Use distributive property to evaluate 4(2x-1) when x=6.

Answer is: 90 ft

Step-by-step explanation:

You multiply the width, height, and length to find the volume.

Cause of its shape.

Hope this helps! :)

Have a good day.

The solution of the given problem of unitary method comes out to be beam's maximum bending moment is 180 Nm.

Here,

=> RA - wL = 0

=> wL = 40 N/m x 2 m = 80 N, where RA =

=> RBv - RA = 0 (sum of forces in the vertical direction)

=> RBh = 0 (sum of forces in the horizontal direction) (sum of forces in the horizontal direction)

To solve for RBv, we obtain:

=> 80 N = RBv = RA

Hence, the responses at support points A and B are as follows:

=> RA = 80 N (vertical response at A) (vertical reaction at A)

=> RBv = 80 N (vertical response at B) (vertical reaction at B)

=> RBh = 0 N (horizontal reaction at B) (horizontal reaction at B)

=> M = 80 N x 2 m - 40 N/m x (2 m)2/2 - 500 Nm

=> -180 Nm, where MB = RA x L - wL2/2 -

Keep in mind that the bending moment is opposite the applied moment, as shown by the negative sign.

Thus, at point B, the beam's maximum bending moment is 180 Nm.

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The starting balance of investment depending on the equation [tex]y = 32000 * (1.035)^{x}[/tex] is $32000.

The equation is [tex]y = 32000 * (1.035)^{x}[/tex] where x represents the number of years since the investment started and y represents the total balance after x years.

To find the value starting balance of the investment we need to put x = 0,

since this represents the initial balance at the start of the investment:

[tex]y = 32000 * (1.035)^{x}[/tex]

put x = 0

[tex]y = 32000 * (1.035)^{0} \\y = 32000[/tex]

Therefore, the starting balance of the investment is $32,000.

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The starting balance of the investment is $32,000, since the initial investment is not multiplied by any factor in the given equation.

Investment refers to the process of allocating resources, such as money or time, to a particular venture or asset with the expectation of generating a return on investment (ROI) in the future. An investment can be made in various forms, including stocks, bonds, real estate, commodities, and mutual funds.

Investing involves taking calculated risks in order to earn a profit or generate income. The level of risk and potential reward associated with an investment depends on various factors, such as the nature of the investment, the economic conditions, and the performance of the particular asset or venture.

There are many different investment strategies and approaches, such as value investing, growth investing, dividend investing, and index investing. Each strategy involves a different approach to selecting and managing investments, depending on the investor's goals, risk tolerance, and investment horizon.

The starting balance of the investment is $32,000, since the initial investment is not multiplied by any factor in the given equation.

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Answer:

12

Step-by-step explanation:

Given that,

f(x) = 2x² - 3x + 7

To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.

Let us solve it now.

f(2.5) = 2(2.5)² - 3×2.5 + 7

f(2.5) = 12.5 - 7.5 + 7

f(2.5) = 12

Answer:

[tex]f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}[/tex]

Answer:

140inch^2

Step-by-step explanation:

5×8=40inch^2

4^2×π= 16π

4^2×π=16π

16π+16π=32π

40+32π=140.53096491487

rounded to the nearest 10th= 140inch^2

The probability that a given person drank between 40 and 45 glasses of water is 13.5%.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number outcomes.

between 40 and 45 glasses of water.

First, we need to standardize the values of 40 and 45 using the z-score formula:

z1 = (40 - 50) / 5 = -2

z2 = (45 - 50) / 5 = -1

Next, we look up the area under the standard normal distribution curve between z = -2 and z = -1. We can use a standard normal distribution table or a calculator to find this area, which is approximately 0.135.

Therefore, the probability that a given person drank between 40 and 45 glasses of water is 13.5%.

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The length and width of the new poster are 240 cm and 288 cm, respectively.

To find the length and breadth of the enlarged poster, we need to multiply the original dimensions by the enlargement ratio.

