Which of the following is equal to the rational expression below when x+112x² – 121x +11A. +11B.X+ 11c. -11XD. X-11

50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.

10m = 90 - 50

10m = 40

m = 40/10

m = 4

Integers are numbers such as

And odd numbers are

Answer

(3/8) × (1/5) = (3/40)

(6/10) × (3/4) = (9/20)

Explanation

We are asked to solve the given expressions

(3/8) × (1/5)

And

(6/10) × (3/4)

For (3/8) × (1/5)

For (6/10) × (3/4)

Hope this Helps!!!

The tangent-secant theorem states that given the segments of a secant segment and a tangent segment that share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.

Graphically,

In this case, we have:

Now, we can solve the equation for x:

Therefore, the value of x is 20/3 or approximately 6.67.

we have the following:

Therefore:

Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.

To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car

Solution:

Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,

It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be

It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.

Therefore:

Combining equation 1 and equation 2

Substitute equation 1 into equation 2

Divide through by 4

Substitute S₁ in equation 1

Hence,

The slower car travels at 43 miles per hour(mph), and

The faster car travels as 51 miles per hour(mph)

Answer:

B. A = 14

C = 4

Explanation:

The system of equation is:

A + 10C = 54

A + 9C = 50

So, we can solve for A using the first equation:

A + 10C = 54

A + 10C - 10C = 54 - 10C

A = 54 - 10C

Now, we can replace A by (54 - 10C) on the second equation, so:

A + 9C = 50

(54 - 10C) + 9C = 50

54 - 10C + 9C = 50

54 - C = 50

54 - C + C = 50 + C

54 = 50 + C

54 - 50 = 50 + C - 50

4 = C

Then, we can replace C by 4 and calculate A, so:

A = 54 - 10C

A = 54 - 10(4)

A = 54 - 40

A = 14

Therefore, the solution of the system is:

A = 14

C = 4

We need to know how to calculate compound interest to solve this problem. The present value is $2577.32

Compound interest is the interest that is earned on interest. Inorder to calculate the compound interest we need to know the principal amount, the rate of interest, the time period and how many times the interest is applied in per time period. In this question we know the amount after 9 years and the rate of interest is 9.5% and the interest is compounded quarterly. We will use the formula for compound interest get the principal value.

A=P[tex](1+\frac{r}{n}) ^{nt}[/tex]

where A= amount, P= principal, t=time period, n= number of times interest applied per time period, r=rate of interest

A=$6000

r=9.5%

t=9 yrs

n=4

6000=P[tex](1+\frac{9.5}{400} )^{36}[/tex]

6000= P x 2.328

P=6000/2.328=2577.32

Therefore the present value that will grow to $6000 in 9 years is $2577.32

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Answer:

B. 1

Explanation:

Given the inequality:

To find the critical number, first, change the inequality sign to the equality sign :

Next, solve for x:

Therefore, from the options, 1 is the critical number.

The correct option is B.

The solution:

Given:

Required:

To compare the volume and area of bot shapes.

The Sphere:

The Cube:

Clearly, we can see that:

Both shapes have approximately the same volume.

But the cube has a greater volume than that of the sphere.

Therefore, the correct answer is [option 4]

Let's begin by listing out the information given to us:

To complete the perfect square ((x-h)²) we add and subtract constants:

Explanation:

The equation for a line in the slope-intercept form is:

Where 'm' is the slope and 'b' is the y-intercept.

We can find both with only two points from the line. The slope is:

(x1, y1) and (x2, y2) are points on the line.

With only one of these points, once we know the slope, we can find the y-intercept by replacing x and y by the point. For example:

And then solve for b.

In this problem we can use any pair of points from the table. I'll use the first two:

• (3, -4.5)

• (5, -9.5)

The slope is:

And the y-intercept - I'll use point (3, -4.5) to find it;

Answer:

• Slope: -5/2

• y-intercept: 3

The correct answer is option B

x = 0,1 are the real solutions of the equation .

What are real solutions in math?

 4x³ - 8x² + 4x = 0

x( 4x² - 8x + 4 ) = 0

x( 4x² - 4x - 4x + 4 ) = 0

x ( 4x ( x - 1) -4 ( x - 1 )) = 0

x ( ( 4x - 4 ) ( x - 1 ) ) = 0

x = 0

4x - 4 = 0 ⇒ x = 1

x - 1 = 0 ⇒ x = 1

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step1: Write out the formula for exponential growth

Hence we have

Step2: substitute into the formula in step 1

Hence the right option is A

Given:

The sequence of number of stars is 2,4,8,16

a) To find the common ratio of the pattern.

Hence the common ratio is 2.

b) To find the explicit formula for the pattern.

The general for a geometric progression sequence is,

Hence, the formula for the above pattern will be,

c) To find the number of stars in 11th set.

Substitute n=11 in the explicit formula of the pattern.

Hence, the number of stars in 11th set will be 2048.

The number of kilometers per hour in 880 feet / minute can be found to be 16.09 kilometers per hour

Based on the conversion rates between kilometers and feet, the number of feet per minute for each kilometer per hour is 54.6807 feet per minute.

In other words, 1 km / h is equal to 54.6807 feet per minute.

If there are 880 ft / minute therefore, the number of kilometers per hour is:

= Speed in feet per minute / feet per minute per kilometer per hour

= 880 / 54.6807

= 16.09 kilometers per hour

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Multiply both sides by t:

Multiply both sides by 10:

Divide both sides by 12:

Answer

The least likely to occur is Event C

Explanation

A.

