solve |3x-.5|>1.5, |3x-.5|=1.5,|3x-.5|<1.5

According to the given expression some are shortlisted factored expressions are [tex]4(3a^3 + 2a) for 12a^3 + 8a , 6(4a^4 + 3) for 24a^4 + 18, 4a^3(4a^2 - 5) for 16a^5 - 20a^3.[/tex]

Expressions in mathematics are numerical, variable, and operation combinations that are used to indicate a quantity or a relationship between values.

One or more variables or numbers are combined with one additional operation to form an expression. An illustration of an expression is X + 1.

The completely factored expressions are:

[tex]4(3a^3 + 2a) for 12a^3 + 8a\\\6(4a^4 + 3) for 24a^4 + 184a^3(4a^2 - 5) for 16a^5 - 20a^3[/tex]

So the correct answers are:

[tex]12a^3+8a=4(3a^3+2a)24a^4+18=6(4a^4+3)16a^5−20a^3=4a^3(4a^2−5)[/tex]

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Step-by-step explanation:

y ( 2y + 5 )   + 4 ( 2y+3)

2y^2 + 5y     +  8y + 12  

 2y^2   + 13 y   + 12

Answer:

Step-by-step explanation:

Ans:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The value of x is 2 !

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hope it helps:)

The value of solution of expression is,

⇒ x = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 7 + 4x - 9 = 6

Now, We can simplify as;

⇒ 4x - 2 = 6

⇒ 4x = 4 + 2

⇒ 4x = 8

⇒ x = 2

Thus, The value of solution of expression is,

⇒ x = 2

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This statement is false. Therefore, the original equation has no solution.

How to solve an equation?

To solve the equation 5x + 3x = 2(4x - 5) - 2, we need to simplify each side of the equation using the order of operations (PEMDAS).

First, we simplify the left side of the equation by combining like terms. 5x + 3x equals 8x, so we have:

8x = 2(4x - 5) - 2

Next, we simplify the right side of the equation using the distributive property of multiplication. We multiply the 2 by each term inside the parentheses:

8x = 8x - 10 - 2

We can simplify further by combining like terms on the right side of the equation:

8x = 8x - 12

Now we have an equation with variables on both sides. To solve for x, we want to isolate the variable on one side of the equation. We can do this by subtracting 8x from both sides:

0 = -12

This statement is false. Therefore, the original equation has no solution.

The equation 5x + 3x = 2(4x - 5) - 2 is an example of a contradiction. It means that there is no value of x that makes both sides of the equation equal. In this case, we can see that the left side of the equation is always greater than or equal to the right side, no matter what value of x we choose. Therefore, the equation has no solution.

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Answer: it is one of the last two

Step-by-step explanation:

The surface area of the rectangular prism is 348 square meters.

Hello! I'd be happy to help you find the surface area of a rectangular prism with dimensions 6 m by 4 m by 15 m. The surface area can be calculated using the formula:

Surface Area = 2lw + 2lh + 2wh

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

Given the dimensions 6 m (length), 4 m (width), and 15 m (height), we can plug in the values

The surface area can be calculated using the formula:

Surface Area = 2(6)(4) + 2(6)(15) + 2(4)(15)
Surface Area = 48 + 180 + 120
Surface Area = 348 m²

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Answer:

approximately 0.0018 feet, or about 0.0216 inches.

Step-by-step explanation:

The volume of the suitcase is:

V_suitcase = height x length x width

V_suitcase = 5 ft x 4 ft x 4 ft

V_suitcase = 80 cubic feet

The volume of each supply is:

V_supply = base area x height

We know that the base area of each supply is 9 square feet. Let's assume that the height of each supply is h.

So, the total volume of all the supplies that can be put in the suitcase is:

V_total_supplies = V_supply x number of supplies

V_total_supplies = (9 ft^2 x h) x 5120

We want to find the height of each supply, so we can rearrange the equation above to solve for h:

h = V_total_supplies / (9 ft^2 x 5120)

Substituting the values we know:

h = (80 ft^3) / (9 ft^2 x 5120)

Simplifying, we get:

h = 0.0018 ft

So the height of each supply is approximately 0.0018 feet, or about 0.0216 inches.

The volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.

What is volume ?

Volume is a physical quantity that refers to the amount of space occupied by an object or a substance. In mathematical terms, volume can be defined as the measure of the three-dimensional space enclosed by a closed surface or shape.

