THE number of bass and pike in a lake are estimated to be in the ratio of 5:3. There are approximately 500 fish in the lake.

When using substitution to solve this system of equations, what is the result of the first step x=6y+3

myrzilka [38]

First step: you have to plug in 6y+3 into the equation and solve
Example: 6y+3+2y = 5

3 0

3 years ago

Determine whether PQ and UV are parallel,

lys-0071 [83]

Answer:

The answer is below

Step-by-step explanation:

The slope of a line (m) is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

Two lines are parallel if they have the same slope and perpendicular if the product of their slope is -1.

1)

$Slope\ of\ PQ=\frac{1-(-2)}{9-(-3)}=\frac{1}{4} \\\\Slope\ of\ UV=\frac{-2-6}{5-3}=-4$

Since the product of their slope is -1, they are perpendicular

2)

$Slope\ of\ PQ=\frac{1-7}{2-(-10)}=-\frac{1}{2} \\\\Slope\ of\ UV=\frac{1-0}{6-4}=\frac{1}{2}$

Since the slope is not the same or product of their slope is not -1, they are neither parallel or perpendicular

3)

$Slope\ of\ PQ=\frac{8-1}{9-1}=\frac{7}{8} \\\\Slope\ of\ UV=\frac{8-1}{2-(-6)}=\frac{7}{8}$

Since the slopes are the same, they are parallel

4)

$Slope\ of\ PQ=\frac{3-0}{9-(-4)}=\frac{3}{4} \\\\Slope\ of\ UV=\frac{6-(-3)}{8-(-4)}=\frac{3}{4}$

Since the slopes are the same, they are parallel

5)

$Slope\ of\ PQ=\frac{1-2}{0-(-9)}=-\frac{1}{9} \\\\Slope\ of\ UV=\frac{-1-8}{-2-(-1)}=9$

Since the product of their slope is -1, they are perpendicular

6 0

3 years ago

Read 2 more answers

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books

laila [671]

Let, the number of books on Monday = m
On Tuesday = 2m
On Wednesday = 2m - 6

Equation: m + 2m + (2m - 6) = 19
You can solve it:
5m = 19 + 6
m = 25/5
m = 5

In short, He sold 5 books on Monday

Hope this helps!

7 0

4 years ago

Chad has a bag with 2 mint sticks, 11 jelly treats, and 7 fruit tart chews. If he eats one piece every 4 minutes, what is the pr

scoray [572]

Answer:

first you add all the candies together to get 20 in the bag

2+11+7=20

jelly treat:

now we divide 11 by 20 to get a decimal

11/20= .55

multiply .55 by 100 to change it to a percentage

.55*100=55

first part of answer: He has a 55% chance of getting a jelly treat

mint stick:

divide 2 by 20 to get a decimal

2/20=.1

change .1 to a percent by multiplying by 100

.1*100=10

second part of answer: he has a 10% chance of getting a mint stick

Step-by-step explanation:

7 0

3 years ago

Given the following: What is the value of x? What is the value of y? What is the m∠A? Show all work.

kondaur [170]

Answer:

angle A=angle C

angle B =angle D

to find x

$x + 45 = 3x - 85 \\ x - 3x = - 85 - 45 \\ - 2x = - 130 \\ x = 75$

to find y

$x + 45 + 3x - 85 + y + y = 360 \\ 4x + 40 + 2y = 360 \\ 4(75) + 2y = 360 - 40\\ 300 + 2y = 320 \\ 2y = 20 \\ y = 10$

3 0

3 years ago

Read 2 more answers