What is the solution of the equation (x-5)2 + 3(x-5)+9=0? Use u substitution and the quadratic formula to solve.
-3±3-√3
2
O x-
7±3-√√3
2
Ox-2
Ox=8

Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.

Algebraic progression is a series of numbers where each term following the first is derived by multiplying the previous president by a constant known as the common difference (d). An arithmetic progression often takes the form: A, A+D, A+2D, A+3D,... where "a" stands for the initial keyword and "d" for the common distinction.

given

The sequence's initial term is 7, and the shared discrepancy is 15. We can continuously add 15 to the preceding word to find the next terms.

As a result, the arithmetic sequence's first four terms are:

Initial term = 7

Term two: 7 plus 15 equals 22

Third term = 22 plus 15 equals 37

Fourth term: 37 plus 15 equals 52

Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.

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Answer:

Center= -4,8

Radius=7

Step-by-step explanation:

The value of y that makes the hanger balance is 3.

The value of y can be solved considering linear equation method.

A linear equation is an algebraic equation in which the highest power of the variable(s) is always 1. It represents a straight line when graphed on a Cartesian coordinate plane. A linear equation can have one or more variables.

To solve for y in the equation 5 + y = 8, you can follow these steps:

Step 1: Subtract 5 from both sides of the equation to isolate the term with y on one side.

5 + y - 5 = 8 - 5

This simplifies to:

y = 3

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y is a function of x.

A mathematical relationship between an input (x) and an output (y) where each input has exactly one output is known as a function. There are no multiple possibilities of y for a single value of x in the preceding equation, which expresses y as a combination of x², x, and a constant term. As a result, the equation meets the criteria for a function.

Yes, y = 2x² - 4x + 10 is a function.

A function is a mathematical rule that assigns to each input (x-value) exactly one output (y-value). In the given equation, for any value of x, we can calculate the corresponding value of y using the given equation. Therefore, y is a function of x.

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The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.

A this double shape's perimeter is the space encircling its outside edge. It is the length of the object's sides. As an illustration, the perimeter of a rectangle is equivalent to the total of its four sides' lengths.

given

Assume that the rectangular field has a width of "x" yards.

The problem states that the field's length is three times its breadth, or three times yards.

The lengths of all the sides make up the rectangle's perimeter, therefore we can write:

[tex]Perimeter = 2 (length + width).[/tex]

In place of the values we hold:

[tex]400 = 2(3x + x)\\400 = 2(4x) (4x)\\400 = 8x\\x = 50[/tex]

The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.

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Answer: The primary rectangle contains a length of 2a units (since it is labeled as "2a" within the diagram), so its zone is 2a x a = 2a^2 square units.

The moment rectangle contains a length of 3a units (since it is labeled as "3a" within the diagram), so its range is 3a x a = 3a^2 square units.

The third rectangle contains a length of 4a units (since it is labeled as "4a" within the graph), so its range is 4a x a = 4a^2 square units.

To discover the overall region of the expansive rectangle, able to include the zones of these three rectangles:

Add up to zone = 2a^2 + 3a^2 + 4a^2

Disentangling this expression, we are able combine the like terms (2a^2, 3a^2, and 4a^2) to urge:

Add up to range = (2 + 3 + 4) a^2

Step-by-step explanation:

the total number of boxes with at least 20 but fewer than 60 broken crayons is  33.To answer this question, we need to use the stem-and-leaf plot to count the number of boxes with at least 20

what is at least ?

"At least" is a phrase that is used to indicate a minimum quantity or degree of something. It means that the stated quantity or degree is the smallest amount that is acceptable or possible. For example, if someone says "I need at least 10 dollars,"

In the given question,

To answer this question, we need to use the stem-and-leaf plot to count the number of boxes with at least 20 but fewer than 60 broken crayons.

From the stem-and-leaf plot, we can see that the stems 2, 3, 4, and 5 have leaves that add up to at least 20 but fewer than 60:

Stem 2 has leaves 3 and 8, which add up to 11.

Stem 3 has leaf 3, which adds up to 3.

Stem 4 has leaves 0 and 9, which add up to 9.

