Graph X-3<8 and 6x<72

Answer: c. 9

Step-by-step explanation:

Thus, the unknown side length of rectangle for the given area and one side length is found to be 5.5 m.

Every day, rectangles are all around us. All of these objects—doors in a home, windows in a structure, and books in a library—are rectangles.

Given that:

Area of rectangle A = length * width

width = area / length

width = 11 / 2

width =  5.5

Thus, the missing side of rectangle for the given area and one side length is found to be 5.5 m.

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Complete question:

Find the unknown side length of the rectangle if its area is 11 m² and one of its side is 2 m.

Answer:

68/25

Step-by-step explanation:

Thus, the height of flagpole from the ground is found as 23.34 feet.

The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.

The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.

Given data:

Using the trigonometric ratios in the right triangle ABE.

tan 35 = h / 30

h = 30* tan(35)

h = 18.34

Height of flagpole = 18.34 + 5 = 23.34 feet

Thus, the height of the flagpole from the ground is found as 23.34 feet.

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Answer:

mean: 20mins

Step-by-step explanation:

add them all together to get 240

then divide by how many there are

240÷12=20

so the mean is 20mins

Answer:

[tex]3 {( - 5)}^{2} + 5( - 5) + 7 = 57[/tex]

[tex] {( - 5)}^{3} - 5c + 202 = 57[/tex]

[tex] - 125 - 5c + 202 = 57[/tex]

[tex]77 - 5c = 57[/tex]

[tex] - 5c = - 20[/tex]

[tex]c = 4[/tex]

For this value of c, these graphs will intersect at (-5, 57).

Please use your graphing calculator to confirm that this is the only point of intersection.

The distance PQ cannot be expressed as k√5, where k is a rational number given that PQ = √18

To find dy/dx, we can use implicit differentiation:

4xy = 2(x² + 4y²) - 9x

Differentiating both sides with respect to x, we get:

4y + 4xy' = 4x + 8yy' - 9

Simplifying and solving for y', we get:

y' = (4x - 4y - 9)/(4x - 16y)

Hence, dy/dx = (4x - 4y - 9)/(4x - 16y).

At point P, the tangent to the curve is parallel to the y-axis.

This means that dx/dy = 0 at P.

We can find the coordinates of P by solving the following equations simultaneously

4xy = 2(x² + 4y²) - 9x

dx/dy = 0

From 4xy = 2(x² + 4y²) - 9x, we have:

4xy + 9x = 2(x² + 4y²)

Dividing both sides by x², we get:

4y/x + 9/x = 2 + 4y²/x²

Since dx/dy = 0, we have:

dy/dx = 0

Using the formula for dy/dx that we derived in part (a), we get:

(4x - 4y - 9)/(4x - 16y) = 0

Solving for y, we get:

y = (4x - 9)/4

Substituting this into 4xy = 2(x² + 4y²) - 9x, we get:

4x * (4x - 9)/4 = 2(x² + 4[(4x - 9)/4]²) - 9x

Simplifying and solving for x, we get:

x = 9/2 and 3/2

Substituting these values of x into y = (4x - 9)/4, we get the coordinates of P:

y = 9/4 and y = -3/4

This means that

P(9/2, 9/4) and P(3/2, -3/4)

At point Q, the tangent to the curve is parallel to the x-axis.

This means that dy/dx = 0 at Q.

Using the formula for dy/dx that we derived in part (a), we get:

(4x - 4y - 9)/(4x - 16y) = 0

Solving for x, we get:

x = (4y + 9)/4

Substituting this into 4xy = 2(x² + 4y²) - 9x, we get:

4 * [(4y + 9)/4] * y = 2([(4y + 9)/4]² + 4y²) - 9 * (4y + 9)/4

Simplifying and solving for y, we get:

y = -3/4, 9/4

Substituting these values of y into x = (4y + 9)/4, we get the coordinates of Q:

x = 3/2 and x = 9/2

This means that

Q(3/2, -3/4) and Q(9/2, 9/4)

Using the distance formula, we can find the distance PQ:

PQ = √[(9/2 - 3/2)² + (9/4 + 3/4)²] or √[(3/2 - 9/2)² + (-3/4 - 9/4)²]

Simplifying, we

PQ = √18 or √18

So, we have

PQ = √18

This gives

k√5 = √18

So, we have

k = √18/√5

Evaluate

k = √3.6

√3.6 is not a rational number

Hence, the distance PQ cannot be expressed as k√5

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Answer:

28°

Step-by-step explanation:

If the angles are supplementary, they add up to 180°.

