Question 4(Multiple Choice Worth 4 points)
(06.06)

A rectangle with width of 5. There is a vertical line that splits rectangle into two sections with different lengths. One length is x the other is 3.

5(x + 3) represents the area of the rectangle above. Which expression below is equivalent by the Distributive Property?

Answer:

V = 4*8

V= 32

(x+x) * (x+x) = 2x * 2x = 4x^2

Your question is incomplete. Below you will find the missing content.

Which series of transformations will not map figure H onto itself?

A. O(x+0, y-2), reflection over y = 1

B. O(x+2, y-0), reflection over x=3

C. O(x+3, y+3), reflection over y = -x +7

D. O(x-3, y-3), reflection over y = -x +2

The correct option is Option D: the series of transformation O(x-3, y-3), reflection over y = -x +2 will not map figure H onto itself.

Here given a square with its 4 vertices at coordinates (2,1), (1,2), (2,3) and (3,2).

By checking all the options

Option A:

1st transformation (x+0, y-2) will map 4 vertices of the square into points of coordinates such as

(2,1) → (2,-1)

(1,2) → (1,0)

(2,3) → (2,1)

(3,2) → (3,0)

next transformation which is the reflection over y=1 gives the coordinates (x,2-y)

(2,-1) → (2,3)

(1,0) → (1,2)

(2,1) → (2,1)

(3,0) → (3,2)

These new points are exactly the same as the vertices of the initial square.

Option B:

1st transformation (x+2, y-0) will map 4 vertices of the square into points of coordinates such as

(2,1) → (4,1)

(1,2) → (3,2)

(2,3) → (4,3)

(3,2) → (5,2)

next transformation which is the reflection over x=3 gives the coordinates (6-x,y)

(4,1) → (2,1)

(3,2) → (3,2)

(4,3) → (2,3)

(5,2) → (1,2)

These new points are exactly the same as the vertices of the initial square.

Option C:

1st transformation (x+3, y+3) will map 4 vertices of the square into points of coordinates such as

(2,1) → (5,4)

(1,2) → (4,5)

(2,3) → (5,6)

(3,2) → (6,5)

next transformation which is the reflection over y=-x+7 gives the coordinates such as

(5,4) → (3,2)

(4,5) → (2,3)

(5,6) → (1,2)

(6,5) → (2,1)

These new points are exactly the same as the vertices of the initial square.

Option D:

1st transformation (x-3, y-3) will map 4 vertices of the square into points of coordinates such as

(2,1) → (-1,-2)

(1,2) → (-2,-1)

(2,3) → (-1,0)

(3,2) → (0,-1)

next transformation which is the reflection over y=-x+2 gives the coordinates such as

(-1,-2) → (4,3)

(-2,-1) → (3,4)

(-1,0) → (2,3)

(0,-1) → (3,2)

These new points are not matching with the vertices of the initial square.

Therefore the correct option is Option D: O(x-3, y-3), reflection over y = -x +2 will not map figure H onto itself.

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Answer:

25 percent chance or 13/52 for drawing a diamond and 4/52 for a queen

Step-by-step explanation:

There are 13 diamonds in a stack of 52 cards, hence 13/52 or 25 percent chance of drawing a diamond.

Since there are only 4 queens in a stack of 52 cards, so 4 out of 52 cards are queens

We need to understand circles and colinear points in order to use the building tool to create a circle.

It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.

Draw arcs such that they all bisect one another at a point, which will be the center of the circle, starting with three non-colinear points (points A, B, and C).

Additionally, the radius will match the distance between the arcs' centers and their correspondingly drawn arcs.

Hence we need to understand circles and colinear points in order to use the building tool to create a circle.

