MULTIPLE CHOICE PRACTICE
9. For the function defined by the equation y=2 x²-10, which of the following represents the output when the input is -3 ?
(1) 6
(3) -10
(2) 8
(4) -28
10. If a function is defined by the equation y=-5 x+1 and the domain is the set {-2,0,2,4\}, which set below represents the range of the function?
(1) {11,12,13,14}
(3) {-10,-1,9,19}
(2) {-19,-9,1,10}
(4) {51,53,55,57}
11. A function is given by the set: {(-6,2),(-4,7),(0,5),(2,-4),(5,2),(7,5)}. Which of the following gives a pair of inputs that have the same output?
(1) -6and -4
(3) -4 and 2
(2) 5 and 7
(4) 0 and 7

For the given equation, 1/x + 2/x+10 = 1/3,

1)The least common denominator is x+10. Option c is correct.

2)The equation will have 2 valid solutions. Option a is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is,

1/x + 2/x+10 = 1/3

[tex]\frac{1}{x}+\frac{2}{x+10}=\frac{1}{3}[/tex]

Cross-multiply the given equation,

[tex]3\left(x+10\right)+6x=x\left(x+10\right)[/tex]

The obtained value of x after simplifying the equation is,

[tex]\\\ x=5,\:x=-6[/tex]

Thus, for the given equation, 1/x + 2/x+10 = 1/3, the least common denominator is x+10. Option c is correct and the equation will have 2 valid solutions. Option a is correct.

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The slopes of the linear equations are:

a) -1

b) 0

c) undefined, it is a vertical line.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

1) The points are (3, 5) and (2, 6), so the first slope is:

a = (6 - 5)/(2 - 3)  =1/-1 = -1

2) The points are (-3, 2) and (7, 2)

Notice that this is a horizontal line of the form y = 2, so the slope is zero.

3) The points are (6, 8) and (6, -2)

This is a vertical line of the form x = 6, so the slope is undefined.

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                                    [tex]\large\boldsymbol{\rm{Slope}}[/tex]

[tex]\bf{Intro}[/tex]

To find the slope of a line, given that it passes through two points, use the slope formula:

[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Substitute the known values and simplify:

[tex]\bf{m=\dfrac{6-5}{2-3}}[/tex]

[tex]\bf{m=\dfrac{1}{-1}}[/tex]

[tex]\bf{m=-1}[/tex]  {slope}

[tex]\rule{250}{1}[/tex]

Substitute the known values and simplify:

[tex]\bf{m=\dfrac{2-2}{7-(-3)}}[/tex]

[tex]\bf{m=\dfrac{0}{7+3}}[/tex]

[tex]\bf{m=\dfrac{0}{10}}[/tex]

[tex]\bf{m=0}[/tex]    {slope}

[tex]\rule{250}{1}[/tex]

Substitute the known values and simplify:

[tex]\bf{m=\dfrac{-2-8}{6-6}}[/tex]

[tex]\bf{m=\dfrac{-10}{0}}[/tex]

[tex]\bf{m=not\:de fined}[/tex]

✦ Therefore, the slopes are: -1, 0, not defined.

a) The monthly repayment amount is $466.67.

b) The total interest paid on loan is $21,000.

Interests on student loans are computed using the simple interest system, instead of compound interest.

The total interest payable is a function of the outstanding balance (principal amount plus accumulated interest) during the non-payment period, the interest rate, and the number of years of payment.

Unsubsidized Loans plus Accumulated Interest = $35,000

Interest rate (APR) = 6%

Repayment period = 120 months (10 years x 12)

Interest on the student loan = $21,000 ($35,000 x 6% x 10)

Total amount to repay for 10 years = $56,000

Monthly repayment = $466.67 ($56,000 ÷ 120)

Thus, the monthly repayment will be $466.67, which is determined by adding the total interest for 10 years to the outstanding balance and dividing the result by 120 months.

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Answer:

Rhs

Step-by-step explanation:

angle N (R)

pq=mq ( h)

Nq (s)

The pros and cons regarding the methods of the polynomial include:

Graphing the related system eliminates the need to rewrite the equation in order to set it equal to 0. It is simpler because you can graph each side of the equation separately.

It can be difficult to locate the system's intersection point at times. You may need to zoom in or learn how to resize the window. Using the related function allows you to find the points by focusing on the x-axis.

A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations such as addition, subtraction, multiplication, and division.

The formula is ax² + bx + c = 0, where a and b are coefficients, c is a constant, and the polynomial degree is 2. A trinomial equation is a polynomial with three variable terms. It is also known as a cubic equation. To be a polynomial term, an expression must contain no square roots of variables, no fractional or negative powers on variables, and no variables in the denominators of any fractions.

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1. If a polynomial function with rational coefficients has -4 and 8 as roots, it means we can factor this polynomial this way :

What is rational coefficients?

A coefficient is a number that is placed in front of a variable. A variable and a rational number are preceded by a rational coefficient, which may be an integer, decimal, or fraction.

(x - (-4))(x-8) = (x+4)(x-8) = x² - 8x + 4x - 32 = x² - 4x - 32

1x² - 4x - 32 is a polynomial function of least degree with rational coefficients that satisfices the given conditions. The leading coefficient here is 1, we call this a monic polynomial.

2. There may be something missing in the question here

3. We can use the factoring techniques to find the roots :

x^3 - 5x² + 9x - 45 let us group x^3 with -5x² and 9x with -45 :

(x^3 - 5x²) + (9x - 45) = x²(x - 5) + 9(x - 5)

We can notice now that there is a common factor : (x-5) this allows us to factor again by (x-5) :

Y = (x-5)(x²+9)

This is the maximum we can do on R, but on C the set of complex we can still factor again.

x² + 9 has a negative discriminant : Δ = b² - 4ac where b = 0 , a = 1, c = 9

Δ < 0, Δ = - 36

Applying the formulas for the roots x1 and x2 we get x1 = -3i, and x2 = + 3i

Y = (x-5)(x-3i)(x+3i)

So the solution is S = {5, 3i, -3i} the three roots of the function.

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The predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.

The given results of regression:

y = –0.693x + 28.802

The formula for regression equation is:

y = ax + b

So, given that:

a = –0.693

b = 28.802

r2 = 0.571536

r = 0.756

Back to the given results of regression:

y = –0.693x + 28.802

In this case, y represents the number of sit-ups a person can do, and x represents the hours of TV watched per day.

Thus, the predicted number of sit-ups for a person who watches x = 6 hours of TV is:

y = –0.693x + 28.802

y = –0.693 * 6 + 28.802

y = –4.158 + 28.802

y = 24.644

Hence, the predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.

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Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.

But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.

So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.

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The slant height of the cone is 12.6 units

What are solids ?

A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

h= 12

diameter = d = 8

so, radius, r = d/2 = 8/2 = 4

Formula for slant height , l is:

l = √(h² + r²) = √(12² + 4² )

 = √(144 + 16) = √160 = 12.649 ≈ 12.6 units

The slant height of the cone is 12.6 units

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electricity consumed:28 units

charge upto 20 units : 20 * Rs 3 : Rs 60

charge from (21 to 28) : 8 * Rs 6.50 : 52

total charge including service charge : Rs 60 + Rs 52 + Rs 50 : Rs 162

The ratio of the number of men to women to adults is 5 : 3 : 4 and the number of women is 360

From the question, we have the following ratios that can be used in our computation:

Men : Women = 5 : 3

Children : Adults = 1 : 2

This means that

Children : Men : Women  = 1 : 2(Men : Women)

So, we have the following representation

Children : Men : Women  = 1 : 2(5/8 : 3/8)

Open the brackets

Children : Men : Women  = 1 : 5/4 : 3/4

Multiply through by 4

Children : Men : Women  = 4 : 5 : 3

Rewrite the ratio as

Men : Women : Children 5 : 3 : 4

Here, we have

People = 1440

Recall that

Men : Women : Children 5 : 3 : 4

So, we have

Women = 3/(5 +3 + 4) * 1440

Evaluate the sum

Women = 3/12 * 1440

Evaluate the products

Women = 360

Hence, the number of women is 360

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The number of shirts Samuel can fold in 2 minutes is 12

From the question, we have the following parameters that can be used in our computation:

Number of Shirts 3 6 ?

Time (minutes) 0.25 0.50 2

Represent the missing value with x

So, we have the following representation

Number of Shirts 3 6 x

Time (minutes) 0.25 0.50 2

From the above table of values, we have the following equation

6 : x = 0.5 : 2

Multiply the second ratio by 12

So, we have

6 : x = 6 : 12

By comparison, we have

x = 12

Hence, the number of shirts is 12

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The equation of the graph in slope intercept form is y = x + 2

The equation of a graph can be represented in slope intercept form as follows:

y = mx + b

where

Hence, let's find the slope using (1, 3) and (2, 4)

Therefore,

slope = 4 - 3 / 2 - 1

slope = 1 / 1

slope = 1

Let's find the y-intercept using (1, 3)

y = x + b

3 = 1 + b

b = 3 - 1

b = 2

Therefore, the equation is y = x + 2

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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The CD be worth in 5 years is

We would use the following formula to calculate compound interest:

A = P(1 + r / n) nt

Where

A is the CD's total value after t years.

The interest rate is represented by r.

The periodic interval at which it was compounded is represented by n.

P stands for the principal, or the amount of the CD purchase.

Considering the data provided,

P = 1500

r = 6% = 6/100 = 0.06

Since it was compounded 12 times in a year, n = 12.

The phrase changes.

A = 1500(1+0.06/12)^12 × t

A = 1500(1+0.005)^12t

A = 1500(1.005)^12t

1) If t is five years,

A = 1500(1.005)^12 × 5

A = $2023.3

2) If t equals ten years,

A = 1500(1.005)^12 × 10

A = $2729.1

3) If t equals 486 months, then 486/12 is 40.5 years.

A = 1500(1.005)^12 × 40.5

A = $16935

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Answer:

#4 is one, and #5 is two.

