True or False
Corresponding angles must be proportional.
O True
O False

ANSWER

C and D

EXPLANATION

Step 1: Given that:

Step 2: Simplify matrix D

Hence, matrices C and D are equal.

Dimensions of rectangle after dilation of scale factor 7/8 will be

[tex] (\frac{7}{2},14),  (\frac{-7}{2},14),  (\frac{-7}{2},-14),  (\frac{7}{2},-14) [/tex]

Dilation means the area of any rectangle increases or decreases due to change in it's dimensions but the shape of that rectangle will remain same.

Now Consider the point of dilation as the center of rectangle and assume that the center of given rectangle is at the origin.

As given the length and width of rectangle is 32ft and 8ft respectively.

∴ The Dimensions of rectangle will be (4,16), (-4,16), (-4,-16) and (4,-16).

Now As the rectangle is diluted by the factor of 7/8.

So Now New Dimensions are Calculated by simply multiplying the available dimensions with the scale factor of dilation.

∴ new Dimension after dilation will be

[tex] (4(\frac{7}{8}),16(\frac{7}{8})), (-4(\frac{7}{8}),16(\frac{7}{8})), (-4(\frac{7}{8}),-16(\frac{7}{8})), (4(\frac{7}{8}),-16(\frac{7}{8})) [/tex]

∴ Dimension after dilution will be ;

[tex] (\frac{7}{2},14),  (\frac{-7}{2},14),  (\frac{-7}{2},-14),  (\frac{7}{2},-14) [/tex]

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Given:

a.) The admission fee at a small fair is $2.50 for children and $4.00 for adults.

b.) On a certain day, 2400 people enter the fair and $7140 is collected.

Let,

x = total number of children

y = total number of adults

Let's generate two equations based on the given scenario:

EQUATION 1: Total number of children and adults entered the fair.

EQUATION 2: Total money collected from the admission.

We will be using the substitution method. We get,

Substitute to Equation 2:

Therefore, 1,640 children went to the fair.

For the adults,

x + y = 2400

1,640 + y = 2400

y = 2400 - 1,640

y = 760 adults

In summary: 1,640 children and 760 adults went to the fair.

Answer:

Step-by-step explanation:

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Functions are special relaionships that connect an element of one set of numbers, with one element in another set of numbers.

The most comon way to represent functions is connecting elements of a set of Real numbers called the "Domain", to another number in a set called the Range (and whose elements are identified with the letter "y")

Using math operations one can relate x values with y values via an equation of the type:

y = 2 x - 5

where you have a mathematical form of that relationship, that allows you to know given the value of one member (x) of the Domain what number is associated with it in the Range.

For example, try the number x = 0

and see which y number connects with it:

y = 2 (0) - 5 = 0 - 5 = -5

Then you say that the number 0 in the Domain connects with the number -5 in the Range.

This relationship can also be given with coordinate pairs of the form:

(x, y) mentioning in the first position (where the x is), the number in the Domain that connects to the "y" number of the Range). The y goes in the second place. so for example in the relationship we found above, x = 0 connects with y=-5, you would have a shortcut way to write it as the pair: (0, -5) that tells you which x connects with which y.

The functions can also be given in graph form by plotting the relationship between members of the Domain and the Range on the plane. Graphing a point in the plane location that corresponds to the connected x and y values (like you do in the game "battlefield" when you locate ships on the board.

I know this is very general, but hopefully you got the idea ofa function as a special relationship between numbers, and that they can be expressed in different fashions.

Using the greatest common factor, it is found that the greatest number of cards that she can place in a row is of 14.

The number of cards for each family is given as follows:

We want to find a way to distribute them having the same number of cards in each row, hence this is possible finding the greatest common factor (GCF) of the numbers of 154 and 140.

The GCF is found factoring both numbers 154 and 140 simultaneously by prime factors, as follows:

154 - 140|2 (both 154 and 140 are divisible by 2).

77 - 70|7 (both 77 and 70 are divisible by 11).

11 - 7

There are no numbers for which both 11 and 7 are divisible by, hence the greatest number of cards that she can place in a row is:

gcf(154, 140) = 2 x 7 = 14.

The complete problem is:

April is arranging place cards for a wedding reception on a table. The bride's family has 154 cards and the groom's family has 140 cards. She wants the arrangements for the two families to have the same number of cards in each row. What is the greatest number of cards that she can place in a row?

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The slope of the line passing through the coordinates (2, 12) and (4, 3) is -9/2.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1( 2, 12 )

Point 2( 4,3 )

To determine the slope, plug the given x and y values into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 3 - 12 )/( 4 - 2 )

Slope m = ( -9 )/( 2 )

Slope m = -9/2

Therefore, the slope of the line is -9/2.

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Checking if the results of the following divisions are true or false.

a) -5/-1 = 5 ↔ True

The fraction, (remembering that it is a division), -5/-1​ can be simplified to 5 by removing the negative sign from the numerator and denominator.

b) (0/-4) = 0 ↔ True

We know that any number divided by zero, the result will always be zero.

c) -3/1 = -3 ↔ True

Any number divided by one equals the same number.

d) -8/0 = 0 ↔ False

A normal number simply cannot be divided by 0.

The three previous divisions are true, that is, your answers are correct. While the last one can't, since it can't be divided by 0, this one is false.

The equation of a line that passes through the point ( -5, 6) and has a slope equal to 3 is  y = 3x + 21

The equation of the line passes through the point (-5, 6) and has a slope equal to 3.

Therefore, the equation of a line can be represented as follows;

y = mx + b

where

Therefore,

y = 3x + b

slope = 3

using (-5, 6), let's find the y-intercept

6 = 3(-5) + b

6 = - 15 + b

b = 6 + 15

b = 21

Therefore, the equation of the line is y = 3x + 21

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The given function is:

The theorem states that the factors are p/q where p is the factors of the last term (constant term) and q is the factors of the leading coefficient.

Here the leading coefficient is -25 and the constant term is -1.

The factors are listed below:

So the value of p/q can be the values shown below:

Hence the possible zeroes of the given function are:

Answer:

perpendicular

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 )

y = - [tex]\frac{2}{3}[/tex] x + 5 ← is in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

3x - 2y = 4 ( subtract 3x from both sides )

- 2y = - 3x + 4 ( divide through by - 2 )

y = [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form

with slope m = [tex]\frac{3}{2}[/tex]

• Parallel lines have equal slopes.

clearly the slopes are not equal, so not parallel.

• the product of the slopes of perpendicular lines = - 1

- [tex]\frac{2}{3}[/tex] × [tex]\frac{3}{2}[/tex] = - 1

then the lines are perpendicular to each other.

Answer:

The lines are perpendicular.

Step-by-step explanation:

[tex]3x -2y=4[/tex]

Step 1: Add -3x to both sides.

[tex]3x-2y+-3x=4+-3x[/tex]

[tex]-2y=-3x+4[/tex]

Step 2: Divide both sides by -2.

[tex]\frac{-2y}{-2} =\frac{-3x+4}{-2}[/tex]

[tex]y=\frac{3}{2} x-2[/tex]

Finally...

[tex]y=\frac{3}{2} x-2\neq y=-\frac{2}{3} x+5[/tex] so the lines are not parallel.

However, [tex]\frac{3}{2}[/tex] is the opposite reciprocal of [tex]-\frac{2}{3}[/tex], so, the lines are perpendicular.

(You can also try drawing the lines.)

The equation whose graph is parallel to that of line 2x - y = - 1 is →

y = - 2x - 1

The general equation of straight line is -

y = mx + c

Given is an equation of line as → 2x - y = - 1

The equation of the line whose graph will be parallel to that of the graph of line 2x - y = -1, will have same slope as that of given line itself.

2x - y = - 1

y = -2x - 1

m = -2

The equation whose graph is parallel to that of 2x - y = -1 is -

y = - 2x - 1

Therefore, the equation whose graph is parallel to that of line 2x - y = - 1 is → y = - 2x - 1

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Answer: [tex]x=-1 \pm \sqrt{15}[/tex]

Step-by-step explanation:

[tex](x+1)^2 =15\\\\x+1 =\pm \sqrt{15}\\\\x=-1 \pm \sqrt{15}[/tex]

The solution of the given equation in quadratic form will be; (x^{2} -6x - 8)/(x^{2} -4 )

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

WE have been given an algebric equation as;

x/x+2 - 4/x-2

Solving it;

[tex]\dfrac{x}{x+2 }- \dfrac{4}{x-2}\\\\\\\dfrac{x(x-2)}{x+2 }- \dfrac{4(x+2 )}{x-2}\\\\\\\dfrac{x(x-2)- 4(x+2 )}{(x+2 )(x-2)}\\\\\\\dfrac{x^{2} -2x- 4x - 8}{x^{2} -2^{2} }\\\\\\\dfrac{x^{2} -6x - 8}{x^{2} -4 }[/tex]

Hence, the solution of the given equation in quadratic form will be;

(x^{2} -6x - 8)/(x^{2} -4 )

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Solution

We want to find the area of the triangle given te sides

b = 20

a = 29

c = 21

Note: Hero formula for calculating the Area of a Triangle

We will first find S

To find the Area

Therefore, the area is

As a fraction 3.83 (3 repeating )is 3x 83/99

what is repeating decimals ?

Repeating decimal values are created by fraction that  do not divide evenly. when converting a repeating decimal to a fraction we can ignore the units in the start as the units remain unchanged ,which allows us to  convert our decimal values and then the units back in afterward.

so ,

To convert the 3.83 to a fraction , we ignore the units as they will remain units.

we then set up one equation of our unknown x being equal to 0.83333......and another that is 100 times greater , 100x = 83.33333....

by subtracting these two equation from each other we can then divide by the coefficient of x to create our fraction .

10x=83.3333...

    x= 0.83333...

  99x = 82.5

we now divide both sides by 99 to isolate x:

99x=82.5

99x/99=82.5/99

x= 82.5/99

x = 82.5 x10/99x10

x = 825/990

x = 165/198

we cannot simplify this fraction any more

finally we add back the 3 units we set aside at the beginning ,making our fraction 3x165/198

so , the fraction 3.83 is 3x 83/99

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Considering the area and the perimeter of a square, it is found that:

Each length of the large square floor is of 21 meters, and each length of the small square floor is of 3 meters.

Supposing a square of side length s, the area and the perimeter are given as follows:

The area of the figure is given by the subtraction of the area of the large square, of side length x, by the area of the small square, of side length y, hence:

A = x² - y²

x² - y² = 432.

The perimeter of the figure is the perimeter of the square of side length s added to two edges of the smaller square of side length s, hence:

P = 4x + 2y

4x + 2y  = 90.

Then the system of equations to find the dimensions is given as follows:

The solution of this system is given by:

The problem is completed by the image given at the end of the answer.

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We are given a circle whose diamter is 100 feet. To find out if 140 feet of hedges will fit into it given all the oother dimensions, we will have to calculate the lengths of the chords that correspond to the hedges.

First, let us solve for AE.

We used θ = 50 degrees because we know that the measurement of the arc is equal to the measurement of the central angle.

Now, to solve for the length of ED, we need to find out the measurement of the central angle that subtend it.

Segments AD and EC intersect, thus the following equation must be true for the angles that they form and the arcs that they subtend:

Again, using the formula for finding the length of a chord, we can now solve for the length of ED.

Finally, we need to calculate the length of BC. But we know that BC = ED because the diameters meet at a 90-degree angle and so the chords that they subtend are all congruent. You may also think of ∠BYC as being vertical to ∠EYD. So BC should be equal to ED either way. BC = 100

So the total length of the hedges is:

Therefore, the numbers given by the designers are not reasonable. 140 feet is too short for the hedges.

90 letters out of the inspected sample of 900 letters will be found to be open

Inspection is done by mail carrier for every 20th letter

Inspection rate = 1/20*100 = 5%

It is a form of inspection where a sample of the same unit's manufactured goods, produced using the same procedures, is taken and examined, as opposed to the entire unit being examined. In general, the unit relates to the lot, and the lot determines whether the things are acceptable or rejectable.

Number of letters found open in 600 letters = 3 letters

Rate of letter found open = 3/600*100 = 0.5%

The sample being mailed = 18000 letters

Number of letters that were inspected for being open = 5% of 18000 = 900

letters

The number of letters found open = 0.5% of 18000 = 90

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The most appropriate choice for volume of cuboid and cylinder will be given by-

Total mass of sculpture is 10.0464 tonnes

What is volume of cuboid and cylinder?

Cuboid is a three dimensional figure that has 6 faces, 12 edges and 8 vertices.

Volume of cuboid is given by the formula length [tex]\times[/tex] breadth [tex]\times[/tex] height

Cylinder is a three dimensional round figure that has two circular bases at the end

If r is the radius of the cylinder and h is the height of the cylinder, volume of the cylinder is given by the formula

V = [tex]\pi \times r^2 \times h[/tex]

Here,

Radius of cylinder = 40 cm

Height of cylinder = 70 cm

Volume of cylinder = [tex]\pi \times r^2 \times h[/tex]

                                = [tex]\frac{22}{7} \times (40)^2 \times 70\\[/tex]

                                = 352000 [tex]cm^3[/tex]

Length of cuboid = 80 cm

Breadth of cuboid = 80 cm

Height of cuboid = 140 m

Volume of cuboid = [tex]80 \times 80 \times 140[/tex]

                              = 896000 [tex]cm^3[/tex]

Total volume of sculpture = (352000 + 896000) [tex]cm^3[/tex]

                                           = 1248000 [tex]cm^3[/tex]

Density of sculpture = 8.05 [tex]g / cm^3[/tex]

Mass of sculpture  = [tex]1248000 \times 8.05[/tex]

                               = 10046400 g

                               = 10046.4 kg

                                = 10.0464 tonnes

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Answer:

9.38%

Step-by-step explanation:

First this is the solution I used:

Percentage change = actual change/original amount x 100

Hope this helps.

Answer:

[tex]y = - \frac{1}{2} x + 3[/tex]

Step-by-step explanation:

Please see the attached images for the full solution.

Note that when y is replaced with f(x), it is known as a function instead of an equation.

The inequality that represents the number of hours you will need to work in order to afford the video game is x ≥ 5.58.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤ 

Let the number of hours be represented as x.

The person is paid $10.75 an hour at your job and the newest video game costs $60.00. This will be illustrated as:

10.75x ≥ 60

Divide

x ≥ 60 / 10.75

x ≥ 5.58

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Erica worked 4 hours  to prepare 26 flower arrangements.

Erica prepared 13 flower arrangements after working 2 hours.

Time Erica took to prepare 1 flower arrangement = 2 / 13 hours.

Therefore time Erica took to prepare 26 flower arrangement = 2/13 x 26 hours.

=4 hours.

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Answer:

63r-27s+90

Step-by-step explanation:

9 times 7 is 63

9 times -3 is -27

9 times 10 is 90

Answer:

8x17.50

Step-by-step explanation:

the groups generated by two elements of order 2 are K4  and dihedral group.

We are given that G be  a finite group with  x, y belong to G have two elements of order two.

We have to prove that <x,y> is either abelian or isomorphic  to a dihedral group.

<x,y> means the group generated by two elements of order 2.

We know that  Zn is a cyclic group and  number of elements of order 2 is always odd in number and generated by one element  .So , given group is not isomorphic to Zn

But we are given that two elements of order 2 in given group

Therefore, group G can be K4 or dihedral group

Because the groups generated by two elements of order 2 are K4  and dihedral group.

We know that  is abelian group of order 4 and every element of K4  is of order 2 except identity element and generated by 2 elements of order 2 and dihedral group can be  also generated by two elements of order 2

Hence, <x,y> is isomorphic to K4 or D2.

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Answer:

answers are in the photo

Answer:

No, it doesn't satisfy.

Step-by-step explanation:

2x - 6y = -3

let us post the ordered pair in the equation and solve it

2(3) - 6(7/2) = -3

6 - 21 = -3

-15 = -3  ......  which isn't equal

so we conclude that the given ordered pair doesn't satisfy the equation.