Part A: Describe the solution(s) to 9x² - 36x + 36 = 0 by just determining the radicand. Show your work. (10 points) Part B: Describe the solution (s) to x²-x + 4 = 0 by just determining the radicand. Show your work. (10) points) Part C: Solve 4x² + 23 – 35 using an - appropriate method. Show the steps of your work and explain why you chose the method used. (15 points) (35 points)​

Answer:

( 3, -2 )

Step-by-step explanation:

3, -2 is on the line so it is a solution

the rest of the points aren't in the shaded area or on the line therefore they are not a solution

Have a great day! :)

Answer:

Ans= 6720 ways

Step-by-step explanation:

From Combination rule from Permutation and Combination, nCr

We use 8^C3 or 8C3,

8x7x6x5x4x3x2x1

--------------------------  =6,720

3x2x1

or

8x7x6x5x4x3! /3!, here the 3! cancels each other out, and we're left with 8x7x6x5x4, which equals 6720.

Answer:

1942

Step-by-step explanation:

31072 / (2^4) = 31072

Hope This Helped

Question

What is 131072 divided by 2 to the power of 4?

Solution in steps:

Answer:

∆ADB is ~ ∆BEC because <D and <E are right angles which are equal to 90°.

A right angle is defined as an angle that is formed when two straight line are perpendicular at an intersection creating a 90° angle when measured.

From the diagram, ∆ADB is ~ ∆BEC because <D and <E are right angles which are equal to 90°.

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Answer:

See below

Step-by-step explanation:

h^2 - 5h = 84

h^2 - 5h - 84 = 0

The  letters of the word "UNDERDOG" can be arranged in 144 ways.

There are only two letters that are the same which are D, then the remaining letters are 6 letters.

V, E, O are vowels

         N  R  G

The vowels are not joined together

For N, R, G  A³3

There are 4 openings A³4

Hence:

A³4· A³3=4×3×2×3×2×1

A³4· A³3=144

Therefore the  letters of the word "UNDERDOG" can be arranged in 144 ways.

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When Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.

It should be noted that when an angle turns through a particular degree, it'll be said to have an identical degree.

In this case, when Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.

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Answer:

6 cm²

Step-by-step explanation:

The formula to find the area of the parallelogram is :

Area = Base × Height

Given that,

Base ⇒ 3cm

Height ⇒ 2 cm

Let us find now.

Area = Base × Height

Area = 3cm × 2cm

Area = 6 cm²

Answer:

4.97

Step-by-step explanation:

h(x) = -3x² + 5

h(0.1)

x = 0.1

h(0.1) = -3(0.1)² + 5

0.1² = 0.01

-3(0.01) + 5

-3(0.01) = -0.03

-0.03 + 5 = 4.97

An equation is formed of two equal expressions. The original height of the water in the pool in feet is 5.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the equation, 4.75 = x + (-0.25) can be used to find x, the original height of the water in a pool. Therefore, the height of the fool in the beginning is,

4.75 = x + (-0.25)

4.75 + 0.25 = x

x = 5

Hence, the original height of the water in the pool in feet is 5.

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Answer:

A and B are arithmetic sequences. they have a set and consistent increase/decrease in each term.

Step-by-step explanation:

The value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

From the graph:

P(X ≤ 1) = 0.05

P(X ≤ 2) = 0.1

P(X ≤ 3) = 0.15

P(X ≤ 4) = 0.2

P(X ≤ 5)= 0.2

Add all the probability:

P = 0.05+0.1+0.15+0.2+0.2 = 0.7

P(X≤a)=0.6  (that means the value of the area under the curve 'a' is 0.6)

So the value of a should be 5

Thus, the value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.

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Answer:

Put 5 in the input

Step-by-step explanation:

after subtracting the monthly fee (which she has to pay, even if she does not make a single call) we have

66.9 - 15 = $51.90

for actual phone call minutes.

1 minute is $0.05

so, in the month with the lowest charge she had used

51.9 / 0.05 = 1038 minutes for calls.

since this was the minimum, for all the numbers of minutes m she used in a month we have

m >= 1038 minutes

The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.

Conversion means to convert the same thing into different units.

Convert the degree measure to the radian measure.

⇒ 75°

We know the conversion is given as

180° = π radian

   1° = π/180°

Then we have

75° = 75° x π/180° radian

75° = 1.30899 radian

75° ≅ 1.31 radian

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The correct answer is 6 / 7 as it is closer to 1.

The fraction is defined as the division of the whole part into an equal number of parts.

The number near 1 will be calculated as:-

7/ 6 = 1.1666

6 / 7 = 0.8571

Difference of the first ratio from one.

1.1666 - 1  = 0.1666

Difference of the second ratio:-

1 - 0.8571 = 0.1429

So the difference of 6 / 7 is lower than the difference of the fraction 7 / 6 from one.

Therefore the correct answer is 6 / 7 as it is closer to 1.

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Answer:

See below ~

Step-by-step explanation:

⇒ Number of years since = 0 ⇒ t = 0

⇒ Apply in the formula

⇒ n(0) = 73e^(0.02 × 0)

⇒ n(0) = 73e⁰

⇒ n(0) = 73,000,000 rats

=============================================================

⇒ Number of years since 1993 : 2009 - 1993 = 16 ⇒ t = 16

⇒ Applying in the formula

⇒ n(16) = 73e^(0.02 × 16)

⇒ n(16) = 73e^(0.32)

⇒ n(16) = 73 × 1.37712776 × 10⁶

⇒ n(16) = 100.530326 x 10⁶

⇒ n(16) = 100,530,326 rats

Answer:

Given function:  

[tex]\large \text{$ n(t)=73e^{0.02t} $}[/tex]

where:

To calculate the rat population in 1993, substitute [tex]t = 0[/tex] into the function:

[tex]\large \begin{aligned}\implies n(0) & =73e^{0.02(0)}\\& = 73 \cdot 1\\& = 73 \sf \: million\end{aligned}[/tex]

To calculate a prediction of the rat population in 2009, first determine the value of t by subtracting the initial year of 1993 from the given year of 2009:

[tex]\large \text{$ \implies t=2009-1993=16 $}[/tex]

Substituting the found value of t into the function to find the predicted number of rats in 2009:

[tex]\large \begin{aligned}\implies n(16) & =73e^{0.02(16)}\\& = 73e^{0.32}\\& = 100.5303268...\\ & = 100.5 \sf \: million\:(1\:dp)\end{aligned}[/tex]

The size of the unknown angle "x"

We'll have to check which one is appropriate from SOHCAHTOA.

In this question hypotenuse and adjacent is given so, we'll have to use cos.

[tex]\large\boxed{Formula: cos \: (A)= \frac{adj}{hyp}}[/tex]

Let's solve!

Let's substitute the values according to the formula.

[tex]cos \: x= \frac{8}{11}[/tex]

We'll have to use cos inverse.

[tex]x= {cos}^{-1}( \frac{8}{11} )[/tex]

[tex]x= 43.34175823[/tex]

Now we'll have to round off to 1 decimal place.

The value in hundredths place is less than 5 so we won't have to round up.

So, the final answer is:

[tex]\large\boxed{x= 43.3°}[/tex]

Therefore, the size of the unknown angle "x" is 43.3°

[tex]\large\boxed{Formula:\frac{sum \: of \: interior \: angles}{n}}[/tex]

n means the number of sides.

Sum of interior angles of a dodecagon is 1800°

Let's substitute the values according to the formula.

[tex]\frac{1800}{12}[/tex]

[tex]\large\boxed{ = 150°}[/tex]

Now, we can find the size of one exterior angle.

[tex]\large\boxed{Formula:\frac{360}{n}}[/tex]

n means the number of sides.

A dodecagon has 12 sides.

Let's substitute the values according to the formula.

[tex]\frac{360}{12}[/tex]

[tex]\large\boxed{ = 30°}[/tex]

Hence, the size of 1 interior angle of a dodecagon is 150° and 1 exterior angle is 30°

Step-by-step explanation:

x = number of bottles Paula sold

y = number of bottles Pedro sold

x + y = 72

x = 72 - y

x/y = 3/5

(72 - y)/y = 3/5

5(72 - y) = 3y

360 - 5y = 3y

360 = 8y

y = 45

x + y = 72

x + 45 = 72

x = 27

so,

Paula sold 27 water bottles, and Pedro sold 45.

Answer:

2(x-5)

Step-by-step explanation:

Hope this helps

Answer:

2 · (x - 5)

Step-by-step explanation:

2 · (x - 5)

2 ·

"2 times"

when multiplication- or "times" is said, it can be shown in multiple ways. Multiplication can be shown as a×b , a·b , (a)(b)

(x - 5)

"difference of x and 5"

when difference is noted, the first number listed is the one written first. The difference between 2 and x is ( 2 - x ); the difference between x and 2 is ( x - 2).

Answer:

see the attachment photo!

Answer:

hope it helpssssssss youj

Step-by-step explanation:

if I understand this correctly, then

1 was rolled 77 times

2 89 times

3 73 times

4 69 times

5 110 times

6 82 times

remember, a probability is always desired cases over total possible cases.

a)

the experimental probability to roll an odd number (1, 3, 5) is the number of desired cases (77 + 73 + 110) over the total cases (500).

260 / 500 = 26/50 = 13/25 = 0.52

b)

if the cube would be totally equal, so that every side has truly the same probability to appear we would have for every roll 6 total possible outcomes (1 .. 6), and 3 desired outcomes (1, 3, 5).

so the theoretical probability is

3/6 = 1/2 = 0.5

c)

if the cube is truly "fair" (all sides really have the same probability to show), then the first answer is true.

the more rolls of the die, the greater the likelihood that both probabilities will get closer and closer.

that is actually a main point of probabilities : to find the most likely behavior or structure of a large number of items or objects out of the structure or behavior of a smaller sample. or out of theoretical considerations that can be tested with smaller samples.

Answer:

  1 plane

Step-by-step explanation:

In Euclidean geometry, three non-collinear points will define exactly one plane.

__

Two points will define a line. That line can exist in an infinity of different planes.

A third point not on the line can only lie in exactly one plane with that line.

Three non-collinear points in Euclidean geometry can lie on one unique plane.

In Euclidean geometry, any three non-collinear points (points not lying on the same line) uniquely determine a plane.

This means that there is only one plane that contains all three of those points.

So, given three non-collinear points, you can find exactly one plane that passes through all of them.

Hence, if the three points not on the same line can lie on one plane.

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Answer:

Bonds

Step-by-step explanation:

A bond is a fixed-income instrument that represents a loan made by an investor to a borrower (typically corporate or governmental).

Answer:

3600 ways

Step-by-step explanation:

person A has 7 places to choose from :

→ He has 2 places ,one to the extreme left of the line ,the other to the extreme right of the line

If he chose one of those two ,person B will have 5 choices and the other 5 persons will have 5! Choices.

⇒ number of arrangements = 2×5×5! = 1 200

→ But Person A also , can choose one of the 5 places in between the two extremes .

If he chose one of those 5 ,person B will have 4 choices and the other 5 persons wil have 5! Choices.

⇒ number of arrangements = 5×4×5! = 2 400

In Total they can be arranged in :

1200 + 2400 = 3600 ways

Using function concepts, it is found that the correct statement is given by:

all of the x-intercepts of f(x) are common to those of g(x).

They are the values of x when x = 0, hence:

Hence, the first statement is correct, and the x-intercept x = -1 of f(x) is common to the x-intercept x = -1 of g(x).

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The total amount of water that Kiesha drinks in 12 days is 20 quarts

The average amount of water she drinks per day is 1 2/3 quarts

The number of days that Keshia drinks at least the average amount of water is 6 days

If she drinks 1 quart of day 13, the average reduces.

The total amount of water drank in the 12 days can be determined by adding the quarts for each day together. When they are added together, the number is 20 quarts.

Average = total amount drank / number of days 1 2/3 quarts

New average = 20 + 1 / 13 = 21 / 13 = 1 7/13 quarts

The average reduces because the quart drank on the 13th day is less than the amount of water drank on the other days.

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