If f(x) is a decreasing function, which of the following statements must be true? Select all that apply.

(Assume that f(x) is always decreasing.)

a) f(5)−f(1) / 5−1 > 0
b) f(5)−f(1) / 5−1 < 0
c) For some value of x≠5, f(x)=f(5)
d) f(5) < f(1)
e) f(5) > f(1)

[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]

Answer:

C. 32 - 4x = 12

Step-by-step explanation:

Answer: 19

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

Step-by-step explanation:

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

Answer:

37 subsets

Step-by-step explanation:

yeah just copy that and that's all

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.

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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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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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 amount in the bank account at the end of 4 years will be = $6540

The amount deposited by Michas in the savings account = $6000

Interest rate = 2.25% annually

No. of years principal is invested = 4 years

Calculating the amount in the bank account after 4 years, using the formula:

Simple interest = P*R*T/100

where P = principal invested

R = rate of interest annually

T = number of years amount is invested

So, Simple interest on the principal invested for 4 years= 6000*2.25*4/100 = 540

The amount in the bank account at the end of 4 years will be = 540 + 6000 = $6540

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The equation of line which passes through (1, -4) and whose slope is 0 is y = -4.

According to the given question.

A line passes throught the point (1, -4) and its slope is 0.

Let the equation of the line be y = mx + b.

Where,

m is the slope of the line

and b is the y intercept.

Since, the line is passing through (1, -4) and slope is 0 i.e. m = 0.

Therefore, m = 0 and (x, y) = (1, -4) must statisfy y = mx + b.

-4 = 1(0) + b

⇒ -4 = b

⇒ b = -4

Therefore, the equation of line which passes through (1, -4) and whose slope is 0 is y = -4.

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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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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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The linear model tells you about the rental cost of apartments in the complex that is $410.6

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = MX + c. Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

A linear equation is given as y = MX + b

where m is the rate of change, b is the initial value of y, and, x are variables.

Assume that y represents the monthly rental price and x represents the square footage.

Given the equation:

Predicted Rental Price = 391+0.98· Area

For the rental price versus area (in square feet) for 20 apartments.

Predicted Rental Price = 391+0.98· Area

Predicted Rental Price = 391 +0.98· (20)

= 410.6

The  linear model tells you about the rental cost of apartments in the complex that is $410.6

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Answer:

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

Please see the attached picture for full solution!

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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.

Answer:

9,887,674 ≈ 10,000,000

69,954,943 ≈ 70,000,000

47,546,804 ≈ 48,000,000

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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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:

  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.

Answer:I think it's 8.702 L

Step-by-step explanation:

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!

Answer:

$3900

Step-by-step explanation:

100*30=$3000

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

3000*1.3=$3900

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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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

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