Mrs. Forsyth has 130 pieces of candy. She wants to split it into fifths for each of her classes. How
many pieces of candy will each class get?

Considering the definition of parallel and perpendicular line:

A linear equation o line can be expressed in the form y = mx + b.

where

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 9x+8y=-2. Expressed in the form y = mx + b, you get:

8y= -2 - 9x

y= (-9x -2)÷ 8

y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex]

Two lines are parallel if they have the same slope. So, in this case, the parallel line has a slope of  -[tex]\frac{9}{8}[/tex] and has a form of: y= -[tex]\frac{9}{8}[/tex]x + b

The line passes through the point (-3, 2). Replacing in the expression for parallel line:

2= -[tex]\frac{9}{8}[/tex]× (-3) + b

2= [tex]\frac{27}{8}[/tex] + b

2- [tex]\frac{27}{8}[/tex]= b

- [tex]\frac{11}{8}[/tex]= b

Finally, the equation of parallel line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{11}{8}[/tex].

The line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex].

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  -[tex]\frac{9}{8}[/tex]. So:

-[tex]\frac{9}{8}[/tex]× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-[tex]\frac{9}{8}[/tex])

slope perpendicular line= [tex]\frac{8}{9}[/tex]

So, the perpendicular line has a form of: y= [tex]\frac{8}{9}[/tex]x + b

The line passes through the point (-3, 2). Replacing in the expression for parallel line:

2= [tex]\frac{8}{9}[/tex]× (-3) + b

2= -[tex]\frac{8}{3}[/tex] + b

2+ [tex]\frac{8}{3}[/tex]= b

[tex]\frac{14}{3}[/tex]= b

Finally, the equation of of perpendicular line is y= [tex]\frac{8}{9}[/tex]x + [tex]\frac{14}{3}[/tex].

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Answer: The surface area is 173.2 mm²

Step-by-step explanation: If the four triangles are equilateral and one of the sides is 10 then all the other sides must be 10 as well, meaning that the surface area of each triangle is 43.3 mm². That means that to find the surface area of the whole pyramid you must multiply 43.3 by 4 because there are 4 separate triangles.

43.3 × 4 = 173.2

Answer:

b

Step-by-step explanation:

4 - 8 = -4 times 2 = -8

Answer:

Yes, by ASA congruence.

Step-by-step explanation:

Solving :

Hence, as 2 angles and a side of the triangles are equal, we can say they are congruent by ASA congruence.

[tex]\huge\underline{{\sf Answer}}[/tex]

[tex] \textbf{Let's check if the two triangles are } [/tex][tex] \textbf{congruent} [/tex] ~

[tex] \large\textsf{Given information } [/tex]:

[tex] \textsf{Two angles of a triangle is equal to corresponding} [/tex] [tex] \textsf{two angles of another triangle, and they} [/tex][tex] \textsf{have one side in common (should be equal} [/tex][tex] \textsf{for both) } [/tex]

[tex] \textsf{So, after analyzing this information, we can } [/tex][tex] \textsf{conclude that the two triangles are congruent by} [/tex][tex] \textsf{AAS congruency criteria.} [/tex]

[tex] \texttt{[ since two angles are equal and one} [/tex][tex] \texttt{non included side is common/equal ]} [/tex]

Answer:

[tex]\frac{8}{30}[/tex]

Step-by-step explanation:

Card(AUBUC)= Card(A)+card(B)+card(C)-Card (A∩B) -Card( A∩C)-Card(B∩C) +Card(A∩B∩C)

= 21 + 14 + 15 - 10 - 8 - 4 + 2

= 30

Then

Card(AUBUC) = 30

Card( A∩C) = 2 + 6 = 8

[tex]p\left( A\cap C\right) =\frac{card\left( A\cap C \right) }{card\left( A\cup B\cup C \right) }[/tex]

               [tex]=\frac{8}{30}[/tex]

Answer:

B. 11

Step-by-step explanation:

Hope this helps! ;-)

Answer:

11

Step-by-step explanation:

15-12/3

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

15-4 = 11

Answer:

B. 325

Step-by-step explanation:

y = the total value of the amount of papers he has to deliver each week

44x + 61 = y

(7 days in a week - sunday = 6 days)

44(6) + 61 = y

264 + 61 = y

325 = y

Answer:a function whose value decreases as the independent variable increases over a given range.

Step-by-step explanation:

Answer:

Your kid will be 9 years old.

Step-by-step explanation:

It's not relevant, that you are 14 now.

Answer: 9

Step-by-step explanation: Regardless of if you are 14 or not, 30-21=9

Statement 8 (x = 10/5 or x = 2) is given by the division property of equality. Then the correct option is B.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Suppose that we're taking about

It means, we divide p into q equal parts.

