The graph of the parent function f(x) = xº is translated to form the graph of g(x) = (x - 4) 3 - 7. The point (0, 0) on the
graph of f) corresponds to which point on the graph of g(x)?

Answer:

NM = 13

Step-by-step explanation:

pythagorean theorem: \(a^{2} + b^{2} = c^{2}\)

a or NO = 5

b or OM = 12

c or NM = ?

plug in what is known:

⇒ \(5^{2} + 12^{2} = c^{2}\)

⇒ \(25 + 144 = c^{2}\)

⇒ 169 = \(c^{2}\)

square root each side of the equation:

⇒ \(\sqrt{169} = \sqrt{c^{2} }\)

solve:

⇒ 13 = c

Answer:

The exact solutions in the interval [0,2π) are x = π/6, 5π/6, 7π/6 and 11π/6

Step-by-step explanation:

yw;)

The value of i th sample point is xi = 9i/n.

a) The given function is f(x) = x² + 3 and we need to find the area under the curve of the function on [0, 9]. Here a is the lower limit of the interval and b is the upper limit of the interval.

So, we have a = 0 and b = 9.

b) We are required to use n subintervals to evaluate the area.Δx is the width of each subinterval.

So, we have

Δx = (b - a) / n

= (9 - 0) / n

= 9/n

c) The sample points for the right endpoints for each interval can be determined as follows:

x1 = a + Δx

= 0 + 9/n

= 9/nx2

= a + 2

Δx = 0 + 2(9/n)

= 18/n

x3 = a + 3

Δx = 0 + 3(9/n) = 27/n

and in general

xi = a + i

Δx = 0 + i(9/n) = 9i/n

Therefore, the value of i th sample point is xi = 9i/n.

Note: As we need to find the area using limit definition, the expression would be a summation of f(xi)Δx where i goes from 1 to n, i.e., ∑f(xi)Δx from i = 1 to n.

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x-value that corresponds to the z-score of 2.33 is 81.65.

Mean = 70

Standard deviation = 5

z score = 2.33

Using the z-score formula:

z = (x - mean) / SD

Plug the values:

2.33 = (x-70)/5

    x = 5(2.33) +70

    x = 81.5

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The modified Reynolds analogy, also known as the Chilton-Colburn analogy, is expressed mathematically as Nu = f * Re^m * Pr^n. It relates the convective heat transfer coefficient (h) to the skin friction coefficient (Cf) in fluid flow. This equation is widely used in heat transfer analysis and design applications involving forced convection.

The modified Reynolds analogy is a useful tool in heat transfer analysis, especially for situations involving forced convection. It provides a correlation between the heat transfer and fluid flow characteristics. The Nusselt number (Nu) represents the ratio of convective heat transfer to conductive heat transfer, while the Reynolds number (Re) characterizes the flow regime. The Prandtl number (Pr) relates the momentum diffusivity to the thermal diffusivity of the fluid.

The equation incorporates the friction factor (f) to account for the energy dissipation due to fluid flow. The values of the constants m and n depend on the flow conditions and geometry, and they are determined experimentally or by empirical correlations. The modified Reynolds analogy is widely used in engineering calculations and design of heat exchangers, cooling systems, and other applications involving heat transfer in fluid flow.

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Answer:-7.5

Step-by-step explanation:

If we take out the negative and make it 24 ÷ 3.2, it would be 7.5 since 3.2 would go into 24 7.5 times. But since we changed it to figure it out, we have to change it back with the rule that "a negative x negative is a positive" meaning that the

24 ÷ 3.2 = 7.5

would change to

24 ÷ (-3.2) = -7.5 OR

Positive ÷ negative = negative

(And this goes with any operation)

Answer:

2x-8

Step-by-step explanation:

Answer:

2x-8

Step-by-step explanation:

If your doing distributive property then you multiply the 2 by the x and the 8 which will give you

2x-8

Answer:

216

Step-by-step explanation:

gof(6) means g(f(6))

f(6)=2(6)-6=6

g(6)=6^3=216

The disjunction of -p or -q can be written as (-p) v (-q). So, we have to find the truth value of (-p) v (-q). So, the compound statement for the disjunction of -p or -q is (-p) v (-q), and its truth value is true.

using the following statements: p: There are 14 inches in 1 foot.

q: There are 3 feet in 1 yard.

