A wolf leaps out of the bushes and takes a hunter by surprise. Its trajectory can be mapped by the equation f(x) = −x2 + 11x − 18. Write f(x) in intercept form and find how far the wolf leaped using the zeros of the function. (1 point)
y = (x − 3)(x + 6); the wolf leaped a distance of 9 feet using zeros −6 and 3
y = −(x − 3)(x − 6); the wolf leaped a distance of 3 feet using zeros 3 and 6
y = −(x − 2)(x − 9); the wolf leaped a distance of 7 feet using zeros 2 and 9
y = (x + 2)(x − 9); the wolf leaped a distance of 11 feet using zeros −2 and 9

The angle that has been formed and is shown as x is shown as 52.1°.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. The tangent function is denoted as tan.

We can see that we need to find the tangent of the angle;

Tan x = 36/28

x = Tan-1(36/28)

x = 52.1°

Thus it is clear from the calculation that we have done above that the angle that is marked x is 52.1°.

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Answer:

We can start by finding the value of the expression inside the tangent function: tan(1/2 (0 + π/2)) = tan(π/4) = 1

Now we can substitute this value into the original equation and simplify:

y = -3 + tan(1/2 (0 + π/2))

y = -3 + 1

y = -2

The vertical shift of the graph is the constant term in the equation, which is -2. Since this value is negative, the graph is shifted downwards. Therefore, the correct answer is (A) 3 units down

The horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.

To answer the question, we need to use trigonometry. In this case, we can use the sine function, which relates the opposite side of a right triangle to its hypotenuse. In this case, the ladder is the hypotenuse, and the horizontal distance between the base of the ladder and the wall is the opposite side.

The angle formed by the ladder and the ground is the angle of interest.

Let x be the horizontal distance between the base of the ladder and the wall. Then, using the sine function, we have:

sin(64 degrees) = x/18

Multiplying both sides by 18, we get:

x = 18 sin(64 degrees) ≈ 16.2 feet

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.

It is important to note that when using trigonometry, we need to use the appropriate trigonometric function depending on the sides and angles we are given. In this case, we were given the hypotenuse and the angle opposite the horizontal distance, so we used the sine function.

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the solution to the equation log2x + log4x + log16 = 7  the logarithms using the properties of Logarithms is x ≈ 53.408.

To solve the equation log2x + log4x + log16 = 7, we can simplify the logarithms using the properties of logarithms.

First, we can use the property loga + logb = log(ab) to combine the logarithms:

log2x + log4x + log16 = log(2x * 4x * 16)

Next, we simplify the expression inside the logarithm:

log(2x * 4x * 16) = log(32x^3)

Now, our equation becomes:

log(32x^3) = 7

To eliminate the logarithm, we can rewrite the equation in exponential form:

32x^3 = 10^7

Simplifying further:

32x^3 = 10,000,000

Now, we can solve for x by dividing both sides of the equation by 32:

x^3 = 10,000,000 / 32

x^3 = 312,500

To find the value of x, we take the cube root of both sides:

x = ∛312,500

x ≈ 53.408

Therefore, the solution to the equation log2x + log4x + log16 = 7 is x ≈ 53.408.

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Answer:

Sin θ = 3/5 cos θ = 4/5 tan θ= 3/4

The total number of teams that are in the NFC from the given two way frequency table is: 16 teams

A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.

Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data

From the attached two way table, we see that:

Total number of animals = 15

Total number of non-animals = 17

Total Number of NFC = 16

Total number of AFC = 16

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For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth.

For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.

Received message. For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth. For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.

hopes thats help thank you

Step-by-step explanation:

One rectangle  10 x 6 = 60 cm^2

Two sqaures     2 *    4x4 =  32 cm^2      Total = 92 cm^2

Answer:

The Answer is 80√3 or 138.56 to 2d.p

Step-by-step explanation:

sin 60=L/8

L=sin60×8

L=4√3

Area of rectangle =L×W

A=20×4√3

A=80√3=138.56 to 2d.p

Answer:

[tex]\huge\boxed{\sf 0.00008\ km}[/tex]

Step-by-step explanation:

= 8 cm

= 8 / 100,000 km

[tex]\rule[225]{225}{2}[/tex]

Answer:

0.00008

80 cm is 0.0008 so you know I just assumed

Answer: [tex]x\approx 6.2[/tex]

Step-by-step explanation:

Detailed explanation is attached below.

Answer: 2916 cubic feet

Step-by-step explanation:

V=(4/3)*3*(9^3)

V=(4/3)*3*729

V=2916

Answer: 2^(4/5)=16

Step-by-step explanation:

log a (b)=c

this converts to:

a^c=b

so...

2^(4/5)=16

The transformations to the parent function are given as follows:

The parent function for this problem is given as follows:

y = 1/x.

The transformed function for this problem is given as follows:

y = 3/(x + 5) - 3.

Hence the  transformations to the parent function are given as follows:

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Answer:

Use systems of equations to solve.

Let x represent the cost per pound of the espresso coffee beans and

y represent the cost per pound of the vanilla coffee beans.

6x + 5y = 77.50

20x + 13y = 234.50, both of these are given.

Rewrite these equations so you can eliminate one of the variables;

60x + 50y = 775, Multiply both sides of the equation by 10

60x + 39y = 703.5, Multiply both sides of the equation by 3

Now Subtract equation 2 from equation 1,

11y = 71.5

y = 6.5

Solve for x,

6x + 5(6.50)= 77.50

x = 7.50

Therefore, the cost per pound of the espresso coffee beans is $7.50, and

the cost per pound of the vanilla coffee beans is $6.50.

Answer:

70cm^2

Step-by-step explanation:

10×5=50cm^2 is the area of the rectangle

18-10=8 is the height of the triangle

8×2.5=20

20÷2=10 is area of half the triangle

10+10=20cm^2 is the area of the triangle

50cm^2+20cm^2=70cm^2

Answer:

Question 3:    5

Question 4:    91

Step-by-step explanation:

[tex](x+5)2-y[/tex]

[tex]x = -2[/tex]

[tex]y =1[/tex]

[tex](-2 + 5)2 - 1[/tex]

[tex](3)2-1[/tex]

[tex]6-1 = 5[/tex]

[tex]3x +4y^2[/tex]

[tex]x = -3[/tex]

[tex]y=5[/tex]

[tex]3(-3)+4(5)^2[/tex]

[tex]-9 + 100[/tex]

[tex]=91[/tex]

Answer:

The answer is number 2

The straight-line distance from your starting point at the end of driving is approximately 24.4 miles.

To find the straight-line distance from your starting point, we can use the Pythagorean states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The distance you drove west and turned left forms two sides of a right triangle, and the straight-line distance from the starting point will be the hypotenuse.

Given:

Distance driven west = 20 miles

Distance driven south = 14 miles

Using the Pythagorean:

Hypotenuse² = (Distance driven west)² + (Distance driven south)²

Hypotenuse² = 20² + 14²

Hypotenuse² = 400 + 196

Hypotenuse² = 596

To find the length of the hypotenuse (straight-line distance), we take the square root of both sides:

Hypotenuse = √596

Hypotenuse ≈ 24.4 miles (rounded to the nearest tenth)

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The scatter plot that accurately describes the data is given as follows:

Scatter plot A.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

The input and output variables for this problem are given as follows:

Hence the points are given as follows:

(13, 23), (17, 17), (21, 17), ..., (70,30).

And all these points are marked on the scatter plot given by option A.

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The mode of the data is 0

Central tendency is defined as the statistical measure identifying a single value as representative of an entire distribution.

It provides an accurate description of the entire data.

The three major measures of central tendency are given as;

The mode is defined as the measure of central tendency representing the most occurring number in a given data set

From the information given, we have;

0, 4 , 3, 4, 0, 9, 1

Then, the mode is 0

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Answer:

Angles 1 and 8 are alternate exterior angles.

Answer:

Step-by-step explanation:

The calculated value of the conditional probability P(Not A | Not B) is 0.8125

From the question, we have the following parameters that can be used in our computation:

The table of values

The probability P(Not A | Not B ) is calculated as

P(Not A | Not B ) = (Not A and Not B)/(Not B)

Using the above as a guide, we have the following:

(Not A and Not B) = 0.65

(Not B) = 0.80

Substitute the known values in the above equation, so, we have the following representation

P(Not A | Not B ) = 0.65/0.80

Evaluate

P(Not A | Not B) = 0.8125

Hence, the probability P(Not A | Not B) is 0.8125

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The polynomial function in factored form with roots x = 7, x = -10, and x = 3, each with a multiplicity of 1, is  [tex]f(x) = x^3 - 76x + 210.[/tex]

To write a polynomial function in factored form with the given roots, we can use the factored form equation:

f(x) = (x - r1)(x - r2)(x - r3)...

Where r1, r2, r3 represent the roots of the polynomial.

Given the roots x = 7, x = -10, and x = 3, we can write the factored form equation as:

f(x) = (x - 7)(x + 10)(x - 3)

Expanding this equation will give us the polynomial function in factored form:

[tex]f(x) = (x - 7)(x + 10)(x - 3)[/tex]

[tex]= (x^2 - 7x + 10x - 70)(x - 3)[/tex]

[tex]= (x^2 + 3x - 70)(x - 3)[/tex]

[tex]= x^3 - 3x^2 + 3x^2 - 9x - 70x + 210[/tex]

[tex]= x^3 - 76x + 210[/tex]

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The statement which is true is he has enough of each type of juice to make 1 recipe, the correct option is B.

We are given that;

Orange juice cup= 6

Pineapple juice cup=3

Now,

PART A: To answer this question, we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Felicia has pineapple juice in fluid ounces. We can use the fact that 1 cup = 8 fluid ounces to convert Felicia’s amount of pineapple juice to cups:

32 fluid ounces = 32 / 8 cups = 4 cups

The recipe requires 3 cups of pineapple juice, so Felicia has more than enough pineapple juice. The correct answer is B.

PART B: we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Jared has each type of juice in pints. We can use the fact that 1 pint = 2 cups to convert Jared’s amounts of juice to cups:

8 pints = 8 * 2 cups = 16 cups

Jared has 16 cups of each type of juice. The recipe requires 6 cups of orange juice, 3 cups of pineapple juice, and 1 cup of cranberry juice. This adds up to 10 cups of juice for one recipe. So, Jared has enough of each type of juice to make one recipe and have some left over. However, he does not have enough of each type of juice to make two recipes, since that would require 20 cups of juice in total. T

Therefore, by unitary method the answer will be He has enough of each type of juice to make 1 recipe.

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Answer:

The length of the second book is 10.5 inches, while the first book's thickness is in a ratio of 2:1.5, which simplifies to 4:3. Similarly, the length of the first book is also in a ratio of 4:3 with the second book. Hence, we can calculate the second book's length as 14 divided by 4, multiplied by 3, which equals 10.5 inches.

The total number of teams that are in the NFC from the given two way frequency table is: 16 teams

A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.

Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data

From the attached two way table, we see that:

Total number of animals = 15

Total number of non-animals = 17

Total Number of NFC = 16

Total number of AFC = 16

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The interval representing the range of the graphed function in this problem is given as follows:

a) (0, ∞).

From the image of the problem, the output y of the function is composed by the positive values, hence the interval representing the range is given as follows:

(0, ∞).

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