Use the graph of the function f to answer the question.
Find the​ numbers, if​ any, at which f has a local minimum. What are the local​ minima?
A. f has a local minimum at x= -1; the local minimum is - 1 у B. f has no local minimum C. f has a local minimum at x= - 1 and r; the local minimum is - 1 D. f has a local minimum at x = 0; the local minimum is 1 . х AV -T T 31 2 2 2

The correct answer is d. happens when A is not in [-pi/2, pi/2]. The inverse sine function, sin^-1, or arcsin, is the function that reverses the sine function.

It is defined for values in the range [-1, 1] and has a range of [-pi/2, pi/2]. This means that if A is not in the range [-pi/2, pi/2], then sin^-1 (sin A) will not equal A.

For example, if A = pi, then sin A = 0, but sin^-1 (0) = 0, not pi. This is because pi is not in the range [-pi/2, pi/2], so the inverse sine function cannot return it as an answer.

Therefore, The correct answer is d. happens when A is not in [-pi/2, pi/2].

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Easton needs to complete 3 more jumps to reach his goal of completing 70% of the jumps on the skateboard course.

Easton's goal is to complete 70% of the jumps on the skateboard course. This means he needs to complete 70% of the total number of jumps.

We know that Easton has already completed 18 jumps out of 30, which is equivalent to completing 60% of the jumps.

The total number of jumps on the skateboard course is 30.

Easton's goal is to complete 70% of the jumps, which is:

0.7 x 30 = 21 jumps

Easton has already completed 18 jumps, so he needs to complete:

21 - 18 = 3 more jumps

So, he needs 3 more jumps

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We use standard units when measuring an object because :

A. Standard units are used because they are relatively permanent.

B. Standard units enable communication over time.

C. Standard units enable communication over distance.

D. Standard units are exact.

We use standard units when measuring an object because they are relatively permanent and enable communication over time, distance, and exactness.

Standard units are used because they are relatively permanent. This means that they do not change over time and are consistent. Standard units enable communication over time. Since they are consistent, they allow for accurate communication of measurements even if they are taken at different times.

Standard units enable communication over distance. They allow for accurate communication of measurements even if the people communicating are in different locations. Standard units are exact. This means that they are precise and accurate, allowing for consistent measurements.

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The length of line LN is 25.

What is Similarity of Triangles?

Two triangles are similar if they have the same shape but possibly different sizes. This means that their corresponding angles are congruent and their corresponding sides are proportional.

Since line MN is parallel to line JK, we can use the property that corresponding angles are congruent to set up the following proportion:

LN/KJ = NM/JK

Substituting the given values, we have:

LN/40 = 25/40

Multiplying both sides by 40, we get:

LN = 25

Therefore, the length of line LN is 25.

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The simplified expression is 45°, which is closest to option a. 38°.

Lines are one-dimensional geometrical objects that extend infinitely in both directions. Angles are formed when two lines intersect, and they measure the amount of rotation between the lines.

We can use the formula:

arctan(x) + arctan(y) = arctan[(x + y) / (1 - xy)]

to simplify the expression.

Setting x = 1/3 and y = 2/3, we have:

arctan(1/3) + arctan(2/3) = arctan[(1/3) + (2/3) / (1 - (1/3)(2/3))]

= arctan(1)

= 45°

Therefore, the simplified expression is 45°, which is closest to option

a. 38°.

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a)P(number greater than 8) = 4/12 = 1/3 ≈ 0.3

b)P(number less than 6) = 5/12 ≈ 0.4

c)If each face has an equal chance of rolling, the solid is fair. The solid is fair since the faces are numbered sequentially from 1 to 12 and each face has an equal chance of being rolled.

One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

from the question:

a) A solid has 12 equal-sized faces with numbers ranging from 1 to 12. The chance of getting a number larger than 8 is calculated by dividing the total number of faces by the number of faces with numbers greater than 8. Given that there are 4 faces (12 - 8) with numbers greater than 8, the likelihood of drawing one is:

P(number more than 8) = 4/12 = 1/3 =  0.35

b) Similarly, the chance of receiving a number less than 6 is calculated by dividing the total number of faces by the number of faces that have numbers less than 6. Given that there are 6 - 1 = 5 faces with numbers lower than 6, the likelihood of drawing one is as follows:

P(less than six) = 5/12=  0.4

c) If each face has an equal chance of rolling, the solid is fair. The solid is fair since the faces are numbered sequentially from 1 to 12 and each face has an equal chance of being rolled.

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Answer:

The width of the window is 122 inches

Step-by-step explanation:

654- known two sides(410) =244

divide 244/2, to get both unknown sides of the rectangular window, 122 inches

The fifth term of the expansion of (x − 5)⁶ is found as:  937x².

The Pascal triangle has a lengthy history. It may be traced back to India's Pingala people in the second century BC, who also knew various other binomial formulas at the same time.

Using the binomial series:

(n C r) = n! / (r1(n - r)!

Given equation: (x − 5)⁶

On comparing:

a = x, b = -5 and n = 6

x⁶ + (6C1).x⁶.(-5)¹ + (6C2).x⁴.(-5)² + (6C3)x⁴(-5)³ + (6C4).x²(-5)⁴ + (6C5).x¹.(-5)⁵ + (-5)

Using binomial calculator to solve the expression as;

x⁶ - 30x⁵ + 375x⁴ - 2500x³ + 937x² - 1870x + 15625

Thus, the fifth term of the expansion of (x − 5)⁶ is found as:  937x².

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The excluded values of u in the expression (u-7)/(u^2-14u+49) are 7.

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Answer:

15=2.00x+1.50y

Step-by-step explanation:

Answer: 240 more cards than Alex!

Step-by-step explanation:

After 8 months, Filip will have more trading cards than Alex. This is because over 8 months, Filip will have bought 8 boxes of 30 cards and Alex will have bought 8 boxes of 22 cards, meaning that Filip will have a total of 8*30 = 240 more cards than Alex.

Answer:

240 more

Step-by-step explanation:

The simplified expression is [tex](z^{(16))}(y^{(12))}/(100663296)(x^{(8))}[/tex].

To simplify the expression ((4x^(2)z^(-4))/(20y^(-3)))^(-4) using the properties of exponents, we need to follow the steps below:

1. First, we need to distribute the exponent of -4 to each term inside the parentheses. This will give us:

(4^(-4))(x^(2*-4))(z^(-4*-4))/(20^(-4))(y^(-3*-4))

2. Next, we need to simplify the exponents by multiplying them. This will give us:

[tex](4^(-4))(x^(-8))(z^(16))/(20^(-4))(y^(12))[/tex]

3. Now, we need to simplify the terms with negative exponents by moving them to the opposite side of the fraction. This will give us:

[tex](z^(16))(y^(12))/(4^(4))(x^(8))(20^(4))[/tex]

4. Finally, we need to simplify the terms with the same base by adding their exponents. This will give us:
[tex](z^(16))(y^(12))/(4^(4))(x^(8))(2^(8))(5^(8))[/tex]

5. We can further simplify the expression by simplifying the terms with the same base. This will give us:

(z^(16))(y^(12))/(16^(2))(x^(8))(2^(8))(5^(8))

6. Now, we can combine the terms with the same base to get our final answer:

(z^(16))(y^(12))/(256)(x^(8))(256)(390625)

7. Our final answer is:

(z^(16))(y^(12))/(100663296)(x^(8))

Therefore, the simplified expression is (z^(16))(y^(12))/(100663296)(x^(8)).

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The expressions that can be used to determine the total area, in square feet, of Rajiv's garage after he removes the wall are

We have to solve for the total area of the garage of Rajiv after he had removed the wall

This is given as

12 * x + 12 * 14.5

= 12(14.5 + x)

Option B

When we expand the expression 12(14.5 + x)

174 + 12x

re written as

12x + 174

Option G

The expression that can be used to determine the total area, in square feet, of Rajiv's garage after he removes the wall is given as 12(14.5 + x), 12x + 174

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d

2/3 is the same as 4/6 and 25/100 is the same as 1/4. -1.3 is transferred to the beginning of the equation

The equation is true, the point (-1,6) does indeed lie on the line (-3,5).

The equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. In order to determine whether or not the point (-1,6) lies on the line (-3,5), we need to plug in the x and y values of the point into the equation of the line and see if the equation is true.

First, we need to find the slope of the line. The slope is the difference in the y values divided by the difference in the x values:

m = (5 - 6)/(-3 - (-1)) = -1/-2 = 1/2

Next, we need to find the y-intercept of the line. We can do this by plugging in one of the points and solving for b:

5 = (1/2)(-3) + b

b = 5 + (3/2) = 13/2

Now we have the equation of the line: y = (1/2)x + 13/2

Finally, we can plug in the x and y values of the point (-1,6) to see if the equation is true:

6 = (1/2)(-1) + 13/2

6 = -1/2 + 13/2

6 = 12/2

6 = 6

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Using the area formula, it is obtained that Tanner has enough spray paint to cover the arrow with one can of spray paint.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

To determine if Tanner has enough spray paint for his arrow, we need to find the total area of the arrow and compare it to the coverage of one can of spray paint.

The arrow consists of a rectangle and a triangle.

The rectangle has a length of 2 feet and a width of 5 1/3 feet, so its area is -

Area of rectangle = length × width

= 2 ft × 5 1/3 ft

= 10 2/3 sq. ft.

The triangle has a base of 3 feet and a height of the difference between the width of the rectangle (5 1/3 feet) and the width of the arrow (6 feet):

Height of triangle = 6 ft - 5 1/3 ft = 2/3 ft

Area of triangle = 1/2 x base x height = 1/2 x 3 ft x 2/3 ft = 1 sq. ft.

The total area of the arrow is the sum of the area of the rectangle and the area of the triangle -

Total area of arrow = Area of rectangle + Area of triangle

Total area of arrow = 10 2/3 sq. ft. + 1 sq. ft.

Total area of arrow = 32/3 sq. ft. + 1 sq. ft.

Total area of arrow = 11 2/3 sq. ft.

Therefore, since one can of spray paint covers up to 12 square feet, Tanner has enough spray paint to cover the arrow with one can of spray paint.

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The amount of interest earned on Jenna's loan of $8000 for 15 years is $7200

The given variables and their values from the question are listed as follows:

Principal = 8000

Rate = 6%

Time = 15 years

The general formula to calculate simple interest is:

Simple interest = Principal * Rate * Time

By replacing the given values into the equation mentioned above, we obtain the subsequent expression

Simple interest = 8000 * 6% * 15

Evaluate the products in the expression

Simple interest = 7200

Hence, the amount of interest is $7200

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Complete question

Jenna borrows 8,000 for college at a yearly simple interest rate of 6 she takes 15 years

Determine the amount of interest

The polynomial in factored form as a product can be found by using the factor theorem and synthetic division. The factor theorem states that if f(a) = 0, then (x-a) is a factor of f(x). We can use synthetic division to find the factors of f(x)=12x^(5)+5x^(4)-39x^(3)+9x^(2)+19x-6.

First, we need to find a value of x that makes f(x) = 0. We can use the rational root theorem to find possible rational roots. The possible rational roots are ±1, ±2, ±3, ±6. We can use synthetic division to test these possible roots.

Using synthetic division with x = 1, we get a remainder of -1, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of f(x).

Now we can divide f(x) by (x+1) using synthetic division to get the quotient 12x^(4)-7x^(3)-32x^(2)+41x-6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this quotient.

