10. The table represents the relationship between the base length and the height of some parallelograms, Both measurements are in inches. What is the relationship between the base length and height of these parallelograms?

The true statement is The value of g(1) is 3 .

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

g(x)=f(x-3)

When x= 1

g(1) = f(-2)= 3

and, When x= -1

g(1) = f(-2)= -1

Hence, the true statement is The value of g(1) is 3 .

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Step-by-step explanation:

This is a Taylor series because our center is non-zero.

The goal of Taylor series is to approximate non polynomial functions using Calculus.

So let's be intuitive.

In order to be accurate, we need to match the center value at some center a.

We know that cos(pi/2)=0, so our first constant should be 0.

[tex]q(x) = 0[/tex]

Next, we must be spot on with the linear approximation

at x=pi/2

we know that

[tex] \frac{d}{dx} \cos(x) = - \sin(x) = - \sin( \frac{\pi}{2} ) = - 1[/tex]

We also want to divide this by 1! , which is just one so our constant there is

-1, since we want to use this as an linear approximation and we want to be general, and we have a center to stay in respect to,

our next term is

[tex] 0 - 1(x - \frac{\pi}{2} ) {}^{1} [/tex]

Next, up, we must be similar in concavity.

So we take the second derivative of cosine which is just

[tex] - \cos(x) = - \cos( \frac{\pi}{2} ) = 0[/tex]

Since our constant is 0, we can skip this, even if we divide by 2!

Our fourth term is the third derivative of cosine

which is

[tex] \sin(x) = \sin( \frac{\pi}{2} ) = 1[/tex]

We then divide that by 3!, which becomes

[tex] \frac{1}{6} [/tex]

since we want to use this as an cubic approximation and we want to be general, and we have a center to stay in respect to,

our next term is

[tex] - (x - \frac{\pi}{2} ) {}^{} + \frac{1}{6} (x - \frac{\pi}{2} ) {}^{3} [/tex]

Let do one more term,

we know the 5th term is the fourth derivative of cosine evaluated at x=pi/2, which is just 0 so we can skip it.

The 6th term is the fifth derivative of cosine evaluated at x=pi/2, which is -1, then we divide by 5!, so we get

[tex]q(x) = - (x - \frac{\pi}{2} ) + \frac{1}{6} (x - \frac{\pi}{2} ) {}^{3} - \frac{1}{120} ( x - \frac{\pi}{2} ) {}^{5} [/tex]

Using the approximations, plug in 1.5 for x and we get approximately

0.0707

Answer:

Step-by-step explanation:

1 foot=12inch

3000 feet=12 ×3000=36000 inches

72,000 inches=2 miles

36000 inches=(2÷72,000)×36,000=1 mile

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin x= 12/ 13

So, B = √13² - 12² = √169 - 144 = √25 = 5

cos x= -5/ 13

So, sin 2x= 2 sin x cos x =2 (12/13)(-5/13) = -120/169

and, cos 2x= 1- 2 sin²x

                  = 1- 2( 144 / 169)

                  = -119/ 169

and, tan 2x = sin 2x/ cos 2x = 120/ 169 / (- 119/ 169)= 120/ 119

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Answer:

  HAEC

Step-by-step explanation:

You want the code letters associated with lines 1–4 on the graph.

Has a y-intercept of -4, and a rise/run if 1/4. The equation is ...

  y = 1/4x -4  (H)

Has a y-intercept of -4, and a rise/run of 4/1 = 4. The equation is ...

  y = 4x -4  (A)

Has a y-intercept of 3, and a rise/run of -2/1 = -2. The equation is ...

  y = -2x +3  (E)

Has a y-intercept of +1 and a rise/run of 2/1 = 2. The equation is ...

   y = 2x +1  (C)

The code is HAEC.

The vertical intercepts is (4/3,0) (3,0) (1,0) and The horizontial intercepts is (0,72)

The end behavior is as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.

Function is a type of relation, or rule, that maps one input to specific single output.

Given the G(x) = -2(3x + 4)(x - 1)(x – 3)^2 as a polynomial function.

Since all the exponets will equal 0. The constant will just add to the term.

The leading degree is even. Thus Even Degree Polynomials like Quadratics tend to go approach positive infinity vertically as x approaches positive infinity, and as x approaches negative infinity, it approaches positive infinity vertically.

Our leading coefficient is negative which means our quadratic will get reflected across the x axis.

