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Marta_Voda [28]
3 years ago
7

Recall that two angles are complementary if the sum of their measures is​ 90°. Find the measures of two complementary angles if

one angle is five
times the other angle.
Mathematics
1 answer:
lorasvet [3.4K]3 years ago
5 0
The measure of angle one is 75 degrees and the other measure is 15 degrees
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Rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$
solniwko [45]

Rewrite the expression  6j^2 - 4j + 12$ in the form $c(j + p)^2 + q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$

The ratio of \frac{q}{p}  = - 34

How to solve such questions?

Such Questions can be easily solved just by some Algebraic manipulations and simplifications. We just try to make our expression in the form which question asks us. This is the best method to solve such questions as it will definitely lead us to correct answers. One such method is completing the square method.

Completing the square is a method that is used for converting a quadratic expression of the form ax^{2} + bx + c to the vertex form

a(x - h)^{2} + k. The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: a(x + m)^{2} + n, such that the left side is a perfect square trinomial

$6j^2 - 4j +12$

=  $6(j^2 - \frac{2}{3} j )+12$

= $6(j^2 - \frac{2}{3} j  +  \frac{1}{9}  )+\frac{102}{9}                   (Completing Square method)

=6( j- \frac{1}{3} )^{2}  +  \frac{34}{3}

On comparing with the given equation we get

p = - \frac{1}{3}     and q = \frac{34}{3}

∴ \frac{q}{p} = \frac{\frac{34}{3} }{\frac{-1}{3} }

= - 34

Learn more about completing the square method here :

brainly.com/question/26107616

#SPJ4

7 0
2 years ago
Translate the following verbal expression into a algebraic expression Ten more than the absolute value of a number
Butoxors [25]

Answer:

x + 10

Step-by-step explanation:

X is used to represent a variable or any number. This letter can be changed if you'd like

6 0
3 years ago
1. In the picture below, if major arc BC is 258
WINSTONCH [101]

The answer is attached.

4 0
3 years ago
The function f(x) = 3x² + 12x +11 can be written in
Viktor [21]

Answer:

3)  f(x) = 3(x + 2)^2 - 1.

Step-by-step explanation:

f(x) = 3x² + 12x +11

f(x) = 3(x^2 + 4x) + 11        Completing the square:

f(x) =  3[(x + 2)^2 - 4] + 11

f(x) = 3(x + 2)^2 -+3*-4 + 11

f(x) = 3(x + 2)^2  - 12 + 11

f(x) = 3(x + 2)^2 - 1.

6 0
3 years ago
How many years (approximately) will it take $6,000 to amount $8,000 if it is invested at an annual rate of 9.0% compounded conti
quester [9]

Answer:

It should take roughly 3.5 years

Step-by-step explanation:


6 0
3 years ago
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