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3 years ago

What number would you add to both sides of x2 + 7x = 4 to complete the square? 22 72

Mathematics

2 answers:

Studentka2010 [4]3 years ago

6 0

In order to complete the square with the numbers that you have, you would have to add 12.25 to both sides.

In order to complete the square, you always have to add half of the x coefficient squared. Since the x coefficient is 7, we take half of that (3.5) and square it to get 12.25.

Harlamova29_29 [7]3 years ago

5 0

(7/2)^2

is the answer

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Mrs. Smith's class is working on a variety of science experiments. Each

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

If there are n students, then the number of pairs is $\frac{n(n-1)}{2}$ .

With 12 students, $\frac{12(12-1)}{2} = \frac{132}{2}=66$ pairs can be formed.

The reason the formula works is this: Each of the 12 students can be paired with 11 other students (no student is paired with him/her self). But counting 12 x 11 = 132 counts each pair twice. Example: student A can be paired with student B,..., student B can be paired with student A. The pair was counted two times.

See the attached image that shows pairings of 5 students. There are

5(5 - 1)/2 = 5(4)/2 = 10 pairs.

8 0

2 years ago

Need help on these !! 13 and 14! Please!!

katen-ka-za [31]

Question # 13

Answer:

The required equation for the given function is y = 4sin(x/2+2π/3) -2 , as shown attached graph diagram.

Step-by-step explanation: 

As the general sine function is given by

$y=asin(bx+c)+d$ .......[A]

amplitude = a
period = 2π ÷ b
Phase shift = -c ÷ b
Vertical shift = d

As in the question,

amplitude = a = 4
period = 4π
phase shift = -4π/3
Vertical shift = d = -2

period = 2π ÷ b

b = 2π/period

b = 2π/4π ∵ period = 4π

b = 1/2

Also

Phase shift = -c/b

-4π/3 = -c/b ∵ phase shift = -4π/3

4π/3 = c/b

c = b × 4π/3

c = 1/2 × 4π/3

c = 4π/6

c = 2π/3

So, putting Amplitude ⇒ a = 4, Vertical shift ⇒ d = -2, b = 1/2 ,

and c = 2π/3 in Equation [A] would bring us the required equation for the given function.

$y=asin(bx+c)+d$

y = 4sin(x/2+2π/3)+(-2)

y = 4sin(x/2+2π/3) -2

Note: The graph is also shown in attached diagram.

Question # 14

Answer:

The required equation for the given function is y = cot(x+π/3)+2, as shown in attached graph diagram.

Step-by-step explanation: 

As the general cotangent function is given by

$y=acot(bx+c)+d$ .......[A]

amplitude = a
period = π ÷ b
Phase shift = -c ÷ b
Vertical shift = d

As in the question,

period = π
phase shift = -π/3
Vertical shift = d = 2

period = π ÷ b

b = π/period

b = π/π ∵ period = 4π

b = 1

Also

Phase shift = -c/b

-π/3 = -c/b ∵ phase shift = -π/3

π/3 = c/b

c = b × π/3

c = 1 × π/3

c = π/3

So, putting vertical shift ⇒ d = 2, b = 1 and c = π/3 in Equation [A] would bring us the required equation for the given function.

$y=acot(bx+c)+d$

y = cot(x+π/3)+2

Note: The graph is also shown in attached diagram.

Keywords: amplitude, period , phase shift , vertical shift

Learn more about trigonometric functions of equations from brainly.com/question/2643311

#learnwithBrainly

7 0

3 years ago

Consider function f.

tekilochka [14]

Given:

The function is:

$f(x)=\sqrt{7x-21}$

To find:

The steps of finding the inverse function $f^{-1}(x)$ .

Solution:

We have,

$f(x)=\sqrt{7x-21}$

The steps of finding the inverse function are:

Step 1: Substitute $f(x)=y$ .

$y=\sqrt{7x-21}$

Step 2: Interchange x and y.

$x=\sqrt{7y-21}$

Step 3: Taking square on both sides, we get

$x^2=7y-21$

Step 4: Adding 21 on both sides, we get

$x^2+21=7y$

Step 5: Divide both sides by 7.

$\dfrac{1}{7}x^2+3=y$

Step 6: Substitute $y=f^{-1}(x)$ .

$\dfrac{1}{7}x^2+3=f^{-1}(x)$ , where $x\geq 0$ .

Therefore, the inverse of the given function is $f^{-1}(x)=\dfrac{1}{7}x^2+3$ and the arrangement of steps is shown above.

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3 years ago

In destroit at 10 am,the temperature was -6 degrees.By 2 pm,it had increased 20 degrees.what was the temperature at 11 am? (hint

MAVERICK [17]

Answer:

Step-by-step explanation:

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3 years ago

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Answer:

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2 years ago