31 points
2a) Why wouldn’t a 2x2 area model (2 rows, 2 columns) with 4 smaller areas work to multiply
(x + 3)(2x
4 − 3x
3 − 2x
2 − 4x − 1) ? In your explanation, include a description of how to determine the correct rows

and columns for the area model [be sure to refer to and include the correct number of ‘terms’ and correct dimensions]

2b) Show what the area model SHOULD look like with the
correct lengths and widths labeled. DO NOT MULTIPLY!

2c) Draw an area model to find the ‘total area’ of a rectangle if the length is (x + 8) and the width is (x − 5). Write
your final ‘total area’ as a polynomial in Standard Form.

Final Area:

Therefore, Kallie will need to use a total of 6 teaspoons of water conditioner for all the water in 12 fish tanks.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign, with the expression on the left being equal to the expression on the right. Equations are used to represent various relationships and situations in mathematics and other fields, and are solved to find the values of variables that make the equation true.

Here,

First, we need to determine the total amount of water in all 12 fish tanks. Since each fish tank is filled with 20 quarts of water, the total amount of water in all 12 fish tanks is:

12 fish tanks * 20 quarts per fish tank = 240 quarts of water

To convert quarts to gallons, we divide by 4 (since there are 4 quarts in a gallon):

240 quarts / 4 quarts per gallon = 60 gallons of water

Now, we can use the given conversion factor to determine how many teaspoons of water conditioner are needed for 60 gallons of water. Since for every 10 gallons of water, Kallie uses 1 teaspoon of water conditioner, for 60 gallons of water, she will use:

60 gallons / 10 gallons per teaspoon = 6 teaspoons of water conditioner

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Answer:

This is a guess but I think it's 5 min per table.

Step-by-step explanation:

The reason being:

if we know that she has 9 tables to get to and each table can seat 4 people, we would have to multiply both numbers to find how many TOTAL people are in the restaurant during the first few hours.

9x4 = 36 people in total

then, we need to convert 3hrs into minutes to get a more accurate rep as to how much time she would spend at each table (she isn't going to spend the entire 3 hrs with only one table now, is she?)

so for this, we convert 3hrs into minutes

1 min = 60 secs

1 hr = 60 minutes

3hrs -> 60 x 3 = 180 minutes

now, to understand how many time she spends at each table, we need to figure out by dividing the # of people by the amount of minutes.

180 minutes/36 people = 5 mins per table.

The biker wοuld travel 20 miles in 20 minutes.

The speed οf an οbject, alsο knοwn as v in cοmmοn parlance and kinematics, is the size οf the change in pοsitiοn per unit οf time οr the size οf the change in pοsitiοn οver time; as such, it is a scalar quantity. The average speed οf an οbject in a given periοd οf time is equal tο the distance traveled by the οbject divided by the length οf the interval the instantaneοus speed is the upper limit οf the average speed as the length οf Velοcity and speed are different cοncepts.

We can nοw substitute this expressiοn fοr s in the previοus equatiοn:

t = 48 miles / (48 miles / t)

Simplifying this equatiοn, we get:

t = t

Therefοre, we can cοnclude that the biker travelled fοr exactly 1 minute fοr every mile travelled.

b. If the biker travelled fοr 20 minutes, we can use the fοrmula:

d = s x t

Substituting the values we knοw, we get:

d = s x 20 minutes

We alsο knοw frοm the previοus calculatiοn that the biker travels 1 mile fοr every minute traveled. Therefοre, the speed οf the biker is:

s = 1 mile / minute

Substituting this value, we get:

d = 1 mile/minute x 20 minutes = 20 miles

Therefοre, the biker wοuld travel 20 miles in 20 minutes.

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Therefore, the quantity of heat absorbed by 70 g of water that warms from 30∘C to 90∘C is 17,645.6 J (joules).

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equals sign (=). The expressions on either side of the equals sign can contain numbers, variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

Here,

The amount of heat absorbed by a substance can be calculated using the formula:

Q = mcΔT

where Q is the amount of heat absorbed, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. For water, the specific heat capacity is 4.184 J/g⋅K.

Using the given values, we can calculate the amount of heat absorbed as follows:

m = 70 g

c = 4.184 J/g⋅K

ΔT = (90 - 30)∘C = 60∘C

Q = mcΔT

Q = (70 g) x (4.184 J/g⋅K) x (60∘C)

Q = 17645.6 J

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Therefore , the solution of the given problem of angles comes out to be

Angle QMR = 30.

The place where the lines that make up a skew's ends meet determines the size of its largest and smallest walls. It is conceivable for two routes to cross at a junction. Angle is another outcome of two things interacting. They mirror dihedral shapes the most. A two-dimensional curve can be created by arranging two line beams in various configurations between their ends.

Here,

Angle QRM counts 90 degrees because it is a right angle (represented by the square in the diagram).

We can use the knowledge that the sum of all angles in a straight line is 180 degrees to determine angle QPR. A straight line is formed by angles QPB and BPR, so:

=> Angle QPB + Angle BPR =  180°.

Given that the triangular is equilateral, angle QPB is equal to 60 degrees.

=> BPR angle = 180 - 60 = 120 degrees.

We can now use the knowledge that a triangle's total angles equal 180 degrees to determine angle QMR. Triangle formed by angles QMR, QRM, and BMR results in:

Angles QMR, QRM, and BMR add up to 180 degrees.

=> Angle QMR+90+120=180

=> Angle QMR = 180 - 90- 120,

=> Angle QMR = 30

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Step-by-step explanation:

Find the 360° circumference of the circle ( pi * d)   then you want                   90 / 360ths of that

Radius  = 10 mi       then  d = 20 miles

Circumference = pi * 20  = 20 pi miles

    90 / 360   * 20 pi =  15.7 mi

the number of students that offer Mathematics is 11

The sum of the fractions of the pie chart should be equal to 1 since it represents the whole class of 80 students.

Let's write the fractions for each subject in terms of x:

Math: 5x/80

French: (16x-24)/80

English: (6x+12)/80

Hausa: (4x+12)/80

Physics: 5x/80

The sum of these fractions must equal 1:

5x/80 + (16x-24)/80 +  (6x+12)/80 + (4x+12)/80 + 5x/80 = 1

Multiplying both sides by the least common multiple (LCM) of the denominators, which is 80, we get:

5x + 16x - 24 + 6x + 12 + 4x + 12 + 5x = 80

Combining like terms, we get:

36x = 80

So, we have

x = 80/36

For maths, we have

Maths = 5 * 80/36

Maths = 11

Therefore, 11 students offer Mathematics.

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Answer:

There are 1760 yards in one mile and the rink is 250 yard in perimeter.

This means 3 miles is 5280 yards.

If Sam has already gone around the whole rink 6 times, that means he was traveled a total of 1500 yards.  

Sam has 3780 more yards to travel 3 miles.

This means he needs to do 15.12 more laps around the rink.  Or 16 if you are rounding.

Answer:

[tex]f(x) = {x}^{2} - 14x + 45[/tex]

Step-by-step explanation:

[tex]f(x) = (x - 5)(x - 9)[/tex]

[tex]f(x) = {x}^{2} - 14x + 45[/tex]

Answer:

30

Step-by-step explanation:

41.25-10=31.25

31.25/1.25=25

25+5=30

Hope this helps!

Answer:

The height of a rectangular prism is 26 inches and its base is a rectangle with an area of 6 cubic inches. What is the volume of the prism in cubic inches?

Step-by-step explanation:

The height of a rectangular prism is 26 inches and its base is a rectangle with an area of 6 cubic inches. What is the volume of the prism in cubic inches?

A sketch of the algebra-tile shape is shown in the image attached below.

An expression for the perimeter of the shape is 4x + 4.

The perimeter for each of the given values of x are 32 units, 26 units, and 13.33 units respectively.

In Mathematics and Geometry, the perimeter of a rectangular shape can be calculated by using this mathematical expression;

P = 2(L + B)

Where:

Based on the sketch of the algebra-tile shape, an expression for its perimeter is given by:

Perimeter of the shape = 4x + 4

When x = 7 units, the perimeter of the shape can be calculated as follows;

Perimeter of the shape = 4(7) + 4

Perimeter of the shape = 32 units.

When x = 7 units, the perimeter of the shape can be calculated as follows;

Perimeter of the shape = 4(5.5) + 4

Perimeter of the shape = 26 units.

When x = 7 units, the perimeter of the shape can be calculated as follows;

Perimeter of the shape = 4(7/3) + 4

Perimeter of the shape = 13.33 units.

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After answering the provided question, we can conclude that As a result, function Joel cannot satisfy the constraints by purchasing two games and six puzzles.

A function appears to be a hyperlink between two sets of numbers in mathematics, where each member of the first set (referred as the domain) corresponds to a certain representative of the second set (called the range). In other utterance, a function takes input from a set and produces output by another. Inputs are frequently represented by the variable x, and outputs are represented by the variable y. A function can be represented by a formula or a graph. The method y = 2x + 1 is an example of a conceptual model in which each value assigned to x yields a value of y.

