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Greeley [361]
3 years ago
15

Can someone help me with several questions?

Mathematics
1 answer:
juin [17]3 years ago
8 0

Answer:

1.) -1

2.) 5.6

3.) -1

4.) 12

You might be interested in
-1 3/5 divided by -2/3
Cloud [144]
<h2>Answer:</h2>

12/5

alternative forms:

2 2/5, or 2.4

<h2>Step-by-step explanation:</h2>

-1 3/5÷ -2/3

convert mixed number to an improper fraction

-8/5÷ -2/3

divide

8/5•3/2

reduce numbers

4/5•3

multiply

---------

12/5

---------

7 0
3 years ago
Read 2 more answers
For the function f(x) = x2 ­ -12, find (f o f­-1)(4) A. 0 B. 4 C. 10 D. 6
slega [8]

We actually don't need to do any computation. By definition, the inverse function f^{-1} changes the role of input and output. So, if a function f maps x onto y, the inverse function maps y onto x.

You have to think like this: if the function makes a step further, the inverse function makes that same step back.

This means that the composition f \circ f^{-1} is always the identity function f(x) = x. In fact,

(f\circ f^{-1})(x) = f(f^{-1}(x)) = x

So, for every function, you have

(f\circ f^{-1})(4) = f(f^{-1}(4)) = 4

5 0
3 years ago
X^+17x+72=12 factoring quadratic equation
Tom [10]

Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, -17x its coefficient is -17 .

The last term, "the constant", is +60

Step-1 : Multiply the coefficient of the first term by the constant 1 • 60 = 60

Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -17 .

-60 + -1 = -61

-30 + -2 = -32

-20 + -3 = -23

-15 + -4 = -19

-12 + -5 = -17 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -5

x2 - 12x - 5x - 60

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-12)

Add up the last 2 terms, pulling out common factors :

5 • (x-12)

Step-5 : Add up the four terms of step 4 :

(x-5) • (x-12)

Which is the desired factorization

Equation at the end of step

1

:

(x - 5) • (x - 12) = 0

STEP

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-5 = 0

Add 5 to both sides of the equation :

x = 5

Solving a Single Variable Equation:

2.3 Solve : x-12 = 0

Add 12 to both sides of the equation :

x = 12

Supplement : Solving Quadratic Equation Directly

Solving x2-17x+60 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-17x+60

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.5000

Plugging into the parabola formula 8.5000 for x we can calculate the y -coordinate :

y = 1.0 * 8.50 * 8.50 - 17.0 * 8.50 + 60.0

or y = -12.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-17x+60

Axis of Symmetry (dashed) {x}={ 8.50}

Vertex at {x,y} = { 8.50,-12.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 5.00, 0.00}

Root 2 at {x,y} = {12.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2-17x+60 = 0 by Completing The Square .

Subtract 60 from both side of the equation :

x2-17x = -60

Now the clever bit: Take the coefficient of x , which is 17 , divide by two, giving 17/2 , and finally square it giving 289/4

Add 289/4 to both sides of the equation :

On the right hand side we have :

-60 + 289/4 or, (-60/1)+(289/4)

The common denominator of the two fractions is 4 Adding (-240/4)+(289/4) gives 49/4

So adding to both sides we finally get :

x2-17x+(289/4) = 49/4

Adding 289/4 has completed the left hand side into a perfect square :

x2-17x+(289/4) =

(x-(17/2)) • (x-(17/2)) =

(x-(17/2))2

Things which are equal to the same thing are also equal to one another. Since

x2-17x+(289/4) = 49/4 and

x2-17x+(289/4) = (x-(17/2))2

then, according to the law of transitivity,

(x-(17/2))2 = 49/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(17/2))2 is

(x-(17/2))2/2 =

(x-(17/2))1 =

x-(17/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(17/2) = √ 49/4

Add 17/2 to both sides to obtain:

x = 17/2 + √ 49/4

Since a square root has two values, one positive and the other negative

x2 - 17x + 60 = 0

has two solutions:

x = 17/2 + √ 49/4

or

x = 17/2 - √ 49/4

Note that √ 49/4 can be written as

√ 49 / √ 4 which is 7 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2-17x+60 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -17

C = 60

Accordingly, B2 - 4AC =

289 - 240 =

49

Applying the quadratic formula :

17 ± √ 49

x = —————

2

Can √ 49 be simplified ?

Yes! The prime factorization of 49 is

7•7

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 49 = √ 7•7 =

± 7 • √ 1 =

± 7

So now we are looking at:

x = ( 17 ± 7) / 2

Two real solutions:

x =(17+√49)/2=(17+7)/2= 12.000

or:

x =(17-√49)/2=(17-7)/2= 5.000

Two solutions were found :

x = 12

x = 5

Step-by-step explanation:

please mark my answer in brainlist

8 0
2 years ago
Please answer the question from the attachment.
Mars2501 [29]
We have to calculate the pizza´s area.
r=radius
Area (circle)=π*r²
diameter=30 cm
radius=diameter/2=30 cm/2=15 cm

Area(pizza)=π*(15 cm)²=225π cm²≈706.86 cm².

solution: 706.86 cm²
3 0
3 years ago
Only question numer 10.​
leva [86]
Out of the six, only “u” wouldn’t work so the answer is d. 5

Hope this helps and hope you have a great day! Please make brainiest
4 0
2 years ago
Read 2 more answers
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