P(spade card) = 13/52

P(queen) = 4/51 Note: Without replacement

⇒ 13/52 x 4/51

= 52/2652

= 0.0196

B.

P(a spade) = 13/52

P( another spade) = 12/51 Note: Without replacement

⇒ 13/52 x 12/51

= 156/2652

= 0.0588

C.

P(an ace) = 4/52

P(king) = 4/51

⇒ 4/52 x 4/51

= 16/2652

= 0.006

∴ The least likely to occur is Event C

For statement one:

We need to add up to complex numbers and their sum must give us equal to 10.

Also, we need to use the complex numbers:

5+i√15 and 5-i√15.

Then, we can use:

(5+i√15)+( 5-i√15) =

5+i√15+5-i√15 =

5+5+ i√15-i√15 =

= 10 + 0

= 10

For the second statement:

We need to show the product of complex numbers:

Then, we use:

(5+i√15)(5-i√15))=

5*5 - 5*i√15) +5*i√15) +√15*√15=

25 + 0 + 15=

40

5x + 2y = -12 (a)

3y + 5x =-8 (b)

First, write (b) in the ax+by=c form:

5x + 3y = -8 (b)

Now, subtract (b) to (a) to eliminate x

5x + 2y = -12

-

5x + 3y = -8

__________

-y = -4

solve for y:

Multiply both sides by -1

y=4

Replace y=4 on (a) and solve for x:

5x + 2 (4) = -12

5x + 8 = -12

5x = -12-8

5x = -20

x = -20/5

x = -4

Solution: (-4,4)

In order to corroborate that the points belong to the equation, we must subtitute the points into the equation.

If we substitute the points from option A, we get

for (1,8), we have

then, option A is false.

Now, if we substitute the points in option B, for point (2,5), we have

which is correct. Now, for point (-1.8) we obtain

Since all the points fulfil the equation, then option B is an answer.

Lets continue with option C and D.

If we substitute point (1,8) from option C, we have

then, option C is false.

If we substite point (4,11) from option D, we get

then, option D is false.

Therefore, the answer is option B.

We get 1.45 dollars per pound when we convert 3.2 Euros per kilogram to dollar per pound.

According to the question,

We have the following information:

3.2 Euros per kilogram

We need to convert its units into dollars per pounds.

We know that 1 Euro is approximately equal to 1 US dollar and 1 kilogram of weight is equal to 2.205 pounds.

(Note that there are various conversions from Euro to dollars which have 1 Euro equal to 1.00755 and many other values. In this case, we have rounded it off to 1 to avoid any confusion.)

(We know that per means the unit given is in divide.)

So, we have:

(3.2*1)/(1*2.205)

3.2/2.205

1.45 dollar per pounds

Hence, the conversion to dollars per pounds is 1.45 dollar per ponds from Euros per kilogram.

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We will have the following:

The surface area of the onion can be best modeled by a sphere. Base on the model, the approximate area of the onion is 38.5 square inches:

The addition is the operation that puts together two quantities of numbers. It is represented by the signal "+". To add the two numbers we can use a visualization method as shown below:

We have two sticks on the left and two sticks on the right, we need to add them both, this is the same as joining them together, the result is 4 sticks. The answer is 4.

Answer:

the answer is 11

duuuh

Step-by-step explanation:

We will see that the function f(x) is:

f(x) = 15*(x - 3)

Evaluating it in x = -3 we can see that:

f(-3) =  -90

We know that when we divide f(x) by (x - 3), the quotient is 15. (that is the statement given in the question)

so we can write the equation:

f(x)/(x - 3) = 15

And we can solve this for f(x) as if it were a variable, then we get:

f(x) = 15*(x - 3)

Now, if we evaluate the function in x = -3 (this is replacing the variable x with the number -3), we will get:

f(-3) = 15*(-3 - 3) = 15*(-6) = -90

So the statement:

f(-3) = 15

Is false

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SOLUTION

For rational approximation of 37, it means we are to obtain the close estimate for the square root of 37.

using perfect squares,

The perfect square number immediately lower than 37 is

The perfect square number immediately higher than 37 is

Then we set up the problem as in the image below

The distance between 36 to 37 is lower than the distance between 49 to 37, hence the rational aproximation of 37 will be closer to the square root of 36 than the square root of 49.

This accouunt for the sqaure root of 37 in the image above

Therefore

The rational aprosimation of 37 using perfect square is 6.1

Explanation

Step 1

Let

then

I hope this helps you

The formula for the logistic regression model that best fits the data is,

The graph, tables and details of the population data will be shown below

a) The equation that best fits the regression model is,

Substitutes the data above into the equation

Hence,

b) In the year 2030, t = 20

Hence, the answer is

c) Given that

Multiply both sides by 1+3.98e^{-0.02t}

Subtract 1 from both sides

Divide both sides by 3.98

Apply exponent rule

Divide both sides by -0.02

Hence, the population will reach 23million in the year 2023.

d) The carrying capacity for Florida's population is equal to the value of a.

Hence, the carrying capacity fof Florida's population is

ok! to graph your first point, you know the y-intercept is 1, so your point is (0,1)

graph that

because we knkow the slope is 2/3 and it's y change/x change, move up 2 and left 3 for your next point, which is (2,4)

we can graph a third point for accuracy, and move up 2 and left 3 again to get (4,7)

create a line connecting all the points