7.1 (1 mark) Write --2x2-14x+12 **-6) in terms of a sum of partial fractions Answer You have not attempted this yet 7.2 (1 mark) Uue partial fractions to evaluate the integral 5x2–2x+23 dx (x+1)(x+5) Note. If you require an inverse trigonometric function, recall that you must enter it using the are nime, c.parcsin (not in arcot (not co), Also, if you need it, to get the absolute value of something use the abs function exis entered as ant() Answer You have not attempted this yet

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

STEP 2: Multiply the constant with the leading term

STEP 3: Write the possible factors of the result in product form

STEP 4: Find the factors that will give the second term (-7x) when added

STEP 5: Substitute these factors for -7x in the expression in step 1

STEP 6: Factorize by grouping

Hence, the factors of the given expression are:

Answer:

y = - 1

Step-by-step explanation:

\(\frac{4}{y}\) + 2 = \(\frac{10}{5y}\)

multiply through by 5y to clear the fractions

20 + 10y = 10 ( subtract 20 from both sides )

10y = - 10 ( divide both sides by 10 )

y = - 1

Answer:

y=4x+1

Step-by-step explanation:

First find the gradient of the straight line

Then substitute the gradient in the formula y=mx+c.

Substitute one of the given coordinates in the line to find the value of c.

After finding the value of c substitute it in the formula but do not write the values of x and y in the formula

Answer:

Step-by-step explanation:

Remember PEMDAS

2 - 8 : (2^4 : 2) =

2 - 8 : (16 : 2) =

2 - 8 : 8 =

2 - 1 =

a)  u · v, is -34 + 23 = -12 + 6 = -6. b)  v · v, is 44 + 33 = 16 + 9 = 25.

c) The squared norm of vector u, ||u||², is (-3)² + 2² = 9 + 4 = 13.

d) the dot product of u and v with v. In this case, (-6)(4, 3) = (-24, -18).

In the first paragraph, the dot product of vectors u and v is calculated by multiplying the corresponding components of the vectors and summing them. For u · v, (-34) + (23) = -12 + 6 = -6.

In the second paragraph, the other calculations are performed. For v · v, (44) + (33) = 16 + 9 = 25. The squared norm of vector u, ||u||², is found by squaring each component of u and summing them. (-3)² + 2² = 9 + 4 = 13. Finally, the expression (u · v)v represents the projection of vector u onto vector v and is obtained by multiplying the dot product of u and v with v. (-6)(4, 3) = (-24, -18).

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer:

D

Step-by-step explanation:

The expression is equal to 1/300

D is the only other one equal to 1/300

Answer:

w = 6 / 21.

Step-by-step explanation:

To solve this equation, we first need to get all of the terms with the variable w on one side of the equation and all of the constants on the other side. To do this, we can use the distributive property to combine like terms on each side of the equation.

We can use the distributive property to combine the two terms on the left side of the equation to get 5 + 16w = 21w. This gives us the equation 21w = 6 - 45.

Next, we can add 45 to both sides of the equation to get 21w + 45 = 6 + 45. This simplifies to 21w + 45 = 51.

Finally, we can divide both sides of the equation by 21 to get the value of w. This gives us the equation w = (51 - 45) / 21 = 6 / 21.

Therefore, the solution to the equation is w = 6 / 21.

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer: 5 < 10x - 3

Step-by-step explanation:

Answer:

B.     $2253.65

Step-by-step explanation:

Use the formula for compound interest.

F = P(1 + r/n)^(nt)

F = future value

P = present value

r = interest rate (written as decimal)

n = number of times interest is compounded each year

t = number of years

F = unknown

P = $2000

r = 4% = 0.04

n = 4

t = 3

F = $2000(1 + 0.04/4)^(4 × 3)

F = $2253.65

The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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Sophie needs approximately 14.82 ounces of flour to bake her cake .

To convert grams to ounces, we can use the conversion factor that 1 ounce is approximately equal to 28.35 grams . The mass m in grams (g) is equal to the mass m in ounces (oz) times 28.34952

1 ounces = 28.35 gram

So, to find the number of ounces of flour Sophie needs, we can divide the weight in grams by the conversion factor .

420 g × 1 ounces / 28.35 g

420 g / 28.35 g = 14.82 ounces

Therefore, Sophie needs approximately 14.82 ounces of flour to bake her cake .

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In testing for differences between the means of 2 independent populations the null hypothesis is zero.

This is defined as a statistical hypothesis which has no statistical significance in a set of given observations.

In testing for differences between the means of 2 independent populations the null hypothesis is the difference between the two population means and is not significantly different from zero which is denoted below:

H₀: µ₁ - µ₂ = 0

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Answer:

I dont get it, what is this?

Step-by-step explanation:

Answer:

correct answers: 2 question: Solve the given system of equations using any method and then choose the correct ordered pair from the given choices: x + y = 33x - y ... Select one: O a. (2.1) O b.(-2,-1) O c. (1,2) O d. (-1,2)​. answer. Answers: 2. Get ... Asine function has the following period =4 amplitude = 4 midline y = 1.

