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Dominik [7]
3 years ago
14

Mike and Alice recycled 147 bottles altogether. Mike recycled 6 times as many bottles as Alice. How many bottles did Alice recyc

le?
Mathematics
1 answer:
ValentinkaMS [17]3 years ago
8 0

Answer:

The number of bottles recycle by Alice is 21.

Step-by-step explanation:

Given:

Mike and Alice recycled 147 bottles altogether. Mike recycled 6 times as many bottles as Alice.

Now, to find the quantity of bottles Alice recycle.

Let the number of bottles recycle by Alice = x.

And the number of bottles recycled by Mike = 6x.

So, according to question:

x+6x=147

⇒7x=147

<em>Dividing both sides by 7 we get:</em>

⇒x=21.

Therefore, the number of bottles recycle by Alice is 21.

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Which equation matches the statement: "The sum of -4x and 2 is 9"??
neonofarm [45]

Answer:

A

Step-by-step explanation:

sum means addition

the problem says sum of -4x and 2 meaning -4x + 2

the word "is" right before 9 means equals 9

6 0
3 years ago
!!! HELP ME !!!
antoniya [11.8K]

Answer:

DHGB

Step-by-step explanation:

Let's start with 1.  

The equation is in standard form (ax+by=c): -4x+2y=8

we'll put it into slope intercept form.

Add 4x onto both sides

2y=4x+8

divide by 2

y=2x+4

Parallel lines have the same slope, but a different y intercept. (the line parallel to this one will have a slope of 2 but a y intercept different from +4)

Looking at the answer choices, the only choice with a slope of 2 is D (y=2x-5)

So the answer to 1  is D

Now 2.

we're given 3 points. One of the points crosses the y axis, which is the y intercept. In this case, the line crosses the point (0,3)

That means the y intercept of the line is (0,3)

here's the line so far:

y=mx+3 (m is a placeholder for the slope)

when given a graph, we can use rise/run. Starting from the point (3,2), we can move 3 spaces to the left, and one up.

In a graph, if you move to the left or downwards, it's a negative move. If you move up or to the right, it's a positive move.

Since we went 1 space up (rise) and 3 spaces to the left, (run) the slope is -1/3

So the line is y=-1/3x+3

Perpendicular lines are negative and reciprocal. If you multiply their slopes, they will equal -1. Their y intercepts don't matter at all.

So to find the slope, we can use this equation.

-1/3m=-1

multiply by -3 on both sides

m=3

Looking at the answer choices, H is the only answer with a slope of 3. So the answer to 2 is H.

Now, 3

You can do the graph method like above for 2, but I'll just calculate the slope.

We're given two points, (-1,-2) and (0,2)

the formula for slope is (y2-y1)/(x2-x1)

we can label the points.

x1=-1

y1=-2

x2=0

y2=2

now, substitute into the equation.

m=(2--2)/(0--1)

m=4/1

the slope is 4.

Now let's use point slope form, which is y-y1=m(x-x1)

once again, sub. into the equation.

y+2=4(x+1)

do distributive prop

y+2=4x+4

subtract by 2

y=4x+2

As said above, parallel lines have the same slope.

Looking at the answer options, G also has the slope of 4

so the answer to 3 is G

Finally, #4

Equation: 3x+y=1

subtract 3x from both sides

y=-3x+1

As said above, perpendicular lines have slopes that multiply to equal -1.

-3m=-1

multiply by -1/3

m=1/3

so the slope of the line will be 1/3.

Looking at the answer options, B also has a slope of 1/3.

So the answer to 4 is B

The code is DHGB

Hope this helps!

4 0
3 years ago
The area of a rectangle whose perimeter is a fixed 80 feet is given by A=40w - w2 , where w is the width of the rectangle. Deter
Stolb23 [73]

Answer:

Width=20 feet

Since Length=Width=20 feet, the rectangle is a Square.

Step-by-step explanation:

Area, A=40w - w^2

To determine the width of the rectangle that gives the maximum area, we take the derivative of A and solve for its critical point.

A'=40 - 2w\\$When A'=0\\40-2w=0\\40=2w\\w=20 feet

The width of the rectangle that gives the maximum area =20 feet.

Perimeter of a rectangle=2(l+w)

Perimeter of the rectangle=80 feet

2(l+w)=80

2l+2(20)=80

2l=80-40

2l=40

l=20 feet

Since the length and width are equal, the special type of rectangle that produces this maximum area is a Square.

7 0
3 years ago
Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her
Tatiana [17]
<span>The equation is e = 300 - 10t. t is greater or equal than 0 and given that e cannot be negative, 300 - 10 t greaetr or equal than 0 => 10 t greater or equal than 300, and t greater or equal than 300/10 = 30. This is the viable points are times from 0 to 10 and elevation from 300 to 0. Some points are (0,300) which is the initial point (when Rory is on the top); (1, 290); (2, 280); (3, 270); (4, 260); (5, 250); (6, 240); (10, 200), (20, 100), (30, 0).</span>
7 0
3 years ago
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Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50. Ques
ivann1987 [24]

Answer:

9 months

Step-by-step explanation:

4 0
3 years ago
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