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Answer:

62m^2

Step-by-step explanation:

From the figure above, we have two rectangles

For one rectangle,

Lenghts= 7m

Width = 6m

Area = lenght× width = 7×6= 42m^2

For the sect rectangle

Lenght = 5cm

Width = 4cm

Area = 5×4 = 20cm^2

Area of jack patio = 42+20= 62m^2

Answer:

[tex]\boxed {\frac{F -32}{9} = \frac{C }{5}}[/tex]

Step-by-step explanation:

The correct relation between degrees Celsius, °C, and degrees Fahrenheit, °F is :

[tex]\boxed {\frac{F -32}{9} = \frac{C }{5}}[/tex]

Mikaela's team's score is 8.33

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Viktoria's team's score = 7

According to question,

= 2+ 7*2 = 16

so, Mikaela team score= 16/3+3= 8.33      

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Step-by-step explanation:

The are two angles ie. 45 and 80 than find the third angle

80 will be vertically opposite and alternative angle to a

Answer:

2 ± i

Step-by-step explanation:

by 5, I assume you mean +5

x² - 4x + 5 = 0

x = (-b±(√(b²-4ac)) / 2a

x = (4 ± (√(16 - 20)) / 2

x = (4 ± (√(-4)) / 2

√-4 = √4√-1 which is 2i

x = (4 ± 2i) / 2

x = 2 ± i

The given quadratic equation is

[tex]2 {x}^{2} - x - 3 = 0[/tex]

comparing with

[tex] {ax}^{2} + bx + c = 0[/tex]

We get ,

[tex]a = 2 \\ b = - 1 \\ c = - 3[/tex]

formula :

[tex]D = {b}^{2} - 4ac \\ \\ D = {( - 1)}^{2} - 4 \times 2 \times ( - 3) \\ \\ D = 1 - ( - 24) \\ \\D = 1 + 24 \\ \\D = 25.[/tex]

Discriminant of given quadratic equation is 25 .

option (B) 25 ✔

Answer: [tex]-x^3-x^2+11x\\[/tex]

Step-by-step explanation:

Combine Like Terms:

[tex]=3x+2x^3+-5x^2+4x+6x+-2x+-3x^2+7x^2+-3x^3\\\\=(2x^3+-3x^3)+(-5x^2+-3x^2+7x^2)+(3x+4x+6x+-2x)\\\\=(-x^3)+(-8x^2+7x^2)+(7x+4x)\\\\=-x^3-x^2+11x\\[/tex]

Answer:

B. g(x) is shifted 5 units right and 2 units up from f(x).

g(x) = [tex]\frac{1}{x-5}[/tex] + 2 is compared to the parent function, f(x) = [tex]\frac{1}{x}[/tex] by g(x) is shifted 5 units right and 2 units up from f(x).

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given parent function is,

f(x) = [tex]\frac{1}{x}[/tex]

And the translated function is,

g(x) = [tex]\frac{1}{x-5}[/tex] + 2

When f(x) becomes g(x), the first change occurred is [tex]\frac{1}{x}[/tex] changes to [tex]\frac{1}{x-5}[/tex].

That is f(x) changes to f(x-5).

This translation occurs when the function undergoes horizontal translation towards right.

Then [tex]\frac{1}{x-5}[/tex] is translated to [tex]\frac{1}{x-5}[/tex] + 2.

That is, f(x-5) is changed to f(x-5) + 2.

This occurs for the vertical translation towards up.

Hence the translation occurred is g(x) is shifted 5 units right and 2 units up from f(x).

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Answer:

-12 ≤ p ≤ 12

Step-by-step explanation:

If the absolute value inequality is

|p| ≤ 12,

then the answer is

-12 ≤ p ≤ 12

The net interest she would get on the amount deposited is $57,000.

The net interest is the total interest earned less tax.

Interest = amount deposited x simple interest x time

200,000 x 0.1 x 3 = $60,000

Net interest = $60,000 x (1 - 0.05)

$60,000 x 0.95

$57,000

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The question was incomplete. Below you will find the missing graph image.

The range contain all the real numbers greater than or equal to –3 .

Range of function : The set of outputs of a function is called range of that function. Range of a function is also called co-domain of the function.

Example : If f(x) = x² is the function with domain as all real numbers, then the range of that function is the set of all non-negative real numbers.

We have to find the range of the function on the graph.

We can see by the graph minimum value of y of function is -3 and the graph continues to extend upward in the positive direction.

So, the range contain all the real numbers greater than or equal to –3 .

Therefore, the range contain all the real numbers greater than or equal to –3 .

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Answer:

[tex]\huge\boxed{\sf x = -2/3}[/tex]

Step-by-step explanation:

3x + 2 = 0

Subtract 2 to both sides

3x = 0 - 2

3x = -2

Divide 3 to both sides

x = -2/3

[tex]\rule[225]{225}{2}[/tex]

Answer:

Her sales after 6 months are = 127units

Step-by-step explanation:

Percentage increase:- The degree to which a value increases expressed in percent form is known as percentage increase.

formula for % increase = (final value - initial value)/initial value(100)

Here in the question,

percentage increase after every month is = 5%

initial value  =  95 units

therefore by applying above formula :-

[(x-95)/95]×100 = 5          [where x is the value of her sales goals after 1 month]

x = (5/100)×95+ 95

x = 99.75

Now this x will be the initial value for the next month

x₂ = (5/100)99.75+ 99.75             [ x₂ = sales goal after 2 months]

x₂ = (5/100)×99.75+ 99.75

x₂ = 104.73

similarly,

(x₃-104.73/104.73)100 = 5       [x₃ = sales after 3 months]

x₃ = 109.96

similarly for 4th month,

(x₄ -109.96/109.96)100 = 5       [x₄ = sales after 4 months]

x₄ = 115.45

for 5th month,

(x₅ -115.45/115.45)100 = 5       [x₅ = sales after 5 months]

x₅ = 121.22

finally for the 6th month

(x₆-121.22/121.22)100 = 5        [x₆ = sales after 6 months]

x₆ = 127.28

therefore,

her sales after 6 months are = 127.28 units or 127 units by rounding off

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The probability that at least 40 jobs will be submitted in 15 minutes is 0.79162.

The number of jobs submitted per minute follows Poisson Distribution.

A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as  [tex]P(X= x) = e^{-\lambda} \frac{\lambda^{x} }{x!}[/tex] .

In the question, we have the random variable x = 40.

The mean λ = Average jobs per minute*time = 3*15 = 45.

We are to find the probability that at least 40 jobs will be submitted in 15 minutes, which is represented as P(X ≥ 40) = P(X > 39).

P(X > 39) = 1 - P(X ≤ 39) = 1 - poissoncdf(45,39)

As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).

Therefore, P(X > 39) = 1 - 0.20838 = 0.79162.

Therefore, the probability that at least 40 jobs will be submitted in 15 minutes is 0.79162.

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The categories of nominal level distribution do not have to be listed in any particular order

These characteristics include:

Therefore, the categories of nominal level distribution do not have to be listed in any particular order

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Answer:

A = 1.5 π in² ≈ 4.7 in²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{\frac{\pi }{3} }{2\pi }[/tex]

  = π × 3² × [tex]\frac{1}{6}[/tex]

  = 9π × [tex]\frac{1}{6}[/tex]

  =  1.5π in²

  ≈ 4.7 in² ( to the nearest tenth )

The complete question says: Let v, w, be vectors of [tex]\mathbb{R}^4[/tex]. Let A be a matrix with 4 columns v, w, 2v+w, v-w. What are the possible values for rank(A)?

The possible values for rank A = 2

A vector space is a space that contains vectors as well as the associative including the commutative operation of vector addition and the associative, as well as, distributive operations of vector multiplication by scalars.

From the information given:

where;

However, the vectors 2v+w and v-w can be expressed as a linear combination of the given values of v and w(independent vectors).

We can conclude that the maximum no. of independent rows = 2. Hence, the possible rank of matrix A is 2.

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Answer:

-63

Step-by-step explanation:

3 - 6(12 - 1) = 3 - 6(11) = 3 - 66 = -63

The correct answer is option A which is the equations which represent relationship  between c and f is c = 7 / 3f.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

Given that:-

From the given data we can see that the amount of flour required is [tex]9\dfrac{1}{3}\[/tex] Cups or [tex]\dfrac{28}{3}[/tex] Cups for making 4 cakes.

So the expression will be written as:-

[tex]9\dfrac{1}{3}f = 4c[/tex]

[tex]\dfrac{28}{3\\}f = 4c[/tex]

[tex]c = \dfrac{28}{3\times 4}f[/tex]

c = [tex]\dfrac{7}{3}[/tex]f

Therefore the correct answer is option A which is the equation that represents the relationship between c and f is c = 7 / 3f.

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The area of the triangle is given as: ≈ 70.50cm²

Area of shaded region = Area of the sector less Area of the Triangle.