(3x) + (2x + 40) = 180

5x + 40 = 180

     - 40   - 40

5x = 140

x = 28°

The finance charge for Antoni Gaudi's bedroom set purchase is $731.08.

An installment refers to a sum of money that is paid back in parts over a period of time, typically with interest.

A loan is a financial agreement between a lender and a borrower, in which the lender provides the borrower with a specific amount of money or assets, which the borrower agrees to pay back with interest over a predetermined period of time. Loans can be used for a variety of purposes, such as purchasing a home, starting a business, or paying for education.

Based on the given information, the bedroom set sells for $2,650, and the financing requires a 15% down payment, which is $397.50 ($2,650 x 0.15).

Therefore, the amount financed is $2,252.50 ($2,650 - $397.50).

To calculate the finance charge, we need to know the total amount of payments Antoni Gaudi will make over the 42-month period. Each monthly payment can be calculated using the following formula:

Monthly Payment = (Amount Financed x (APR/12)) / (1 - (1 + APR/12)^-n)

Where:

APR is the annual percentage rate (12% in this case)

n is the total number of payments (42 in this case)

Plugging in the values, we get:

Monthly Payment = ($2,252.50 x (0.12/12)) / (1 - (1 + 0.12/12)^-42)

= $70.99 (rounded to the nearest cent)

Therefore, the total amount of payments Antoni Gaudi will make over the 42-month period is $2,983.58 ($70.99 x 42).

The finance charge can be calculated as follows:

Finance Charge = Total Payments - Amount Financed

= $2,983.58 - $2,252.50

= $731.08

Therefore, the finance charge for Antoni Gaudi's bedroom set purchase is $731.08.

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x ≤ 4, -2≤ y ≤ 2  are the domain and range of the graph of this function.

What is the domain and domain of the function in the graph?

Another way to identify domains and feature sets is with graphs. Domain refers to the set of possible input values, so a chart's domain consists of all input values ​​displayed on the x-axis.

                                    A range is the set of possible output values ​​plotted on the y-axis. To find the domain and domain of the equation y = f(x), find the value of the independent variable x for which the function is defined. 

y = f(x)

according to the graph value of y

 x ≤ 4,

-2≤ y ≤ 2

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Answer:

[tex]25.5h = 153[/tex]

[tex]h = 6[/tex]

The height is 6 feet, so A is correct.

Answer: a. To find the number of barrels that should be refined to maximize profit, we need to find the critical point of the function P(x), which occurs where the derivative of P(x) equals zero.

P(x) = 8x - 0.02x²

P'(x) = 8 - 0.04x

Setting P'(x) = 0, we get:

8 - 0.04x = 0

Solving for x, we get:

x = 200

Therefore, 200 barrels should be refined to maximize the profit.

b. To find the maximum profit, we substitute x = 200 into the profit function P(x):

P(200) = 8(200) - 0.02(200)²

P(200) = 1600 - 800

P(200) = 800

Therefore, the maximum profit is $800.

Step-by-step explanation:

Answer:

It is irrational, because the product of an irrational number and a rational number is irrational.

Step-by-step explanation:

sqrt 27 is  irrational =5.19615.......

3 is rational

  subtracting 3 from the irrational number just creates a smalller irrational number    ....then multiplying by 9 just creates a larger irrational number

The probability of exactly 3 successes in 15 trials with a probability of success on a single trial of 0.77 is approximately 0.1648.

To find the probability of exactly 3 successes in a binomial distribution with n=15 trials and a probability of success on a single trial q=0.77, we can use the formula for the probability mass function of the binomial distribution:

P(X=k) = (n choose k) * q^k * (1-q)^(n-k)

Substituting the given values into the formula, we get:

P(X=3) = (15 choose 3) * 0.77^3 * (1-0.77)^(15-3)

P(X=3) = (15!/((15-3)!3!)) * 0.77^3 * 0.23^12

P(X=3) = 0.1648.

