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3 years ago

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Mathematics

1 answer:

tia_tia [17]3 years ago

5 0

Answer:

Step-by-step explanation:-

Triangle ABC lies on the

coordinate plane with vertices

located at A (8,6), B (2,-5), and

C (-5, 1). The triangle is

< transformed using the rule

(x,y) - (x + 3,2y) to create

triangle A'B'C'.

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2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

3 years ago

(4x^3 - x^2 +4x) + (x^3 -x^2 - 4x)

madreJ [45]

Answer:

5x³ - 2x²

Step-by-step explanation:

Step 1: Write out expression

4x³ - x² + 4x + x³ - x² - 4x

Step 2: Combine like terms (x³)

5x³ - x² + 4x - x² - 4x

Step 3: Combine like terms (x²)

5x³ - 2x² + 4x - 4x

Step 4: Combine like terms (x)

5x³ - 2x²

4 0

3 years ago

PLEASE HELP ITS DUE TODAY!!

Lena [83]

Answer:

a) 5 pizzas need to be ordered and half of a pizza will be left over aka 0.5

b) $45

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Please help with these questions!!:))

Sonbull [250]

Answer:

The first one : decay

The second one : growth

When the argument of the exponential expression is bigger that 1 then it represents a growth

When it's less than 1 and above 0 then it's a decay

8 0

3 years ago

You begin a hike in Death Valley, California, an elevation of -86 meters meters. You hike to a point of elevation at 45 meters.

KIM [24]

-41 would be your answer

6 0

3 years ago