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3 years ago

The measures of two supplementary angles are (2x – 8)° and (3x - 2)°. What is the measure of the

Mathematics

1 answer:

saw5 [17]3 years ago

4 0

Answer:

68°

Step-by-step explanation:

Here,

Two supplementary angles are (2x – 8)° and (3x - 2)°.

As we know that the sum of two supplementary angles are 180°. So,

→ (2x – 8)° + (3x – 2)° = 180°

→ 2x° – 8° + 3x° – 2° = 180°

→ 5x° – 10° = 180°

→ 5x° = 180° + 10°

→ 5x° = 190°

→ x = 190° ÷ 5°

→ x = 38°

Supplementary angles are,

1st angle = (2x – 8)°

→ 2(38°) – 8

→ (76 – 8)°

→ 68°

2nd angle = (3x – 2)°

→ 3(38°) – 2

→ (114 – 2)°

→ 112°

Therefore, the measure of the smaller angle is 68°.

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22. Many rectangles have a perimeter of 81 feet. Find the dimensions for the one with the maximum enclosed area.

melisa1 [442]

Let
x----------> the length of the rectangle
y---------> the width of the rectangle

we know that
perimeter of rectangle=2*[x+y]
area of rectangle=x*y
P=81 ft
so
81=2*[x+y]-----------> 40.5=[x+y]

case A) 20.25 feet × 20.25 feet
P=2*[20.25+20.25]-----> 81 ft----------> the perimeter is ok
A=20.25*20.25-----> 410.06 ft²

case B) 11 feet × 29.5 feet
P=2*[11+29.5]-----> 81 ft----------> the perimeter is ok
A=11*29.5-----> 324.5 ft²

case C) 9 feet × 9 feet
P=2*[9+9]-----> 36 ft----------> the perimeter is not 81
A=9*9-----> 81 ft²

case D) 17.5 feet × 23 feet
P=2*[17.5+23]-----> 81 ft----------> the perimeter is ok
A=17.5*23-----> 402.5 ft²

the answer is
case A) 20.25 feet × 20.25 feet

5 0

3 years ago

(-10m^4n^7)(-3m^4n) the answer should be a simplified monomial

Brilliant_brown [7]

(-10m^4n^7)(-3m^4n)

= -10*-3 m^4*m^4 * n^7* n^1

= 30m^8n^8

3 0

3 years ago

The panthers won 4/5 of their games,. If they lost 7 games, how many games did they win?

Varvara68 [4.7K]

Answer:

They have won 28

Step-by-step explanation:

The team has lost 1/5 of their games. You can do how many they have lost, 7, times the amount of the denominator, 5. Doing this gives you 35, the TOTAL games played. Since we are looking for the games won, you do the total, 35, minus the games lost, 7. You get 28.

7 0

4 years ago

Show all worked identify the asymptotes and state the end behavior of the function F(x)=6x over x-36

astraxan [27]

Solution

Asymptote:

Vertical Asymptote

- The vertical asymptotes of a rational function are determined by the denominator expression.

- The expression given is:

$f(x)=\frac{6x}{x-36}$

- The denominator of (x- 36) determines the asymptote line.

- The vertical asymptote defines where the rational function isundefined. Iin order for a rational function to be undefined, its denominator must be zero.

- Thus, we can say:

$\begin{gathered} x-36=0 \\ Add\text{ 36 to both sides} \\ \\ \therefore x=36 \end{gathered}$

- Thus, the vertical asymptote is

$x=36$

Horizontal Asymptote:

- The horizontal asymptote exists in two cases:

1. When the highest degree of the numerator is less han the degree of the demnominator. In this case, the horizontal asymptote is y = 0

2. When the highest degee sof the numerator and tdenominator are the same. In this case, the horizontal asymptote is

$\begin{gathered} y=\frac{N}{D} \\ where, \\ N=\text{ Coefficient of the highest degree of the numerator} \\ D=\text{ Coefficient of the highest degree of the denominator} \end{gathered}$

- For our question, we can see that the highest degrees of the numerator and denominator are the same. Thus, we have the Horizontal Asymptote to be:

$y=\frac{6}{1}=6$

End behavior:

- The end behavior is examining the y-values of the function as x tendsto negative and positive infinity.

- Thus, we have that:

$\begin{gathered} f(x)=\frac{6x}{x-36} \\ \\ \text{ Divide top and bottom by }x \\ f(x)=\frac{6x}{x-36}\times\frac{x}{x} \\ \\ f(x)=\frac{\frac{6x}{x}}{\frac{x-36}{x}}=\frac{6}{1-\frac{36}{x}} \\ \\ As\text{ }x\to-\infty \\ f(-\infty)=\frac{6}{1-\frac{36}{-\infty}}=\frac{6}{1+\frac{36}{\infty}}=\frac{6}{1+0}=6 \\ \\ \text{ Thus, we can say: }x\to-\infty,f(x)\to6 \\ \\ Also, \\ As\text{ }x\to\infty \\ f(\infty)=\frac{6}{1-\frac{36}{\infty}}=\frac{6}{1-0}=6 \\ \\ \text{ Thus, we can also say: }x\to\infty,f(x)\to6 \end{gathered}$

Final Answers

Asymptotes: