1) Sarah received three fifths of her sister's book collection. If Sarah received 18
books, how many books did her sister have before giving any to Sarah?

The sequence of transformations that produces the blue figure from the red figure are;

A geometric transformation is the change to a geometric figure or shape by translating, reflecting, dilating, or rotating the figure.

The coordinates of the vertices of the red triangle are;

A(2, -2), B(2, -4), C(5, -4)

AB = -2 - (-4) = 2

BC = 5 - 2 = 3

AC = √((5 - 2)² + (-4 - (-2))²) = √(13)

The coordinates of the vertices of the blue triangle are;

D(-5, 5), E(-5, -1), and F(4, -1)

DE = 5 - (-1) = 6

EF = 4 - (-5) = 9

DF = √((4 - (-5))² + (-1 - 5)²) = 3·√(13)

The lengths of the sides of the blue triangle are DE/AB = 6/2 = 3 times the length of the sides of the red triangle

The points of the image of the red triangle following a dilation by a scale factor of 3 are;

A(2, -2) [tex]\underrightarrow{D_3}[/tex] A'(2 × 3, -2 × 3) = A'(6, -6)

B(2, -4)  [tex]\underrightarrow{D_3}[/tex] B'(2 × 3, -4 × 3) = B'(6, -12)

C(5, -4)  [tex]\underrightarrow{D_3}[/tex] C'(5 × 3, -4 × 3) = C'(15, -12)

The difference between the coordinates of the points A' and D are;

Horizontal translation = -5 - 6 = -11

Vertical translation = 5 - (-6) = 11

The triangle A'B'C' is translated 11 units to the 11 units to the left and 11 units upwards using the rule, [tex]T_{(-11,\, 11)}[/tex]

The sequence of transformation is a dilation by a scale factor of 3, centered at the origin, [tex]D_{3, \,O}[/tex] followed by a translation of 11 units to the left and 11 units to upwards.

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Answer:

C

Step-by-step explanation:

there are 1 x values that have the 2 different y value

Answer:

  7

Step-by-step explanation:

You want the integer length of the shortest third side that will form a triangle with sides 12 and 18.

The triangle inequality requires the sum of any two sides exceed the measure of the third side. If x is the short side, we want ...

  x +12 > 18

  x > 6 . . . . . . subtract 12

The smallest integer greater than 6 is 7.

The third side must be at least 7 units long.

__

Additional comment

Some authors write the triangle inequality as a+b≥c. If you use that version, then the shortest side can be 6 units. The resulting "triangle" will have zero area, and will look like a line segment 18 units long.

Answer:

1 yes y does vary directly with x

2 to find slope apply the given formula,

y2-y1/m2-m1

2/3 is slope

then the equation should be

y=2/3x

good luck

The two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14).

The general equation of a quadratic equation is -

y = ax² + bx + c

It has two possible roots. It has a degree of 2.

Given is the graph of the function, f(x) = x² - 5x - 7.

We have the following -

f(x) = x² - 5x - 7.

We will draw the graph of this function.

Now, the graph cuts the [x] axis at (-1.14) and (6.14).

Therefore, the two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14). The graph opens upwards.

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Answer:

-43.2

Step-by-step explanation:

2 x (6^2 (0.5-1.1))

2 x (6^2 (-0.6))

2 x (-36 x -0.6)

2 x (-21.6)

- 43.2

Answer:

Step-by-step explanation:2[6²(0.5-1.1)]

2[6²(-0.6)]

2[6×6(-0.6)]

2[36(-0.6)]

2[-21.6]

=> -43.2

a) The terms are:  10x, 12y,300

  The Coefficients are: 10,12

b) x intercept is (30,0). y intercept is (0,25)

c)  The three possible solutions:

(1,24), (8,18) , (6,20)

what are terms and coefficients?

Term could be a single number (positive or negative), a single variable (a letter), or a combination of multiple variables multiplied but never added or removed. Variables with numbers in front of them can be found in some terms. A coefficient is the number that appears in front of a phrase.

10x +12y=300

Terms:  10x, 12y,300

Coefficients: 10,12

Refer to the attachment for graph:

b) The locations on a Cartesian coordinate system known as intercepts are where the graph of an equation or function crosses the x- and y-axes.