It is usually expressed in cubic units such as cubic meters, cubic feet, or cubic centimeters, depending on the system of measurement being used.

the length of the prism is 7 feet, the width is 2 feet, and the height is 3.5 feet.

Volume = Length x Width x Height

Volume = 7 ft x 2 ft x 3.5 ft

Volume = 49 cubic feet

So, the volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.

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[tex]\:\: \:\: \:\star[/tex] We are asked to find out the distance between (1,5) and (-6,-2).We know the formula to find the distance between two points is given by -

[tex] \:\: \star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]

As per question, points are -

Now that we are given the points, so we can put them into the formula and solve for distance between them.Which is -

[tex]\:\: \:\: \:\star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]

[tex] \longrightarrow \sf Distance_{(AB)} = \sqrt{ (-2-5)^2 + (-6-1)^2 }\\[/tex]

[tex]\:\:\:\:\:\longrightarrow \sf Distance_{(AB)}= \sqrt{ (-7)^2 + (-7)^2 }\\[/tex]

[tex]\:\:\:\:\longrightarrow \sf Distance_{(AB)} = \sqrt{ 49+49 }\\[/tex]

[tex]\: \:\:\:\: \:\longrightarrow \sf Distance _{(AB)}= \sqrt{ 98}\\[/tex]

[tex]\: \:\:\: \:\longrightarrow \sf Distance_{(AB)} = \sqrt{49 \times 2}\\[/tex]

[tex]\:\: \:\: \:\:\longrightarrow \sf\underline{ Distance_{(AB)} = 7√2}\\[/tex]

[tex]\: \:\:\: \:\:\longrightarrow \sf Distance_{(AB) }= 9.89949......\\[/tex]

[tex]\: \:\:\: \:\:\longrightarrow \sf \underline{Distance_{(AB) }= 9.9\:(Approx)}\\[/tex]

Therefore, the distance between (1,5) and (-6,-2) is 7√2 or, 9.9 ( Approx).

Answer:

Step-by-step explanation:

The correct answer is "The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80."

The slope of the line of fit represents the rate of change in the dependent variable (total cost, y) with respect to the independent variable (number of donuts, x). In other words, it represents the amount by which the total cost increases or decreases for each unit increase in the number of donuts sold.

In this case, the slope of the line of fit is 4/5, which means that for each additional donut sold, the total cost is predicted to increase by $0.80. This indicates that the donut shop should expect to make a profit of $0.80 for each donut sold, assuming that all other factors remain constant. This information can be used by the donut shop to determine the optimal price to sell its donuts and maximize its profits.

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The area of the rectangle is 40 square inches.

For a rectangle that is 8 inches long, 3 inches on the bottom, and 5 inches on the side, there are a few things you can do.

The perimeter of a rectangle is the sum of the lengths of all four sides.

To calculate the perimeter, add the lengths of the top and bottom sides (8 + 3 = 11) and the lengths of the two side lengths (5 + 5 = 10).

To find the area of a rectangle with an 8-inch long side, a 3-inch bottom side, and a 5-inch side, follow these steps:
Identify the dimensions of the rectangle.
The dimensions are given as 8 inches long, 3 inches on the bottom, and 5 inches on the side.

However, a rectangle only has two different side lengths, so we can assume that the 3-inch measurement is irrelevant.
Confirm the side lengths.
In this case, the side lengths are 8 inches and 5 inches. The 8-inch side is the length, and the 5-inch side is the width.
Calculate the area of the rectangle.
To find the area, multiply the length by the width. In this case, that is 8 inches (length) multiplied by 5 inches (width).
Area = Length × Width
Area = 8 inches × 5 inches
Area = 40 square inches

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The van would have traveled approximately 8 miles of distance after 12 minutes.

To calculate the distance traveled by the van after 12 minutes, we can use the formula:

y = mx

Where m is the rate of travel, and x is the time in minutes.

To find the value of m, we can use the first two data points:

m = (y2 - y1) ÷ (x2 - x1)

m = (8 - 0) ÷ (10 - 0)

m = 8 ÷ 10

m = 4 ÷ 5

Therefore, the formula becomes:

y = (4 ÷ 5) x

Now, we can substitute x = 12 to find the distance traveled after 12 minutes:

y = (4 ÷ 5) × 12

y = 0.8 × 12

y = 9.6

y ≈ 8 miles

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The complete question is:

A van travels at a constant speed. The table shows the distance y (in miles) that the van travels after x minutes. How far does the van travel after 12 minutes?

