What is the range of the function

x ≈ 17.8 cm (rοunded tο 1 decimal place).

The trigοnοmetric functiοns in mathematics are real functiοns that relate the angle οf a right-angled triangle tο the ratiοs οf its twο side lengths. They are alsο knοwn as circular functiοns, angle functiοns, οr gοniοmetric functiοns.

All geοsciences, including navigatiοn, sοlid mechanics, celestial mechanics, geοdesy, and many οthers, use them extensively. They are sοme οf the mοst straightfοrward periοdic functiοns, and as a result, Fοurier analysis is frequently used tο study periοdic phenοmena.

Tο sοlve fοr x, we can use the trigοnοmetric functiοn cοsine since we have the adjacent side and the hypοtenuse.

cοs(θ) = adjacent/hypοtenuse

cοs(38°) = x/hypοtenuse

We knοw that the perpendicular is y = 11 cm, sο we can use the Pythagοrean theοrem tο find the hypοtenuse:

\(\rm hypotenuse^2 = perpendicular^2 + base^2\)

\(x^2 = y^2 + (adjacent)^2\)

\(x^2 = 11^2 + (x cos(38^\circ))^2\)

\(x^2 = 121 + (x 0.7880107536)^2\)

\(x^2 = 121 + 0.6201117996x^2\)

\(0.3798882004x^2 = 121\)

\(x^2 = 318.5022183\)

x ≈ 17.84 cm (rounded to 1 decimal place)

Therefore, x ≈ 17.8 cm (rounded to 1 decimal place).

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For the quadratic function,

(a) Standard form: f(x) = (x + 1)^2 - 7

(b) Its graph will be a parabola opening upward

(c) Minimum value: f(x) = -7

(a) To express the quadratic function f(x) = x^2 + 2x - 6 in standard form, we complete the square.

f(x) = (x^2 + 2x) - 6
To complete the square, take half of the linear coefficient (2) and square it: (2/2)^2 = 1.

Now, add and subtract this value inside the parentheses:
f(x) = (x^2 + 2x + 1 - 1) - 6
f(x) = (x + 1)^2 - 7

So, the standard form is f(x) = (x + 1)^2 - 7.

(b) Since the leading coefficient (1) is positive, the graph of this quadratic function opens upward. The vertex is at the point (-1, -7), which is the minimum point. To sketch the graph, plot the vertex and draw a parabola opening upward.

(c) The minimum value of the function is the y-coordinate of the vertex: f(x) = -7.

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Answer:

Step-by-step explanation:

The width of a rectangle is 4 meters less than twice the length. The area is 96 square meters. Find dimensions

The average rate of change of the function in the interval [x,x+h] is [7h(x + 2a) - (x + h + 2a)] / (x + h + 2a)(x + 2a). The domain of the function f(x) is all real numbers except -2a and is given by (-∞,-2a) U (-2a,∞).

The given function is f(x)= 7x−1x+2

a) The average rate of change of f(x) in the interval [-1,3] is given by;[f(3) - f(-1)] / (3 - (-1)).

Therefore, to find the value of f(3), substitute x = 3 in the given function:

f(x) = 7x−1x+2a

f(3) = 7(3) - 1 / (3 + 2a)

f(3) = 21 - 1 / (3 + 2a)

f(3) = 20 / (3 + 2a)

Similarly, to find the value of f(-1), substitute x = -1 in the given function:

f(x) = 7x−1x+2ax

f(-1) = 7(-1) - 1 / (-1 + 2a)

f(-1) = -8 / (-1 + 2a)

Therefore, the average rate of change of the function in the interval [-1,3] is;

= [f(3) - f(-1)] / (3 - (-1))

= [20 / (3 + 2a)] - [-8 / (-1 + 2a)] / 4

= [20 / (3 + 2a)] + [8 / (1 - 2a)] / 4

= 4[20 / (3 + 2a)] + [8 / (1 - 2a)] / 4

= (20 / (3 + 2a)) + (2 / (1 - 2a))

The average rate of change of the function in the interval [x,x+h] is [7h(x + 2a) - (x + h + 2a)] / (x + h + 2a)(x + 2a).The domain of the function f(x) is all real numbers except -2a and is given by (-∞,-2a) U (-2a,∞).

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Answer:

m ÷ 7

Step-by-step explanation:

"Quotient" means you're dividing, so this just means you're dividing m by 7.

Answer:

7629.39453125

Step-by-step explanation:

The formula for the n-th term is:

\(k_n = \frac{5^{n-1}}{2^{n-2}}\)

So:

\(k_{10} = \frac{5^9}{2^8}\) = 1953125 / 256 = 7629.39453125

Answer:

7629.395 correct answer

To estimate the area under the graph of f(x) = \(5 + 2x^2\) from x = -1 to x = 2, we can use the method of rectangles with right endpoints. By dividing the interval into three rectangles, the estimated area can be calculated.

To estimate the area using three rectangles with right endpoints, we divide the interval [-1, 2] into three equal subintervals: [-1, -0.333], [-0.333, 1.333], and [1.333, 2]. The width of each rectangle is (2 - (-1)) / 3 = 1, as the interval is divided into three equal parts.

Similarly, for the second rectangle, the right endpoint is 1.333, giving us a height of f(1.333) = 5 + 2(1.333)^2 = 9.778. Finally, for the third rectangle, the right endpoint is 2, resulting in a height of f(2) = \(5 + 2(2)^2\) = 13.

The estimated area using three rectangles is R3 = (1 * 5.222) + (1 * 9.778) + (1 * 13) = 28.

To improve the estimate, we can use six rectangles. We divide the interval [-1, 2] into six equal subintervals, each with a width of (2 - (-1)) / 6 = 0.5. We repeat the process of calculating the heights at the right endpoints of each subinterval and sum up the areas of the six rectangles.

By using six rectangles and repeating the calculations, we obtain R6 = (0.5 * 5.056) + (0.5 * 5.778) + (0.5 * 6.889) + (0.5 * 9.222) + (0.5 * 11.778) + (0.5 * 13) = 30.611.

Therefore, the improved estimate using six rectangles is R6 = 30.611.

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Answer:

6 Liters

Step-by-step

4 Lemons = 3 Liters

8 Lemons = 6 Liters

So its basicly multiplying it by 2  ^O^

Answer:

X = 6

Step-by-step explanation:

number of lemons. Liters

4 ---> 3

8 ---> X

= 4:8 = 3: X

= 4 = 3

8 X

= 4X = 3×8

= X = 3 × 8

4

= X = 6 answer X=6

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Answer:the answer is 9

Step-by-step explanation:

To determine the number of smaller boxes that would contain the same amount of cereal as a larger box, we set the expressions representing the cereal content equal to each other. Solving the equation, we find that 15 smaller boxes are required to match the cereal quantity in the larger box.

To find the number of smaller boxes that equal the same amount of cereal in a larger box, we need to equate the two expressions and solve for n.

Setting the expressions equal to each other:

10 + 6.3n = 7 + 6.5n

Simplifying the equation:

6.3n - 6.5n = 7 - 10

-0.2n = -3

Dividing both sides by -0.2:

n = -3 / -0.2

n = 15

Therefore, 15 smaller boxes would equal the same amount of cereal as the larger box.

The problem states that the expressions 10 + 6.3n and 7 + 6.5n represent the amount of cereal in the new larger box. The variable n represents the number of smaller boxes.

To find how many smaller boxes are equivalent to the larger box, we need to set the two expressions equal to each other and solve for n. This equation represents the balance between the amount of cereal in the larger box and the combined amount of cereal in the smaller boxes.

By simplifying the equation and solving for n, we find that 15 smaller boxes are needed to equal the same amount of cereal as the larger box.

This means that if the cereal manufacturer wants to package the same amount of cereal as the larger box, they would need to use 15 smaller boxes instead. This calculation helps the manufacturer determine the number of smaller boxes needed to maintain the same quantity of cereal while changing the box size.

