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2 years ago

What number must be added to the expression below to complete the square? x2 - 11x

Mathematics

2 answers:

mart [117]2 years ago

5 0

Since we are to complete the square, therefore I believe the correct given should be:

x ^ 2 – 11 x

Take note of the symbol ^ which denotes that 2 is an exponent of x.

The general form of a binomial equation is in the form of:

a x^2 + b x + c

Where in this case:

a = 1

b = -11

c = unknown

To complete the square, we have to find for the value of c. This is calculated using the formula:

c = (b / 2) ^ 2

c = (-11 / 2) ^ 2

c = 30.25

Therefore the complete equation is:

x ^ 2 – 11 x + 30.25

Contact [7]2 years ago

4 0

30.25 is correct but apex asks for a fraction so 121/4

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The Thomas family went for a Sunday drive. Before they left, Mr. Thomas noticed the gas tank was ¾ full. When they returned home

JulijaS [17]

Answer:

7.5 gallons

Step-by-step explanation:

Given:

The Thomas family went for a Sunday drive.

Before they left, Mr. Thomas noticed the gas tank was ¾ full.

When they returned home the gas tank was ⅓ full.

Total capacity of the gas tank = 18 gallons

Question asked:

How many gallons of gas did the car use on the drive?

Solution:

Before they left, quantity of gas in the tank = $\frac{3}{4} \times18=\frac{54}{4} =13.5\ gallons$

When they returned, quantity of gas in the tank = $\frac{1}{3} \times18=\frac{18}{3} =6\ gallons$

Quantity of gas used on the drive = 13.5 - 6 = 7.5 gallons

Therefore, 7.5 gallons of gas used on the drive by Thomas family.

4 0

2 years ago

"You measure 34 dogs' weights, and find they have a mean weight of 67 ounces. Assume the population standard deviation is 13.5 o

liraira [26]

Answer:

The 95% confidence interval for the true population mean dog weight is between 62.46 ounces and 71.54 ounces.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96*\frac{13.5}{\sqrt{34}} = 4.54$

The lower end of the interval is the sample mean subtracted by M. So it is 67 - 4.54 = 62.46 ounches.

The upper end of the interval is the sample mean added to M. So it is 67 + 4.54 = 71.54 ounces.

The 95% confidence interval for the true population mean dog weight is between 62.46 ounces and 71.54 ounces.

7 0

3 years ago

Using a rule why is = to 3 x + 4 find the value of y when x is 2

Alex73 [517]

X=2 so 2+4=6 so y=6. I just gone ovee this unit aswell.

4 0

3 years ago

Solve the following system of equations:

Vladimir79 [104]

Answer:

(-1,1)

Step-by-step explanation:

We can solve this by either graphing and finding ther point the lines intersect, or mathematically, I'll do both.

Graphing:

Mathematically:

−2x + 4y = 6

y = 2x + 3

See the attached graph. The lines intersect at (-1,1)

--------------------

I'll rearrange the first equation (to make it easier for me):

−2x + 4y = 6

4y = 2x + 6

y = (1/2)x + 1.5

Now lets substitute the second equation into the first so that we can eliminate y:

y = 2x + 3

[(1/2)x + 1.5] = 2x + 3

- (3/2)x = (3/2)

x = -1

If x = -1:

y = 2(-1) + 3

y = 1

The solution is x = -1 and y = 1, or (-1,1)

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

Both approaches give us (-1,1), the solution to the system of equations. It is the only point that satisfies both equations.

3 0

1 year ago

5- pls help!!!! math -

Sedbober [7]

Answer:

5,-1

Step-by-step explanation:

2,3

+ 3,-4

5, -1

6 0

1 year ago

Read 2 more answers