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kipiarov [429]
3 years ago
12

Solve the system by substitution. y = 2x 3x + 2y = 21

Mathematics
2 answers:
soldier1979 [14.2K]3 years ago
6 0
\left \{ {{y=2x} \atop {3x+2y=21}} \right \longrightarrow \left \{ {{y=2x} \atop {3x+2\cdot2x=21}} \right. \longrightarrow \left \{ {{y=2x} \atop {7x=21}} \right.\longrightarrow \left \{ {{y=2x} \atop \boxed{{x=3}}} \right.  \\\\y=2x\longrightarrow y=2\cdot3\longrightarrow \boxed{y=6}
Alexandra [31]3 years ago
6 0
Y=2x;3x+2y=21

Solve y=2x for y

 Substitute (2x) for y in 3x+2y=21

3x+2y=21

3x+22x=21

7x=21 (Simplify)

7x / 7 = 21 / 7(Divide both sides by 7)

x=3

Substitute (3) for x in y=2x:

y=2x

y=(2)(3)

y=6 (Simplified)

y=6 and x=3

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Answer:

6.24 units.

Step-by-step explanation:

Use the Pythagorean theorem.

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4 years ago
A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are ma
Marrrta [24]

Answer:

the cost function is Cost=7000 m*$ /R + 50.265 $/m² * R²

Step-by-step explanation:

then the cost function is

Cost= cost of side area+ cost of top + cost of bottom = 2*π*R*L * 5$/m² +

π*R² * 8$/m² +  π*R² * 8$/m²

since the volume V is

V=π*R²*L → V/(π*R²)=L

then

Cost=2*π*R*V/(π*R²) * 5$/m² +  π*R² * 8$/m² +  π*R² * 8$/m²

replacing values

Cost=2*700 m³ /R * 5$/m² +  π*R² * 16$/m² = 7000 m*$ /R + 50.265 $/m² * R²

thus the cost function is

Cost=7000 m*$ /R + 50.265 $/m² * R²

4 0
3 years ago
Read 2 more answers
Factor x2+4x-12 , Your help is sincerely appreciated and is not taken lightly. Once again. I thank you.
Vikki [24]
The correct answer is:  [C]:  " (x + 6)(x - 2) " .
_______________________________________________________
4 0
4 years ago
Cam rode her bike 5 times as far as Dante did. Dante rode 187 meters farther than Michael did. Cam rode 15.25 Kilometers. How ma
kiruha [24]
Let Dante's distant be x, Cam's will be 5x
Given that Cam rode 15.25 km
then
5x=15.25
x=3.05 km

thus Dante rod 3.05 km
but
1 km=1000m
thus
3.05 km=3050 m
But Dante rod 187 m more than Michael, the distance Michael will ride then  will be:
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4 0
3 years ago
The class average on a math test was an 82 with a standard deviation of 5. If the 
Alex787 [66]

Answer:

Option 3 and 4.

Step-by-step explanation:

The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:

z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation

Given that mean (μ) = 82, standard deviation (σ) = 5

1) For x = 74:

z=\frac{x-\mu}{\sigma} \\\\z=\frac{74-82}{5} =-1.6

Option 1 is incorrect

2) For x < 87

z=\frac{x-\mu}{\sigma} \\\\z=\frac{87-82}{5} =1

From the normal distribution table, P(x < 87) = P(z < 1) = 0.8413 = 84.13%

Option 2 is incorrect

3) For x = 95:

z=\frac{x-\mu}{\sigma} \\\\z=\frac{95-82}{5} =2.6

Option 3 is correct

4) For x < 77

z=\frac{x-\mu}{\sigma} \\\\z=\frac{77-82}{5} =-1

From the normal distribution table, P(x < 77) = P(z < -1) = 0.16 = 16%

Option 4 is correct

5) For x > 92

z=\frac{x-\mu}{\sigma} \\\\z=\frac{92-82}{5} =2

From the normal distribution table, P(x > 92) = P(z > 2) = 1 - P(z < -2) = 1 - 0.9772 = 0.0228 = 2.28%

Option 5 is incorrect

8 0
3 years ago
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