***WORTH 40 POINTS*** [−3−4x≤21]

Answer:

Average Rate = -14/7

Step-by-step explanation:

f(3) = 3^2 - 3 - 8 = -2

f(-4) = (-4)^2 - (-4) - 8 = 12

interval: [-4, 3]

Average Rate = [f(b) - f(a)]/(b - a) interval: [a, b]

= [(-2) - 12] / [3 - (-4)]

= -14/7

Answer: 4t+109.99=347.95

Step-by-step explanation:

Answer:

Step 1: Move the decimal point so that you have a number that is between 1 and 10. ...

Step 2: Count the number of decimal places moved in Step 1 . ...

Step 3: Write as a product of the number (found in Step 1) and 10 raised to the power of the count (found in Step 2).

Step-by-step explanation:

To prove that the matrix A^p is symmetric for any positive integer p, we can use mathematical induction.

First, we establish the base case for p = 1. If A is a symmetric matrix, it means that A^T = A, where A^T represents the transpose of matrix A. In this case, A^1 = A, which satisfies the condition for symmetry.

Next, we assume that A^k is symmetric for some positive integer k. This assumption forms the induction hypothesis.

Now, we need to prove that A^(k+1) is also symmetric based on the induction hypothesis. We have:

(A^(k+1))^T = (A^k * A)^T

Using the property of matrix transpose, we have:

(A^k * A)^T = A^T * (A^k)^T

Since A is symmetric, A^T = A. Therefore, we have:

(A^k * A)^T = A * (A^k)^T

Now, using the induction hypothesis, we can rewrite (A^k)^T as A^k:

A * (A^k)^T = A * A^k = A^(k+1)

Thus, we have shown that (A^(k+1))^T = A^(k+1), which means A^(k+1) is symmetric.

By using mathematical induction, we have proven that if A is a symmetric matrix, then A^p is also symmetric for any positive integer p. This result holds because each step of the induction preserves the symmetry property, and the base case establishes the initial condition for p = 1. Therefore, we can conclude that the matrix A^p is symmetric for all positive integers p.

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Answer:

42/100

Step-by-step explanation:

The clerk walked approximately 0.371π meters during the 132 minutes of delivering along the hallway.

To find the number of 3-meter segments the clerk walked during the 132 minutes, we need to integrate the velocity function over the given time interval.

v(t) = 4π sin(t)

The clerk starts at one end and takes 13 minutes to finish deliveries, so the time interval is from t = 0 to t = 13.

To calculate the distance walked, we integrate the absolute value of the velocity function over the given interval:

Distance = ∫[0, 13] |v(t)| dt

Let's calculate the integral:

Distance = ∫[0, 13] |4π sin(t)| dt

Since the absolute value of sin(t) is positive for the given interval, we can simplify the integral to:

Distance = 4π ∫[0, 13] sin(t) dt

Using the integral of sin(t), which is -cos(t), the expression becomes:

Distance = -4π cos(t) |[0, 13]

Now we can evaluate the integral over the given interval:

Distance = -4π (cos(13) - cos(0))

Simplifying further:

Distance = -4π (cos(13) - 1)

Calculating the value:

Distance ≈ -4π (0.907 - 1)

Distance ≈ -4π (-0.093)

Distance ≈ 0.371π meters

Therefore, the clerk walked approximately 0.371π meters during the 132 minutes.

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Answer:

\(\displaystyle a^{-7}=\frac{1}{a^7}\)

Step-by-step explanation:

Recall that if you raise a base to a negative exponent, you take the reciprocal of the base raised to the positive exponent.

Thus, \(a^{-7}=\frac{1}{a^7}\).

The measure of the angle x is 32 degree after applying the sin law of triangle.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have a triangle given in the diagram.

To find the measure of the angle x we must apply the sin law of triangle.

\(\rm \dfrac{17}{sin116} = \dfrac{10}{sinx}\)

Sinx = 10(sin116)/17

Sinx = 0.528

x = 31.91 ≈ 32 degree

Thus, the measure of the angle x is 32 degree after applying the sin law of triangle.

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Answer:

He Spent 24.0624 Dollars

Step-by-step explanation:

25.86-25.68*7%=24.0624 Dollars

Hope This Helps!

The final transformation is y = 3 f ( x - 5 ) + 5.

A function g is given as g ( x ) =  3x + 5.

Identify the parent function.

Then use the steps for graphing multiple transformations of functions to list, in order, the transformations applied to the parent function to obtain the graph of g.
Parent function: f(x) = x
Given, g(x) = 3x + 5
Shift the graph off to the right 5 units, shrink the graph vertically 1 by a factor of 3 and shift the graph upward by 5 units.
Thus, the transformation steps are:
Shift right by 5 units
Shrink vertically by a factor of 3
Shift upward by 5 units
The final transformation is y = 3 f ( x - 5 ) + 5.

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Answer:

8.50 divided by 1.25 then when u get the answer subtract 40

Answer:

25

Step-by-step explanation:

so instantly 40-8.50=31.5

The question is very vague because it doesn't state the number of rides he wants to go on in minimum.

if you do 1.25x25=31.25

According to that, he will leave with a change of 0.25 and obv u cannot go on half a ride...

So in about 2 mins i guess it is 25???

Add me on instagram: vnshl

Answer:

(1, 0) and (3, 0)

Step-by-step explanation:

y=2x²-8x+6

x- intercept when y=0

Answer:

(1, 0) / (3, 0)

Step-by-step explanation:

Answer:

its F

Step-by-step explanation:

Its f since when you do the reflection on a grid you will get (1,-4)  No problem ;D

Answer:

YES

Step-by-step explanation:

Answer:Any positive improper fraction is larger than any positive proper fraction: ie: 44/25 > 1 > 19/ ie: - 44/25 < -1 < - 19/

Step-by-step explanation:

Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.

No, dividing two polynomials may not result in another polynomial. It can produce a rational function.

A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.

If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.

A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.

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Answer:

2/12

Step-by-step explanation:

There is a 1/6 chance of rolling a 3 once because there are six sides and only one 3, double that ratio if your want the probability of rolling that same number twice in a row.

Answer:

To find the degree measures of all angles with cosine 1/2, we can use the unit circle, which is a circle with a radius of 1 centered at the origin of the coordinate plane. The x-coordinate of a point on the unit circle represents the cosine of the angle formed between the positive x-axis and the line segment connecting the origin to the point.

When cosine is 1/2, we know that the x-coordinate of the point on the unit circle is 1/2. We can use the Pythagorean theorem to find the y-coordinate of the point:

1^2 + y^2 = 1^2

y^2 = 1 - 1/4

y^2 = 3/4

y = ±√(3/4)

y = ±(√3)/2

So the two angles with cosine 1/2 are the angles whose terminal sides intersect the unit circle at the points (1/2, √3/2) and (1/2, -√3/2). To find these angles in degrees, we can use the inverse cosine function:

cos⁻¹(1/2) ≈ 60

cos⁻¹(1/2) + 360 ≈ 300

Therefore, the degree measures of all angles with cosine 1/2 are approximately 60° and 300°.

Step-by-step explanation: :)

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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Answer:

30.

Step-by-step explanation:

The amount he opened the investment account with, his principal = $8600

This principal = 100% of his investment

If after a year the amount in his account increased by 24.5%, the total percentage now = 100 + 24.5 = 124.5%

By ratio, we can find the increase thus

His increase = 10707 - 8600 = $2107

At the end of last year, he had $10707 in his account

Dry-by-step explanation:

Kznyuszc kubysadnuailsdaieubvaeryulbvaulybeffn

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Answer:

y =(x-9)^2 +2

Step-by-step explanation:

The vertex form of a quadratic is

y = a(x-h)^2 +k  where (h,k) is the vertex and a is a constant

y = a(x-9)^2 +2

We can choose a if not given another point so I choose a = 1

y =(x-9)^2 +2

Answer:

N/A

Step-by-step explanation:

the question is not in depth could you add a photo

The expression with fewest possible terms is written as, 21t/40 - 73/4

Expression:

Basically, the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between is known as expression

Given,

Here we have the expression:

(3/4t - 5 + 2/5t) - (5/8t + 17)

Now, we have to simplify the given expression.

in order to solve this expression we have to divide the expression into two parts like the following:

A = (3/4t - 5 + 2/5t)

B = (5/8t + 17)

First, we have to solve the A part, then we get,

=>  (3/4t - 5 + 2/5t)

In order to solve this one we have to make the denominator equal,

So, the expression is rewritten as follows:

=> (15t - 25 + 8t)/20

=> (23t - 25)/20

Now, we have to solve the part B, then we get,

=> A - B = (23t - 25)/20 - (5/8t + 17)

=> [46t - 50 - 25t - 680]/40

=> (21t - 730)/40

It can be expanded as,

=> 21t/40 - 730/40

=> 21t/40 - 73/4

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The surface area that can be painted with one complete rotation of the roller is 1508 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 8 inches

h = height of the cylinder = width = 30 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(8*30)

SA = 150.7.966 = 1508 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 1508inches².

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Answer:

It depends.

Step-by-step explanation:

If it is two straight lines, then no, there is no way for the lines to intersect in more than one place. If the line is a parabola, then the lines would intersect in 2 places. It depends on what type of line you have.  

Answer:

Guava has the most, Nelli juice has second most, Mango juice has third most Papaw juice has 4th most, Woodaple has the least

Step-by-step explanation:

Answer:

From smallest portion to biggest

Wood apple juice,

Papaw juice,

Mango juice,

Nelli Juice

Step-by-step explanation:

By looking at this graph we cam tell Guava juice has the most since it has the biggest section.

Now we can tell Wood apple juice isn't a popular option because it has the smallest section

Now to fill in the gaps, Papaw juice has the second least amount, then Nelli has third least amount, and and Guava Juice has the most.

  By using triangle sum theorem in triangle EFG, measure of the unknown angle ∠G will be 68°.

Measures of the angles in a triangle has been given as,

m∠E = 97°

m∠F = 15°

By triangle sum theorem,

m∠E + m∠F + m∠G = 180° (Sum of interior angles of a triangle is 180°)

97° + 15° + m∠G = 180°

m∠G = 180 - 112

m∠G = 68°

  Therefore, measure of the third angle (∠G) of ΔEFG will be 68°.

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Answer:

3.99

Step-by-step explanation:

The total sum of central angle of circle is 360 which mean the area of the circle = (12.36 x 360)/89

A=πr^2

=> (12.36 x 360)/89 = 3.14(r^2)

r^2 = 15.92

r = 3.99