Stem 5 has leaves 1 and 9, which add up to 10.

Therefore, the total number of boxes with at least 20 but fewer than 60 broken crayons is 11 + 3 + 9 + 10 = 33.

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Here, we want to get the final volume

From the general gas equation, we have it that:

[tex]\dfrac{P_1V_1}{T_1} =\dfrac{P_2V_2}{T_2}[/tex]

From the question, we have it that:

P1 is the initial pressure which is 475 torr

V1 is the initial volume which is 296 mL

T1 is the initial temperature which we have to convert to absolute value by adding 273.15 K ([tex]68 + 273.15 = 341.15 \ \text{K}[/tex])

P2 is the final pressure that is the same as the initial which is 475 torr

V2 is the final volume that we want to calculate

T2 is the final temperature which is 273.15 K (0 degrees Celsius is 273.15 K)

Substituting the values, we have:

            [tex]\dfrac{475\times296}{341.15}=\dfrac{475\times V_2}{273.15}[/tex]

[tex]V_2=\cfrac{475\times296\times273.15}{341.15\times475} =\boxed{\bold{237 \ mL}}[/tex]

We could have solved this by using Charles' law that relates temperature to volume (volume is directly proportional to temperature)

The correct option is (D) A, B, C, E, G, I

What is the cube?

A cube is a three-dimensional solid shape that has six square faces of equal size. It has twelve edges and eight vertices, and all angles between the faces are right angles. The cube is a regular polyhedron, which means that all its faces are congruent and all its edges have the same length.

The net of a cube is the one that has the faces arranged in such a way that it makes a complete cubic structure

A) In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

B)  In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

C) In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

D) In the given figure, the net can be folded into a cube when its faces are folded one over the other. Therefore, it is a cube net.

Hence, The correct option is (D) A, B, C, E, G, I.

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Answer:

11 dimes and nickels.

Step-by-step explanation:

22 total coins divided by 2 equals 11 for each.

the number 2 represents the dimes and nickels, 22 for the total amount of coins, and 11 for the answer.

Answer:15 nickels  and  7 dimes.

Step-by-step explanation:

The total miles drive by Suzy in 18 hours when she can drive 53 miles in 1 hour is equal to 954 miles.

If Suzy can drive 53 miles in 1 hour,

Using the formula of speed based on distance and time we have,

Speed = Distance / Time

Substitute the values in the formula we get,

⇒ Speed = 53 miles / 1 hour

⇒ Speed  = 53 miles/hour

Use this information to find out how far Suzy can drive in 18 hours we get,

Now, Speed =  53 miles/hour

Time = 18 hours

Distance = Speed x Time

Substitute the value of speed and time we get,

⇒ Distance  = 53 miles/hour x 18 hours

⇒ Distance = 954 miles

Therefore, Suzy can drive 954 miles in 18 hours.

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In order to achieve $4,000 in three years at 4.5% simple interest, the principal must be equal to $29,629.63.

In Mathematics, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

By substituting the given parameters into the simple interest formula, we have;

4,000 = P × 4.5/100 × 3

4,000 = P × 0.045 × 3

4,000 = 0.135P

Principal, P = 4,000/0.135.

Principal, P = $29,629.63

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Answer:72

Step-by-step explanation:you would add the 9 to the other side and then it would give you the answer of x=72. You do this because it is -9 if it were say x+9 then you would subtract 9 from both sides

The blanks when completed are

In a scale drawing, the scale factor represents the ratio of the size of an object in the drawing to the size of the corresponding object in real life.

In the given scale drawing, we have

Longest side in B = 12

So, the scale factor is

scale factor = size of object in drawing / size of corresponding object

This gives

scale factor = 12 / 4

scale factor = 3

This means that

Every side length in A grew by a factor of 3

Using the scale ratio formula, we have

A length in B/A corresponding length in A = 3

Lastly, the size of the angles remain unchanged

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10 x 8 face as the base for prism 1

10 x 3 face as the base for prism 2

To find the area of the base, you simply multiply the length and width:

Base area = length x width = lw

Therefore, for rectangular prism 1 we get:

10 x 8

For rectangular prism 2 we get:

10 x 3

Similarly, if the base of the prism is a triangle, you would need to use the formula for the area of a triangle, which is:

Base area = 1/2 x base x height

where base and height are the base and height of the triangle respectively.

