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xeze [42]
3 years ago
14

Kesha sharpened 4 colors of pencils for her teacher. She sharpened equal amounts of red and green pencils. Then she sharpened tw

ice as many blue and yellow pencils in equal amounts. How many of the 42 pencils were yellow?
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
7 0
Variables are taken from the first letter of the color, ex: green = g.

Given:
r = g
2r = b = y
Total =42

So then:
r+ r + 2r + 2r = 42
6r = 42
r = 7

y = 2r
y = 2(7)
14 of the 42 pencils were yellow.
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anastassius [24]

Step-by-step explanation:

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3 years ago
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Miriam has 62 feet of fencing to make a rectangular vegetable garden. Which dimensions will give Miriam the garden with greatest
lidiya [134]
Perimeter: P=62 feet
P=2(b+h)
62=2(b+h)
Dividing both sides of the equation by 2:
62/2=2(b+h)/2
31=b+h
b+h=31   (1)

Area: A=bh   (2)

Isolating h in equation (1)
(1) b+h=31→b+h-b=31-b→h=31-b   (3)

Replacing h by 31-b in equation (2)
(2) A=bh
A=b(31-b)
A=31b-b^2

To maximize the area:
A'=0

A'=(A)'=(31b-b^2)'=(31b)'-(b^2)'=31-2b^(2-1)→A'=31-2b

A'=0→31-2b=0
Solving for b:
31-2b+2b=0+2b
31=2b
Dividing both sides by 2:
31/2=2b/2
31/2=b
b=31/2=15.5

Replacing b by 31/2 in equation (3)
h=31-b
h=31-31/2
h=(2*31-31)/2
h=(62-31)/2
h=31/2

The dimensions are 31/2 ft x 31/2 ft = 15.5 ft x 15.5 ft
The area with these dimensions is: A=(15.5 ft)(15.5 ft)→A=240.25 ft^2

These dimensions are not in the options

1) The first option has an area of: A=(18 ft)(13 ft)→A=234 ft^2
2) The second option has an area of: A=(19 ft)(12 ft)→A=228 ft^2
3) The third option has an area of: A=(17 ft)(14 ft)→A=238 ft^2

The third option has the largest area.

Answer: Third option  
 
4 0
3 years ago
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Find the equation of the line. Use exact numbers
romanna [79]

Answer:

y = -3/2x + 3

Step-by-step explanation:

We can get 2 points from the graph

(0,3)

(2,0)

from (0,3) we know that the b in the equation is 3

now to calculate m or slope we use \frac{y1-y2}{x1-x2}

\frac{0 - 3}{2-0} = -3/2

so we plug our m and b into y = mx + b and get

y = -3/2x + 3

6 0
3 years ago
In a geometric sequence, the ratio between consecutive terms is...
Leokris [45]
<h3>Answer: The same or equal</h3>

========================================================

Explanation:

Consider an example like 3, 6, 12, 24, 48, ...

The ratio between consecutive terms is

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Each time we divide any given term over its previous one, we get the same ratio 2. We call this the common ratio. In terms of notation, the variable r is used for the common ratio, so r = 2 in this case.

As another example, the geometric sequence 5, 50, 500, 5000, ... has r = 10 as the common ratio because we multiply each term by 10 to get the next one. Moving forward has us multiply by r, moving backward and we divide by r. The value of r cannot be zero, but it can be negative.

An example with r being negative would be something like

1, -1, 1, -1, 1, -1, ....

we just bounce back and forth between those two values. In this case, r = -1.

6 0
3 years ago
What is this? I’m too dumb.
gavmur [86]

Answer:

its 35

Step-by-step explanation:

y = 6

and 6 times 6 is 36

and 36 minus 1 is 35

:)

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