Every week Marcela deposits $45 in a bank account that she opened with an initial
deposit of $250, so that after n weeks her balance (in dollars) is 250 + 45n. Her
brother Ronnie withdraws $30 each week from his own bank account, which he
opened with an initial deposit of $145, so that after n weeks his balance is 145-
30n. Express the ratio of Marcela's balance to Ronnie's as a rational function, and
simplify

Segment AC was dilated by a scale factor of 2 to form A'C' measuring 16  units

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

Let us assume that segment AC was dilated by a scale factor of 2 to form C'A', hence:

A'C' = 2 * AC = 2 * 8 = 16 units

Segment AC was dilated by a scale factor of 2 to form A'C' measuring 16  units

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Home is 0.6 miles away from the store

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed x Time

Given:-

Total time taken by girl to complete the trip = 15 minutes = [tex]\frac{1}{4}[/tex] hours

Speed while riding going = 6 miles per hour

Speed while coming back = 4 miles per hour

Total time taken by girl  =

Time taken while going +   Time taken while coming back      - (1)

  Let x be distance from home to store

       [tex]\frac{x}{6}[/tex] =  Time taken while going

[tex]\frac{x}{4}[/tex] = Time taken while coming back

    Substituting in (1) we get

      [tex]\frac{1}{4} = \frac{x}{6} + \frac{x}{4}[/tex]

      [tex]\frac{1}{4} = \frac{2x + 3x}{12}[/tex]

       [tex]\frac{1}{4} = \frac{5x}{12}[/tex]

      [tex]x= \frac{12}{20}[/tex]

    x = 0.6 miles

Thus home is 0.6 miles away from the store

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The value of b in the expression is -2.

a + a + b = 14

b + b + c = 8

a + b + c = 18

Therefore,

2a + b = 14

2b + c = 8

c = 8 - 2b

Hence,

a + b + 8 - 2b = 18

a - b = 18 - 8

a - b = 10

2a + b = 14

a - b = 10

3a = 24

a = 8

8 - b = 10

b = 8 - 10

b = -2

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Answer:

a = 8

b = -2

c = 12

Step-by-step explanation:

a + a + b = 14

2a + b = 14 ⇒ ( 1 )

b + b + c = 8

2b + c = 8 ⇒ ( 2 )

a + b + c = 18 ⇒ ( 3 )

First, let us make a as the subject in equation 1.

2a + b = 14

2a = 14 - b

[tex]a=\frac{14-b}{2} \\a = 7-\frac{b}{2}[/tex]   ⇒ ( 4 )

Let us make c as the subject in equation 2.

2b + c = 8

c = 8 - 2b ⇒ ( 5 )

Now it is clear for us that, we can replace a & c with ( 7 - b / 2 ) & ( 8 - 2b ) respectively.        

And now let us solve the equation 3 to find the value of b.

[tex]a+b+c=18\\\\7-\frac{b}{2} +b+8-2b=18\\\\Combine\: \:like\:\: terms.\\\\[/tex]

[tex]15-\frac{b}{2} -b=18\\\\\frac{15*2}{1*2} -\frac{b}{2}-\frac{b*2}{1*2}=18\\\\\frac{30}{2} -\frac{b}{2}-\frac{2b}{2}=18\\\\\frac{30-3b}{2} =\frac{18}{1} \\\\Use\:\: cross\;\: multiplication[/tex]

[tex]30-3b=18*2\\\\30-3b=36\\\\30-36=3b\\\\-6=3b\\\\-2 = b[/tex]

And now let us find  the value of a

For that, let us use the equation 1. There, we can replace b with ( -2 ) to find the value of a.

[tex]2a+b=14\\\\2a-2=14\\\\2a = 14+2\\\\2a=16\\\\a=8[/tex]

Now, let us find the value of c.

For that, let us take the equation 2. There also, we can replace b with -2 to find the value of c.

[tex]2b+c=8\\\\2*-2+c=8\\\\-4+c=8\\\\c=8+4\\\\c=12[/tex]

Using the side-splitter theorem, the segment length that would complete the proportion is GJ.

It should be noted that the side splitter theorem states that when a line intersects two sides of a triangle and is also parallel to the third side, then it'll divide the sides proportionally.