The end behavior is as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.

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Answer:

Step-by-step explanation:

ax² + bx + c = 0

D = b² - 4ac

If D > 0 , then quadratic equation has 2 roots.

If D = 0 , then quadratic equation has 1 roots.

If D > 0 , then quadratic equation has No roots in the set of real numbers.

~~~~~~~~~~~~~~~~~~~~

2y² + 4y = 3

2y² + 4y - 3 = 0

a = 2 , b = 4 , c = - 3

D = 4² - 4(2)( - 3) = 40 > 0 ( 2 solutions )

[tex]y_{12}[/tex] = ( - 4 ± 2√10 ) ÷ 4

[tex]y_{1}[/tex] = [tex]\frac{-2+\sqrt{10} }{2}[/tex]

[tex]y_{2}[/tex] = [tex]\frac{-2-\sqrt{10} }{2}[/tex]

Answer: 18

Step-by-step explanation:

[tex]\triangle HJK \cong \triangle HLK[/tex] by HL. Therefore, [tex]JK=2[/tex] by CPCTC.

Using the segment addition postulate, [tex]GK=9[/tex].

Furthermore, [tex]\triangle HGK \cong \triangle HMK[/tex] by HL. This means that [tex]MK=9[/tex] by CPCTC.

Using the segment addition postulate again, [tex]GM=9+9=18[/tex].

The distance AB between the two points is 5.7 units

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

A = (2, 2) and B =(-2, -2)

The distance between the two points can be calculated using the following distance equation

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where

(x, y) = (2, 2) and (-2, -2)

Substitute (x, y) = (2, 2) and (-2, -2) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

distance = √[(2 + 2)² + (2 + 2)²]

Evaluate

distance = 5.7

Hence, the distance is 5.7 units

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5.5km/hr is the speed at which he walks.

Two or more expressions with an Equal sign is called as Equation.

Given

w = walking speed

t = time walking = 2

Given, A man walks for 2 hours at a certain speed which is 2w

He then cycles at three times that seed for 4 hours.

We can form a equation by given data

2w + 3×w×4 = 77

2w+12w=77

14w = 77

Divide both sides by 14

w = 5.5 km/hr

Hence, 5.5km/hr is the speed at which he walks.

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The changes to the slope and y-intercept of this transformation are

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

g(a) = f(a) + k

Also, from the question, we have

k = 2

Using the above as a guide, we have the following:

Substitute the known values in the above equation, so, we have the following representation

g(a) = f(a) + 2

This means that

Slope of f(a) = Slope of g(a)

Also, we have

y-intercept of g(a) = y-intercept of f(a) + 2

Hence, the y-intercept of g(a) is 2 greater than the y-intercept of f(a)

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The time required to match the record is 41.37 seconds. The correct option is (c).

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The given problem can be solved as follows,

The remaining time for matching the record is given by,

73.4 - (20(¹/₄) + 11.78)

= 73.4 - (81/4 + 11.78)

= 73.4 - (20.25 + 11.78)

= 73.4 - 32.03

= 41.37

Hence, the time Julie have left to match the record is 41.37.

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The range of possible values for x is 0<x<20

The Range is the difference between the lowest and highest values.

In any triangle, the smallest angle is opposite to the smallest side.

So, In ΔABD , the side which faces ∠ABD is AD whose length is 32 units.....(1)

And, in ΔCBD, the side which faces ∠CBD is CD whose length is 20 units....(2)

Now, from equations (1) and (2) We get,

∠ABD < ∠CBD

So, ∠ABD lies between 0° to 48°

0<4x+8<48

Subtract 8 on both sides

-8<4x<40

Divide by 4

-2<x<10

As ∠ABD lies between 0° to 48°, so 0<x<10 is the range.

Hence, 0<x<10 is the range of possible values for x.

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Answer:

24

Step-by-step explanation:

60% of 40 is 24 because to find a percentage, multiply the percent you are trying to find (60%) by the number you are trying to find percent of (40) and divide the answer of 60x40 by 100.  60x40 is 2,400. 2,400 divided by 100 is 24. The width of the rectangle is 24ft

Answer:

1. Supplementary

2. Alternate exterior

Step-by-step explanation:

1. ∠1 and ∠2 are complementary because they both lie on the same straight line. If you had the values of these angles, they would add up to 180°

2. ∠1 and ∠8 are alternate exterior angles because they are on opposite sides of the transversal (the diagonal line from the bottom left to the top right) and they are on the outsides of the parallel lines. (∠1 is above the top horizontal line and ∠8 is below the bottom horizontal line.)

The inverse function of f(x) = -3x + 3 in slope-intercept form is g(y) = (-1/3)y + 1.

What is the inverse function?

The inverse function of a function f(x) is a function g(x) such that g(f(x)) = x for all x in the domain of f.

The given function is f(x) = -3x + 3. To find the inverse function, we can solve for x in terms of y:

y = -3x + 3

0 = -3x + y + 3

-y = -3x + 3

x = (-y + 3) / -3

The inverse function is then g(y) = (-y + 3) / -3. Rewriting this in slope-intercept form gives:

g(y) = (-1/3)y + 1

Hence, the inverse function of f(x) = -3x + 3 in slope-intercept form is g(y) = (-1/3)y + 1.

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For given data,

a) A scatter diagram is as shown below.

b) the coefficient of correlation is, r = 0.63

c) the linear regression equation (least-squares equation of the line) to predict weekly sales from advertising expenditures is : y = 3.2208x + 343.71, where x is the Advertising Costs and y be the Sales in dollars

d) when advertising costs are $32, the weekly sales would be 446.78 dollars.

In this question, we have been given that a retail merchant made a study to determine the relation between weekly advertising expenditures and sales.

The following data were recorded:

Advertising Costs, $ 40 20 25 20 30 50 40 20 50 40 25 50

Sales, $ 385 400 395 365 475 440 490 420 560 525 480 510

a) a scatter plot for the above data is as shown below.

b) the coefficient of correlation is:

r = √0.403

r = 0.63

c) the linear regression equation is:

y = 3.2208x + 343.71

where x is the weekly Advertising Costs and y be the Sales in dollars

d) the weekly sales when advertising costs are $32:

y = 3.2208(32) + 343.71

y = 446.78

So, when advertising costs are $32, the weekly sales would be 446.78 dollars.

Therefore, for given data:

a) A scatter diagram is as shown below.

b) the coefficient of correlation = 0.63

c) the linear regression equation: y = 3.2208x + 343.71

d) when advertising costs are $32, the weekly sales would be 446.78 dollars.

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The shortest distance between the two points is √[(c + 5)² + (6 - d)²]

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

G = (c, 6) and H = (-5, d)

The distance between the two points can be calculated using the following distance equation

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where

(x, y) = (c, 6) and (-5, d)

Substitute (x, y) = (c, 6) and (-5, d) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

distance = √[(c + 5)² + (6 - d)²]

Hence, the distance expression is √[(c + 5)² + (6 - d)²]

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Cost to fill the container = $ 462

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Various forms have various volumes.

The formula for the volume of a rectangular container is given by  

Here we have,

Dimensions of a container are 3yd × 5yd × 7 1/3 yd  

Here 7 1/3 = 22/3 yd

From the given formula,  

Area of the container =  3yd × 5yd × 22/3 yd  

= [tex](3 \times 5 \times \frac{22}{3} )yd^{3}[/tex]

= [tex]( 5 \times 22 )yd^{3}[/tex]      

= 110 yd³  

Given the cost per 1 yd³ = $ 4.20

=> cost of 110 yd³ = 110 × $ 4.20 = $ 462

Therefore,

Cost to fill the container = $ 462

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D, graph with a line from 0 comma 0 to 90 comma 30 and an x axis labeled time seconds and a y axis labeled sit ups represents the proportional relationship.

Explanation:

y = 3x

where x is the passage of time.

y stands for how many sit-ups there were.

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Average rate of change for interval 5 to 11 boxes is 4.5 , 11 to 20 boxes is 6 and 20 to 25 boxes is 3.2

Average rate of change can be defined as slope of function between two fixed values of x. It can also be defined as change in function per unit or we can say as an average.

Average rate of change (from x = a to x=b) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Given table can we represented as No.of boxes = x

Total weight = y

So, for x = 5 , y = 18

x = 11 , y = 45

x = 20 , y = 99

x = 25 , y = 115

(a) Average rate of change for Intervals

5 to 11 boxes = [tex]\frac{45 - 18}{11-5}=\frac{27}{6} = \frac{9}{2}[/tex]

= 4.5

11 to 20 boxes = [tex]\frac{99-45}{20-11} = \frac{54}{9}[/tex]

= 6

20 to 25 boxes = [tex]\frac{115-99}{25-20}=\frac{16}{5}[/tex]

= 3.2

(b) for interval of 11 to 20 boxes we have greatest average weight per box.

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Answer:

Coefficient of x

Write in the slope intercept form

35

Step-by-step explanation:

165 - 105x + 3y = 0  Subtract 165 from both sides and and 105x to both sides

3y = 105x - 165  Divide all the way through by 3

y = 35x - 55

The slope is the coefficient of x when the equation is written in the slope intercept form of the line.

The slope is 35

Answer:

-6v-1+v

collect the like terms

-6v + v - 1

you have

-5v-1

Answer:

answer is 5v-1

Step-by-step explanation:

add the common varribles which are V,

Answer:

Step-by-step explanation:

115 woman

Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.

What is the half-life of a substance?

Half-life is the time required for the amount of something to fall to half its initial value. The converse of half-life is doubling time.

The half-life of a substance is the time it takes for half of the initial mass of the substance to decay.

Since the half-life of Palladium-100 is 4 days, after 4 days, the mass of the sample will be reduced to half of its initial value. After 8 days, it will be reduced to a quarter of its initial value, and after 12 days it will be reduced to an eighth of its initial value.

We are given that after 12 days, the mass of the sample is 6 mg. This means that the initial mass of the sample was 8 * 6 mg = 48 mg.

After 7 weeks (7 * 7 = 49 days), the mass of the sample will be reduced by a factor of

              =  [tex]8^{(49/4) }[/tex]

             = [tex]8^{12.5}[/tex] =

approximately [tex]2.6 * 10^6[/tex]. The mass of the sample after 7 weeks will be approximately [tex]\frac{6 mg }{2.6 * 10^6}[/tex] = approximately [tex]2.3 * 10^{-6}[/tex] mg.

Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.

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The probability that the marble is red or blue is 0.6923 or 69.23% if the bag contains five red marbles, four blue marbles, and four yellow marbles. You randomly pick a marble.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

We have the total number of marbles = 5+4+4 =13

Total number of red and blue marble = 5+4 = 9

The probability that the marble is red or blue = 9/13 = 0.6923 or

= 69.23%

Thus, the probability that the marble is red or blue is 0.6923 or 69.23% if the bag contains five red marbles, four blue marbles, and four yellow marbles. You randomly pick a marble.

Hope this helps!!! :)

(Special thanks to JaneWright Brainly tutor!!!)

Answer:

66% and 2/3

Step-by-step explanation:

100% divided by 3 is 33% and 1/3

Hope that helps! :)

Therefore by solving the equations we get to know that 196 children and  200 adults were present on that day.

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.

Let's initially configure our system by giving the letters x and y meanings. Assume x is the number of kids and y is the number of adults.

Children are priced at $1.50, while adults are priced at $4.00. We multiply the total number of children, x, by 1.5 to get how much each child will cost. 1.5x is used to indicate this. We will use 4y for adults, whose entry fee is $4. On the specified day, $1094 in total revenue was earned. This sum requires the addition of 1.5x and 4y.

1.5x + 4y = 1094 works for the money equation involved.

Second equation: The total number of individuals present on the day is 283. X and Y, or the number of children and adults, must be added together to arrive at this figure.

x + y = 396

System of equations:

1.5x + 4y = 1094

x +   y = 396

Thus,

x + y = 396  

y = 396- x

Substitute y = 396 - x into the first equation.

1.5x + 4 (396 - x) = 1094

1.5x + 1584 - 4x = 1094  

1584 - 2.5x = 1094      

-2.5x = -490                  

x = 196

Substitute x =196 back into y = 396 - x

y = 396 - 196 = 200

Therefore by solving the equations we get to know that 196 children and  200 adults were present on that day.

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Using proportions, Angela can make 9.5 batch of cookies and the equation to model the solution is y = 2.25x

Proportion is an equation that defines that the two given ratios are equivalent to each other. However, in this case, we can write out an equation that shows the number of cookies she can make with the number of cups of flour available.

To do this, we need to set up a proportional equation with a constant of proportionality.

This is often written as

y = kx

For each batch, she needs 2 1/4 cups

Let's convert this into decimal which will give us 2.25 cups of flour.

y = 2.25x

A. The number of batch she can make will be

21 3/8 ÷ 2 1/4 = 9.5 batch

B) The equation to model the solution is y = 2.25x

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