Please explain and help me

The height of the prism is 5x + 3 units.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

Given:

The volume of a rectangular prism is given by the expression

10x^3 + 46x^2 – 21x – 27. The area of the base of the prism is given by the expression 2x^2 + 8x – 9.

We have to find the height of prism.

Volume of the rectangular prism = Base × Height

The expression is in the Question be

10x ³ + 46 x² - 21x -27

And the  area of the base of the prism is given by the expression

2x² + 8x - 9 .

Put in the formula

10x ³ + 46 x² - 21x -27  = 2x² + 8x - 9  × Height

The factor of 10x ³ + 46 x² - 21x -27 are (5x +3 )(2x² + 8x - 9) .

put in the formula

(5x +3 )(2x² + 8x - 9) = (2x² + 8x - 9) × Height

Cancelled 2x² + 8x - 9 on both side.

(5x+3)unit = Height

Hence, the height of the prism is 5x + 3 units.

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The region inside cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ) is equal to [tex]\frac{\pi}{4}[/tex]

Now, According to the question:

We will first draw both of them on the same plane and then find their point of intersection. Then using the given information, we will shade the region whose area we have to find.

The point of intersection of  r = 1 + cos(θ) and  r = 3 cos(θ)

1 + cos(θ)  = 3 cos(θ)

1 = 2 cos(θ)

=> cos(θ) = 1/2

=> θ = [tex]cos^-^1[/tex][tex]\frac{1}{2}[/tex]

=> θ = ±[tex]\frac{\pi }{3}[/tex]

So, two curves intersect at θ = ± [tex]\frac{\pi }{3}[/tex]

Area of the cardioid,

[tex]A_1 = \int\limits^\pi _\frac{\pi }{3} {\frac{1}{2}(1+cos\theta)^2 } \, d\theta= \frac{1}{2} \int\limits^\pi _\frac{\pi }{3} (1+cos^2\theta+2cos\theta) } \, d\theta=\frac{1}{2}[/tex]

          [tex]\int\limits^\pi _\frac{\pi }{3} {(1 + \frac{cos2\theta+1}{2} +2cos\theta)} \, d\theta[/tex]

 => [tex]A_1 = \frac{1}{2}[\theta+\frac{1}{2}(\frac{sin2\theta}{2} +\theta)+2sin\theta ]^\pi _\frac{\pi }{3}[/tex]

=> [tex]A_1= \frac{1}{2}[\frac{3\pi }{2}+0+0-\frac{\pi }{2}-\frac{\sqrt{3} }{8} -\sqrt{3} ][/tex]

=> [tex]A_1= \frac{1}{2} [\pi +\frac{-9\sqrt{3} }{8} ]\\\\A_1 = \frac{\pi }{2} - \frac{9\sqrt{3} }{16}[/tex]

Area of the circle,

[tex]A_2 = \int\limits^\frac{\pi }{2} _\frac{\pi }{3} {\frac{1}{2}(3cos\theta)^2 } \, d\theta \\\\A_2 = \frac{9}{2} \int\limits^\frac{\pi }{2} _\frac{\pi }{3} \frac{cos2\theta+1}{2}d\theta\\ \\A_2 = \frac{9}{4}[\frac{sin2\theta}{2}+\theta ]^\frac{\pi }{2}_\frac{\pi }{3}[/tex]

[tex]A_2 = \frac{9}{4}[0+\frac{\pi }{2} -\frac{\sqrt{3} }{4} -\frac{\pi }{3} ][/tex]

[tex]A_2=\frac{9}{4}[\frac{\pi}{6}-\frac{\sqrt{3} }{4} ][/tex]

[tex]A_2= \frac{3\pi }{8}-\frac{9\sqrt{3} }{16}[/tex]

Area of the shaded region,

[tex]A = A_1-A_2[/tex]

[tex]A = \frac{\pi }{2} - \frac{9\sqrt{3} }{16} - \frac{3\pi }{8}+\frac{9\sqrt{3} }{16}[/tex]

[tex]A = \frac{\pi }{8}[/tex]

This is the area of the shaded region in the first and the second quadrant. We see that by symmetry, the area of the shaded region in the first and the second quadrant is equal to the area of the shaded region in the third and the fourth quadrant.