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The statement that (sin 2x) / (1 + cos 2x) = tan x can be proven.

To prove that (sin 2x) / (1 + cos 2x) = tan x, we will use trigonometric identities.

(sin 2x) / (1 + cos 2x)

(2sin x × cos x) / (1 + (cos²x - sin²x))

(2sin x × cos x) / (cos²x + 2sin x × cos x + sin²x)

We can rewrite the denominator using the Pythagorean identity sin²x + cos²x = 1:

(2sin x × cos x) / (1 + 2sin x × cos x)

(2sin x × cos x) × (1 - 2sin x × cos x) / (1 - (2sin x × cos x)²)

((2sin x × cos x) - (4sin²x × cos²x)) / (1 - 4sin²x × cos²x)

(2sin x - 4sin²x) / (1/cos²x - 4sin²x)

Since tan x = sin x / cos x, we can rewrite the expression:

(2tan x - 4tan²x) / (sec²x - 4tan²x)

(2tan x - 4tan²x) / (1 + tan²x - 4tan²x)

(2tan x - 4tan²x) / (1 - 3tan²x)

2tan x × (1 - 2tan²x) / (1 - 3tan²x)

tan x

So, we have proved that (sin 2x) / (1 + cos 2x) = tan x.

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The function has a vertical asymptote at x = 1, x-intercepts are x = 1 and x = 5, hole at x = 5 and horizontal asymptote is y = 0.

A rational function is a function that can be expressed as the ratio of two polynomial functions. In other words, it is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to zero for any value of x.

To plot the rational function f(x) = (x² - 6x + 5)/(-x + 1)

Vertical asymptote: The denominator of the function (-x + 1) is equal to zero when x = 1.

Therefore, there is a vertical asymptote at x = 1.

x-intercept: To find the x-intercept, we set the numerator equal to zero and solve for x:

x² - 6x + 5 = 0

This quadratic equation can be factored as:

(x - 5)(x - 1) = 0

Therefore, the x-intercepts are x = 1 and x = 5.

y-intercept: To find the y-intercept, we set x equal to zero:

f(0) = (0² - 6(0) + 5)/(-0 + 1) = 5

Therefore, the y-intercept is (0, 5).

Hole: The function has a hole at x = 5 because both the numerator and the denominator become zero at x = 5.

Horizontal asymptote: To find the horizontal asymptote, we need to compare the degrees of the numerator and the denominator. The degree of the numerator is 2 and the degree of the denominator is 1, so the horizontal asymptote is y = 0.

Now, we can plot the function by choosing some values of x and calculating the corresponding values of y:

x y = f(x)

-1 4

0 5

0.5 3.25

1 undefined

2 -1

Image is attached below.

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Equation of circle in standard form- (x + 1)² + (y + 2)² = 1².  radius of the circle is found as 1. centre -(h,k) =  (-1, -2)

We can solve quadratic equations that lack a factor by completing square.

In order to make the left side of an equation a perfect square trinomial, the equation's form must be adjusted.

Given equation is-

x² + y² + 2x + 4y + 4 = 0

Add and subtract 1 in the equation:

x² + y² + 2x + 4y + 4 + 1 - 1 = 0

rearranging:

(x² + 2x + 1) + (y² + 4y + 4) - 1 = 0

This can be written as:

(x² + 2*1x + 1²) + (y² + 2*2y + 2²) = 1

(x + 1)² + (y + 2)² = 1²  ...eq 1

Thus, the standard form of the equation of circle is:

(x - h)² + (y - k)² = r²  ..eq 2

On comparing eq 1 and eq 2

In which radius of the circle is found as 1.

centre -(h,k) =  (-1, -2)

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Step-by-step explanation:

x = 6 x = -5

x - 6 = 0 x + 5 = 0

f(x) = 2(x-6)(x+5)

f(x) = 2(x² +5x - 6x - 30)

f(x) = 2(x² - x - 30)

f(x) = 2x² - 2x - 60

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According to the question the volume formula to find the height of the pyramid is 9 units.

