Find the slope of the line that passesthrough these two points.(-3,2)(6,5)my2-yiX2-X1m=Simplify Completely.

Answer:

  A. Divide both sides by 2/3, then subtract 57 from both sides.

Step-by-step explanation:

You want to know the steps to solve 2/3(y +57) = 178 for y.

The variable has 57 added to it, and the sum is multiplied by 2/3. To solve for y, you need to undo these operations in reverse order.

First, you divide by 2/3.

  y +57 = 267

Then you subtract 57.

  y = 210

Answer:

\(v = \frac{32\pi}{3}\)

or

\(v=33.52\)

Step-by-step explanation:

Given

\(f(x) = 4x - x^2\)

\(g(x) = x^2\)

\([a,b] = [0,2]\)

Required

The volume of the solid formed

Rotating about the x-axis.

Using the washer method to calculate the volume, we have:

\(\int dv = \int\limit^b_a \pi(f(x)^2 - g(x)^2) dx\)

Integrate

\(v = \int\limit^b_a \pi(f(x)^2 - g(x)^2)\ dx\)

\(v = \pi \int\limit^b_a (f(x)^2 - g(x)^2)\ dx\)

Substitute values for a, b, f(x) and g(x)

\(v = \pi \int\limit^2_0 ((4x - x^2)^2 - (x^2)^2)\ dx\)

Evaluate the exponents

\(v = \pi \int\limit^2_0 (16x^2 - 4x^3 - 4x^3 + x^4 - x^4)\ dx\)

Simplify like terms

\(v = \pi \int\limit^2_0 (16x^2 - 8x^3 )\ dx\)

Factor out 8

\(v = 8\pi \int\limit^2_0 (2x^2 - x^3 )\ dx\)

Integrate

\(v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0\)

\(v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0\)

Substitute 2 and 0 for x, respectively

\(v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])\)

\(v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])\)

\(v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ]\)

\(v = 8\pi [ \frac{16}{3} - \frac{16}{4} ]\)

Take LCM

\(v = 8\pi [ \frac{16*4- 16 * 3}{12}]\)

\(v = 8\pi [ \frac{64- 48}{12}]\)

\(v = 8\pi * \frac{16}{12}\)

Simplify

\(v = 8\pi * \frac{4}{3}\)

\(v = \frac{32\pi}{3}\)

or

\(v=\frac{32}{3} * \frac{22}{7}\)

\(v=\frac{32*22}{3*7}\)

\(v=\frac{704}{21}\)

\(v=33.52\)

Answer:

A). The ratio of a circle's circumference to its diameter

Step-by-step explanation:

The difference of two squares expression is (c) (5x + 3y)(5x - 3y)

The difference of two squares expression is represented as:

a^2 - b^2 = (a + b)(a - b)

Using the above as a guide, we have the following expression in option (c)

(5x + 3y)(5x - 3y)

Hence, the difference of two squares expression is (c) (5x + 3y)(5x - 3y)

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from the well known theorem that, primes are multiple of 6 ±1 ( eg 5,7,11,13,17,19...)

and one of them has \(-1\) and other has $+1$ from the multiple of 6

let , $p=6n-1$, so $p+2=6n+1$

$\implies p+1=6n$

$\therefore 6|(p+1)$

QED

The expansion will be 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

We can expand (2d+3)^6 using the binomial theorem, which states that:

(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn-1 * a^1 * b^(n-1) + nCn * a^0 * b^n

where nCk is the binomial coefficient, given by:

nCk = n! / (k! * (n-k)!)

Expanding (2d+3)^6 using this formula, we get:

(2d+3)^6 = 6C0 * (2d)^6 * 3^0 + 6C1 * (2d)^5 * 3^1 + 6C2 * (2d)^4 * 3^2 + 6C3 * (2d)^3 * 3^3 + 6C4 * (2d)^2 * 3^4 + 6C5 * (2d)^1 * 3^5 + 6C6 * (2d)^0 * 3^6

Simplifying each term using the binomial coefficient formula, we get:

(2d+3)^6 = 1 * 64d^6 * 1 + 6 * 32d^5 * 3 + 15 * 16d^4 * 9 + 20 * 8d^3 * 27 + 15 * 4d^2 * 81 + 6 * 2d * 243 + 1 * 1 * 729

Simplifying each term further, we get:

(2d+3)^6 = 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

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The measure of the complement of a 1-degree angle is 89 degrees.

