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Which equation represents a linear function?
y – 2 = –5(x – 2)
x + 7 = –4(x + 8)
y – 3 = y(x + 4)
y + 9 = x(x – 1)

Answer:

Option A y-3=2(x-1)

Step-by-step explanation:

we know that

The equation of a line into point slope form is equal to

y-y1=m(x-x1)

In this problem we have

(x1,y1)=(1,3)

m=2

substitute

y-3=2(x-1)

Answer:

The correct answer is option C.  -6x³ - 6x

Step-by-step explanation:

It is given an expression,

(4x³ + 3x² - 6x) - ( 10x³ + 3x²)

To find the simplified form

(4x³ + 3x² - 6x) - ( 10x³ + 3x²) = 4x³ + 3x² - 6x - 10x³ - 3x²

 = 4x³ - 10x³ + 3x² - 3x² - 6x

 = -6x³ + 0 - 6x

 = -6x³ - 6x

Therefore the correct answer is option C.  -6x³ - 6x

Answer:  −6x3 − 6x

Step-by-step explanation:

Answer:

68°

Step-by-step explanation:

To find the angles represented by the percentages , you should have in mind that the total sum of all angles in the pie-chart equals 360°

The percentages given are;

The total percentages for the items

[tex]=34+8+11+12+15+20=100[/tex]

To get the angles represented by each percentage

Angle x=item/100 ×360°

Where x is the angle of an item in the circle graph

Calculating angles for carrot and potatoes

[tex]C=\frac{11}{100} *360=39.6\\\\\\P=\frac{8}{100} *360=28.8\\\\\\P+C=39.6+28.8=68.4[/tex]

The combined angle will be 68.4°

Answer:

Acute, Equilateral

Step-by-step explanation:

Acute because all angles (which are 60 degrees) are less than 90 degrees.

Equilateral because all sides are equal.

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Answer:

The correct options are

A.  Acute

E. Isosceles

F. Equilateral

Step-by-step explanation:

From the figure we can see a triangle.

To find the correct options

1). From figure we get  all the angles are equal.

Each angle is equal to 60°

60 < 90

Option A. Acute is TRUE

2). Also all the sides of the triangles are equal,

Therefore the given triangle is equilateral triangle.

Option F. Equilateral is TRUE

Every equilateral triangle is Isosceles triangle.

Therefore option D. is also true

Answer:

Option C.

[tex]x=2\sqrt{2}[/tex]

[tex]y=2\sqrt{6}[/tex]

Step-by-step explanation:

step 1

Find the value of x

In the right triangle of the figure

[tex]sin(30\°)=\frac{x}{4\sqrt{2}}[/tex] -----> opposite side angle of 30 degrees divided by the hypotenuse

Remember that

[tex]sin(30\°)=\frac{1}{2}[/tex]

so

[tex]\frac{1}{2}=\frac{x}{4\sqrt{2}}[/tex]

[tex]x=\frac{4\sqrt{2}}{2}[/tex]

[tex]x=2\sqrt{2}[/tex]

step 2

Find the value of y

In the right triangle of the figure

[tex]cos(30\°)=\frac{y}{4\sqrt{2}}[/tex] -----> adjacent side angle of 30 degrees divided by the hypotenuse

Remember that

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{\sqrt{3}}{2}=\frac{y}{4\sqrt{2}}[/tex]

[tex]y=\frac{4\sqrt{6}}{2}[/tex]

[tex]y=2\sqrt{6}[/tex]

the equation of the trend line is y = -7x + 4.

To find the equation of the trend line using two points, we need to determine the slope (m) and the y-intercept (b) of the line. The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.

For the points (-4, 32) and (7, -45), the slope would be:

m = (-45 - 32) / (7 - (-4))

m = (-77) / (11)

m = -7

Now, we use the slope and one point to find the y-intercept using the point-slope form of the equation of a line, y - y1 = m(x - x1), and then we convert it to the slope-intercept form, y = mx + b.

Using point (-4, 32), the equation becomes:

32 = -7(-4) + b

32 = 28 + b

b = 32 - 28

b = 4

So, the equation of the trend line is y = -7x + 4.

Answer:

[tex]\large\boxed{V=\dfrac{4}{3}\pi R^3=\dfrac{D^3}{6}\pi}\\\\\boxed{V=\dfrac{500\pi}{3}\ in^3\approx523.33\ in^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{A diameter}\ D=2R\Rightarrow R=\dfrac{D}{2}.\\\\\text{Therefore}\\\\V=\dfrac{4}{3}\pi\left(\dfrac{D}{2}\right)^3=\dfrac{4}{3}\pi\left(\dfrac{D^3}{8}\right)=\dfrac{D^3}{6}\pi[/tex]

[tex]\text{We have the dimater}\ D=10in.\ \text{Substitute:}\\\\V=\dfrac{10^3}{6}\pi=\dfrac{1000}{6}\pi=\dfrac{500\pi}{3}\ in^3[/tex]

For this case we have that by definition, the volume of a sphere is given by:

[tex]V = \frac {4} {3} \pi * r ^ 3[/tex]

Where:

r: It is the radius of the sphere

We are told as data that the diameter of the sphere is 10in, so the radius is 5in:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi\\V = 523.33in ^ 3[/tex]

Answer:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi[/tex]

Any of the three given expressions can be used to find the volume of the sphere.

Answer:

[tex]\boxed{2n+2}[/tex]

Step-by-step explanation:

You remove parenthesis.

-n-3+3n+5

Group like terms

 ↓

-n+3n-3+5

Add numbers from left to right.

-n+3n=2n

2n-3+5

Adding and subtracting numbers from left to right.

-3+5=2

2n+2 is the correct answer.

Answer:

2n+2

Step-by-step explanation:

-n+(-3)+3n+5

Combine like terms

-n +3n -3+5

2n +2

Answer:

180°

Step-by-step explanation:

(8y+17)°=(6x-7)°

(3x-29)°+(8y+17)°=180°

so,

(3x-29)°+(6x-7)°=180°

To solve the expression (6x-7)+(3x-29), we combine like terms. The 'x' terms (6x + 3x) sum up to 9x and the constants (-7 and -29) sum up to -36. Therefore, the simplified expression is 9x - 36.

The student wants to solve the expression (6x-7)+(3x-29). To do this,  you should combine like terms, which means you should add together the terms that have the same variable.

Step 1: Add the 'x' terms together. This would give us 6x + 3x which equals 9x.

Step 2: Then add the constants together, in this case -7 and -29, you get -36.

So, the simplified result of the expression (6x-7)+(3x-29) is 9x - 36.

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Answer:

OE. (2,0)

Step-by-step explanation:

Since x is by itself x equals 1 so the x value would be 1/1. The y intercept is 2 which means you began on the y axis 2 and x axis 0 and then you move 1/1 from that spot because of your x value or slope.

Answer:

6x - 10 + 10 = 5x - 13

6x = 5x -13

x = -13

Answer:

[tex]y=-0.10x+60[/tex]

Step-by-step explanation:

Let

y -----> gallons of water remaining in the barrel

x-----> number of minutes elapsed

we know that

Water leaks out of the barrel at a rate of 1 gallon every 10 minutes

so

[tex]1/10=0.10\frac{gal}{min}[/tex]

The linear equation that represent this situation is  

[tex]y=-0.10x+60[/tex]

The graph in the attached figure

Answer:

x^2-3x+6/x^2-2x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Options b and D

Step-by-step explanation:

It's a question of Boolean's algebra

We will find the truth values of each statement p, q, r, and s first.

p : An isosceles triangle has two congruent sides.

Means truth value is True

q ; A right angle measures 90°

Truth value of this statement will be True

r : Four Points are always coplanar.

Truth value of this statement will be False.

s : A decagon has 12 sides

Truth value of the statement will be False.

Now we come to the options.

a. Four points are always coplanar and a right angle measures 90°.

Here "and" means conjunction and truth value of conjuncion of two statements will be true if only both the statements are true.

r        q         r ∧ q

T        T            T

But the truth value is given as false so not the correct option.

b. Four points are always coplanar and a right angle measures 90°.

As we have discussed in option a. truth value of the conjunction is True so this option will be the correct option.

c. Four points are always coplanar or a right angle measures 90°

OR means it's a disjunction and truth value of disjunction is false only when both the statements are False.

r         q        r ∨ q

T        T           T

But the truth value is given as False, so this option is not correct.

d. Four points are always coplanar or a right angle measure 90°

As discussed in option c. Truth value will be True. so this option will be the correct option.

Options b and d are the correct options.  

Answer:

A=62cm

Step-by-step explanation:

Length : 5 cm

Width: 3 cm

Height: 2 cm

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Answer:

62 cm^2

Step-by-step explanation:

Each two lengths given forms a rectangle. There are two rectangles of each size. Find their areas and add them up.

2(5 cm * 3 cm) + 2(5 cm * 2 cm) + 2(3 cm * 2 cm) =

= 2(15 cm^2) + 2(10 cm^2 + 2(6 cm^2)

= 2(15 cm^2 + 10 cm^2 + 6 cm^2)

= 2(31 cm^2)

= 62 cm^2

Answer:

4 cm.

Step-by-step explanation:

Area of the shape =

136 =  6 * 14 + (h/2)(12 + 14)      where the last part is the area of the trapezoid.

84 +  13h = 136

13h = 138 - 84 = 52

h = 4 (answer).

Answer:

112

Step-by-step explanation:

Monday=14

Tuesday=2x14=28

Wednesday= 2x28=56

Thursday= 2x56=112

[tex]|\Omega|=9[/tex]

b)

[tex]|A|=2\\\\P(A)=\dfrac{2}{9}\approx22\%[/tex]

c)

[tex]|A|=3\\\\P(A)=\dfrac{3}{9}=\dfrac{1}{3}\approx33\%[/tex]

a) The possibility space is completed with the potential outcomes of spinning both spinner A and spinner B.

b) The probability of getting a negative score is 2/9.

c) The probability of scoring more than 3 is also 2/9.

a) **Possibility Space:**

```

                            Spinner A

                             2         4         6

Spinner B    3       1          -1        -3

                       6       4          0         -2

                       9       7          3          1

```

In the possibility space, each cell represents the outcome of spinning both spinner A and spinner B. The score is obtained by subtracting the number on spinner A from the number on spinner B.

b) **Probability of Getting a Negative Score:**

To calculate the probability of getting a negative score, count the number of occurrences where the result is negative and divide it by the total number of possible outcomes. In this case, there are two instances (-1 and -2) where the score is negative. The total number of outcomes is 9.

Probability of negative score = Number of negative outcomes / Total number of outcomes

Probability of negative score = 2 / 9

c) **Probability of Scoring More Than 3:**

To find the probability of scoring more than 3, count the number of occurrences where the result is greater than 3 and divide it by the total number of possible outcomes. In this case, there are two instances (4 and 7) where the score is more than 3.

Probability of scoring more than 3 = Number of outcomes > 3 / Total number of outcomes

Probability of scoring more than 3 = 2 / 9

Answer:

Step-by-step explanation:

The answer is TS ≅ HG. C

Answer:

The correct option is TS ≅ HG. As, The side TS is ≅ to side HG.

Step-by-step explanation:

Given information;

The triangle GHJ is rotated about a point x.

Which results in formation of another triangle STR.

Now, according to the given information if any triangle is rotated 90 degree about a point the two side will be ≅ to each other.

Hence, The side TS is ≅ to side HG.

Hence, option (c) is correct.

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Answer: D is correct dotted and shaded below

Step-by-step explanation:

It’s a dotted line because the symbol is < or >

Everything below the line will be shaded because it’s y<, if it were y> then everything would be shaded above

Answer:

A shaded region below a dashed boundary line

Step-by-step explanation:

Conveniently it has been established, that in inequalities graph dashed lines indicate that all the points ∈ line expressed by y< -1/2x+5 part of the inequality are not included. So we represent by shaded regions below dashed lines.

If this inequality was then expressed by y<= -1/2x +5 then a solid line would then represent.

Check it out below

bearing in mind that the rate of change will just be the slope or namely the derivative of the expression.

[tex]\bf f(x)=3+e^x(x-5)^3\implies \cfrac{df}{dx}=0+\stackrel{\textit{product rule}}{e^x(x-5)^3+\stackrel{\textit{chain rule}}{e^x\cdot 3(x-5)^2\cdot 1}} \\\\\\ \cfrac{df}{dx}=e^x(x-5)^3+3e^x(x-5)^2\implies \cfrac{df}{dx}=\stackrel{\textit{common factor}}{e^x(x-5)^2[(x-5)+3]} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{df}{dx}=e^x(x-5)^2(x-2)~\hfill[/tex]

Answer:

The resulting vector b - a is <-5 , 7>

The resulting vector 2a - b is <8 , -9>

Step-by-step explanation:

* Use the graph to solve the problem

- The vector a is <3 , -2>

- The vector b is <-2 , 5>

* We can add and subtract the vectors

∵ a = <3 , -2>

∵ b = <-2 , 5>

- To find b - a subtract a from b

∴ b - a = <-2 , 5> - <3 , -2> = <(-2 - 3) , (5 - -2)> = <(-5) , (7)>

∴ The resulting vector b - a is <-5 , 7>

* 2a means multiply vector a by 2

∵ a = <3 , -2>

∴ 2a = <(2 × 3) , (2 × -2) = <6 , -4>

* Now lets find the resulting vector 2a - b

- Subtract b from 2a

∵ 2a = <6 , -4>

∵ b = <-2 , 5>

∴ 2a - b = <6 , -4> - <-2 , 5> = <(6 - -2) , (-4 - 5> = <(8) , (-9)> = <8 , -9>

∴ The resulting vector 2a - b is <8 , -9>

Answer:

(-3,4)

Step-by-step explanation:

That means to reflect the point across the y-axis... If you draw (3,4) on the coordinate plane you should see (-3,4) is the reflection across the y-axis from that point.

Answer:

P' = (- 3, 4 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ), hence

P(3, 4 ) → P'(- 3, 4 )

Answer:

[tex]\large\boxed{x<\dfrac{6}{7}}[/tex]

Step-by-step explanation:

[tex]\dfrac{7x}{3}<2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{7x}{3\!\!\!\!\diagup_1}<(3)(2)\\\\7x<6\qquad\text{divide both sides by 7}\\\\x<\dfrac{6}{7}[/tex]

Answer:

x<6/7

Step-by-step explanation:

Multiply by 3 from both sides of equation.

3*7x/3<2*3

Simplify.

7x<6

Divide by 7 from both sides of equation.

7x/7<6/7

Simplify, to find the answer.

x<6/7 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

Possible values of dimensions are (24,16,2) or (24,8,4)

Step-by-step explanation:

We are given the volume of the Cuboid and length . We are required to find the possible values of width and height from this information.

Let us say that the width is x and height is y

Length = 24

Volume of a cuboid = length * width * height

Volume = 768

768=24*x*y

[tex]xy=\frac{768}{24}\\xy=32\\[/tex]

xy=32

Now the possible factors of 32

32=1*32 ( Which shall not be taken into consideration as length is already given as 24 and width or height can  not be more length)

32=2*16

32=4*8

Hence the possible values width are 8, 16 and that of height 4 and 2

Hence the possible values of dimensions are (24,16,2) or (24,8,4)

Answer:

x = 98

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠x is an exterior angle and

∠GFH and ∠FHG are the 2 opposite interior angles, hence

x = 53 + 45 = 98

The value of x is 98 degree.

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠GFH and ∠FHG are the 2 opposite interior angles to exterior angle 'x',

x = 53 + 45

x = 98

Hence, the value of x is 98 degree.

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For this case we must simplify the following expression:

[tex]\frac {\frac {4t ^ 2-16} {8}} {\frac {t-2} {6}} =[/tex]

Applying double C we have:

[tex]\frac {6 (4t ^ 2-16)} {8 (t-2)} =[/tex]

Simplifying:

[tex]\frac {3 (4t ^ 2-16)} {4 (t-2)} =[/tex]

We take common factor 4 from the parentheses of the numerator:

[tex]\frac {3 * 4 (t ^ 2-4)} {4 (t-2)} =[/tex]

We simplify:

[tex]\frac {3 (t ^ 2-4)} {(t-2)} =[/tex]

We factor the numerator:

[tex]t ^ 2-4 = (t + 2) (t-2)[/tex]

We rewrite the expression:

[tex]\frac {3 (t + 2) (t-2)} {(t-2)} =[/tex]

We simplify:

[tex]3 (t + 2) =\\3t + 6[/tex]

Answer:

[tex]3t + 6[/tex]

Answer:

B

Step-by-step explanation:

It is a function because it passes the vertical line test... (There is no vertical line you can draw that will go through 2 or more than 2 points.)