Formula is a mathematical rule or equation expressed symbolically, that describes the relationship between different variables. It is a set of symbols or terms that expresses a relationship between different entities, such as numbers, objects, ideas, or concepts. Formulas are used to calculate, analyze, and predict data, and are essential in many scientific and mathematical fields.

The volume of a pyramid is given by the formula V = (1/3) × b × h, where b is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is a right triangle, we can use the formula to find the area of a right triangle, A = (1/2) × b × h, to find the base of the pyramid.
A = (1/2) × 8 × 9 = 36
Now we can use the volume formula to find the height of the pyramid:
V = (1/3) × 36 × h

108 = (1/3) × 36 × h

108 = 12 × h

h = 9 units

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The unit twenty-six point seven ounces in terms of milligrams is 756932.3  

To convert ounces (oz) to milligrams (mg), we can use the following conversion factor:

1 oz = 28,349.5 mg

Therefore, to convert 26.7 oz to mg, we can multiply 26.7 by the conversion factor as follows:

26.7 oz × 28,349.5 mg/oz = 756932.3  mg

So, there are approximately 756932.3 milligrams in 26.7 ounces of mass.

Comparing the calculated answer with the options given, we see that the answer is closest to 756,498.15 mg, which is not one of the options.

Therefore, we cannot choose any of the options given.

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Answer:

Step-by-step explanation:

Given:-

•α=

•β=

To Find:-

♦The Quadratic Equation using the Given details?

AnsWer:-

↓Quadratic Formula↓

→k[x²-(α+β)x+αβ]

→α+β=+

•Take LCM•

→α+β=+

→α+β=

→αβ=×

→αβ=

↑Using these Values in The Formula↑

→k[x²-(x)+() ]

★Let k=8★

→8[x²-(x)+() ]

→8x²-(-2x)+(-3)

→8x²+2x-3=quadratic Equation

The three consecutive integers are 18, 19, and 20.

Consecutive integers are integers that follow each other in order, without any gaps, and differ by 1. For example, 3, 4, and 5 are consecutive integers because they follow each other in order and differ by 1.

Let's assume that the three consecutive integers are x, x+1, and x+2. Then, according to the problem statement:

4x + (x+2) = 92

Simplifying this equation, we get:

5x + 2 = 92

Subtracting 2 from both sides, we get:

5x = 90

Dividing both sides by 5, we get:

x = 18

Therefore, the three consecutive integers are 18, 19, and 20. We can check that these integers indeed satisfy the condition given in the problem:

4 times the first integer is 4*18 = 72, and when we add the third integer 20 to it, we get 72 + 20 = 92, as required.

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The equation of the linear function represented by the table in slope-intercept form is:

y = 3x + 2

We can find the equation of the linear function represented by the table using the slope-intercept form:

y = mx + b

where "m" is the slope of the line and "b" is the y-intercept.

To find the slope, we can use any two points from the table. Let's use the first and last points:

slope (m) = (y2 - y1) / (x2 - x1)

slope (m) = (14 - 5) / (4 - 1)

slope (m) = 3

Now we can find the y-intercept "b" by substituting one of the points and the slope into the slope-intercept form:

y = mx + b

5 = 3(1) + b

5 = 3 + b

b = 2

So the equation of the linear function represented by the table in slope-intercept form is:

y = 3x + 2

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Answer:

height= 3cm

Step-by-step explanation:

to find the base of each triangle just half the bottom to get 4cm

a^2+b^2=c^2

a^2+4^2=5^2

a^2+16=25

a^2=9

a=√9

a=3

In triangle ABC

a) The value of x = 29⁰

b) The angle c equal to 93⁰

A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.

In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.

We know that:

angle a = 35⁰

angle b = 52⁰

angle c = 3(x+2)⁰

Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:

angle a + angle b + angle c = 180

Substituting the values we know, we get:

35 + 52 + 3(x+2) = 180

Simplifying the equation, we get:

87 + 3x + 6 = 180

3x + 93 = 180

3x = 87

x = 29

Therefore, x = 29⁰

To find angle c, we can substitute the value of x into the equation we were given for angle c:

angle c = 3(x+2)

angle c = 3(29+2)

angle c = 3(31)

angle c = 93

Therefore, angle c is equal to 93⁰.

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Answer:

20 ..............................