Which expression is equivalent to 9x - (x − 8)(x + 1) + 10x? - x² + 19x+8 -x^2+26x+8 8x^2 + 10x+8 8x^2 +26x+8

Use the definition of the derivative to find dsk Answer for the function G() = 2/3. To use the definition of the derivative to find the Answer for the function G() = dG = 2/3, we use the following formula; G'(x) = lim(h→0) [G(x + h) - G(x)] / h

Now, we can integrate both sides of the equation with respect to x. This is the required implicit solution of the given differential equation. Thus, the solution is (2xy + y²)² = C(7x² + 2xy)⁵/16. The solution in implicit form is where C is an arbitrary constant. From the definition of the derivative we have the following formula G'(x) = lim(h→0) [G(x + h) - G(x)] / h

For the given function, G(x) = 2/3. Then,

G'(x) = lim(h→0) [G(x + h) - G(x)] / h We substitute G(x) with 2/3 to get;

G'(x) = lim(h→0) [(2/3) + h - (2/3)] / h

G'(x) = lim(h→0) h / h

G'(x) = 1 Thus, dG / dx

= G'(x)

Then we found f(g(1)) by looking at the point where the graph of f(x) intersects the horizontal line y = g(1). Finally, to evaluate f(3) + g(3), we found the y-values where the graphs of f(x) and g(x) intersected the vertical line x = 3 and added them together.

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Answer:

Step-by-step explanation: 40 see attachment

The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.

To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.

So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.

To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.

Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1

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The value of (3a - 2b) · (b + 4a) is 68.

To find the value of (3a - 2b) · (b + 4a), we need to calculate the dot product of the two vectors. Given that |a| = 5 and |a + b| = 5√3/3, we can use these magnitudes to find the individual components of vectors a and b.

Let's assume vector a = (a₁, a₂, a₃) and vector b = (b₁, b₂, b₃).

Given that |a| = 5, we have:

√(a₁² + a₂² + a₃²) = 5

And given that |a + b| = 5√3/3, we have:

√((a₁ + b₁)² + (a₂ + b₂)² + (a₃ + b₃)²) = 5√3/3

Squaring both sides of the equations and simplifying, we get:

a₁² + a₂² + a₃² = 25

(a₁ + b₁)² + (a₂ + b₂)² + (a₃ + b₃)² = 25/3

Expanding the second equation and using the fact that a · a = |a|², we have:

a · a + 2(a · b) + b · b = 25/3

25 + 2(a · b) + b · b = 25/3

Simplifying, we get:

2(a · b) + b · b = -50/3

Now, we can calculate the value of (3a - 2b) · (b + 4a):

(3a - 2b) · (b + 4a) = 3(a · b) + 12(a · a) - 2(b · b) - 8(a · b)

= 12(a · a) + (3 - 8)(a · b) - 2(b · b)

= 12(25) + (-5)(-50/3) - 2(b · b)

= 300 + 250/3 - 2(b · b)

= 900/3 + 250/3 - 2(b · b)

= 1150/3 - 2(b · b)

Since we don't have the specific values of vector b, we cannot determine the exact value of (3a - 2b) · (b + 4a). However, we can conclude that it can be represented as 1150/3 - 2(b · b).

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Given Integral is ∫cos 2x/ (sin^2x + cos^2x + 2sinxcosx) dx.Let us solve it using integration by substitution,Let u = sin x + cos x, then du/dx = cos x − sin xMultiplying numerator and denominator by 2,

we get:∫cos 2x/ (sin^2x + cos^2x + 2sinxcosx) dx=∫cos 2x/ (sin x + cos x)^2 dx=∫cos2x/ u2 duNow substitute v = tan(x/2)So sin x = 2v/(1 + v^2), cos x = (1 − v^2)/(1 + v^2), and dx = 2/(1 + v^2) dvUsing the half-angle identities, we can simplify the integrand into:cos 2x/ (sin x + cos x)^2 = 4v2/ (1 + v2)4dvcos 2x = 2 cos2(x) − 1 = 2(1 − sin2(x)) − 1 = 1 − 2 sin2(x)Substituting the expression for cos 2x and simplifying, we obtain:∫cos 2x/ (sin^2x + cos^2x + 2sinxcosx) dx=∫1/ (1 + v^2) (1 − 2 sin2(x)) 4v^2/(1 + v^2)^2 dv=∫4v^2/(1 + v^2)^3 dv= 2[1/(1 + v^2)] + ln|(v^2 + 1)/2| + C.Substituting back v = tan(x/2), we have:∫cos 2x/ (sin^2x + cos^2x + 2sinxcosx) dx= 2(1 − tan2(x/2)) − 1/2 ln|(1 + tan2(x/2))/2| + C= ½ ln(cos2(x) + 2) + C.

We conclude that the correct answer is option C.

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The value of x that is not a zero of the function is 3.

The zero of a function is any replacement for the variable that will produce an answer of zero.

In a simpler terms, the zeros of a function are the values of x when f(x) is equal to 0.

Therefore,

f(x) = x³ + 3x² - x  - 3

0 = x³ + 3x² - x  - 3

Let's try the values of x options.

let's try 1

(1)³ + 3(1)² - 1  - 3 = 0

let's try -1

(-1)³ + 3(-1)² + 1  - 3 = 0

let's try 3

(3)³ + 3(3)² - 3 - 3 = 48

let's try -3

(-3)³ + 3(-3)² + 3 - 3 = 0

Therefore 3 is not a zero of the function.

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Answer:

152 calories

Step-by-step explanation:

The calories count, composition of carbohydrates, fat and protein are related by;

C = 4h + 9f + 4p

where C, h, f, and p have there given meaning.

Given that the serving of a type of nut contains; f = 12 grams, h = 6 grams and p = 5 grams, then;

C = 4(6) + 9(12) + 4(5)

  = 24 + 108 + 20

  = 152

C = 152 calories

Therefore, there are 152 calories in the serving of the certain type of nut.

Answer:

see below

Step-by-step explanation:

we are given a exponential function

\( \displaystyle y = \left(1/5\right) ^{x} \)

we want to figure out the missing values of y for x i.e (-2,-1, and 2) to do we can consider substituting so,

when x is -2 y should be

\( \displaystyle y = \left(1/5\right) ^{ - 2} \)

rewrite ⅕ in exponent notation:

\( \displaystyle y = \left((5) ^{ - 1} \right) ^{ - 2} \)

by law of exponent we obtain:

\( \displaystyle y = (5) ^{ 2} \)

simplify square:

\( \displaystyle y = \boxed{ 25}\)

when x is -1:

\( \displaystyle y = \left(1/5\right) ^{ - 1} \)

rewrite ⅕ in exponent notation:

\( \displaystyle y = \left((5) ^{ - 1} \right) ^{ - 1} \)

use law of exponent which yields:

\( \displaystyle y = \boxed5 \)

when x is 3:

\( \displaystyle y = \left(1/5\right) ^{ 3} \)

by law of exponent we obtain:

\( \displaystyle y = 1/ {5}^{3} \)

simplify square which yields:

\( \displaystyle y = \frac{1}{ \boxed{125}} \)

Answer:

25 5 1/125

Step-by-step explanation:

Answer:

I thik it is B

Step-by-step explanation:

Answer:

\(3.8 \times 52 \\ \frac{988}{5} \\ 197.6\)

Answer:

65 degrees

Step-by-step explanation:

y is a right angle and a is 30 degrees. this means that the supplementary engle of x is 45 plus 70 which is 115. 180-115 = 65 degrees.

Answer:

A. 40-30i is your answer.

For the polynomials p(x) = 1 - x + 4x² and q(x) = x - x², (p, q) = 10, ||p|| = √18, ||a|| = √18, and d(p, q) cannot be determined. For the vectors u = (0, 2, 3) and v = (2, 3, 0), (u, v) = 6, ||u|| = √13, ||v|| = √13, and d(u, v) cannot be determined.

In the first scenario, we have p(x) = 1 - x + 4x² and q(x) = x - x². To find (p, q), we substitute the coefficients of p and q into the inner product formula:

(p, q) = (1)(0) + (-1)(2) + (4)(3) = 0 - 2 + 12 = 10.

To calculate ||p||, we use the formula ||p|| = √((p, p)), substituting the coefficients of p:

||p|| = √((1)(1) + (-1)(-1) + (4)(4)) = √(1 + 1 + 16) = √18.

For ||a||, we can use the same formula but with the coefficients of a:

||a|| = √((1)(1) + (-1)(-1) + (4)(4)) = √18.

Lastly, d(p, q) represents the distance between p and q, which can be calculated as d(p, q) = ||p - q||. However, the formula for this distance is not provided, so it cannot be determined. Moving on to the second scenario, we have u = (0, 2, 3) and v = (2, 3, 0). To find (u, v), we use the given inner product formula:

(u, v) = (0)(2) + (2)(3) + (3)(0) = 0 + 6 + 0 = 6.

To find ||u||, we use the formula ||u|| = √((u, u)), substituting the coefficients of u:

||u|| = √((0)(0) + (2)(2) + (3)(3)) = √(0 + 4 + 9) = √13.

Similarly, for ||v||, we use the formula with the coefficients of v:

||v|| = √((2)(2) + (3)(3) + (0)(0)) = √(4 + 9 + 0) = √13.

Unfortunately, the formula for d(u, v) is not provided, so we cannot determine the distance between u and v.

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The last option; intersecting, but not perpendicular

Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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Answer: its (4f 5) ^3

Step-by-step explanation:

This can be expressed as (1 - (1 - 0.001)^N) ≤ 0.25. Solving this equation will give us the maximum frame length N that satisfies the target efficiency reduction of 75%.

