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2 years ago

Solve the following simultaneous equations 2x+5y=0 and 3x-4y=23

Mathematics

1 answer:

Elodia [21]2 years ago

7 0

Answer:

x = 5, y = -2

Step-by-step explanation:

2x + 5y = 0 --- Equation 1

Equation 1×3: 6x + 15y = 0 --- Equation 2

3x - 4y = 23 --- Equation 3

Equation 3×2: 6x - 8y = 46 --- Equation 3

We will be eliminating 6x from Equation 2.

Equation 3-2: 6x - 8y - 6x - 15y = 46-0

-23y = 46

y = 46 ÷ -23

y = -2

Substitute y = -2 into Equation 1:

2x + 5y = 0

2x + 5(-2) = 0

2x + (-10) = 0

2x - 10 = 0

2x = 10

x = 10 ÷ 2

x = 5

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In mathematics given that x=L2-L1/L1(O2-O1).

Assoli18 [71]

Answer:

1. L1 = $\frac{L2}{X(O2 -O1)}$

2. O2 = $\frac{L2 - L1(1 + XO1)}{XL1}$

Step-by-step explanation:

Given: x = $\frac{L2 - L1}{L1(O2 -O1)}$

1. To make L1 the subject of formula;

x = $\frac{L2 - L1}{L1(O2 -O1)}$

cross multiply to have;

L2 - L1 = xL1(O2 - O1)

collect like terms,

L2 = xL1(O2 - O1) + L1

factorize the right hand side;

L2 = L1[x(O2 - O1)]

L1 = $\frac{L2}{X(O2 -O1)}$

2. To make O2 the subject of formula;

x = $\frac{L2 - L1}{L1(O2 -O1)}$

cross multiply to have;

L2 - L1 = xL1(O2 - O1)

open the bracket to have;

L2 - L1 = xL1O2 - xL1O1

⇒ xL1O2 = L2 - L1 + xL1O1

O2 = $\frac{L2-L1 + XL1O1}{XL1}$

= $\frac{L2 - L1(1 + XO1)}{XL1}$

4 0

2 years ago

a perfect is to be chosen from a class of 16 girls and 14 boys.what is the probability that the prefect is a girl

LiRa [457]

Answer:

Step-by-step explanation:

$16\:girls \\14\:boys\\\\Probability = \frac{Event}{Total \:possible\:outcome}\\\\ Event=16\\\\ Total\:possible\:outcome = 16+14=30\\\\P = \frac{16}{30}\\ \\Probability = \frac{8}{15}$

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3 years ago

For the polynomial 6xy2 – 5x2y? + 9x2 to be a trinomial with a degree of 3 after it has been fully simplified, the missing expon

Karolina [17]

Consider the polynomial $6xy^2-5x^2y^?+9x^2$ .

For this polynomial to be trinomial with a degree of 3. We have to identify the missing exponent of the 'y' term.

Let the missing exponent of the 'y' term be 0

So, the polynomial will be $6xy^2-5x^2y^0+9x^2$

= $6xy^2-5x^2+9x^2$

= $6xy^2+4x^2$ which is not a trinomial, which is a binomial.

So, the missing exponent of 'y' can'not be zero.

Let the missing exponent of the 'y' term be 2

So, the polynomial will be $6xy^2-5x^2y^2+9x^2$

= $6xy^2-5x^2y^2+9x^2$

= $6xy^2-5x^2y^2+9x^2$ which is a trinomial of degree 4.

So, the missing exponent of 'y' can'not be '2'.

If we will take the missing exponent of 'y' more than 2, than the degree of the given polynomial will not be 3 anymore.

Let the missing exponent of the 'y' term be 1

So, the polynomial will be $6xy^2-5x^2y^1+9x^2$

= $6xy^2-5x^2y+9x^2$

= $6xy^2+4x^2$ which is a trinomial of degree 3

So, the missing exponent of 'y' is 1.

7 0

3 years ago

Read 2 more answers

A random sample of of 100 voters in a town is selected, and 24 are found to support an annexation suit. Find the 96% confidence

lbvjy [14]

Answer: 0.24 +/- 0.088 = (0.152, 0.328)

Step-by-step explanation:

The point estimate p is given by;

p= 24/ 100 = 0.24

Z value for 96% confidence interval is 2.05

The solution for the given confidence interval is derived using the equation

p +/- z√(pq/n)

Where p = 0.24 q= 1-p = 0.76, n=100 z= 2.05

= 0.24 +/- 2.05√(0.24×0.76/100)

= 0.24 +/- 2.05(0.0427)

=0.24 +/- 0.088

= ( 0.152, 0.328)

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3 years ago

Given measure of arcs, solve for the unknown angles

IRINA_888 [86]

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