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Zielflug [23.3K]
2 years ago
14

What is the measure of the missing angle?

Mathematics
1 answer:
Semenov [28]2 years ago
3 0
Hello! every triangle’s interior angles add up to 180. here would be how I solve this equation.

180-75-40=65 (find missing angle)
65+x=180 (supplementary angles)
180-65=x (substitution)
115=x (simplify)
x=115 (reflexive property of equality)
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<img src="https://tex.z-dn.net/?f=5x-%20%5Cdfrac%7B%20%5Csqrt%7B%209%20%7B%20x%20%7D%5E%7B%202%20%7D%20-6x%2B1%20%5Cphantom%7B%5
Morgarella [4.7K]

Answer:

=5x+1          or          =5x-1

Step-by-step explanation:

One is given the following equation:

5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}

The problem asks one to simplify the expression, the first step in solving this equation is to factor the equation.  Rewrite the numerator and denominator of the fraction as the product of two expressions. Remember the factoring patterns:

(a-b)^2=a^2-2ab+b^2

=5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}

=5x-\frac{\sqrt{(3x-1)^2}}{-(3x-1)}

Now simplify the numerator. Remember, taking the square root of a squared value is the same as taking the absolute value of the expression,

=5x-\frac{\sqrt{(3x-1)^2}}{1-3x}

=5x-\frac{|3x-1|}{-(3x-1)}

Rewrite the expression without the absolute value sign in the numerator. Remember the general rule for removing the absolute value sign:

|a-b|\\=a -b           or           (-a-b) = b-a

=5x-\frac{|3x-1|}{-(3x-1)}

=5x-\frac{3x-1}{-(3x-1)}          or          =5x-\frac{-(3x-1)}{-(3x-1)}

Simplify both expressions, reduce by canceling out common terms in both the numerator and the denominator,

=5x-\frac{3x-1}{-(3x-1)}          or          =5x-\frac{-(3x-1)}{-(3x-1)}

=5x-(-1)          or          =5x-(1)

Simplify further by rewriting the expression without the parenthesis, remember to distribute the sign outside the parenthesis by the terms inside of the parenthesis; note that negative times negative equals positive.

=5x-(-1)          or          =5x-(1)

=5x+1          or          =5x-1

6 0
3 years ago
Please translate each algebraic expression to English phrase
ludmilkaskok [199]

1. x - 8

2. 13 + 2y

3. 4 ( x+ 5)

4. 7x

5. m + 6
5 0
2 years ago
Read 2 more answers
Is a rectangular prism has a length width and height of 3/8cm, 5/8cm and 7/8 in a meter respectively then the volume of the pris
myrzilka [38]

The volume of a rectangular prism is given by the multiplication of its three dimensions: if w, h, l are the width, height and length of the prism, the volume is

V = w\cdot h\cdot l

So, in your case, you have

V = \dfrac{3}{8} \cdot \dfrac{5}{8} \cdot \dfrac{7}{8} = \dfrac{3\cdot 5 \cdot 7}{8\cdot 8 \cdot 8} = \dfrac{105}{512}

4 0
3 years ago
In Mr. Scott’s class the ratio of boys to girls is 2:3. The total number of students in Mr. Scott’s class is 30. What percent of
Yuri [45]

Answer:

40% of the class is Girls, so 12 students are girls

Step-by-step explanation:

add up the ratio

2+3=5

divide by 5

30/5=6

multipy ratio to find totial number of students

2*6=12

2*3=18

divide the number of students to get the pecentage

12/30=0.4=40%

18/30=0.6=60%

5 0
3 years ago
How to simplify this question
ANEK [815]
Simplification = 3.5x + 2.5x
Result = 6x
6 0
4 years ago
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