The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.

Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:

1 degree + x degrees = 90 degrees.

To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:

x degrees = 90 degrees - 1 degree.

Simplifying the right side, we get:

x degrees = 89 degrees.

In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.

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The measure of <BDC is 68 degree.

The fundamental characteristics listed below make it simple to recognise parallel lines.

First, Interior of ( 2y+ 34) = 180 - (2y + 34)

                                         = 146- 2y

Now, using Corresponding Angle

74 = 146 - 2y

2y= 72

y= 72 / 2

y= 36

Second, Using Linear Pair

-7x+ 12 + (-8x+ 48)= 180

-7x + 12 - 8x + 48 = 180

-15x + 60 = 180

-15x = 120

x= -8

So, <BDC = -7x+ 12 = 56+ 12 = 68 degree

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Answer:

odd

Step-by-step explanation:

take example of 2^3 +3^3 it's odd

now others try yourself

Answer:

a) 53.33 miles per hour

b) 1.7 pages per minute

c)2.25 $ per avocado

Step-by-step explanation:

a) 320/6 = 53.33333

b) 68/40 = 1.7

c) 27 /12 = 2.25

Answer:

9^3 times 7^2

Step-by-step explanation:

The equation you used is correct, but the differential equation does not include the growth rate. The growth rate is proportional to the current population, so the differential equation should look like this:  dp/dt = kP - 20,000t

dp/dt = kP - 20,000t  , Where k is the growth rate. To solve this equation, we can use the separation of variables: dp/P = kdt - 20,000tdt

Integrating both sides, we get:

ln|P| = kt - 20,000t^2/2 + C, Where C is the integration constant. To find C, we can use the initial population of 200,000:

ln|200,000| = -0.099t - 20,000t^2/2 + C

=>C = ln|200,000| + 0.099t + 20,000t^2/2  .Therefore, the population of mosquitoes at any given time t is:

P = 200,000e^(-0.099t - 20,000t^2/2 + ln|200,000| + 0.099t + 20,000t^2/2)  = 200,000e^(ln|200,000|)  = 200,000

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Answer:

12 + 12 = 24

12 x 2 = 24

Step-by-step explanation:

The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

The variance = 2916,

The mean life of a battery, m = 518 min,

The total number of samples, n = 81

Calculate the probability of a mean battery life of lower than 526.4 minutes by the following formula,

z = x - m / (σ / √ n)

Here, x is the expected value, σ is the deviation, and z is the probability.

Substitute the values,

z = 526.4 - 518 / (54 / √81)         [σ = √ variance = √2916  = 54]

z = 1.4

Consult the cumulative standard normal table

P (z < 526.4) = 0.9192,

But we know that

P (z > 526.4) = 1 - P (z < 526.4)

P (z > 526.4) = 1 - 0.9192 = 0.0808

Therefore, The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

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Answer:

Solve for x, y, and z. 1st Equation: 2x + 2y + 4z = 48. 2nd Equation: 2x + 9y + 7z = 105. 3rd Equation: x + 4y + z = 37. Subtract the 2nd Equation from the 1st Equation. This will eliminate the variable “x”.

Step-by-step explanation:

Answer:

D. x>5

Step-by-step explanation:

\(3x + 2 < 4x - 3 \\ = 3x - 4x < - 3 - 2 \\ = - x < - 5 \\ = x > 5\)

To solve the equation \(3 \csc ^{2} (x) = 5 - 5 \cot(x) \), we will start by rewriting the right-hand side of the equation using the identity \(\cot x = \frac{1}{\tan x}\):

\(3 \csc ^{2} (x) = 5 - 5 \frac{1}{\tan(x)}\)

Next, we will use the identity \(\csc^2 x = \frac{1}{\sin^2 x}\) to rewrite the left-hand side of the equation:

\(\frac{3}{\sin ^{2} (x)} = 5 - 5 \frac{1}{\tan(x)}\)

Now, we will use the identity \(\sin^2 x + \cos^2 x = 1\) to rewrite the denominator on the left-hand side:

\(\frac{3}{1 - \cos^2 x} = 5 - 5 \frac{1}{\tan(x)}\)

Next, we will use the identity \(\tan^2 x = \sec^2 x - 1\) to rewrite the fraction on the right-hand side:

\(\frac{3}{1 - \cos^2 x} = 5 - 5 (\sec^2 x - 1)\)

Now, we will distribute the negative sign on the right-hand side:

\(\frac{3}{1 - \cos^2 x} = 5 - 5 \sec^2 x + 5\)

Combining like terms on the right-hand side gives us:

\(\frac{3}{1 - \cos^2 x} = 10 - 5 \sec^2 x\)

Adding 5 to both sides and then dividing both sides by 10 gives us:

\(\frac{3 + 5}{10} = 1 - \frac{5}{10} \sec^2 x\)

Simplifying the left-hand side gives us:

\(\frac{8}{10} = 1 - \frac{5}{10} \sec^2 x\)

Multiplying both sides by 10 and rearranging terms gives us:

\(\sec^2 x = \frac{10 - 8}{5} = \frac{2}{5}\)

Taking the square root of both sides gives us:

\(\sec x = \pm \frac{\sqrt{2}}{\sqrt{5}}\)

To find the values of x that satisfy the equation, we need to find the values of x in the interval \(-\pi \leqslant x \leqslant \pi\) that give us a positive value for \(\sec x\). Since the secant function is positive for all values of x in the interval \(0 \leqslant x < \pi\), all values of x in this interval will satisfy the equation.

Therefore, the solution to the equation is \(x \in \left[ 0, \pi \right)\).

Answer:

A, how much more soil did natasha add than dina?

B, Dina added 5/6 and Natasha added 11/8

C, subtraction

D, 11/8-5/6 or 33/24-20/24

E, 13/24

F, Natasha added 13/24 more of the bag than Dina did.

Step-by-step explanation:

Answer:3.5 pies

Step-by-step explanation:

Team Crusty = 28 pies / 8 hours = 3.5 pies per hour.

Hope This Helped!

:D

The equation can you use to find the rental cost, d, of each day they used the RV is 895=8d+55

What does $895 comprises of?

The $895 paid  for the duration of the trip consists of the payments for the RV for 8 days and additional amount of $55 which is for the outdoors upgrade.

The equation that can be used to determine rental cost per , d , per day considers that the total rental cost is number of days, 8 days  multiply by the rental  cost per day, which is d, and also that the final $55 is specifically for outdoors upgrade

Total cost=d*8+$55

Remember total cost of the trip is $895

$895=8d+$55

Which we can rewrite the expression by ignoring the dollar sign as below:

895=8d+55

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Answer:

\(3d + 2f = 21 \\ 2f = 21 - 3d \\ f = \frac{21 - 3d}{2} \)

The solution of equation 3d + 2f = 21 for f in terms of d is f = ( 21 - 3d ) / 2

To solve for f in the equation 3d + 2f = 21, follow these steps:

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value.

Subtract 3d from both sides of the equation :

2f = 21 - 3d

Divide both sides of the equation by 2 :

f = ( 21 - 3d ) / 2

So, the solution for f in terms of d is :

f = ( 21 - 3d ) / 2

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

Work Shown:

x = the other number

(5+4i)*x = 41

x = 41/(5+4i)

x = 41*(5-4i)/( (5+4i)*(5-4i) ) ..... see note below

x = 41*(5-4i)/( 41 )

x = (41/41)*(5-4i)

x = 5 - 4i  

As a way to check, (5+4i)*(5-4i) = 5^2+4^2 = 25+16 = 41

The rule used is (a-bi)(a+bi) = a^2 + b^2

-----------

Note:  I multiplied top and bottom by (5-4i) to get rid of the imaginary term in the denominator.

