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3 years ago

If using the method of completing the square to solve the quadratic equation

Mathematics

1 answer:

Mrac [35]3 years ago

7 0

Answer:

81/4

Step-by-step explanation:

Given the equation x^2 – 9x + 38 = 0

Subtract 38 from both sides

x^2 – 9x + 38 - 38= 0 - 38

x^2 - 9x = -38

Next is to complete the square, to do this we will add the square of the half of coefficient of x to both sides as shown;

Coefficient of x is - 9

Half of -9 will be (-9/2)

Squaring the result will give (-9/2)² = 81/4

Hence the number that would have to be added to "complete the

square" is 81/4 to have;

x^2 - 9x + 81/4= -38 + 81/4

(x-9/2)² = -38 + 81/4

Hence the required value is 81/4

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PLEASE ANSWER WILL GIVE POINTS!!!!!!!!!!!

iris [78.8K]

Given:

The figure of a right triangle ABC.

To find:

The trigonometric ratios $\sin B, \tan A, \cos B$ .

Solution:

Using Pythagoras theorem,

$Hypotenuse^2=Perpendicular^2+Base^2$

$AB^2=AC^2+BC^2$

$(10)^2=(6)^2+BC^2$

$100-36=BC^2$

$64=BC^2$

Taking square root on both sides.

$\sqrt{64}=BC$

$8=BC$

So, measure of BC is 8 units.

Now,

$\sin \theta=\dfrac{Opposite}{Hypotenuse}$

$\sin B=\dfrac{AC}{AB}$

$\sin B=\dfrac{6}{10}$

$\sin B=\dfrac{3}{5}$

Similarly,

$\tan \theta=\dfrac{Opposite}{Adjacent}$

$\tan A=\dfrac{AC}{BC}$

$\tan A=\dfrac{6}{8}$

$\tan A=\dfrac{3}{4}$

And,

$\cos \theta=\dfrac{Adjacent}{Hypotenuse}$

$\cos B=\dfrac{BC}{AB}$

$\cos B=\dfrac{8}{10}$

$\cos B=\dfrac{4}{5}$

Therefore, the required trigonometric ration are $\sin B=\dfrac{3}{5}, \tan A=\dfrac{3}{4}, \cos B=\dfrac{4}{5}$ .

6 0

3 years ago

Which expression represents the change from a $20 bill when you purchase an item that costs d dollars

Anettt [7]

Expression that represents the change from $20 after the purchase of an item that costs d dollars is:
20-d

6 0

3 years ago

Gary and Joey share a 16-ounce box of cereal. By the end of the week, Gary has eaten 3/8 of the box, and Joey has eaten 1/4 of t

V125BC [204]

Answer:

3/8 of the box is left so 6 ounces is left.

Step-by-step explanation:

Make the 1/4, 2/8 then add 2/8 by 3/8 to get 5/8 then subtract 8/8 by 5/8 to get 3/8 then multiply it by 2 to get 6/16.

So the answer is 6/16 or 6.

6 0

3 years ago

Read 2 more answers

Use the order of operations and the digits 2, 4, 6, and 8 to create an expression with a value of 2

Naya [18.7K]

4÷(6-(8÷2))=2

Do the order of operations, and the end value will be 2.

Do you understand how I got that? Good luck by the way!

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4 years ago

What is the value of x in the solution to the system of equations below?

son4ous [18]

If you would like to know the value of x in the solution to the system of equations, you can find this using the following steps:

6x + 3y = 13
3x - y = 4 ... y = 3x - 4
___________
<span>6x + 3y = 13
</span>6x + 3 * (3x - 4) = 13
6x + 9x - 12 = 13
15x = 13 + 12
15x = 25
x = 25/15
x = 5/3

The correct result would be 5/3.

6 0

3 years ago