Compare the following functions:

Function A: y = 4x −5
Function B: _______.

What is the slope/rate of change of Function A? ______.

What is the slope/rate of change of Function B between f(0) and f(1)? ______.

What is the slope/rate of change of Function B between f(1) and f(2)? ______.

What is the slope/rate of change of Function B between f(2) and f(3)? _____.

The slope of Function A is _______.
The slope of Function B is _______.

Answer:

[tex]\textsf{(a)} \quad \boxed{9a-3}[/tex]

[tex]\textsf{(b)} \quad \boxed{-9a-3}[/tex]

[tex]\textsf{(c)} \quad \boxed{-9a+3}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x) = 9x - 3[/tex]

Part (a)

To find f(a), substitute x = a into the function:

[tex]\implies f(a)=9a-3[/tex]

Part (b)

To find f(-a), substitute x = -a into the function:

[tex]\implies f(-a)=-9a-3[/tex]

Part (c)

To find -f(a), first substitute x = a into the function:

[tex]\implies f(a)=9a-3[/tex]

Then make the function negative:

[tex]\begin{aligned}\implies -f(a)&=-(9a-3)\\&=-9a+3 \end{aligned}[/tex]

Answer:

three

Step-by-step explanation:

o 13, 19, 7

Horizontal asymptotes of the given graph is given by y = -4.

As given in the question,

From the given graph we observed :

Value of each unit on x -axis is equal to 1

Value of each unit on y -axis is equal to 1.

For the standard equation of line y = mx + b

When input values tends to ∞ or -∞ graph approaches to infinity to both the ends.

Horizontal asymptote is given y = b as per the value of b .

Here in the given graph ,

When input values tends to to ∞ or -∞ graph approaches to infinity to both the ends then horizontal asymptote is given by y = -4.

Therefore, horizontal asymptotes of the given graph is given by y = -4.

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The main features that can be easily seen then a quadratic function is given are parabola, axis of symmetry, a maximum OR minimum value, and an y-intercept of the graph.

A quadratic function is in the form ax²+bx+c=y where a, b and c are real integers.

How to find the features of a quadratic equation?

Every quadratic equation has the following features:

When the quadratic function is graphed, it will enable us to find the other features of the function when these are identified.

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Answer:

f(-2)= -2

f(-0.75)= -1

f(1)= 1

Respuesta:

5

Explicación paso a paso:

28- (2*4)= 20

20/4=5

28 es el total de horas

2 horas por la mañana durante cuatro días

20 es el total de horas por la noche

4 días trabajados

5 es horas cada día durante la noche

Answer:

Durante cada turno de la noche Esther trabajo 5 horas

Step-by-step explanation:

Primero hallemos cuantas horas trabaja Esther en un día

[tex]2 + x = horas\ en \ un\ dia[/tex]

2 es el número de horas que trabaja en cada turno de la mañana y [tex]x[/tex] el número de horas que trabaja en su turno de la noche (en este momento desconocemos el valor de [tex]x[/tex] y es el que queremos hallar). Ahora se tiene que en 4 días ester trabaja 28 horas en total, por lo tanto, multiplicamos 4 a ambos lados de la ecuación para conservar la igualdad

[tex]4\times (2 + x) = horas\ en \ cuatro \ dias[/tex]

[tex]8+4x= 28[/tex]

Ahora se despeja [tex]x[/tex] de la ecuación anterior

[tex]4x=28-8=20\\x=\frac{20}{4} =5[/tex]

De tal manera que Esther en cada turno nocturno trabaja 5 horas

The options given in the question are wrong. The correct answer should be 25

The value of x is 25

(x-7)2 = 36

x-7 = 36/2

x-7 = 18

x = 18+7

x = 25

We can solve the linear equation in one variable by moving the variables to one side of the equation, and the numeric part on the other side of the equation. For example, x - 1 = 5 - 2x can be solved by moving the numeric parts on the right-hand side of the equation which is summed up to be 6, while keeping the variables on the left side which sums up to be 3x. Hence, we get x + 2x = 5 + 1. Thus, 3x = 6. This gives x = 2.

Similarly, we got the value of x which is 25.

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The integer which satisfies both inequalities  -4 ≤ x ≤ 3 and -5x -3 > 8 are -3 and -4.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

As per the given first inequality,

-4 ≤ x ≤ 3

The integer associated with the above inequality is -4,-3,-2,-1,0,1,2,3.

As per the given second inequality,

-5x -3 > 8

-5x > 8 + 3

-5x > 11

x < -11/5

x < -2.2

The integer associated with the above inequality is -3,-4....

The integer satisfies both inequalities are -3 and -4.

Hence "The integer which satisfies both inequalities  -4 ≤ x ≤ 3 and -5x -3 > 8 are -3 and -4".

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Answer:

2 + (-10) = 2 - 10 = -8

Answer:

We use the attached graph

a. The maximum profit is the y value that is the value of P(x) that reaches maximum. From the graph the maximum value of P(x) is 675

So the maximum profit the florist will earn from selling bouquets = $675

b. Break even is the point where the profit p(x) becomes 0

From the graph we can see that P(x) =0 at x= -10 and x=20

x=-10 is invalid

So, break even after 20 one- dollar decreases

c. The interval of number of one dollar decreases is where the profit P(x) is greater than 0.

From the graph its very clear that the profit P(x) is greater than 0 in the interval 0 to 20.

So, The interval of number of one dollar decreases for which the florist makes a profit from celebration bouquet is (0, 20)

The number of three letter words that can be formed from the 4 letters "FGHI" is

(a) when repetition allowed is 64

(b) when repetition not allowed is 24 .

In the question ,

the four letters are given as "FGHI" ,

we need to find the how many 3 letter words  can be formed ,

(a) when repetition is allowed

= (selecting a letter from 4 given letters)×(selecting a letter from 4 given letters)×(selecting a letter from 4 given letters) .

= ⁴C₁ × ⁴C₁ × ⁴C₁

= 4 × 4 × 4              .... because ⁴C₁ = 4

= 64

(b)  when repetition not allowed

= (selecting a letter from 4 given letters)×(selecting a letter from the remaining 3 letters)×(selecting a letter from the remaining 2 letters)

= ⁴C₁ × ³C₁ × ²C₁

= 4 × 3 × 2

= 24

Therefore , The number of three letter words that can be formed from the 4 letters "FGHI" is  (a) when repetition allowed is 64  , (b) when repetition not allowed is 24 .

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The expression of time taken for the submarine to descend in

d(t)= mt + b  is

data gotten from the question

after 2 minutes a submarine had descended -390 feet

-390 = 2m + b

after 9 minutes the submarine had descended to -600 feet

-600 = 9m + b

The data from the question gives two linear equations with two unknown

-600 = 9m + b

-390 = 2m + b

solving the equations gives

m = -30

b = -330

the equation is then written as

d(t) = -30t - 330

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1) The interest that will accumulate for Marlie during the 4.5-year non-payment period is $3,629.34.

2a) The new principal when Marlie begins making loan payments will be $22,429.34.

2b) Marlie will pay an additional $9,622.19 in interest for 10 years, including the 4.5-year period interest of $3,629.34 to make a total of $13,251.53.

3. If Marlie paid interest during the 4.5-year period, the total interest she will pay, thereafter, is $8,065.20.

4. Marlie's only interest payment due on January 1 is $67.21.

5a) With a private loan at 7.8% APR, Marlie's monthly payment is $226.11.

5b) The total amount Marlie will pay back with a private loan at 7.8% APR is $27,133.67.

5c) Based on a private loan, Marlie's total interest is $8,333.67.

The interest on federal student loans is based on simple interest, unlike the interest on private loans, which is compounded.

We can compute simple interest using the simple interest formula (PRT/100) and compounded interest using an online finance calculator.

Student loan amount = $18,800

Interest rate = 4.29%

Non-payment period = 4.5 years

Loan repayment period = 10 years

Interest for the 4.5-year non-payment period = $3,629.34 ($18,800 x 4.29% x 4.5 years)

New Principal after 4.5 years = $22,429.34 ($18,800 + $3,629.34)

Additional interest on the loan after 4.5 years = $9,622.19 ($22,429.34 x 4.29% x 10 years).

Total interest = $13,251.53 ($9,622.19 + $3,629.34)

Interest for 10 years on principal = $8,065.20 ($18,800 x 4.29% x 10 years).

Only Interest monthly payment = $67.21 ($18,800 x 4.29% x 1/12)

N (# of periods) = 120 months (10 years x 12)

I/Y (Interest per year) = 7.8%

PV (Present Value) = $18,800

FV (Future Value) = $0

Results:

Monthly payments (PMT) = $226.11

Sum of all periodic payments = $27,133.67

Total Interest = $8,333.67

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The length of the rectangle-shaped classroom is 15 meters.

We have a classroom. The shape of the classroom is rectangular. The length of the classroom is 3 meters more as compared to its width. The area of the rectangular classroom is 180 square meters. We need to find the length of the classroom.

Let the width of the rectangle be represented by the variable "x". The length of the rectangle is "x + 3". We will use the formula for the area of a rectangle. The area of a rectangle is the product of its length and width.

A = x*(x + 3)

180 = x² + 3x

x² + 3x - 180 = 0

We will use the quadratic formula to solve for the values of "x".

x = [-3 ± √(3² - 4(1)(-180))]/2(1)

x = [-3 ± √(9 + 720)]/2

x = [-3 ± √729]/2

x = [-3 ± 27]/2

The values of the variable "x" are -15 and 12. The negative value is rejected because the measure of a dimension cannot be negative. Hence, the value of "x" is 12. The length of the rectangular classroom is x + 3 = 12 + 3 = 15 meters.

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Answer: d> 5 1/2

Step-by-step explanation:

34 + (12 × d) > 100

34 + 12d > 100

12d > 100 - 34

12d > 66

d > 66 / 12

d > 5 1/2 days

Therefore, the number of days, (d), it will take Katie to collect over 100 seashells is 5 1/2 days.

Answer: 52 miles per hour

Step-by-step explanation:

 15/60=.25

4 hours

221 miles

221/4.25

52 miles per hour

Answer:

The correct answer is 0.00604

Step-by-step explanation:

Tip: Think of how a number line is displayed: negative numbers are on the left side of the mid-point, zero in most cases, and positives numbers are to the right of the mid-point.

Since the exponent is a negative number, you know that you need to move the decimal point to the left the same number of places as the exponent. In this problem, the exponent is –3, meaning that you need to move the decimal point 3 places to the left.

*Remember to fill in any gaps with a zero after moving the decimal point.* Your answer should look like this: 6.04 in standard form is 0.00604

Hope that helps! Have an amazing rest of your day! Brainliest welcome! :)

Answer: 1. 12.5 miles per hour 2. 0.36 hours

Step-by-step explanation:

Please refer to this explanation:

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Answer:

d = 24

Step-by-step explanation:

[tex] \rm \implies - \dfrac{2}{3} d - \dfrac{1}{4} d = - 22 \\ \\ \rm \implies - \frac{2}{3} d \times \frac{4}{4} - \frac{1}{4} d \times \frac{3}{3} = - 22 \\ \\ \rm \implies - \frac{8}{12} d - \frac{3}{12} d = - 22 \\ \\ \rm \implies \frac{ - 8d - 3d}{12} = - 22 \\ \\ \rm \implies \cancel{- } \frac{11}{12} d = \cancel{-} 22 \\ \\ \rm \implies d = 22 \times \frac{12}{11} \\ \\ \rm \implies d= 2 \times 12 \\ \\ \rm \implies d= 24[/tex]

The graph of the given logarithmic function is (see in attachments).

Graph:

In mathematics, a graph is an orderly visual representation of any data. The graph shows how the variable quantities are related to one another. A graph is used in graph theory to represent the collection of objects that are interconnected in some way. The edges between the nodes reflect the connections between the nodes, while the vertices or nodes of the objects are essentially mathematical concepts.

Numerous types of graphs are used to visually display data in mathematics and statistics. Graph theory is the study of points and lines. It is a field of mathematics that focuses on graph analysis.

This image provides a visual representation of the mathematical truth. Graph theory is a method for studying relationships.

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The correlation coefficient, r, of the data (1 , 6) , (3 , 4) , (5 , 2) is calculated as: r = -1

The correlation coefficient can be described as a numerical value that ranges from -1 through 0, to 1. It is a test of the strength of the relationship between two different variables. It is denoted as "r".

The formula for finding the correlation coefficient (r) between two variables x and y is given as:

r = Σ(xi - mean of x)(yi - ȳ) / √(Σ[xi - mean of x)²Σ(yi - ȳ)²]

Given the following data:

(1 , 6) , (3 , 4) , (5 , 2)

Therefore, the table in the attached diagram shows how to derive each of the variables in the formula used for calculating the correlation coefficient, r, between X and Y.

Thus, applying the formula, we have:

Correlation coefficient (r) = -8/√(8*8)

Correlation coefficient (r) = -1

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Answer:

$25.67

Step-by-step explanation:

120 - 43 = 77

77/3 = 25.67

The value of k in the equation k over 12.6 equals 7.4 is A. 93.24

Temperature simply means the degree of hotness and coldness in a body.

Based on the information given, the equation is expressed as k over 12.6 equals 7.4. This will be:

k / 12.6 = 7.4

Cross multiply

k = 12.6 × 7.4

k = 93.24

Therefore, the correct option is A.

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The quadratic function is increasing on the interval:

(-∞, 0)

Here we want to see on which intervals is the quadratic function increasing.

Or function is:

f(x) = 5 - 2x^2

Notice that we have a negative leading coefficient, which means that the parabola opens downwards.

Then the function will be increasing from negative infinity to the x-value of the vertex.

Remember that for the general quadratic:

y = a*x^2 + b*x + c

the x-value of the vertex is:

x = -b/2a

In this case we don't have a linear term, so b = 0, then the vertex is at x = 0.

Which means that the function is increasing on the interval (-∞, 0)

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Answer: (8,3)

Step-by-step explanation:

See the picture attached

Answer:

From least to greatest

= -7, -3, 2, 5

Absolute values from least to greatest

= 2, 3, 5, 7

(Absolute value is the distance of a number from 0 in the number line regardless of the direction, so I think this is the answer)

The x- and y-intercept of the line -1.2x + 8.2y = 39.36 are -32.8 and 4.8

An intercept is a point at which the line crosses the axis of a graph. The point at which the line crosses the x-axis is known as the x-intercept, whereas if a line crosses the y-axis at a point, then the point will be the y-intercept.

Here we have,

-1.2x + 8.2y = 39.36

To find x - intercept substitute y = 0

=> -1.2x + 8.2(0) = 39.36

=> -1.2x = 39.36

=> x = 39.36/1.2

=> x = -32.8

To find y - intercept substitute x = 0

=> -1.2(0) + 8.2y = 39.36

=> 8.2y = 39.36

=> y = 39.36/8.2

=> y = 4.8  

Therefore

The x- and y-intercept of the line -1.2x + 8.2y = 39.36 are -32.8 and 4.8

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Answer:

Positive

Step-by-step explanation:

Appears to be a POSITIVE correleation

   as height increases   so  does weight

Answer:

  3, 4, 5

Step-by-step explanation:

You have parallel lines crossed by a transversal, and one obtuse angle marked as 99°. You want the angle designators of the congruent angles.

Where a transversal crosses parallel lines, corresponding angles are congruent. In this figure, angle 3 corresponds to the one marked 99°, so it is congruent.

Anywhere that lines cross, vertical angles are congruent. Angles 3 and 4 are vertical angles, as are angle 5 and the one marked 99°.

Hence angles 3, 4, 5 are all congruent to the one marked 99°.

__

Additional comment

You may have observed that the listed congruent angles are all of the obtuse angles in the figure. Similarly, all acute angles in the figure are congruent. Since the acute and obtuse angles are supplementary (form linear pairs), angles 1, 2, 6, 7 are all 81°.

Ooo this is like a riddle. Let me attempt to answer:

Let's start with one of the brothers. That's 1 child. There has to be 1 more brother for each brother to have one other brothers. Then for that brother to have two sisters, they have to have two girls. This is 4 children.

Now from a girl's perspective. You are a girl so you are already 1 child. To have one brothers, there has to be 1 boy. Then to have two sisters, there has to be two additional girls. That's 3 girls and one boy - which are still 4 children in all.

Of course two parents are two parents for all.

The fewest number of children the parents have is 4

I hope this helps!