The inequality that represents the situation is (1/2)m + (1/4) ≤ F ≤ 2.

What are Linear Inequalities?

Linear inequalities are mathematical statements that involve two expressions connected by an inequality symbol (such as <, >, ≤, or ≥) and describe a relationship between these expressions that is not necessarily equal. They are often used to represent constraints or conditions in real-world problems involving variables.

Let's start by defining a variable to represent the amount of food that Martin's dog eats: m.

According to the problem, Felicity's dog eats at least one-quarter cup more than one-half of the amount Martin's dog eats. One-half of the amount Martin's dog eats is (1/2)m, and one-quarter cup more than that is (1/2)m + (1/4).

So, the amount of food that Felicity's dog eats can be represented by the inequality:

F ≤ (1/2)m + (1/4)

where F is the amount of food that Felicity's dog eats.

However, we also know that Felicity's dog eats no more than two cups of dog food per day. Therefore, we can add another constraint to the inequality:

F ≤ 2

Putting these two constraints together, we get:

(1/2)m + (1/4) ≤ F ≤ 2

or, in a simplified form:

(1/2)m + (1/4) ≤ F ≤ 2

So, the inequality that represents the situation is (1/2)m + (1/4) ≤ F ≤ 2.

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Answer:

15:10

Step-by-step explanation:

15:10 can be reduced into 3:2 by dividing with 5

and 9:6 can be reduced to 3:2 by dividing with 3

keep smiling.

Answer:

D

Step-by-step explanation:

just got in edg 2021

Answer: 6/8 inch

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

according to BODMAS

6÷2=3

3+3=6

4^2=16

16-6=10

Answer:

\( - \frac{1}{3} \)

Step-by-step explanation:

\( - 3.7 = - 5.4x - 5.5 \\ - 3.7 + 5.5 = - 5.4x \\ 1.8 = - 5.4x \\ \ - \frac{1.8}{5.4} = x = - \frac{1}{3} \)

So if we know the perimeter of the circle we can find it's radius using the formula for perimeter:

\(p = 2\pi(r)\)

So we can solve for radius:

\(r = \frac{10.71}{2\pi} \)

Then we can plug this radius into the formula for the area of a circle:

\(a = \pi {r}^{2} \)

\(a = \pi( \frac{10.71}{2\pi} ) ^{2} \)

Then it only wants a quarter of that area so we divide that value by 4 which upon simplification becomes the answer:

\(2.28 {ft}^{2} \)

Answer:

\( \boxed{Area \: of \: quarter \: circle = 7.065 \: square \: feet} \)

Given:

Perimeter of quarter circle = 10.71 feet

To find:

Area of quarter circle

Step-by-step explanation:

First we need to calculate the radius of quarter circle:

Let the radius of quarter circle be 'r'

\(Perimeter \: of \: quarter \: circle = \frac{\pi r}{2} + 2r\)

\( \implies 10.71 = \frac{\pi r}{2} + 2r \\ \\ \implies 10.71 = \frac{\pi r}{2} +2r \frac{2}{2} \\ \\ \implies 10.71 = \frac{\pi r}{2} + \frac{4r}{2} \\ \\ \implies 10.71 = \frac{\pi r + 4r}{2} \\ \\ \implies 10.71 \times 2 = \pi r + 4r \\ \\ \implies 21.42 = \pi r + 4r \\ \\ \implies 21.42 = (\pi + 4)r \\ \\ \implies 21.42 = (3.14 + 4)r \\ \\ \implies 21.42 = 7.14r \\ \\ \implies 7.14r = 21.42 \\ \\ \implies r = \frac{21.42}{7.14} \\ \\ \implies r = 3 \: ft\)

\( Area \: of \: quarter \: circle = \frac{\pi {r}^{2} }{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi \times {(3)}^{2} }{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi \times 9}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3.14 \times 9}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{28.26}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =7.065 \: {ft}^{2} \)

Answer:

5/3

Step-by-step explanation:

on both sides we can see that the orginal length of 3 increased to five

therfore if we multiply 3 by 3/5 we get five which means the scale factor is 5/3

When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.