Solution: We know that 1 foot = 12 inches, which means that there are 14 inches in 1 foot can be written as 14 < 12. But this statement is false because 14 is not less than 12. Therefore, the negation of this statement is true, which gives us (-p) as true.

Now, we know that 1 yard = 3 feet, which means that there are 3 feet in 1 yard can be written as 3 > 1. This statement is true because 3 is greater than 1. Therefore, the negation of this statement is false, which gives us (-q) as false.

Now, we can use the values of (-p) and (-q) to find the truth value of (-p) v (-q) using the disjunction rule. The truth value of (-p) v (-q) is true if either (-p) or (-q) is true or both (-p) and (-q) are true. Since (-p) is true and (-q) is false, the disjunction of (-p) v (-q) is true. Hence, the compound statement for the disjunction of -p or -q is (-p) v (-q), and its truth value is true.

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Answer:

120°

Hope it helped you

Answer:

1200

Step-by-step explanation:

A difference of 2 squares factors in general as

a² - b² = (a - b)(a + b) , then

103² - 97²

= (103 - 97)(103 + 97)

= 6 × 200

= 1200

The correct answer is 1200.

Where one perfect square is subtracted from another, is called a difference of two squares. It arises when (a − b) and (a + b) are multiplied together. This is one example of what is called a special product.

A difference of 2 squares factors in general is written as

a² - b² = (a - b)(a + b) , then

103² - 97²

= (103 - 97)(103 + 97)

= 6 × 200

= 1200

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The correct answer is (D) AB is 4 x 4, BA is 2 x 2.

What is order of a matrix?

The order of a matrix refers to the number of rows and columns in the matrix. If a matrix has m rows and n columns, we say that it is an m x n matrix. The order of the matrix is written as "m x n".

In general, if A is an m x n matrix and B is an n x p matrix, then the product AB is an m x p matrix and the product BA is an n x n matrix.

In this case, A is a 4 x 2 matrix and B is a 2 x 4 matrix. Therefore, the product AB is a 4 x 4 matrix, and the product BA is a 2 x 2 matrix.

So the answer is (D) AB is 4 x 4, BA is 2 x 2.

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The two inequalities in the system for Keitaro to reach his monthly goal of at least 36 miles but not more than 90 miles are: 3w + 6r ≥ 36 and 3w + 6r ≤ 90, where w represents the number of hours he walks and r represents the number of hours he runs.

To form the inequalities, we need to consider the distances covered by Keitaro while walking and running, as well as the minimum and maximum monthly goals.

Let's start with the minimum goal of 36 miles. We know that the walking pace is 3 miles per hour. Therefore, the distance covered by walking can be expressed as 3w, where w represents the number of hours Keitaro walks. Similarly, the distance covered by running can be expressed as 6r, where r represents the number of hours he runs.

To reach at least 36 miles, the total distance covered (3w + 6r) must be greater than or equal to 36. Hence, the first inequality is 3w + 6r ≥ 36.

Now let's consider the maximum goal of 90 miles. To ensure that the total distance covered is not more than 90 miles, the second inequality is 3w + 6r ≤ 90.

Therefore, the system of inequalities is 3w + 6r ≥ 36 and 3w + 6r ≤ 90, where w represents the number of hours Keitaro walks and r represents the number of hours he runs. These inequalities ensure that Keitaro's monthly distance falls within the desired range of at least 36 miles but not exceeding 90 miles.

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Answer:

83

Step-by-step explanation:

The 126 angle is an exterior angle of the triangle.

The 43 and x angles are the two remote interior angles of the 126 angle.

Theorem:

The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles.

x + 43 = 126

x = 83

Answer:

x = 83

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

126 = x+43

Subtract 43 from each side

126-43 = x+43-43

83 = x

Answer:

D & B

Step-by-step explanation:

Answer:235

Step-by-step explanation:i got it right on test

Answer:

Lesser x = -14

Greater x = 0

Step-by-step explanation:

Given equation:

\(\sf (x+7)^2-49=0\)

Add 49 to both sides:

\(\implies \sf (x+7)^2-49+49=0+49\)

\(\implies \sf (x+7)^2=49\)

Square root both sides:

\(\implies \sf \sqrt{(x+7)^2}=\sqrt{49}\)

\(\implies \sf x+7=\pm7\)

Solve for x:

\(\implies \sf x+7=7 \implies x=0\)

\(\implies \sf x+7=-7 \implies x=-14\)

As -14 < 0

Answer:

Positive: Decimals are a part of a whole just like fractions are a part of a whole. Therefore, a positive decimal is always greater than a negative decimal.

Negative: When you have two negative decimals, the one closer to zero is always greater. The farther a negative decimal is from zero, the smaller its value.

All of it put together (same text as above):

Decimals are a part of a whole just like fractions are a part of a whole. Therefore, a positive decimal is ALWAYS greater than a negative decimal. When you have two negative decimals, the one closer to zero is always greater. The farther a negative decimal is from zero, the smaller its value.

To prove that e(h) has a minimum at h = 3€/M, we need to first understand the terms involved. The upper bound for total numerical error E h2 eh) + M h 6 refers to the maximum possible error in a numerical computation.

It includes two types of error: the truncation error (E h2) which results from approximating a mathematical function using a finite number of terms, and the round-off error (eh) which results from the limited precision of computer arithmetic.
The numerical error e(h) is a function of the step size h used in numerical approximations. It is given by e(h) = E h2 + M h 6 + eh.
Now, to prove that e(h) has a minimum at h = 3€/M, we can take the derivative of e(h) with respect to h and set it to zero.
de(h)/dh = 2Eh - Mh5 + eh'
Setting this equal to zero, we get:
2Eh - Mh5 + eh' = 0
Rearranging and solving for h, we get:
h = (2E/Me')^(1/4)
Substituting this value of h in e(h), we get:
e(h) = (4/3)^(3/4) * (EM)^(1/4) * eh'
Since eh' is a constant, e(h) is minimized when EM is minimized.
Therefore, we need to find the minimum value of EM, which is achieved when h = 3€/M.
Thus, we can conclude that e(h) has a minimum at h = 3€/M.

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roots = {-2, -6}

Factors: (x + 6) and (x + 2)

Answer:

Height of building is 57.12 m.

Step-by-step explanation:

Let us try to understand the given dimensions as per the attached diagram.

Please refer to attached image (Right angled \(\triangle OBT\))

with \(\angle B =90^\circ\)

Let O be the point where the Surveyor is standing.

B be the point of the base of building.

T be the point of top of building.

As per question statement,

\(\angle O = 55^\circ\)

Side OB = 40 m

To find: Side BT = ?

Using tangent trigonometric identity:

\(tan\theta =\dfrac{Perpendicular}{Base}\)

\(tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m\)

So, height of building is 57.12 m.

Answer:

a) 64

b) 9

c) 1

d) 49

Step-by-step explanation:

8^2 = 64

same as 8*8

1^2 = 1

same as 1*1

3^2 = 9

same as 3*3

7^2 = 49

same as 7*7

a: 64, b:9, c:1, d:49

Step-by-step explanation:

because 8 squared is 64, 3 squared is 9(3×3=9), 1 squared is 1(1×1), and 7 squared is 49.

Answer:

WX

Step-by-step explanation:

The distance between vertex X and vertex W is much smaller then from X to Y or W to Y.

Answer:

c

Step-by-step explanation:

The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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The approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.

We can approximate the area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 using a Riemann sum with 4 rectangles of equal width. The left-hand endpoint of each subinterval will be used.

The width of each rectangle is the length of the interval (5-(-1)) divided by the number of rectangles (4). Therefore, the width of each rectangle is

(5-(-1))/4 = 6/4 = 1.5.

Since we are using the left-hand endpoint of each subinterval, the x-values of the left-hand endpoints of the rectangles are

-1, -1+1.5

-1+1.5+1.5

-1+1.5+1.5+1.5 = -1+4.5=3.5

The height of each rectangle is determined by the value of y at the corresponding x-value.

Therefore, the heights of the rectangles are

3(-1)^2+1=2

3(-1+1.5)^2+1=7.125

3(3.5)^2+1=35.125

3(3.5+1.5)^2+1=46.875

The area of each rectangle is the product of its width and height, so the areas of the rectangles are

2*1.5=3

7.125*1.5=10.6875

35.125*1.5=52.6875

46.875*1.5=70.3125.

Therefore, the approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.

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Answer:

19

Step-by-step explanation:

-8+8=0

0+19=19

Hope it helps.

Answer:

19

Step-by-step explanation:

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