Larry and Donna bought a sofa at the sale price of $1,152. The original price of the sofa was $1,920.
Find the amount of discount in dollars.

The digit that occurs in the 2023rd place after the decimal point is; 1

A repeating decimal has another name called a recurring decimal, and it is defined as a number whose decimal representation eventually becomes periodic

Now, we are given the fraction as 1/7 which is a repeating decimal because its decimal representation is periodic for every 6 decimal units as shown below; 1/7 = 0.142857142857...

Now, the digits are repeated after every 6 digits and as such to get the digit in the 2023rd place;

2023/7 = 337 remainder 1

Thus, the sequence 142857 would be repeated 337 times after which the next digit which is the 2023rd digit will be 1.

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If I manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. Where I have in stock 500 eggs and 1,050 cups of cream. The number of quarts of each flavor that I would make in order to use up all the eggs and cream is: 150 quarts of Vanilla and 200 Quarts of Mocha.

Let x and y be the number of Quarts of Vanilla and Mocha respectively.

The total number of eggs used is given as:

2x+y = 500

And the total cups of cream is:

3x + 3y = 1050

Removing the second equation from three times the first, we get:

3(2x + y) - (3x + 3y) = 3(500) -1050

6x + 3y - 3x - 3y = 1500 - 1050

⇒ 3x = 450

⇒ x = 450/3

x = 150

By substituting x back in tot he first equation we find:

2x+y = 500

2 (150) + y = 500

300 + y = 500

y = 500 - 300

y = 200.

Thus, to use up al the eggs and cream, 150 quarts of Vanilla and 200 quarts of Mocha should be produced.

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The acccceleration will be 1m/s² and the average speed is 47m/s.

For the acceleration problems, you must draw a tangent on curved velocity-time graphs. Since it requested acceleration at t = 10 seconds, we must create a straight line that only touches the graph once, at 10 seconds.

Now, when drawing tangents, you must be as precise as you can because they can only contact the line once.

Next, determine the gradient using the tangent. You can accomplish this by creating a triangle out of two additional lines drawn from the tangent, then dividing the rise by the run, or Y/X. The triangle that comes before the Y and the X simply denotes the Greek letter delta, which symbolizes change. Change in Y so prevails over Change in X. So 10/10 = 1. So 1m/s^2.

If we estimate the speed at 5 seconds intervals, then we have

Average speed = (36 + 46 + 49 + 50 + 50 +50 + 50) ÷ 7

Average speed = 331/7 = 47.29 m/s

Average speed = 47 m/s

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Answer:

Step-by-step explanation:

You want a couple of interior angles and the value of x given the parallelogram in the figure.

The diagonals of a parallelogram bisect each other, and divide the figure into two pairs of congruent triangles. Here, the congruent triangles of interest are ...

  ∆NKJ≅∆NML

In these triangles, that means ...

  ∠J ≅ ∠L = 50° = ∠NJK

  ∠K ≅ ∠M = 42° = ∠NKJ

The halves of diagonal JL are congruent, so we have ...

  4x -3 = 13

  4x = 16 . . . . . . . . add 3

  x = 4 . . . . . . . . . divide by 4

Answer:

13.25

Step-by-step explanation:

1. you have to subract the cost of the drink:

94.25-1.50=92.75

2.you have to divide to get the individual cost of pizzas by doing

92.75÷7=13.25

so therefore your answer is 13.25 per pizza

The use of internal rhyme affect the poem by: C. It helps create and maintain the poem's playful tone

Internal rhyme tend to occurs when words that are in the same line of a poem rhyme with one another.

The use of internal rhyme can tend to  add  more musical quality to a poem and it as well help to create cohesion within a line or stanza. Internal rhyme also help to a sense of playfulness in the poem.

Therefore we can conclude that the correct option is C.

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The expression 4√72 can be simplified by first taking the square root of both sides, which gives us 2√72. Then, we can factor out a 6 from both sides, which gives us 24√6. Therefore, the simplified expression is 24√6.

Expression is the process of conveying one’s thoughts, emotions, ideas, and beliefs through speech, writing, art, or any other form of communication. Expression is a form of communication that allows people to express themselves in a way that is meaningful and personal to them. It is a powerful way for individuals to express their thoughts, feelings, and opinions without fear of judgement or criticism. Expression is an important part of self-expression, and it can be used to connect with others through shared experiences, to create a sense of community, and to grow and learn from one another. Expression is an invaluable tool for self-expression, creativity, and communication.

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The scale factor for each of the dilation is given as -

Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -

y = Kx

K = y/x

where -

{K} is scale factor. It also tells by how many times is {y}, greater than {x}.

Given is a line segment and its dilated image.

The scale factor is given by -

K = y/x

[1] -

K₁ = 18/12 = 3/2

[2] -

K₂ = 8/12 = 2/3

[3] -

K₃ = 12/12 = 1

[4] -

K₄ = 6/12 = 1/2

Therefore, the scale factor for each of the dilation is given as -

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Answer: The fractional increase in Gershon's broccoli sprouts is 7/4 and the percent increase in Gershon's broccoli sprouts is 175%.

Step-by-step explanation:

The fractional increase in Gershon's broccoli sprouts is the difference between the final amount and the initial amount divided by the initial amount.

So in this case, it would be (11 - 4) / 4 = 7 / 4.

The percent increase in Gershon's broccoli sprouts is the fractional increase multiplied by 100.

So, it would be (7 / 4) * 100 = 175%.

It means Gershon's broccoli sprouts increased by 175% from 4 pounds to 11 pounds.

The coordinates of the triangle before and after dilation is

preimage        image

R (6, 9)             R' (2, 3)

S (3, -9)            S' (1, -3)

T (-6, -3)           T' (-2, -1)

The rule that best describes the transformation is

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we have

preimage                             image

R (6, 9)  → (1/3 * 6, 1/3 * 9) → R' (2, 3)

S (3, -9) → (1/3 * 3, 1/3 * -9) → S' (1, -3)

T (-6, -3) → (1/3 * -6, 1/3 * -3) → T' (-2, -1)

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Answer:

Step-by-step explanation:

The balance of an account after a year, when the interest rate is 3% per year and there are no additional withdrawals or deposits, can be represented by the formula:

Balance = Principal + Interest

where Principal is the initial amount of money invested (m) and Interest is the interest earned on that amount for the year.

Interest is calculated as the product of the principal, the interest rate, and the time period. In this case, the interest rate is 3% (or 0.03), and the time period is one year. Therefore the Interest can be represented by the following expression:

Interest = Principal * Interest Rate * Time

Substituting the given values:

Interest = m * 0.03 * 1

So the expression that represents Arianys balance after a year is:

Balance = m + (m*0.03)

= m + 0.03m

= 1.03m

This expression represents her balance after a year, assuming she makes no additional withdrawals or deposits.

Answer:

Step-by-step explanation:

Let the other diagonal be d.

From the Pythagorean theorem,

d2 = 82 + 1442

d2 = 64 + 20736

d2 = 20800

d = √20800

d = 144 cm

The correct solution set for the given graph include the following: D. {infinite set of points on the line}.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Generally speaking, the solution set of a graph simply refers to all of the points that lie on its line. By critically observing the graph of lines a and b, we can reasonably infer and logically deduce that they both have the same slope, solution set, as well as increasing and decreasing infinitely.

In this context, the correct solution set lies in both Quadrant II and Quadrant III because both lines move towards negative and positive infinity i.e [-∞, ∞].

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Answer:

see explanation

Step-by-step explanation:

[tex]\frac{5}{x}[/tex] - [tex]\frac{2}{x^2}[/tex] = 2

multiply through by x² ( x ≠ 0 ) to clear the fractions

5x - 2 = 2x² , that is

2x² = 5x - 2 ( subtract 5x - 2 from both sides )

2x² - 5x + 2 = 0 ← in standard form

(2x - 1)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x - 2 = 0 ⇒ x = 2

since x₁ < x₂ , then

x₁ = [tex]\frac{1}{2}[/tex] and x₂ = 2

Then

3x₁ + x₂

= 3 × [tex]\frac{1}{2}[/tex] + 2

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

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

= [tex]\frac{7}{2}[/tex]

The solutions for the given function are (-2, 0) and (2, 0).

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

The given function is f(x)=√(x²-4).

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,−2]∪[2,∞),{x|x≤−2,x≥2}

Range: [0,∞),{y|y≥0}

Therefore, the solutions for the given function are (-2, 0) and (2, 0).

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The height of the cuboid is 4 cm  

What is a cuboid?

A cuboid is a solid shape or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has eight vertices, twelve edges, and six rectangular faces. A rectangular prism is another name for a cuboid. A cube is an object with six square faces on a cuboid.

volume of a cuboid = l *w*h

where, l= length, w=width, h= height

=> 364 = 7*13*h

=> h=364/(7*13) = 364/91

=> h= 4 cm

Thus, the height of the cuboid is 4 cm  

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Answer:It means almost everywhere

Step-by-step explanation:

The value of AE is, 10 units.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Here, From the given figure we can see that two triangle ABE and DEC are similar.

Therefore, The ratio of corresponding sides are equal.

Hence, From figure we get,

⇒ ED/AE = CD/AB

Substitute all the values, we get;

⇒ (x + 6)/(2x + 6) = 8/10

⇒ 10(x + 6) = 8(2x + 6)

⇒ 10x + 60 = 16x + 48

⇒ 16x - 10x = 60 - 48

⇒ 6x = 12

⇒ x = 2

So, The value of AE is,

AE = 2x + 6

AE = = (2 × 2 ) + 6

AE = 4 + 6

AE = 10

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Answer:

Let's call the amount Erica earned from her job at the college "x". We know that:

Total income = $67,160

Income from store = 3x + 1,550

Total income = Income from store + Income from college

67,160 = 3x + 1,550 + x

67,160 = 4x + 1,550

Now we can solve for x:

67,160 - 1,550 = 4x

65,610 = 4x

x = 16,402.5

Erica earned $16,402.50 from her job at the college.

Using scientific notation, the number of gallons of water saved in two years by the wireless soil monitors is 1.2 x 10^12.

Scientific notation is a shorthand way of writing very large numbers or very small numbers in a simpler form.

The parts of a scientific notation are coefficient, base, and exponent.

We state that a number is written in standard notation when the number is between 1 and 10 and it is multiplied by a power of 10.

The number of gallons of water per year saved by wireless soil monitors = 6 trillion

The number of gallons of water saved by wireless soil monitors in 2 years = 12 trillion

In scientific notation, 12 trillion = 1.2 x 10^12.

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The given triangles are not similar because the sides given are not proportional.

Similar triangles are those triangles which has the same shape but different size.

The length of sides and angles are proportional in similar triangles.

Given are two triangles QRS and TUV.

Also given the measure of two sides of each triangle and an included angle of these sides of each triangle.

From the figure, given angles are equal.

If we prove that the sides including these angles are proportional, we can say the given triangles are similar by SAS similarity theorem.

7 / 35 = 1/5

But 13/55 ≠ 1/5

So they are not proportional.

Hence the given triangles are not similar.

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The number of people that uses exactly one of gym, swimming pool and track is 49people

A set is the mathematical model for a collection of different things. A set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

The number of people that uses gym= 73- ( 32-14+ 36-14 + 14)

73-(18+22+14)

73 - (54) = 19 people

The number of people that use pool only = 73-(36-14+35-14+14)

= 73-(22+21+14)

= 73-(57)

= 16people

The number of people that use track only = 67-(32-14+35-14+14)

= 67-(18+21+14)

= 67-53

= 14people

therefore the number of people that use one of the facility is 19+16+14 = 49people

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Plan A has the majority of votes.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given this,  the school board in Wichita Falls, Texas, began planning for new and renovated high school facilities.

thus we can say the total number of members who voted is 7.

Therefore, 4 votes are required for the majority.

Therefore, there is no plan that receives a majority of votes.

1st choice votes to A=3

1 choice votes to B=3 1st choice votes to C=1

So, C is to be eliminated and his 1 vote is to be transferred to A (as A is the next choice after C in column 3 of the table)

First choice vote to A = 3 + 1 = 4

First choice vote to B = 3

Since A gets the majority of votes A is the winner

Thus, Plan A has the majority of votes.

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Complete question:

Answer:

Angle 6 = 70

Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.

Answer: The distance formula is a mathematical formula used to find the distance between two points in a plane. One way to find the distance formula is by using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The distance formula can be derived from the Pythagorean theorem by considering the two points as the two endpoints of a line segment. The formula is as follows:

Distance = √(x2 - x1)^2 + (y2 - y1)^2

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this formula, the difference in the x-coordinates is squared and the difference in the y-coordinates is also squared. Then, these two values are added and the square root of the result gives the distance between the two points.

For example, if we have two points (x1, y1) = (2, 3) and (x2, y2) = (5, 8), we can use the distance formula to find the distance between these two points:

Distance = √((5 - 2)^2 + (8 - 3)^2)

Distance = √(3^2 + 5^2)

Distance = √(9 + 25)

Distance = √(34)

Distance = 5.83

Therefore, the distance between the two points is 5.83 units.

Step-by-step explanation:

Answer:

To find f(-3), substitute -3 for x in the equation for f(x):

f(-3) = 2(-3) + 5 = -6 + 5 = -1

Answer:

f(-3) = -1

To find g(x) - h(x), first substitute x into both g(x) and h(x) and then subtract h(x) from g(x):

g(x) - h(x) = -3x^2 + 2x - 6 - (-4 - x) = -3x^2 + 3x - 2

Answer:

g(x) - h(x) = -3x^2 + 3x - 2

To solve for x when f(x) = h(x), first substitute x into both f(x) and h(x), and then solve for x:

2x + 5 = -4 - x

3x = -9

x = -3

Answer:

x = -3

To determine which of the functions are linear, we need to look at the degree of the polynomials in each function. Linear functions have a degree of 1, while non-linear functions have a degree greater than 1.

f(x) = 2x + 5 is linear because it has a degree of 1

g(x) = -3x^2 + 2x - 6 is non-linear because it has a degree of 2

h(x) = -4 - x is linear because it has a degree of 1

Answer:

f(x) and h(x) are linear, while g(x) is non-linear.

Answer:

The equation of this line is y>1/2x-3

Step-by-step explanation:

This is an inequality equation that represents a line that is greater than 1/2x-3. The inequality symbol ">" indicates that all the y-coordinates that are on the same side of the line as the y-axis are greater than 1/2x-3.

In other words, all the points that lie above the line will satisfy the inequality, while all the points that lie below the line will not.

It's worth noting that the line y<1/2x-3 represents the same line but the inequality symbol "<" indicates that all the y-coordinates that are on the same side of the line as the x-axis are less than 1/2x-3.

y>2x-3 and y<2x-3 represent different lines, the first one represents a line with a slope of 2 and the second one represents a line with a slope of -2.

Value of g(x) with given values of x:

                      x -5 -4 -3 -2 -1

                   g(x) 7 1 -1 1 7

Given: the functional equation:

                          g(x) = 2(x + 3)^2 – 1

Solution:

Value of g(x), when x= -5

g(x) = 2 (-5 +3)^2 – 1

      = 2 (-2)^2 – 1

      = 2* (-2)* (-2) – 1

      = 8 – 1

      = 7

Value of g(x), when x= -4

g(x) = 2 (-4 +3)^2 – 1

      = 2 (-1)^2 – 1

      = 2* (-1)* (-1) – 1

      = 2 – 1

      = 1

Value of g(x), when x= -3

g(x) = 2 (-3 +3)^2 – 1

      = 2 (0)^2 – 1

      = 2* 0  – 1

      = 0 – 1

      = - 1

Value of g(x), when x= -2

g(x) = 2 (-2 +3)^2 – 1

      = 2 (1)^2 – 1

      = 2* (1)* (1) – 1

      = 2 – 1

      = 1

Value of g(x), when x= -1

g(x) = 2 (-1 +3)^2 – 1

      = 2 (2)^2 – 1

      = 2* (2)* (2) – 1

      = 8 – 1

      = 7

The next two numbers on the number pattern will be 12.2, 12.9 the correct option is A

To obtain the next two points on the number pattern, first we must identify what is the meaning of pattern.

The pattern is given as follows;

The double of an amount is calculated.

Now 0.7 is increased to double the amount, and we return to step 1, doubling the value.

The final term is 6.1, which is obtained after the addition of 0.7 to 5.4. Double 6.1 is obtained multiplying the number by 2, as follows;

2 x 6.1 = 12.2.

Then the number obtained after 0.7 is added to 12.2 is given as follows;

0.7 + 12.2 = 12.9.

It implies that the correct answer of the given number pattern is 12.2, 12.9

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The diameter of the circle would be given as = 10

Diameter is defined as the length of a line through the center that touches two points on the edge of the circle.

The diameter of the circle can be found through finding first the radius of the circle.

The radius of the circle is half of the diameter. it is the line DI which is also the longer line of the triangle DGI.

Using the Pythagorean formula c² = a² + b²

The lines that represents ;

a= DG

b= EI/2 = 4.8

C= DI = ?

C² = DI

a² = 1.8²

b² = (9.5/2)² = 4.8²

c² = 2.24 + 23.04 = 25.28

C =√25.28

C = 5

Therefore the diameter of the circle = 5×2 = 10

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The debts to assets ratio is 0.63

The formula for calculating debts to assets ratio is

total liabilities/total assets

The total liabilities is $3,228

The total assets is $5,091

Therefore the debts to assets ratio is

3228/5091

= 0.63

Hence the debts to assets ratio is 0.63

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