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kompoz [17]
3 years ago
12

6r+7=13+7r show work please​

Mathematics
1 answer:
yulyashka [42]3 years ago
8 0

Answer:

r=-6

Step-by-step explanation:

6r-7r=13-7

-r=6

r=-6

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PLEASE HELP ME ON THESE PROBLEMS, ITS URGENT! (Help for any of these would be greatly appreciated!)
Anvisha [2.4K]
1.) We can solve the problem by developing a linear model.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
\left\begin{array}{c}x+y=80 . . . (1)\\70x+80y=76(80) . . . (2)\end{array}\right  \\   \\ \Rightarrow  \left\begin{array}{c}80x+80y=6400 . . . (3)\\70x+80y=6080 . . . (4)\end{array}\right  \\  \\ \Rightarrow10x=320 \\  \\ \Rightarrow x=32 \\  \\ \Rightarrow y=80-32=48
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.


2.) Volume of alcohol in the original mixture
\frac{35}{100} \times 40=14 quarts

Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
\frac{48}{100} \times (40+x)=14+x \\  \\ \Rightarrow19.2+0.48x=14+x \\  \\ \Rightarrow0.52x=5.2 \\  \\ \Rightarrow x=10

Therefore, 10 quarts of pure alcohol should be added


3.) Original proportion of white paint in the mixture
=\frac{5}{5+11}=\frac{5}{16}

Let x be the number of gallons of white paint to be added, then
\frac{5+x}{16+x}=\frac{2}{3} \\  \\ \Rightarrow3(5+x)=2(16+x) \\  \\ \Rightarrow15+3x=32+2x \\  \\ \Rightarrow x=32-15=17
Therefore, 17 gallons of white paint should be added.


4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
x - 2 + x + x + 2 = 25 \\  \\ \Rightarrow3x=25\Rightarrow x=8.33
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.

4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
x - 2 + x + x + 2 = 45 \\ \\ \Rightarrow3x=45\Rightarrow x=15
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.


5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
\frac{1}{t} = \frac{1}{9} + \frac{1}{12} - \frac{1}{15} = \frac{20+15-12}{180} = \frac{23}{180} \\  \\ \Rightarrow t= \frac{180}{23} =7.83
Therefore, it will take 7.83 hours to get the tank filled up.
3 0
3 years ago
Can someone please help
choli [55]

Answer:

(6, -4)

Step-by-step explanation:

If ABCD is dilated by a factor of 2, you multiply the coordinates by 2. For the coordinate D', you would multiply 3 by 2 to get 6 and you would multiply -2 by 2 to get -4. Answer: (6, -4)

3 0
3 years ago
I’m I right? I kinda but kinda don’t get this question I lost my notes and I just learnt this
belka [17]

Yes, you are correct

3 0
2 years ago
Read 2 more answers
Is c+3/5=15 an identity
Mademuasel [1]
No, becuase c has to be a certain number to equal 15
6 0
2 years ago
Find all solutions to the equation in the interval [0, 2π). cos 2x - cos x = 0
Jlenok [28]
This is the concept of algebra, to solve the expression we proceed as follows;
cos 2x-cosx=0
cos 2x=cosx
but:
cos 2x+1=2(cos^2x)
thereore;
from:
cos 2x=cos x
adding 1 on both sides we get:
cos 2x+1=cos x+1
2(cos^2x)=cosx+1
suppose;
cos x=a
thus;
2a^2=a+1
a^2-1/2a-1/2=0
solving the above quadratic we get:
a=-0.5 and a=1
when a=-0.5
cosx=-0.5
x=120=2/3π
when x=1
cos x=1
x=0
the answer is:
x=0 or x=2/3π

4 0
3 years ago
Read 2 more answers
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