the other khan academy assignment

Answer:  

1

Step-by-step explanation:

8-1,2,4.....

25-1,5...

first we will open bracket by squaring all the digits, then we will take LCM of the denominators and write in the standard form, it cant be further solved

Answer:

x²/9 - x/6 + 1/16

Step-by-step explanation:

Using (a - b)² = a² - 2ab + b, expand the expression:

x²/9 - 2x/12 + 1/16

reduce the fraction with two:

x²/9 - x/6 + 1/16

and you're done!

Answer:

m=0

Step-by-step explanation:

3^0=1

Answer:

Step-by-step explanation:

ok

Answer:

6/7

Step-by-step explanation:

First, cancel out 16 and 56 by a common factor of 8. The resulting expression is -2/5*-15/7. Then, simply 5 and 15 by a common factor of 5. Then, you will get: -2*(-3/7). The negatives cancel out, so the answer is 6/7.

Answer:

a =  120

b =  80

c =  40

d =  0.5

e =  50%

Step-by-step explanation:

Answer:

he is right

Step-by-step explanation:

A survey indicates that there are approximately 120 dairy farms in a given area. If there are exactly 400 farms, and exactly 20% of them are dairy farms, what is the percent error? Fill in the table below.

a =

✔ 120

b =

✔ 80

c =

✔ 40

d =

✔ 0.5

e =

✔ 50%

Answer:

20.92 %.  

Step-by-step explanation:

Add the individual probability of 0, 1, 2, and 3 late days out of 15

P(0 days) = (2/3)15    Notice that I have made P the probability of NOT being late.

P(1 day) = 15(2/3)14(1/3)

Hope this helps!

The inverse Laplace transform of G(s) is:

g(t) = (2/3) \(e^{-t}\) - (1/3) \(e^{-2t}\) - (1/3) \(e^{-3t}\)

The inverse Laplace transform of the function G(s) using the partial fraction expansion coefficients obtained from MATLAB, we need to express G(s) in terms of partial fractions.

G(s) = (2s³ + 5s² + 3s + 6) / (s³ + 6s² + 11s + 6)

The denominator of G(s) can be factored as:

s³ + 6s² + 11s + 6 = (s + 1)(s + 2)(s + 3)

Let's write G(s) in terms of partial fractions as follows:

G(s) = A / (s + 1) + B / (s + 2) + C / (s + 3)

To find the values of A, B, and C, we can multiply both sides of the equation by the denominator and equate the coefficients of like powers of s.

(2s³ + 5s² + 3s + 6) = A(s + 2)(s + 3) + B(s + 1)(s + 3) + C(s + 1)(s + 2)

Expanding the right side and collecting like terms, we have:

2s³ + 5s² + 3s + 6 = (A + B + C)s² + (5A + 4B + 3C)s + (6A + 3B + 2C)

Comparing the coefficients of like powers of s, we get the following equations:

A + B + C = 0

5A + 4B + 3C = 5

6A + 3B + 2C = 3

Solving these equations, we find:

A = 2/3

B = -1/3

C = -1/3

Therefore, the partial fraction expansion of G(s) becomes:

G(s) = (2/3) / (s + 1) - (1/3) / (s + 2) - (1/3) / (s + 3)

Now, we can use the linearity property and known Laplace transforms to find the inverse Laplace transform of each term.

Taking the inverse Laplace transform, we have:

g(t) = (2/3) \(e^{-t}\) - (1/3) \(e^{-2t}\) - (1/3) \(e^{-3t}\)

Therefore, the inverse Laplace transform of G(s) is:

g(t) = (2/3) \(e^{-t}\) - (1/3) \(e^{-2t}\) - (1/3) \(e^{-3t}\)

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First we are supposed to find 30% of 451

30/100×451 = 135.3

So, 451 - 136= 315.7

Therefore I would be left with 315.7

Answer:

$315.70

Step-by-step explanation:

the sum of these is 451 so to find 30 percent we multiply 451 by 30 percent

First turn 30 percent into a decimal by moving the decimal point to places to the left

0.30 and now we multiply

0.3x451

135.30 is 30% of 451 and since someone is taking it we subtract it by 451

451-135.30

315.70 is what you are left with

But if it was tax you would add this to the total amount you are spending

Hopes this helps please mark brainliest

Answer:

-7

Step-by-step explanation:

Answer:

x=-7

Step-by-step explanation:

:)

Answer: x>-1

Step-by-step explanation:

Dotted line on the axis is covering y infinitely, so theres an inequality on x, and the line is at -1, so x should be > - 1

Answer:

C. x > -1

Step-by-step explanation:

The line intersects on the x-axis at -1 and is shaded towards the right, which are all numbers greater than -1. The inequality that matches this is x > -1.

If the variable was y, then the line would be horizontal on the y-axis. If the inequality was x > 1, then the line would intersect on the x-axis on positive 1. This is why the other options are incorrect.

hope this helps!

The limits of integration for x will be from x = 0 to x = 4.

We can now evaluate the integral as follows:

∫∫ y dA,

\(D = \int 0^4 \int0^{(1-(1/4)x)}\ y\ dy\ dx\)

\(= \int0^4 [y^2/2]0^{(1-(1/4)x)} dx\)

= ∫0⁴ [(1/2)(1-(1/4)x)²] dx

= (1/2) ∫0⁴ (1- (1/2)x + (1/16)x²) dx

= (1/2) [(x-(1/4)x²+(1/48)x^3)]0⁴

= (1/2) [(4-(1/4)(16)+(1/48)(64))-0]

= (1/2) (4-4+4/3)

= 2/3

Therefore, ∬ ydA = 2/3.

To evaluate ∬ ydA,

we need to integrate the function y over the region D.

The region D is a triangular region with vertices (0,0), (1,1), and (4,0). Therefore, we can evaluate the integral as follows:

∬ ydA = ∫∫ y dA, D

The limits of integration for y will depend on the limits of x for the triangular region D.

To find the limits of integration for x and y, we need to consider the two sides of the triangle that are defined by the equations y = 0 and

y = 1 - (1/4)x.

The limits of integration for y will be from y = 0 to y = 1 - (1/4)x.

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Answer:$20.79

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Sorry for late response just saw your other comment. Also good luck

Answer:

B.

Step-by-step explanation:

To describe the goal of the writers in creating the constitution

Answer:

73.1 cm

Step-by-step explanation:

In the drawing, the rubber track is in black and the wheels are in light gray.

As we can see in the figure, the rubber track will have a length of two halfs of a circunference of radius 8 cm plus six diameters of 8 cm. So the total length is:

Length of rubber track = pi * 8 + 6 * 8 = 25.13 + 48 = 73.133 cm

Rounding to one decimal place, we have that the length is 73.1 cm

This question is incomplete because it lacks the diagram of the 4 circular wheels.

Find attached to this answer the appropriate diagram

Answer:

100.5cm

Step-by-step explanation:

The formula to be used in this calculation is the circumference of a circle.

The circumference of a circle can be defined as the actual length of a circle when it is stretch out(opened up) or the distance around a circle.

The formula for the circumference of a circle is given as 2πr where r = radius of the circle

Or πD where D = Diameter of the circle

In the question, we are given the diameter of the circle = 8cm

So we use the Formula

= πD

The length of the rubber track around one wheel is

= π × 8cm = 25.132741229cm

From the attached diagram, we can see we have 4 wheels.

The length of the rubber track that goes around the four wheels is calculated as

4 × 25.132741229cm = 100.53096491cm.

Approximately to one decimal place = 100.5cm

Therefore, the length of the rubber track that goes around the four wheels to one decimal place is 100.5cm

Answer:

C)  (-1, -4) and (4, 6)

Step-by-step explanation:

\(\textsf{Equation 1}:y=2x-2\)

\(\textsf{Equation 2}:y=x^2-x-6\)

Substitute Equation 1 into Equation 2 and solve for x:

\(\implies 2x-2=x^2-x-6\)

\(\implies x^2-3x-4=0\)

Find two numbers that multiply to -4 and sum to -3:  -4 and 1

Rewrite the middle term as the sum of these two numbers:

\(\implies x^2-4x+x-4=0\)

Factorize the first two terms and the last two terms separately:

\(\implies x(x-4)+1(x-4)=0\)

Factor out the common term \((x-4)\):

\(\implies (x+1)(x-4)=0\)

\(\implies (x+1)=0 \implies x=-1\)

\(\implies (x-4)=0 \implies x=4\)

Substitute the found values of x into Equation 1 and solve for y:

\(x=-1 \implies y=2(-1)-2=-4\)

\(x=4 \implies y=2(4)-2=6\)

Therefore, the solution to the system of equations is:

(-1, -4) and (4, 6)

Answer:

   5x/7y^3

Step-by-step explanation:

Something to the power of -1/2 is saying 1 over square-root of that something. Let's pretend x is that something. If we have something like this \(x^{-\frac{1}{2} }\), then it can be written like this: \(\frac{1}{\sqrt{x}}\).

In our problem, we have the chunk to the -1/2 power. So the reciprocal of the chunk would become \(\sqrt{\frac{25x^{2} }{49y^{6}}\)

It's easy to solve now. The square root of the numerator becomes 5x and the denominator becomes 7y^3. The simplified version is \(\frac{5x}{7y^\power{3}}\)

To find the measure of an angle in a triangle that is isosceles, you can use the fact that the two equal sides of the triangle are congruent to each other.  The measure of each of these angles can be found by subtracting the measure of the third angle from 180 degrees.

Determine which two sides of the triangle are equal in length (these are called the "congruent sides").

Find the measure of the angle opposite one of the congruent sides. This angle is called the "base angle."

Subtract the measure of the base angle from 180 degrees. This will give you the measure of the other two angles in the triangle (since the three angles in any triangle must add up to 180 degrees).

For example, if the measure of the base angle is x degrees, then the measure of the other two angles would be (180-x) degrees.

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The measure of angles in an isosceles triangle can be found using the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.

To find the measure of an angle in a triangle isosceles, you can use the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.

Let's look at an example. Suppose you have an isosceles triangle and you know that two of its angles measure 50 degrees and 60 degrees. To find the measure of the third angle, you would subtract 110 (the sum of the two known angles) from 180. This gives you 70 degrees as the measure of the third angle.

In addition to the Triangle Angle Sum Theorem, you can also use the Isosceles Triangle Theorem to find the measure of an angle in an isosceles triangle. The Isosceles Triangle Theorem states that the angles opposite the two equal sides of an isosceles triangle are equal. This means that if you know one of the angles in the triangle, you can determine the measure of the other two angles, since they will both be equal to the measure of the known angle.

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Answer:

x = 9

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

B x = 3 or -12

Step-by-step explanation:

(btw this / is a fraction sign and this ^ is the power of sign)

Let's solve your equation step-by-step.

x^2+9x−36=0

For this equation: a=1, b=9, c=-36

1x^2+9x+−36=0

Step 1: Use quadratic formula with a=1, b=9, c=-36.

x= −b±√b^2−4ac/2a

x= −(9)±√(9)2−4(1)(−36)/2(1)

x= −9±√225/2

= x= 3 or x= -12

The completely factored form of the polynomial is :\(\(12x^2 + 2x - 4 = 2(2x + 4)(3x - 1)\)\)

To completely factor the polynomial \(\(12x^2 + 2x - 4\)\), we need to find expressions that can be multiplied together to obtain the given polynomial.

First, we can look for common factors. In this case, all the coefficients are divisible by 2, so we can factor out a 2:

\(\(2(6x^2 + x - 2)\)\)

Now, we focus on factoring the quadratic expression \(\(6x^2 + x - 2\)\). We need to find two binomials that, when multiplied, give us this quadratic.

To factor \(\(6x^2 + x - 2\)\), we look for two numbers whose product is equal to \(\(6 \times -2 = -12\)\) and whose sum is equal to the coefficient of the middle term, which is 1.

After trying different combinations, we find that the numbers 4 and -3 satisfy these conditions:

\(\(6x^2 + x - 2 = (2x + 4)(3x - 1)\)\)

Putting it all together, the completely factored form of the polynomial is:

\(\(12x^2 + 2x - 4 = 2(2x + 4)(3x - 1)\)\)

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The equation of the line of best fit for the points is y = -2x + 3

The distance between two points is referred to as a line. The standard equation of a line in slope-intercept form is expressed according to the equation

y = mx + b

where:

m is the slope

b is the intercept

Using the coordinate points (-1, 5) and. (5, -7)

Slope = -7-5/5-(-1)

Slope = -12/6

Slope = -2

Find the y-intercept

-7 = -2(5) + b

-7 = -10 + b

b. = 3

Determine the equation

y = mx + b

y = -2x + 3

This gives the required equation of line of best fit.

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The value of the line integral f · dr over the curve C is 20 i + 39 j.

Let's first find a parameterization of the line from the point (2,5) to the point (4,7). We can choose t as the parameter and write the parameterization as:

x = 2 + 2t

y = 5 + 2t

where 0 ≤ t ≤ 1.

Next, we need to evaluate f · dr along this curve C. Substituting the parameterization into f · dr, we get:

\(f · dr = (x^2 i + y^2 j) · (dx i + dy j)\)

\(= x^2 dx + y^2 dy\)

\(= (2 + 2t)^2 dt i + (5 + 2t)^2 dt j\)

\(= (4t^2 + 8t + 4) dt i + (4t^2 + 20t + 25) dt j\)

Finally, we integrate f · dr over the range of t from 0 to 1 to get the line integral:

f · dr C = ∫(0 to 1) (\(4t^2\) + 8t + 4) dt i + ∫(0 to 1) (\(4t^2\) + 20t + 25) dt j

=\([4/3t^3 + 4t^2 + 4t]\) from 0 to 1 i + \([4/3t^3 + 10t^2 + 25t]\) from 0 to 1 j

= \((4/3 + 4 + 4) i + (4/3 + 10 + 25) j\)

= \(20 i + 39 j\)

Therefore, the value of the line integral f · dr over the curve C is 20 i + 39 j.

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Answer:

144 000

Step-by-step explanation:

960 000 × 0.15

= 144 000

Answer:

144,000

Step-by-step explanation:

\( \frac{15}{100} \times 960000 \\ 15 \times 9600 \\ 144000\)

The estimate for 3√65 is 49/12.

To use a linear approximation (or differentials) to estimate the given number 3√65, follow these steps:

1. Choose a number close to 65 that has an easy-to-calculate cube root, such as 64 (since the cube root of 64 is 4).

2. Define the function f(x) = 3√x.

3. Calculate the derivative f'(x) = (1/3)x^(-2/3).

4. Evaluate f'(x) at the chosen number (x=64): f'(64) = (1/3)(64)^(-2/3) = 1/12.

5. Apply the linear approximation formula: Δy ≈ f'(x)Δx, where Δy is the change in f(x) and Δx is the change in x.

6. Find the change in x (Δx): Δx = 65 - 64 = 1.

7. Calculate the change in y (Δy): Δy ≈ f'(64)Δx = (1/12)(1) = 1/12.

8. Add the change in y (Δy) to the initial function value f(64): 3√65 ≈ 3√64 + Δy = 4 + 1/12 = 49/12.

So, using linear approximation, the estimate for 3√65 is 49/12.

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The acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

To find the acceleration of the particle at \(t = 2\) seconds, we need to differentiate the position function twice with respect to time. First, let's differentiate the position function \(s(t)\) once to find the velocity function \(v(t)\). Using the chain rule, we have:

\(\(v(t) = \frac{d}{dt}[(4t+1)^{3/2}]\)\)

To simplify the differentiation, we can rewrite the function as\(\(v(t) = (4t+1)^{3/2}\)\) . Applying the power rule, the derivative becomes:

\(\(v(t) = \frac{3}{2}(4t+1)^{1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(v(t) = 6(4t+1)^{1/2}\)\)

Next, we differentiate the velocity function \(v(t)\) to find the acceleration function \(a(t)\):

\(\(a(t) = \frac{d}{dt}[6(4t+1)^{1/2}]\)\)

Using the power rule again, we get:

\(\(a(t) = 6 \cdot \frac{1}{2}(4t+1)^{-1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(a(t) = 12(4t+1)^{-1/2}\)\)

Now we can find the acceleration at \(t = 2\) seconds by substituting \(t = 2\) into the acceleration function:

\(\(a(2) = 12(4 \cdot 2 + 1)^{-1/2}\)\)

\(\(a(2) = 12(9)^{-1/2}\)\)

Simplifying the expression, we have:

\(\(a(2) = \frac{12}{3} = 4\) cm/s²\)

Therefore, the acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

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To determine the slant height of the cone, we will apply the Pythagorean theorem to the right triangle ABC.

From the Pythagorean theorem we get that:

We are given that:

Therefore:

Finally, solving for AC, we get:

Answer:

percentage loss = 20%

Step-by-step explanation:

percentage loss is calculated as

\(\frac{loss}{CP}\) × 100% ( CP is the cost price )

loss = SP - CP ( SP is selling price )

loss = CP - SP = 350 - 280 = 70 , then

percentage loss = \(\frac{70}{350}\) × 100% = 0.2 × 100% = 20%