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3 years ago

What are the next two numbers in this pattern? 5, –30, 180, –1080, . . .

Mathematics

2 answers:

Amiraneli [1.4K]3 years ago

4 0

6480 is the next one, and the second next one is -38880. You can determine this by multiplying the number twice by 36.

OLEGan [10]3 years ago

4 0

Since the pattern is to multiply by negative 6, the next numbers are; 6480, and -38880

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3 years ago

A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y. Corn costs $215 per acre to produce, and cotton costs

tatyana61 [14]

Answer:

The system that represent the scenario is

$x+y\leq500$

$215x+615y\leq 187,500$

The solution in the attached figure

Step-by-step explanation:

Let

x-----> the acres of corn

y----> the acres of cotton

we know that

$x+y\leq500$ ------> inequality A

$215x+615y\leq 187,500$ -----> inequality B

using a graphing tool

the solution is the shaded area in the attached figure

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3 years ago

Read 2 more answers

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.

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