Step-by-step explanation:

Answer:

10(-x + 1)

Step-by-step explanation:

-2x - 8x + 20

-10x + 20

10(-x + 1)

The length of the diagonal of the right triangle is 21.2 units.

The game is played on a square court divided into four smaller squares that meet at the centre.

A right triangle QTS is formed, where QTS is 45°. Using trigonometric function, the length of the diagonal can be found as follows:

Therefore,

sin 45 = opposite / hypotenuse

opposite side = 15 feet

hypotenuse side = 15 feet

The hypotenuse side is the diagonal.

Hence,

sin 45° = 15 / h

cross multiply

h = 15 / sin 45

h = 15 / 0.70710678118

h = 21.2132034356

h = 21.2 units

Therefore,

length of diagonal = 21.2 units

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a) The percentage of $680 which is $490 is 72.06%.

b) When a price is reduced from $680 to $490, the percentage decrease is 27.94%.

The percentage is the ratio of a value to another.

Percentages are depicted as fractional values expressed over 100.

To determine percentages, the smaller value is expressed as the numerator, while the more considerable value is described as the denominator.

The result is then multiplied by 100.

For instance:

$490 of $680 is 72.06% ($490/$680 x 100)

Price reduction from $680 to $490, the percentage decrease is computed as the difference between $680 and $490 divided by $680, multiplied by 100.

Thus, the percentage decrease in price from $680 to $490 is 27.94%, showing that the original price of the good or service has been reduced from 100% to 72.06%.

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Answer:

is there a pitcher with it

Step-by-step explanation:

The maximum number of individuals who can visit the amusement park is 4.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question

The number of persons who can visit the theme park will be determined by the inequality that can be used to compute x and the information provided in the question:

8 + 23(x) ≤ 100

8 + 23x ≤ 100

23x ≤ 100 - 8

23x ≤ 92

x ≤ 92/23

x ≤ 4

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The value of x is 18 if ∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

It is given that:

∠C and ​ ∠D ​ are vertical angles.

5x-7 = 8x-55

Subtract 5x from both sides:

-7 = 3x -55

Add 55 to both sides:

3x = 48

x = 48 /3

x = 16

Thus, the value of x is 18 if ∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.

∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55. What is m∠D ?

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Answer:

width is 2.75 and $6.60

Step-by-step explanation:

first divided by 132 by 12 which gives you 11 then divided 11 by 4 and you get 2.75.

Dubble Check: to chock multiply 12 x 4 x 2.75 which gives you 132.

Cost: Multiply 132 times 5 and you get 660 then place a decimal point between 6 and 6 to get $6.60

The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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The set A ∩ (/B ∪ C) is given as { 1, 6 }

From the information given, we have the sets as;

U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A= {1, 2, 4, 6}

B= {3, 7}

C= {1, 3, 6, 7, 8}

Note that;

B∪C = { 1, 3, 6, 7, 8}

A ∩ (/B ∪ C) = { 1, 6 }

Hence, the set is { 1, 6 }

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If ∠2=10x+7 and one angle is 67 degrees then value of x is 6.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that the triangle has two equal sides which makes the triangle as isosceles.

In an isosceles triangle the two sides will be always equal and the angles will be also equal.

One angle of the triangle is 67 degrees

We need to find the ∠2.

As we know that the equal sides make equal angles.

∠2=67 degrees

and from given ∠2=10x+7

Now equation 67 with the 10x+7 to find the value of x.

So 67=10x+7

subtract 7 from both sides

67-7=10x+7-7

60=10x

Divide both sides by 10

x=60/10

x=6

Hence, the value of x is 6.

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Answer:

(a) 6.33 miles per hour

(b) $4.33 per hour

(c) $0.68 per mile

Step-by-step explanation:

Li drove 6 hours (5pm - 11pm) for a total of 38 miles
[tex]\textrm{(a) Her average speed is determined by the formula}\\\\\dfrac{\textrm{Distance Travelled}}{\textrm{Time taken for travel}}[/tex]

[tex]\textrm{So average speed }=$\dfrac{38}{6} = 6.33$ \;\textrm{miles per hour}}\\\\[/tex]

(b) She paid $26 for 6 hours of usage
[tex]\textrm{So cost per hour } = \dfrac{26}{6} = \$4.33\;\textrm{per hour}\\\\[/tex]

(c) Cost per mile, c, can be computed as follows
[tex]c = \dfrac{\textrm{Total Cost}}{\textrm{Miles Traveled}}[/tex]

[tex]\longrightarrow \dfrac{26}{38} = \$0.68\; \textrm{per mile}[/tex]

Answer:

Equation in terms of k about the average age is:

(2k + 61) / 5 = 17

After solving the equation, k = 12 years

Step-by-step explanation:

Age of Roxanne = k years

Age of the sister = (k + 8) years

Age of brothers = 21, 18 and 14 years

Total number of siblings = 5

Average age of siblings = [k + (k + 8) + 21 + 18 + 14] / 5

or, 17 = [2k + 61] / 5

or, 85 = 2k + 61

or, 24 = 2k

or, 12 = k

So, k = 12 years