5. What is the equation, in slope-intercept form, of the line that is perpendicular to the one shown and goes through the point (-1,-4)? :

Please step by step

Answer:

y = -1x -2

Step-by-step explanation:

For Igor's answer, there are 6 pencils in each pack. For Elsa's answer, there are 18 pencils in 3 packs. You just need to devide 36 by 3 and 6 to find each of their answers.

The required value of x is 22 degrees for the given figure.

Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.

As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:

According to the given figure, it can be written as follows:

2x + 24 + 6x - 20 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176/8

x = 22

Therefore, the required value of x is 22 degrees for the given figure.

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The complete question is as follows:

Find the value of x for the below figure.

The complete square of the given numbers are-

Part a: 6(x + 1/4)^2 + 69/8

Part b: (x + 5/2)^2 + 27/2

Part c: -(x + 3)^2 + 18

For the given question

Part a: 6x^2+3x+9

Tale 6 commom;

6(x^2 + x/2 + 3/2)

Add and subtract 1/16 to the equation;

6(x^2 + x/2 + 1/16 - 1/16 + 3/2)

6((x^2 + x/2 + 1/16) - 1/16 + 3/2)

6((x + 1/4)^2 + 23/16)

6(x + 1/4)^2 + 69/8

Part b: x^2+5x+26

Add and subtract 25/4 to the equation;

x^2 + 5x + 25/4 - 25/4 + 26

(x^2 + 5x + 25/4) - 25/4 + 26

(x + 5/2)^2 + 27/2

Part c: -x^2+6x+9

Taking - 1 common.

-(x^2 - 6x - 9)

Add and subtract 9 in the equation;

-(x^2 - 6x + 9 ) - 9  - 9)

-((x^2 - 6x + 9 ) - 9  - 9)

-((x + 3)^2 -18)

-(x + 3)^2 + 18

Thus, the complete square of the umber are found.

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Answer: 123

Step-by-step explanation:

what you mean bae

The number of cans required to paint an area of 2000 square units is equal to 5 cans.

As given in the question,

Total area to be painted is equal to 2000 square units.

Area covered by one can of paint is equal to 400 square units

400 square units = 1 can of paint

⇒ 1 square units = ( 1 / 400 ) cans of paint

⇒ 2000 square units =  ( 2000 / 400 ) cans of paint

⇒ 2000 square units = 5 cans of paint

Therefore, the number of cans required to paint an area of 2000 square units using given can is equal to 5 cans.

The above question is incomplete, the complete question is:

How many cans of paint are needed to cover an area of 2000 square units if one can of paint covers in area 400 square units?

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In school suspension

The marginal cost of the function C(Q) = aQ^3 + bQ^2 + cQ + d is given by MC(Q) = 3aQ^2 + 2bQ + c.

To find the marginal cost, we need to differentiate the cost function C(Q) with respect to Q. Let's differentiate each term separately:

d/dQ (aQ^3) = 3aQ^2

d/dQ (bQ^2) = 2bQ

d/dQ (cQ) = c

Adding these differentials together, we get the marginal cost:

MC(Q) = 3aQ^2 + 2bQ + c

The critical Q* at which the cost is minimized can be found by setting the marginal cost MC(Q) equal to zero and solving for Q. However, to determine the condition on a, b, c, and d for cost minimization, we would need more information or constraints related to the problem.

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The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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Answer:

3u+12

Step-by-step explanation:

The number, in this case 3, is being multiplied by the terms inside the parenthesis, u and 4.

3*u=3u

3*4=12

So the simplified version is 3u+12.

-hope it helps

The function is symmetric, we can again simplify the calculation by integrating it from 0 to x and then multiplying the result by 2.

(i) To determine the required relation between the constants a and b, we can start by noting that for any probability distribution function, the area under the curve must equal 1. In this case, we need to find the value of a that makes the area under the curve equal to 1.
Since the given function f(x) is an exponential function, we can integrate it over the entire real line to find the area under the curve. However, since the function is symmetric around the y-axis, we can simplify the calculation by integrating it over the positive x-axis and then multiplying the result by 2.
∫[0,∞] a * exp(-b * x) dx = 1
Solving this integral equation will give us the required relation between the constants a and b.
(ii) To determine the probability distribution function F(x), we can integrate the probability density function f(x) from negative infinity to x. Since the function is symmetric, we can again simplify the calculation by integrating it from 0 to x and then multiplying the result by 2.
F(x) = 2 * ∫[0,x] a * exp(-b * t) dt
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Answer: Yes, the two triangles are similar.

Step-by-step explanation:

The triangle on the right needs to be turned. But you don't necessarily have to do that for this problem, just match up the two highest numbers, the two middle, and the two lowest.