From the information given, it can be deduced that EF and HJ are parallel while H is on the side EG and J is on GF. Therefore, according to the theorem, GH/HE = GJ/JF

Therefore, the correct option is GJ.

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Answer: C.

Step-by-step explanation:  Trust Me! It was correct on the Edge quiz! :)

The given equality 2 divided by 9 = 5/2 divided by 5/4 is seen to be; False because LHS ≠ RHS

We are given the equality;

2 divided by 9 = 5/2 divided by 5/4

We want to check whether the left hand side of the equality is equal to the right hand side. Thus;

Left hand side can be expressed as;

2 divided by 9 = 2/9

Now, right hand side can be expressed as;

5/2 ÷ 5/4

⇒ (5/2) * (4/5)

⇒ 2

Therefore we can see that LHS is not equal to RHS and so the equality is false.

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The question is incomplete. Below you will find the missing part of the question.

How many rabbits were there after x years? Write a function to represent this scenario.

[tex]8(2)^{x}[/tex] rabbits were there after x years.

The function form is [tex]f(x)=8(2)^{x}[/tex]

The number of rabbits released each year is 8.

During 0 year, there will be 8 rabbits;

During year 1, the number of rabbits will be 8+8 = 16, i.e. 8×2¹ = 16

Similarly, during the year 2, the number of rabbits will be  16+16 i.e. 8×2² = 32

So, according to the pattern we can say that the function would be  

[tex]f(x)=8(2)^{x}[/tex]

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Answer:

7 (option B)

Step-by-step explanation:

the area of a trapezoid can be found using the formula:

[tex]A = \frac{a+b}{2}h[/tex]

where

A: area

a: base

b: other base

h: height

here, we can plug in our known variables to solve for h (height)

A: 119

a: 10

b: 24

h: ??

[tex]A = \frac{a+b}{2}h[/tex]

[tex]119 = \frac{10+24}{2}h[/tex]

{now, simplify!}

[tex]119 = \frac{10+24}{2}h[/tex]         {add 10 + 24}

[tex]119 = \frac{34}{2}h[/tex]            {divide 34 by 2}

119 = 17 · h

119     =    17 · h

÷ 17       ÷17             {divide both sides by 17to isolate h}

7 = h

So, the height (h) of this trapezoid is 7

hope this helps! have a lovely day :)

The end behavior of the function is [tex]\mathrm{as}\:x\to \:+\infty \:,\:h\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:h\left(x\right)\to \:-\infty \:[/tex]

The function is given as:

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

Next, we plot the graph of the function (see attachment)

From the attached graph, we can see that:

The function approaches negative infinity, irrespective of the direction of the x value

Hence, the end behavior of the function is [tex]\mathrm{as}\:x\to \:+\infty \:,\:h\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:h\left(x\right)\to \:-\infty \:[/tex]

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Social-desirability biases is the sort of response bias that is the tendency of the survey respondent to answer the question in a manner that is favorable to others.

As Maria found that most respondents 98% of the voters were open to support women candidates. The social desirably bias poses a serious problem during the self-reporting as the bias interferes with the interpretations of the average tendencies.

As however during the anonymous survey of the voters or respondents showed only 80% of them would support the women candidate.

Hence the social desirability bias is the main culprit for such a response.

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The parabola opens down, the sign of the second difference is positive and the equation of the axis of symmetry is x = 1

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have given a graph of a parabola.

From the graph:

The parabola opens down.

The sign of the second difference is positive.

The coordinates of the vertex is at (1, 3)

The equation of the axis of symmetry is x = 1

The optimal value of the parabola is at y = 3

The optimal value is considered a max value.

The x-intercepts is at (-1, 0) and (3, 0)

The y-intercept is at (0, 5/2)

Thus, the parabola opens down, the sign of the second difference is positive and the equation of the axis of symmetry is x = 1

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The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ

An equation is an expression that shows the relationship between two or more variables and numbers.

Let f(x) and g(x) represent the value in the savings account of Jack and Susie respectively after x years. Hence:

f(x) = 1000(1.015)ˣ, g(x) = 800(1.015ˣ

Hence:

Total savings = 1000(1.015)ˣ + 800(1.015)ˣ = (1.015)ˣ[1000 + 800] = 1800(1.015)ˣ

The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ

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Based on the calculations, the total volume which the pair have altogether is equal to 19.8 Liters.

In Science, volume is a unit of measurement which indicates the capacity of a container and it has the following units:

Next, we would convert the volume of Madison's diesel in centiliter to liter as follows:

1 centiliter = 0.01 liter

940 centiliter = X liter

Cross-multiplying, we have:

X = 940 × 0.01

X = 9.4 L.

Total volume = 9.4 + 10.4

Total volume = 19.8 Liters.

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Answer: no solution

Step-by-step explanation:

if we simplify this equation, we derive that 9=2.

this is a false statement, which means this equation has no real solutions.

Answer: B: 11 and 12

Step-by-step explanation:

- An integer is simply a whole number

- So consecutive integers are simply whole numbers that follow each other (ex: 1, 2, 3)

- The square root of 125 (in decimals) is 11.1803398875, meaning it is higher than 11 but less than 12

- So 11.1803398875 falls between 11 and 12, making the answer B

hope this helps :)

The number of possible outcomes are 180.

To find the total number of possible outcomes for two or more events, multiply the number of outcomes for each event together.

Given that,

We have two types of rings Gold and platinum

For this event (material) we have 2 outcomes.

Each ring is available in 10 style

For this event (style) we have 10 outcomes.

Each ring is fitted with 9 gemstones

For this event (gem) we have 9 outcomes.

Total number of possible outcomes  = 2×10×9

                                                            = 180

Hence, The number of possible outcomes are 180.

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Answer:

Step-by-step explanation:

There are several ways you can find the values of an exponential function for different values of the independent variable. You can read them from its graph, evaluate the formula, or recognize the relationship between the values.

The graph shows you the population is 10 in year 1, up by a factor of 2 from the population of 5 in year 0. The exponential nature of the function means the population will double in each of the next few years:

  2 years: 2 × 10 = 20

  3 years: 2 × 20 = 40

  4 years: 2 × 40 = 80

__

Additional comment

You can always use a calculator to evaluate the function for different values of t.

Answer: False

Step-by-step explanation:

   This is not a function because the single input [x] of 6 has outputs [y] of 2 and 4, and the single input [x] of 12 has outputs [y] of 2 and 4.

   A function must have only one output [y-value] for every input [x-value].

The term that describes point N is centroid. The correct option is C. Centroid

The centroid of a triangle is the point in which the three medians of the triangle intersect.

The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.

In the given diagram, we can observe that the lines join the midpoints of each side to the corresponding opposite vertex.

Point N is the point where the lines intersect.

Hence, the term that describes point N is centroid. The correct option is C. Centroid

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Answer:

B. Circumcenter

Have an Amazing day/night!!

Answer:

(5d⁴ − 8)²

Step-by-step explanation:

I hope this is helpful!

Answer:

a. The graph is concave up in the interval 0 ≤ x ≤ +∞

b. The graph is concave down in the interval -∞ ≤ x ≤ 0

To answer the question, we need to know what intervals are

Intervals are range of values in which a function is valid. It can either be the range of values of input or output of the function.

From the graph, we see that the function is concave up in the interval 0 ≤ x ≤ +∞

So, the graph is concave up in the interval 0 ≤ x ≤ +∞

From the graph, we see that the function is concave down in the interval -∞ ≤ x ≤ 0

So, the graph is concave down in the interval -∞ ≤ x ≤ 0

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Subtract the largest power of 2 from 798 such that the difference is not negative.

2⁹ = 512 and 2¹⁰ = 1024, so the largest power of 2 smaller than 798 is 2⁹, and

798 = 512 + 286 = 2⁹ + 286

Repeat this process with the remainder, 286.

2⁸ = 256, so

286 = 256 + 30 = 2⁸ + 30

⇒   798 = 2⁹ + 2⁸ + 30

2⁴ = 16 and 2⁵ = 32, so

30 = 16 + 14 = 2⁴ + 14

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 14

2³ = 8, so

14 = 8 + 6 = 2³ + 6

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 6

2² = 4, so

6 = 4 + 2 = 2² + 2¹

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 2² + 2¹

or more completely,

798 = 1×2⁹ + 1×2⁸ + 0×2⁷ + 0×2⁶ + 0×2⁵ + 1×2⁴ + 1×2³ + 1×2² + 1×2¹ + 0×2⁰

Then the base-2 representation of 798 is

11 0001 1110₂

The largest possible volume of the given box is; 96.28 ft³

Let b be the length and the width of the base (length and width are the same since the base is square).

