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3 years ago

13

What is the supplementary angle to an angle that has 112 degrees?

1 answer:

olga55 [171]3 years ago

7 0

Supplementary means they add up to 180°.
180-112= 68
The answer is 68°

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Solve the system using substitution. Check your solution.<br> 2x - y= 65<br> 5y = x

lyudmila [28]

Answer:

The solutions to the system of equations are:

$x=\frac{325}{9},\:y=\frac{65}{9}$

Step-by-step explanation:

Given the system of the equations

$\begin{bmatrix}2x-y=65\\ 5y=x\end{bmatrix}$

isolate 'x' for 2x-y

$2x-y=65$

Add y to both sides

$2x-y+y=65+y$

$2x=65+y$

Divide both sides by 2

$\frac{2x}{2}=\frac{65}{2}+\frac{y}{2}$

$x=\frac{65+y}{2}$

$\mathrm{Subsititute\:}x=\frac{65+y}{2}$

isolate 'y' for $5y=\frac{65+y}{2}$

$5y=\frac{65+y}{2}$

$10y=65+y$

subtract y from both sides

$10y-y=65+y-y$

$9y=65$

Divide both sides by 9

$\frac{9y}{9}=\frac{65}{9}$

$y=\frac{65}{9}$

$\mathrm{For\:}x=\frac{65+y}{2}$

$\mathrm{Subsititute\:}y=\frac{65}{9}$

$x=\frac{65+\frac{65}{9}}{2}$

$x=\frac{325}{9}$

The solutions to the system of equations are:

$x=\frac{325}{9},\:y=\frac{65}{9}$

3 0

3 years ago

Total of 581 students. if the ratio of girls to boys in the class is 3:4, how many more boys than girls are in the class

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Since the ratio is 3:4 there are a total of 7 parts. Divide the 581by 7 to find that each part is 83.

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sertanlavr [38]

Answer:

$Dom\{g(x)\} = Dom\{f(x)\} = (g, h)$ .

$Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)$

Step-by-step explanation:

From Mathematics we remember that the domain of a functions corresponds to the set of values of the independent variable ( $x$ in this case) so that images exist and the range of a function is the set of images.

In this case, we know the domain and range of $f(x)$ and we must find the domain and range of $g(x)$ .

Domain

The domain of $g(x)$ is the domain of $f(x)$ . That is, $Dom\{g(x)\} = Dom\{f(x)\} = (g, h)$ .

Range

We have to define the bounds of the range of $g(x)$ , given that range $f(x)$ is modified by streching and horizontal translation operations:

Lower bound ( $f(x) = j$ )

$g(x) = m\cdot j +p$

Upper bound ( $f(x) = k$ )

$g(x) = m\cdot k +p$

In consequence, the range of $g(x)$ is $Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)$

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