Find angle x giving your answer to one decimal place

The required slope, y-intercept, and x-intercept are -2.5, 15, and 7.5 respectively.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,
Locate two points on the graph,
(0, 15) and (7.5, 0)

The slope is given as,
m = -15/7.5
m = -2.5

The slope of the graph represents the rate of fuel i.e. 2.5 gallons per hour.

Now,
y-intercept from the graph is 15, and the x-intercept in the graph is 7.5, which represents the amount of fuel initally in the car, and in 7.5 hours no fuel will be left respectively.

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A recipe for a rice dish calls for 6 oz of pure wild rice and 14 oz of a rice mixture that is 10% wild rice , the mixture is 37% wild rice.

we need to find how much wild rice is in the 14 oz of the rice mixture. We can do this by multiplying the weight of the rice mixture (14 oz) by the percentage of wild rice in the mixture (10%).

14 oz * 10% = 1.4 oz

Now we add the amount of wild rice in the rice mixture (1.4 oz) to the amount of pure wild rice (6 oz) to find the total amount of wild rice in the mixture:

1.4 oz + 6 oz = 7.4 oz

Now we divide the total amount of wild rice (7.4 oz) by the total weight of the mixture (20 oz) and multiply by 100% to find the percentage of wild rice in the mixture:

(7.4 oz / 20 oz) * 100% = 37%

So, the mixture is 37% wild rice.

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The measure of the reference angle is: [tex]$$\cos (\theta)=\frac{\sqrt{3}}{2}$$[/tex]

The reference angle of an angle is the smallest acute angle between the terminal arm of a quadrant and the x-axis.

Given that:

[tex]$$\theta=\frac{11 \pi}{6}$$[/tex]

First, we convert to degrees

[tex]& \theta=\frac{11 \pi}{6} * 180 \pi \\[/tex]

[tex]& \theta=\frac{11}{6} * 180 \\[/tex]

[tex]& \theta=11 * 30 \\[/tex]

[tex]& \theta=330^{\circ}[/tex]

[tex]$$\alpha=30$$[/tex]

Hence, the measure of the reference angle Is: [tex]$30^{\circ}\alpha=30[/tex]$ means that the reference angle is in the first quadrant [tex]$\theta=330^{\circ}$[/tex] means that this angle is in the fourth quadrant

In the first and the fourth quadrants,

[tex]$$\cos (\theta)=\cos (\alpha)$$[/tex]

Substitute [tex]$\alpha=30$[/tex]

[tex]$$\cos (\theta)=\cos (30)$$[/tex]

In trigonometry:

[tex]$$\cos (30)=\frac{\sqrt{3}}{2}$$[/tex]

So:

[tex]$$\cos (\theta)=\frac{\sqrt{3}}{2}$$[/tex]

[tex]$$\cos (\theta)=\frac{\sqrt{3}}{2}$$[/tex]

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Answer:

Step-by-step explanation:

If the arithmetic sequence is f(x) = 3x-7, x stands for the position of the number in the sequence. In other words, we are looking to solve for x when f(x) = 8:

8 = 3x - 7 and

15 = 3x so

x = 5. The position of the number 8 is the 5th position.

What does this problem ask for:

 --> position of '8' in the sequence

Since our general formula: f(x) = 3x - 7

 --> 'x' represents the position of the term in the sequence

    --> f(x) is the term in the sequence

 --> therefore, if we plug '8' into f(x)

    --> we can find 'x' which is the position of 8 in the sequence

Thus:

 [tex]8=3x-7\\3x=8+7\\3x=15\\x=5[/tex]

8 is the 5th term

Answer: 5th term

Table of Values:
Number of Pylons: 0 | Height: 27 cm
Number of Pylons: 1 | Height: 32 cm
Number of Pylons: 2 | Height: 37 cm
Number of Pylons: 3 | Height: 42 cm
Number of Pylons: 4 | Height: 47 cm
Number of Pylons: 5 | Height: 52 cm
Number of Pylons: 6 | Height: 57 cm
Number of Pylons: 7 | Height: 62 cm
Number of Pylons: 8 | Height: 67 cm
Number of Pylons: 9 | Height: 72 cm
Number of Pylons: 10 | Height: 77 cm
Number of Pylons: 11 | Height: 82 cm
Number of Pylons: 12 | Height: 87 cm
Number of Pylons: 13 | Height: 92 cm
Number of Pylons: 14 | Height: 97 cm
Number of Pylons: 15 | Height: 102 cm
Number of Pylons: 16 | Height: 107 cm
Number of Pylons: 17 | Height: 112 cm
Number of Pylons: 18 | Height: 117 cm
Number

There are two real number solutions for x2 − 5x + 7 = 0: x = 2 and x = 7.

1. x2 − 5x + 7 = 0

2. (x - 2)(x - 7) = 0

3. x = 2 or x = 7

When solving for the real number solutions of x2 − 5x + 7 = 0, we first need to factor the equation into two linear terms: (x - 2)(x - 7) = 0. From here, we can use the Zero Product Property to determine that x = 2 and x = 7 are the two real number solutions of this equation. This means that when x is equal to 2 or 7, the equation will equal 0 and all other values of x will result in a non-zero answer. Therefore, the only two real number solutions of x2 − 5x + 7 = 0 are x = 2 and x = 7.

