Solve the system of equations 3y+2z=12 and y-z=9

Answers

Answer 1

Answer: mulitply second equation by 2 and add to first

3y+2z=12
2y-2z=18 +
5y+0z=30

5y=30
divide 5
y=6

sub back
y-z=9
6-z=9
minus 6
-z=3
times -1
z=--3

x=-3
y=6

Related Questions

A cylinder has a radius of 12 m and a height of 9 m.What is the exact volume of the cylinder? 108π m³ 216π m³ 972π m³ 1296π m³
Find the answer to (6!) in math
What is 782,444 rounded to the nearest hundred thousand
Find the value of Y 600 x Y = 240,000
What is the solution to the equation 1.6m − 4.8 = −1.6m?m = 0.5 m = 0.7 m = 1.5 m = 3

Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π?

Answers

recall that to get the x-intercepts, we set the f(x) = y = 0, thus

$\bf \stackrel{f(x)}{0}=-4cos\left(x-(\pi )/(2) \right)\implies 0=cos\left(x-(\pi )/(2) \right)\n\n\ncos^(-1)(0)=cos^(-1)\left[ cos\left(x-(\pi )/(2) \right) \right]\implies cos^(-1)(0)=x-\cfrac{\pi }{2}\n\n\nx-\cfrac{\pi }{2}=\begin{cases}(\pi )/(2)\n\n(3\pi )/(2)\end{cases}$

$\bf -------------------------------\n\nx-\cfrac{\pi }{2}=\cfrac{\pi }{2}\implies x=\cfrac{\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{2\pi }{2}\implies \boxed{x=\pi }\n\n-------------------------------\n\nx-\cfrac{\pi }{2}=\cfrac{3\pi }{2}\implies x=\cfrac{3\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{4\pi }{2}\implies \boxed{x=2\pi }$

Solve the following quadratic by factoring1) x²+5x+6=0
2) x²+10x+21=0
3) x²+8x+15=0
4) x²+9x+14=0
5) x²-2x35=0

Answers

Answer:

Step-by-step explanation:

To solve these quadratic equations by factoring, you need to find two numbers that multiply to the constant term (the number without x^2) and add up to the coefficient of the linear term (the number with x). Here are the solutions for each of the equations:

1. x² + 5x + 6 = 0

We need two numbers that multiply to 6 and add up to 5. The numbers are 2 and 3.

So, we can factor the equation as (x + 2)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

x + 2 = 0 => x = -2

x + 3 = 0 => x = -3

So, the solutions are x = -2 and x = -3.

2. x² + 10x + 21 = 0

We need two numbers that multiply to 21 and add up to 10. The numbers are 7 and 3.

So, we can factor the equation as (x + 7)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

x + 7 = 0 => x = -7

x + 3 = 0 => x = -3

So, the solutions are x = -7 and x = -3.

3. x² + 8x + 15 = 0

We need two numbers that multiply to 15 and add up to 8. The numbers are 5 and 3.

So, we can factor the equation as (x + 5)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

x + 5 = 0 => x = -5

x + 3 = 0 => x = -3

So, the solutions are x = -5 and x = -3.

4. x² + 9x + 14 = 0

We need two numbers that multiply to 14 and add up to 9. The numbers are 7 and 2.

So, we can factor the equation as (x + 7)(x + 2) = 0.

Now, set each factor equal to zero and solve for x:

x + 7 = 0 => x = -7

x + 2 = 0 => x = -2

So, the solutions are x = -7 and x = -2.

5. x² - 2x - 35 = 0

To factor this equation, we need two numbers that multiply to -35 and add up to -2. The numbers are -7 and 5.

So, we can factor the equation as (x - 7)(x + 5) = 0.

Now, set each factor equal to zero and solve for x:

x - 7 = 0 => x = 7

x + 5 = 0 => x = -5

So, the solutions are x = 7 and x = -5.

0.7(3s+4)−1.1s=7.9 I need a answer

Answers

First, expand the bracket

2.1s + 2.8 - 1.1s = 7.9

Next, collect like terms

s + 2.8 = 7.9

Lastly subtract 2.8 from 7.9 to get your answer.

s = 5.1

(Hope this helps! ^^)

Answer:

$\boxed {s = 5.1}$

Step-by-step explanation:

Solve for the value of $s$ :

$0.7(3s + 4) - 1.1s = 7.9$

-Use Distributive Property:

$0.7(3s + 4) - 1.1s = 7.9$

$2.1s + 2.8 - 1.1s = 7.9$

-Combine like terms:

$2.1s + 2.8 - 1.1s = 7.9$

$s + 2.8 = 7.9$

-Subtract $2.8$ to both sides:

$s + 2.8 - 2.8 = 7.9 - 2.8$

$\boxed {s = 5.1}$

So, the value of $x$ is $5.1$ .

What is APR=(1+i/12)^t-1

Answers

The given formula is the Effective Annual Percentage rate formula where i signifies the nominal interest in terms of month. This formula is used in converting nominal interest rate to an effective interest rate since nominal interest rates are hard to compare unless their period are on the same basis.

Which box is greater a 1.5 pound box of raisins or a 650 gram box of raisins?

Answers

The 1.5 pound box of raisins
Convert the 650 grams to pounds and you will get 1.433 pounds which we would round to 1.4

1.5 is definitely greater than 1.4

1.5 gram= 680 grams
it means 1.5 gram box is greater than 650 gram box

hope u understand

4. Find the length of side EG.

Answers

Answer:

42 cm

Step-by-step explanation:

the first triangle is 7 times bigger than the second triangle. ( 4 x 7 = 28)

so to find out line EG, you times 6 cm by 7. which is 42

Other Questions

HELP What function models the data shown on the graph? f(x) = 2(x – 5)(x – 1) f(x) = –2(x – 5)(x – 1) f(x) = 2(x + 5)(x + 1) f(x) = –2(x + 5)(x + 1)

A store buys shoes for $40, then sells them to customers for $160. What is the percent mark-up for the price of the shoes?

A music festival offers one-day and three-day passes. A one day pass costs $100 and a three-day pass costs $250. write an expression for the total ticket sales if (n) one day passes and (t) three day passes are sold.

Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.