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2 years ago

Can anyone help me out with this please

Mathematics

1 answer:

musickatia [10]2 years ago

4 0

First, let's factor the equation to make it easier to solve for the intercepts:

f(x) = x² + 12x + 32
f(x) = (x + 8)(x + 4)

To find the x-intercepts of a function, set the y value (f(x)) to 0:

0 = (x + 8)(x + 4)
x = -8, -4

Similarly, to find the y-intercept, set the x values to 0:

f(x) = (0 + 8)(0 + 4)
f(x) = (8)(4)
f(x) = 32

*Note that you can see 32 as the y-intercept in the parabola's original equation

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Can someone help??plzzz..

Sav [38]

When you are multiplying 2 numbers with exponents, you need to add the exponent. When you multiply an exponent with an exponent, you multiply them.

So,
(3^2 x 7^4) ^9
First multiply the base and add exponents = ( 21^6) ^9
= 21 ^6x9
21^54
The same rule applies for variables, just pretend there is an imaginary 1.

4 0

3 years ago

The product of two rational numbers is 9⁄7 and one of them is 15⁄14. Then the other rational number is

Rasek [7]

Answer:

The other rational number in the operation given is:

6/5

Step-by-step explanation:

To obtain the number in the operation given, we're gonna represent the operation:

r * 15/14 = 9/7

Where:

r = the other rational number.

Now we are going to solve r to identify its value in numbers:

r * 15/14 = 9/7

$r = \frac{\frac{9}{7} }{\frac{15}{14}}$ (We pass a number that is multiplying to the left of the equal, to divide to the right of the equal symbol)

$r = \frac{6}{5}$

As you can see, when we operate, the result is 6/5, and we can prove this multiplying as we had in the original equation, replacing r by 6/5:

r * 15/14 = 9/7
6/5 * 15/14 = 9/7
9/7 = 9/7

In this form, we know the result is correct.

8 0

3 years ago

2x^3-x^2-3x=210 the answer is 5 but I want to know why.

mel-nik [20]

Answer:

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

Step-by-step explanation:

1) Move all terms to one side.

$2x^{3} -x^{2} -3x-210=0$

2) Factor $2{x}^{3}-{x}^{2}-3x-210$ using Polynomial Division.

1 - Factor the following.

$2x^{3} -x^{2} -3x-210$

2 - First, find all factors of the constant term 210.

$1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210$

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

$2*1^{3} -1^{2} -3*1-210=-212$

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

$2(-1)^{3} -(-1)^{2} -3*-1-210=-210$

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

$2*2^{3} -2^{2} -3*2-210=-204$

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

$2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224$

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

$2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174$

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

$2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264$

Substitute 5 into x. Since the result is 0, x-5 is a factor..

$2\times {5}^{3}-{5}^{2}-3\times 5-210 =0$

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

⇒ $x-5$

4) Polynomial Division: Divide $2{x}^{3}-{x}^{2}-3x-210$ by $x-5$ .

$2x^{2}$ $9x$ $42$

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

$x-5$ | $2x^{3}$ $-x^{2}$ $-3x$ $-210$

$2x^{3}$ $-10x^{2}$

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

$9x^{2}$ $-3x$ $-210$

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

$42x$ $-210$

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

5) Rewrite the expression using the above.

$2x^2+9x+42$

$(2x^2+9x+42)(x-5)=0$

3) Solve for $x.$

$x=5$

4) Use the Quadratic Formula.

1 - In general, given $a{x}^{2}+bx+c=0$ , there exists two solutions where:

$x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}$

2 - In this case, $a=2,b=9$ and $c = 42.$

$x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}$

3 - Simplify.

$x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

5) Collect all solutions from the previous steps.

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

4 0

2 years ago

Read 2 more answers

Please Help practice #3

algol [13]

Answer:

(2x+5)(4x+3)

Step-by-step explanation:

Given the expression 8x^2 + 26x + 15

Factorize

8x^2 + 26x + 15

= 8x^2 + 6x + 20x + 15

= 2x(4x+3) + 5 (4x+3)

= (2x+5)(4x+3)

Hence the factored form of the expression is (2x+5)(4x+3)

5 0

3 years ago

Circle all of the equations

Tanzania [10]

Answer:

B and C

Step-by-step explanation:

Just not linear lol

3 0

3 years ago