Put them over each other:

32/48, 30/45, 24/36

Divide.

Each ratio equals 2/3

Answer:

9x² + 12x + 16

Step-by-step explanation:

(27x³ - 64) / (3x - 4)

= (3x - 4)(9x² + 12x + 16) / (3x - 4)

= 9x² + 12x + 16

The two positive integers that maximize the sum of their squares while satisfying the constraint x + y = 10 are x = y = 5.

To set up the optimization problem, let x and y be the two positive integers we are trying to find. Then, we want to minimize and maximize the sum of their squares, which can be expressed as:

Minimize: \(f(x, y) = x^2 + y^2\)

Subject to: x + y = 10 and x, y > 0

Maximize: \(g(x, y) = x^2 + y^2\)

Subject to: x + y = 10 and x, y > 0

Note that the constraint x, y > 0 means that we are looking for positive integers, and the constraint x + y = 10 means that their sum must be 10.

To solve the minimization problem, we can use the method of Lagrange multipliers. The Lagrangian function is:

L(x, y, λ) = \(x^2 + y^2 + λ(10 - x - y)\)

Taking the partial derivatives with respect to x, y, and λ, we get:

∂L/∂x = 2x - λ = 0

∂L/∂y = 2y - λ = 0

∂L/∂λ = 10 - x - y = 0

Solving these equations simultaneously, we get:

x = y = 5

λ = 10

Therefore, the two positive integers that minimize the sum of their squares while satisfying the constraint x + y = 10 are x = y = 5. The minimum value of the sum of their squares is:

\(f(5, 5) = 5^2 + 5^2 = 50\)

To solve the maximization problem, note that the function x^2 + y^2 is a continuous and increasing function of x and y. Since x and y must sum to 10 and be positive integers, the maximum value of their sum of squares occurs when one of them is as large as possible, which is 5. Thus, the maximum value of the sum of their squares is:

\(g(5, 5) = 5^2 + 5^2 = 50\)

Therefore, the two positive integers that maximize the sum of their squares while satisfying the constraint x + y = 10 are x = y = 5.

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Answer:

79

Step-by-step explanation:

80 divided by 8+72-3

10+72-3

82-3

79

Hope this helps!

Answer:

it is c

Step-by-step explanation:

Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, height of the water tower is 40.16 feet tall.

To calculate the height of the water tower, we can use the formula for the volume of a cylinder. This formula is V = πr^2h, where V is the volume, π is the constant pi (3.14), r is the radius of the cylinder, and h is the height of the cylinder. In this case, the radius of the cylinder is 10 feet and the volume of the cylinder is 12,560 gallons. We can rearrange the formula to solve for h, giving us h = V/πr^2. Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, the water tower is 40.16 feet tall.

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Given fractions can be written as  2/4 = 2*1/4 , 2/6 = 2*1/6 and5/2  = 5*1/2

what is a fraction?

A fraction is a numerical quantity that represents a part of a whole. Fractions are typically written in the form of a numerator (the top number) over a denominator (the bottom number), separated by a horizontal line. For example, 3/4 is a fraction that represents three parts out of a total of four equal parts.

Fractions can be proper (when the numerator is less than the denominator, e.g., 2/5) or improper (when the numerator is greater than or equal to the denominator, e.g., 7/4).

Fractions can also be equivalent (representing the same part of a whole in different ways, e.g., 2/4 and 1/2), or they can be added, subtracted, multiplied, and divided to obtain new fractions. Fractions are used in a variety of mathematical operations, including measurements, ratios, and percentages.

1. 2/4 = 2/1*1/4 = 2*1/4

so here it is given that , 2/4 = 2* ? / 4
so here the numerator could be 1

so we get, 2/4 = 2*1/4

similarly ,

2. 2/6 = 2/1*2/6 = 2*1/6

3. 5/2 = 5/1*1/2 = 5*1/2

4. 3/3 = 3/1*1/3 = 3*1/3

5. 10/8 = 10/1*1/8 = 10*1/8

6. 2/5 = 2/1*1/5 = 2*1/5

7. 1/6 = 1/1*1/6 = 1*1/6

8. 9/5 = 9/1*1/5 = 9*1/5

9. 9/3 = 9/1*1/3 = 9*1/3

10. 9/10 = 9/1*1/10 = 9*1/10

11. 9/12 = 9/1*1/12 = 9*1/12

12. 8/10 = 8/1*1/10 = 8*1/10

13. 6/3 = 6/1*1/3 = 6*1/3

14. 6/8 = 6/1*1/8 = 6*1/8

15.  4/12 = 4/1*1/12 = 4*1/12

Therefore, Given fractions can be written as  2/4 = 2*1/4 , 2/6 = 2*1/6 and5/2  = 5*1/2