Part A:

8x + 12y 96

x + y ≥ 9

x ≥ 0

Part B

If Joel purchases two games and six puzzles, he will spend:

[tex]2 * $12 + 6 * $8 = $48 + $48 = 96\\8x + 12y \leq 96\\8(6) + 12(2) = 48 + 24 = 72 < 96\\x + y \geq 9\s6 + 2 = 8 < 9[/tex]

As a result, Joel cannot satisfy the constraints by purchasing two games and six puzzles.

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An approximate of 68% of American women have shoe sizes that are between 6.54 and 9.58.

To use the empirical rule, we need to assume that the distribution of women's shoe sizes is approximately normal. Given a mean of 8.06 and a standard deviation of 1.52, we can standardize the values of 6.54 and 9.58 by subtracting the mean and dividing by the standard deviation:

Ζ1 = (6.54 - 8.06) / 1.52

Ζ1 = -1.00

Ζ2 = (9.58 - 8.06) / 1.52

Ζ2 = 1.00

The standardized values tell us that the value of 6.54 is 1 standard deviation below the mean, while the value of 9.58 is 1 standard deviation above the mean. According to the empirical rule, about 68% of the data falls within one standard deviation of the mean. Therefore, we can say that: [tex]P(6.54 < x < 9.58) = P(-1.00 < z < 1.00) = 68%[/tex]

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Solving a system of equations we can see that they have 4 lizards and 5 spiders.

We know that each spider has 8 legs, and each lizard has 4 legs.

Now we can define the variables:

x = number of lizards.

y = number of spiders.

We know that the total number of animals is 9, so:

x + y = 9

And the total number of legs is 56, then we can write:

4x + 8y = 56

Then we have a little system of equations:

x + y = 9

4x + 8y = 56

We can isolate x in the first equation to get:

x = 9 - y

Replacing that in the other one, we wll get:

4*(9 - y) + 8y = 56

36 - 4y + 8y = 56

4y = 56 - 36

4y = 20

y = 20/4 = 5

They have 5 spiders, and the other 4 animals must be lizards.

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Answer:

Step-by-step explanation:

To find sin(alpha-beta), we can use the trigonometric identity:

sin(alpha - beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)

We are given that sin(alpha) = 11/12 in the second quadrant and cos(beta) = 15/17 in the fourth quadrant. We can use the Pythagorean theorem to find sin(beta):

sin^2(beta) + cos^2(beta) = 1

sin(beta) = sqrt(1 - cos^2(beta))

sin(beta) = sqrt(1 - (15/17)^2)

sin(beta) = sqrt(1 - 225/289)

sin(beta) = sqrt(64/289)

sin(beta) = 8/17 (since sin(beta) is positive in the fourth quadrant)

Now we can plug in the values we know into the identity:

sin(alpha - beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)

sin(alpha - beta) = (11/12)(15/17) - cos(alpha)(8/17)

We still need to find cos(alpha), which we can do using the Pythagorean identity:

sin^2(alpha) + cos^2(alpha) = 1

cos(alpha) = sqrt(1 - sin^2(alpha))

cos(alpha) = sqrt(1 - (11/12)^2)

cos(alpha) = sqrt(23/144)

Now we can substitute this value into the expression for sin(alpha - beta):

sin(alpha - beta) = (11/12)(15/17) - cos(alpha)(8/17)

sin(alpha - beta) = (11/12)(15/17) - sqrt(23/144)(8/17)

sin(alpha - beta) ≈ 0.210

Therefore, sin(alpha - beta) is approximately equal to 0.210.

For the given statements f(-x) = -4|x| - 5x^3 = -f(x), we can conclude that f(x) is an even function.

A function that fulfils f(-x) = f(x) for any x inside the function's domain is said to be even. The graph of an even function displays reflected y-axis symmetry geometrically. The even functions [tex]f(x) = x^2 and f(x)[/tex] = cos are two examples (x).

A function is considered odd if it meets the condition f(-x) = -f(x) for all x inside its domain. An odd function's graph displays origin rotational symmetry geometrically. Odd functions include such like [tex]f(x) = x^3 and f(x) = sin (x).[/tex]

The given function is [tex]f(x) = -4|x| + 5x^3.[/tex]

An even function is a function that satisfies f(-x) = f(x).

For the function:

[tex]f(-x) = -4|-x| + 5(-x)^3[/tex]

[tex]f(-x) = -4|x| - 5x^3[/tex]

[tex]f(x) = -4|x| + 5x^3[/tex]

Since[tex]f(-x) = -4|x| - 5x^3 = -f(x)[/tex], we can conclude that f(x) is an even function.

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Answer: 1/3

Step-by-step explanation:

Quotient is another word for the solution to a division problem.

So in this case the quotient is the answer to -5/-15.

When you divide a negative by another negative, you get a positive answer. The same can be said about dividing a positive number by another positive number.

So, in this case, we can change -5/-15 to 5/15.

Now we just need to simplify by finding a GCF (greatest common factor)

Both 5 and 15 shares 5 as a factor, so divide them both by 5.

Then you would get 1/3 or .33333333333333333...

Answer:

Step-by-step explanation:

[tex]24\div 6+2\times 9 =4+18=22[/tex]

÷  and × first followed by + and -.  But otherwise work left to right.

Answer:  22

Step-by-step explanation:

1.)  Solve using PEMDAS.

Answer:

2+5/9 is the answer

If you add 2 to 5/9, that makes the statement true

The factory has 172 litres of dye available.

Liters (also spelled litres) is a unit of volume in the International System of Units (SI). It is commonly used to measure the volume of liquids, gases, and solids that can be poured or contained in a container. One liter is equivalent to 1000 cubic centimeters (cc) or milliliters (ml), and it is roughly equal to 1.057 quarts or 0.264 gallons.

In the given question,

First, we need to find out how much dye is needed for one roll of fabric. We know that 43 liters of dye are needed for 1 roll of fabric that is 1,067 feet long. Therefore, we can say that:

1 roll of fabric = 43 liters

1,067 feet

To find out how much dye is needed for 5 rolls of fabric, we can multiply both sides of this equation by 5:

5 rolls of fabric = 5 × 43 liters

1,067 feet = 215 liters

1,067 feet

So, 5 rolls of fabric would require 215 liters of dye.

Next, we need to check if the 4 buckets of dye are enough to dye 5 rolls of fabric. Each bucket contains 43 liters of dye, so 4 buckets would contain:

4 buckets of dye = 4 × 43 liters

= 172 liters

Therefore, the factory has 172 liters of dye available.

Since 215 liters of dye are required for 5 rolls of fabric, and the factory has only 172 liters of dye available, it cannot dye 5 rolls of fabric with the given amount of dye.

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According to the information, the volume of the three-dimensional rhombus is 61.92 cm³.

The three-dimensional rhombus is a geometric solid in the shape of a prism whose lateral faces are rhombuses and the bases are parallelograms. To calculate its volume, the area of the base must be multiplied by the height of the prism.

In this case, the height of the prism is 3 cm and the dimensions of the base rhombus are 5.2 cm wide and 8 cm long. Since the rhombus has two diagonals of equal length, its area can be calculated using the formula (major diagonal x minor diagonal) / 2.

First, the length of the diagonals of the base rhombus must be calculated using the Pythagorean theorem, since its width and length are known:

Then, the area of the base rhombus can be calculated:

Finally, the volume of the prism can be calculated:

Therefore, the volume of the three-dimensional rhombus is 61.92 cm³.

Note: This question is incomplete. Here is the complete information:

Find the volume of the prism

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Answer:

The answer is 13.6

Step-by-step explanation:

4 x 3.4 = 13.6

Step-by-step explanation:

As your post is written   90 dL  *  L / dl  = 90 L

But I think what you really want is the conversion factor for L to dL :

one liter is 10 dL  :

        L / 10 dL

then you question becomes

   90 dL   * L / 10 dL  =  9 liters      

Step-by-step explanation:

23-x >19

make x the coefficient by subtracting 23 from both sides

23-23 - x > 19 - 23

-x > -4

Divide both sides by -1, thus making the sign to change

-x / -1 > -4/-1

x < 4

A negative return means that the investment has lost value within a certain period of time. It is a loss on paper unless the investment is redeemed. The return may become positive again the next day or the next quarter.

What is meant by investment?

Investment is the use of money or capital to acquire an asset or securities for the purpose of earning income or profits over time. It can be various forms of financial instruments such as stocks, bonds, mutual funds, real estate, and others.

What is a quarter?

A quarter is a unit of currency equal to one-fourth of a dollar in the United States and some other countries. It is also commonly used to denote a period of three months in a calendar year.

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Answer:

(6,-5)

Step-by-step explanation:

Parallel lines have the same slope.