8. Complete the table below by drawing an example of each shape.

Answer:

8 units

Step-by-step explanation:

ratios  

(x-3) /( x+1)  = (x-2)/(x+3)     cross multiply

x^2 -x -2 = x^2 - 9

  -x - 2 + 9 = 0

    x = 7          

           so TS = x + 1 = 8 units

Answer:

1 : 4

Step-by-step explanation:

3.5 : 14 ( divide both parts by 3.5 )

= 1 : 4

Answer:

16.5 meters

Step-by-step explanation:

The length of an arc of a circle = 2πr(C/360°) ;where:

C is the central angle of the arc,

R is the radius of the arc

Length of the arc = 2π(7)(135/360)

= 16.493

= 16.5 metres (approx.)

Answer:

Arc Length: 5.25π or [tex]\frac{21}{4} \pi[/tex]

Explanation:

An arc is the part of the circumference of a circle.

Formula:

[tex]\sf Arc \ Length = \dfrac{\theta}{360} \ \times \ 2\pi \ \times radius[/tex]

If applied:

[tex]\sf Arc \ Length = \dfrac{135}{360} \ \times \ 2\pi \ \times 7[/tex]

[tex]\sf Arc \ Length = \dfrac{3}{8} \ \times \ 14\pi[/tex]

[tex]\sf Arc \ Length = \dfrac{21}{4} \pi[/tex]

[tex]\sf Arc \ Length = 5.25 \pi[/tex]

Buford should use 7.5 pounds of the 50% corn bag.

A system of linear equation is an equation containing two different equations with variables and the coefficient.

From the given information, let:

Sp, we can a system of a linear equation that says:

x + y = 30

0.5x + 0.9y = 0.8(30)

Using elimination method

x + y = 30

-

x - 1.8y = -48

0 - 0.8y = -18

y = 18/0.8

y = 22.5

From x + y = 30

x = 30 - 22.5

x = 7.5

Therefore, we can conclude that he should use 7.5 pounds of the 50% corn bag.

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If there are 12 coins under the couch and every coin is either a nickel or a penny and together they are forming 32 cents then the equations which represent the problem will be x+y=12, 0.01x+0.05y=0.32. The correct option is B which is x+y=12, 0.01x+0.05y=0.32.

Given There are 12 coins and total money is 32 cents.

Let the number of pennies be x and the number of  nickels be y.

According to question there are 12 coins so the first equation becomes:

x+y=12.

Then we have been told that together they amount to 32 cents.

We know that 1 penny is 1 cent coin and 1 nickel is 5 cent coin so the equation becomes :

1*x+5*x=32

x+5y=32

converting into dollar

0.01x+0.05y=0.32.

Hence the right equations showing the problem of nickel and pennies are x+y=12, 0.01x+0.05y=0.32.

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The limit of the nth term of a sequence does not exist option (D) is correct.

A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.

We have an expression:

[tex]= \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]

Applying limit:

[tex]= \lim_{n \to \infty} \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]

[tex]=\lim _{n\to \infty \:} n \left(\dfrac{2+\dfrac{25}{n^3}+\dfrac{32}{n^4}-\dfrac{15}{n^5}}{6+\dfrac{2}{n}-\dfrac{11}{n^2}-\dfrac{2}{n^3}+\dfrac{17}{n^4}}\right)[/tex]

= ∞ = The limit does not exist

Thus, the limit of the nth term of a sequence does not exist option (D) is correct.

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Answer:

8 is correct.

Mark as brainlist, thanks me, and rate. Hope it helps you!!!

Answer:

(x-7)(x+6)

Step-by-step explanation:

Answer:

y= 2x - 3

Step-by-step explanation:

To calculate the slope (or gradient) of a line, take two points on the line whose x and y values are easy to read. Then divide the difference of they y-coordinate values by the difference of their x-coordinate values.

Here I have taken the points p (3, 3) and q (1, -1) to calculate the slope.

• slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex]

         = [tex]\frac{3 - (-1)}{3 - 1}[/tex]

         = [tex]\frac{4}{2}[/tex]

         = 2  

The intercept is the y-coordinate value of the point at which the line crosses ("intercepts") the y-axis. I've marked the intercept point with a green line.

• intercept = -3

The slope-intercept equation of a line takes the form:

y = mx + c

where 'm' is the slope and 'c' is the y-intercept.

Substituting the values we found into the equation gives us:

y = 2x + (-3)

∴ y = 2x - 3

See below for the verification of ∠ACD =  ∠ABC + ∠BAC

The following proof works for both triangles.

The sum of angles in a triangle is 180 degrees.

So, we have:

∠ABC + ∠BAC + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ABC - ∠BAC

The sum of angles on a straight line is 180 degrees.

So, we have:

∠ACD + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ACD

Substitute ∠ACB = 180 - ∠ACD in ∠ACB = 180 - ∠ABC - ∠BAC

180 - ∠ACD = 180 - ∠ABC - ∠BAC

Subtract 180 from both sides

- ∠ACD = - ∠ABC - ∠BAC

Multiply both sides by -1

∠ACD =  ∠ABC + ∠BAC

Hence, ∠ACD =  ∠ABC + ∠BAC has been verified

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Answer:

2ab(b + 4a​)

Step-by-step explanation:

2ab² + 8a²b​

Factor Out the 2:

2(ab² + 4a²b​)

Factor Out the a:

2a(b² + 4ab​)

Factor Out the b:

2ab(b + 4a​)

Answer:

16.6

Step-by-step explanation:

Add the numbers together.

13.2+20=33.2

Now divide the number by 2.

33.2/2=16.6

Hope this helps!

If not, I am sorry.

Answer: x = 2

Step-by-step explanation:

First, let's take the root of 256 to find the length of each side before the addition of x.

[tex]\sqrt{256} = 16[/tex]

This means 16 cm is the length of each side before the addition of x.

Then increase each side by X to get

[tex](16 + x)(16 + x) = 324[/tex]

[tex]256 + 16x + 16x + x^2=324[/tex]

[tex]x^2+32x -68=0[/tex]

[tex]x=2[/tex]  or   [tex]x=-34[/tex]

The value cannot be negative so x has to be 2

The required Pythagorean triplets are hypotenuse, perpendicular and base is 13, 12 and 5 respectively.

In a right angled triangle, its side, such as hypotenuse, perpendicular and base  is Pythagorean triplets.

We have

Hypohypotenuse = 13
perpendicular = 12
base = 5
Which satisfies the condition of the Pythagorean theorem.

[tex]a^2+b^2=c^2\\12^2+5^2=c^2\\169=c^2[/tex]

and c = 13

Thus, the required value of Pythagorean triplets satisfies the Pythagorean theorem.  

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The value of the give expression is  [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴

From the question, we are to determine the value of

2(5+34-67/45*43)^2

This can be written as

[tex]2 (\frac{5+34-67}{45 \times 43 })^{2}[/tex]

First, we will simplify the bracket

[tex]2 (\frac{-28}{1935 })^{2}[/tex]

Then, we get

[tex]2 \times \frac{-28}{1935 }\times \frac{-28}{1935 }[/tex]

= [tex]\frac{1568}{3744225}[/tex]

= [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴

Hence, the value of the give expression is  [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴

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The equation of line is 2x  - 3y = 6.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

The x-intercept is 3 and the y-intercept is -2.

So, the line passes through the points  (3, 0) and (0, -2)

Now, slope of line is

m= -2-0/ 0-3 = 2/3

Equation of line is

y = 2/3 x - 2

y = 2x-6 /3

3y= 2x -6

2x  - 3y = 6

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The transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).

A dilation transformation is a transformation that changes the size of the original figure but the shape remains unchanged.

If any figure is dilated by a scale factor k with the center of dilation as the origin.

Then the change of transformation in each of the vertices of the figure is given:

(x,y) → (kx, ky)

It is given a point C which is located at C(9,3).

Hence, here k=3

We get:

C(9,3) → C'(9×3,3×3)

C(9,3) → C'(27,9) = C'(3,1)

Hence, the transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).

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Answer:

(5,5)

Step-by-step explanation:

count from the center

Answer:

38.667°

Step-by-step explanation:

the total sum of 3 angles in a triangle is 180

in triangle PQR this means:

P+Q+R = 180

so:

64+x+2x=180

64+3x=180

3x=116

x=116/3=38.667

So Q=X=38.667

Step-by-step explanation:

if it is cloudy, then it is snowing. False.  This is obviously not true since sometimes it's just cloudy and it's also cloudy when it rains.

all quadrilaterals are rectangles. False. A quadrilateral has four straight sides which don't have to be parallel to each other unlike a rectangle which has four straight sides with all four sides being parallel to one other side.

All chocolates like students? False? Not sure if I'm writing the converse correctly for this one but if I am this isn't true because chocolate doesn't have feelings...

All triangles with two or more congruent angles are a right triangle. False. This is only true when those two congruent angles add up to 90 which is when they're both 45. But they could also both be 30, 29, 28, etc... which won't result in a right triangle.

Answer:

If it is cloudy, then it is snowing.

   Counter-argument: It can be cloudy in the summer.

If a figure is a quadrilateral, then it is a rectangle.

   Counter-argument: Trapezoids are not rectangles.

If someone likes chocolate, then they are a student.

    Counter-argument: many people like chocolate who are not students.

If a triangle has 2 or more congruent angles, then it is a right triangle.

    Counter-argument: Equilateral tr6iangles have 3 congruent angles.

    None are right angles.

Step-by-step explanation:

Converse statements reverse the If Then in the original.

Answer:

g(x) = -5x²

(option B)

Step-by-step explanation:

we know that our original graph, f(x) = x² is a parabola.

So, we can consider what happens when we adjust the function/equation of a parabola.

when we "vertically stretch" a parabola, we are increasing the value of x.

 think of it this way: the steepness of a slope is rise over run. If we rise ten, and run one, that's going be a lot more steep than if we rise 1, run 1.

Let's say our x = 5

if f(x)=x²

f(5) = 25

> y value / steepness is 25

f(x) = 3x²

f(5) = 75

 > y value / steepness is 75

So, we are looking for an equation with an increase in x present.

When a parabola has been flipped over the x-axis, we know that the original equation now includes a negative

suppose that x = 1

if y = x² ; y = 1² = 1

if y = -(x²) ; y = -(1²) ; y = -1

So, when we set x to be negative, we make our y-values end up as negative also (which makes the graph look as if it has been flipped upside-down)

This means that we are looking for a function with a negative x value.

So, we are looking for a negative x-value that is multiplied by a number >1

The graph that fits our requirements is g(x) = -5x²

hope this helps!!

Elaine saw statistics showing that union employees make an average of 30 percent more than nonunion workers, so when she was looking for a new job, she looked for one at a company that was unionized. Elaine was motivated by Economic needs.

By economic need Elaine is trying to get a company that would pay her more. Hence the need to go for the Unionized company.

This is given that the Unionized company is said to earn more than the other company. Hence her motivation is due to her economic needs.

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Answer:

2,

Step-by-step explanation:

The vertex is the very highest or very lowest point. X coordinates are listed first, then Y.

Answer:

the algebraic expression is; x+3=14

Answer:

(-5,0)

Step-by-step explanation:

The x intercept is where it crosses the x axis

It crosses the x axis where x = -5

The y value is 0

(-5,0)

Answer:

A  

Step-by-step explanation:

The x -intercept is 'shorthand' for  x - AXIS intercept

  where the graph crosses the x - axis

      this will always have a   ZERO  value for the 'y'- coordinate

looking at the graph this point is   -5,0

7h-15h+40=-72

40+72=15h-7h

112=8h

h=14

Answer:

16

Step-by-step explanation:

consider X  = Damon's age

3x + 8 = 2x

x = 8

so Damon will be 16 in 8 years ( 8+8)

Answer:

16

Step-by-step explanation:

24/3 8

24+8=32

8+8=16

16/32=1/2

Answer:

C

Step-by-step explanation:

2 equal angles are said to be congruent