-6x+4y=-18 -x-y=2 solve by subsitution

Explain what are all of the properties of real numbers and use an example for each.

Arada [10]

Answer:

mark me as a brainlist answer

Step-by-step explanation:

Give examples to explain the properties of real numbers

Property (a, b and c are real numbers, variables or algebraic expressions)Examples8.Additive Inverse Property a + (-a) = 04 + (-4) = 09.Multiplicative Inverse Property10.Zero Property of Multiplication a • 0 = 04 • 0 = 011.Closure Property of Addition a + b is a real number10 + 5 = 15 (a real number)

6 0

3 years ago

Selene's checking account balance was -$33, and then she withdrew $42 more. What is her checking account balance after the withd

Rainbow [258]

Answer:

-75

Step-by-step explanation:

WIthdrew = Negative

-33 - 42 = -75

7 0

3 years ago

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Simplify the expression csc(-x)/1+tan^2x)

Charra [1.4K]

Assuming ya meant $\frac{csc(-x)}{1+tan^2(x)}$

to slimplify, we use a variation of the pythagorean identity and a decomposition into the sin and cos

for the pythaogreaon identity
$cos^2(x)+sin^2(x)=1$
divide both sides by $cos^2(x)$
$1+tan^2(x)=sec^2(x)$ since $\frac{sin(x)}{cos(x)}=tan(x)$
subsitute
$\frac{csc(x)}{sec^2(x)}$

recall that $csc(x)=\frac{1}{cos(x)}$
also that cos(x) is an even function and thus cos(-x)=cos(x)
therfore $csc(-x)=\frac{1}{cos(-x)}=\frac{1}{cos(x)}=csc(x)$
so we get

$\frac{csc(x)}{sec^2(x)}$
decompose them into $\frac{1}{cos(x)}$ and $\frac{1}{sin^2(x)}$ to get $\frac{\frac{1}{cos(x)}}{\frac{1}{sin^2(x)}}$
multiply by $\frac{sin^2(x)}{sin^2(x)}$ to get
$\frac{sin^2(x)}{cos(x)}$
we can furthur simlify to get
$(\frac{sin(x)}{cos(x)})(sin(x))=tan(x)sin(x)$
the expression simplifies to tan(x)sin(x)

5 0

3 years ago

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Rai compares two cable plans from different companies. Which equation gives the correct value of m, the number of months for whi

tekilochka [14]

Answer:

D. 75m = 50(12)+125(m-12)

Step-by-step explanation:

m = months.

Equation for which Plans A and B cost the same.

In Plan A:

No initial fees.

$75 per month

1 month = $ 75

then;

for m month =$75 m

Total cost for plan A = 75m

In Plan B:

$50 per month for first 12 month.

1 month = $50

12 months = 50(12)

Similarly,

$125 per month for each additional month after that.

additional month= (m-12)

Plan B additional month

= 125(m-12)

Total cost for plan B = 50(12)+ 125(m-12)

Since, Plans A and B cost the same.

75m = 50(12)+125(m-12)

3 0

3 years ago

Complete each statement in the steps to solve x2 – 6x – 7 = 0 using the process of completing the square. Isolate the constant b

Tomtit [17]

"Isolate the constant by adding 7 to both sides of the equation."
This step separates the non-squareable 7 and the squareable $x^2 - 6x$ .

"Add 9 to both sides of $x^2 - 6x = 7$ to form a perfect square trinomial while keeping the equation balanced."
After separating the non-squareable, add the number which makes the first or left side a perfect square trinomial. The formula to find the number is: $c = {\frac{b}{2} }^{2}$ .
When we plug the values: $c = { \frac{ - 6}{2} }^{2}$
Simplify: $c = {( - 3)}^{2} = 9$

"Write the trinomial $x^2 - 6x + 9$ as $(x - 3)$ squared."
When you factor $x^2 - 6x + 9$ , you will get $(x - 3) \times (x - 3)$ .

"Use the square root property of equality to get $x - 3 = ± \sqrt{16}$ ."
The 16 is coming from the part when we add 9. We needed 9 on the left side for a perfect square, but to protect the balance of the equality, we need to add 9 to the right side too. When we add 7 and 9, we got 16, and that is where it came from.

"Isolate the variable x to get solutions of -1 and 7."
To isolate x we branched the plus-minus sign:
$x - 3 = 4 \: \: \: x = 4 + 3 = 7 \\ \\ x - 3 = - 4 \: \: \: x = - 4 + 3 = - 1$

8 0

3 years ago

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