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3 years ago

Find the slope of the line through the following pair of points and draw the line through the points (4,1) (-1,-5)

1 answer:

7 0

Slope formula : (y2 - y1) / (x2 - x1)
(4,1)...x1 = 4 and y1 = 1
(-1,-5)...x2 = -1 and y2 = -5
now we sub and solve
slope = (-5 - 1) / (-1 - 4) = -6/-5 = 6/5 <==

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Prove A-(BnC) = (A-B)U(A-C), explain with an example

NikAS [45]

Answer:

Prove set equality by showing that for any element $x$ , $x \in (A \backslash (B \cap C))$ if and only if $x \in ((A \backslash B) \cup (A \backslash C))$ .

Example:

$A = \lbrace 0,\, 1,\, 2,\, 3 \rbrace$ .

$B = \lbrace0,\, 1 \rbrace$ .

$C = \lbrace0,\, 2 \rbrace$ .

$\begin{aligned} & A \backslash (B \cap C) \\ =\; & \lbrace 0,\, 1,\, 2,\, 3 \rbrace \backslash \lbrace 0 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace \end{aligned}$ .

$\begin{aligned}& (A \backslash B) \cup (A \backslash C) \\ =\; & \lbrace 2,\, 3\rbrace \cup \lbrace 1,\, 3 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace\end{aligned}$ .

Step-by-step explanation:

Proof for $[x \in (A \backslash (B \cap C))] \implies [x \in ((A \backslash B) \cup (A \backslash C))]$ for any element $x$ :

Assume that $x \in (A \backslash (B \cap C))$ . Thus, $x \in A$ and $x \not \in (B \cap C)$ .

Since $x \not \in (B \cap C)$ , either $x \not \in B$ or $x \not \in C$ (or both.)

If $x \not \in B$ , then combined with $x \in A$ , $x \in (A \backslash B)$ .
Similarly, if $x \not \in C$ , then combined with $x \in A$ , $x \in (A \backslash C)$ .

Thus, either $x \in (A \backslash B)$ or $x \in (A \backslash C)$ (or both.)

Therefore, $x \in ((A \backslash B) \cup (A \backslash C))$ as required.

Proof for $[x \in ((A \backslash B) \cup (A \backslash C))] \implies [x \in (A \backslash (B \cap C))]$ :

Assume that $x \in ((A \backslash B) \cup (A \backslash C))$ . Thus, either $x \in (A \backslash B)$ or $x \in (A \backslash C)$ (or both.)

If $x \in (A \backslash B)$ , then $x \in A$ and $x \not \in B$ . Notice that $(x \not \in B) \implies (x \not \in (B \cap C))$ since the contrapositive of that statement, $(x \in (B \cap C)) \implies (x \in B)$ , is true. Therefore, $x \not \in (B \cap C)$ and thus $x \in A \backslash (B \cap C)$ .
Otherwise, if $x \in A \backslash C$ , then $x \in A$ and $x \not \in C$ . Similarly, $x \not \in C \!$ implies $x \not \in (B \cap C)$ . Therefore, $x \in A \backslash (B \cap C)$ .

Either way, $x \in A \backslash (B \cap C)$ .

Therefore, $x \in ((A \backslash B) \cup (A \backslash C))$ implies $x \in A \backslash (B \cap C)$ , as required.

8 0

2 years ago

What’s the area of this triangle?

tankabanditka [31]

Answer:

26.75

Step-by-step explanation:

There are two ways to do this. You can use the base*height/2 formula for the area of the triangle, or use the complex formula of determining triangle area without height.

The first is A=(b*h)/2

In this case you need to find the height using a²+b²=c²

Take your base (7.6) and divide it by 2 this will give you the bottom side of your triangle (3.8) now plug this, and the side value of 8 into the formula. Remember c is the hypotenuse (diagonal side) and x is the height.

3.8²+x²=8²

14.44+x²=64

x²=49.56

x=7.039 -now you have the height for the triangle and can use this to find the area

A=b*h (in this case we dont have to divide by two since we need two triangles because we split the original in two to find the base of 3.8)

so it's 3.8*7.039=26.75

(If you need more help look up Silicon Valley High school's video titled, "How to find the area of a triangle (without the height)"

It will teach you the formula $A=\sqrt{s(s-a)(s-b)(s-c)}$ which teaches you to find the area of any triangle when all you are given is three sides

3 0

2 years ago

Marina correctly simplified the expression (-4a^-2 b^4)/(8a^-6b^-3) assuming that a does not equal 0 and b does not equal 0. Her

Elza [17]

For this case we have the following expression:
(-4a ^ -2 b ^ 4) / (8a ^ -6b ^ -3)
We can rewrite the expression using properties of exponents.
We have then:
(-4/8) * ((a ^ (- 2 - (- 6))) (b ^ (4 - (- 3))))
Rewriting we have:
(-2/4) * ((a ^ (- 2 + 6)) (b ^ (4 + 3)))
(-1/2) * ((a ^ 4) (b ^ 7))
-1 / 2a ^ 4b ^ 7
Answer:
The exponent of the variable b in Marina's solution should be 7

7 0

3 years ago

Read 2 more answers

Which rule represents a linear function?<br><br> y=5x² y=5x

nevsk [136]

Answer:

The answer is y=5x²

Step-by-step explanation:

If you put y=5x² on a graph paper it will be in a staright line.

7 0

2 years ago

Find the slope-intercept equation of the line that has a slope of -2 and goes through the point (5,-2).