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Since the graph of g is translated vertically downward by 3 units, the graph of function h is equal to h(x) = 2x² - 10.

In Mathematics, there are different types of transformation and these include the following:

A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

Since the graph of g is translated vertically downward by 3 units, the graph of function h would be represented by the following expression:

Note: g(x) = 2x² - 7

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

h(x) = 2x² - 7 - 3.

h(x) = 2x² - 10.

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Answer:

Step-by-step explanation:

Based on the dimensions of the semicircle and the rectangle, the approximate area that Ysau paints is  514 ft²

First, find the area of the rectangle:

= 24 x 12

= 288 ft²

The area of the semi-circle is the area of a circle divided by two. The radius is half of the longer side of the rectangle:

= 24 / 2

= 12 ft

Area of the semicircle is:

= (22/7 x 12 x 12) / 2

= 226 ft²

The total approximate area is:

= 226 + 288

= 514 ft²

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Answer:

25 miles per gallon

Step-by-step explanation:

Because if 2 gallons is 50 miles then one gallon has to be 25 miles per gallon

the probability that a random selected student walks to the school is 19.5%, the correct option is D.

We want to find the probability that a random selected student walks to the school.

To find it, we just need to take the quotient between the number of students that walk to the school and the total number of students.

The number of students that walk to the school is:

42 + 36 = 78

The total number of students is:

85 + 77 + 30 + 47 + 42 + 36 + 44 + 39 = 400

Then the probability is:

P = 78/400 = 0.195

To get this in percentage form, we just multiply by 100%.

0.195*100% = 19.5%

The correct option is D.

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The value of x on the line segment is 8

The given parameters are:

AB = 2x + 7

AC = 7x - 3

BC = 4x - 2

The above means that the point B is on the line segment AC

So, we have:

AC = AB  + BC

This gives

2x + 7 + 4x - 2 = 7x - 3

Evaluate the like terms

-x = -8

Divide both sides by -1

x = 8

Hence, the value of x on the line segment is 8

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Total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

As given in the question,

Macro earns commission rate of 6% for the first $6500

And 9% on sales over $6500

Out of $10,500

For first $6500 Commission =(6500 × 6)/ 100

                                            = $390

For $ (10,500 - 6,500 = 4000) commission = (4000 × 9)/ 100

                                                                   = $360

Total graduated commission on sales of $10,500 = $( 390 + 360)

                                                                             = $750

Therefore, total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

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Fraction of members in the club that prefer hot chocolate = [tex]\frac{7}{40}[/tex]

It's Given that :

A sports club has 80 participants.

Senior Members = 25

Junior Members = 18

Adult Members = 80 - (25 + 18) = 80 - 43 = 37

JUNIOR MEMBERS :

Prefers tea = 10

Prefers Coffee = 2

Prefers hot chocolate = 18 - (10 + 2) = 18 - 12 = 6

SENIOR MEMBERS :

Prefers tea = 4

Prefers coffee = 13

Prefers hot chocolate = 25 - (4 + 13) = 25 - 17 = 8

ADULT MEMBERS :

Prefers tea = 28 - (10 + 4) = 28 - 14 = 14

Prefers coffee = 37 - 14 = 23

Prefers hot chocolate = 0 (none)

Calculation of Fraction of members in the club that prefer hot chocolate = 8 + 6 = 14 members out of 80 members

= [tex]\frac{14}{80} = \frac{7}{40}[/tex]

Therefore 7 / 40 of members prefer hot chocolate.

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Answer:

46, 94

Step-by-step explanation:

hope this works for you :)

(a)Symmetric matrix -

Let matrix A be of order 3×3 =

                                  [tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]

So, the transpose of A will be -

A' =

                                  [tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]

So, we can say that A=A'. So, it is symmetric.

(b) Skew - symmetric matrix -

Let us consider a matrix B =

                                  [tex]\left[\begin{array}{ccc}0&-6&4\\-6&0&7\\4&7&0\end{array}\right][/tex]

matrix B is said to be skew-symmetric if aij =−aji.