In a stop-and-wait ARQ (Automatic Repeat Request) system, the sender transmits a frame and waits for an acknowledgment from the receiver before sending the next frame. To determine the maximum frame length, we need to consider the effect of bit errors on the system's efficiency.

The probability of bit error is given as 0.001, which means that for every 1000 bits transmitted, approximately one bit will be received incorrectly. The efficiency of the system is affected by the need for retransmissions when errors occur.

To meet the target efficiency reduction of 75%, we must ensure that the system's efficiency remains at least 25% of the error-free efficiency. In other words, the number of retransmissions should not exceed 25% of the frames transmitted.

Assuming a frame length of N bits, the probability of an error-free frame is (1 - 0.001)^N. Therefore, the probability of an error occurring is 1 - (1 - 0.001)^N. The number of retransmissions is directly proportional to the probability of errors.

To meet the target, the number of retransmissions should be less than or equal to 25% of the total frames transmitted. Mathematically, this can be expressed as (1 - (1 - 0.001)^N) ≤ 0.25. Solving this equation will give us the maximum frame length N that satisfies the target efficiency reduction of 75%.

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ANSWER:

6 and -6

STEP-BY-STEP EXPLANATION:

We have the following equation:

We solve for x:

It means that the value of x is 6 and -6

Cluster Sample is the sampling method used in this type of data collection.

Cluster sampling is a sampling technique used in statistics that divides the total population under consideration into externally homogeneous but internally heterogeneous groupings known as clusters. Each cluster essentially serves as a miniature representation of the overall population.

Using simple random sampling, some clusters are picked after the clusters have been identified, while the remaining clusters are left out of the study. A researcher must determine the right sampling strategy for each cluster after identifying the clusters.

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Answer:

\(\boxed{47.089 \;meters} \\\\\)

Step-by-step explanation:

For any function f(x), the maximum or minimum value can be determined by 1. Finding the first derivative f(x) with respect to x i.e. f'(x)

2. Setting this first derivative to 0, solving for x

3. Substituting for x in the original function to get the maximum/minimum value

\(\textrm{The equation for the function f(t) is }\\f(t) = -4.9t^2 + 20.58t + 25.48\\\\\)

\(\textrm{The first derivative of this function with respect to t is }\\\\f'(t) = - 2\cdot 49t + 20.58\\= -9.8t + 25.48\\\\\)

\(\textrm{Setting this first derivative equal to 0 gives:}\\\\-9.8t + 20.58 = 0\\\\-9.8t = -20.58 \;\;\;\;\;\textrm{(Subtracting 20.58 from both sides)}\\\\9.8t = 20.58 \;\;\;\;\;\; \textrm{ (Multiplying both sides by -1)}\)

\(\textrm{Therefore }\\\\t = \dfrac{20.58}{9.8}\\\\t= 2.1 \textrm{ seconds}\)

\(\textrm{Therefore, at = 2.1 seconds, the ball will reach its maximum height.}\)

To find what this maximum height is, substitute t = 2.1 in the original equation and solve for h(t)

\(h(t)\;at\;t=2.1 \\h(2.1) = 4.9\cdot \:2.1^2+20.58\cdot \:2.1+25.48=47.089 \;meters\\\\\)

\(\textrm{ The maximum height the ball achieves before landing is } \boxed{47.089 \;meters} \\\\\)

\(\textrm {This occurs 2.1 seconds after launch }\)

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer:

y=3.5

Step-by-step explanation:

y=3(0.5)+2

y=1.5+2

y=3.5

Answer:

E,C

Step-by-step explanation:

circumference formula is 2 times radius times pi or diameter times pi

E is the diameter of the flower bed times pi by just multiplying 4 by 2 to get 8

C is correct alone because it uses the pi formula

Hopes this helps please mark brainliest

Answer:

The Circumference of the circle shown in the picture is 87.96

Step-by-step explanation:

The formula in order to find the circumference is C=2πr.

r in this example is 14

so C= 2 * π * 14

π is always a constant value so all you have to do is add it to the calculator to get your answer.

Hope this helps!

Answer:

there are 4 terms and x is the constant

Answer:

- 20

Step-by-step explanation:

Step 1:

10 - 2v = - 5v - 50      Equation

Step 2:

10 + 3v = - 50    Add 5v on boh sides

Step 3:

3v = - 60      Subtract 10 on both sides

Step 4:

- 60 ÷ 3      Divide

Answer:

v = - 20

Hope This Helps :)

Answer:

The table on the far left is a linear function.

Step-by-step explanation:

The table on the far left is the function

\(y = \frac{1}{2} x\)

Answer:  n ≤ 52

Step-by-step explanation:

less than or equal to is usually write as ≤.

n - 15 ≤ 37

  +15    +15 [Add 15 to the both sides]      

     n ≤ 52

Answer:

32 is the present age of Timothy

Answer:

32

Step-by-step explanation: