All categories

3 years ago

Let 2x-5y=16 and 5x+3y=9. what is the value of 12x+y

1 answer:

3 0

2x-5y=16 =>10x-25y=80
5x+3y=9 => 10x+6y=18
subtract one from the other: (6-(-25)y=(18-80), 31y=-62, y=-2
plug y=-2 in 2x-5y=16 to find x: 2x+10=16, x=3
12x+y=12*3-2=34

You might be interested in

Would appreciate the help !

aleksandr82 [10.1K]

This is one pathway to prove the identity.

Part 1

$\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{1}{\tan(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\cot(\theta) = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)*\sin(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)(1-\cos(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\$

Part 2

$\frac{\sin^2(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)-\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-(\cos(\theta)-\cos^2(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-\cos(\theta)+\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\$

Part 3

$\frac{\sin^2(\theta)+\cos^2(\theta)-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)} \ \ {\checkmark}\\\\$

As the steps above show, the goal is to get both sides be the same identical expression. You should only work with one side to transform it into the other. In this case, the left side transforms while the right side stays fixed the entire time. The general rule is that you should convert the more complicated expression into a simpler form.

We use other previously established or proven trig identities to work through the steps. For example, I used the pythagorean identity $\sin^2(\theta)+\cos^2(\theta) = 1$ in the second to last step. I broke the steps into three parts to hopefully make it more manageable.

3 0

2 years ago

F.8=8f? What is the answer

sveta [45]

Hey there!

f.8=8f

0.8f = 8f

SUBTRACT 8f to BOTH SIDES

0.8f - 8f = 8f - 8f

SIMPLIFY IT!

-7.2f = 0

DIVIDE -7.2 to BOTH SIDES

-7.2f/-7.2 = 0/-7.2

CANCEL out3 -7.2/-7.2 because it give you 1

KEEP: 0/-7.2 because it help solve for the f-value

NEW EQUATION: f = 0/-7.2

SIMPLIFY IT!

f = 0

Therefore, your answer is: f = 0

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

3 0

2 years ago

A cabin in the shape of a regular pentagonal pyramid has a slant height of 16 feet and a base edge length of 12 feet. Paint for

s2008m [1.1K]

Answer:

Step-by-step explanation:

You were so mean I needed help and you become insensetive and just typed "cool"for the points I will show you back one day

5 0

2 years ago

Jenna often babysits to earn extra money. On Friday nights , she made $42 for for babysitting 3 hours.

aivan3 [116]

She made 14 dollars and hour if that was your question

8 0

2 years ago

Mark is going to an awards dinner and wants to dress appropriately. He is running behind schedule and asks his little brother to

Cerrena [4.2K]

Answer:

The answer is " $\bold{\frac{2}{3}}$ ".

Step-by-step explanation:

Pick a shirt first: 3 choices

Pick slacks next: 2 choices

Then choose a tie: 1 choice

Total: $3 \times 2 \times 1 = 6$ outfits.

These will be similarly divided between the two slacks, so 3 black slack outfits of $6 = \frac{1}{2}$ . Similarly, the 6 styles are also divided between the option of 3 shirts. 2 blue shirt outfits $6 = \frac{1}{3}$

To recognize that over outfits are a mix of a blue shirt and black slack, it would be twice many more to add $\frac{1}{2} \ and \ \frac{1}{3}$ . Add $\frac{1}{2} \ and \ \frac{1}{3}$ , and remove the chance for both the black slack shirt and outfit and are one of the six outfits:

$\to \frac{1}{2} + \frac{1}{3} -\frac{1}{6} =\frac{3+2-1}{6} =\frac{4}{6} = \frac{2}{3}$

8 0

2 years ago

Read 2 more answers