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3 years ago

If r = -18, s = 27, and t = -15, what is the value of r - s - t

Mathematics

2 answers:

7nadin3 [17]3 years ago

8 0

-18- -27 = -45 -45- -15 = -30

noname [10]3 years ago

6 0

We know that:

r = -18

s = 27

t = -15

You want to find the value of r - s - t

Frist plug each corresponding value into r - s - t

-18 - 27 - (-15)

To solve this you will need to subtract from left to right.

-18 - 27 - (-15)

-18 - 27 <<< When subtracting with a negative number you will do something called "Same-Add-Opposite." This means that you will keep the first number in the expression (in this case that is -18) the same. Then turn the subtraction sign into an addition sign. Finally you will take the "opposite" sign of the second number. When I say "opposite sign" I mean that if this number is positive it will become negative. If it was negative it will become positive.

Here is your expression after applying same - add - opposite:

-18 + (-27)

When adding a negative number with a negative number you will simply just add the two numbers together and the sign of the answer will be negative as well.

-45

This is the remaining expression:

-45 - (-15)

^^^Apply same - add - opposite to this as well

-45 + 15

When adding a positive number with a negative number you will act as if you are subtracting the two numbers, then take the sign of the largest number (disregarding the signs). In this case the largest number is 45 (disregarding the signs) and its sign is negative. Your answer will have a negative sign.

-30

Hope this helped!

~Just a girl in love with Shawn Mendes

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2 years ago

Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6

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Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. $2x-4y=12$

$-3x+6y=-15$

b. $2x-4y=12$

$-5x+3y=10$

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

$A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0$

1. One solution:

There will be one solution to the system of equations, If we have:

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

2. Infinitely Many Solutions: (Identical lines in the system)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}$

3. No Solution:(Parallel lines)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Now, let us discuss the system of equations one by one:

a. $2x-4y=12$ OR $2x-4y-12=0$

$-3x+6y=-15$ OR $-3x+6y+15=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15$

Here, the ratio:

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}$

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Therefore, no solution i.e. parallel lines.

b. $2x-4y=12$ OR $2x-4y-12=0$

$-5x+3y=10$ OR $-5x+3y-10=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10$

$\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}$

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

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Answer:

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Step-by-step explanation:

Henry places £6000 in an account which pays 4.6% compound interest each year. Calculate the amount in his amount after 2 years

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A = P(1 + r/n)^nt

A = Final Amounrt

P = Principal = £6,000

r = Interest rate = 4.6%

t = Time in years = 2 years

n = Compounding frequency = Yearly = 1

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r = R/100

r = 4.6%/100

r = 0.046 per year,

Then, solve our equation for A

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