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Answer:

208.25

Step-by-step explanation:

2/5 * 595 = 2*119=238

therefore, total number of 8th graders is 238

so, 7/8 * 238 = 7*238÷8=208.25

The number of full hours that the school will be charged would be = 6 full hours.

The amount of money charged for 2 hour = $49

The amount of money charged for 5 hours = 122.50

Therefore the amount of money charged for an hour= 49/2 = $24.5

The amount of money charged for reservation fees = $25

The amount of money the school has to spend on artist fee alone = $175 - 25 = $150

The amount of hours they can hire the artist should be the cost that is within $150 = cost for an hour + cost for 5 hours = 122.50 + $24.5 = $147.

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Answer:

i wish i could help but i never learned that

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

B using the perpendicular theorem

Since MB is a perpendicular bisector of JK , then JB = BK

and Δ JMK is isosceles with congruent legs , so

JM = MK ( substitute values )

9x - 18 = 3x ( subtract 3x from both sides )

6x - 18 = 0 ( add 18 to both sides )

6x = 18 ( divide both sides by 6 )

x = 3

The missing dimensions are 4.5 in. and 75 in. respectively.

Given are model and actual dimensions of two items.

After the dilation, the relation between final and initial dimensions of the image is -

y = Kx

where -

{K} is a dimensionless quantity called scale factor.

For the figure skates -

{Model/Actual} = {1/15}

1/15 = {x}/67.5

{x} = 67.5/15

{x} = 4.5 in.

For the pipe -

{Model/Actual} = {1/15}

1/15 = 5/{y}

{y} = 5 x 15

{y] = 75 in.

Therefore, the missing dimensions are 4.5 in. and 75 in. respectively.

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Answer:

Step-by-step explanation:

its 8 1/10

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Now, According to the question:

Is a negative slope horizontal or vertical?

Negative slope means that as we move from left to right on the graph, the line falls. Zero slope means that the line is horizontal: it neither rises nor falls as we move from left to right. Vertical lines are said to have "undefined slope," as their slope appears to be some infinitely large, undefined value.

Hence, The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

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X and Y are independent random variables, and a and b are constants is

Var(X-Y) = Var(X) + Var(Y)

Now, According to the question:

Let's Know:

Independent random variable:

Two random variables X and Y are independent if

E(XY) = E(X)E(Y).In case of n random variables the formula is extended as

[tex]E(X_1,X_2,X_3....X_n)=E(X_1)E(X_2)E(X_3)...E(X_n)[/tex]

Are the random variables X and Y independent?

If X and Y are two random variables and the distribution of X is not influenced by the values taken by Y, and vice versa, the two random variables are said to be independent.

Hence, X and Y are independent random variables, and a and b are constants is

Var(X-Y) = Var(X) + Var(Y).

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A percent is a unit of measurement used to express a ratio as part of 100. It is often used to express a proportion of a whole quantity.

The percentage is defined as a ratio expressed as a fraction of 100.

When a part of a whole is represented as a percent, it means that it is expressed as a fraction of 100.

For example, if a quantity is represented as 50%, it means that it is equal to 50/100 or 1/2 of the whole.

Therefore, part of a whole is represented by a percent that is a fraction of 100, with the numerator representing the part and the denominator representing the whole. The value of the fraction is then multiplied by 100 to express the ratio as a percentage.

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Answer:

N = X^a × Y^b × Z^c

Step-by-step explanation:

For the graphs you use the the method of

Rise(Up) / Run(Down) = Slope

for exmaple the first graph

The rise is 4 (up) and the run (down) is 6 so you divide that being 2/3 the slope.

For the secound part you use the formula

m= rise/run = y2-y1/x2-x1

for exmaple for number 7

(4,9) and (1,6) being (x1, y1) and (x2,y2)

so your rise is 3 and your run is 3 that being 3/3 = 1 so your slope is 1 or m=1

Statistics, or what we say to as ‘Stats’ in general parlance, is fully a useful branch of mathematics that can help in analyzing and solving mass everyday problems.

It has a broad range of applications in various fields, right from medicine, and engineering, to sports, etc. So, let us know more about it.

The benefits of statistics include collecting data in the form of numerical figures, analyzing and interpreting the data, grouping and presenting the data, and arriving at novel information organized from the data.

in the branch of mathematics, statistics is a very main idea to learn.

Population mention to a group of people or objects as a whole, while a sample is a subset of the whole. By examine samples of a population, you can learn more about that population.

A branch of statistics also deals with analyzing certain outline in a macroscopic way where we work with a given population and a sample.

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Apples and pears were purchased by Catherine for the school picnic. The right formula will be y = 100-x and y < x if the total number of fruits is less than 100.

Equations are mathematical expressions with two algebraic operators on either side of the equal (=) symbol. To illustrate this relationship, the phrases on the left and right are shown to be equal to one another. A basic, straightforward equation is L.H.S. = R.H.S. (left-hand side = right side).

As per the given data in the equation,

Catherine bought apple and pears.

The overall quantity is less than 100

Let the number of apples is x and,

The number of pears is y.

She bought more apples than pears,

y < x.

And y < 100 - x.

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Solving the provided question we can say that the quadratic equation - y =  a( x - h)^2 + k => y = 2 + k

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here,

the quadratic equation -

y =  a( x - h)^2 + k

here x = 0l h =1 and a = 2

y = 2 + k

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Answer:-3+(n-1)*7

Step-by-step explanation:

Nth term = -3+(n-1)*7

The slope of the line passing through the points (3, 2) and (-2, 2) is 0.

In the given question, we have to find an equation of the line that passes through the points (3, 2) and (-2, 2).

The point-slope approach is typically used when two points that sit on a specific line are specified.

A line's equation is written as y - y(1) = m(x - x(1)), where y(1) is the Y-axis coordinate, m is the slope, and x(1) is the X-axis coordinate.

Firstly we find the value of m using the formula

m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

From the given points x(1) = 3, y(1) = 2, x(2) = -2, y(2) = 2.

Now putting the value

m = [tex]\frac{2-2}{-2-3}[/tex]

Now solving

m = [tex]\frac{0}{-5}[/tex]

m = 0

Hence, the slope of the line passing through the points (3, 2) and (-2, 2) is 0.

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The complete question is:

What is the slope of the line passing through the points (3, 2) and (-2, 2)?

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Given that the triangles are similar?

i)        Corresponding angles of both the triangles are equal, and

ii)       Corresponding sides of both the triangles are in proportion to each other.

Properties

Formulas

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Factored form of the equation of the parabola from the given graph can be represented by : f (x) = A ( x - t ) ( x - q ).

As given in the question,

Standard equation of the parabola is given by :

f (x ) = ax² + bx + c

Let us consider the x - intercept of the given graph of parabola where graph of the parabola cuts x -axis at ( t , 0) and ( 0 ,q )

Then factored form for the given roots of the equation can be represented as:

f (x) = A ( x - t ) ( x - q )

t, q are the x-intercepts and A is called the leading coefficient.

Therefore, the factored form the parabola from the given graph is equal to f (x) = A ( x - t ) ( x - q ).

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Answer: D

Step-by-step explanation: Because its Deeeeee

The premium of the policy will be $4,536.30. The goal of insurance is to spread the risk of potential losses among a large group of people, so that any individual loss is not too devastating for one person to bear.

Insurance is a contract between an individual or organization and an insurance company, where the individual or organization pays a premium to the insurance company in exchange for financial protection or reimbursement in the event of an unforeseen loss or event. The insurance company agrees to pay for any covered losses or damages, up to the limits specified in the insurance policy. Insurance can be used to protect against a variety of risks, including death, injury, property damage, and liability.

The premium of the policy can be calculated using the formula:

Premium = (Probability of death * Benefit amount) + Administrative costs

In this case, the probability of death is 18.1452%, the benefit amount is $25,000, and the administrative costs are $45.

Then, the premium of the policy would be:

(0.181452 * 25,000) + 45 = $4,536.30

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Answer:  $4581.30

Step-by-step explanation:

The rate is the height of the pile changing when it is 8 feet is:

dh/dt=60/256π

The volume of a cone is defined as the amount of space or capacity a cone occupies, and it is measured in cubic units like cm³, m³, and in³.

The volume of a cone is given as V = (1/3)πr²h.

If the radius of the base of the cone is "r"

height of the cone is "h",

Let r = radius of the base at time t

    h = height at time t

    V = volume of cone at time t

Given:  dV/dt = 20

Find dh/dt when h = 8

V = (1/3)πr²h   Since 2r = 4h, r = 2h

V = (1/3)π[2h]²h

  = (2/3)πh³

dV/dt = (4/3)πh²(dh/dt)

Now, substitute the values we get

20 = (4/3)π(8)²(dh/dt)

20=4/3π×64(dh/dt)

20=256π/3(dh/dt)

60/256π=dh/dt

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The blocks will be filled as follows -

y = 5(x) + b

33 = b

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the slope of the line passing through the point (4, 53).

Now, from the question, we can write -

y = 5x + b

For the point -

(4, 53)

We can write -

53 = 5 x 4 + b

b = 53 - 20

b = 33

Therefore, the blocks will be filled as follows -

y = 5(x) + b

33 = b

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The range of given parabolic function [tex]x^2+3[/tex] is [3,∞).

Domain: the domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The fact that the fraction's denominator is not equal to zero and that the digit inside the square root bracket is positive both point to the domain.

Range: the range of a function is the set of all possible values for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.

[tex]f(x)=x^2+3\\[/tex]

here domain of the given function is R.

and for x=0, f(x)=3 which is the lower range of given function and for higher range is infinity.

so range of given function is [3,∞).

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