what is this ???????/ 9.1 ∙ 102

Answer:

y = - 4x + 38

Step-by-step explanation:

A(3, 9)

B(5, 1)

\(m_{AB}\) = \(\frac{1-9}{5-3}\) = - 4

CD║AB

C(9, 2)

y - 2 = - 4(x - 9)

y = - 4x + 38

The answer is 1) V = \(2\pi\int\limits(2)+ {x} \, dx\); 2) V = \(2\pi \int\limits(1 - 2x) - 2x dx\); 3) V =\(2\pi \int\limits {\sqrt{2} } \, dx\) ; 4) V = \(2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx\) .

1) The volume of the shell is then given by the product of the area of its curved surface and its height. The height is equal to 2 - (-2) = 4, and the radius is equal to the minimum of the distances from x = 2 to the two curves, which is x = 2 - () = 2 + . The volume of the solid is then given by the definite integral:

V = \(2\pi\int\limits(2)+ {x} \, dx\) = \(2\pi [(/3) + 2x]\) evaluated from 0 to 1 = (4/3)π.

2) The height of the region is equal to  - (2x) =  -2x, and the radius is equal to the minimum of the distances from x = 1 to the two curves, which is x = 1 - (2x) = 1 - 2x. The volume of the solid is then given by:

V = \(2\pi \int\limits(1 - 2x) - 2x dx\)=\(2\pi [/5 - 2/3 + /2]\) evaluated from 0 to 1 = (8π/15).

3) The height of the region is equal to (2-x) -  = 2-x. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = The volume of the solid is then given by:

V =\(2\pi \int\limits {\sqrt{2} } \, dx\) = \(2\pi [(x^4/4)]\) evaluated from 0 to √2 = (π/2).

4) The height of the region is equal to () - (2-) = 2 - 2. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = √((2-)/2). The volume of the solid is then given by:

V = \(2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx\) = \(4\pi [(2/3)\± (2\sqrt{2} /3)]\)

The complete Question is:

Use the shell method to find the volumes of the solids generated by revolving the regions bounded by the curves and lines in about the

1.  y = x, y = -x/2, and x = 2

2. y = 2x, y = x/2, and x = 1

3. y = x/2, y = 2-x, and x = 0

4. y = 2-x/2, y = x/2, and x = 0

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Answer is \(2\sqrt{2}\) mi

Given,

Kaylib’s eye-level height is 48 ft

Addison’s eye-level height is 85 and one-third ft above sea level.

From the formula d= \(\sqrt{3h/2}\),

get the difference as:

\(d=\sqrt{(3*(85+1/3))/2} - \sqrt{(3*48)/2}\)

=\(\sqrt{256/2} - \sqrt{3*24}\)

=\(\sqrt{128} - 6\sqrt{2}\)

=\(8\sqrt{2} - 6\sqrt{2}\)

d=\(2\sqrt{2}\)

Therefore, Addison sees \(2\sqrt{2}\)mi to the horizon

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The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer:

The answer is 1054ft³

Step-by-step explanation:

Volume of rectangular prism =1/3LWH

V=1/3×31/2×51/3×12

V=1054ft³

We have a triangle formed by the t

Answer:

H

Step-by-step explanation:

180-48=132

We have that:

The tangent line and radius form a 90° angle.

The sum of the internal angles of a triangle is 180°.

Therefore:

Where:

Substitute the value:

Solve for x:

Answer: 68

Answer:

r=17%

Step-by-step explanation:

P is the investment

A is the targeted amount

t= time (25-18=7 years)

A=P(1+r)^t

30000=10000(1+r)^7

(1+r)^7=30000/10000

r=\root(7)(3)-1

r=0.16993 ≅0.17= 17%

check: A=P(1+r)^t ⇒10000(1+0.17)^7=30012≅30000

Answer:

The first account, she invested = $4200 and in the second = $4800

Step-by-step explanation:

Let us assume that Genevieve invests $x at 6% ,

Hence, she invests ($9000 - $x ) at 4% ,

It's given that the combined interest from both of the above accounts is $444,

So,

0.06x + 0.04 (9000 - x) = 444

=> 0.06x + 360 - 0.04x = 444

=> (0.06x - 0.04x) + 360 = 444

=> 0.02x = 444 - 360

=> 0.02x = 84

=> x = 84/0.02

=> x = 8400/2 (By multiplying the denominator and numerator)

=> x = 4200

Therefore, 9000 - x = 9000 - 4200 = 4800

$4200 at 6% and $4800 at 4%

Therefore, the first account, she invested = $4200 and in the second = $4800

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The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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Answer:

x

Step-by-step explanation:

Step-by-step explanation:

3x+2x=180

5x=180

x=36°

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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When multiplying two terms with the same base, add their exponents. For example, \(a^m * a^n = a^(m+n)\) . When dividing two terms with the same base, subtract their exponents. For example,\(a^m / a^n = a^(m-n).\)

Rewriting the expression (8^x)^3x as (8^x)^(3*x) using the exponent rules, the equation becomes:

\((8^x)^(3*x) = 24\)

Using the property of exponents that says  \((a^b)^c = a^(b*c),\) we can simplify the left-hand side of the equation:

\(8^(x3x) = 24\)

\(8^(3x^2) = 24\)

Now, taking the logarithm of both sides with base 2 (log2), we get:

\(log2(8^(3x^2)) = log2(24)\)

Using the property of logarithms that says loga(b^c) = c*loga(b), we can simplify the left-hand side of the equation:

\(3x^2*log2(8) = log2(24)\)

Recall that log2(8) = 3, so we can substitute this value:

\(9x^2 = log2(24)\)

Finally, solving for x, we get:

\(x = ±sqrt(log2(24)/9)\)

Since x must be non-negative (as given in the original problem), we take the positive root:

\(x = sqrt(log2(24)/9) ≈ 0.8179\)

Therefore, the equivalent expression is:

\(x = sqrt(log2(24)/9) ≈ 0.8179.\)

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The above question is incomplete. the complete question is given below:

Which of the following is equivalent to (8^x)^3x=24 where x≥0 ?

According to the information, we can infer that the correct expression is (10 * 7) + (2 * 7) (option D).

To find the correct expression we must look at the graph and interpret the information it has. In this case, some tiles are white and others are gray, so they would represent different elements. In this case, the white area is 10 * 7 tiles, so this would be the first part of the expression.

On the other hand, the second part of the expression would be 7 * 2, which represents the length, length and width of the gray area. According to the above, the correct expression would be (10 * 7) + (2 * 7), the first part in parentheses represents the white area and the second part in parentheses represents the gray area.

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Answer:

20\(c^{6}\)

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × \(c^{(3+3)}\)

= 20\(c^{6}\)

The maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

To convert the maximum effective monthly rate of 1% into an APR with quarterly compounding, we can use the formula:

\(APR = [(1 + \dfrac{r}{n})^n - 1] \times 4\)

Where r is the effective monthly rate and n is the number of compounding periods per year. In this case, we want to find the maximum APR with quarterly compounding that the borrower will accept, so we can substitute r = 1% and n = 3:

\(APR = ((1 + \dfrac{0.01}{3})^3 - 1) \times 4\)

APR = (1.0100333³ - 1) x 4

APR = 0.04033 x 4

APR = 0.16132 or 16.132%

Therefore, the maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

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Answer:

first, dilate triangle ABC with respect to the origin by scale factor of 2.

then rotate it 90 degrees counterclockwise about the origin

Step-by-step explanation:

Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.

The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

We have,

For Matthew's investment, the continuous compounding formula can be used:

\(A = P \times e^{rt}\)

Where:

A = Final amount

P = Principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case,

Matthew's money has tripled,

So A = 3P.

For Parker's investment, the formula for compound interest compounded annually is used:

\(A = P \times (1 + r)^t\)

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

We need to find t when Matthew's money has tripled in value.

