1. Let

U = {(x, y, z) = R³ | x+y=2z = 0 = x - y},

and let

V = span {(1, 0, -1), (3, 1, 2)}.

Determine the dimensions of both U and V, proving your results.
Note that to prove the dimension, you should use the definition, which
means you need to find a basis. It is not enough to just state a basis,
you must explain why it is a basis.

h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.

Here,

We can draw the graph as

h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)

h(x) = f(x) + 5

The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.

Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

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Answer:

D

Step-by-step explanation:

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{3}{4}[/tex]  Use the common denominator of 8 Multiply [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{2}[/tex]

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{6}{8}[/tex]

7[tex]\frac{9}{8}[/tex]

7 + [tex]\frac{8}{8}[/tex] + [tex]\frac{1}{8}[/tex]  Another name for [tex]\frac{8}{8}[/tex] is 1

7 + 1 + [tex]\frac{1}{8}[/tex]

8[tex]\frac{1}{8}[/tex]

Answer:

k=4

Step-by-step explanation:

[tex] \frac{1}{2} k - \frac{4}{1} k = - 8 - 6[/tex]

[tex] \frac{(1 \times 1) - (4 \times 2)}{(2 \times 1)} k = - 14[/tex]

[tex] \frac{1 - 8}{2}k = - 14[/tex]

[tex] - \frac{7}{2} k = - 14[/tex]

[tex] \frac{ - \frac {7}{2} }{ - \frac{7}{2} }k = \frac{ - 14}{ - \frac{7}{2} } [/tex]

[tex]k = 4[/tex]

The required temperature in Beijing China is -7°C on Tuesday.

As mentioned in the numeral,

On Monday in December
The temperature in Harbin China is  -8°C,

Now,
The Temperature in Beijing china is -2°C
According to the condition, the temperature on the next day in Beijing is 5° degrees colder than it was yesterday since the temperature is becoming colder implying that the temperature is getting decreased by -5°C.

The temperature on Tuesday is given as,
T = -2°C - 5°C  [subtracting -5 because the temperature is decreased]
T = - 7°C

Thus, the required temperature in Beijing China is -7°C on Tuesday.

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From the classification angles, it was possible to find the arcs:

UL=40, UY= 90, TY=50, YLE =270, LE=140 and UET=220.

If UE= 180 and TE=40, you have:

UET=UE+TE

UET=180+40

UET=220

They are a lot of classifications for angles like complementary angles, supplementary angles, right angles, and others. See below:

The question gives mTE=40, and it asks:

UL is opposite the arc TE, therefore its value is also 40.

The figure shows a right angle, then UY is equal to 90.

If UY is equal 90, YE is equal to 90 too, because they are supplementary. If YE=90 and TE=40, you have:

TE+TY=90

40+TY=90

TY=90-40

TY=50

YLE = YE+UE. The figure shows YE=90 and UE represents a semicircle (180). Thus,

YLE= 90+180=270

If UE= 180 and UL=40, you have:

UE=UL+LE

180=40+LE

LE=180-40

LE=140

If UE= 180 and TE=40, you have:

UET=UE+TE

UET=180+40

UET=220

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Answer:

(3,18)

Step-by-step explanation:

You do not give the center of dilation, so I am using the origin (0,0)

You multiply the x and y by 3

(1,6)

1 x 3 = 3

(1,6)

6 x 3 = 18

(3,18)

The function's general shape is a downward-opening parabola.

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

f(x)=-x^4+8x^3+8x^2-96x-144

Express properly

So, we have

f(x) = -x⁴ + 8x³ +8x² - 96x - 144

Next, we plot the graph (see attachment)

From the attached graph, we can see that the function opens down

This means that the general shape is a downward-opening parabola.

The function faces down (as shown on the graph)

Here, we set x = 0

So, we have

f(0) = -(0)⁴ + 8(0)³ + 8(0)² - 96(0) - 144

Evaluate

f(0) = -144

So, the y-intercept is -144

We start by setting the factor to 0

So, we have

x - 6 = 0

Solve for x

x = 6

From the graph;

When x = 6, y = 0

This means that x - 6 is a factor

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2 copies of 1/10 can be written as 2/10

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given here 2 copies of 1/10 thus 2×1/10=2/10

                                                                =1/5

Hence, 2 copies of 1/10 can be written as 2/10

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Dirk will make 70 pars or better.

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 that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.

Out of 90 holes, Dirk made par or better on 42 holes.

At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.

Then, Out of 150 holes, Dirk will make par or better on -

(42/90 x 150) holes

(42/90 x 150)

70

Therefore, Dirk will make 70 pars or better.

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Answer:

which one is correct about HRM?

The cost of the order can be expressed as 7x + 5, where x is the number of t-shirts ordered.

In this expression, "7x" represents the cost of the t-shirts, where each shirt is $7 and the number of shirts is represented by "x". The "$5" represents the flat shipping fee for the entire order, which does not change regardless of the number of shirts being ordered.

By adding the cost of the shirts and the shipping fee, we can find the total cost of the order. It's important to understand that the value of "x" must be specified to evaluate the expression.

For example, if 3 shirts are ordered, then x = 3 and the expression becomes:

So the total cost of the order would be $26.

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The points to be graphed are (6, 0) and (0, 3). The graph of the equation is shown in the attached image

y = - 1/2x + 3

In order to graph the equation of the line:

First, find the value of x when y = 0:

y = - 1/2x + 3 , when y = 0:

0 = - 1/2x + 3

1/2x = 3

x = 3 × 2

x = 6

Also, find the value of y when x = 0:

y = - 1/2x + 3, when x = 0:

y = - 1/2(0) + 3

y = 3

Therefore,  the values to be plotted on our graph are (6, 0) and (0, 3). The image of the graph is attached

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Answer:

1.8 meters

Step-by-step explanation:

Multiply 12 by 0.15 to get your answer. You multiply because the question says "15% of 12 meters" which means you need to multiply.

Answer: 1.8

Step-by-step explanation:

Multiply 12 by .15 (15% as a decimal), and you'll get 1.8 meters. You multiply, because it says 15% of 12 meters.

Step-by-step explanation:

TRY WITH SOME Trigonometric FUNCTION.

IF SOMETHING IS Wrong . I AM STILL A STUDENT

40 minutes of 8 hours as a fraction is 1/12.

Fractions represent the parts of a whole or collection of objects. A fraction has two parts namely numerator (upper part) and denominator (lower part).

Given are 40 minutes to 8 hours.

We can write -

(40 minutes/8 hours)

{40 minutes/(8 x 60)}

(40/480)

1/12

Therefore, 40 minutes of 8 hours as a fraction is 1/12.

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One possible set of perimeters for the two figures is 4x and 16x.

Dilation is one of the type of transformation where the size of the object is made smaller or larger without affecting the shape.

Let A be the area of the original figure.

New area after dilation = 16A

Suppose that the figure is a square.

Area of a square is the square of it's side length and perimeter is four times the length of one side.

Let 'x' be the length of a side of the original figure.

Area of the original figure, A = x²

Perimeter of original figure = 4x

New area = 16 A = 16 x² = (4x)²

So the side length of new figure = 4x

Perimeter of new figure = 4 (4x) = 16x

Hence one of the possible set of perimeters for the two figures given is 4x and 16x.

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The total amount that Latoya ended up paying for the machinery, was $ 13, 080 .96

The amount of interest that Latoya paid was $ 980.96

The total amount paid by Latoya for the machinery can be found as :

= Down payment of the machinery + ( Monthly payments x Number of months per year x Number of years )

= 1, 800 + ( 313. 36 x 12 x 3 )

= $ 13, 080 .96

The total interest paid on the loan was :

= ( Monthly payments x Number of months per year x Number of years ) - Worth of the machine - down payment

= ( 313. 36 x 12 x 3 ) - 12, 100 - 1, 800

= $ 980.96

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Therefore , the solution of the given problem of population is . Sample - The 400 clients that the insurance company included in this study

In common parlance, a population is a distinct group of people who share a common citizenship, identity, or set of traits. A population is a sampling that is typical of a broader group of individuals (or even objects) that share one or more variables characteristics.

Here,

A party promises to reimburse another party in exchange for a fee in the case of a certain loss, damage, or injury as a way of financial loss protection. It is a method of risk management that is primarily employed to protect against the risk of a potential loss.

a. Parameter - The average health care cost each year for all of the insurance company's clients

b. Population - All of the insurance company's clients

c. Sample - The 400 clients that the insurance company included in this study

d. Statistic - The average health care costs each year for the 400 clients that the insurance company included in this study

e. Data - The list of the 400 annual health care costs for the clients that the insurance company includes in the study

f. Variable - The cost each year for health care

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The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.

What does rate of change mean?

An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then the rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.

Surafce area of a prism is equal to

2(Area of base) + (perimeter of base)(height)

2b^2+4bh

[tex]S=2b^2+4bh[/tex]

[tex]\frac{ds}{dt}=4b\frac{db}{dt} + 4b\frac{db}{dt} + 4h\frac{db}{dt} \\[/tex]

It is given that db/dt= -7 and dh/dt -=10.

At a particular instant b= 4km, h=9 km.

Now we will substitute the values in this formula:

[tex]\frac{ds}{dt}=-4*4*7-4*4*7+ 4*9*10\\\frac{ds}{dt}=136[/tex]

The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.

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If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

First step:-

Right triangular prism=1⁵/₆ inches= 11/6 inches

Height of the base=8²/₃ inches = 26/3 inches

Second step:-

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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The probability of P(B and C) is 1/6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. It is more likely that an event will occur if its probability is higher.

For e.g., A straightforward illustration is tossing a fair (impartial) coin.

