Simplify (x + 5)2 using the square of a binomial formula.
x² + 10x + 25
x²-10X-25
x²-10x+25
x² + 10x - 25

The rational function f(x)= x/x+3 is graphed in the figure.

What is rational function?

A rational function is the function which can be expressed in terms of the ratio of p and q.

f(x)= p(x)/q(x)

From the given graph , the vertical asymptote is at x=-3

Now, let's find out the vertical asymptote of each function

In order to find out vertical asymptote, we set the denominator =0

a. f(x)= x/(x+3)

x+3=0

x=-3

b. f(x)= x-3/x

x=0

c. f(x)= x/3

3≠0

d. f(x)= 3/x

x=0

The first function has vertical asymptote at x=-3.

Hence, the first option f(x)= x/x+3 is graphed in the figure.

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Answer: 204

Step-by-step explanation:

2 goes into 12 six times. 34x6=204

hence, your answer.

Note that the number of students, in a dass of 35, who improve their score from the first midterm to the second midterm is a discrete variable.

A discrete variable is one that can only have particular, unique values and cannot have any other values in between. The number of students who increase their score is a whole number that can only take on specific values (e.g., 0, 1, 2, etc.), indicating that it is a discrete variable.

A quantitative variable in mathematics and statistics can be continuous or discrete depending on whether it is normally obtained by measuring or counting. The variable is continuous in that interval if it can take on two specific real values while simultaneously taking on all real values between them.

Thus, it is correct to state that the number of students, in a dass of 35, who improve their score from the first midterm to the second midterm is a discrete variable.

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Full Question:

Is the following variable best thought of as discrete or continuous?

The number of students, in a class of 35 , who improve their score from the first midterm to the second midterm

The area of a circle with a diameter of 6 is A=π(3)². Option C

It is important to note that the area of a circle is expressed with the formula;

A = πr² or πd²/4

Where;

From the information given, we have that the diameter is 6

Radius = diameter/2 = 6/ 2 = 3

Substitute the value into the formula for area

Area, A = π(3)²

Hence, the area of the circle is  π(3)²

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Answer:48 counters

Step-by-step explanation:8x3=2, 3x8=24, 24+24+48

The product of a, b and c is equal to 18.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is are the expression as -

[tex]$\frac{\sqrt[4]{81x^{4} y^{2} } }{x^{-1} 2y^{-1} }[/tex]

The given expression is -

[tex]$\frac{\sqrt[4]{81x^{4} y^{2} } }{x^{-1} 2y^{-1} }[/tex]

We can rewrite it as -

[tex]$\frac{(81x^{4} y^{2}) ^{\frac{1}{4} } }{x^{-1} (2y)^{-1} } = \frac{(3^{4} x^{4} y^{2})^{\frac{1}{4} } }{x^{-1} (2y)^{-1} } = 6xy^{\frac{1}{2} } xy[/tex]

Now, we can write -

[tex]6xy^{\frac{1}{2} } xy = 6x^{2} y^{(\frac{1}{2} + 1) } = 6x^{2} y^{(\frac{3}{2}) }[/tex]

On comparing, we get -

a = 6

b = 2

c = 3/2

So -

a x b x c = 6 x 2 x 3/2 = 18

a x b x c = 18

Therefore, the product of a, b and c is equal to 18.

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it is 57 understand the way is down there

Step-by-step explanation:

j

k

h

a

h

a

The concept given is Graphs. A graph is a chart showing the relationship between magnitudes of variables, usually two variables, each measured along a pair of orthogonal axes.

Charts and tables are powerful visual tools because they present information quickly and easily. that graphics are commonly used in print and electronic media.

Sometimes data is easier to understand in a chart than in a table because a chart can show a trend or comparison.

A) bar graph and pie chart.

B) histogram, stem plot, and box plot.

C) histogram, stem plot, and box plot.

D) time plot.

E) bar graph and pie chart.

F) normal quantile plot.

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What is Constant of Proportionality?

The ratio between two proportional quantities' constant values is known as the constant of proportionality.

The formula for calculating slope is expressed as:

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

Given: the coordinate points (5,225) and (3, 135). The constant of proportionality is expressed as:

m =  [tex]\frac{135-225}{3-5}[/tex]

m = [tex]\frac{-90}{-2}[/tex]

m = 45

Hence, Constant of Proportionality is 45.

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The height of the totem tree after solving the equation is 1/6 units

An equation is an expression that shows how numbers and variables relate with each other.

Mathematical operations include addition, subtraction, division and multiplication. Mathematical operations are used in equations

Let h represent the height of the totem pole.

Ronald carved 3/3/8 of a totem pole. he says that the totem pole is 3/4 completed. Hence:

(3/4)h = 3÷3÷8

(3/4)h = 3 * (1/3) * (1/8)

(3/4)h = 1/8

Cross multiplying gives:

h = (4 * 1)/(3 * 8)

h = 1/6

The height of the tree is 1/6 units

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Answer: c is correct

Answer:

c

Step-by-step explanation:

Answer: The selling price of a T-shirt would be $107.

Step-by-step explanation: The amount paid by the shopkeeper for the Tshirts would be $2170 ÷ 10 = $217

Since the jeans cost twice as much as the T-shirts, we can multiply the cost of the T-shirts by 2 to find the cost of a pair of jeans: $217 x 2 = $434.

We know that the shopkeeper sold the clothes for more than 20% more than he paid for, i.ee, 100 - 20 = 80.

To find the selling price of a T-shirt, we'll divide the cost of the T-shirts by the markup percentage as a decimal: $217 / (80/100) = $107.

Answer:

B

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{4}{5}[/tex] x + 1 ← is in slope- intercept form

with slope m = [tex]\frac{4}{5}[/tex] and y- intercept c = 1

The probability of selecting the letter C or the coin landing tails up is given by the following option:

3/5.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

From the table representing the sample space, the number of total outcomes is given as follows:

10.

The desired outcomes are given as follows:

(as the or statement means that at least one of the conditions have to be satisfied, that is, one is enough).

Hence the probability is obtained as follows:

p = 6/10

p = 3/5. (dividing both the numerator and the denominator by 2).

Meaning that the last option is the correct option.

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Answer:

$7.40

Step-by-step explanation:

Therefore , the solution of the given problem of parallel line comes out to be   MP =22.

Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.

Here,

Given :  PQ || MN

=> PQ =MP+2

=> PO = 12 , MN = 12

So,

=> PO + MN = 12 + 12

=> PQ = 24

=> PQ = MP +2

=>24 = MP +2

=> MP =22

Therefore , the solution of the given problem of parallel line comes out to be   MP =22.

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The simplified expressions for (A), (B) and (C) are:

(A) [tex]f(x+h) = 4x + 4h - 6[/tex]

(B) [tex]f(x+h) * f(x) = 16x^2 + 4xh - 24x + 4h^2 - 24h + 36[/tex]

(C) [tex]f(x+h) - f(x) / h = 4[/tex]

To simplify we use the given method.

A)

[tex]f(x+h) = 4(x+h) - 6 = 4x + 4h - 6[/tex]

B) [tex]f(x+h) * f(x) = (4x + 4h - 6) * (4x - 6) = 16x^2 + 4xh - 24x + 4h^2 - 24h + 36[/tex]

C)

[tex]f(x+h) - f(x) / h = (4x + 4h - 6) - (4x - 6) / h = 4h / h = 4[/tex]

So the simplified expressions for (A), (B) and (C) are:

(A) [tex]f(x+h) = 4x + 4h - 6[/tex]

(B) [tex]f(x+h) * f(x) = 16x^2 + 4xh - 24x + 4h^2 - 24h + 36[/tex]

(C) [tex]f(x+h) - f(x) / h = 4[/tex]

Please note that in (C) the difference of the functions is divided by h, not multiplied.

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The midpoint of the segment joining points (a,b) and (j,k) is, (a+j)/2, (b+k)/2)

The midpoint of the segment joining two points (x1, y1) and (x2, y2) is given by the point ((x1 + x2)/2, (y1 + y2)/2).

So, to find the midpoint of the segment joining the points (a, b) and (j, k), we need to take the average of the x-coordinates and the average of the y-coordinates:

((a + j)/2, (b + k)/2)

So the midpoint of the segment joining points (a,b) and (j,k) is  (a+j)/2, (b+k)/2).

