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3 years ago

How do you solve -3x+y=7 5x+2y=3 by substitution method??

Mathematics

2 answers:

JulsSmile [24]3 years ago

8 0

Yes you would have to solve this problem by substitution method

lakkis [162]3 years ago

8 0

Answer:

(-1,4)

Step-by-step explanation:

-3x + y = 7......y = 3x + 7

so sub in 3x + 7 in for y back into the other equation

5x + 2y = 3

5x + 2(3x + 7) = 3 ...distribute thru the parenthesis

5x + 6x + 14 = 3....subtract 14 from both sides

5x + 6x = 3 - 14...combine like terms

11x = - 11...divide both sides by 11

x = -11/11

x = -1

now that we know x = -1, we can sub that back into either of the original equations to find y

y = 3x + 7

y = 3(-1) + 7

y = -3 + 7

y = 4

so we have (-1,4) as a solution....but lets check it first

-3x + y = 7

-3(-1) + 4 = 7

3 + 4 = 7

7 = 7 (correct)...it checks out

so ur solution is : x = -1 and y = 4 or (-1,4)

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you are riding a bicycle which has tires with a 25-inch diameter at a steady 15-miles per hour, what is the angular velocity of

motikmotik

Answer:

The angular velocity is 6.72 π radians per second

Step-by-step explanation:

The formula of the angular velocity is ω = $\frac{v}{r}$ , where v is the linear velocity and r is the radius of the circle

The unit of the angular velocity is radians per second

∵ The diameter of the tire is 25 inches

∵ The linear velocity is 15 miles per hour

- We must change the mile to inch and the hour to seconds

∵ 1 mile = 63360 inches

∵ 1 hour = 3600 second

∴ 15 miles/hour = 15 × $\frac{63360}{3600}$

∴ 15 miles/hour = 264 inches per second

Now let us find the angular velocity

∵ ω = $\frac{v}{r}$

∵ v = 264 in./sec.

∵ d = 25 in.

- The radius is one-half the diameter

∴ r = $\frac{1}{2}$ × 25 = 12.5 in.

- Substitute the values of v and r in the formula above to find ω

∴ ω = $\frac{264}{12.5}$

∴ ω = 21.12 rad./sec.

- Divide it by π to give the answer in terms of π

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3 0

3 years ago

You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar

Verizon [17]

Answer:

$Length=10.5\ ft$

$Width=10.5\ ft$

$Area=110.25\ ft^{2}$

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

$P=2(x+y)$

we have

$P=42\ ft$

$42=2(x+y)$

simplify

$21=(x+y)$

$y=21-x$ ------> equation A

Remember that the area of rectangle is equal to

$A=xy$ ----> equation B

substitute equation A in equation B

$A=x(21-x)$

$A=21x-x^{2}$ ----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point $(10.5,110.25)$

see the attached figure

$x=10.5\ ft$

Find the value of y

$y=21-10.5=10.5\ ft$

The garden is a square

the area is equal to

$A=(10.5)(10.5)=110.25\ ft^{2}$ ----> is equal to the y-coordinate of the vertex is correct

6 0

3 years ago