So, the total area is 2 ×[tex]\frac{\pi}{8}[/tex] = [tex]\frac{\pi}{4}[/tex]

Hence, the region inside cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ) is equal to [tex]\frac{\pi}{4}[/tex]

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Answer: z=23

Step-by-step explanation:

Since the sum of all interior angles of a triangle is 180, let's use that to solve this problem.

First, let's set up an equation.

z+62+95=180

Next step is to simplify the left side of the equation, which leaves us with:

z+157=180

Lastly, subtract 157 from both sides of the equation and we get the final answer:

z = 23

Answer:

the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together

Step-by-step explanation:

angle addition postulate formula is ∠AOB + ∠BOC = ∠AOC

an incline plane to lift a heavy object to the top of a shelving unit with a height of 5 ft. The base of the incline plane is 221 ft from the shelving unit

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Answer:

Step-by-step explanation:

The height of her pear tree is 20 inches

First subtract 46 from 26 to get 20. So 20+26=46inches

x=20

Step-by-step explanation:

you know how to transform an equation ?

you need to apply the same operating to both sides of the equation. always. otherwise the equality relation is destroyed.

x + 26 = 46

to get to "x = ..." the "+ 26" is in the way.

clearly we need to subtract 26. but we need to do it on both sides.

x + 26 - 26 = 46 - 26

x = 20

that simply means the last tree is 20 in.

it is 26 in shorter than 46 in (fig tree).

that's all there is to it.

Answer: x = 81

Step-by-step explanation:

Quite a straightforward question.

Given equation is 61+20=x

So you just need to add 61 and 20 to get the value of x,

x=81

∠3 is congruent to ∠1. Hence, proved.

Two angles are said to be complementary angles if they add up to 90 degrees. In other words, when complementary angles are put together, they form a right angle (90 degrees).

Given that, ∠3 and ∠2 are complementary; m∠2 + m∠3 = 90°---------(I)

From the given figure,

m∠1 + m∠2 = 90°---------(II)

From the given equation (I) and (II), we get

m∠1 + m∠2=m∠2 + m∠3

m∠1 ≅ m∠3

Hence, proved.

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Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.

The original capital is multiplied by the interest rate, the loan term, and other factors to calculate simple interest. A simple return is equal to the principal plus interest hrs. This method of calculating interest is the simplest. The most typical method is to calculate it as a fraction of the principal amount. For instance, he was only liable for paying his portion of the interest if he acquired $100 from a buddy and agreed to repay the money on 5% interest. $x (0.05) = $5. When you make loans or lend money, you both have to pay interest. Interest is frequently determined as a percentage of a loan.

Here,

Given  :  interest = 9%

time  =35 years

amount = 800000

Using formula :

=> FV.( r / [tex](1+r) ^{n}[/tex] -1)

=>  800000 (0.09/12 / [tex](1 + 0.09/12 )^{12*35}[/tex] - 1 )

=> 271.94

Therefore,

the total amount you deposit will only be

=> 35*12 times $271.94, or

roughly total amount => 35*12*271.94= 114214.8 dollars, out of the estimated $800,000.

The balance will be what the account earns or accumulates over the next 35 years.

Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.

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The correct equations to represent Ted's total September costs are: (3600+ 1.50) x 12.000 1.50(3600+) 12,000.

Cost is the total expenditure or loss incurred in the production, acquisition, or use of a product or service. It can be calculated as the sum of fixed costs (such as rent and labor costs) plus variable costs (such as materials and energy). Cost can be expressed both in monetary terms (such as dollars or euros) or in terms of resources (such as time or effort). In business, cost is a crucial factor for determining profitability and should be taken into consideration when making decisions about production, sales, and pricing strategies.
The first equation calculates the cost of the fixed monthly costs plus the cost of the 16 ounce bags of coffee multiplied by the total number of bags sold. The second equation calculates the cost of the 16 ounce bags of coffee multiplied by the fixed monthly costs plus the total number of bags sold.

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The probability of being born on a Tuesday is= 18/343

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability.

A straightforward illustration is tossing a fair (impartial) coin.

The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).

Hence, The probability of being born on a Tuesday is= 18/343.

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Answer:

D

Step-by-step explanation:

There are no black shoelaces

The values of the expression are given by the inequality below:

11/3 < 5/x + 2 < 9/2

Here we want to find the possible values of the expression:

5/x + 2

Where we have the restriction:

2 < x < 3

Notice that x is on the denominator, so when x takes the largest value x = 3, we will have a lower bound for the expression:

5/3 + 2 = 5/3 + 6/3 = 11/3

When x takes the smallest value, we will get the upper bound:

5/2 + 2 = 5/2 + 4/2 = 9/2

Then the possible values of the expression are:

11/3 < 5/x + 2 < 9/2

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If y equals 7 when x equal 2/3, so when x =7/3 the y is equal to 14/7

If y varies inversely with x, this means that the product of x and y is a constant. So if we know that y = 7 when x = 2/3, then we can set up the equation: x*y = k, where k is the constant.

Substituting the known values we get: (2/3)*7 = k.

So we know that k = 14/3

Now, we can use this value of k to find the value of y when x = 7/3.

x*y = k

(7/3)*y = 14/3

y = 14/7

So, when x = 7/3, y = 14/7

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Therefore , the solution of the given problem of equation comes out to be x² + z²= y, a circular paraboloid.

When a math formula employs the equals symbol (=), it appears to be a rule that connects two expression and denotes equality. An equation in algebra is a factual declaration that shows that several mathematical variables are all equal. For instance, the values ptdc + 6 and 12 in the equation obd + 6 = 12 have an equal sign. The link between the words on either side of each letter is described by a mathematical formula. The sentence and the insignia are frequently same.

Here,

The vector solution is r(s, t) = s, t, t² - s².

When comparing to r(s, t) = x, y, and z, x = s, y = t, and z = 2 - s²

So, z = y² - x²

, a hyperbolic paraboloid (2)

r(s, t) = s sin³t, s², s cos³t is the vector equation that is presented.

When comparing with withr(s, t) = x, y, and z,

x = ssin³t, y = s², and z = s* cos³t²

As a result, x2 + z2 = s2 (sin23t + cos23t),

sin23t + cos23t = 1,

x² + z² = s², s² = y, and x² + z²= y,

a circular paraboloid.

Therefore , the solution of the given problem of equation comes out to be x² + z²= y, a circular paraboloid.

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The value of j by solving with one-step equation solution method will be of the option C i.e. 2/30.

What are one-step equations?

A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true.

To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself. The inverse operations are:

Addition and subtraction

Multiplication and division

The most important thing to remember is that whatever you do to one side of the equation, you have to do the same thing to the other side.

Now,

given that,

19/30=j+17/30

To find j, subtract 17/30 from both side,  (Using one-step equation method)

19/30-17/30=j+17/30-17/30

2/30=j

Hence, the value of j will be 2/30.

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Answer:

23.35 cubic feet

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula: V = π * r^2 * h, where r is the radius of the circular base, h is the height of the cylinder.

To find the radius, we use the formula for the circumference of a circle: C = 2πr

The circumference of the circular base is 2.6 feet, so we can set this equal to 2πr and solve for r: 2.6 = 2πr, r = (2.6) / (2π) = 0.816

Now that we know the radius, we can substitute it into the volume formula: V = π * (0.816)^2 * 4.4 = 23.35 cubic feet

So the answer is 23.35 cubic feet, which closest to A. 23.35 cubic feet

Answer:

I don't know the answer to this question

$2094.28 interest will she pay by the time the loan is repaid.

What is compounded monthly?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

As we know the formula of per month installments

[tex]E.M.I = \frac{P*r*(1+r)^n}{(1+r)^n^-^1}[/tex]

By putting the value of P (loan applied for)=$5500

r (Monthly rate of interest)  [tex]= \frac{6.8}{12*100}[/tex]

n = number of monthly installments = 10 × 12 = 120

[tex]E.M.I = \frac{5500*(\frac{6.8}{12*100} )(1+\frac{6.8}{1200} )^1^2^0}{(1+\frac{6.8}{1200} )^1^2^0-1}\\ E.M.I= \frac{5500*0.00567*1.971}{1.971-1}\\ E.M.I = \frac{61.461}{0.971} \\E.M.I = 63.29[/tex]

E.M.I.=$63.29

Total Installments of loan =120

Therefore total amount paid against loan = $63.39 × 120 = 7594.28

So interest paid = 7594.28 - 5500= $2094.28

Hence, $2094.28 interest will she pay by the time the loan is repaid.

