A line has this equation: -10x + y = -5

Murrr4er [49]

$\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
\\
&& y={{k }}x
\end{array}\\\\
-------------------------------\\\\$

$\bf \textit{we know that }\qquad 
\begin{cases}
y=42\\
x=6
\end{cases}\implies 42=k6\implies \cfrac{42}{6}=k
\\\\\\
7=k\impliedby \textit{constant of variation}
\\\\\\
thus\qquad \qquad y=7x
\\\\\\
\textit{what is "y" when x=5?}\qquad y=7(5)\impliedby \textit{solve for "y"}
\\\\\\
\textit{what is "x" when y=28?}\qquad 28=7x\impliedby \textit{solve for "x"}$

6 0

4 years ago

How many solutions does this linear system have y=2x-5. -8-4y=20

ollegr [7]

Answer:

One solution

Step-by-step explanation:

y = 2x – 5. –8x – 4y = –20. one solution: (–2.5, 0)

4 0

4 years ago

Which expression represents the phrase?

Alecsey [184]

Answer:

D. (5 + x) - 6

Step-by-step explanation:

"6 less than the sum of 5 and x."

I can try sum of 5 and x first

(5 + x)

then 6 less than it.

(5 + x) - 6

3 0

4 years ago

Calculate the area of the following figure correct to 2 decimal places if can show or explain work

grin007 [14]

The way we approach a question like this, is by looking at what portion of the circle we actually have to calculate the area of. We know that a circle is a shape that goes 360 degrees around a point. Therefore we know that, for example, a semicircle, or half a circle, would cover half the amount of degrees. This is important, because as well as covering half the number of degrees, it also covers half the area. For the figure in your picture, we are told that the portion missing from the circle is 90 degrees (shown by the right angle symbol in the center).
this means that 90 degrees worth of the circle is missing, so if we do 360÷90, we find that the answer equals $\frac{3}{4}$ . This means that we are dealing with $\frac{3}{4}$ of a circle. So, we simply find the area of the circle normally, and then multiply by $\frac{3}{4}$ :
The formula for area of a circle is $\pi r^{2}$ , so in this case, it can be said to be $\pi (10^{2} )$ , which is equal to 314.15
Now we simply take that area and multiply it by the fraction we established earlier:
314.15 x $\frac{3}{4}$ = 235.61
Therefore the area of the figure is 235.61 $cm^{2}$
I hope this helped and please remember to try and not only understand the answer, but the maths that worked it out too :))

3 0

4 years ago

Which biconditional is NOT a good definition

ZanzabumX [31]

The answer is: [C]: Two angles form [a] linear pair if and only if the angles are adjacent.
_____________________________
{Your answer choice is correct! Good job!}.
_______________________________________
Explanation:
__________________
Consider the answer choice given in: "Answer choice: [C]" :
_______________________
"Two angles form linear pair if and only if the angles are adjacent."
_____________________________
Then, consider the following:
__________________
1) "Two angles that are supplementary form a linear pair."
Is this true? Yes, but not always. (In other words, "sometimes"). A "linear pair" of angles IS supplementary (by definition); however, NOT ALL supplementary pairs of angles are linear angles. Supplementary pairs of angles must ALSO be ADJACENT in order to be "linear angles" as well.
2) "Two angles that are vertical are adjacent." Is this true? No; this is NEVER true
_____________
As such, this biconditional is NOT a good definition; and by examining all the other answer choices given, we see that this answer choice "C" is correct.
__________________
Consider the other answer choices given:
_________________________________________
Answer choice: [A]: "Two angles are supplementary if and only if the sum of their angles measures 180." ;
 is INCORRECT because it is a good definition:
1) If 2 angles are supplementary, then the sum of their measures is 180 degrees.
2) If the sum of the measures of two angles is 180 degrees, then the angles are supplementary.
___________________________________
Answer choice: [B]: "Two angles are vertical angles only if they are not adjacent to each other and are formed by two intersecting lines.";
is INCORRECT because it is a good definition:
1) If two angles are vertical, then they are nonadjacent angles formed by two intersecting lines.
 2) If two angles are nonadjacent angles formed by two intersecting lines, then the angles are vertical angles.
_____________________________________
Answer choice: [D]: "The sum of two angles is 90 if and only if those angles are complementary" ;
is INCORRECT because it is a good definition:
1) If two angles are complementary, then the sum of their measures is 90 degrees.
 2) f the sum of [the measures of] two angles is 90 degrees, then the angles are complementary.
_______________________________________________

7 0

4 years ago

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