 28))/4 = 4/4×(3 x + 28) = 3 x + 28:

(3 x + 28) = -8×4

4 (-8) = -32:

3 x + 28 = -32

Subtract 28 from both sides:

3 x + (28 - 28) = -28 - 32

28 - 28 = 0:

3 x = -28 - 32

-28 - 32 = -60:

3 x = -60

Divide both sides of 3 x = -60 by 3:

(3 x)/3 = (-60)/3

3/3 = 1:

x = (-60)/3

The gcd of -60 and 3 is 3, so (-60)/3 = (3 (-20))/(3×1) = 3/3×-20 = -20:

Answer: x = -20

The quotient of the expression [tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5}[/tex] is [tex]x^{2} - 3x + 7 + \frac{-20x+36}{x^{2}-5}[/tex].

In mathematics, the outcome of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Constant: An absolute numerical number is referred to as a constant.

Variable: A symbol without a set value is referred to as a variable.

Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.

Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.

Consider the expression,

[tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5}[/tex]

Now,

[tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5} = x^{2}+\frac{-3x^{3}+7x^{2}-5x+1}{x^{2}-5}[/tex]

[tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5} = x^{2} - 3x + \frac{7x^{2}-20x+1}{x^{2}-5}[/tex]

[tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5} = x^{2} - 3x + 7 + \frac{-20x+36}{x^{2}-5}[/tex]

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Answer:

9,887,674 ≈ 10,000,000

69,954,943 ≈ 70,000,000

47,546,804 ≈ 48,000,000

The fraction of the original mass that was lost in the second month is 1/12.

A fraction is a non-integer that is made up of numerators and denominators. An example of a fraction is 1/6.

Weight lost in the first month = 1/6 x 120 = 20kg

Weight lost in the second month = 1/10 x (120 - 20)

=  1/10 x 100 = 10kg

Fraction of the original mass that was lost in the second month : weight lost in the second month / total mass

10 kg / 120 = 1/12

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The coordinates of point S are (12,₋9)

Given, coordinates of T are (0,5)

midpoint of ST is (6,₋2)

When it is necessary to determine the precise center point between two specified points, the midpoint formula is used. So you may use this method to determine the point that divides a line segment specified by two points in half.

coordinates of S are = ?

we know the midpoint formula is (x₊x₁)/2 , (y₊y₁)/2

The midpoint calculation is the same as averaging two numbers. As a result, by adding any two integers together and dividing by two, you may find the midpoint between them.

substitute the given values in the formula.

(6,₋2) =  (x₊0)/2 , (y₊5)/2

for the x value of S:

x/2 = 6

x = 12

for the y value of S:

y₊5/2 = ₋2

y ₊ 5 = ₋4

y = ₋4 ₋ 5

y = ₋9

Therefore the coordinates of S are (12,₋9)

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The common difference and the first four terms are - 12 and 3, -9, -21 , -33 respectively

Given that the sum of an arithmetic sequence is  6n-3n²

S1  = a1 = 6(1) - 3(1)² = 6 - 3 = 3

S4 = a1 + a2 + a3 + a4 = 6(4) - 3(4)² = -24

a1 + a2+ a3 + a4 + d = -24

4(a1) + d = -24

4(3) + d = -24

12 + d = -24

d = -24 + 12

d = -12

The first four terms are;

T2 = 3 + (2-1) -12

T2 = 3 -12

T2 = -9

T3 = 3 + 2(-12)

T3 = 3 - 24

T3 = -21

T4 = 3 + 3(-12)

T4 = 3 - 36

T4 = -33

Thus, the common difference and the first four terms are - 12 and 3, -9, -21 , -33 respectively

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Answer: 19

Step-by-step explanation: 13+6=19

The [tex]\lim_{x \to 1} 7x-3=7(1)-3=4[/tex] using the ε − δ definition of a limit.

The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

The limit of f(x) at x = c is L according to the epsilon-delta definition of limits if ε > 0 there's a δ > 0 such that if the distance of x from c is less than, then the distance of f(x) from L is less than ε. The idea that we can approach L as closely as we like is expressed in this way.

[tex]\lim_{x \to a}f(x)= L[/tex] if ∀ ε > 0, ∃ δ > 0

0 < | x − a| < δ

⇒ | f(x) − L | < ε

Now, consider the limit

[tex]\lim_{x \to 1} 7x-3=4[/tex]

Here, f(x) = 7x - 3, a = 1, L = 4

Proof:

∀ ε > 0, ∃ δ = ε > 0

0 < | x - 1 | <  δ

⇒ | 7x - 3 - 4 | = | x - 1 | <  δ = ε

Hence, [tex]\lim_{x \to 1} 7x-3=4[/tex]

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Answer:

p= 3

Step-by-step explanation:

Answer:

p = 3

Step-by-step explanation:

Solving for the value of p,

→ 9p - 12 = -3p + 24

→ 9p + 3p = 24 + 12

→ 12p = 36

→ p = 36/12

→ [ p = 3 ]

Thus, the value of p is 3.

Answer:

[tex] \large{ \boxed{ \tt{3 {x}^{2} - 12x - 1 }}}[/tex]

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