Park rangers at a game preserve in Africa observed a cheetah run 3

Eduardo puts $40 into his piggy bank and plans to add $5 each month. Write an equation to represent this.

igomit [66]

Answer:

40+5x

Step-by-step explanation:

Eduardo put $40 in so the 40 is what he has already put in. Next you have $5 added in but it doesn’t say for how many months just that it’s each month so we put the x to represent out unknown so we can solve the equation.

4 0

3 years ago

A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the rati

AnnyKZ [126]

Answer:

3:7

Step-by-step explanation:

So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or <em>20%</em> is alcohol. So let's just say that x=alcohol and y=water, this means that: $x+y=c$ where c is the total amount in the glass. This means that: $x=0.20c$

Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: $j+k=c$ and that: $j=0.40c$ .

So if we're going to add the two glasses, we simply add the two sides, and get: $j+x+k+y=2c$ . Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: $(0.4c+0.2c)+x+k=2c$ Now we can add like terms to get the equation: $0.6c+y+k=2c$ . We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.

3 0

2 years ago

Read 2 more answers

Write the equation in y=mx+b form please????

Solnce55 [7]

ANSWER

$y = - 2x - 5$

EXPLANATION

We can use any two points to determine the slope.

The line passes through;

(-3,1) and (-5,5).

The slope is given by

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

This implies that;

$m = \frac{5 - 1}{ - 5 - - 3}$

$m = \frac{4}{ - 2} = - 2$

We can now find the equation using the formula;

$y-y_1=m(x-x_1)$

$y - 1 = - 2(x + 3)$

Expand:

$y = - 2x -6 + 1$

$y = - 2x - 5$

6 0

3 years ago

Four students were discussing how to find the unit rate for a proportional relationship. Which method is valid? “Look at the gra

AlladinOne [14]

The correct answer is: [A]: " Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate."

<h3>What is y-value?</h3>

The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). Also called "Ordinate".

Here, The "y-axis" is located on the "vertical axis" that represents the "dependent variable" (or, at times, the "control value") that cannot be "manipulated" / controlled/ or "selected" / since it represents the "y-value" of the corresponding coordinate to which the "x-value" happens to corresponds to at the given value for "x" .

Thus, the correct answer is: [A]: " Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate."

Learn more about Y-value from:

brainly.com/question/3319387

#SPJ1

8 0

2 years ago

Please help. Don’t understand this math problem!

oksian1 [2.3K]

Answer:

{ 4 }

Step-by-step explanation:

First you need to solve the equation. Then you need to write the solutions as a set.

__

I like to use a graphing calculator to solve equations involving roots. That helps avoid extraneous solutions. Here, the graph of the left side intersects the graph of the right side at x=4. There is exactly one solution, so the solution set is ...

{ 4 }

__

Solving this algebraically, you would isolate the radical, then "undo" it by squaring both sides of the equation. Then solve the resulting quadratic. That will have 2 solutions, only one of which will work in the original equation.

√(5x +16) -2 = 3x -8 . . . . given

√(5x +16) = 3x -6 . . . . . . add 2

5x +16 = (3x -6)^2 . . . . . square both sides

5x +16 = 9x^2 -36x +36 . . . . expand the square

9x^2 -41x +20 = 0 . . . . . . subtract (5x+16) to put into standard form

Factors of 9·20 = 180 that have a sum of 41 are 5 and 36, so we can rewrite this equation as ...

9x^2 -36x -5x +20 = 0

9x(x -4) -5(x -4) = 0 . . . . . . factor by pairs

(9x -5)(x -4) = 0

The values of x that make this equation true are the values that make the factors be zero: 5/9 and 4. Trying these in the equation, we find ...

√(5(5/9) +16) -2 = 13/3 -2 = 2 1/3 . . . . value of the left side for x = 5/9

3(5/9) -8 = -6 1/3 . . . . . . value of the right side for x=5/9; not the same

x = 5/9 is NOT A SOLUTION

__

√(5(4)+16) -2 = √36 -2 = 4 . . . . value of the left side for x = 4

3(4) -8 = 12 -8 = 4 . . . . . . value of the right side for x=4. These are the same, so ...

x = 4 is a solution

The set of solutions is then ...

{ 4 } . . . . . solution set

5 0

3 years ago