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Answer:

3 (x + y) (x - y)

Step-by-step explanation:

3x²-3y²​

GCF is 3

3(x² - y²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = (a+b) (a−b) where a = x  and b = y.

So, the answer is 3 (x + y) (x - y)

Based on the word problem, the answer is not one of the given options (E. NOTA).

In this case, we have 9 letters and we want to select all of them, so n = 9 and r = 9. Therefore:

A = 9!

A = 362,880

B) The hypotenuse of a right triangle can be found using the Pythagorean theorem:

c^2 = a^2 + b^2

In this case, we have a = 9 and b = 12. Therefore:

c^2 = 9^2 + 12^2

c = 15

So, B = 15.

y - 9 = 3(x - 6)

y - 9 = 3x - 18

y = 3x - 9

The y-intercept of this line is -9, so C = -9.

Therefore, A + B + C = 362,880 + 15 - 9 = 362,886.

So the answer is not one of the given options (E. NOTA).

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Answer:

PMT = $52,023.26

Step-by-step explanation:

To calculate how much Fiona must deposit into her retirement account each year, we can use the formula for annuity payments:

PMT = PV x (r / (1 - (1 + r)^(-n)))

Where:

PMT is the periodic payment

PV is the present value (or desired future value) of the annuity

r is the interest rate per period (in this case, the annual yield of 6% divided by the number of periods per year, which is 1)

n is the total number of periods (in this case, 20 years)

We know that Fiona wants to have a total of $600,000 in her retirement account by the time she retires, so PV = $600,000. We also know that the interest rate per period is 6% / 1 = 0.06, and the total number of periods is 20.

Plugging these values into the formula, we get:

PMT = $600,000 x (0.06 / (1 - (1 + 0.06)^(-20)))

PMT = $600,000 x (0.06 / (1 - 0.312))

PMT = $600,000 x (0.06 / 0.688)

PMT = $52,023.26

Therefore, Fiona would need to deposit approximately $52,023.26 into her retirement account each year for the next 20 years to have a total of $600,000 by the time she retires, assuming the annual yield remains constant at 6%.

The value of x is given as follows:

x = 4.2 cm.

The value of x is obtained applying the proportions in the context of the problem.

The ratio between the volumes is given as follows:

3375/512 = 6.59

The side lengths are measured in units, while the volume is measured in cubic units, hence the proportion to obtain the value of x is given as follows:

8/x = cubic root of 6.59

8/x = 1.9

x = 8/1.9

x = 4.2 cm.

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a.The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b.  the probability is 0.1399.

c. the quarterback can expect to throw about 2.27 passes before completing one.

d. the probability is 0.1865.

e. the probability is 0.7349.

The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.

a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:

P(X=k) = [tex](1-p)^{k-1}[/tex]×p

where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.

The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:

P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰

= 0.56²×0.44

= 0.1399

Therefore, the probability is 0.1399.

c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:

E(X) = 1/p

where p is the probability of completion on each attempt.

In this case, p = 0.44, so the expected number of passes is:

E(X) = 1/0.44

= 2.27

Therefore, the quarterback can expect to throw about 2.27 passes before completing one.

d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:

P(X > 5) = 1 - P(X <= 5)

= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]

= 0.1865

Therefore, the probability is 0.1865.

e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:

P(X ≥ 4) = 1 - P(X < 4)

where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.

Using the binomial probability distribution table or calculator, we can find:

P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]

= 0.7349

Therefore, the probability is 0.7349.

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===================================================

Explanation:

We have 5 green in the 1st row and 4 green in the 2nd row.

The LCM is 5*4 = 20.

The ratio [tex]6 \text{ yellow} = 5 \text{ green}[/tex] scales up to [tex]24 \text{ yellow} = 20 \text{ green}[/tex] after multiplying both sides by 4.

