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3 years ago

M^ 2 + m − 90 factorize

Mathematics

2 answers:

laiz [17]3 years ago

5 0

Answer:

(m+10)(m-9)

Step-by-step explanation:

To factor this equation we want to find two numbers that multiply to -90 but also add/subtract to 1.

Those two numbers are 10 and -9 (10×-9=-90, 10-9=1)

cluponka [151]3 years ago

3 0

Answer:

$(m-9)(m+10)$

Step-by-step explanation:

When you are given an expression in this format

$ax^2+bx+c$

You must find two numbers that add up to <em>b</em> while the product is <em>c</em>.

You do trial and error to figure it out for your equation.

$m^2+m-90$

Hmm... what two numbers add up to 1 and multiplied together equal -90.

Start off with pairs that can equal 90.

45 2

18 5

9 10

Ok, well 45 * 2 does equal 90 but 45 + 2 = 47and 45 + -2 = 43 but there's no way I can make it equal to 1. Next!

18 * 5 equals 90 but 18 + -5 = 13 and 18 + 5 = 23, I can just tell that there's no way I can make this equal to 1.

9 * 10 equals 90, 9 + 10 = 19 but 9 + -10 = -1. Now, that's interesting, We have -1 but we need 1. All we have to do is flip the order. 10 + -9 = 1. And -9 * 10 = -90, PERFECT!

Now use the two numbers and put it in factored form.

$(m-9)(m+10)$

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(08.07 HC)

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

$\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

C) See attachment.

Step-by-step explanation:

Given function:

$f(x)=2x^2-x-10$

To factor a <u>quadratic</u> in the form $ax^2+bx+c$ <em> , </em>find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

Therefore, the two numbers are -5 and 4.

Rewrite $b$ as the sum of these two numbers:

$\implies f(x)=2x^2-5x+4x-10$

Factor the first two terms and the last two terms separately:

$\implies f(x)=x(2x-5)+2(2x-5)$

Factor out the common term (2x - 5):

$\implies f(x)=(x+2)(2x-5)$

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

$\implies (x+2)(2x-5)=0$

Therefore:

$\implies (x+2)=0 \implies x=-2$

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

$x=-2, \:\:x=\dfrac{5}{2}$

The x-value of the vertex is:

$\implies x=\dfrac{-b}{2a}$

Therefore, the x-value of the vertex of the given function is:

$\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}$

To find the y-value of the vertex, substitute the found value of x into the function:

$\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}$

Therefore, the vertex of the function is:

$\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0

2 years ago

HELPPPP!!!!!!!!!!!!!

juin [17]

I think its C Because Aob is a given angle Boc is where we prove Aob so Im 95% sure its c

4 0

2 years ago

The perimeter of a square is 60 inches. Find the area.

Marianna [84]

Answer 225

Step-by-step explanation:

60/4=15. 15*15= 225

5 0

3 years ago

Counting how many errors are in one chapter of a book is an example of measuring what kind of quality characteristics

AnnZ [28]

Answer: Attributes.

Step-by-step explanation:

An attribute is characterized as a person, position, or thing's quality or characteristic. Individuals in real life and fictional characters have different characteristics. Someone could be called attractive, charming, funny, or intelligent, for instance. Well, in math, an attribute is a characteristic of a math object - it's what this object has. An attribute of the book is the number of errors in a chapter of the book.

8 0

3 years ago

A bag cost 4 times as much as a dress if the bag cost $276 how much will Toni speed on the bag and 3 such dresses

timama [110]

276 divides by 4 = 69
So 3x69 = 207 + 276 = $483

6 0

3 years ago