PLZ MARK BRAINLIEST I NEED IT ALSO HOPE THIS HELPS

The matrix is a not invertible when it's column do not span because it is not linearly independent.

According to the statement

we have find that the matrix can be a invertible or not when its column is spaned.

So, For this purpose, we know that the

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.

And according to the statement it is not possible for thr matrix to be invertible.

Because for matrix it is not a possible because it is not independent,

In other words, No, if the columns don't span R5 -> NOT linearly independent -> not invertible.

So, The matrix is a not invertible when it's column do not span because it is not linearly independent.

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(A)Therefore, the probability that a randomly selected student score will be less than 690 points is 0.9738.(B) Therefore, the probability that a randomly selected student score will be between 400 and 590 is 0.2257.

A: The given data implies that the mean of SAT scores is 400, and the standard deviation is 150. The z-score is calculated by z = (x - μ) / σ. The z-score corresponding to 690 is (690 - 400) / 150 = 1.93. This z-score can be used to find the probability that a randomly selected student score will be less than 690 points using the normal distribution table. This is equivalent to finding the area to the left of the z-score.

The area to the left of 1.93 can be obtained from the normal distribution table or calculator. Using the normal distribution table, we find that the area to the left of 1.93 is 0.9738.

Therefore, the probability that a randomly selected student score will be less than 690 points is 0.9738.

B: The probability that a randomly selected student score will exceed 690 points is equivalent to finding the area to the right of the z-score of 1.93. The area to the right of 1.93 can be obtained from the normal distribution table or calculator.

Using the normal distribution table, we find that the area to the right of 1.93 is 0.0262. Therefore, the probability that a randomly selected student score will exceed 690 points is 0.0262. C: The probability that a randomly selected student score will be between 400 and 590 can be obtained by finding the area under the curve between the z-scores corresponding to 400 and 590.

The z-score corresponding to 400 is (400 - 400) / 150 = 0, and the z-score corresponding to 590 is (590 - 400) / 150 = 0.6. Therefore, we need to find the area between 0 and 0.6. This area can be obtained from the normal distribution table or calculator. Using the normal distribution table, we find that the area between 0 and 0.6 is 0.2257.

Therefore, the probability that a randomly selected student score will be between 400 and 590 is 0.2257.

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Answer:

Mixed Number: 5 \(\frac{7}{10}\)

Improper Fraction:\(\frac{57}{10}\)

Step-by-step explanation:

A mixed number is when you express the decimal as a fraction, 0.7 is the same as \(\frac{7}{10}\), so 5\(\frac{7}{10}\) is your answer.

An improper fraction is a fraction where the numerator is bigger than the denominator, to do this you multipy the whole number 5, which can be written as \(\frac{5}{1}\), by \(\frac{10}{10}\).

\(\frac{5}{1}\)·\(\frac{10}{10}\)=\(\frac{50}{10}\)

Then add 0.7, or \(\frac{7}{10}\).

\(\frac{50}{10}\)+\(\frac{7}{10}\)=\(\frac{57}{10}\)

Would you please mark my answer brainliest if it helped you? :D

Answer:

∠e = 105° because ∠e and the 105° angle are vertically opposite angles

∠h = 75° because ∠h and the 105° angle are supplementary angles

∠f = ∠h = 75° because ∠f and ∠h are vertically opposite angles

∠c = 105° because ∠c and the 105° are corresponding angles

∠b = 75° because ∠b and ∠f are corresponding angles

∠a = 105° because ∠a and ∠e are corresponding angles

∠d = 75° because ∠d and ∠h are corresponding angles

Step-by-step explanation:

The given diagram includes two parallel lines having a common transversal that crosses both (parallel) lines

By sing angle properties, we have;

∠e = 105° because ∠e and the 105° angle are vertically opposite angles formed by the same two straight lines and are therefore always equal

∠h = 180° - 105° = 75° because ∠h and the 105° angle are angles that form a straight line and are therefore supplementary angles which are angles that sum up to 180°. Therefore, ∠h + 105° = 180°, therefore ∠h = 75°

∠f = ∠h = 75° because ∠f and ∠h are vertically opposite angles

∠c = 105° because ∠c and the 105° are corresponding angles and corresponding angles are equal

Similarly, we have;

∠b = ∠f = 75° because ∠b and ∠f are corresponding angles

∠a = ∠e = 105° because ∠a and ∠e are corresponding angles

∠d = ∠h = 75° because ∠d and ∠h are corresponding angles

Events a and b are not independent. The probability of both events occurring is 0.2, which is less than the product of their individual probabilities (0.7 x 0.4 = 0.28).

If events a and b were independent, the probability of both events occurring would be the product of their individual probabilities (P(a) x P(b)). However, in this scenario, the probability of both events occurring is 0.2, which is less than the product of their individual probabilities (0.7 x 0.4 = 0.28). This suggests that the occurrence of one event affects the occurrence of the other, indicating that they are dependent events.

Independence between events a and b refers to the idea that the occurrence of one event does not affect the probability of the other event occurring. In other words, if events a and b are independent, the probability of both events occurring is equal to the product of their individual probabilities. However, in this scenario, we are given that the probability of event a occurring is 0.7, the probability of event b occurring is 0.4, and the probability of both events occurring is 0.2. To determine whether events a and b are independent, we can compare the probability of both events occurring to the product of their individual probabilities. If the probability of both events occurring is equal to the product of their individual probabilities, then events a and b are independent. However, if the probability of both events occurring is less than the product of their individual probabilities, then events a and b are dependent.

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Answer:

(4/3)πr^3 = 12348π

r^3 = 9261

r = cuberoot(9261) = 21

SA = 4πr^2 = 4π(441) = 1764π square inches.

I think this is the answer, hope this helps!

r = 14.3384653 in

A = 2583.54009 in2

C = 90.0912347 in

The result of the Fourier Transform (Ω) X ( Ω ) of the signal x() = ((−1)−(+1))cos(200) is

x(t) = 1/(2π) ∫[-j∞, j∞] (s/(s^2 + 4π^2f0^2) + (s + 2/T)/(s^2 + 4π^2f0^2)) e^{st} ds

Given that the signal x()=((−1)−(+1))cos(200)  

The Fourier transform (Ω) X (Ω) is given by;

X (Ω) = ∫[-∞, ∞] x(t) e^{-jΩt} dt

Taking Laplace transform of the signal x(t);

x(t) = (−1)^(t/T)cos(2πf0t)

= cos(2πf0t) - 2cos(2πf0t)u(-t/T)

The Laplace transform of the first term is L(cos(2πf0t)) = s/(s^2 + 4π^2f0^2)

The Laplace transform of the second term is given by

L(cos(2πf0t)u(-t/T)) = (s + 2/T)/(s^2 + 4π^2f0^2)  

which is derived using partial fraction decomposition

Hence, the Laplace transform of the signal is given by

X(s) = L{x(t)}

= s/(s^2 + 4π^2f0^2) + (s + 2/T)/(s^2 + 4π^2f0^2)

Taking inverse Laplace transform of X(s) we have;

x(t) = 1/(2π) ∫[-j∞, j∞] X(s) e^{st} ds

= 1/(2π) ∫[-j∞, j∞] (s/(s^2 + 4π^2f0^2) + (s + 2/T)/(s^2 + 4π^2f0^2)) e^{st} ds

After solving this integral we will get the result of the Fourier Transform (Ω) X ( Ω ) of the signal x() = ((−1)−(+1))cos(200).

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Answer:

if i see the picture

i can probaly help

Step-by-step explanation:

The given coins [1, 2, 5] and the value 11, the minimum number of coins needed is 2.

Here are the steps to find the minimum number of coins:

1. First, we create an array of size equal to the given value, initialized with a very large number. This array will store the minimum number of coins needed to make each value from 0 to the given value.

2. We set the first element of the array to 0, as it doesn't require any coins to make a value of 0.

3. Next, we iterate through all the coins available and for each coin, we iterate through all the values from the coin value to the given value.

4. For each value, we calculate the minimum number of coins needed by taking the minimum of the current minimum and the value obtained by subtracting the coin value from the current value and adding 1 to it.

5. Finally, we return the value stored in the last element of the array, which represents the minimum number of coins needed to make the given value.

Let's consider an example to better understand the process:

Given coins: [1, 2, 5]
Given value: 11

1. Initialize the array with [INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF] (INF represents infinity).

2. Set the first element of the array to 0, so it becomes [0, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF].

3. For the first coin (1), iterate through the array from index 1 to 11.

  - For index 1, the minimum number of coins needed is 0 + 1 = 1.
  - For index 2, the minimum number of coins needed is 0 + 1 = 1.
  - For index 3, the minimum number of coins needed is 0 + 1 = 1.
  - ...
  - For index 11, the minimum number of coins needed is 0 + 1 = 1.

  The array becomes [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

4. For the second coin (2), iterate through the array from index 2 to 11.

  - For index 2, the minimum number of coins needed is 1 (minimum of 1 and 0 + 1 = 1).
  - For index 3, the minimum number of coins needed is 1 (minimum of 1 and 0 + 1 = 1).
  - For index 4, the minimum number of coins needed is 1 (minimum of 1 and 1 + 1 = 2).
  - ...
  - For index 11, the minimum number of coins needed is 1 (minimum of 1 and 1 + 1 = 2).

  The array becomes [0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2].

5. For the third coin (5), iterate through the array from index 5 to 11.

  - For index 5, the minimum number of coins needed is 2 (minimum of 2 and 0 + 1 = 1).
  - For index 6, the minimum number of coins needed is 2 (minimum of 2 and 1 + 1 = 2).
  - ...
  - For index 11, the minimum number of coins needed is 2 (minimum of 2 and 2 + 1 = 3).

  The array becomes [0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2].

6. The minimum number of coins needed to make the given value (11) is 2.

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Answer:

between one and 6

Step-by-step explanation:

musrbe the answer

Answer:

Just plot one point on (0, 5) and the other one on (6, 8)

Step-by-step explanation:

You just plot (0, 5) then you go 1 up and 8 to the right and plot another point there.

Hope it helps!