From the graph, x intercept is (30,0). y intercept is (0,25)

c) solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

10x +12y=300

Find y when x=1:

10(1)+12y=300

10+12y=300

12y=300-10=290

y= 24.2 ≈ 24

Similarly, the three possible solutions:

(1,24), (8,18) , (6,20)

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The value of investment after 4 years would be $12600

What is investment?

Spending money on an item with the intention of seeing its value rise over time is known as investing. Sacrificing any current item, whether time, money, or effort, is necessary for investment. In the world of finance, investing is done in order to profit from the asset that is being put up for investment.

Main body:

f(n) = 3000(1.05)n

where n= no. of years invested

here n= 4

so total investment = 3000*1.05*4

                                = $12600

Hence the value of investment is $12600.

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The real width of the building is given by 47 meters.

Given that the actual length of the building is 62 meters.

In a scale drawing, the length of the building is 12.4 cm.

So, 12.4 cm = 62 meters

1 cm = 62/12.4 = 620/124 = 5 meters.

Also given that the width of building on scale drawing = 9.4 cm

Hence the real width of the building = 9.4 * 5 = 47 meters.

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The function h(x) is a translation of 4 units to the left, so the correct options is B.

h(x) = √(x + 4)

We know that h(x) is a transformation on the parent square root function:

f(x) = √x

If we look at the graphs, we can see h(x) is translated 4 units to the left.

Now, for a function f(x), we define a horizontal translation of N units as:

h(x) = f(x + N)

if  N < 0, the translation is to the right.

if N > 0, the translation is to the left.

In this case we have a translation of 4 units to the left, then N = 4, so we can write:

h(x)= f(x + 4)

Replacing the function f(x) we get:

h(x) = √(x + 4)

So the correct option is B.

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The equation is, 250+x =400

From the question, we have

The old energy level is 250.

Let the bar is added to the bag = x.

The new energy level is 400.

The equation is, 250+x =400

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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Answer:

16.57894736842105

Step-by-step explanation:

A/Q=

The multiplier of 0.5% is 0.005

A percentage multiplier is a number that is used to calculate a percentage of an amount

In order to determine 0.5% of a number we can multiply the number by a multiplier:

0.5% = 0.5/100 = 0.005

Therefore, 0.005 is the multiplier

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Answer:

(0, [tex]\frac{5}{3}[/tex] )

Step-by-step explanation:

3x + 6y = 10 → (1)

2x + 3y = 5 → (2)

multiplying (2) by - 2 and adding to (1) will eliminate y

- 4x - 6y = - 10 → (3)

add (1) and (3) term by term to eliminate y

- x + 0 = 0

- x = 0

x = 0

substitute x = 0 into either of the 2 equations and solve for x

substituting into (2)

2(0) + 3y = 5

3y = 5 ( divide both sides by 3 )

y = [tex]\frac{5}{3}[/tex]

solution is (0, [tex]\frac{5}{3}[/tex] )

Qualitative graphs depict the relationship between two quantities without including numerical values.

The benefit is that it only shows the overall trend of the effect. When we experiment with these variables, we can immediately see how the graph will look. This could validate our findings.

A quantitative relationship emerges as one variable influencing another, which can be seen with a graph. Examine how each variable is represented on the graph, as well as how quantitative relationships are stated using equations.

Quantitative data refers to data that's represented by numbers.

This is the result of graphing all of the data points. Look at that, our data points have formed a straight line! We can draw the line in using a ruler to make it more visible. We'll notice that the line passes through all of the points in our data, indicating that there is a definite relationship in our quantitative data.

Thus, qualitative graphs depict the relationship between two quantities without including numerical values.

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The equation for the total cost for Sports Haus is 500 + 10x and the equation for Fitness First is  50 + 25x   .

In the question ,

it is given that ,

Francie wants to join the health Club .

For the Sports Haus the initiation fees = $500

per month charge = $10

let the number of months be= "x" ,

so , the equation to represent the total cost for Sports Haus Club for x months is  500 + 10x .

For the Fitness First the initiation fees = $50

per month charge = $25

so , the equation to represent the total cost for Fitness First Club for x months is  50 + 25x .

Therefore , The equation for the total cost for Sports Haus is 500 + 10x and the equation for Fitness First is  50 + 25x   .

The given question is incomplete , the complete question is

Francine wants to join a health club and has narrowed it down to two choices. The Sports Haus charges an initiation fee of $ 500 and $ 10 per month. Fitness First has an initiation fee of $ 50 and charges $ 25 month . write an equation for the total cost of each health club for x months .

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After collision, Car A moves with a velocity of 4.1 m/s

An elastic collision is a collision in which there is no net loss in kinetic energy in the system due to the collision. Both momentum and kinetic energy are conserved in an elastic collision. It can be either one-dimensional or two-dimensional. In the real world, perfectly elastic collision is impossible because there is bound to be some energy conversion, however small. However, though there is no change in the linear momentum of the whole system, there is a change in the individual momenta of the involved components, which are equal and opposite in magnitude and cancel each other out and the initial energy is conserved.

The formula of elastic collision is given as

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Assuming after collision, car B has a velocity of 0m/s

281(2.82) + 209(1.72) = 281 * v + 0

792.42 + 359.48 = 281v

1151.9 = 281v

v = 1151.9 / 281

v = 4.1 m/s

The velocity of car A after collision is 4.1 m/s

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Answer: 7th Graders

Explanation:

Several people have gotten this question and 7th graders are the right choice

Answer:7th grade should be awarded !

Step-by-step explanation:

Answer:

it describes the proportion of individuals in a sample with a certain characteristic or trait

Step-by-step explanation:

to find sampling proportion, u have to divide the number of people or items who have the characteristic of interest by the total number of people/items in the sample.

It describes the percentage of people in a sample who possess a particular quality or attribute.

What is a sampling proportion?

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

Formula to calculate sampling proportion

p′ = x / n

where,

x: the number of successes

n: the sample size

p′:  sample proportion

Hence, it describes the percentage of people in a sample who possess a particular quality or attribute.

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The new function's equation is g(x) = (x - 2)² + 6

Given,

The parent function, f(x) = x²

We have to determine the equation for the new function g(x)

Vertical shift:

The parent function is clearly pushed 6 units upward from the graph.

The general formula to increase the c units on the graph is f(x) + c

As a result, by using the rule, the new function g(x)of vertical shift is provided by g(x) = x² + 6

Horizontal shift:

It is clear from the graph that the parent function has been moved 2 units to the right.

To move the graph's c units to the right, follow this basic formula: f(x - c)

Consequently, the new function g(xhorizontal )'s shift is given by g(x) = (x - 2)²

The new function g( x ) is as follows:

The equation results in the new function being shifted 2 units to the right and 6 units upward.

g(x) = (x - 2)² + 6

Therefore, the new function's equation is g(x) = (x - 2)² + 6

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The graph g(x)=log(-3x + 9)+4 is the outcome of a transformation on the function, f (x) = log (x), which can be visualized as a reflection across the y-axis. Then you contract by a factor of 3 horizontally, 3 to the right, and 4 to the up.

The connection between an independent variable and a dependent variable is established by a mathematical expression, rule, or law (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function:

Parent function: f(x) = log(x)

Transformation function: g(x) = log(-3x + 9) + 4

Step 1 -  Shift 3 unit right, to achieve the function

y = log (x - 3) (x - 3)

Step 2 - Reduce the graph by thrice by multiplying x by three:

y = log 3(x - 3) (x - 3)

Step 3 -  The formula y = log 3(x - 3) to line -3 = x is to be reflected to obtain: y = -3 (x - 3)

Step 4 - The function y = log 1 - 3(x - 3) should be translated by four units to reach

Therefore, the function can be transformed by reflection and translation.

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If she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be 3.

In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.

Given,

if she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be: 3.

$7.5= 1 hour various days

Sunday: $9.50 or ($7.50+$2.00) = 1 hour

Sunday = 4 + $9.50 = 38

Let Monday equal x $7.5 = 7.5x.

Let Wednesday equal x $7.5 equal x.

Let the total income be $83

Let x be the amount of hours.

Hence:

The first step is to create

Equation:

7.5x+7.5x+38=83

The next step is to determine the number of hours Laurie worked on Monday.

x =83-38÷ 7.5+7.5

x=83-38÷15

x=45÷15

3 hours =  x

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Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 3 and y- intercept c = 7 , then

y = - 3x + 7 ← equation of line

The total change in temperature is 58°F.

It should be noted that temperature simply means the degree of hotness and coldness in a body.

In this situation, the temperature in a town increased 18°F in 4 hours and the temperature decreased 40°F in the next 6 hours.

The change in temperature will be:

= Old temperature - New temperature

= 18°F - (-40°F)

= 18°F + 40°F

= 58°F

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Answer:

-10/9

Step-by-step explanation:

Use the slope formula: s=(y2-y1)/(x2-x1)
It doesn't matter the order.

Let's say 0 is x2 and 5 is y2; 9 is x1 and -5 is y1

Plug in the equation: s=[(5)-(-5)]/[(0)-(9)]

Simplify and solve: s=[5+5]/[-9]
                               s = -10/9

Answer:

Step-by-step explanation:

Ok:

First Problem with coin!

1. A coin has 2 sides and one of them is going to land up or down which means it has a chance of 1 out of 2.

1 out of 2=

1/2= 50%

Second Problem with spinner

2. There are 12 spaces on the spinner and three of those spaces are blue.

SO: 3 out of 12=

3/12=

1/4=

25%

Answers: 50% and 25%

IN FRACTION FORM: 1/2 and 1/4

Answer:

  see attached

Step-by-step explanation:

You want to construct an inscribed square in circle C with vertex A.

Reference the attached figure.

The desired inscribed square is AKFL.

The determinant of nxn matrix A  2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.

From the given information, the matrix will appear as follows

[tex]A= \left[\begin{array}{ccccc}2&1&......&1 &1\\0&2&......&1 &1\\0&0&2 ......&1 &1\\0&0&0 ......&2 &1\\0&0&0 ......&2 &1\\0&0&0 ......&0 &2\end{array}\right][/tex]

The matrix is nxn, there are n rows and n columns. As we can see, this matrix has an upper diagonal, and in terms of linear algebra, its determinant is the sum of all its principal diagonal members. As a result, the matrix's determinant is: 2^n

Therefore, the determinant of a n x n matrix A with 2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.

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The equation of the function g(x), considering the transformations, is given as follows:

[tex]g(x) = -3\log_5{(-x)} - 4[/tex]

The equation of function g(x) is obtained applying the transformations to the parent function f(x).

The parent function f(x) is given as follows:

f(x) = log5(x).

The vertical stretch by a factor of 3 is represented by a multiplication of f(x) by 3, hence:

g(x) = 3log5(x).

The reflection over the x-axis is represented by a multiplication of the function by -1, hence:

g(x) = -3log5(x).

The reflection over the y-axis is represented by a multiplication by -1 inside the domain of the function, hence:

g(x) = -3log5(-x).

The shift down by four units is represented by a subtraction of the function by four, hence:

g(x) = -3log5(-x) - 4.

Using Latex for better visualization:

[tex]g(x) = -3\log_5{(-x)} - 4[/tex]

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Answer: A number which is divided by 5, with the result as 50 less than if the number had been divided by 6 would be; -1500

How to solve Algebra Word Problems?

Let the number be x. We are asked that it is divided by 5, and the result is 50 less than if the number had been divided by 6;

(x/6) - (x/5) = 50

Multiply by 30 to get;

5x - 6x = 1500

-x = 1500

x = -1500

Let the older turtle be represented x and the younger one be y.

Todays age,

Older turtle = 11y years

Younger turtle = y years

Also the equation form as;

11y + 24 = 7(y + 24)

11y + 24 = 7y + 168

11y - 7y = 168 - 24

4y = 144

y = 144/4

y = 36

Thus;

Age of older turtle today = 396 years

Age of younger turtle today = 36 years

Therefore,

3(36 + t) = 396 + t

108 + 3t = 396 + t

2t = 292

t = 292/2

t = 146 years

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Step-by-step explanation: