A store is having a sale on jelly beans and almonds today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of two purchases today.

Cindy thinks that she can now get the desk chair for free which is false. Then the percent off that she will receive with both the sale and the coupon will be 75%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Let X be the price of a new desk chair.

Cindy is shopping for a new desk chair at a store where the desk chairs are 50% off. Then the cost of a new desk chair after 50% off will be

⇒ 50% of X

⇒ 0.50X

She also has a coupon for 50% off any one item. Then the cost of a new desk chair after applying the coupon of 50% will be

Cost = 50% of 0.50X

Cost = 0.25X

Cindy thinks that she can now get the desk chair for free which is false.

Then the percent off that she will receive with both the sale and the coupon will be

Discount = [(X - 0.25X) / X ] * 100

Discount = 0.75 x 100

Discount = 75%.

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Vertically Stretching and Compressing

Multiplying a function by positive constant yields a function whose graph is vertically stretched or compressed relative to the original function's graph. If the constant is greater than 1, it will stretch vertically. If the constant is between 0 and 1, vertical compression is done. You get vertical compression.

Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values ​​are affected.

Solution:

To write the equation of the function y = x with a vertical compression by a factor of 1/4, we will use the formula given below:

y = a · x

This equation means y = a · x, and a is the vertical compression/stretch. Since a = 1/4, we can substitute 1/4 for a.

Therefore, the answer is D, y = 1/4x.

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The following procedure mistakes are listed below:

In this question we find six cases of equations with fractions, whose intended procedures are shown, of which we must determine in what step a mistake is done:

Case 1

x / 2 + 3 = 9                       Given

x + 6 = 18                           Compatibility with multiplication / Distributive property / Definition of multiplication

x = 12                                 Compatability with addition / Existence of additive inverse / Modulative property

A mistake was made in the first step. (Misuse of distributive property)

Case 2

(2 · x - 1) / 3 + x = 3             Given

2 · x - 1 + 3 · x = 3               Compatibility with addition / Distributive property

5 · x - 1 = 3                          Commutative, associative and distributive properties / Definition of addition

5 · x = 2                              Compatibility with addition / Commutative, associative and modulative properties / Existence of additive inverse

x = 2 / 5                             Compatibility with multiplication / Existence of multiplicative inverse / Associative and modulative properties / Result

A mistake was made in the first step. (Misuse of distributive property).

Case 3

(5 · x + 5) / 10 + (2 · x + 6) / 10 = 6             Given

5 · x + 5 + 2 · x + 6 = 60                            Compatibility with multiplication / Existence of multiplicative inverse / Commutative, associative and distributive properties

7 · x + 13 = 60                                            Associative, commutative and distributive properties

7 · x = 47                                                    Compatibility with addition / Existence of additive inverse / Commutative, associative and distributive properties

x = 47 / 7                                                    Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Result

A mistake was made in the first step (Misuse of distributive property and compatibility with multiplication).

Case 4

3 - 5 / (x + 1) = 1                                           Given

3 · (x + 1) - 5 = x + 1                                     Compatibility with multiplication / Distributive, associative and commutative properties

3 · x - 2 = x + 1                                            Distributive property / Definition of subtraction

2 · x = 3                                                      Compatibility with addition / Existence of additive inverse / Commutative, associative and distributive properties

x = 3 / 2                                                      Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Result

A mistake was made in the first step (Misuse of distributive property and compatibility with multiplication).

Case 5

x / 3 + x = 2                                                  Given

5 · x / 3 = 2                                                   Modulative property / Existence of multiplicative inverse / Definition of division

5 · x = 6                                                        Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Definition of division

x = 6 / 5                                                        Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Definition of division / Result

A mistake was made in the first step (Misuse of existence of multiplicative inverse and distributive property).

Case 6

(2 · x + 5) / 5 + 2 = 7                                     Given

2 · x + 7 = 7                                                   Compatibility with multiplication / Distributive, associative and commutative properties

2 · x = 0                                                          Compatibility with addition / Existence of additive inverse / Commutative and associative properties

x = 0                                                               Compatibility with multiplication / Existence of multiplicative inverse / Commutative and associative properties / Cancelative property / Result

A mistake was made in the first step (Misuse of compatibility with addition).

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Two parallelograms will be congruent only when all four corresponding sides are equal in length & one corresponding internal angle is equal.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.

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Answer:

640 km

Step-by-step explanation:

80km/h, x 8 hours = 640 km

The equilateral triangle has three symmetry lines.

So,

Step 1:

Step 2:

Step 3:

(Refer to the graphs below)

Therefore, the equilateral triangle has three symmetry lines.

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Answer: 166 Soft Drinks

Step-by-step explanation:

250 ÷ 1.50 = 166

The simplified form the expression (7 - 5(3)²) is -38.

Simplification is the process involved in replacing a mathematical expression by an equivalent one which is  that is usually simpler and  shorter.

For example;

a + b + 2a + 2b = 3a + 3b.

Given the expression in the question;

7 - 5(3)²

Simply each term, raise 3 to the power of 2

7 - 5(3)²

7 - 5(9)

Multiply -5 and 9

7 - 5(9)

7 - 45

Subtract 45 from 7

-38

Therefore, the simplified form the expression (7 - 5(3)²) is -38.

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The function y=3√-x-3 is graphed only over the domain of {x 1-8 ≤x≤ 8).  is the range of the graph is b) {y  : -5 < x < - 1 }

Range is set of Y values for which the function is define.

So, in order to find the range , we need to find the corresponding y values for given domain.

Put x = -8 in  y = ∛-x -3 then we get,

                y = ∛-x -3

                y = ∛-(-8) -3

                y = ∛8 -3

                y = 2 -3

                 y = - 1

Put x = 8 in  y = ∛-x -3 then we get,

                y = ∛-(8) -3

                y = ∛-8 -3

                y = -2 -3

                 y = - 5

Hence the range of function y = ∛-x -3 over the domain of {x : -8 < x < 8 } is

{y  : -5 < x < - 1 }

correct option is b) {y  : -5 < x < - 1 }

In arithmetic, the range of a function may seek advice from either of  intently associated concepts: The codomain of the feature The image of the function Given two units X and Y, a binary relation f between X and Y is a function if for each x in X there is exactly one y in Y such that f relates x to y.

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For this case, your interest rate will be (. 11 x 100 = 11) 11%. Step 3: Apart from this, you can also calculate your time period involved, principal amount and interest amount paid in a specific time period if you have other inputs available with you. Calculate interest amount paid in a specific time period, I = Prt

Answer:

918.50 in interest over 11 years.

Step-by-step explanation:

Comment

You have to make an assumption here. The assumption is that this is simple interest.

So if the brother pays 10% each year, he is paying

10/100 * 835 each year in interest

10/100 * 835 = 83.50 every year.

There are 11 years, so the total interest paid is 11 * 83.50 = 918.50 dollars in total.. That's more than what he borrowed!

(a). Using the concept given above, PC and AB are the circle's chords.

(b). In the given figure, OC, OP, OA and OB are the radii of the circle.

(c). A chord which is not the diameter of the circle is PC.

A circle is a shape in which all points are the same distance from the center. Circles are named after their centers. Therefore, the right circle is called circle A because its center is at point A. Real-world examples of circles include (the surface of) wheels, dinner plates, and coins.

(a). Circle chords are two-point line segments that connect two different places on the circumference of a circle.

Using the concept given above, PC and AB are the circle's chords.

(b). Line segments formed by joining any point on the boundary on the circle with the center of the circle are known as radii of the circle.

In the given figure, OC, OP, OA and OB are the radii of the circle.

(c). A chord which passes through the center of the circle is known as diameter of the circle.  

A chord which is not the diameter of the circle is PC. ( By using the definition of chord and diameter of the circle.)

The complete question is:

In figure, O is the center of the circle

(a) Name all chords of the circle

(b) Name all radii of the circle

(c) Name a chord, which is not the diameter of the circle

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The scale factor of two suitcases that are similar rectangular prisms is 5/4.

Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar rectangular prisms:

length of A / length  of B = width of A / width of B = height of A / height of B

Scale factor refers to the ratio of the corresponding dimensions of similar solids.

If the smaller suitcase is 68 centimeters long and the larger suitcase is 85 centimeters long, then the scale factor is:

scale factor = length of larger suitcase / length of smaller suitcase

scale factor = 85 cm / 68 cm

scale factor = 5/4

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Answer:

12

Step-by-step explanation:

We'll give Sucely the variable s and Liz l.

s = 3(l - 5)

21 = 3(l - 5) distribute the 3

21 = 3l - 15 add 15 to each side

36 = 3l divide each side by 3

12 = l

So, Liz sent 12 texts

Answer:

g(x + 2) = 10x + 24

g(x) + g(2) = 10x + 28

Step-by-step explanation:

1) If g(x) = 10x + 4, then g(x+2) = 10(x+2) + 4

g(x) = 10x + 20 + 4

g(x + 2) = 10x + 24

2) If g(x) = 10x + 4, then g(x) + g(2) = 10x + 4 + 10(2) + 4

g(x) + g(2) = 10x + 4 + 20 + 4

g(x) + g(2) = 10x + 28

Answer:

secret hukgjkkkkouugvgv uukkoygjo

The required value of the constant of proportion and x is (-12 / 5) and (⅙) respectively.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation and x

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Now, find k for, given x = 3 / 2 and y = -5 / 8, we need to put these values in equation 1, i.e.

-5 / 8 = k(3 / 2)

k = -12 / 5

Further, calculate x for given y = (⅖) and constant of proportion = -12/5 i.e.

2 / 5 = (- 12 / 5) × (x)

x = -⅙

Hence, the required value of constant of variation and z is -12 / 5 and -⅙ respectively.

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For the function f(2) = 9:

1. The value of the output is: 9

2. The value of the input is: 2.

The function, f(2) = 9 is interpreted as, for an input value of 2, we would get an output value of 9.

This means that, when x (independent variable or input) is 2, y (dependent variable or output) would be 9.

Thus, given the function f(2) = 9, we have the following:

1. The value of the output is: 9

2. The value of the input is: 2.

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4y - 7x = 0  is the equation of the line in standard form.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

To find standard equation of a line we will use points (0,0)  and (80,140)

Lets fine the slope of given data,  slope, m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

m = [tex]\frac{140- 0}{80- 0}[/tex]

m = 140/80

m = 7/4

We can now make the slope intercept form that is y = mx

with the given data,

y = 7/4(x)

4y = 7x

subtract 7x both the side and we get

4y - 7x = 0

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If function g(x)= [tex]3(4)^{x}[/tex], then the value of g(2) is 48

The function g(x) = [tex]3(4)^{x}[/tex]

Function is the expression the defines the relationship between between a set of inputs having one output each. The set of all possible input of the function is called domain and set of all possible output of the function is called range

Here the function is  g(x)= [tex]3(4)^{x}[/tex]

The values of x = 2

Substitute the value of x in the function

g(x)= [tex]3(4)^{2}[/tex]

First find the value of [tex]4^{2}[/tex]

g(x)= 3×16

Multiply it

g(x)= 3×16

g(x)=48

The value of g(2) is 48

Hence, If function g(x)= [tex]3(4)^{x}[/tex], then the value of g(2) is 48

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Given set of numbers 65, 72, 88 represent an acute triangle.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.

Now we find the type of triangle.

We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.

the sum of the squares of the two smaller sides is,

= 65² + 72²

= 4225 + 5184

= 9409

= 97²

And 88² = 7744

Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.

Therefore, given set of numbers 65, 72, 88 represents an acute triangle.

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Answer:

(4c + b)(12c - b)

Step-by-step explanation:

- b² + 48c² + 8bc ← rearrange

48c² + 8bc - b² ( split the middle term )

= 48c² + 12bc - 4bc - b² ( factor first/second and third/fourth terms )

= 12c(4c + b) - b(4c + b) ← factor out (4c + b) from each term

= (4c + b)(12c - b)

Answer: a

Step-by-step explanation:

[tex]-3(x+7)-15 > 2x+4\\\\-3x-21-15 > 2x+4\\\\-3x-36 > 2x+4\\\\-36 > 5x+4\\\\-40 > 5x\\\\x < -8[/tex]

[tex]-2x+6 < 4(x-3)\\\\-2x+6 < 4x-12\\\\6 < 6x-12\\\\18 < 6x\\\\x > 3[/tex]

Taking the union, we get that [tex]x < -8[/tex] or [tex]x > 3[/tex].

If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that  can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is:  x=≤ 477.5.

x is the integer

First step is to formulate the inequality

40x≤ 25,500-6,400

Now let determine the x by using the inequality

40x≤ 25,500-6,400

40x≤19,100

x=≤19,100/40

x=≤ 477.5

Therefore If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that  can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is:  x=≤ 477.5.

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The orientation of the vertices stay same after a reflection.

The orientation of the vertices is nothing but The relative arrangements of points following a transformation or after surrounding a geometric shape are known as orientation. In terms of how the points align, orientation is divided into clockwise and counterclockwise. The points are opposite the original shape when the orientation is reflected. Same orientation denotes that the points are simply a reflection of the original figure and are arranged in exactly the same manner.

The orientation of the vertices stay same after a reflection.

When you translate a figure, you slide it left, right, up, or down. This implies that the coordinates for the vertices of the figure will alter on the coordinate plane.

Apply the same change to each point to graph a.

The variations in a reflection's coordinates can be used to identify it. The figure makes a mirror image of itself when it flips across a line in a reflection. Consider the reflection in the image.

Therefore, The orientation of the vertices stay same after a reflection.

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The least common multiple of each pair of polynomials x² - 1 and

x² + 2x +1 is equal to (x-1)(x+1)².

As given in the question,

Given pair of polynomial are x² - 1 and x² + 2x +1

Simplify each pair of polynomial by factorizing them

Apply a² -b² =(a-b)(a +b)

x² -1 =(x-1)(x+1)

Apply (a +b)² =a² +2ab +b²

x² + 2x + 1 =(x+1)²

Least common multiple of (x-1)(x +1) an (x+1)² =(x-1)(x+1)²

Therefore, the least common multiple of each pair of polynomials x² - 1 and x² + 2x + 1 is equal to (x-1)(x+1)².

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Part a: The possible locations for the knight after two moves are a7, a5, e7 or e5.

Part b: A rook would have to move down 5 spaces and right 3 spaces, according to one possible translation.

One of the most well-known and oldest board games, played between two opponents on a checkered board with specifically made contrasting pieces, usually white and black After White moves first, players take turns in compliance with fixed rules, each attempting to force the opponent's main piece, the King, in to the checkmate—a position in which it cannot avoid capture.

Niw, as per the given question;

Part a: The knight's first move can be to a6 (green square 1) or c6 (red square 1). If he lands on a6, he can move on to c7 or c5. He can land on a7, a5, e7, or e5 if he lands on c6.

Part b: The rook would have to move 5 spaces down and 3 spaces right.

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The complete quesion is-

Each chess piece has a path that it can follow to move. The rook, which begins in square a8, can only move vertically or horizontally. The knight, which begins in square b8, can move two squares horizontally and the one square vertically, or two squares vertically and one square horizontally. The bishop, which begins in square f8, can only move diagonally.

a. The knight moves 2 squares vertically and 1 square horizontally on its first move, then two squares horizontally and 1 square vertically on its second move. What are the possible locations for the knight after two moves?

b. After two moves, the rook is in square d3. Describe a possible translation to describe the two moves.

The correct statement for the expression is that 't' should be multiplied by 's'.

Given r/s = t and explain what is wrong with the statement as r * t = s.

Given expression as r/s = t

We can write this expression as

r/s = t/1

By cross multiplication on both sides we get

r * 1 = t * s

r = t * s

This is the correct expression we get. But the given statement r * t = s is false.

We conclude this as 't' should be multiplied by 's'.

Hence, the correct option is option B is correct.

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Answer:week 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

If I name the centre (intersection of diagonals) as O, Angle AOD will be equal to 68°

[Opposite angles are equal]

The diagonals bisect the 4 corner angles of a rectangle in equal halves. So, a = 45°

Also, Angle ADO = 90° - b

[Each of the four angles in a rectangle = 90°]

And In [tex]\triangle[/tex] AOD,

=> Angle AOD + Angle ADO + Angle OAD = 180°

=> 68° + 90° - b + 45° = 180°

=> 203° - b = 180°

=> b = 23°