You place a ladder against the top of a 18-foot building. The bottom of the ladder is 8.5 feet from the bottom of the building. How long is the ladder? Show your work for full credit.

The critical points for the function f(x) = x³ - 12x - 2 are x = -2 and x = 2.

To find the critical points of a function, we need to determine where its derivative is equal to zero or undefined. In this case, the derivative of f(x) is f'(x) = 3x² - 12.

Setting f'(x) equal to zero and solving for x, we get:

3x² - 12 = 0

Factoring out a common factor of 3, we have:

3(x² - 4) = 0

Next, we can factor the quadratic expression inside the parentheses:

(x - 2)(x + 2) = 0

Setting each factor equal to zero, we find:

x - 2 = 0 or x + 2 = 0

Solving these equations, we obtain:

x = 2 or x = -2

Therefore, the critical points of the function f(x) = x³ - 12x - 2 are x = -2 and x = 2. These points correspond to potential extrema or inflection points on the graph of the function.

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Answer:  b) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Explanation: We simply list all the numeric single digits from 0 to 9. We'll leave out the asterisk and pound sign as they aren't numeric digits.

the range in this set of data is 25 inches. To find the range of snowfall amounts, we need to look at the line plot and identify the highest and lowest amounts of snowfall that were recorded.

The range in a set of data is the difference between the maximum and minimum values in the set.

To find the range of snowfall amounts, we need to look at the line plot and identify the highest and lowest amounts of snowfall that were recorded.

Let's say that the highest amount recorded was 30 inches and the lowest amount recorded was 5 inches. Then the range would be:

range = highest amount - lowest amount

range = 30 - 5

range = 25

Therefore, the range in this set of data is 25 inches.

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The product of the volume and total surface area of the given right conical frustum is approximately 146520π². To find the product of the volume and total surface area of a right conical frustum, we first need to determine the individual values of volume and surface area.

The volume of a frustum can be calculated using the formula:

V = (1/3)πh(r₁² + r₂² + r₁r₂),

where h is the height of the frustum, r₁ and r₂ are the radii of the larger and smaller bases, respectively.

In this case, we are given that the radii of the larger and smaller bases are 12 and 9 units, respectively. We also know that the two bases are 4 units apart, which means the height of the frustum is 4 units.

Substituting the given values into the formula, we have:

V = (1/3)π(4)(12² + 9² + 12*9)

 = (1/3)π(4)(144 + 81 + 108)

 = (1/3)π(4)(333)

 = (4/3)π(333)

 ≈ 444π cubic units

Now, let's move on to calculating the total surface area of the frustum. The formula for the total surface area is:

A = π(r₁ + r₂)ℓ + πr₁² + πr₂²,

where ℓ is the slant height of the frustum.

Since the frustum is a right frustum, the slant height ℓ can be found using the Pythagorean theorem:

ℓ = √(h² + (r₁ - r₂)²)

Substituting the given values, we have:

ℓ = √(4² + (12 - 9)²)

 = √(16 + 9)

 = √25

 = 5

Now we can calculate the total surface area:

A = π(12 + 9)(5) + π(12²) + π(9²)

 = π(21)(5) + π(144) + π(81)

 = 105π + 144π + 81π

 = 330π square units

Finally, to find the product of the volume and total surface area, we multiply the two values:

VA = (444π)(330π)

  ≈ 146520π²

Therefore, the product of the volume and total surface area of the given right conical frustum is approximately 146520π².

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The values of x are given as follows:

3) x = 6.

4) x = 9.

Similar polygons are polygons that share these two features presented as follows:

For item 3, we have that the relationship is given as follows:

x/1.5 = 8/2

x/1.5 = 4.

x = 4(1.5)

x = 6.

For item 4, we have that the relationship is given as follows:

6/10 = x/15

0.6 = x/15

x = 15 x 0.6

x = 9.

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a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.

To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.

Applying this rule to the expression 1/58^8, we get:

1/58^8 = 1/(58^8) = 58^-8

Therefore, the correct answer is 58^-8.

It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:

1/58^8 = (1/58)^8 = 58^-8

This simplification shows that the correct answer is still 58^-8.

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The rate of change of the area of the triangle at the given instant is 4 cm²/s. Thus, the correct answer is (B) 4. The rate of change of the area of the triangle can be determined using the formula for the area of a triangle, which is A = (1/2) * base * height.

We are given that the base is increasing at a constant rate of 2 cm/s and the height is decreasing at a rate of 1 cm/s.

At the instant when the height is 5 cm and the area is 5 cm², we can substitute these values into the formula to solve for the rate of change of the area. Let's denote the rate of change of the area as dA/dt.

A = (1/2) * base * height

5 = (1/2) * base * 5

Simplifying the equation, we have:

base = 2

Now, we can differentiate both sides of the equation with respect to time (t):

dA/dt = (1/2) * (dbase/dt) * height + (1/2) * base * (dheight/dt)

Substituting the given rates of change:

dA/dt = (1/2) * (2 cm/s) * 5 cm + (1/2) * 2 cm * (-1 cm/s)

Simplifying further:

dA/dt = 5 cm^2/s - 1 cm^2/s

dA/dt = 4 cm^2/s

Therefore, the rate of change of the area of the triangle at the given instant is 4 cm^2/s. Thus, the correct answer is (B) 4.

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The ride that has the greatest elevation based on the information is B. Lightning bolt : 327 feet.

The term elevation is typically used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface.

Elevations show how your house will appear from various perspectives. Regarding these particular angles, there are many elevation kinds. Some varieties include split elevations, rear elevations, side elevations, and front elevations.

From the information, it was stated that the lightning bolt starts at an elevation of 15ft from the platform and speeds the passengers to an elevation of 327 ft.

It should be noted that the information is to simply find the elevation that is the greatest.

Based on the figures given, the appropriate elevation will be 327 feet.

Therefore, the correct option is B.

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Answer:

The bottom right answer.

Domain -5, -1, 0, 1, 2, 3

Range -4, 0, 2, 3, 4

Step-by-step explanation:

Domain is all the x coordinates, Range is all the y coordinates

To find the Domain, work left to right on the x-axis and list the x coordinates.

-5, -1, 0, 1, 2, 3

To find the Range, work from the bottom to the top of the y-axis and list the y coordinates.

-4, 0, 2, 3, 4

The discounted price of the Dao will be equal to $14315.2.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Dao receives an employee discount on the purchase of a new automobile. The automobile that he is interested in has a sticker price of $18,560.

The discounted price will be calculated as,

Discounted price = 18560 x 0.92

Discounted price = $14315.2

Therefore, the discounted price of the Dao will be equal to $14315.2.

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Answer:

x=30 degrees

Step-by-step explanation:

there are 3theorems that can be used for this

vertical angle theorem: vertical angles congruent

triangle sum theorem: all angles in triangle add up to 180 degrees

straight line?? i forgot the name: a straight line is 180 degrees

refer to image attached

measure of angle BAC is 36 degrees by vertical angle theorem.

look at the angle 105 degrees. it and a unknown degree to the left equal 180 because it makes a straight line. so measure of angle BDC is 180-105 degrees. measure of angle BDC is 75 degrees

then sum of all the angles in triangle ABD is 180

36 +(39+x) +75=180 degrees

solve equation

x +150=180

x=30 degrees

hope this helps !!

Answer:

This should help friend:

Step-by-step explanation:

Hope u r well

give me thanks, brainliest and 5 star plz

The answer to this question is:

No. of cups of milk will Paula use = 3/8

Given that recipe requires 3/4 cups of milk.

Paula is making half (1/2) of the recipe.

And we are asked to find that No. of cups of milk will Paula use.

To solve this question,  we have to multiply the quantity of milk required by the quantity she is going to make.

The quantity of milk required * the quantity she is going to make

= 3/4 * 1/2

= 3/8

Therefore, No. of cups of milk will Paula use = 3/8

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The answer is point C is further from point A than point B

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,

Given here: The points A(-5,8) ,  B(1,0) C(-10,16)

length of AB= \(\sqrt{(-5-1)^2+(8-1)^2}\)

                    =9.22 units

Similarly length of AC= \(\sqrt{(-5+10)^2+(8-16)^2}\)

                                    = 9.433

Hence, point C is further from point A than point B

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Answer:

60 animal balloons

Step-by-step explanation:

15 times 3 equals 45 so 20 times 3 equals 60 balloons

Hope this is helpful

Answer:

60

Step-by-step explanation:

If he can make 20 balloon animals in 15 minutes, then to get the answer you would multiply 20 x 3 = 60. That would be how many animal balloons that Fred can make in 45 minutes.  And 45 minutes is three sets of 15 minutes.

Hope that helps.

The predicted population of the city in the year 2030 is 5,780 person.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

Years = 2030 - 2010 = 20 years.

By substituting given parameters, we have the following:

\(P(t) = I(1 + r)^t\\\\P(t) = 3200(1 + 3/100)^{20}\\\\P(t) = 3200(1 + 0.03)^{20}\)

P(t) = 5,779.56 ≈ 5,780 person.

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Answer:

0

Step-by-step explanation:

125×^6_81=0

×^6 we do not support this expression

ans = 0

The critical numbers of the function f(x) = x³e^(−9x) are:

To find the critical numbers of the function f(x) = x³e^(-9x), we need to find the values of x where the derivative of the function is zero or undefined.

The derivative of f(x) is:

f'(x) = 3x²e^(-9x) - 9x³e^(-9x) = 3x²e^(-9x){1-3x}

The derivative is zero when:

3x²e^(-9x){1-3x} = 0

This equation is zero when x=0 or 1/3.

The derivative is undefined when the exponential term is zero, that is, when:

e^(-9x) = 0

This equation has no solutions because e^(-9x) is always positive and never equal to zero.

Therefore, the critical numbers of the function are: 0, 5/9

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Answer:

5 10/12

Step-by-step explanation:

using BODMAS

1/2×2/3=1/3

THEN; 5 1/4+1/3

Change 5 1/4 to 21/4 then add to 1/3

you get 70/12

divide 70÷12

answer 5 10/12

hope it helped

Answer:

Step-by-step explanation:

Remark

You have an isosceles triangle. That means that the angles opposite the marked sides are equal. So mark the angle on the lower left of the triangle as 50 degrees.

The solution to problem depends on the fact that the sum of the two inside angles of the triangle (each of which is marked as 50 degrees) not supplementary to the exterior angle, are still equal to the exterior angle.

Givens

<1 = 50 degrees

<2 = 50 degrees

Exterior angle = 15x + 25   Substitute the givens into the equation

Equation

<1 + <2 = 15x + 25

Solution

50 + 50  = 15x + 25                       Combine the left side

100 = 15x + 25                               Subtract 25 from both sides

100 - 25 = 15x + 25 - 25                Combine

75 = 15x                                          Divide both sides by 15

75/15 = 15x/15                      

5 = x

Answer

<1 = 50 degrees

<2 = 50 degrees

15x + 25 = 75 + 25 = 100

The smallest perimeter is P = 2L + 2W = 2(2) + 2(2) = 8 in, and the dimensions of the rectangle are 2 in by 4 in.

To find the smallest perimeter for a rectangle with an area of 4 in² using derivatives, we can set up an optimization problem. Let's denote the length of the rectangle as L and the width as W.

The formula for the area of a rectangle is given by A = L × W. Since we know the area is 4 in², we can write the equation as 4 = L × W.

To find the smallest perimeter, we need to minimize the perimeter function P = 2L + 2W while satisfying the area constraint.

We can rewrite the area equation as W = 4/L and substitute it into the perimeter equation to get P = 2L + 2(4/L).

Now, we find the derivative of the perimeter function with respect to L: \($dP/dL = 2 - \frac{8}{L^2}$\).

To find the minimum perimeter, we set the derivative equal to zero and solve for L:

\(2 - \frac{8}{L^2} = 0\\\\ 2 = \frac{8}{L^2}\\\\ L^2 = \frac{8}{2}\\\\ L^2 = 4\\\\ $L = \pm 2$\)

Since we're dealing with lengths, we take L = 2 (we discard the negative solution). Substituting this value back into the area equation, we find W = 4/L = 4/2 = 2

Therefore, the smallest perimeter is P = 2L + 2W = 2(2) + 2(2) = 8 in, and the dimensions of the rectangle are 2 in by 4 in.

Now, consider finding the largest perimeter. Since we're not given any constraints on the dimensions, the largest perimeter is unbounded and not defined for a fixed area of 4 in². As one side of the rectangle approaches infinity, the perimeter also approaches infinity. Therefore, there is no upper limit to the perimeter.

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The inequality for the statement:-2/7 is at most the product of a number and -4/5. is --4x/5 ≤ -2/7

Information from the question

the statement: -2/7 is at most the product of a number and -4/5

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using equal to

at most means the highest value hence the answer is either the number or less.

let the number be x

x * -4/5 ≤ -2/7

--4x/5 ≤ -2/7

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In an ABCAC research design, C refers to a new independent variable. The correct answer is option c. a new independent variable.

An ABCAC research design is a type of single-subject research design that is used to examine the effects of different independent variables on a target behavior. In this design, A refers to the baseline phase, B refers to the first intervention phase, and C refers to the second intervention phase. The purpose of the C phase is to introduce a new independent variable to see if it has an effect on the target behavior.

Therefore, in an ABCAC research design, C refers to a new independent variable that is introduced to examine its effect on the target behavior.

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The function g(x) is exponential.

A function is a mathematical Statement used to find relation between independent and dependent variable.

The data is given for the two functions

From observing the data it can be understood that

g(x) is represented as an exponential function

g(x) = abˣ

The data given is

At year = 1995, x =0 and y = 11008.31

At year = 2000, x =5 and y = 16,174

11008.31 = a b⁰

a = 11008.31

g(x) = 11008.31 bˣ

16174 = 11008.31 bˣ

b = 1.08

g(x) = 11008.31 (1.08)ˣ

At 2005 , x = 10

g(x) = 11008.31 (1.08)¹⁰

g(x) = 23766.11

Therefore the table justifies our answer.

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Answer:

The function g(x) is exponential.

Step-by-step explanation:

Got It right on FLVS!

Answer:

{d,b}={4,3}

Step-by-step explanation:

[1]    11d + 17b = 95

  [2]    d + b = 7

Graphic Representation of the Equations :

   17b + 11d = 95        b + d = 7  

Solve by Substitution :

// Solve equation [2] for the variable  b

 [2]    b = -d + 7

// Plug this in for variable  b  in equation [1]

  [1]    11d + 17•(-d +7) = 95

  [1]    -6d = -24

// Solve equation [1] for the variable  d

  [1]    6d = 24

  [1]    d = 4

// By now we know this much :

   d = 4

   b = -d+7

// Use the  d  value to solve for  b

   b = -(4)+7 = 3

Solution :

{d,b} = {4,3}

Answer:

B = 3

d = 4

Step-by-step explanation:

You can use elimination method. Multiply (d + b = 7) by -11.

11d + 17b = 95

-11d - 11b = -77

add together. D’s will cancel

6b = 18

divide by 6

b = 3

plug in 3 for b in the equation of your choice

d + (3) = 7

subtract 3

d = 4

Using the alternate exterior angles theorem, the value of x is: 127°.

When two parallel lines are intersected by a transversal to form alternate exterior angles that lie outside on each of the parallel lines, the alternate exterior angles theorem states that both angles are equal or congruent to each other.

From the diagram given, we are told that line m is parallel to line n.  transversal t crosses both lines  and n. The angles, x and 127 degrees are alternate exterior angles that lie on each parallel lines.

Therefore, the alternate exterior angles theorem states that, both angles would be equal.

Thus, we can conclude that, x = 127°.

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Since η² ≈ 0.33 and not 0.50, the statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η² = 0.50" is false.

ANOVA, or Analysis of Variance, is a statistical method used to compare the means of two or more groups to determine if there are any statistically significant differences between them. It is commonly used in experimental and observational studies to analyze the variance between group means and within-group variability.

ANOVA tests the null hypothesis that the means of the groups are equal, against the alternative hypothesis that at least one of the group means is different. It calculates the F-statistic, which compares the between-group variability to the within-group variability. If the F-statistic is large enough and exceeds a critical value, it indicates that there is evidence to reject the null hypothesis and conclude that there are significant differences between the group means.

We can determine if η² = 0.50 is true or false by calculating the effect size η² using the provided SS between and SS within values.
η² = SS_between / (SS_between + SS_within)
η² = 20 / (20 + 40)
η² = 20 / 60
η² = 1/3 ≈ 0.33
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True, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.

The formula to calculate eta squared (η2) is:
η2 = SSbetween / (SSbetween + SSwithin)
If SSbetween = 20 and SSwithin = 40, then:
η2 = 20 / (20 + 40) = 0.5
Therefore, η2 = 0.50, which means that 50% of the total variance in the dependent variable can be attributed to the independent variable (or factor) being analyze. The statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η 2 = 0.50" is true. To determine η 2 (eta-squared), you'll need to calculate the proportion of total variance explained by the between-group variation. This can be done using the formula η 2 = SS between / (SS between + SS within). In this case, η 2 = 20 / (20 + 40) = 20 / 60 = 0.50. Therefore, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.

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Answer:

1185

Step-by-step explanation:

A Parallel Line means the slope must be the same as the Given Line. A Perpendicular Line means the slope must be the negative reciprocal of the Given Line.

For Row A: Parallel is 12, Perpendicular is 6

For Row B: Parallel is 2, Perpendicular is 11

For Row C: Parallel is 9, Perpendicular is 16

For Row D: Parallel is 4, Perpendicular is 13

In Row E's case, 0 doesn't have a negative reciprocal, so you go with the equation that has a straight line down but no Y-Intercept.

For Row E: Parallel is 15, Perpendicular is 7

Row A = 72

Row B = 22

Row C = 144

Row D = 52

Row E = 105

Sum = 395

Code = 395 × 3 = 1185

Answer:

If the word problem uses words like divide, quotient, goes into, or how many times. These are all key words to know if you need to divide or not.

Step-by-step explanation: