A manufacturer of graphing calculators has determined that 11,000 calculators per week will be sold at a price of $98. At a price of $93, it is estimated that 13,150 calculators would be sold.
(a) Determine a linear function that will predict the number of calculators y that would be sold at a given price x.
(b) Use this model to predict the number of calculators that would be sold each week at a price of $73.

a: ______ b:______

Step-by-step explanation:

Step 1 :

Break down the fraction with the H.C.F of the numerator and the denominator.

For instance, in Question 5 , the HCF of 20 and 8 is 4. So, 4 will go into 20 five(5) times and 4 will go into 8 two(2) times, leaving 5/2.

Step 2 :

Then 2 (denominator) will go into 5(numerator) two(2) times.

So, you'll get 2 as the whole number .

Step 3:

Multiply the denominator by the whole number (2×2) to get 4.

Then subtract 4 from 5 to get 1 and to form a proper fraction by making 1 the numerator and the 2 the denominator to get 1/ 2

Step 4 :

Then put the 2( whole number) and the 1/2 ( proper fraction) together to get the mixed fraction

We can write this expression as a product of two factors:

(a + 1)³ + x³ = (a + x + 1)(a²- a x + x² + x + a + 1)

HOW TO WRITE expression as a product.?

To write an expression as a product means to represent the expression as the multiplication of two or more factors. The process of writing an expression as a product depends on the type of expression and the algebraic techniques that are available.

Here are some general steps that can be followed to write an expression as a product:

Look for common factors: If there are common factors in the expression, they can be factored out using the distributive property. For example, in the expression 3x + 6, we can factor out 3 to get 3(x + 2).

Use algebraic identities: There are many algebraic identities that can be used to factor expressions. For example, the difference of squares identity (a² - b²= (a + b)(a - b)) can be used to factor expressions that are in the form of a difference of squares.

Look for patterns: Sometimes, expressions can be factored by recognizing patterns. For example, the expression x² + 2x + 1 can be factored as (x + 1)²by recognizing that it is a perfect square trinomial.

Use polynomial division: If the expression is a polynomial with higher degree, polynomial division can be used to factor it into linear and quadratic factors.

Use the quadratic formula: If the expression is a quadratic trinomial that cannot be factored easily, the quadratic formula can be used to find the roots of the equation, which can then be used to write the expression as a product of linear factors.

Overall, writing an expression as a product requires a good understanding of algebraic techniques and a lot of practice.

We can use the formula for the sum of cubes to write the expression as a product:

(a + 1) + x³ = (a + 1 + x)(a² - a x + x²) + x³

Expanding the first factor on the right-hand side using the distributive property, we get:

(a + 1 + x)(a²- a x + x²) + x^3 = a³- a² x + a x² + a² + a x + x²+ x³

Collecting like terms, we can write this expression as a product of two factors:

(a + 1)³ + x³ = (a + x + 1)(a²- a x + x² + x + a + 1)

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The dimensions of the final flag and the number of pieces of construction paper it took would be 9 inches tall and 18 inches long.

Three (3) pieces of  9" x 12" construction paper are needed.

First, let's find out the dimensions of the flag. The flag is twice as long as it is tall. If the height of the flag is H, then the length L would be 2H.

Since there are three equally sized vertical bars, the length of the flag would be 3 times the width of the green bar:

L = 3(18 - a)

Now, we know that L = 2H. So,

2H = 3(18 - a)

Given that the construction paper is 9" x 12", we can try to create the flag with the minimum amount of overlap a. Since the height of the flag should be equal to the short side of the construction paper, H = 9 inches.

Now we can plug in the value of H in the equation we derived above:

2(9) = 3(18 - a)

18 = 54 - 3a

3a = 36

a = 12

Now we can calculate the dimensions of the final flag:

H = 9 inches

L = 2H = 2(9) = 18 inches

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Answer:

[tex]{ \colorbox{lightgreen}{can \: be \: simplified}} \\ \dashrightarrow \: { \sf{ \blue{9x + 6x}}} \: \: \: \: \: \\ \hookrightarrow \: { \mathfrak{simplification}} \: \: \: \\ { \sf{ = (9 + 6)x}} \\ { \underline{ \sf{ \: = 15x \: \: \: \: \: \: \: \: \: \: }}} \\ \\ \dashrightarrow \: { \sf{ \blue{4x + x}}} \: \: \\ \hookrightarrow \: { \mathfrak{simplification}} \\ { \sf{ = (4 + 1)x}} \\ { \underline{ \sf{ \: = 5x \: \: \: \: \: \: \: \: \: \: \: \: }}} \\ \\\dashrightarrow \: { \sf{ \blue{y + 2y}}} \\ \hookrightarrow \: { \mathfrak{simplification}} \\ { \sf{ = (1 + 2)y}} \\ { \underline{ \sf{ \: = 3y \: \: \: \: \: \: \: \: \: \: \: \: }}}[/tex]