Time (minutes), x 0 10 20 30

Distance (miles), y 0 8 16 24

The equation for the new function F(t) is F(t) = 9t - 256/9.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

The conversion formula for converting temperature from Celsius to Fahrenheit is:

F = 9/5C + 32

Substituting the equation for C(t) into F(t) = 9/5C(t) + 32, we get:

F(t) = 9/5(5t - 160/9) + 32

Simplifying this equation, we get:

F(t) = 9t - 320/9 + 32

F(t) = 9t - 256/9

Therefore, the equation for the new function F(t) is F(t) = 9t - 256/9.

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To find the area of a triangle, the correct formula is Area = (base x height) / 2.

A triangle is a 2-dimensional shape with three sides and three angles. It does not have a total surface area like a 3-dimensional shape such as a cube or a sphere.

However, you can find the area of a triangle using the following formula:

Area = (base x height) / 2

where "base" refers to the length of one of the sides of the triangle, and "height" refers to the perpendicular distance from the base to the opposite vertex.

Once you have calculated the area of the triangle, you can use this value to find other quantities such as the perimeter or the length of other sides using various formulas.

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The solution to the equation [tex]4x^2 = 5(4x - 5)[/tex] is x = 5/2."

To solve the equation [tex]4x^2[/tex] = 5(4x - 5), we first simplify the right-hand side by using the distributive property:

Next, we bring all the terms to one side of the equation by subtracting 20x and adding 25 to both sides:

[tex]4x^2 - 20x + 25 = 0[/tex]

This equation is now in the form of a quadratic equation [tex]ax^2[/tex] + bx + c = 0, where a = 4, b = -20, and c = 25. We can solve for x using the quadratic formula:

[tex]x = (-b ± sqrt(b^2 - 4ac)) / 2a[/tex]

Substituting the values of a, b, and c, we get:

x = (-(-20) ±  - 4(4)(25))) / 2(4)

x = (20 ± sqrt(400 - 400)) / 8

x = 5/2

Solve 4 x squared equals 5 left parenthesis 4 x minus 5 right parenthesis.

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We can write √a⁵ as √a⁴ × a.Therefore, a factor out of each square root  of √a⁵ = a²√a.

A factor in mathematics is an algebraic expression or number that divides another expression or number without producing a residue.

For instance, 1, 2, 3, 4, 6, and 12 are factors of 12 because they can divide 12 equally.

Then, using the property of square roots that √ab = √a × √b, we can simplify this to:

√a⁴ × a = (√a²)² × √a = a²√a

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The steps that should be taken to calculate the volume of the right triangular prism are;

Base = 8 meters

Height = 14 meters

Length of the prism = 7 meters

Area = ½ × base × height

= ½ × 8 × 14

= 56 square meters

Volume of the rectangular prism = Area × length of the prism

= 56 square meters × 7 meters

= 392 cubic meters

Ultimately, the volume of the right triangular prism is 392 cubic meters

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For a total of $2,400, the coach purchased 30 hoodies and 15 long sleeve shirts. A hoodie costs $60 and a long sleeve shirt is $45.

Let x represent the number of hoodies ordered and y represent the number of long sleeve shirts ordered. To describe the provided data, we may construct the following system of two equations:

x + y = 45 (because there are 45 players) (since there are 45 players)

60x + 45y = 2400 (the total cost of the order) (the total cost of the order)

We may determine that x = 30 and y = 15 by solving for x and y. As a result, the coach placed orders for 15 long sleeve jerseys and 30 hoodies. We can confirm that the total price is $2400: (30 x $60) + (15 x $45) = $1800 + $675 = $2400

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The missing property is the distributive property of multiplication.

The distributive property of multiplication is a mathematical property that allows you to simplify expressions that involve multiplying a number or variable by a sum or difference of other numbers or variables.

For the addition of 5 terms with 1z, we have that the term 1 is common to all the factors in the expression, hence the expression can be written as follows:

1z + 1z + 1z + 1z + 1z = 1(z + z + z + z + z) = 5z.

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Since lines l and m are parallel, we know that angles 1 and 5 are corresponding angles and are therefore congruent. Also, angles 4 and 8 are corresponding angles and are congruent.

We also know that angles 1 and 4 are vertical angles, so they are congruent, and angles 2 and 3 are vertical angles, so they are congruent.

Thus, we can set up the following equation:

m∠7 = m∠8 - m∠5 = m∠4 - m∠5

We are given that m∠2 = 120°, so we can use this to find m∠1:

m∠1 + m∠2 = 180° (since angles 1 and 2 are supplementary)

m∠1 + 120° = 180°

m∠1 = 60°

Since angles 1 and 5 are congruent, we know that m∠5 = 60°.

We are also given that angles 1 and 3 are complementary, so we can use this to find m∠3:

m∠1 + m∠3 = 90°

60° + m∠3 = 90°

m∠3 = 30°

Now we can find m∠4:

m∠1 + m∠4 = 180° (since angles 1 and 4 are supplementary)

60° + m∠4 = 180°

m∠4 = 120°

Finally, we can use these values to find m∠7:

m∠7 = m∠4 - m∠5

m∠7 = 120° - 60°

m∠7 = 60°

Therefore, m∠7 is 60°.

The function is   [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Here the principal p = $8100

Rate of interest r = 3.7% = 3.7/100 =0.037

Compounded daily then n= 365

Now using compound interest formula then,

=> CI = [tex]P(1+\frac{r}{n})^{nt}[/tex]

=> CI = [tex]8100(1+\frac{0.037}{365})^{365t}[/tex]

=> CI = [tex]8100(1+0.000101369)^{365t}[/tex]

=> CI = [tex]8100(1.000101369)^{365t}[/tex]

Then the function is f(t) = [tex]8100(1.000101369)^{365t}[/tex] .

Now percentage of growth per year is ,

=>  [tex]8100(1.000101369)^{365t}[/tex][tex]\times\frac{1}{100}\%[/tex]

Put t=1 then

=> 8,405.30[tex]\times\frac{1}{100}\%[/tex]

=> 84%

Hence the function is   [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.

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Answer:

balls

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

because I took the test

Answer: I think it's a. 84 cubic units

Hope it helped : D

Answer:

a) 2 new printers

b) 11 min

Step-by-step explanation:

Given:

5 old printers take 30 min to produce a batch of comic books

4 new printers take 18 min to produce a batch of comic books

.

a) First, we need to find how long does one old and new printer take to produce a batch of comic books:

.

Since 5 old printers take 30 min to do the job, one printer would take 5 times more than this (5 printers work together and they do the job faster than one, that's why we have to multiply):

.

1 old printer does the job in:

5 × 30 = 150 min

1 new printer does the job in:

4 × 18 = 72 min

.

Since one old printer does the job in 150 min, 6 old printers would do this job 6 times faster (that's why we divide):

6 old printers would take:

150 / 6 = 25 min

2 new printers would take:

72 / 2 = 36 min

.

25 < 36

That means, 2 new printers would do this job faster

.

b) In order to find how much less time would this take, we have to subtract:

.

36 - 25 = 11 min

Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter

The proportion of a circle's circumference to its diameter is denoted by the mathematical constant pi (). It cannot be written as a simple fraction since it is an irrational number. Pi is approximately equal to 3.141592, or 3.15.

We must first determine the circle's radius in order to determine the length of Mr. Chang's string.

C = 2πr, where C is the circle's circumference and r is its radius, is the formula for a circle's circumference.

Given that the circle's circumference is 31.4 meters, we can solve for r using the following method:

C = 2r 31.4

=2x3.14xr

= 31.4/(2x3.14)r

= 3.14/6.28r

r = 5

Thus, the circle's radius is roughly 5 meters.

The diameter of the circle, which is twice as long as its radius, will be equal to Mr. Chang's stake because it is in the center of the circle.

Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter

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The simplified ratio of [tex]2.4:3/4:1 2/3[/tex]  is [tex]28.8:9:20[/tex].

A ratio refers to the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

To solve this ratio, we need to convert all the fractions to a common denominator:

2.4 : 3/4 : 1 2/3 = 2.4 : (3/4) : (5/3)

To eliminate the fractions, we can multiply all terms by the LCD of 12:

2.4 * 12 : (3/4) * 12 : (5/3) * 12

= 28.8 : 9 : 20

So the simplified ratio for the given ratio is: 28.8 : 9 : 20

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