Let's set up the equation:

\(3P = P \times e^{rt}\)

Dividing both sides by P, we get:

\(3 = e^{rt}\)

Taking the natural logarithm of both sides:

ln(3) = rt

Now we can solve for t

t = ln(3) / r

For Matthew's investment,

r = 3 1/8% = 3.125% = 0.03125 (as a decimal).

For Parker's investment,

r = 2 3/4% = 2.75% = 0.0275 (as a decimal).

Now we can calculate t for Matthew's investment:

t = ln(3) / 0.03125

Using a calculator, we find t ≈ 22.313 years.

Now, we can calculate how much money Parker would have in his account at that time:

\(A = P \times (1 + r)^t\)

\(A = $8,000 \times (1 + 0.0275)^{22.313}\)

Using a calculator, we find A ≈ $13,774.

Therefore,

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

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Answer:

20,763

Step-by-step explanation:

I saw the answer after I got it wrong

The angles 5 and 6 which are given in the diagram above are typical example of an adjacent angle.

An adjacent angle is defined as the type of angle that has a common sides which is shared by the two angles that are being compared.

A vertical angle is the type of angle that is usually opposite and they constructed by the intersection of two lines.

Therefore since a common sides exists between angle 5 and 6.

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Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.

We use the fact that parallel lines have the same slope to determine the equation of a line that is perpendicular to a given line and passes through a point. provided that it takes the form y = mx + b, where m is the slope, the provided line has a slope of -8/7. The parallel line will therefore similarly have a slope of -8/7.

The point-slope form of a line is used to determine the y-intercept of a parallel line: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. We obtain: y - 4 = (-8/7)(x + 6) by substituting (-6, 4) and -8/7 for m.

This equation can be simplified to y = (-8/7)x - 40/7.

We make use of the fact that perpendicular lines have opposing reciprocal slopes to determine the equation of a line that is perpendicular to the supplied line and passes through (-6, 4). provided that the provided line has a slope of -8/7, the perpendicular line will have a slope of 7/8.

Again using the point-slope representation of a line, we arrive at: y - 4 = (7/8)(x + 6)

This equation can be simplified to: y = (7/8)x + 25/4

Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.

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Answer: 12.69067

Step-by-step explanation:

2x² - 6x = -7 equation has  imaginary solutions

To determine if an equation has imaginary solutions, we can examine the discriminant of the quadratic equation

x² + 3x - 5 = 0

a = 1, b = 3, c = -5

Discriminant = (3)² - 4(1)(-5) = 9 + 20 = 29

The equation has two real solutions

x⁴ - 5x ^ 2 + 3 = 0

This equation is a quartic equation, not a quadratic equation. Quartic equations can have both real and imaginary solutions

2x² - 6x = -7

2x^2 - 6x + 7 = 0

a = 2, b = -6, c = 7

Discriminant = (-6)²- 4(2)(7) = 36 - 56 = -20

Since the discriminant (-20) is negative, the equation has two complex (imaginary) solutions.

-3x² = -5

Dividing both sides by -3, we get:

x²= 5

a = 1, b = 0, c = -5

Discriminant = 0² - 4(1)(-5) = 20

The equation has two real solutions.

Hence, 2x² - 6x = -7 equation has imaginary solutions

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Answer:

The answer is 14

Step-by-step explanation:

I used a calculator because when you grow older and have a phone, logically you will always have a calculator :)

Answer:

-10

Step-by-step explanation:

Use order of operations, PEMDAS/GEMDAS, 4*(-3)=12, and 2-(-12)=-10

Answer:

32

Step-by-step explanation:

4 times 2 is 8, - -7 is 15 plus 17 is 32

Answer:

7

Step-by-step explanation:

Using fundamental theorem of algebra, there should be 7 roots, if you count multiplicity.

If you're only counting distinct roots, then there should be 4 roots.

Answer:

24 + y = 41

y = 17

Step-by-step explanation:

24 + y = 41

y + 24 = 41

y + 24 - 24 = 41 - 24

y = 17