[tex]{ \colorbox{lightgreen}{cannot \: be \: simplified}} \\ \dashrightarrow \: { \sf{2x + 3y}} \\ \dashrightarrow \: { \sf{7y + 1 \: \: }} \\ \dashrightarrow \: { \sf{4y + 4x}}[/tex]

Answer:

31

Use Bodmas to solve it

7*3 + 10
21 +10
31

31

You can use BODMAS by arranging it multiplication comes first so 7 times 3 which is 21 so agter that addition comes next so that will be 21 plus 10 which gives 31

The five number summary is: Minimum: 60 Q1 (first quartile): 63 ,Median: 70Q3 (third quartile): 75, Maximum: 79

To find the five number summary of the data set 72, 60, 64, 75, 79, 63, 70, 61, 78, follow these steps:

1. Arrange the data in ascending order: 60, 61, 63, 64, 70, 72, 75, 78, 79

2. Identify the minimum value (smallest number): 60

3. Identify the maximum value (largest number): 79

4. Calculate the median (middle number): There are 9 data points, so the median is the 5th number: 70

5. Calculate the first quartile (Q1): The lower half of the data set is 60, 61, 63, 64, 70. The median of this lower half is the

middle number, which is 63.

6. Calculate the third quartile (Q3): The upper half of the data set is 70, 72, 75, 78, 79. The median of this upper half is

the middle number, which is 75.

The five number summary is:

Minimum: 60

Q1 (first quartile): 63

Median: 70

Q3 (third quartile): 75

Maximum: 79

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Answer: is it an A.P or G.P

Answer: 298.41 K

Step-by-step explanation:

given from the problem: T=VPC

where C is a constant

plug in knowns to get C

294= (8000)(0.75)C

C=0.049

T=VP(0.049)

T = (7000)(0.87)(0.049)

T = 298.41 K

Answer: variables

Step-by-step explanation:

mathmeticians made this to where it would leave things out of questions, so factoring would just be your variables my guy

Answer: 25

Step-by-step explanation:

Let x represent the number of pages Broonzy read last night. Then, 5x represents the number of pages she will read tonight. According to her plan, after reading 5x pages tonight and 10 pages tomorrow night, she will complete the remaining 40 pages. The equation can be expressed as:

x (last night) + 5x (tonight) + 10 (tomorrow night) = 40 (total remaining pages)

Combining the terms, we get:

6x + 10 = 40

Now, let's solve for x:

6x = 30

x = 5

So, Broonzy read 5 pages last night. To determine the number of pages she needs to read tonight, we multiply x by 5:

5x = 5 * 5 = 25

Therefore, Broonzy has to read 25 pages tonight to finish her book according to her plan.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.

What is the Pythagorean theorem?

The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

Now,

In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.

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Answer:

-157.7

Step-by-step explanation:

Subtract 12.3 from 23 to get 10.7

10.7 - (166.4 + 2), next add 166.4 and 2 to get 168.4

10.7 - 168.4, finally subtract 168.4 from 10.7 to get -157.7

Answer:

Step-by-step explanation:

the measurements are a Pythagorean triple, therefore it is a right triangle, where 3 and 4 are the legs and 5 is the hypotenuse, we use the formula 1/2 × b × h

A = 1/2 × b × h.

A = 1.5 × 4

A = 6"^2

From a point 100m from a building the angles of elevation to the top and the bottom of a flagpole atop the building are 54.5 degrees and 51.8 degrees. Therefore, the height of the flagpole is 125.6m.

we can use the trigonometric ratios of Sine, Cosine, and Tangent.

First, we need to draw a right triangle with the given information.

The triangle will have two sides:

the 100m side and the side to the flagpole. We can use the angle of elevation of 54.5 degrees to calculate the side of the triangle opposite the flagpole.

To do this, we use the Tangent ratio and solve for the side opposite the flagpole (the height of the flagpole):

Tangent(54.5) = Height/100

Height = 100*Tangent(54.5)

Height = 100*1.256

Height = 125.6m

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The total number of students in Ms. Persons class is 24.

An equation is simply a mathematical formula that expresses the equality of two expressions.

Given the data in the question:

Lets y be the number of students in the class

Hence:

[tex]75\% \ \text{of y = 18}[/tex]

[tex]\text{Lets find y}[/tex]

[tex](\dfrac{75}{100} ) \times y = 18[/tex]

[tex]75 \times y = 18 \times 100[/tex]

[tex]75 \times y = 1800[/tex]

[tex]y = 1800 \div 75[/tex]

[tex]y = 24[/tex]

Therefore, the total number of students in Ms. Persons class is 24.

1 centimeter on the scale drawing of rectangular park represents 15 feet of the actual parking lot.

What is rectangle?

A rectangle is a four-sided flat shape with four right angles. It is a type of quadrilateral. Rectangles have opposite sides that are parallel and equal in length, and all four interior angles are right angles (90 degrees).

We know that the width of the actual parking lot is 48 feet. We also know that on the scale drawing, the width is represented by 3.2 cm. Therefore, we can set up a proportion to find out how many feet are represented by 1 centimeter on the scale drawing:

[tex]$\frac{48 \text{ feet}}{3.2 \text{ cm}} = \frac{x \text{ feet}}{1 \text{ cm}}$[/tex]

where x is the number of feet represented by 1 centimeter on the scale drawing.

We can solve for x by cross-multiplying:

[tex]$48 \text{ feet} \times 1 \text{ cm} = 3.2 \text{ cm} \times x \text{ feet}$[/tex]

Simplifying, we get:

[tex]$x = \frac{48 \text{ feet} \times 1 \text{ cm}}{3.2 \text{ cm}} = 15 \text{ feet}$[/tex]

Therefore, 1 centimeter on the scale drawing represents 15 feet of the actual parking lot.

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[tex]\text{t = total}[/tex]

[tex]\text{equation:} \ t = 25x + 50[/tex]

[tex]m=25[/tex]

[tex]\text{The slope is} \ \bold{25}[/tex]

Answer:

x^2 + 7x - 18 = (x + 9)(x - 2)

The difference between length and width is x + 9 - (x - 2) = x + 9 - x + 2 = 11.

Answer:

-24

Step-by-step explanation:

Hey there!

First we need to find the ratio

ratio = -6/-3 = 2

r = 2

-3, -6, -12, ? , -48

T1 = a

T2 = ar

T3 = ar²

T4 = ar³

T5 = ar⁴

And so on...

T1 means first term, T2 means second term

We're finding the fourth term which is T4

Remember T1 = a = -3

So, T4 = ar³

= -3 × 2³

= -3× 8

= -24

Therefore, the fourth unknown term is -24

You're welcome y'all

If Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie can skip up to 15 days and still finish crocheting at least 3 blankets before she wants to donate them to the homeless shelter.

Let's first calculate how much of a blanket Darcie can crochet in 60 days if she works every day:

1/15 blanket per day * 60 days = 4 blankets

Since Darcie wants to crochet a minimum of 3 blankets, we know that she needs to work for at least 3/4 of 60 days. Let x be the number of days Darcie can skip and still finish the blankets:

(60 - x) * 1/15 >= 3

Simplifying this inequality, we get:

4 - 1/15x >= 3

1/15x <= 1

x <= 15

Therefore, Darcie can skip up to 15 days and still finish crocheting at least 3 blankets before she wants to donate them to the homeless shelter.

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Answer:

Step-by-step explanation:

irregular quadrilateral

Answer:

The name of this shape is (Irregular Pentagon)

Answer:

4.4 m

Step-by-step explanation:

Area of the wheel of a car= 1.54 m²

Area of a circle= [tex]\pi r^{2}[/tex]

                 1.54= 3.14 x r²

                     r²= [tex]\frac{1.54}{3.14}[/tex]

                     r²= 0.49

                      r= 0.7 m

Circumference of the wheel= [tex]2\pi r[/tex]

                                              = 2 x 3.14 x 0.7

                                              = 4.4 m

∴ the circumference of the wheel is 4.4 m

Answer: y=-3/4x-11

Step-by-step explanation: slope= -3/4

y+8=-3/4x+4

y+8=-3/4x-3

y=-3/4x-11

Answer:

3. ( 3, -1 )

Step-by-step explanation:

Answer:

What is 16.00 to 1 decimal place?" is the same as asking, "What is 16.00 rounded to one decimal point?" or "How to round 16.00 to one decimal place."

The main point (pun intended), is that you want to round 16.00 to one digit or place after the decimal point. Thus, we want to eliminate the last digit in 16.00. To eliminate the last digit, we use the following One Decimal Place rules to get the answer:

One Decimal Place Rule #1: If the last digit in 16.00 is less than 5, then remove the last digit.

One Decimal Place Rule #2: If the last digit in 16.00 is 5 or more and the second to the last digit in 16.00 is less than 9, then remove the last digit and add 1 to the second to the last digit.

One Decimal Place Rule #3: If the last digit in 16.00 is 5 or more and the second to the last digit in 16.00 is 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the left of the decimal place.

When rounding 16.00 to one decimal place we use One Decimal Place Rule #1. Therefore, the answer to "What is 16.00 rounded to 1 decimal place?" is:

After answering the provided question, we can conclude that As a result, equation the cost of 2 pounds of candy is $7.00.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9"[/tex] asserts that the statement "[tex]2x + 3[/tex]" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "[tex]x2 + 2x - 3 = 0[/tex]," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

Claim: To calculate the cost of 2 pounds of candy, multiply the cost per pound of candy by 2.

According to the data provided, the cost per pound of candy is $3.50.

Reasoning: In order to determine the cost of 2 pounds of candy, we must first determine the total cost of 2 pounds of candy. Because the price per pound of candy is $3.50, we can calculate the total cost by multiplying the price per pound by the number of pounds. In this case, we want to know how much it costs for two pounds, so we multiply $3.50 by two to get:

2 pounds of candy = $3.50 per pound x 2 pounds = $7.00

As a result, the cost of 2 pounds of candy is $7.00.

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The triangle congruency postulate that proves both triangles are congruent is: SSS

There are different triangle congruence postulates such as:

SSS: This denotes Side Side Side Congruency Postulate

SAS: Side angle Side Congruency Postulate

ASA: Angle Side Angle Congruency Postulate

AAS: Angle Angle Side Congruency Postulate

HL: Hypotenuse Leg Congruency Postulate

Now, from the given two triangles, we can see the following:

BC ≅ UW

AC ≅ UV

AB ≅ VW

Thus, the three sides are congruent and as such it is congruent by SSS congruency postulate

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A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.

This graph represents the solution to this inequality.

What is inequality?

An inequality in mathematics is a relation that compares two integers or other mathematical statements in an unequal way. The majority of the time, height comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.

Given inequality:

(-1/4)*(12x + 8) < -2x + 11

First, we need to solve it for knowing the value of x,

So,

(-1/4)*(12x + 8) < -2x + 11

Or, -3x - 2 < -2x + 11

Or, -2 - 11 < -2x + 3x

Or, -13 < x

A ray with a red dot at minus 13, and it passes through minus 5.

Hence the correct answer is C; a straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.

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When examining the plots, only one displays a straight line going from -17 to -5 and a ray going from -13 to -5. (indicating that x can be any value greater than or equal to -13) Thus, option C is correct.

To solve the inequality, we can simplify it by first distributing the -1/4 on the left side:

[tex]-3x - 2 ≤ -2x + 11[/tex]

Next, we can isolate the variable on one side by subtracting -2x from both sides:

[tex]-x - 2 ≤ 11[/tex]

Finally, we can isolate the variable by adding 2 to both sides:

[tex]-x ≤ 13[/tex]

And since we want to solve for x, we need to multiply both sides by -1, which will flip the direction of the inequality:

[tex]x ≥ -13[/tex]

This means that x can be any value greater than or equal to  [tex]-13[/tex] .

Therefore, Looking at the graphs, the only one that shows a straight line passing from -17 to -5 and a ray starting at -13 and passing through -5 (indicating that x can be any value greater than or equal to -13)

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The range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.

In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element of another set (called the range). Functions are a fundamental concept in mathematics and are used to describe relationships between variables, as well as to model and solve a wide range of mathematical problems.

A function is typically denoted using a letter such as "f", and is defined by an equation or formula that specifies how the input (or domain) values are transformed into output (or range) values. For example, the function "f(x) = 2x + 1" assigns each input value "x" to an output value equal to twice the input value plus one.

To find the range of the function f(x) = x + 3, we need to apply the function to each value in the given domain and collect the resulting outputs.

When the domain is {-1, 3, 5, 7}, we have:

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

f(3) = 3 + 3 = 6

f(5) = 5 + 3 = 8

f(7) = 7 + 3 = 10

Therefore, the range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.

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