The ratio [tex]4 \text{ green} = 3 \text{ purple}[/tex] scales up to [tex]20 \text{ green} = 15 \text{ purple}[/tex] after multiplying both sides by 5.

--------------

These set of ratios

[tex]6 \text{ yellow} = 5 \text{ green}\\\\4 \text{ green} = 3 \text{ purple}\\\\[/tex]

scale up to

[tex]24 \text{ yellow} = 20 \text{ green}\\\\20 \text{ green} = 15 \text{ purple}\\\\[/tex]

The key is the "20 green" on each line. This leads to the ratios linking up.

If A = B and B = C, then A = C (transitive property).

So we can say [tex]24 \text{ yellow} = 20 \text{ green} = 15 \text{ purple}\\\\[/tex]

That simplifies to [tex]24 \text{ yellow} = 15 \text{ purple}\\\\[/tex]

We can divide both sides by 3 to get [tex]8 \text{ yellow} = 5 \text{ purple}\\\\[/tex]

--------------

We now have these set of ratios

[tex]8 \text{ yellow} = 5 \text{ purple}\\\\5 \text{ purple} = 2 \text{ red}\\\\[/tex]

Connect those two equations together to get

[tex]8 \text{ yellow} = 2 \text{ red}\\\\[/tex]

Lastly, divide both sides by 4

[tex]4 \text{ yellow} = 1 \text{ red}\\\\[/tex]

Answer: C

Step-by-step explanation: C



Using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.

The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item.

When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects.

The angle from the horizontal downward to an item is referred to as the "angle of depression."

The line of sight of an observer would be below the horizontal.

So, in the given situation:
We will find the base which is the distance of the boat from the land.

Which means:
hypotenuse/Base

Which is represented by Cosx.

The angle is 24°.

Then, the equation for a solution would be:

cos(24) = x/45

Therefore, using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.

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Answer:

y intercept when x is 0, so the answer is 3

The volume of the complete prism is  1625 cubic in

The volume of the figure is solved by dividing the figure into two sections and solving for each volume then adding the individual volume together.

The divisions are section 1 and section 2

section 1 has dimensions: 20 x 15 x 5

volume = 20 x 15 x 5 = 1500 cubic in

section 2 has dimensions: 5 x 5 x 5

volume = 5 x 5 x 5 = 125 cubic in

Volume of the complete figure

section 1  + section 2

= 1500 cubic in + 125 cubic in

= 1625 cubic in

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Using Integration,  Area of the curve is 16/3 unit² and the maximum height of the curve is 2 unit.

What exactly is integration?

Integration is a fundamental concept in calculus, which is a branch of mathematics that deals with rates of change and accumulated quantities. Integration is the process of finding the integral of a function, which is the inverse of differentiation.

Now,

For the maximum height that the curve has we have to

put dy/dx=0

d(4x-2x²)/dx=0

4-4x=0

x=4/4

x=1

and when x=1 then y=4*1-2*1²

=4-2

=2

So, the maximum height of the curve is 2 unit.

and for the area

we need to find y.dx for the curve

So,

y.dx=(4x-2x²).dx

=4x+2x²-2x³-2x³/3 for x=0 to x=2

=8+8-16-16/3

=16/3 unit²

Hence, Area of the curve is 16/3 unit².

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The standard deviation of the sampling distribution is approximately 0.3292.

The behaviour of the sampling distribution of the mean is described by the central limit theorem, a key conclusion in statistics. It asserts that regardless of how the population distribution is shaped, if a random sample of size n is taken from a population with mean and standard deviation, the distribution of sample means will tend towards a normal distribution as n increases.

Because it enables us to utilise the normal distribution to draw conclusions about the population mean based on sample means, the central limit theorem has significant practical ramifications. Additionally, it offers a foundation for confidence interval estimation and statistical hypothesis testing.

The standard deviation is given by the formula:

SD = σ/√(n)

Now, substituting the value of σ = 40, n = 147,400 we have:

SD = σ/√(n) = 40/√(147400) ≈ 0.3292

Hence, the standard deviation of the sampling distribution is approximately 0.3292.

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