Write the equation of a line perpendicular to the line: y=−5/2x+4 that goes through the point (-6, 0).

The value of x given the length, width and perimeter of the rectangle is 15

Length of the rectangle = 2x - 7

Width of the rectangle = x + 9

Perimeter of the rectangle = 94

Perimeter of a rectangle = 2(length + width)

94 = 2{(2x - 7) + (x + 9)}

94 = 2(2x - 7 + x + 9)

94 = 2(3x + 2)

94 = 6x + 4

subtract 4 from both sides

94 - 4 = 6x

90 = 6x

divide both sides by 6

x = 90/6

x = 15

Therefore, x is given as 15.

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Answer:

25.2minute

Step-by-step explanation:

75ft^2=45 minutes

1 ft^2=45/75

and, 7ft*6ft=42ft^2

42ft^2=45*42/75

=25.2minutes

Hope you like the solution. I am not sure of the answer. Mark me as brainlist.

The mean of the squared deviations

What is Squared deviations?

The sum of all scores' squared deviations from the mean is lower than the sum of all scores' squared deviations from any other number. The least squares concept governs this.

What is Mean ?

The average of a group of values is referred to as the mean. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

The term "mean square" refers to the sample variance in the analysis of variance (ANOVA) table, which calculates the mean squared deviation.

The average of the deviations' squared

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Answer:

SUPPLEMENTARY ANGLES

(ADJACENT ANGLES).

Step-by-step explanation:

< 4 and < 6 are on a straight line - adjacent angles and m < 4 + m <  = 180 degrees.  So they are supplementary angles also.

Answer:

3 more girls than boys.

Step-by-step explanation:

Let's change 4:5 to 4x(boys) and 5x(girls).

Since there are 27 students, the equation would be:

4x+5x=27

Then, you simplify the equation:

9x=27

x=3

We are not finished yet!

Since there is 4x boys and 5x girls,

do 4 times 3 which gets you 12 boys

and 5 times 3 which gets you 15 girls.

15 girls minus 12 boys is 3 more girls than boys!

Hope this helps :)

Answer:

250N is the weight of the table

Answer:

a. C(x(h)) = 600h + 500

b. C(8) = 5,300

c. See below.

Step-by-step explanation:

a. C(x(h)) = C(30h) = 20(30h) + 500 = 600h + 500

b. C(8) = 600(8) + 500 = 5,300

c. 5,300 is the cost of making the number of shovels that can be made in 8 hours.

Answer:

14

Step-by-step explanation:

Ok, 60! is a really big number

\(x!=x(x-1)(x-2)...1\)

So we have 60*59*58...*1

2 times 5 is 10 which makes a terminal zero (ending zero)

We need to count how many fives and twos are in 60!

There are 60/5=12 5^1's

There are 60/25=2 5^2's

So 12+2=14

There are way more 2's than fives so we take the lesser number

So the answer is 14

*Note that 60/25 is not 2, we need an integer rounded down

Answer:

n = -8, 7

Step-by-step explanation:

Your equation is:

\(\displaystyle{n^2+n=56}\)

Arrange the terms in the quadratic expression, ax² + bx + c:

\(\displaystyle{n^2+n-56=0}\)

Factor the expression, thus:

\(\displaystyle{\left(n+8\right)\left(n-7\right)=0}\)

This is because 8n-7n = n (middle term) and 8(-7) = -56 (last term). Then solve like a linear which results in:

\(\displaystyle{n=-8,7}\)

Hello!

