Consider the following function.

h(x)=(x−4)2−1
Step 2 of 4 : Find the x-intercepts, if any. Express the intercept(s) as ordered pair(s).

Answer:

e = 10

Step-by-step explanation:

Vertically opposite angles are the angles formed opposite to each other when two lines intersect.

Vertically opposite angles are equal.

          9e - 8 = 8e + 2

Add 8 to both sides,

                 9e = 8e + 2 + 8

                 9e = 8e + 10

Subtract '8e' from both sides,

         9e - 8e = 10

                   [tex]\boxed{\bf e = 10}[/tex]

Answer:

e = 10

Step-by-step explanation:

According to the Vertical Angle Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Since the two given angles are vertical angles, they are congruent.

Therefore, we can set them equal to each other:

[tex]\implies (9e - 8)^{\circ} = (8e + 2)^{\circ}[/tex]

[tex]\implies 9e - 8= 8e + 2[/tex]

To solve for e, begin by subtracting 8e from both sides of the equation:

[tex]\implies 9e - 8-8e= 8e + 2-8e[/tex]

[tex]\implies e - 8= 2[/tex]

Add 8 to both sides of the equation:

[tex]\implies e - 8+8= 2+8[/tex]

[tex]\implies e=10[/tex]

Therefore, the value of e is 10.

Answer:

(1,2)

Step-by-step explanation:

The solution to a system of equations is the point at which the lines defined by the equations intersect.

On this graph, we can see that the lines meet a point on the graph that is at 1 on the x-axis (horizontal axis) and at 2 on the y-axis (vertical axis).

In Cartesian coordinates, this is written in the format (x, y):

(1, 2)

Step-by-step explanation:

it's radius squared timesed by pi (π)

r^2×π

if u don't have a radius but a diameter then half the diameter to get the radius

Answer:

There are two common formulas that can be used to calculate the area of a circle. Here they are:

Where [tex]\pi[/tex] is the universal value for all circles that expresses the ratio between the length of circumference and the diameter of any circle. It's a rational number and its value is about 3.141592653589793238462643383279502884197..., so you may want to just 3.14.

This is the easiest and simplest formula. Letter "r" represents the length of radius of the circle,

Rarely used formula. In this equation, "C" represents the length of circumference of the circle.

Check the attached image to better understand the meaning of radius, diameter and circumference. Also, provided a second image with all the formulas for the area of a circle.

Answer:

93%

Step-by-step explanation:

651/700 houses were for sale. Write that as a percentage.

651/700=0.93

0.93=93%

Answer:

NO= 18

Step-by-step explanation:

If we dissect the image, we can see that triangle LMN there are two similar triangles; triangle LMN and smaller triangle OPN. By definition of similar triangles, corresponding parts of similar triangles will have the same ratios. So, as we can see, sides NP and NM are corresponding. The ratio of the two sides is 24/44 (just put the smaller side over the longer side). Simplified, the ratio is 6/11. So, we know that the opposite sides' ratio will also be 6/11. So, all we have to do is multiply NL (33) by 6/11, which equals 18.

Check:

24/44=6/11, and 18/33=6/11, so the ratios are the same.

Answer:

5, 8 and 2

Because it has the same angel as 3 there for it's 5 , 8 and 2

Hence, in answering the stated question, we may say that As a result, graphs  P75 equals 80.375.

Mathematicians use graphs to visually explain or chart events or variables. A graph point often indicates a connection between one thing and another. A graph, a non-linear data structure, is constituted of nodes (vertices) and edges. Glue the nodes, which are also called as vertices. This graph has E=1, 2, 1, 3, 2, 4, and (2.5) edges and V=1, 2, 3, 5. (3.5). (4.5). Graphical representations of exponential growth in analytical charts (bar charts, pie charts, line charts, and so on). a graph of a logarithmic triangle.

To get the value of P75, the 75th percentile, we need to discover the score where 75% of the scores fall below it.

z = (x - μ) / σ

where x is the score to be converted, is the mean, and is the standard deviation.

So we can write:

0.75 = P(Z ≤ 0.675)

where Z is the standard normal variable with a mean of 0 and a standard deviation of 1.

We can now rearrange the formula for the z-score to solve for the score x:

x = μ + zσ

Plugging in the values we have:

x = 77.4 + (0.675)(5) (5)

x = 80.375

As a result, P75 equals 80.375.

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The proportional and inverse relationships can be presented as follows;

1. The value of y when x = 36 is 6

2. The value of y when x = 1 is 27

3. The time of fall of an object that falls 144 feet is 3 seconds

4. The length of the string that vibrates 64 times per second is 48 inches long

A proportional relationship is one that can be expressed in the form; y = k × x.

The possible questions, obtained from a similar question posted online, are presented as follows;

1. y varies directly as the square root of x, when y = 4, x = 16, to find y when x = 36;

The value of y can be found by expressing the relationship between y and x using a proportional relation as follows;

y ∝ √x

y = c·√x

4 = c·√(16) = 4·c

Therefore;

c = 4/4 = 1

c = 1

When x = 36, we get;

y = 1 × √(36) = 6

2. The variation of y and x can be presented as follows;

y ∝ 1/x³

y = c/x³

y = 1, when x = 3, therefore;

1 = c/3³ = c/27

c = 27 × 1 = 27

c = 27

The value y when x = 1, can be found as follows;

y = 27/1³

y = 27/1³ =27

3. The relationship between the distance and the time duration the ball can be presented as follows;

Let s represent the distance the ball falls, and let t represent the time the ball falls, we get;

s = k·t²

The distance an object falls in one second = 16 feet

Therefore, we get;

When s = 16, t = 1

16 = k × 1²

k = 16/1² = 16

k = 16

s = 16·t²

When s = 144 feet, we get;

144 = 16 × t²

t² = 144/16 = 9

t = √9 = 3

4. The relationship between the vibration of a string and the tension in the string can be presented as follows;

Let f represent the vibration of the string, and let l represent the length in the string, we get;

f ∝ 1/l

f = c/l

When l = 24, f = 128, we get;

128 = c/24

c = 128 × 24 = 3,072

Therefore, if the string vibrates 64 times per second, we get;

64 = 3,072/l

l = 3,072/64 = 48

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The absolute maximum value occur (3, 4.033) at point x = 3

The function given in the problem is g(x) = 3x³e⁻ˣ

differentiating the function

g(x) = 3x³e⁻ˣ

g'(x) = 3x³(-e⁻ˣ) + e⁻ˣ(9x²)

g'(x) = e⁻ˣ(-3x³ + 9x²)

equating to zero

0 = e⁻ˣ(-3x³ + 9x²)

0 = -3x³ + 9x²

3x³ = 9x²

x = 3

checking intervals close to 3: the check is done using numbers at the left and right to 3 and this numbers will be sufficiently close.

We choose 1 and 5, when the value of g'(x) increases from positive to negative then maximum value occurs

at x = 1, g'(1) = e^(-1)(-3(1)³ + 9(1)²) = 2.2073

at x = 3, g'(3) = e^(-3)(-3(3)³ + 9(3)²) = 0

at x = 5, g'(5) = e^(-5)(-3(5)³ + 9(5)²) = -1.0107

We can say that x = 3 is point of local maxima

g(3) = 3(3)³e^(-3) = 4.03275 = 4.033

from calculation the absolute maximum value occurs at (3, 4.033)

From the graph the absolute maximum value for the domain -1 ≤ x ≤ 5 occurs at (3, 4.033)

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The correct statement regarding the numeric values of the piece-wise function is given as follows:

D. f(1) = 0.

To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

A piece-wise function is a function that has different definitions based on the input of the function, hence before obtaining the numeric value we must obtain the correct definition of the function in the interval.

Choosing the correct definitions of the function, the numeric values are given as follows:

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Answer: y=1x+6

Step-by-step explanation:

goign up by 1/1 y intercpt is 6

Step-by-step explanation:

a) To calculate the amount that Eric will receive after the 6 years, we need to use the formula for simple interest:

I = P * r * t

Where:

- I is the interest earned

- P is the principal amount (the initial investment)

- r is the interest rate (as a decimal)

- t is the time period (in years)

In this case, Eric invested $10,000 at an interest rate of 8% for 6 years. So we can plug in these values:

I = 10,000 * 0.08 * 6

I = 4,800

The interest earned is $4,800. To find the total amount that Eric will receive after the 6 years, we need to add the interest to the principal:

Total = P + I

Total = 10,000 + 4,800

Total = 14,800

Therefore, Eric will receive $14,800 after the 6 years.

b) The total interest that Eric will earn is already calculated in part a) and it is $4,800.

Inequality to find the value of p is 7p - 12 ≤ 45. So correct option is C.  The value of p is at most 8.14 centimeters.

Inequalities can be solved in a similar way to equations, but with some important differences. To solve an inequality, one must find the set of values that satisfy the inequality. This set of values is often expressed as an interval, which is a range of values between two endpoints. For example, the solution to the inequality x < 5 is the interval (-∞, 5), which includes all values of x that are less than 5. The solution to an inequality may also be expressed graphically on a number line or coordinate plane.

The perimeter of an isosceles triangle with sides of length 3p-6, 3p-6, and p is:

Perimeter = (3p-6) + (3p-6) + p

= 7p - 12

We are given that the perimeter is at most 45 centimeters. Therefore, we can write the following inequality to find the value of p:

7p - 12 ≤ 45

Adding 12 to both sides, we get:

7p ≤ 57

Dividing both sides by 7, we get:

p ≤ 8.14

Therefore, the value of p is at most 8.14 centimeters.

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Answer:

-9 and -5

Step-by-step explanation:

-9 + -5 = -14

-9 * -5 = 45

Answer:

- 9 and - 5

Step-by-step explanation:

- 9 × - 5 = 45 and - 9 + (- 5) = - 9 - 5 = - 14

Answer:

The sum of the exterior angles of any polygon, regardless of the number of sides, is always 360 degrees. Each exterior angle of a regular octagon measures 45 degrees, because the sum of the interior and exterior angles at each vertex is 180 degrees, and the octagon has 8 vertices. Therefore, the sum of all the exterior angles of an octagon is:

8 × 45º = 360º

So the answer is option B) 360º.

The intervals for which the rate of change of the quadratic function, f(x) = -(x + 1)² + 8 is faster than the rate of change of g(x) = -x - 6 are; x ≤ -1.5 and x ≥ -0.5

A quadratic function is a polynomial function with one or more variables in which the highest exponent is two.

The slope of f(x) is; f'(x) = -2·(x + 1)

The slope of g(x) = -1

When the rate of change of f(x) is faster than the rate of change of g(x), we get;

The slope of f(x) > The slope of g(x), therefore;

-2·(x + 1) > -1

From which we get;

|-2·(x + 1)| ≥ |-1|

2·(x + 1) ≥ 1

x + 1 ≥ 1/2

x ≥ 1/2 - 1 = -1/2

x ≥ -1/2 = -0.5

The absolute sign indicates that we get;

x + 1 ≤ -1/2

x ≤ -1/2 - 1 = -1 -1/2 = -3/2 = -1.5

x ≤ -1.5

The interval for which the average rate of change of f(x) is faster than the average rate of change of g(x) are; x ≥ -0.5 and x ≤ -1.5

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The probability of having 4 hurricanes in a year is approximately 0.118 or 11.8%.

It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

a. To find the probability of having exactly 4 hurricanes in a year, we use the Poisson distribution with a mean of 6.6:

P(X=4) = (e^-6.6)×(6.6^4)/(4!) ≈ 0.118

Therefore, the probability of having 4 hurricanes in a year is approximately 0.118 or 11.8%.

b. In a 35-year period, the expected number of years with 4 hurricanes is:

μ = λt = 6.635 ≈ 231

Therefore, we can expect to have 231 years with 4 hurricanes in a 35-year period.

c. If in a recent period of 35 years, only 3 years had 4 hurricanes, this is less than what the Poisson distribution would predict (231 years). However, this doesn't necessarily mean that the Poisson distribution doesn't work well here. The Poisson distribution is a theoretical model that assumes certain conditions, and it's possible that those conditions weren't met in this specific case. It's also possible that this was just a rare event that can happen due to chance. Further analysis would be needed to determine whether the Poisson distribution is a good fit for this data.

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A rectangle has a width that is 16 feet shorter than its length and an area that is 35 square feet. The rectangle's length and breadth can be calculated using the equation [tex]3x^2[/tex] - 16x - 35 = 0.

Assume that the rectangle measures "x" feet in length. Then, according to the problem:

The width is 16 feet less than 3 times the length, so the width is 3x - 16 feet.

The area of the rectangle is 35 square feet, so we can write:

Area = Length x Width

35 = x(3x - 16)

To solve for x, we can simplify this quadratic equation by expanding the right-hand side and moving all the terms to one side:

35 = [tex]3x^2[/tex] - 16x

[tex]3x^2 - 16x - 35 = 0[/tex]

The rectangle's length and breadth can be calculated using the quadratic equation shown above.

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As you can see, each number in the pattern is obtained by adding 4 to the previous number.

An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.

Here,

Sure, here's a pattern for the rule a + 4:

a = 1: 1 + 4 = 5

a = 2: 2 + 4 = 6

a = 3: 3 + 4 = 7

a = 4: 4 + 4 = 8

a = 5: 5 + 4 = 9

a = 6: 6 + 4 = 10

a = 7: 7 + 4 = 11

a = 8: 8 + 4 = 12

a = 9: 9 + 4 = 13

a = 10: 10 + 4 = 14

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The distance οn the map that represents οne mile is 5/8 inch.

Tο find οut hοw much distance οn the map represents οne mile, we need tο use a ratiο οf the distance οn the map tο the actual distance.

Let x be the distance οn the map that represents οne mile. Then we have:

1/2 inch : 4/5 miles = x : 1 mile

We can crοss-multiply tο sοlve fοr x:

(1/2 inch) × (1 mile) = (4/5 miles) × x

Simplifying the right-hand side:

(1/2) × 1 = (4/5) × x

1/2 = (4/5) × x

Multiplying bοth sides by 5/4:

(1/2) × (5/4) = x

5/8 = x

Therefοre, the distance οn the map that represents οne mile is 5/8 inch.

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In a casde whereby saac is mountain climbing with Rina and has just climbed a 6.2-meter vertical rock face the distance from the cliff is Rina standing is 7.85m

Base on the given iformation, following the trigonometry rule it can be seen thatr the hypotenus of the triangle is the distance of Isaac  to Rina which can be expressed a C = 10m

The height that was climbed by I saac =  6.2-m. a= 6.2m

the distance from Rina to cliff = b

Then base on pytagoras theorem

c^2= a^2 + b^2

10^2 = 6.2^2 +  b^2

b^2= 10^2 - 6.2^2

b^2= 61.56

b = √61.56

b=7.85m

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In response to the question, we may say that  Value total: 60 cents plus equation 240 cents plus 300 cents equals $3.00.

The equals symbol (=), which indicates equivalence, connects two statements in a mathematical equation. An algebraic equation's mathematical assertion proves the equality of two mathematical propositions. The equal sign, for instance, places a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. Use a mathematical formula to understand how the two sentences on opposite sides of a letter relate to one another. Usually, the logo corresponds to the particular programme. An example would be 2x - 4 = 2.

Let's define our variables first:

Let x represent the amount of quarters in the machine.

10x + 5(8x) = 300

When we simplify and find x, we obtain:

10x + 40x = 300

50x = 300\sx = 6

Hence, the machine has six dime coins. We may determine the quantity of nickels by using the connection between the number of dimes and nickels:

8x = 8(6) = 48

There are 48 nickels in the machine as a result.

Verifying our response:

6 dime is 6 times 10 cents, or 60 cents.

48 nickels is 48 x 5 cents, or 240 cents.

Value total: 60 cents plus 240 cents plus 300 cents equals $3.00.

The vending machine has 48 nickels and 6 dimes, thus our answer is right.

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Answer:

The location of the point (4, 2) is to the right of the triangle RST, therefore,

a dilation from the left or a contraction from the right is required.

The dilation of ΔRST that would result in a line segment with slope of 2

that passes through (4, 2) is C. A dilation with a scale factor of 0.5 centered 12,2

Step-by-step explanation:

Step-by-step explanation:

Divide.

Answer: 680

Step-by-step explanation:

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{D varies directly with G}}{D = k(G)}\hspace{5em}\textit{we also know that} \begin{cases} G=24\\ D=552 \end{cases} \\\\\\ 552=k(24)\implies \cfrac{552}{24}=k\implies 23=k\hspace{5em}\boxed{D=23G}[/tex]

The values of the measures are;

Range = 6

Median = 4

Mean = 4.5

To determine the values of the range, median and mean, we need to note that;

The range of a given set of values is the interval between the smallest number and the largest number in the set.

Given the data set;

3, 4, 5, 7, 8, 8, 9

The range = 9 - 3 = 6

The median of a given set of values is the  middle number of the set when arranged in an ascending or descending form.

Given the set;

3, 4, 4, 6, 6,

The median is 4

The mean of a set of numbers is the average value of the numbers.

Given the set;

2, 9, 7, 5, 2, 2,

The mean = 2 + 9 + 7 + 5 + 2 + 2/6 = 27/6 = 4. 5

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Answer:

simplified expression: 15yz + 12

In response to the given question, we can state that Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.

Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

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a. To find the speed at which the car achieves maximum fuel economy, we need to find the vertex of the function. The vertex of a quadratic function is given by the formula: (-b/2a, f(-b/2a)). In this case, a = -0.008 and b = 1.4. Substituting these values, we get:

Vertex = (-b/2a, f(-b/2a))

= (-1.4/(2*(-0.008)), f(1.4/(2*(-0.008))))

= (87.5, 6.125)

Therefore, the car should travel at a speed of 87.5 miles per hour to achieve maximum fuel economy.

b. To find the maximum fuel economy, we need to find the value of the function at the vertex. Substituting x = 87.5 in the function, we get:

f(87.5) = -0.008(87.5)^2 + 1.4(87.5) = 6.125

Therefore, the maximum fuel economy of the car is 6.125 miles per gallon.

c. To find the fuel economy of the car if it travels at 60 miles per hour, we need to evaluate the function at x = 60. Substituting x = 60 in the function, we get:

f(60) = -0.008(60)^2 + 1.4(60) = 7.6

Therefore, the fuel economy of the car if it travels at 60 miles per hour is 7.6 miles per gallon.

d. The point (40, 43.2) lies on the graph of the function. This means that when the car travels at a speed of 40 miles per hour, its fuel economy is 43.2 miles per gallon. However, this point does not provide any information about the maximum fuel economy or the speed at which it is achieved.