The possible rational roots of the quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of 8, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of the quotient.

We can divide the quotient by (x+1) using synthetic division to get the new quotient 12x^(3)-19x^(2)-13x+6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this new quotient.

The possible rational roots of the new quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of -14, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of the new quotient.

We can divide the new quotient by (x+1) using synthetic division to get the new quotient 12x^(2)-31x+6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this new quotient.

The possible rational roots of the new quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of -13, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 49, so x = -1 is not a root. Using synthetic division with x = 2, we get a remainder of 0, so x = 2 is a root and (x-2) is a factor of the new quotient.

We can divide the new quotient by (x-2) using synthetic division to get the new quotient 12x-3. This quotient cannot be factored further, so the factors of f(x) are (x+1)(x+1)(x+1)(x-2)(12x-3).

Therefore, the polynomial in factored form as a product is f(x) = (x+1)(x+1)(x+1)(x-2)(12x-3).

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The rate of change of f(x) = 2(2) is equal to the rate of change of the function in the graph.

A function is a relation between two sets of values in mathematics. It is a mathematical process that takes an input and produces an output. It is represented as an equation which describes the relationship between the input and the output. A function can also be used to represent a mathematical rule or procedure that takes a set of inputs and produces a set of outputs.

The rate of change, or slope, is the measure of how quickly one variable changes when the other changes. In the graph, the rate of change is a constant, meaning that for every one unit the x-value increases the y-value increases by two. This is the same as the rate of change of f(x) = 2(2), as for every two units the x-value increases the y-value increases by four. Both the graph and the equation of the function have a constant rate of change which is equal to two, so the rate of change of f(x) = 2(2) is equal to the rate of change of the function in the graph.

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If a car is going 100 miles per hour, the car goes 100 miles in one hour.

Answer:36 seconds

Step-by-step explanation:

100 miles per hour, it would take me approximately 36 seconds to travel 1 mile.

The answer is $21,989.34 and Yes, $10,000 invested at 6% interest will double its value in half the time as $10,000 invested at 3% interest.

Now, For the 6% investment:


$10,000 invested at 6% interest will double in 12 years:


$10,000 × (1.06)^12 = $21,989.34


For the 3% investment:


$10,000 invested at 3% interest will double in 24 years:


$10,000 × (1.03)^24 = $21,989.34


Therefore, it will take half the time (12 years) for the 6% investment to double its value compared to the 3% investment (24 years).

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a) The exact distance is 5√2.

b) The midpoint of the line segment is (5.5, 1.5).

Part 1 of 2 (a) The exact distance between the points (9,2) and (2,1) can be found using the distance formula:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Plugging in the given values:

Distance = √[(2 - 9)^2 + (1 - 2)^2]

Simplifying:

Distance = √[(-7)^2 + (-1)^2]

Distance = √[49 + 1]

Distance = √50

Distance = 5√2

Therefore, the exact distance between the points is 5√2.

Part 2 of 2 (b) The midpoint of the line segment whose endpoints are the given points can be found using the midpoint formula:

Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

Plugging in the given values:

Midpoint = [(9 + 2)/2, (2 + 1)/2]

Simplifying:

Midpoint = [11/2, 3/2]

Midpoint = (5.5, 1.5)

Therefore, the midpoint is (5.5, 1.5).

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9 can be expressed as 3² where value larger than the base.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

Given:

A power with a positive base and a positive integer exponent will always have a value larger than the base.

We can take example as

5³ = 125

Here the base is 5 and value is 125 which is larger than base.

So, to express 9 as such form is

3² = 9

Here Base (3) < Value (9)

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TB is both one-to-one and onto, it is an isomorphism.

To prove that TB is an isomorphism, we need to show that it is both one-to-one and onto.

One-to-one: Assume TB(A) = TB(C) for some A, C EM nxn(K). Then, BAB-¹ = CBC-¹. Multiplying both sides by B-¹ on the left and B on the right gives B-¹BAB = B-¹CBC. Since B is invertible, B-¹B = I and we have A = C. Therefore, TB is one-to-one.