(B' =−B)

B'  =    

                                 [tex]\left[\begin{array}{ccc}0&6&-4\\6&0&-7\\-4&-7&0\end{array}\right][/tex]

(c) A + A′ is a symmetric matrix for any square matrix A with real number entries, whereas A - A′ is a skew-symmetric matrix.

Proof: If B = A + A', then B ′ = (A + A ) ′

(A + B)′ = A′ + B′, thus = A′ + (A′)′

(as (A′)′ =A) = A′ + A

= B (because B + A = B + A′)

B = A+A′ is a symmetric matrix as a result.

Let C now equal A-A′.

Why does C' equal (A-A′)′=(A′)′?

= A′ - A (Why?)

=- (A - A′) = - C

A - A′ is a skew-symmetric matrix as a result.

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Answer:

1/8

Step-by-step explanation:

When Mai-Lin's target heart rate is 153, then her age is 16 years.

From the information, the The American Heart Association suggests a target heart rate of T=0.75(220-a),

where T = person's target heart rate

a = his or her age.

Therefore, when the heart rate is 153, the age will be:

T = 0.75(220 - a)

153 = 165 - 0.75a

0.75a = 165 - 153

0.75a = 12

Divide

a = 12/0.75

a = 16

The person's age is 16 years.

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greatest to smallest :  [tex]= \sqrt[3]{88} ,\sqrt{19} ,\frac{28}{9}[/tex]

Fraction: A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator

Square root: In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = 16

Use this fraction calculator for adding, subtracting, multiplying, and dividing fractions. Answers are fractions in the lowest terms or mixed numbers in reduced form.

Input proper or improper fractions, select the math sign, and click Calculate. This is a fraction calculator with steps shown in the solution.

If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.

Solution :

[tex]\sqrt[3]{88} \\\sqrt[3]{2.2.2.11} \\2\sqrt[3]{11} \\\sqrt[3]{11} = 2.224\\2.2.224\\4.448 ...(1)\\\\\\\frac{28}{9} = 3.333 ...(2)\\\\ \sqrt{19} = 4.359 ...(3)\\\\Form 1 , 2 & 3 \\\\greatest number to smallest number = 4.448 , 4.359 ,3.333\\= \sqrt[3]{88} ,\sqrt{19} ,\frac{28}{9}[/tex]

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Answer:

125

Step-by-step explanation:

105 - (-20) = 105 + 20 = 125

Values at one, two and three standard deviations are 77.9, 82.8 and 87.7 respectively. Values at -1, -2 and -3 standard deviations are 68.1, 63.2 and 58.3 respectively.

The average grade given = 73

So, the mean, μ = 73

The standard deviation, σ = 4.9

We need to find the 1,2 and 3 standard deviations and -1, -2 and -3 deviations from the mean.

We use the formula z = μ + nσ to find the values at nth deviations.

When n = 1

z = 73 + 1 x 4.9 = 77.9

When n = 2

z = 73 + 2 x 4.9 = 82.8

When n = 3

z = 73 + 3 x 4.9 = 87.7

When n = -1

z = 73 -1 x 4.9 = 68.1

When n = -2

z = 73 - 2 x 4.9 = 63.2

When n = -3

z = 73 - 3 x 4.9 = 58.3

Hence, these are the required values.

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Answer:

For sure, A and C. However, I cannot fully read the last one.

Step-by-step explanation:

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Ava and Wyatt will take 4 days to be on the same page of the book.

X-values must be chosen and entered into the equation in order to graph a function. You will obtain a y-value once those values have been entered into the equation. A single point's coordinates are made up of its x and y values.

From the given question we can get:

A = 10 ₊ 20t

W = 30 ₊ 15t

Graph the each function to get the number of days.

A function can only be graphed if X-values are selected and put into the equation. Once those values are introduced into the equation, a y-value will be produced. The values of x and y are the coordinates of a single point.

Hence we get the number of days as 4. and the graph is attached below.

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The current time is 08 : 09 pm

The given parameters are

Time = 7 : 40 pm

Minutes added = 89 minutes

The current time is calculated as

Current time = Time + Minutes added

So, we have

Current time = 7 : 40 pm + 89 minutes

Evaluate the sum

Current time = 7 : 129 pm

Rewrite properly as

Current time = 08 : 09 pm

Hence, the current time is 08 : 09 pm

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Answer: I hope this helps.

Step-by-step explanation:

You get 1750 points from the 35 correct moves (35 x 50) and you get -432 points from time taken (144 x -3) therefore you end the game with 1318 points.

1318 Points.

Answer: 204

Step-by-step explanation:

(14+3)(2 x 6)=

(17)(2 x 6)=

(17)(12)=

17*12=

17*(10+2)=

17*10+17*2=

170+34=204

Answer:204

Step-by-step explanation:

The coordinates of the image of the vertices of the polygon are A''(x, y) = (1, - 2), B''(x, y) = (2, - 2), C''(x, y) = (0, - 1), D''(x, y) = (- 1, - 2) and E''(x, y) = (- 2, - 1).

Rigid transformations are transformations applied on geometric loci such that Euclidean distances in such constructions are conserved. Translations and dilations are common examples of rigid transformations.

If we know that A(x, y) = (- 6, 0), B(x, y) = (- 3, 0), C(x, y) = (0, - 3), D(x, y) = (- 3, - 6) and E(x, y) = (- 6, - 3), then the coordinates of the image are determined below:

Translation

A'(x, y) = (- 6, 0) + (9, - 6)

A'(x, y) = (3, - 6)

B'(x, y) = (- 3, 0) + (9, - 6)

B'(x, y) = (6, - 6)

C'(x, y) = (0, - 3) + (9, - 6)

C'(x, y) = (9, - 9)

D'(x, y) = (- 3, - 6) + (9, - 6)

D'(x, y) = (6, - 12)

Dilation

A''(x, y) = (1 / 3) · (3, - 6)

A''(x, y) = (1, - 2)

B''(x, y) = (1 / 3) · (6, - 6)

B''(x, y) = (2, - 2)

C''(x, y) = (1 / 3) · (0, - 3)

C''(x, y) = (0, - 1)

D''(x, y) = (1 / 3) · (- 3, - 6)

D''(x, y) = (- 1, - 2)

E''(x, y) = (1 / 3) · (- 6, - 3)

E''(x, y) = (- 2, - 1)

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Answer: a=2√5

Step-by-step explanation:

We have a right-angled isosceles triangle

Hence, a=2√5

The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given that 180 mg is present at t = 0 hours.

After t = 33 hours, substance left = 90mg

By unitary method, after = 1 hour, substance left = [tex]180-\frac{90}{33}=180 -\frac{30}{11}[/tex]mg

The substance left after t = 43 hours = [tex]180 - \frac{30\times43}{11}= 180 - \frac{1290}{11}=180 - 117=62.7273mg[/tex]

Hence, The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.

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The lateral area of  right octagonal prism = 672 in^2.

An example of a prismatic uniform polyhedron is the octagonal prism, or op. There are 2 octagons as well as 8 squares in it. Each vertex connects two squares and one octagon. As the name implies, it is an octagonal-based prism.

Three-dimensional geometry is a solid figure, item, or shape comprising three dimensions—length, breadth, as well as height.. Three-dimensional structures have height, which is equivalent to thickness or depth, unlike two-dimensional shapes.

Solve for lateral surface area:

altitude = 12

base = 7

AL=8ah

Putting the value we get:

AL=8 * 12 * 7

Al = 672 in^2

the lateral area of  right octagonal prism = 672 in^2.

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The answer choice which correctly represents an equivalent expression to that which is given as in the task content is; −30 + (−70) + (−40).

It follows from the task content that the expression whose equivalent is to be determined is; −30 + (−40) + (−70).

Therefore, since it follows from the associative property of addition that;

a + b + c = a + c + b.

Therefore, same can be said for the expression as given in the task content where;

-30 + (-40) + (-70) = -30 + (-70) + (-40).

Ultimately, the required equivalent expression is; −30+(−70)+(−40); negative 30 plus open parenthesis negative 70 close parenthesis plus open parenthesis negative 40 close parenthesis

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Answer:

y-coordinate

Step-by-step explanation:

x-intercepts lie on the x-axis. On the x-axis, y=0 while the x value is changing.

Answer: Set the Y equal to zero and solve for x

Step-by-step explanation: