g(x)= x²-x-12/x²-4x+4

find g(2)​

Option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

Given integers are m, n, p and q

And q ≠ 0 and p ≠ 0

A = m / p

B = n/ q

Adding A and B

A + B = m / p + n / q

A + B = (mq + np) / pq

as p ≠ 0 and q ≠ 0 so, pq ≠ 0

So, A + B = (mq + np) / pq is a rational number

Therefore, option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

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Given question is incomplete, the complete question is below:

Keisha's teacher gives her the following information:

• m, n, p, and q are all integers, and p≠ 0 and q≠0

•A= m/q and B= n/p

What conclusion can Keisha make?

A: A +B = (mp + nq)/pq, so the sum of a rational number and an irrational number is an irrational number.

B: A•B= (mp + nq)/pq, so the product of two irrational numbers is an irrational number.

C: A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

D: A•B= (mp + nq)/pq, so the product of two rational numbers is a rational number.​

The mean amount for the three bills is  $100  .

In the question ,

it is given that

the electricity bill for June is = $75

the electricity bill for July is = $75

the electricity bill for August is = $150

Sum of the electricity for three months = 75 + 75 + 150 = 300

number of months =  3

The mean of the three months can be calculated using the formula ,

mean = (sum of bill for three months )/( number of months)

Substituting , the  values

we get

mean = 300/3

= 100

Therefore , the mean amount is $100 .

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Answer:

5x+8x-10g+hd

Step-by-step explanation:

please mark me as brainlest

Hey there!

3x + 2x + 6v - 9g + hd + 2v - 1g

= 3x + 2x + 6v - 9g + 1hd + 2v - 1g

COMBINE the LIKE TERMS

= (3x + 2x) + (6v + 2v) - (9g - 1g) + (1hd)

= 3x + 2x + 6v + 2v - 9g - 1g + 1hd

= 5x + 7v - 10g + 1hd

= 5x + 7v - 10g + hd

= hd - 10g + 8v + 5x

Therefore, your answer is:

hd - 10g + 8v + 5x

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

A triangle with side lengths 12,16, and 20 is a right triangle.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.

The formula states that in a right triangle:

The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

(Hypotenuse)² = (Base)² + (Altitude)²

c²=a²+b²

The three numbers which satisfy the above formula are the Pythagorean triplets

properties of right angle:

The largest angle is always 90º and called the hypotenuse which is always the side opposite to the right angle.

The measurements of the sides follow the Pythagoras rule, which cannot have any obtuse angle.

consider c=20 a=12, b=16 substitute in above formula:

20²=12²+16²

⇒400=144+256

⇒400=400

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Answer:

x = -2

Step-by-step explanation:

y = -3x + 2.5

if y = 8.5 then:

8.5 = -3x + 2.5

-3x = 6

x = -2

Given the volume of the sphere as 26667 cm³, we calculated the radius to be approximately 17.7 cm using the formula for the volume of a sphere. By multiplying the radius by 2, we found that the diameter of the sphere is approximately 35.4 cm.

To calculate the diameter of a sphere when given its volume, we can use the formula for the volume of a sphere:

V = (4/3) * π * r³

Where V is the volume and r is the radius of the sphere. Since we are given the volume, we can rearrange the formula to solve for the radius:

r = (\(\sqrt[3]{(3V / (4\pi )}\)))

Substituting the given volume V = 26667 cm³ into the formula, we have:

r = (\(\sqrt[3]{(3 * 26667 / (4\pi )))}\)

Calculating this expression, we find:

r ≈ (\(\sqrt[3]{80001 / \pi ))}\) ≈ 17.7 cm

Now that we have the radius, we can calculate the diameter by multiplying the radius by 2:

d = 2 * r ≈ 2 * 17.7 ≈ 35.4 cm

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Step-by-step explanation:

23, 27, 27, 28, 25, 26, 25, 29, 26, 27, 24, 26, 26, 24, 27, 25, 28, 25, 26, 25, 29, 26, 27, 24, 26

Arranging in ascending order;

23, 24, 24, 24, 25, 25,  25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28,  29, 29

Mean = Sum of mileage / Number of millage

Number of mileage = 25

Sum of mileage = 651

Mean = 651 / 25 = 26.04

Median = Middle Number (13th number) = 26

Mode (Highest occurring) = 26 (7 times)

Answer:

log ( x(x-9)) = 18

Step-by-step explanation:

We know that log a + log b  = log ( a* b)

log x + log (x-9) = 18

log ( x* (x-9)) = 18

log ( x(x-9)) = 18

The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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Answer:

Time when Ben and Melanie are 360 miles apart = 3.871 hours.

Step-by-step explanation:

The question seems unclear, but the sense that could be made from this question is that

Ben leaves with a speed of 51 miles per hour and Melanie also left at the same time in the opposite direction at a speed of 42 miles per hour. My husband wants to find how many hours they both must have been moving to be 360 miles apart.

Let the required time be t.

Let the distance covered by Ben in t hours be x miles.

Let the distance covered by Melanie in t hours be y miles.

Total distance covered = x + y = 360 (eqn 1)

speed = (distance/time)

For Ben

51 = (x/t)

x = (51t) miles

For Melanie

42 = (y/t)

y = (42t) miles

Substituting for x and y in eqn 1

x + y = 360

51t + 42t = 360

93t = 360

t = (360/93) = 3.871 hours.

Ben would have travelled x = 51t = 51 × 3.871 = 197.42 miles

Melanie would have travelled y = 42t = 42 × 3.871 = 162.58 miles

Hope this Helps!!!!

The superposition is the imposing of one wave on the other and resulting in the change of the amplitude of the final wave.

When two or more waves travel through the same space in superposition, their combined amplitudes equal the amplitudes they would have produced individually. For instance, two waves moving in the same direction will pass through each other without causing any distortion on the other side.

The pattern you see when shining light through two slits, the sounds you hear in acoustically sound rooms and music halls, the interference radios receive when moved close to other electronic devices, and any tone produced by a musical instrument are all examples of the superposition principle in action.

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Answer:

Percentage increase = 36%

Step-by-step explanation:

Kitten's weight = 640 grams

Adult's weight = 2918 grams

To find the percentage increase in the kitten's weight;

We will calculate the increase using the formula;

\( Increase = original \; number - new \; number \)

Substituting the values, we have;

Increase = 2918 - 640 = 2278

Mathematically, percentage increase is calculated using the following formula;

\( Percentage \; increase = \frac{increase}{original \; number} * 100\)

\( Percentage \; increase = \frac{2278}{640} * 100\)

\( Percentage \; increase = 3.56 * 100\)

Percentage increase = 35.5 ≈ 36%

Answer:

4b\(\sqrt{5}\)

Step-by-step explanation:

Factor 80\(b^{2}\).

80\(b^{2}\) = 4 * 4 * 5 * b * b

Since there are two 4s and bs, they can be taken out of the square. (Because if you put a square root over 4 squared or b squared, you would get 4 or b.)

Now you are left with 4b\(\sqrt{5}\).

Katie's average speed during the marathon was approximately 12.7 km/h.

To calculate the average speed, we divide the total distance covered by the total time taken. In this case, Katie ran 34 km in a time span of 2.5 hours, which is equivalent to 150 minutes.

Therefore, her average speed is 34 km / 150 min, which is approximately 0.2267 km/min.

To convert this to km/h, we multiply by 60 to get 0.2267 km/min * 60 min/h = 13.6 km/h (rounded to the nearest tenth).

Therefore, Katie's average speed during the marathon was approximately 13.6 km/h.

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Answer:

13

Step-by-step explanation:

Answer:

x=1 y=2

Step-by-step explanation:

Answer:

y= -2x+4

So the y intercept is 4, as its the c in this equation

I think that makes your x intercept as either 8 or 2...

Step-by-step explanation:

Answer:

4.7 * 10 ^9

Step-by-step explanation:

4,700,000,000

Scientific notation is of the form

a * 10 ^b  where a is a number between 1 and less than 10

Move the decimal so that it is a number between 1 and less than 10

4,700,000,000  becomes 4.700000000  and we moved the decimal 9 places to the left  b is +9  ( positive because we moved to the left)  We can drop the extraneous zeros

4.7 * 10 ^9

Answer:

y-intercept=-3

slope=2

The distance from P to l is √10.

To find the distance from point P to l, first we need to find the equation of line l for which we need to calculate slope and y-intercept. After that we have to find the perpendicular distance from point P to l with the help of perpendicular distance formula.

So, the equation of l with points (0,3) and (-4,-9) is:

m = y2 - y1 / x2 - x1

m = -9 -3 / -4 - 0

m = -12 / -4

m = 3

with the help of slope, let's calculate the y-intercept:

y = mx + c

3 = 3(0) + c

c = 3

So, the equation of the line l is y = 3x + 3.

Now, let's calculate the perpendicular distance from point P to line l:

Distance = \(\frac{|Ax1 + By1 + C|}{\sqrt{A^{2} + B^{2} } }\)

Comparing with Ax + By + C = 0, we have A = 3, B = -1, C = 3, and (x1, y1) = (-6, -5). So, after substituting the values in the equation, we get:

Distance = \(\frac{|3(-6) + -1(-5) + (3)|}{\sqrt{3^{2} + (-1)^{2} } }\)

Distance = |-10| / √10

Distance = √10

Therefore, the distance from P to l is √10.

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The equations of the lines that are (a) tangent and (b) normal to the curve y = 2x³ at the point (1, 2) are:

y = 6x - 4 (tangent)y

= -1/6 x + 13/6 (normal)

Given, the curve y = 2x³.

Let's find the slope of the curve y = 2x³.

Using the Power Rule of differentiation,

dy/dx = 6x²

Now, let's find the slope of the tangent at point (1, 2) on the curve y = 2x³.

Substitute x = 1 in dy/dx

= 6x²

Therefore,

dy/dx at (1, 2) = 6(1)²

= 6

Hence, the slope of the tangent at (1, 2) is 6.The equation of the tangent line in point-slope form is y - y₁ = m(x - x₁).

Substituting the given values,

m = 6x₁

= 1y₁

= 2

Thus, the equation of the tangent line to the curve y = 2x³ at the point

(1, 2) is: y - 2 = 6(x - 1).

Simplifying, we get, y = 6x - 4.

To find the normal line, we need the slope.

As we know the tangent's slope is 6, the normal's slope is the negative reciprocal of 6.

Normal's slope = -1/6

Now we can use point-slope form to find the equation of the normal at

(1, 2).

y - y₁ = m(x - x₁)

Substituting the values of the point (1, 2) and

the slope -1/6,y - 2 = -1/6(x - 1)

Simplifying, we get,

y = -1/6 x + 13/6

Therefore, the equations of the lines that are (a) tangent and (b) normal to the curve y = 2x³ at the point (1, 2) are:

y = 6x - 4 (tangent)y

= -1/6 x + 13/6 (normal)

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Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's call the height of the antenna h and the length of the wire connecting the top of the antenna to the ground d.From the problem statement, we know that d = 7 feet and the angle of elevation θ is 75 degrees. The angle of elevation is the angle between the horizontal and the line of sight to the top of the antenna.We can use the tangent function to find h:tan(θ) = opposite / adjacentIn this case, the opposite side is the height of the antenna h, and the adjacent side is the length of the wire d + 0. This is because the wire touches the ground at a point 7 feet away from the base of the antenna, so the total length of the wire is d + 0.Substituting the values we have:tan(75 degrees) = h / (7 feet + 0)Simplifying:h = (7 feet) × tan(75 degrees)Using a calculator:h ≈ 24.16 feetTherefore, the height of the antenna is approximately 24.16 feet.

Answer:

-211

Step-by-step

Answer:

2.5b+2a+5

Step-by-step explanation

Answer:

The third choice or 2.5b+2a+5

Step-by-step explanation:

your welcome!

Answer:

-13

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

Becuase 13's opposite is -13.

(If you still dont understand you can search up negative and positive number lines up to 20!)

Answer:

500

Step-by-step explanation:

answer 500

mark 500 to the question

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Refer to the attachment for figure:

The height of the rectangle = 11 inches

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x= height

Width becomes x+49

Diagonal BD=61 inches

By pythagoras theorem,

BD²=BC²+CD²

61²= (x+49)²+x²

3721=x²+98x+2401+x²

On simplification,

x²+49x-660=0

Find the factors

(x+60)(x-11)=0

x=-60, x=11

Consider positive value for height

height = 11 inches

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i didn’t realize u were chill like that

Step-by-step explanation:

f(1) = f(1 - 1) - 5

f(1 - 1) = f(0) = -20

f(1) = - 5 -20 = -20 - 5

Answer:

my parent said

So definitely - 66666666

Answer:

Jeremy swims 4/5 of a kilometer each day.

Step-by-step explanation:

Since 5 3/5 can be turned into 28/5, then divided by 7/1, you will get 4/5. So Jeremy swims 4/5 of a kilometer each day.

Eli got his answer by multipying 5 3/5 by 7 which was an incorrect process.