This is represented as:

π r² (∅/360) - 1/2 x b x h

= π x 14² x (46/360) - (1/2) x 14 x 10.0708

= 78.6794 - 70.4956

= 8.1838 cm²

Hence, the area of the triangle is (1/2) x 14 x 10.0708

= 70.4956 cm²

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Answer:

Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]

Step-by-step explanation:

Simplify any algebric expression means to write an equivalent expression in which all similar terms combined and remove all symbols such as brackets.

The given algebraic equation is [tex]x^{2} -\frac{4}{x^{2} } +2x[/tex]

now for simplifying it

First of all take L.C.M of [tex]x^{2}[/tex]

= [tex]\frac{x^{2} (x^{2}) -4 + 2x(x^{2} )}{x^{2} }[/tex]

We get [tex]\frac{x^{2} -4+2x^{3}}{x^{2} }[/tex]

Further we can write it as  [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]

Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]

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Answer:

mommy

Step-by-step explanation:

The value of the function [tex]f(x)=3x^{2} -2x[/tex] for x=4 is 40.

The given function is [tex]f(x)=3x^{2} -2x[/tex].

We need to evaluate the given function for x=4.

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

To find the value of the given function replace x with 4 and simplify.

That is, [tex]f(4)=3(4)^{2} -2 \times 4=48-8=40[/tex].

Hence, the value of the function [tex]f(x)=3x^{2} -2x[/tex] for x=4 is 40.

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The KiwiCo earn money from subscriptions in April would be $5555.73.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

KiwiCo charges a subscription fee of $16.99 for each of its members.

$16.99 per 1 person

KiwiCo had 300 subscribers in March.

In April, 50 new people subscribed to KiwiCo, and 23 people canceled their subscriptions.

300 + 50 = 350 - 23 = 327

So,

327×$16.99= 5555.73

Hence, The KiwiCo earn money from subscriptions in April would be $5555.73.

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Answer:

15

Step-by-step explanation:

"one number is three more than twice the second number"

15 * 2 = 30

30 + 3 = 33

15 + 33 = 48

Answer:

15

Step-by-step explanation:

The key to most problems of this type is carefully translating the word problem into math ... an equation.

"The sum of two numbers is 48."

"Sum": Add

"two numbers": we'll need two numbers... let's call them x & y

"is": =

"48": 48

So, the first sentence means:  [tex]x+y=48[/tex]

Note that we have two unknowns here.  To solve for them, we'll need another equation... at least as many equations as unknowns (2 unknowns, needs 2 equations).

"If one number is three more than twice the second number..."

"one number": x

"is": =

"three more than": +3

"twice": 2*

"the second number": y

So, the second sentence introductory clause means: [tex]x=2y+3[/tex]

We have a system of equations. We need as many equations as we have unknowns.  We currently have two equations, and two unknowns.  Let's try to solve the system:

[tex]x+y=48[/tex]

[tex]x=2y+3[/tex]

There are two main methods to solve systems of equations:  Substitution & Elimination

To use the Substitution Method, we'll need to isolate one of the variables in one of the equations, substitute, and solve.

To use the Elimination Method, we'll need to align like terms, find or build matching coefficients with opposite signs, add to eliminate, and solve.

Given that equation 2 already has x isolated, this system is already ready to use the Substitution method, so let's do that.

[tex]x+y=48\\x=2y+3[/tex]

[tex](2y+3) + y = 48[/tex]

[tex]2y+3 + y = 48[/tex]

[tex]3y+3 = 48[/tex]

[tex]3y= 45[/tex]

[tex]y= 15[/tex]

To find x, substitute back into one of the equations:  Equation 2 already has x isolated, so it will be easy to solve for x.

[tex]x=2(15)+3[/tex]

[tex]x=30+3[/tex]

[tex]x=33[/tex]

So the solution we found is x=33 and y=15.

The sum of the numbers is 48:

[tex]x+y=(33)+(15)\\x+y=48[/tex]

One number is three more than twice the second number

[tex]x=2y+3[/tex]

[tex](33)\text{ ?=? }2(15)+3[/tex]

[tex]33=33[/tex]

Our answer satisfies all of the original conditions, so our answer works.

The question finally asks, "...which of the following is the smaller number?"

Of the two numbers, the smaller number is 15.