Onto: Let D EM nxn(K). Then, we can define A = B-¹DB. Since B is invertible, A EM nxn(K) and TB(A) = BAB-¹ = B(B-¹DB)B-¹ = D. Therefore, TB is onto.

Since TB is both one-to-one and onto, it is an isomorphism.

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Answer: 1lb 7oz

Step-by-step explanation:

All you have to do is subtract 9lbs and 2oz by 7lbs and 11oz, which is 1lb and 7oz

(16 oz in a pound)

The division of polynomials "(4x^(3)-5x^(2)+8x-8)/(x^(2)-3x)" gives the expression "4x+7+(29x-8)/(x^(2)-3x)".

To perform the indicated division, we will use polynomial long division.

First, we will divide the first term of the dividend, 4x^3, by the first term of the divisor, x^2, to get 4x. This will be the first term of our quotient.

Next, we will multiply 4x by the divisor, x^2-3x, to get 4x^3-12x^2. We will then subtract this from the dividend to get 7x^2+8x-8.

We will then repeat this process by dividing the first term of the new dividend, 7x^2, by the first term of the divisor, x^2, to get 7. This will be the second term of our quotient.

We will then multiply 7 by the divisor, x^2-3x, to get 7x^2-21x. We will subtract this from the new dividend to get 29x-8.

Since the degree of the new dividend, 29x-8, is lower than the degree of the divisor, x^2-3x, we are done with the division and 29x-8 will be our remainder.

Therefore, the final answer is:

(4x^(3)-5x^(2)+8x-8)/(x^(2)-3x) = 4x+7+(29x-8)/(x^(2)-3x)

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Answer:

The answer is 13.

Step-by-step explanation:

First, we must find the hypotenuse for right angle:

[tex]c^{2} = a^{2} + b^{2}\\ \\\\c^{2} = 12^{2} + 5^{2} \\c^{2} 144 + 25 \\c^{2} = 169 \\c^{2} =\sqrt{169}\\c^{2} = 13[/tex]

The volume of the rectangular prism is 11.28 feet³.

In terms of geometry, a rectangular prism is a polyhedron having two parallel, congruent bases. It also goes by the name cuboid. A rectangular prism is made up of six rectangles, each with twelve edges.

We are given that a rectangular prism has the following dimensions:

Length (l) = 4.7 feet

Width (w) = 1.5 feet

Height (h) = 1.6 feet

We know that

Volume (V) = [tex]l \times w \times h[/tex]

From this, we get

⇒V = [tex]4.7 \times 1.5 \times 1.6[/tex]

⇒V = 11.28 feet³

Hence, the volume of the rectangular prism is 11.28 feet³.

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Answer: Your answer is 11.28 ft³

Step-by-step explanation: 4.7 x 1.5 x 1.6 = 11.28 you have to do it in this order also I did the k12 quiz here's proof.

Hope it helped :D

(a) The exact distance between the points is 2√10.

(b) The midpoint of the line segment is (-7, 2).

(a) To find the distance between the two given points, use the distance formula, which is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²].

In this case, x₁ = -8, y₁ = 5, x₂ = -6, and y₂ = -1.

Plugging these values into the formula gives us:

d = √[(-6 - (-8))² + (-1 - 5)²]

d = √[(2)² + (-6)²]

d = √[4 + 36]

d = √40

d = 2√10

(b) The midpoint of a line segment can be found using the midpoint formula, which is:

(x₁ + x₂)/2, (y₁ + y₂)/2.

In this case, x₁ = -8, y₁ = 5, x₂ = -6, and y₂ = -1.

Plugging these values into the formula gives us:

midpoint = [(-8 + -6)/2, (5 + -1)/2]

midpoint = [(-14)/2, (4)/2]

midpoint = (-7, 2)

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