Let's first find the common ratio between the original poster and the enlarged poster:

Common ratio = Enlarged size / Original size

Common ratio = 5/3

Now, we can find the dimensions of the enlarged/New poster:

Length of enlarged poster = Length of original poster x Common ratio

Length of enlarged poster = 150 cm × 5/3

Length of enlarged poster = 250 cm

Breadth of enlarged poster = Breadth of original poster x Common ratio

Breadth of enlarged poster = 180 cm × 5/3

Breadth of enlarged poster = 300 cm

Therefore, the the dimensions of the new poster is 250cm by 300cm.

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Answer:

Exact SA = 166.4π cm²

Approximate SA = 522.8 cm²

Step-by-step explanation:

SA = 2πr(r + h)

r = d/2 = 8 cm / 2 = 4 cm

h = 16.8 cm

SA = 2π(4 cm)(4 cm + 16.8 cm)

SA = 2π(4 cm)(20.8 cm)

SA = 166.4π cm²

SA = 522.8 cm²

To enable Riley to save up to buy a new television priced $1,200.17, and since he already has $200.34 saved and earns $76.91 per week at her job, she needs to work for 13 more weeks.

To determine the number of weeks Riley has to work to earn enough to buy the new television, we apply the mathematical operations of subtraction and division.

Subtraction and division are two of the four basic mathematical operations, including addition and multiplication.

The total amount that Riley requires = $1,200.17

The amount of savings Riley already has = $200.34

The remaining amount that Riley needs to earn = $999.83 ($1,200.17 - $200.34)

Riley's earnings per week = $76.91

The number of weeks Riley needs to work to save enough money = 13 weeks ($999.83 ÷ $76.91)

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In conclusion  the solution to the system of equations is x = 1 and y = 2.

How to justify each step?

Here are the steps to solve the system of equations:

5x - y = 3

x + 2y = 5

To eliminate y, we can multiply the second equation by 2:

2(x + 2y = 5)

2x + 4y = 10

Now we can add the first equation and the new second equation together, to eliminate y:

5x - y = 3

2x + 4y = 10

7x = 13

To solve for x, we can divide both sides by 7:

7x / 7 = 13 / 7

Simplifying, we get:

x = 1

Now we can use substitution to find y. We can substitute x = 1 into the first equation:

5x - y = 3

5(1) - y = 3

Solving for y, we get:

-y = -2

To solve for y, we can divide both sides by -1:

-y / -1 = -2 / -1

Simplifying, we get:

y = 2

So, the solution to the system of equations is x = 1 and y = 2.

The steps in solving the system of equations are justified using various properties of equality, as follows:

Step 1 uses the multiplication property of equality, which states that multiplying both sides of an equation by the same nonzero number does not change the solution set of the equation.

Step 2 uses the addition property of equality, which states that adding the same quantity to both sides of an equation does not change the solution set of the equation.

Step 3 uses the division property of equality, which states that dividing both sides of an equation by the same nonzero number does not change the solution set of the equation.

Step 4 uses the substitution property of equality, which states that if two expressions are equal, then one can be substituted for the other in any equation or expression without changing the solution set.

Step 5 uses the subtraction property of equality, which states that subtracting the same quantity from both sides of an equation does not change the solution set of the equation.

Step 6 uses the substitution property of equality again.

Step 7 uses the division property of equality again.

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Answer:

2.936

Step-by-step explanation:

32.297 / 11= 2.936090909

Estimate = 2.936

Hope this helps :)

The statement describes the relationships between x and y in these two equations is B. In y = 10x, the value of y is 10 times the value of x, and in y = x + 10, the value of y is 10 more than the value of x.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, the statement describes the relationships between x and y in these two equations is that in y = 10x, the value of y is 10 times the value of x, and in y = x + 10, the value of y is 10 more than the value of x.

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Answer:

[tex]( - 28 \infty )[/tex]

Step-by-step explanation:

We have already found the solution to the inequality, but since we want to represent the solution in interval notation, we have changed it.

hopefully this helps! :)

If you choose a card at random from 1 through 8, there is an 87.5% probability that you will choose a card that is higher than 1.

There are 8 cards in total, and we want to find the probability of picking a card that is greater than 1.

Out of the 8 cards, 7 of them are greater than 1 (2, 3, 4, 5, 6, 7, and 8).

Therefore, the probability of picking a card that is greater than 1 is:

P(greater than 1) = 7/8

To write this as a percentage rounded to the nearest tenth, we can multiply by 100 and round to one decimal place:

P(greater than 1) = 7/8 * 100% = 87.5% (rounded to the nearest tenth)

Therefore, the probability of picking a card that is greater than 1 is 87.5%.

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Answer: a

Step-by-step explanation:

(1/4)(1x^2y + 32)

Substituting x = 8, y = 3, and z = 5/3:

(1/4)(1(8)^2(3) + 32) = (1/4)(192 + 32) = (1/4)(224) = 56

Therefore, the value of the expression is 56.

the area of the larger sector is approximately 7.11 m².

How to solve and what does circle mean?

To find the area of the larger sector with radius 8m and central angle 40°, we can use the formula:

Area of sector = (central angle/360) x πr²2

Plugging in the given values, we get:

Area of sector = (40/360) x π(8)²2

Area of sector = (1/9) x 64π

Area of sector = 7.11 m² (rounded to the nearest hundredth)

Therefore, the area of the larger sector is approximately 7.11 m².

A circle is a closed two-dimensional geometric shape consisting of all points that are at the same distance from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and twice the radius is called the diameter. The circumference of a circle is the distance around its edge, and the area of a circle is the space enclosed within its edge.

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The first five terms of the recursive sequence an = an-1 + 7, where a1 = 5 can be found by applying the recursive formula multiple times.

A recursive formula is a mathematical expression that uses a sequence of previously defined terms to define each successive term. This type of formula is commonly used to define sequences and can be used to define functions as well. The recursive formula is based on the idea of self-similarity, which means that each successive term is defined in terms of the one before it.

Answer:

C.

Step-by-step explanation:

Questions:

1. 6 is not more than z.

2. The value of w is at least 12

3. Josiah plans to complete his 50 minutes of Mappers practice in 5 days and split the practice up evenly. Which inequality can he use to decide how many minutes he must complete each day?

4. Amy has $35.75 for her visit to the zoo. She must pay $7.25 for admission and wants to feed as many animals as she can. Food for the animals costs $1.25 each. What inequality represents the largest number of animal food that Amy can buy?

5. Jacob spent $40 on supplies to make 100 shirts for a baseball team fundraiser. Solve the inequality to help him decode how much to charge for each shirt to make a profit of more than $350.

100t-40 is greater than 350

Answers:

1. 6 is less than or equal to z (2nd option)

2. w is greater than or equal to 12 (1st option)

3. 5x is greater than or equal to 50 (1st option)

4. 1.25x + 7.25 is less than or equal to 35.75 (4th option)

5. t is great than 39 (3rd option)

Answer:

BC = 62

Step-by-step explanation:

There are 3 triangles total in the figure shown, one large triangle, and two smaller triangles created by the segment BC. Now, look at triangle ACD and see that is a scaled version of common right triangle.

Some common right triangles are 3-4-5, 5-12-13, and 7-24-25. You may be able to see a pattern here where the square of the smallest side length is equal to the sum of the other two side lengths. Triangle ACD happens to be a scaled form of a 5-12-13 triangle. The triangle is scaled by a factor of 3. So the respective side length of AD is 12 * 3 = 36.

Now look at triangle ABD. We have two of the three side lengths.

AD = 36

AB = 85

We want to find BC, so we will use the pythagorean theorem, with (x + 15) to represent the length of BD.

35² + (x + 15)² = 85²

1225 + (x + 15)² = 7225

(x + 15)² = 6000

x + 15 = ±√6000

x = -15 ± √6000

Our equation provides two answers, but the negative value doesn't make sense because length can't be negative, so use the positive length for this application.

x = -15 + √6000

x = 62.4596

Rounded to the nearest whole number, the length of BC is 62.

ΔABC is similar to [tex]~[/tex]ΔADE. BC= 162 and m∠ACB≈ 67.86°

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

In  ΔABC and [tex]~[/tex]ΔADE,

m∠ADE=m∠ABC=90⁰

m∠EAD=m∠CAB...(common angle)

Thus, ΔABC is similar to [tex]~[/tex]ΔADE, by AA test of similarity.

Corresponding angles of both the triangles are equal, and

Corresponding sides of both the triangles are in proportion to each other.

In  ΔABC and [tex]~[/tex]ΔADE,

To find the value of x, we can cross-multiply the given equation and solve for x:

AE/AC=DE/BC

230/315 = 120/BC

Multiplying both sides by BC, we get:

230BC/315 = 120

Multiplying both sides by 315, we get:

230BC = 120 * 315

Dividing both sides by 230, we get:

BC= (120 * 315) / 230

Simplifying, we get:

BC= 162

The cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse.

In ΔABC

Cos ∠ACB=BC/AC

Cos ∠ACB=162/315

We can use the inverse cosine function (cos⁻¹) to find the measure of angle ACB:

∠ACB= cos⁻¹(162/315)

Using a calculator, we get:

∠ACB ≈ 67.86°

Therefore, the measure of angle ACB is approximately 67.86 degrees.

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The equation for the line passing through the point (4, 1) and perpendicular to 2x - 3y = 6 is y = (-3/2)x + 7.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

y = mx + b

1 = (-3/2) 4 + b

1 = -6 + b

1 + 6 = b

7 = b

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You're right about the answer

Answer:

-x - 12

Step-by-step explanation:

x- (-12) = x+12. The opposite of x+12 = -x-12. The answer is therefore -x -12, NOT x + 12.

Answer:

the equation's intervals are (0;+∞)

Step-by-step explanation:

Replace x with -12:

-12 - (-12) = -12 + 12 = 0

With -12 this equation is equal to zero, but since x > -12, that means we have to replace x with numbers that are greater that -12 (-11; -10; etc.)

And since there are open intervals ( > ), we do not count the zero.

The calculated  half-life of the radioactive substance is 18.905 years.

% remaining after each year: 100 - 3.1 = 96.9

Solve for t in

1/2 = (0.969)t

t = log(1/2) / log(0.969) ≅ 18.905 years

t1/2 = 18.905 years

The time it takes for a radioactive element's atoms to divide in half from their initial number is known as the half life of the element or substance.

nuclear decay Radioactive decay is the process by which the nucleus of a heavy radioactive element breaks down and releases alpha, beta, and gamma rays.

Radioactivity law says that when a radioactive element breaks down or decays, a new element will either emit alpha particles two places below the original element in the periodic table or beta particles two places above the original element.

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Answer:

Step-by-step explanation:

The volume of a square-based cuboid is given by the formula:

V = l × w × h

where l is the length, w is the width, and h is the height of the cuboid.

If the length is 4 cm, the width is also 4 cm (since it is a square-based cuboid), and the height is 10 cm, we can substitute these values into the formula and calculate the volume:

V = 4 cm × 4 cm × 10 cm

V = 160 cubic centimeters (cm³)

Therefore, the volume of the square-based cuboid is 160 cubic centimeters.

Answer:

Step-by-step explanation:

Unfortunately, I cannot see the diagram you are referring to. However, I can provide you with the formula for calculating the volume of a square-based cuboid.

The volume of a square-based cuboid is calculated by multiplying the length, width, and height of the cuboid together. In other words:

Volume = length x width x height

So if the length of the cuboid is 4 cm, the width is also 4 cm (since it is a square-based cuboid), and the height is 10 cm, the volume can be calculated as:

Volume = 4 cm x 4 cm x 10 cm

Volume = 160 cubic centimeters

Therefore, the volume of the cuboid is 160 cubic centimeters (cc), or cm^3.

Answer:

7a^2(a^4 + 4)(a^4 - 4)

Step-by-step explanation:

To simplify 7a^10 - 112a^2, we need to find the greatest common factor (GCF) of the two terms and factor it out.

The GCF of 7a^10 and 112a^2 is 7a^2.

So, we can factor out 7a^2 from both terms, which gives:

7a^2(a^8 - 16)

Now, we can further simplify the expression by noticing that a^8 - 16 is a difference of squares. We can write it as:

a^8 - 16 = (a^4)^2 - 4^2 = (a^4 + 4)(a^4 - 4)

Therefore, the fully simplified expression is:

7a^2(a^4 + 4)(a^4 - 4)