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Answer:0

<—————|—————>
                0

Step-by-step explanation:

Answer:

x ≈ 11.6 m

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² + 10.7² = 15.8²

x² + 114.49 = 249.64 ( subtract 114.49 from both sides )

x² = 135.15 ( take square root of both sides )

x = \(\sqrt{135.15}\) ≈ 11.6 m ( to the nearest tenth )

Answer:

1st q answer is f(x) is one- to -one function and 2nd q answer is 2

Answer:

Step-by-step explanation:

Let f(x) = y

y = 2x - 3

x = y + 3 / 2

inverse of f(x) = x + 3 / 2

f [g(2)]

f [2+3/2]

f [5/2]

(2×5/2)-3

5-3

= 2

Step-by-step explanation:

The value of 3³ is 27

And

The value of ³√125 is 5.

Hope it will help :)❤

(a) The required value of a cube of 3 or  \(3^3\) is 27.

(b) The required value of a cube root of 125 or ∛125 is 5.

(a)

The value of \(3^3\) (3 raised to the power of 3) is calculated as follows:

\(3^3\) = 3 × 3 × 3 = 27

Therefore, \(3^3\) is equal to 27.

(b)

The cube root of 125 can be found by determining which number, when raised to the power of 3, equals 125. In this case:

∛125 = 5

Therefore, the cube root of 125 is 5.

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Answer:

\(y = \frac{1}{8}x -7\)

Step-by-step explanation:

Find the slope using (8, -6) and (-8, -8):

\(m=\frac{-8-(-6)}{-8-8} \\\\m=\frac{-8+6}{-8-8} \\\\m=\frac{-2}{-16}\\\\m=\frac{2}{16}\\\\m=\frac{1}{8}\)

\(y=mx + b\\\\y = \frac{1}{8}x + b\)

Now, we use either of our points (8, -6) OR (-8, -8) to find b.

I will be using (8, -6):

\(y = \frac{1}{8}x + b\\\\-6=\frac{1}{8}(8) + b\\\\-6=1+b\\\\-1 \ \ -1\\\\-7=b\)

\(y = \frac{1}{8}x + b== > y = \frac{1}{8}x -7\)

Check your answer manually: (-8, -8)

\(y = \frac{1}{8}x -7\\\\-8 = \frac{1}{8}(-8) -7\\\\-8=-1-7\\\\-8=-8\)

This statement is correct.

*You can also view the attached graph to verify the answer, meaning that those two points should lie on the same line.*

Hope this helps!

There is an 88% chance that he will complete his next free throw.

Now, When Steph Curry has an 88% free throw rating, that means on average he makes 88 free throws out of 100 attempts.

Now, let's look at the probability of him making 16 free throws in a row.

Since each free throw is independent of the others, the probability of making 16 in a row is simply 0.88 to the power of 16

since he has an 88% chance of making each one).

That comes out to about, 0.284, or 28.4% chance of making 16 in a row.

Therefore, the probability that he completes his next free throw after making 15 in a row is still 88%,

since each free throw is independent of the others.

So, there is an 88% chance that he will complete his next free throw.

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Answer:

x = \(\frac{qy}{t}\)

Step-by-step explanation:

\(\frac{tx}{q}\) = y ( multiply both sides by q to clear the fraction )

tx = qy ( isolate x by dividing both sides by t )

x = \(\frac{qy}{t}\)

Answer:

-7/3

Step-by-step explanation:

5-(12)/3

-7/3

If "rotor-blades" of a helicopter are 19 ft long , rotating at 190 rpm, then

(a) angular speed of rotor is 119.38 radians/second,

(b) linear speed at tip of blade is .

The "Angular-Speed" is defined as the rate at which an object rotates or revolves around a fixed point or axis.

The Length of the rotor blades is = 19 ft,

The number of Rotations per minute is (rpm) = 190 rpm,

Part (a) : The Angular speed of the rotor (w) is written as follows:

⇒ w = 2 × π × (rpm/60),

where π = 3.14159, rpm = 190,

Substituting the values,

We get,

⇒ w = 2 × 3.14159 × (190/60)

⇒ w ≈ 119.38 radians/second.

So, the angular speed is 119.38 radians/second.

Part (b) : Linear speed of a point on the "tip-of-blade" can be calculated using the formula:

⇒ v = r × w,

where r = length of "rotor-blade" and w = angular speed of rotor.

Substituting the values,

We get,

⇒ v = (19 ft) × (119.38 radians/second),

⇒ v ≈ 2265.22 ft/second,

Therefore, the linear-speed of a point is 2265.22 ft/second.

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