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Answer:

240 seats with tables

Step-by-step explanation:

Let's start by making our fraction out of 10 on the first train to make it easier on us, this fraction would be [tex]\frac{6}{10}[/tex]. Then, to get the number of seats on this train that would have a table, we need to multiply 400 by our fraction, giving us:

[tex]400 * \frac{6}{10} = 2400/10 = 240[/tex]

So, the 1st train should have approximately 240 seats with tables.

Hope this helped!

Given ,

[tex]\bold\red{zeroes \: of \: a \: cubic \: polynomial \: are \: - 2 \:, \: 0 \: and \: 7} \\ [/tex]

[tex]let \:, \\ \boxed{\alpha \: = - 2} \\ \boxed{\beta \: = 0} \\ \boxed{\gamma \: = 7} [/tex]

Now ,

[tex]sum \: of \: zeroes \: = \alpha \: + \: \beta \: + \: \gamma \: \\ \dashrightarrow \: sum = - 2 + 0 + 7 = \underline{5} \\ \\ sum \: of \: product \: of \: zeroes \: taken \: two \: at \: a \: time \: = \alpha\beta \: + \beta\gamma \: + \: \alpha\gamma \\ \dashrightarrow \: ( - 2)(0) \: + \: (0)(7) \: + \: (7)( - 2) \: = \: \underline{ - 14} \\ \\ product \: of \: zeroes \: = \: \alpha\beta\gamma \\ \dashrightarrow \: ( - 2)(0)(7) = \underline{0}[/tex]

We know that ,

[tex] \boxed{cubic \: polynomial \: = {x}^{3} - (\alpha \: + \: \beta \: + \: \gamma \:) \:{x}^{2} + (\alpha\beta \: + \: \beta\gamma \: + \: \alpha\gamma) \:x \: - \: \alpha\beta\gamma} [/tex]

Plugging in the values , we get

[tex]\boxed{f(x) = {x}^{3} - 5 {x}^{2} - 14x + 0}[/tex]

since this polynomial has degree 3 , it is called a cubic polynomial.

hope helpful! :)

The minimum number of poles to be Erected for fencing are 26.

The perimeter of a rectangle is -

P = 2{L + B}

Given is that a rectangular field measures 63.9 meters by 104.6 meters.

The perimeter of the rectangular field will be -

P = 2(63.9 + 104.6)

P = 2(168.5)

P = 337

Let the total number of poles that can be erected are {x}. Then, we can write that -

2.4x ≤ 63.9

x ≤ (63.9/2.4)

x ≤ 26.66

x = 26 {approx.}

Therefore, the minimum number of poles to be Erected for fencing are 26.

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According to Westgard and CLIA , 40-100  specimens should be run by each method on the same day for 8 to 20 days to compare a test method with a comparative method.

CLIA stands for  Clinical Laboratory Improvement Amendments  . The regulations under CLIA includes, the federal standards which is applicable to all U.S. facilities or sites which are test human specimens for health assessment or it is used to diagnose, prevent, or treat disease.

The Federal Register is the official daily publication for federal agencies and the organization's notices, proposed regulations, and final rules, as well as executive orders and other presidential papers. The regulations published in the Code of Federal Regulations and enforced by federal agencies are known as final rules.

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Answer:

0.9583

Step-by-step explanation:

(2-1) * (23÷24)

1*0.983

=0.9583

Answer:

[tex]\frac{23}{24} = 0.95[/tex]

Step-by-step explanation:

According to BODMAS

If g(x) is the inverse function of f(x)  and[tex]$f^{\prime}(x)=\frac{1}{1+x^4}$[/tex], then [tex]$g^{\prime}(x)$[/tex]  is [tex]1+[\mathrm{g}(\mathrm{x})]^4\end{aligned}[/tex]

Correct option is A)

[tex]& \mathrm{g}=\mathrm{f}^{-1} \\[/tex]

[tex]& \mathrm{f}(\mathrm{g}(\mathrm{x}))=\mathrm{x}[/tex]

Differentiate w.r.t.x

[tex]& \mathrm{f}^{\prime}(\mathrm{g}(\mathrm{x})) \cdot \mathrm{g}^{\prime}(\mathrm{x})=1 \\[/tex]

[tex]& \therefore \frac{1}{1+(\mathrm{g}(\mathrm{x}))^4} \cdot \mathrm{g}^{\prime}(\mathrm{x})=1 \\[/tex]

[tex]& \mathrm{~g}^{\prime}(\mathrm{x})=1+[\mathrm{g}(\mathrm{x})]^4\end{aligned}[/tex]

The complete question is,

If [tex]$\mathrm{g}(\mathrm{x})$[/tex]is the inverse function of [tex]$\mathrm{f}(\mathrm{x})$[/tex] and [tex]$\mathrm{f}^{\prime}(\mathrm{x})=\frac{1}{1+\mathrm{x}^4}$[/tex], then [tex]$\mathrm{g}^{\prime}(\mathrm{x})$[/tex]is

A [tex]$1+[\mathrm{g}(\mathrm{x})]^4$[/tex]

B [tex]$1-[g(x)]^4$[/tex]

C [tex]$1+[\mathrm{f}(\mathrm{x})]^4$[/tex]

D [tex]$\frac{1}{1+[\mathrm{g}(\mathrm{x})]^4}$[/tex]

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By completing squares in both the variables and try to get the general equation of the form:

(x - a)^2 + (y - b)^2 = R^2

A general circle equation for a circle whose center is (a, b) and the radius is R, is:

(x - a)^2 + (y - b)^2 = R^2

So, if we have an equation like:

x^2 + cx + d + y^2 + h*y + l = m

We just need to complete squares in both x and y, such that we end with an equation of the form of:

(x - a)^2 + (y - b)^2 = R^2

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Answer:

B.

Step-by-step explanation:

You need to find a common denominator.  In this case, 40.  Convert 2/5 to 16/40 and 3/8 to 15/40.  Add the numerators (16 + 15) together.  The denominator stays the same.

The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).

Take the common terms in the numerator and denominator and remove them from the expression to make it simpler.

The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).Similar to fractions with variables in the denominators, rational expressions appear like them (and often numerators too).

For instance, the expression x 2 x + 3 is a rational expression: x squared, divided by x, plus 3, end fraction.

1)2m^2-4m)/2(m-2)

=[2m(m-2m)]/2(m-2)

= 2m/2

=m

2)m^2-2m+1/m-1

= (m-1)^2/(m-1)

=(m-1)(m-1)/(m-1)

=(m-1)

3)m^2-3m+2/m^2-m

=m^2-m-2m+2/m(m-1)

=m(m-1)-2(m-1)/m(m-1)

= (m-1)(m-2)/m(m-1)

=(m-2)/m

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The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The quadratic regression equation y = –0.1x² + 143.99x – 13,242.84 models expected company profits in terms of the number of pairs of shoes sold.

The profit can the company expect if it sells 400 pairs of shoes will be given as,

y = –0.1(400)² + 143.99(400) – 13,242.84

y = – 16,000 + 57,596 – 13,242.84

y = 28,354

y ≈ 28,400

The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.

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Answer:

First account: $16,000

Second account: $4,000

Step-by-step explanation:

Let x be the amount Christine invested in the 8% account and y be the amount she invested in the 10% account. We know from the problem that:

x + y = $20,000 (the total amount she had to invest)

0.08x + 0.1y = $1920 (the total amount of interest she received)

We can use the first equation to solve for one variable in terms of the other.

x = $20,000 - y

Now we substitute this expression into the second equation:

0.08($20,000 - y) + 0.1y = $1920

Solving for y:

0.08x + 0.1y = $1920

0.08($20,000 - y) + 0.1y = $1920

1,600 - 0.08y + 0.1y = $1920

-0.08y = -320

y = $4,000

Now, we know that Christine invested $4,000 in the 10% account, we can use the first equation again to find out how much she invested in the 8% account:

x + y = $20,000

x + $4,000 = $20,000

x = $16,000

So Christine invested $16,000 in the 8% account and $4,000 in the 10% account