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The required z-score is -0.5 and the probability that the firm WILL have a negative EPS is 30.85%.

Firm has a loss level EBIT of $175m and an expected EBIT of $200m with a standard deviation of $50m.

Z-score = (EBIT - Expected EBIT) / Standard deviation= (175 - 200) / 50= -0.5

Probability of having a negative EPS:

To find the probability that the firm will have a negative EPS, we need to find the area to the left of Z-score. As the Z-score is negative, we will be finding the left-tail probability using the standard normal table from the link below:

The area to the left of Z-score (0.5) is 0.3085 or 30.85%.

Therefore, the probability that the firm WILL have a negative EPS is 30.85%.

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The number of platters that can be made is 8.

Given that you need to make a platter which consists of 1 bagel, 2 eggs, and 3 slices of bacon. Since it is needed to calculate the maximum number of platters that can be made with 9 bagels, 17 eggs and a package of bacon containing 36 slices.

Further, If we make 1 platter then we need 1 bagels, 2 eggs and 3 slices of bacon. Therefore, for 8 platters, the material required would be 8 times of 1 platter, that is 8 bagels, 16 eggs and 24 slices of bacon.

Similarly if I have to create 9 platters , the material required would be 9 times of 1 platter, that is 9 bagels, 18 eggs and 27 slices of bacon.

So we can not make 9 platters because we need that one extra egg.

The number of platters is 8.

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yes, actually it is possible. The mathematical expression f(x)=exp or ex denotes the exponential function.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function. The formula f(x)=2x is a straightforward example.

Hence, yes, actually it is possible.

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Answer:

m = 160

p = 90

w = 10

z = 80

y = 10

Step-by-step explanation:

All the solution of angles are,

⇒ ∠ p = 90°

⇒ ∠y = 20°

⇒ ∠ z = 70°

⇒ ∠ m = 90°

⇒ ∠ w = 70°

We have to given that,

A rhombus shown in image.

Since, Properties of a rhombus,

The sum of interior angles of a rhombus adds up to 360 degrees.

The opposite angles of a rhombus are equal to each other.

The adjacent angles are supplementary.

In a rhombus, diagonals bisect each other at right angles.

The diagonals of a rhombus bisect these angles.

Hence, We get;

⇒ ∠ p = 90°

⇒ ∠y = 20°

⇒ ∠w = 90° - ∠y

⇒ ∠w = 90° - 20° = 70°

⇒ ∠ z = 70°

⇒ ∠ m = 90°

Therefore, All the solution of angles are,

⇒ ∠ p = 90°

⇒ ∠y = 20°

⇒ ∠ z = 70°

⇒ ∠ m = 90°

⇒ ∠ w = 70°

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Following the transformation, every point on the polygon moves two units to the right.

Transformation is a mathematical operation performed to change the shape or orientation of a graph or object

Since a polygon is transformed according to the rule (x, y) (x+2, y). To detremine which direction every point of the polygon moves two units in, we proceed as folllows.

So, we see that every point on the polygon moves two units to the right.

Thus, every point on the polygon moves two units to the right.

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If the degree is odd and and the leading coefficient is negative then the right end of the graph will point down and the left end will point up .

The End Behaviour of the graph of polynomial is said to be defined by the degree and leading coefficient of polynomial .

the end behaviour for the Odd degree polynomial is given as :

(i) If the degree of polynomial is odd and lead coefficient is positive, then the right end of graph will point up and the left end will point down.

(ii) If the degree of polynomial is odd and the lead coefficient is negative, then right end of graph will point down and left end will point up .

So , according to the question , for the given condition , the right end will point down and left end will point up .

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The answer: d. P13 − P14 ≤ 100; P14 − P13 ≥ 100

The correct answer is (d) P13 − P14 ≤ 100; P14 − P13 ≥ 100.

The question is asking us to specify the difference between the production of product 1 in period 3 and period 4. We know that the difference should not be more than 100 units, which means that the difference can be either positive or negative, but its absolute value should be less than or equal to 100.

Therefore, we can write the following inequalities:

- P13 - P14 ≤ 100 (the difference is not more than 100 units)
- P14 - P13 ≥ -100 (the difference is not less than -100 units, which is the same as saying it is not more than 100 units in the other direction)

Simplifying the second inequality, we get:

- P13 - P14 ≤ 100 (same as the first inequality)
- P14 - P13 ≥ 100 (we multiplied both sides by -1 to make the inequality easier to read)

So, the correct answer is (d) P13 − P14 ≤ 100; P14 − P13 ≥ 100.

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Answer:

1/9

Step-by-step explanation:

You combine the fractions finding the least common denominator. Once you do that, you get your answer of 1/9.

I hope this information was of any use to you.

Answer:

-12/25

Step-by-step explanation: We already know that -48/100=-0.48, so we can just write -48/100 in simplest form which is -0.48. So, your answer is -0.48

Answer:

d

Step-by-step explanation:

only a scalence triangle has all sides with different length

Answer: 2 3/5ths are left or 13/5

Step-by-step explanation: 1 2/5 + 2 3/5 = 4 total walls

Answer: angle A is none of those

Step-by-step explanation:

the sum of all angles in a triangle = 180

one of the triangles is 90

we can form an equation:

90 + (x+69) + (x+39) = 180

90 + 2x + 108 = 180

198 + 2x = 180

2x = 180 - 198

2x = -18

x = - 9

angle A = x+39

substitute x = -9

angle A = -9 + 39 = 30

so angle A is none of those

Answer: A . Drivers older than 65 had no DUIS I just did it on USA test prep.

Step-by-step explanation:

The integer that represents the change in temperature from morning to afternoon is 18.

To find the change in temperature from morning to afternoon, we need to calculate the difference between the afternoon temperature and the morning temperature.

The morning temperature was given as -8.7 F, which means the temperature was 8.7 degrees below the freezing point of water. The afternoon temperature was given as 9.3 F, which means the temperature was 9.3 degrees above the freezing point of water.

To find the change in temperature, we subtract the morning temperature from the afternoon temperature.

9.3 F - (-8.7 F) = 9.3 F + 8.7 F

Here, we add a negative number because we are subtracting a negative number. This gives us

= 18.0 F

So, the change in temperature from morning to afternoon is 18.0 F

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As per the concept of dot plot the team never scored exactly 2 goals in a single game.

In math the term dot plot which is also known as a strip plot or dot chart is referred as a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis.

Here we have given that goals scored per game a dot plot going from 0 to 5. 0 has 3 dots, 1 has 2 dots, 2 has 0 dots, 3 has 5 dots, 4 has 3 dots, 5 has 8 dots.

And we need to find a true statement about the dot plot.

As we know that these types of charts are used to graphically depict certain data trends or groupings.

Here we know that the team never scored exactly 2 goals in a single game, based on this we can says the team never scored exactly 2 goals in a single game and the dot plot shows 0 dots in number 2.

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Answer: yes kevin skied as long as lori

The radius at the point where the surface area is equal to the given value is the radius of the cylinder.

The surface area of a cylinder can be calculated using the following formula:

Surface Area = 2πr2 + 2πrh

Where r is the radius, and h is the height of the cylinder.

To calculate the radius of the cylinder, we need to rearrange the equation to solve for r.

r = (Surface Area - 2πrh) / 2πr

For example, if the surface area is 400π, and the height is 20, then the radius is calculated as follows

r = (400π - 2π(20)) / 2π

r = (400π - 40π) / 2π

r = 360π / 2π

r = 180 / 2

r = 90

So, the radius of the cylinder with a surface area of 400π and a height of 20 is 90.

Graphically, the radius of a cylinder can be found by plotting the surface area of the cylinder on a graph. The height will be represented by the y-axis, and the radius by the x-axis. The surface area is equal to the area of the rectangular shape formed by the two axes. The radius at the point where the surface area is equal to the given value is the radius of the cylinder.

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