And each part is of value p/q

Statement 7 is given below.

5x - 10 = 0

Then statement 8 is given by the division property of equality.

5x = 10

 x = 10/5

 x = 2

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[tex]\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}[/tex]

Absolute value of a graph formula:

Identify the vertex : (h, k) = (6, -7)

Take two points: (6, -7), (9, -5)

 [tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}[/tex]

Join them to build the equation:   [tex]\bf{y = \dfrac{2}{3} |x - 6| - 7}[/tex]

Answer:

[tex]g(x)=\dfrac{2}{3}|x-6|-7[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]

-----------------------------------------------------------------------------------------

Parent function:  [tex]f(x)=|x|[/tex]

[tex]f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}[/tex]  

From inspection of the graph, the vertex of the transformed function is at (6, -7).  Therefore, there has been a translation of:

[tex]\textsf{6 units right}\implies f(x-6) =|x-6|[/tex]

[tex]\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-7[/tex]

From inspection of the graph, we can see that it has been stretched parallel to the y-axis:

[tex]\implies a\:f(x-6)-7=a|x-6|-7[/tex]

The line goes through point (0, -3)

Substituting this point into the above equation to find [tex]a[/tex]:

[tex]\implies a|0-6|-7=-3[/tex]

[tex]\implies 6a=4[/tex]

[tex]\implies a=\dfrac{2}{3}[/tex]

Therefore,

[tex]\implies g(x)=\dfrac{2}{3}|x-6|-7[/tex]

Answer:

(x-3) (x-3)

Step-by-step explanation:

[tex]4x {}^{2} - 24x + 36 \\ dividing \: through \: by \: 4 \\ x {}^{2} - 6x { }^{} + 9 \\ two \: numbers \: such \: that \: when \: you \: add \: them \: they \: give \: you \: - 6 \: and \: when \: you \: multiply \: them \: they \: give \: 9 \\ the \: numbers \: are \: \: - 3 \: and \: - 3 \\ x {}^{2} - 3x - 3x + 9 \\ x( x - 3) - 3(x - 3) \\ (x - 3)(x - 3)[/tex]

The expression for the amount of Meghan's newspaper for three months will be T = C - (9.95 x  3).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, expansion and division.

The account balance total can be calculated with the following equation where the variable T represents the final balance while the variable C represents her current balance before the three months.

T = C - (9.95 * 3)

The monthly charge is multiplied by the three months that Megan will be charged and then discounted from her current balance in order to give the new Total Balance after paying the subscription for the three months.

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Answer:

8000

Step-by-step explanation:

Natalie

Divide 40k by 2 to get 20k and divide 20k by 5 to get 4k we are at 10%

4k / 5 = 800 that means that every 2% is 800 now we multiply by 4x

To get 8% and we get 3200 and multiply by 20 representing the yrs

3200 x 20 = 64k + 40+ = 104k

Mackenzie

40k divide by 2 to get 50% 40k / 2 = 20k and now we divide by 5 to get 10% 20k / 5 = 4k now we divide by 10 to get the amount of each percents worth 4k / 10 = 400 we multiply by 9 to get the compounded interest

400 x 9 = 3600 multiply by 20 to get the compounded daily investment after 20yrs 3600 x 20 = 72k + 40k = 112k

112k - 104k = 8k

Answer: 153.93791 inches³

Step-by-step explanation:

Area of a circle = pi * r²

Area of a circle = pi * 7²

Area of a circle = 3.14159 * 49

Area of a circle = 153.93791 inches³

We can't see you answer choices, so select the best answer choice that is closest to 153.93791 in³

An ERRAND is a chore, but it is not a game and A CONNECTION is a bond, but it is not a separation.

An ERRAND is a chore, but it is not a game.

The correct vocabulary word from each drop-down menu that correctly complete the first sentences is errand.

A CONNECTION is a bond, but it is not a separation

The correct vocabulary word from each drop-down menu that correctly complete the second sentences is connection.

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Answer:

Step-by-step explanation:

Finding the hypotenuse of the triangular side :

Finding Surface Area :

Finding Volume :

The solution from the system of inequalities is (a). Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.

Let P represent the perimeter.

So, we have:

The perimeter is calculated using:

P = 2(x + y)

So, we have:

2(x + y) ≤ 28

y ≥ (x - 2)²

Next, we plot the system of inequalities (see attachment)

From the attached graph, we have some negative x values in the shaded region.

This means that not all solutions are viable

Hence, the true statement is (a)

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The probability that it will not rain on both Saturday and Sunday will be 0.2268.

From the information, meteorologist predicts that there is a 42% chance of rain on Saturday and a 54% chance of rain on Sunday.

The probability that it will not rain on both Saturday and Sunday will be:

= (1 - 42%) × (1 - 54%)

= 0.58 × 0.46

= 0.2268

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3:7 =

3/7

3/7 = x/35

7x = 105

x = 15

answer : clara borrowed 15 books

I think it would be 15, because 3 doesn't go in evenly into 35. You might have the order of the ratio messed up.

Probability that the next person will purchase more than one costume as a fraction in simplest form is; 11/113

We are given the data for number of people who visited the website and the number of costumes purchased in a single day as;

Number of visitors that purchased no costume = 27 visitors

Number of visitors that purchased exactly one costume = 75

Number of visitors that purchased more than one costume = 11

Total number of visitors = 27 + 75 + 11 = 113

Thus;

Probability that the next person will purchase more than one costume as a fraction in simplest form is;

P(purchase more than one costume) = 11/113

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Answer:

418

Step-by-step explanation:

The next term of the given sequence using first and second differences is; 104

We are given the sequence as;

8, 11, 19, 35, 62,.....

Thus, using the first and second differences, we have the sequence pattern as;

8          11            19           35               62         104

    3            8            16            27               42

            5           8             11             15

                   3            3             4

From the above pattern, we can see that the next term of the sequence is 104

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Answer:

x = 27.19

Step-by-step explanation:

Sin(54) =22/x

0.81=22/x

x0.81= 22

x = 27.19

[tex]f(x) = 3^x + \ln x -108 x\\\\f'(x) = 3^x \ln 3 + \dfrac 1x - 108\\\\f''(x) = 3^x \cdot 0+ \ln 3\cdot 3^x\cdot \ln (3)-x^{-1-1}-0= 3^x \cdot \ln^2 3 -x^{-2}\\ \\f'''(x) = 3^x \cdot 0 + \ln^2 (3) \cdot 3^x \cdot \ln (3) +2x^{-2-1} = 3^x \ln^3 (3)+2x^{-3}\\\\f''''(x) = 3^x \cdot 0 + \ln^3 (3) \cdot 3^x \ln(3) -3\cdot 2 x^{-3-1} = 3^x\ln^4 (3)-6x^{-4} \\\\\text{Hence the fourth derivative of f(x) is}~~ 3^x\ln^4 (3)-6x^{-4}.\\\\[/tex]

[tex]\textbf{Note:}\\\\\dfrac{d}{dx}(uv) = u \dfrac{dv}{dx} + v\dfrac{du}{dx}\\\\\dfrac{d}{dx} \ln (x) = \dfrac 1x\\\\\dfrac{d}{dx} a^x = a^x \ln a\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} (\text{Constant}) = 0[/tex]

The statement about the graphs is true is:  Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.

Graph curve is above the horizontal axis.

Let determine the area under the curve using this formula

Base of left and right triangle

Left  

Base = -3 - (-5)

Base= 2

Right

Base= 3 - (-3)

Base= 6

Right and left height

Height= 0.25

Hence:

Total area=(base× height)/2

Total area=[ (2×0.25)/2] + (6×0.25)/2

Total area=0.25+0.75

Total area=1

Therefore  Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.

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Answer:

Area=154.062 [tex]m^{2}[/tex]

Step-by-step explanation:

As Circumference of a circle is given by;

[tex]C=2\times \pi\times r[/tex]

As the circumference is 44m so we can calculate the value of r by using the above formula.

[tex]44=2\times \pi \times r\\\\\frac{44}{2\pi} =r\\\\\implies r=\frac{22}{\pi} =7.003 m[/tex]

Now to Calculate the Area of a Circle.

As the area of a circle is,

[tex]Area =\pi \times r^{2}\\ Area=\pi \times (7.003)^{2} \\Area=\pi \times 49.039\\Area=154.062m^{2}[/tex]

Answer:

A≈391.18

Step-by-step explanation:

The formula to find the surface area of a triangular prism is as follows:

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

Plug in . .

A=ah+bh+ch+[tex]\frac{1}{2}[/tex][tex]\sqrt{ a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4}[/tex]

A = 6 * 20 + 6 * 20 + 6 * 20 + [tex]\frac{1}{2}[/tex] * [tex]\sqrt{64 + 2 * (6 * 6)2 + 2 * (6 * 6)2 - 64 + 2 *(6 * 6)2 * 64}[/tex]

A≈391.18

Answer:

391.2 square cm

Step-by-step explanation:

  l = 20 cm  

Base area = 15.6 square cm

   [tex]\sf \boxed{\text{Surface area of triangular prism = Perimeter of base * l + 2*base area}}[/tex]

                                                        = (6+6+6)*20 + 2*15.6

                                                        = 18*20 + 31.2

                                                        = 360 +31.2

                                                         = 391.2 square cm