What equation results from completing the square and then factoring? x^2-8x=39

Final answer:

Marisol's bedroom is 99 square feet, and the rug area is 48 square feet. By subtracting the rug area from the total room area, we find that 51 square feet of floor will not be covered by the rug.

Explanation:

To find out how many square feet of Marisol's bedroom floor will not be covered by the rug, we must first calculate the area of her entire room and then the area of the rug. The area of a rectangle is found by multiplying the length by the width. The area of Marisol's room is 9 feet × 11 feet = 99 square feet. The area of the rug is 6 feet × 8 feet = 48 square feet.

Next, we subtract the area of the rug from the area of the entire room to find the uncovered floor area.

Uncovered floor area = Total room area – Rug area
= 99 square feet – 48 square feet
= 51 square feet

Therefore, 51 square feet of Marisol's bedroom floor will not be covered by the rug.

Answer:

Lower value: 14

Highest value: 41

Lower quartile: 24.5

Upper quartile: 34.5

Median: 28

Step-by-step explanation:

The equation of the circle shown in the graph is equal to [tex](x + 6)^2 + (y - 4)^2 = 36[/tex]

Form the graph, we can deduce the following points:

The center of the circle is denoted by the black dot and we can see that the values are -6 and 4 respectively.

Also, the diameter of the circle is:

Diameter = 12 units

Radius = [tex]\frac{Diameter}{2} = \frac{12}{2} = 6 \;units[/tex]

Mathematically, the standard form of the equation of a circle is given by;

  .....equation 1

Where;

Substituting the values into eqn 1, we have:

[tex](x - [-6])^2 + (y - 4)^2 = 6^2\\\\(x + 6)^2 + (y - 4)^2 = 36[/tex]

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GL parallel to HI in the pre-image ensures AB remains parallel to FE in the translation.

Given that GL and HI are parallel, we can infer that AB and FE will also remain parallel in the translation. The parallelism of lines GL and HI suggests that their corresponding sides, AB and FE, will exhibit the same parallel relationship during the translation process. This is a consequence of the consistent geometric transformation applied to all points on lines GL and HI. As each point on GL undergoes translation, its corresponding point on HI experiences the same displacement, preserving the parallelism.

Therefore, we can confidently state that AB and FE maintain their parallel orientation, aligning with the geometric properties of the translation that preserves parallel lines. The parallelism observed in the original configuration persists throughout the translation, ensuring that AB and FE remain parallel to each other.

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Answer:

[tex]x=28[/tex]

Step-by-step explanation:

[tex]-10+\sqrt{x+8}=-4[/tex]

⭆ Add 10 to both sides:-

[tex]-10+\sqrt{x+8}+10=-4+10[/tex]

[tex]\sqrt{x+8}=6[/tex]

⭆ Square both sides:-

[tex]x+8=36[/tex]

⭆ Subtract 8 from both sides:-

[tex]x+8-8=36-8[/tex]

[tex]x=28[/tex]

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Answer:

A. 24 miles

Step-by-step explanation:

Using 3.14 for π, we have ...

... Area = πr^2

... √(Area/π) = r = √(1808.64/3.14) = √576 = 24 . . . . miles

Answer:

its 24 miles so the correct answer would be A

Step-by-step explanation:

Answer:

C. Access to cash

Step-by-step explanation:

Bank provides access to cash in multiple manners, you can debit the money from your savings account, apply for different type of loans, draft your DD etc.

While for the other options like printing paychecks are done by any company in order to  provided paychecks to its employees, Insurance companies provides vehicle insurance services to anyone will to get their vehicle insured and printing money is provided only by central bank of any country, not every bank is allowed to print money.

To convert 6 liters of solution into gallons, given that 1 gallon is equivalent to 3.79 liters, you divide 6 by 3.79 which gives you 1.58 gallons of solution.

The question is asking to find the number of gallons in 6 liters of a solution, given that 1 gallon is equivalent to 3.79 liters. The conversion from liters to gallons is a basic concept in measurement conversion. Here is a step-by-step explanation to help you understand the process:

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The amount of fresh berries that contain 80% water is 7.2 pounds.

Amount of water in fresh raspberry = 80%

It means the amount of raspberry only in a fresh raspberry =20%

Amount of water in dry raspberry =20%

A percentage is a value per hundred.

So, the amount of raspberry only in 36 lbs fresh berries = 20% of 36

20% of 36 = (20/100)*36 = 7.2 lbs

So, the amount of raspberry only in 36 lbs of fresh berries =  7.2 lbs

Therefore, we get 7.2 lbs from 36lb fresh berries.

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We have been given that Greg's Jumble has 666 classical songs, 777 rock songs, and 999 rap songs.

Therefore, total number of songs are

[tex]666+777+999\\ =2442[/tex]

The formula for probability is given by

[tex]P(E)=\frac{n(E)}{n(s)}[/tex]

Let us first find the probability for rap song

[tex]P(\text{rap song})= \frac{999}{2442} \\  P(\text{rap song})= \frac{9}{22}[/tex]\\

Therefore, we have

[tex]P(\text{ not rap song})=1- P(\text{rap song})\\ \\ P(\text{ not rap song})=1-\frac{9}{22} \\ \\ P(\text{ not rap song})=\frac{13}{22} =0.59[/tex]

Hence, we have

P(not rap song)=0.59

The expression for the total number of bacteria at t = 3 hours, given an initial 1000 bacteria at t = 0, is:  [tex]\[ 1000 + \int_0^3 R(x) \, dx \][/tex]

To find the number of bacteria in the container at time t = 3 hours, given that the rate of increase is [tex]\( R(t) \)[/tex] bacteria per hour and there are 1000 bacteria at time t = 0, you can use the following steps:

Start with the initial condition :

  You are given that there are 1000 bacteria at t = 0.

So, the initial condition is [tex]\( N(0) = 1000 \),[/tex]  where N(t) represents the total number of bacteria at time t.

Integrate to find the change in number of bacteria over time :

  Since the rate of increase is R(t), the total increase in bacteria from time t = 0 to t = t is given by integrating R(t) with respect to time.

This integral provides the cumulative increase in bacteria:

[tex]\[ \int_0^t R(x) \, dx. \][/tex]

Add the initial bacteria to the increase :

  Since there are already 1000 bacteria at t = 0, the total number of bacteria at time t is given by:

  [tex]\[ N(t) = 1000 + \int_0^t R(x) \, dx. \][/tex]

Find the expression for t = 3 hours :

  To find the total number of bacteria at t = 3 hours, you substitute t = 3 into the expression derived in step 3:

  [tex]\[ N(3) = 1000 + \int_0^3 R(x) \, dx. \][/tex]

Thus, the expression [tex]\( 1000 + \int_0^3 R(x) \, dx \)[/tex] gives the number of bacteria in the container at time t = 3 hours.

Question :

the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours?

The correct expression that gives the number of bacteria in the container at time t = 3 hours is D.  [tex]1000 + \int_0^3 R(t) \, dt[/tex]

The problem asks us to find the number of bacteria in a container at t = 3 hours, given that the number of bacteria increases at a rate of R(t) bacteria per hour and there are 1000 bacteria at time t = 0.

To solve this, we need to integrate the rate function R(t) to find the total change in the number of bacteria over the interval from t = 0 to t = 3.

1. Initial number of bacteria:

At t = 0, the number of bacteria is 1000.

2. Change in number of bacteria:

The rate of change of the number of bacteria is given by R(t) bacteria per hour.

To find the total number of bacteria added over the time interval from t = 0 to t = 3, we need to integrate R(t) from 0 to 3.

Total change in number of bacteria = [tex]\int_0^3 R(t) \, dt[/tex]

3. Total number of bacteria at t = 3 hours:

This is the sum of the initial number of bacteria and the total change in the number of bacteria over the 3 hours.

Number of bacteria at t = 3 hours = [tex]1000 + \int_0^3 R(t) \, dt[/tex]

Complete Question:

The number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0, which of the following expressions gives the number of bacteria in the container at time t=3 hours?

(A) R(3)

(B) 1000+R(3)

(C) [tex]$\int_0^3 R(t) d t$[/tex]

(D) [tex]$1000+\int_0^3 R(t) d t$[/tex]