\(\sf n^2 + n = 56\\\\n^2 + n - 56 = 0\\\\\\n = \dfrac{-b\±\sqrt{b^2-4ac} }{2a} \\\\\\n = \dfrac{-1\±\sqrt{1^2-4*1*(-56)} }{2*1}\\\\\\n = \dfrac{1\±15}{2} \\\\\\\boxed{\sf n = 7 ~or ~-8 }\)

The trigonometric relations from the triangles are

a) tan A = 5/12

b) sin C = 3/5

c) cos X = 3/5

d) sin Z = 4/5

e) tan Z = 4/3

f) tan X = 12/5

Here, we have,

Given data ,

a)

The triangle is ΔABC

tan A = opposite side / adjacent side

Substituting the values in the equation , we get

tan A = 10/24

tan A = 5/12

b)

The triangle is ΔABC

sin C = opposite side / hypotenuse

Substituting the values in the equation , we get

sin C = 24/40

sin C = 3/5

c)

The triangle is ΔXYZ

cos X = adjacent side / hypotenuse

Substituting the values in the equation , we get

cos X =21/35

cos X = 3/5

d)

The triangle is ΔXYZ

sin Z = opposite side / hypotenuse

Substituting the values in the equation , we get

sin Z = 32/40

sin Z = 4/5

e)

The triangle is ΔXYZ

tan Z = opposite side / adjacent side

Substituting the values in the equation , we get

tan Z = 28/21

tan Z = 4/3

f)

The triangle is ΔXYZ

tan X = opposite side / adjacent side

Substituting the values in the equation , we get

tan X = 12/5

Hence , the trigonometric relations are solved from the triangles

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complete question;

Find the value of each trigonometric ratio

The negative sign indicates that the power is flowing in the negative x-direction.

To solve this problem, we can use the relationships between the electric field (E), magnetic field (H), and power density (P) in electromagnetic waves.

Given:

Incident H field phasor: H = ay8e30x (A/m)

Relative electrical permittivity of the dielectric medium: εr = 4

Boundary surface area radius: r = 60 cm = 0.6 m

We'll go through each part of the problem step by step:

a) Electric field phasor:

The relationship between the electric field and magnetic field in a plane wave is E = (1/η) x H, where η is the intrinsic impedance of the medium.

The intrinsic impedance of a dielectric medium is given by η = η0/√εr, where η0 is the impedance of free space (approximately 377 Ω).

Substituting the values, we have:

η = η0/√εr = 377/√4 = 188.5 Ω

Thus, the electric field phasor is:

E = (1/η) x H = (1/188.5) x (ay8e30x) = (ay4.22e-2x) V/m

b) Average incident power density vector:

The average power density (P) of an electromagnetic wave is given by P = (1/2)Re(E x H*), where H* denotes the complex conjugate of H.

Taking the real part, we have:

P = (1/2)Re(E x H*) = (1/2)Re[(ay4.22e-2x) x (ay8e30x)*]

= (1/2)Re[(-32.16ae28x)] = -16.08e28x W/m²

The negative sign indicates that the power is flowing in the negative x-direction.

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All humans are considered to be consumers. A consumer is an organism that obtains its energy and nutrients by feeding on other organisms.

As humans, we consume food to provide our bodies with the energy and nutrients necessary for survival. Whether we eat meat, plants, or a combination of both, we are still consumers. In the case of herbivores, they consume only plant matter, but they are still considered consumers because they are obtaining their energy and nutrients from other living organisms (plants). Therefore, regardless of our dietary choices, all humans are classified as consumers in ecological terms.

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Suppose $11,000 is invested at 5% interest compounded continuously. We need to find the time that it will take for the investment to grow to $22,000. We will use the formula for continuous compounding which is given by the model:

A = Pert

where A is the final amount, P is the principal amount, r is the interest rate, and t is the time.

We can solve for t by substituting the given values:

A = $22,000
P = $11,000
r = 0.05 (5% expressed as a decimal)

$22,000 = $11,000e^{0.05t}

Dividing both sides by $11,000, we get:

2 = e^{0.05t}

Taking the natural logarithm of both sides, we get:

ln 2 = 0.05t

Solving for t, we get:

t = ln 2 / 0.05 ≈ 13.86

Therefore, it will take approximately 13.86 years for the investment to reach $22,000.

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The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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The volume of the shape will be 50cm3.

It should be noted that the volume van be found by multiplying the area by the height. The volume will be:

= 10 × 5

= 50cm³

The standard deviation volume will be:

= 0.1 × 50

= 5cm

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The volume of a sphere is given by the following formula:

Where r is the radius of the sphere.

By replacing 2.2 for r and 3.14 π, we get:

Then, the volume of the sphere equals 4.58 cubic centimeters

Answer:

505

Step-by-step explanation:

you first do 2020x2020 because you can see from the pattern, the inside squares are 1x1, 2x2, 3x3, so the 2020th inside squares would be 2020x2020. then, you would do 2020x4 for the shaded squares because if you see from the pattern, its 1x4, 2x4, 3x4, so the 2020th would be 2020x4. then you divide \(\frac{2020*2020}{2020*4}\) which is 505.

Answer: 84

Step-by-step explanation:

21 * 4=84

Always multiply by 4.

Answer:

0.01190476, but since you have to round to the nearest hundredth your answer should be 0.01

Answer:

0.01

Step-by-step explanation:

6800 seconds converted into weeks is 0.011243386

If you round it to the nearest hundredth, the number next to the second 1 from 0.011243386 the second one tells the first one to stay the same so you get 0.01.

Hope this helps!!

Option a) ab + bc > ac is correct.

The first method by which we can solve this question is,

We have to know about the property of the triangle,

According to the property of the triangle, if we consider a triangle with lines ab, bc, ac and  -

Therefore, we can conclude that ⇒ ab + bc > ac and ab - bc < ac

In the second method, let us consider the given triangle as right-angled,

So, according to the property of the right-angled triangle or Pythagoras' Theorem,

The square of the hypotenuse is equal to the square of the other two sides, let us consider the sides of the triangle = ab, bc, ac.

ABC is a right-angled triangle -

\(ab^{2} + bc^{2} = ac^{2}\)

\(ab + bc > ac\)

Therefore, we can conclude that, options a) ab + bc > ac is correct.

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Using the slope concept, it is found that:

In this problem, the vertical change is the altitude of 10,000 feet.

The minimum horizontal distance is with an angle of 35º, hence:

\(\tan{35^{\circ}} = \frac{10000}{d}\)

\(d = \frac{10000}{\tan{35^{\circ}}}\)

\(d = 14281.5\)

The maximum horizontal distance is with an angle of 33º, hence:

\(\tan{33^{\circ}} = \frac{10000}{d}\)

\(d = \frac{10000}{\tan{33^{\circ}}}\)

\(d = 15398.6\)

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Given that the company charges $31.95 for the day and $0.35 per mile to rent a 10 foot truck.

(A) The aim is to find the cost of renting a 10 foot moving truck for a day.

Assume that m is the number of miles are driven and B is total cost.

(B) The aim is to find the cost at 70 miles,

(C) The aim is to find x if B is 150.

To find the exact value of cos(a - B), where angle a lies in Quadrant II and angle B lies in Quadrant I, we can use trigonometric identities and the given information.

In the second paragraph, we will explain how to find the values of sin a and sin B using the given information. Then, using the difference formula for cosine, we will calculate the exact value of cos(a - B).

Since angle a lies in Quadrant II, we know that tan a = -3/4. We can use the properties of tangent to find the value of sin a. Since tangent is negative in Quadrant II, we can write tan a = -sin a / cos a. Substituting the given value of tan a, we have -3/4 = -sin a / cos a. Cross-multiplying and rearranging, we get sin a = 3/4.

Similarly, since angle B lies in Quadrant I, we know that cos B = 3/8. We can use the Pythagorean identity sin^2 B + cos^2 B = 1 to find the value of sin B. Substituting the given value of cos B, we have sin^2 B + (3/8)^2 = 1. Solving for sin B, we get sin B = √(1 - (3/8)^2) = √(1 - 9/64) = √(55/64) = √55/8.

Now that we have the values of sin a and sin B, we can use the difference formula for cosine: cos(a - B) = cos a * cos B + sin a * sin B. Substituting the known values, we have cos(a - B) = cos a * cos B + sin a * sin B = cos a * (3/8) + (3/4) * (√55/8).

To determine the exact value of cos(a - B), we need the value of cos a. Since we don't have that information given, we cannot provide an exact numerical answer. However, you can substitute the given values of cos B and the calculated values of sin a and sin B into the formula to obtain the exact expression for cos(a - B).

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eighteen thirds

two thirds refers to : \(\sf \sf \dfrac{2}{3}\)

\(\sf \rightarrow 9 * \dfrac{2}{3}\)

\(\sf \rightarrow \dfrac{9*2}{3}\)

\(\sf \rightarrow \dfrac{18}{3}\)     [ also refereed as eighteen thirds ]

Answer:

\(6\\six~is~2/3~of~9\\this~can~also~be~looked~at~as\\2 * 3 = 6\\\)

↓ Second problem

\(11/27\\18/27\\11/3\\18/3\)

                                          Hope it helps, be great!

Answer:

Cost of peach is 72 p each.

Step-by-step explanation:

Total amount was 5x100 = 500 p

Amount of apples were ( 4 x 60) = 240 p

Received change = 44p

Total amount for 3 peaches were = 500-240-44 = 216

Cost of 1 peach = \(\frac{216}{3}\)

= 72p

Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

The work done by the force is found to be  254 J.

Given,F = 4i - 8j + 9k

Initial position of object = (0, 6, 4)

Final position of object = (4, 14, 18)

The work done by the force to move the object from initial position to final position is calculated using the formula:

W = F · d

where F is the force and d is the displacement or distance traveled by the object along a straight line from initial position to final position.

In order to find displacement vector d, we need to find the difference between final and initial positions.

That is,

d = (4i - 8j + 9k) - (0i + 6j + 4k)  = 4i - 14j + 14k

Therefore, the displacement vector is

d = 4i - 14j + 14k.

To find the work done, we need to calculate the dot product of F and d.

That is,

W = F · d

= (4i - 8j + 9k) · (4i - 14j + 14k)

= (4 * 4) + (-8 * -14) + (9 * 14)

= 16 + 112 + 126

= 254 J

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The algorithmic complexity is O(7n), which means the running time is proportional to 7 times the size of the problem.

The algorithmic complexity of an algorithm with a problem size of n is expressed as O(7n). This means that the running time of the algorithm is proportional to 7 times the size of the problem. In other words, when the problem size increases, the running time of the algorithm increases in a linear fashion, with the running time being directly proportional to the number of basic operations being performed. This is because each of the 7 basic operations must be performed for each element of the problem size, and so the larger the problem size, the longer it takes for the algorithm to run. Thus, the algorithmic complexity of the algorithm is O(7n).

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If 0 = pi/ radians. Then the terminal point is (1, 0), and tanθ = 0.

Given the equation 0 = π /  radians.

To find the terminal point we need to use the below formula,θ = 2πn + α

Where,θ = Angle of Terminal Point = Number of revolutions

α = Remaining Angle Thus, here α = 0 radians = 2πn + 0n solving the above equation,

we get,n = 0, 1, 2, ... etc.

As the radian measure is given in the equation, we know that the angle is at the 3 o'clock position on the unit circle, which is also known as the standard position.

So, the terminal point is (1, 0).To find tanθ, we have to use the formula given as tanθ = y / x, where x and y are the coordinates of the terminal point.

Here, x = 1 and y = 0. Hence, tanθ = y / x = 0 / 1 = 0.

Therefore, the terminal point is (1, 0), and tanθ = 0.

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Answer:

3

Step-by-step explanation:

i think because 12-9=3