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Since one angle measures 18°, and the other angle measures (8x − 28)°, the value of x is equal to 12.5.

In Mathematics, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).

Mathematically, a complementary angle can be calculated by using this mathematical expression:

Q + R = 90°

Where:

Q and R are measure of the angles subtended.

Substituting the given parameters into the complementary angle formula, the sum of the angles is given by;

(8x - 28)° + 18° = 90°

8x - 10 = 90

8x = 90 + 10

8x = 100

x = 100/8

x = 12.5

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Yes , i agree with Rosa in linear equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

3/4 is equal to 0.75 and 0.75 > 0.25

Or 0.25 is equal to 1/4,

and 1/4 < 3/4

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The volume of the cylindrical pipe in terms of π is 76π ft³.

The volume of the cylindrical pipe using ALEKS calculator is 238.76 ft³.

The radius of a cylindrical construction pipe is 2 ft, and its length is 19 ft. The exact volume of the cylindrical pipe can be found as follows:

The answer is in terms of π.

Therefore,

volume of a cylinder = πr²h

where

Therefore,

volume of the cylindrical pipe =  πr²h

where

volume of the cylindrical pipe =  π × 2² × 19

volume of the cylindrical pipe =  π × 4 × 19

volume of the cylindrical pipe =  76π ft³

Hence, let's approximate the volume of the cylindrical pipe using π in an ALEKS calculator.

Therefore,

volume of the cylindrical pipe = 76 × π = 238.761041673 = 238.76 ft³

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Answer:

Step-by-step explanation:

It would be -5 3-5=-2

Therefore,  the solution of given problem of probability is there is a 0.397 percent chance that a randomly chosen male will have a systolic blood pressure below 100.

A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A possibility is a number from 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or chance that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages ranging from 0% to 100% and from 0 to 1.

Here,

Considering the query

In a particular municipality, men's systolic blood pressure has a median of 105 as well as a standard deviation = 9, which is considered to be regularly distributed.

Probability that the systolic blood pressure of a man chosen at random will be less than 100

P(x < 100)

Through the use of normalized normal distribution

=> N(100 -105)/9 \s=> N (-5/9)

We have a>0 and N(-a) = 1 - N(a).

=> 1 - N (-5/9)

=> 1 - N(0.556) (0.556)

=>1 - 0.6026

=> 0.3979

≈ 0.397 (nearest hundredths) (nearest thousandth)

Therefore, there is a 0.397 percent chance that a randomly chosen male will have a systolic blood pressure below 100.

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(2x + 3)(x - 1) = 0
x = (-b ± √(b^2 - 4ac))/ 2a, where a = 2, b = 12, and c = -3.
2x^2 + 12x = 3
(6/2)^2 = 9
2x^2 + 12x + 9 - 9 = 3 - 9
factor out the 2x^2 + 12x + 9 = 0

Answer:

J: -5,10

K: -5,5
L: -2,1
M: -2,6

Hope I helped<3

Answer: 30.48

Step-by-step explanation:

2.54x12=30.48

The standard deviation of the sampling distribution is; Option A: 3.750

Standard deviation is defined as a measure of how spread out numbers usually are. It is further said to be the square root of the Variance, and then the variance is the average of the squared differences from the Mean.

Now, we are given;

Population standard deviation; σ = 15

Sample size; n = 16

Formula for sample standard deviation in this regards is;

s = σ/√n

Plugging in the relevant values gives;

s = 15/√16

s = 15/4

s = 3.750

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Therefore . the solution of the given problem of distance comes out to be it follows that there are √17 units separating the two points.

Distance is a measure of an object's travels. Distance, put simply, is what an item travels over in a particular amount of time, or t. The shortest path an object can take while moving is displacement, nevertheless. We commonly incorporate the physical quantities of distance and displacement.

Here,

provided are (6, -3) & (2, -2)

Now, the separation between points (a, b) & (c, d) is

d= √(c-a)² + ( d- b) ²

Therefore, d= √(-3+2)² + (2-6)²

d= √ 1 + 16

d= √17

It follows that there are √17 units separating the two points.

Therefore . the solution of the given problem of distance comes out to be it follows that there are √17 units separating the two points.

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