Someone help this is due today worth half my grade!!

Answer:

hi I tried but I think it's confusing as well.

The Linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

The point-slope equation for a line is of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Given the point-slope equation y - 5 = 3(x - 2),

we can see that the slope of the line is 3 and it passes through the point (2, 5).

To find the linear function for the line, we need to write the equation in slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line intersects the y-axis).

To get the equation in slope-intercept form, we need to isolate y on one side of the equation.

We can do this by distributing the 3 to the x term:y - 5 = 3(x - 2)  y - 5 = 3x - 6  y = 3x - 6 + 5  y = 3x - 1

Therefore, the linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

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\( \: \: \: \: \: \: \: \)

GCF OF 48

The greatest common factor of 8, 28, and 48 is 4.

The largest common factor out of all the numbers in the given set is known as Greatest Common Factor.

Factors of 8, \(8=2\times 2\times 2\)

Factors of 28, \(28=2\times 2\times 7\)

Factors of 48, \(48=2\times 2\times 2\times 2\times 3\)

The common factors in the above set of numbers are 2and 2.

So, the Greatest Common Factor of 8, 28, and 48 is  \(2\times 2=4\).

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Answer:

99

Step-by-step explanation:

-x-=+

18x6=108

108-6=99

Answer:

32, 40, 48, 56

Step-by-step explanation:

\(a_n= 8(n+3)...(given) \\\\ a_1= 8(1+3) = 8 \times 4 = 32 \\ \\ \: a_2= 8(2+3) = 8 \times 5 = 40 \\ \\ a_3= 8(3+3) = 8 \times 6 = 48 \\ \\ a_4= 8(4+3) = 8 \times 7 = 56 \\ \)

The location of all the relative and absolute extrema is (0, 0) (local minimum); (1, 1) (local maximum); (3, 3) (absolute maximum)

To find the relative and absolute extrema of the function f(x) = 2x - x^2 on the domain (0,3), we first take the derivative:

f'(x) = 2 - 2x

Setting this equal to zero, we find the critical point:

2 - 2x = 0
x = 1

To determine the nature of the critical point, we need to examine the second derivative:

f''(x) = -2

Since the second derivative is negative at x = 1, this critical point is a local maximum. To find the absolute extrema, we also need to examine the endpoints of the domain, x = 0 and x = 3:

f(0) = 0
f(3) = 3

So the function has an absolute maximum at x = 3 and an absolute minimum at x = 0. Therefore, the location of all the relative and absolute extrema, from smallest to largest x, is:

(0, 0) (local minimum)
(1, 1) (local maximum)
(3, 3) (absolute maximum)

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Answer:

9 x 2 + 7x

18 + 7x - 6

18 - 6 = 12

12 + 7x

Is your simplified expression

Answer:

12 + 7x

Step-by-step explanation: there

Answer:

Q7: -4 ; Q8: 2.6x + 8

Step-by-step explanation:

For the first one, since they are like terms, you can just normally subtract:

3x - 7x = -4x

Its a negative since 3 - 7 = -4 not positive 4.

You did question 8 correctly.

Answer:

6 x(6x)+6x*-1+1(6x)+1*-1  SIMPLIFIED: 36x^2-1

Step-by-step explanation:

Use foil and distributive property

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

A

Step-by-step explanation:

Answer:

(A) would be the answer

Answer:

The question is not clearly stated, below is a possible match of the clearly and completely stated question:

Tony is writing a fraction equivalent to 2/7 using the formula 2*m/7*n. Which statement about m and n must be true so that tony fraction has the same value as 2/7

A. M/n has to be greater than 1

B. M/n has to equal 7

C. M/n has to be greater than 2

D. M/n has to equal 1

Answer:

m/n has to equal 1 (D)

Step-by-step explanation:

\(original\ fraction = \frac{2}{7} \\equivalent\ fraaction = \frac{2\ \times\ m}{7\ \times\ n} \\equivalent\ fraction\ = \frac{2}{7} \times\ \frac{m}{n} \\\)

since the target for the equaivalent fraction is the same as the equivalent fraction (\(\frac{2}{7}\)), the value of \(\frac{m}{n}\)  must be equal to 1, so that the multiplication will be:

\(\frac{2}{7} \times 1 = \frac{2}{7}\)

The symbols p,x, and s represent sample statistics.

- p (pronounced "p-hat") is the sample proportion. It is used to estimate the population proportion. It is computed as the number of successes in the sample divided by the sample size.

-x (pronounced "x-bar") is the sample mean. It is used to estimate the population mean. It is computed as the sum of all the values in the sample divided by the sample size.

- s is the sample standard deviation. It is used to estimate the population standard deviation. It measures how spread out the data is in the sample. It is computed as the square root of the sum of the squared deviations from the sample mean divided by the sample size minus one.

These sample statistics are used to make inferences about the corresponding population parameters, which are denoted by Greek letters such as μ (mu) for the population mean and σ (sigma) for the population standard deviation.

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The answer is 4) for some c, such that a < c < b, the derivative g'(c) =0. While it is possible.

Is g'(c)=0 necessary between a and b?

4) for some c, such that a < c < b, the derivative g'(c) is equal to zero.

The statement "g hasa minimum value on [a, b]" is true by the extreme value theorem, which states that a continuous function on a closed interval must have both a maximum and minimum value.

Similarly, the statement "g has a maximum value on [a,b]" is also true by the same theorem.

The statement "g(c) = 0 for some c, such that a < c < b" is also true by the intermediate value theorem for continuous functions, which states that if g(a) and g(b) have opposite signs, then there exists a value c between a and b such that g(c) = 0.

Therefore, the only statement that is not necessarily true is "for some c, such that a < c < b, g'(c) = 0." While it is possible for g'(c) to equal zero at some point between a and b, it is not a necessary condition for the given conditions in the question.

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The equation of the circle expressed in the form x²+y²+ax+by+c=0 is (x+3)² + (y+4)² - 100 = 0.

Center of the circle = (-3,-4)Point on the circumference of the circle = P(5,2) We know that the equation of the circle is given by: (x−a)²+(y−b)²=r² where the center of the circle is (a, b) and the radius is r.

Step 1: Find the radius of the circle using the distance formula Distance between the center of the circle and point

P = radius of the circle.

We get

r = √((-3-5)² + (-4-2)²)r = √64+36r = √100 = 10

Step 2:Find the equation of the circle substituting the center and the radius into the equation of the circle

(x−a)²+(y−b)²=r²(x-(-3))² + (y-(-4))² = 10²(x+3)² + (y+4)² = 100(x+3)² + (y+4)² - 100 = 0

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Answer: y=Mx+b

Step-by-step explanation:

67 is a prime number and 1 is neither prime nor composite number.

What is prime number and composite number?

A prime number is a number which has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer.

The given two numbers are 1 and 67.

Since, the prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

67 has exactly two factors i.e. 1 and the number 67 itself.

Therefore, 67 is a prime number.

Due to the fact that it only has one factor, 1, number is not a prime.

Hence, 67 is a prime number and 1 is neither prime number nor composite number.

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Answer:

To the lump sum needed to be invested to receive $10,000 in 10 years at 6.6% interest compounded daily, we can use the present value formula:

PV = FV / (1 + r/n)^(n*t)

where PV is the present value or the initial investment, FV is the future value or the amount we want to end up with, r is the annual interest rate in decimal form, n is the number of times the interest is compounded per year, and t is the time in years.

Plugging in the numbers, we get:

PV = 10000 / (1 + 0.066/365)^(365*10)

= 4874.49

Therefore, the lump sum needed to be invested is about $4,874.49.

The distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

As per the question statement, two points having coordinates (4, -4) and

(9, -2) plotted on the cartesian plane.

We are required to calculate the distance between the above mentioned two points, rounded to the nearest tenth.

To solve this question,  we need to know the Distance-formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by √[(x₂ - x₁)² + (y₂ - y₁)²]"

Assuming that [(x₁, y₁) = (4, -4)] and [(x₂, y₂) = (9, -2)], and substituting these values in the above-mentioned distance formula, we get,

√[(9 - 4)² + {(-2) - (-4)}²]

= √[(9 - 4)² + {(-2) + 4}²]

= √[(9 - 4)² + (4 - 2)²]

=√[(5)² + (2)²]

=√(25 + 4)

=√29

= 5.38 units.

Therefore, rounding (5.38) to the nearest tenth, we get, 5.40.

That is, the distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

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We can write the given series as:

∑ (-1)^n / (n*2^n), n=1 to infinity

To approximate the sum of the series using the first six terms, we can simply add up the first six terms:

(-1)^1 / (12^1) - (-1)^2 / (22^2) + (-1)^3 / (32^3) - (-1)^4 / (42^4) + (-1)^5 / (52^5) - (-1)^6 / (62^6)

Simplifying this expression, we get:

1/2 - 1/8 + 1/24 - 1/64 + 1/160 - 1/384

= 0.5279 (rounded to four decimal places)

Therefore, the sum of the series, approximated by using the first six terms, is approximately 0.5279.

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Answer:

y=2x-7

Step-by-step explanation:

y-y1=m(x-x1)

y-3=2(x-5)

y=2x-10+3

y=2x-7

Please mark me as Brainliest if you're satisfied with the answer.

Answer:

Levi saved 3/5 of the amount he needs to buy a 75 dollar video game. he earns 7.50 per hour working at the pizza shopping town how many hours will he need to work to pay for the rest of the game show all of your work to solve this problem explain the Steps you used! thank you 6th grade form please

Step-by-step explanation:

Answer:

Hello, Jaesuk Sakai Here!! (^^

Step-by-step explanation:

Words in 2 minutes = 90

Words in a minute = 90 / 2

                             = 45

So rate is 45 words/minutes

Happy to Help~ jaesuk sakai!

The surface of the top half of the "Mount Donut" is modeled by the equation z = f(x, y), where the specific form of the function f(x, y) is not provided.

The phrase "Mount Donut" is a playful way to refer to a mathematical surface that resembles a donut shape. The top half of this surface can be represented by the equation z = f(x, y), where f(x, y) is the mathematical function that describes the height of the surface at each point (x, y) on the xy-plane.

To fully understand and analyze the surface, we would need more information about the specific form of the function f(x, y). Without the explicit equation for f(x, y), it is challenging to provide a detailed explanation or solve any specific problems related to the surface.

However, we can make some general observations about surfaces and their modeling in mathematics. Surfaces can be represented using various mathematical techniques, including explicit equations, implicit equations, parametric equations, or even through computer-generated models. Each approach has its advantages and is chosen based on the specific problem at hand.

In the case of the "Mount Donut," the surface is defined implicitly by the equation z = f(x, y), indicating that the height of the surface depends on the values of x and y. The specific form of the function f(x, y) would determine the shape, contours, and features of the surface.

To further analyze or work with the surface, additional information or specifications about the function f(x, y) would be needed, such as its specific equation, its properties, or any constraints imposed on the surface.

In conclusion, while the surface of the top half of the "Mount Donut" is represented by the equation z = f(x, y), without further details about the function f(x, y), it is not possible to provide a more in-depth analysis or solve specific problems related to the surface.

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Answer:

non linear im pretty sure

The parametric equations for the line that is tangent to the curve at t = 0 is x = 1 + t y = 0 + t z = 0 - t.

We are given that;

\(r(t)=eti+(sint)j+ln(1−t)k\) at t=0

Now,

To find parametric equations for the line that is tangent to the curve;

r(t) = eti + (sin(t))j + ln(1 - t)k at t = 0,

Here, line can be obtained by plugging in t = 0 into the given curve:

\(r(0) = e^0i + (sin(0))j + ln(1 - 0)k = i + 0j + ln(1)k = i\)

So (1, 0, 0)  plugging in t = 0:

\(r’(t) = eti + (cos(t))j - (1 / (1 - t))k r’(0) = e^0i + (cos(0))j - (1 / (1 - 0))k = i + j - k\)

So <1, 1, -1> is a direction vector for the line.

Now, using the point and the direction vector, we can write parametric equations for the line as follows;

x = 1 + t y = 0 + t z = 0 - t

Therefore, by the equation the answer will be x = 1 + t y = 0 + t z = 0 - t.

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Answer:

6ft/hour

Step-by-step explanation:

Answer:

6 feet/hour

Step-by-step explanation:

I first found out exactly the amount of feet that was added. \(80-32=48\)

Then I divided that by the amount of hours.  48 ÷ 8 = 6

Answer:

Step-by-step explanation:

surface are of triangular prism =(a+b+c)h+bh

=(5+5+4)11+4*6

=14*11+24

=154+24

=178 yd^2

A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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There are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$. For a number to end in the digit $3$ in base-$b$ representation, it must be congruent to $3$ modulo $b$.

We can rewrite $2013$ as $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$. Now, if $2013$ is congruent to $3$ modulo $b$, it means that $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$ is also congruent to $3$ modulo $b$.

Simplifying the expression, we have $2000 + 0 + 10 + 3$. Since the base-$b$-representation is formed by multiplying each digit by the corresponding power of $b$, we can rewrite the expression as $2 \cdot b^3 + 1 \cdot b^1 + 3 \cdot b^0$. We can now observe that the constant term $3 \cdot b^0$ will always be congruent to $3$ modulo $b$. However, the other terms $2 \cdot b^3$ and $1 \cdot b^1$ will not be congruent to $3$ modulo $b$ for any positive value of $b$. Therefore, the base-$b$-representation of $2013$ cannot end in the digit $3$ for any value of $b$.

Hence, there are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$.

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