Given that, the probabilities, P(A) = 1/8, P(C) = 1/4, and P(A and B) = 1/12

P(A and B) = P(A)×P(B)

Therefore,

1/12 = 1/8 × P(B)

P(B) = 8/12 = 2/3

Now,

P(B and C) = P(C)×P(B)

P(B and C) = 1/4×2/3

P(B and C) = 1/6

Hence, P(B and C) = 1/6

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Answer:

(8, -2)

Step-by-step explanation:

Given:

[tex]\textsf{If P = (8, 2), Find $\sf R_{x-axis}(P)$}[/tex]

[tex]\sf R_{x-axis}(P)[/tex] means to reflect the given point P in the x-axis.

When a point is reflected in the x-axis, the x-value is unchanged, but the y-value becomes negative:

Therefore:

[tex]\sf R_{x-axis}(P)=(8,-2)[/tex]

Answer:

144

Step-by-step explanation:

9+2+4+6+123=

11+10+123
21+123
144

Answer:

Step-by-step

Closure property is true for division except for zero.

The essays that she can review in 1 hour would be; 2 2/3.

A fraction represents a part of a number or any number of equal parts.

We are given that English teacher reviewed 2 /3 of an essay in 1/ 4 of an hour.

Thus, Fraction of the essay reviewed = 2/3

Amount of time used = 1/4

Therefore, the fraction of essay for an hour can be calculated as;

= Fraction of the essay reviewed / Amount of time used

= 2/3 ÷ 1/4

= 2/3 × 4

= 8/3

= 2 2/3

Hence, She will review 2 2/3 essay.

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Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

The term "volume" refers to how much general space an object occupies. Unlike mass, volume changes depending on the surroundings. The mass of a substance in a given volume is referred to as its "density." It describes the relationship between mass and volume.

Here,

A cylinder has a volume of V = r2h.

As a result, V = r2[(1/3)]h is obtained by multiplying h by 1/3.

The (1/3) can be moved to the front to obtain V = [(1/3)]r2h because you are free to multiplied in any ratio you choose.

Thus, you would receive one-third of the initial mass.

What would occur if you increased the radius by 1/3 in contrast to this?

Next, you would have

=> V = π[(1/3)r]2h

=> V = π(1/9)r2h

=> V = (1/9)πr2h

You would then possess 1/9 of the volume.

Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

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Answer:

78

Step-by-step explanation:

a + 8b = 6 + 8 x 9 = 6 + 72 = 78

Answer: 78

Step-by-step explanation:

value of a=6

value of b=9

a+8b= 6+8*9

as the 8 will be multiplied by 9

6+8*9= 6+72

6+72 = 78

The transformation of f (x) exists g (x) = f (x) - 4.

A mathematical function using the following formula is an exponential function: f (x) = an x. where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

A function that has a positive constant increased to a variable exponent, other than 1, is referred to as an exponential function. By solving at a certain input value, a function is assessed. When the beginning value and growth rate are known, an exponential model can be discovered.

We observed that:

f (0) = 2

For the function g (x) we have:

g (0) = -2

Therefore,

g (x) = f (x) - 4

Looking for intersection with axis and we have:

g (0) = f (0) - 4

g (0) = 2 - 4

g (0) = -2 (correct demonstration)

The transformation of f (x) is: A. g (x) = f (x) - 4

Therefore, the correct answer is option A. g (x) = f (x) - 4.

The complete question is;

Two exponential functions, f and g, are shown in the figure below, where g is a transformation of f.

Which of the rules given below shows the transformation of f?

A. g(x) = f(x) - 4

B. g(x) = f(x - 4)

C. g(x) = f(x) + 4

D. g(x) = f(x + 4)

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When convert it into rectangular form we get x=-1/2 and y=0.

To convert a point in polar coordinates (r, θ) to rectangular coordinates (x, y), you can use the following formulas:

[tex]x = r * cos(θ) \\y = r * sin(θ)[/tex]

Where r is the distance from the origin to the point, and θ is the angle in radians between the positive x-axis and the line connecting the point to the origin.

Alternatively, you can also convert from rectangular to polar coordinates using the following formulas:

[tex]r = sqrt(x^2 + y^2)\\θ = atan2(y, x)[/tex]

Where x, y are the rectangular coordinates and atan2 is a function that computes the angle of a point in a cartesian plane.

In general, it's worth noting that the polar coordinates are often used in some physics and engineering problems, while the rectangular coordinates are often used in computer graphics, analytic geometry and other fields.

The angle of 1's inverse tangent is 45°. This is the outcome of translating to polar coordinates in the form (r,theta).

To convert it into rectangle equation we have

[tex]x=rcos(theta)\\y=rsin(theta)\\r=1\\theta= 3*pi/2\\x= cos(3*pi/2)\\x= -1/2\\y=sin(3*pi/2)\\y=0[/tex]

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