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3 years ago

5

Write the quadratic equation whose roots are 5 and 1, and whose leading coefficient is 5

1 answer:

zepelin [54]3 years ago

3 0

Answer: the equation is

5x^2 -30x - 25

Step-by-step explanation:

A quadratic equation is one in which the highest power of the unknown is 2.

The general form of a quadratic equation is expressed as

ax^2 + bx + c

Where c is a constant and a is the leading coefficient

Assuming we want to write the quadratic equation in x, from the information given, the given roots are 5 and 1 and the leading coefficient is 5. We will just multiply the expression by the leading coefficient.

Therefore, the linear factors of the quadratic will be (x-5) and (x-1)

With the leading coefficient as 5, the equation becomes

5(x-5)(x-1)

= 5(x^2 - x - 5x + 5)

= 5(x^2 - 6x + 5)

= 5x^2 -30x - 25

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A sheet of origami paper is in the shape of a square with a side length of 7 inches, as shown. What is the area of the sheet of

vlabodo [156]

??... what lol good job tho

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3 years ago

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s2008m [1.1K]

Answer:

126

Step-by-step explanation:

Add (24x5) to 6

i'm assuming that the first number of the sequence is 6 not 11

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3 years ago

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sergejj [24]

Answer:

A

Step-by-step explanation:

We are given the function:

$\displaystyle f(x) = \left\{ \begin{array}{ll} 2\cos(\pi x) \text{ for } x \leq -1 \\ \\ \displaystyle \frac{2}{\cos(\pi x)}\text{ for } x > -1 \end{array} \right.$

And we want to find:

$\displaystyle \lim_{x\to -1}f(x)$

So, we need to determine whether or not the limit exists. In other words, we will find the two one-sided limits.

Left-Hand Limit:

$\displaystyle \lim_{x\to-1^-}f(x)$

Since we are approaching from the left, we will use the first equation:

$\displaystyle =\lim_{x\to -1^-}2\cos(\pi x)$

By direct substitution:

$=2\cos(\pi (-1))=2\cos(-\pi)=2(-1)=-2$

Right-Hand Limit:

$\displaystyle \lim_{x\to -1^+}f(x)$

Since we are approaching from the right, we will use the second equation:

$=\displaystyle \lim_{x\to -1^+}\frac{2}{\cos(\pi x)}$

Direct substitution:

$\displaystyle =\frac{2}{\cos(\pi (-1))}=\frac{2}{\cos(-\pi)}=\frac{2}{(-1)}=-2$

So, we can see that:

$\displaystyle \displaystyle \lim_{x\to-1^-}f(x)=\displaystyle \lim_{x\to -1^+}f(x) =-2$

Since both the left- and right-hand limits exist and equal the same thing, we can conclude that:

$\displaystyle \lim_{x \to -1}f(x)=-2$

Our answer is A.

8 0

3 years ago

Translate the phrase into a variable expression: twice the sum of a number and 5

DIA [1.3K]

Answer:

'Twice the sum of a number and 5' can be translated into variable expression such as:

2(n + 5)

Step-by-step explanation:

Given the phrase

<em>Twice the sum of a number and 5</em>

First, let us breakdown the English Phrase

Let the number be = n

The sum of a number 'n' and 5 = n + 5

now, twice the sum of a number and 5 can be determined by multiplying (n+5) with 5.

Thus,

'<em>Twice the sum of a number and 5</em>' can be translated into variable expression such as:

2(n + 5)

7 0

3 years ago

Please look at the picture and answer it thank you.

ElenaW [278]

Answer:

x = 17

Step-by-step explanation:

The sum of all angle measures in any triangle is 180 degrees.

Thus, 23 + 5x - 18 + 90 = 180.

Step 1: Simplify both sides of the equation.

$(5x)+(23+90-18)=180$
$5x+95=180$

Step 2: Subtract 95 from both sides.

$5x+95-95=180-95$
$5x=85$

Step 3: Divide both sides by 5.

$5x/5=85/5$
$x=17$

Step 4: Check if solution is correct.

$(5*17-18)+23+90=180$
$67+23+90=180$
$180=180$

Thus, x = 17.

6 0

2 years ago