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Dafna11 [192]
3 years ago
12

Solve the simultaneous linear equation: 6x-y=233y+6x=11​

Mathematics
1 answer:
xeze [42]3 years ago
3 0

Answer:

( \frac{10}{3}, - 3 )

Step-by-step explanation:

Given the 2 equations

6x - y = 23 → (1)

3y + 6x = 11 → (2)

Subtracting (2) from (1) term by term eliminates the term in x

(6x - 6x) + (- y - 3y) = (23 - 11), that is

- 4y = 12 ( divide both sides by - 4 )

y = - 3

Substitute y = - 3 into either of the 2 equations and solve for x

Substituting in (1)

6x - (- 3) = 23

6x + 3 = 23 ( subtract 3 from both sides )

6x = 20 ( divide both sides by 20 )

x = \frac{20}{6} = \frac{10}{3}

Solution is ( \frac{10}{3}, - 3 )

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The area of a rectangle is 20 cm². The height is 4 cm longer than thrice the width.
Ludmilka [50]

Answer:

width = 2 cm

Step-by-step explanation:

are of rectangle is equal to length times width

x is the width, then length is 3x + 4

so x(3x + 4) = 20

3x^2 + 4x = 20

3x^2 + 4x - 20 = 0

The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a

so a = 3

    b = 4

    c = -20

substitute in the formula

x = [-4 +/-√(4^2 - 4(3)(-20))]/2(3)

x = [-4 +/- √(16 + 240)]/6

x = [-4 +/- 16]/6

x1 = (-4 + 16)/6 = 2

x2 = (-4 - 16)/6 = -20/6

since the width can't be a negative number, x2 is not the right answer

so x = 2

8 0
3 years ago
Can y’all help me please I need help
Illusion [34]

Answer:

503 inches (rounded to the nearest whole number)

Step-by-step explanation:

First, we must calculate the wheel's circumference, or in other words, the distance around the wheel. We can do this by using the below equation:

C=\pi d when d is the diameter

Because we know that the wheel's diameter is 16 inches, we can plug it into the equation:

C=\pi (16)\\C=16\pi

Now, because we know that the wheel makes 10 revolutions, we calculate the distance it travelled by multiplying the circumference by 10.

16\pi *10\\= 160\pi

= 503 inches when rounded to a whole number

Therefore, the wheel travelled approximately 503 inches.

I hope this helps!

8 0
3 years ago
7925 divided by 72. It keeps coming out wrong as I do it so I need help
emmainna [20.7K]

Answer:

110 R 5

Step-by-step explanation:

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4 0
3 years ago
Read 2 more answers
What is the circumference of a circle of a circle with a diameter of 2.9 use 3.14 for pi
sweet [91]

Answer:

9.106

Step-by-step explanation:

The circumference of a circle with a given diameter is: C=\pi d

We are given the diameter of 2.9 units.

Using 3.14 for pi:

C=3.14 * 2.9\\\\\boxed{C=9.106}

The circumference is about 9.106 units.

7 0
3 years ago
A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a
jeka94

Answer:

0.2 or 20%

Step-by-step explanation:

If the times of arrival vary uniformly, there is an equal chance of an employee reporting at any given time between 8:40 and 9:30.

The range between 8:40 and 9:30 is 50 minutes.

The range between 9:00 and 9:10 is 10 minutes.

Therefore, the  probability that a randomly chosen employee reports to work between 9:00 and 9:10 is:

P(9:00\leq X\leq 9:10)=\frac{10}{50}=0.20=20\%

The probability is 0.2 or 20%.

6 0
3 years ago
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