Let h be the height of the box.

The surface area of the box is;

S = b² + 4bh

We are given S = 100 ft². Thus;

b² + 4bh = 100

h = (100 - b²)/4b

Volume of the box in terms of b will be;

V(b) = b²h = b² * (100 - b²)/4b

V(b) = 25b - b³/4

The volume is maximum when dV/db = 0. Thus;

dV/db = 25 - 3b²/4

25 - 3b²/4 = 0

√(100/3) = b

b = 5.77 ft

Thus;

h = (100 - (√(100/3)²)/4(5.77)

h = 2.8885 ft

Thus;

Largest volume = [√(100/3)]² * 2.8885

Largest Volume = 96.28 ft³

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The correct matching of the ordered pairs and the line they are on are:

The slope of the first pair is:

= (3 - (-3)) / (-5 - (-5))

= No slope as slope is 0

The slope of the second pair is:

= (-7 - (-1)) / (-1 - (-7))

= -1

The slope for the third pair is:

= (-2 - (-2)) / (6 - (-6))

= 0 or No slope

Rest of the question is:

slope = -1

No slope

No slope

slope = 2

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Answer: vertical line- (-5,-3) and (-5,3)

neither- (-7,1) and (-1,-7)

horizontal line- (-6,-2) and (6,-2)

hopefully this helps

Step-by-step explanation:

Answer:

They get 15×9=135

135÷15=9 is your answer

Answer: 15, 15, 16, 21, 23, 29

Step-by-step explanation:

The change in volume is -88π

The volume is nothing but the amount of space occupied by a three-dimensional figure as measured in cubic units.

Volume Change is defined as the variation in the existing volume of the service type which is provided by the Supplier under the Agreement

The radius is decreasing at 2 inches per minute

The height is given as decreasing at 4 inches per minute

So let [tex]\frac{dr}{dt}=-2[/tex] and

[tex]\frac{dh}{dt}=-4[/tex]

and we have radius r=6,

                     height h=5

The volume of the cone is represented by V as V=[tex]\frac{1}{3}\pi r^{2}h[/tex]

Then

[tex]\frac{dv}{dt}=\frac{\pi }{3}[r^{2}\frac{dh}{dt} +h*2r\frac{dr}{dt}][/tex]

[tex]=\frac{\pi }{3}[6^{2}(-4)+5*2(6)(-2)][/tex]

[tex]=\frac{\pi }{3}[36(-4)+5(12)(-2)]\\ =\frac{\pi }{3}[-144+(-120)]\\ =\frac{-264}{3}\pi \\ =-88\pi[/tex]

So the volume change is [tex]-88\pi[/tex]

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Work Shown:

f(x) = 5x - 7

f(3) = 5(3) - 7 .... every x replaced with 3

f(3) = 15 - 7

f(3) = 8

[tex] \: [/tex]

Given :

To Find :

Calculating the value of x :

[tex]\sf : \implies \: 5x - 7[/tex]

[tex]\sf : \implies \: 5(3) - 7[/tex]

[tex]\sf : \implies \: 15 - 7[/tex]

[tex]\bf : \implies \: 8[/tex]

Hence,

[tex] \implies \boxed{ \bf \: \therefore \: The \: value \: of \: x \: is \: 8 \: } \\ \\ [/tex]

[tex]\sqrt{(24-0)^{2}+(10-0)^{2}}=\boxed{26}[/tex]

Answer:

26

Step-by-step explanation:

√(24 - 0)2 + (10 - 0)2

= √(24)2 + (10)2

= √676 and that would equal

26

The expected value on playing this game is -5/36.

Given: 2 gold marbles, 9 silver marbles, and 24 black marbles.If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.

To find: Expected value on playing the game

Chance of occurrence of  gold = 1/36

Chance of occurrence of silver = 9/36

Chance of occurrence of  black = 26/36

On multiplying the given probability of occurence with the amount you would lose or win

we get,

1/36 * 3 + 9/36 * 2 - 26/36 * 1

3/36 + 18/36 - 26/36

=$ -5/36

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Answer:

none

Step-by-step explanation:

(8-5)=3

8-5÷23

=179/23