All categories

4 years ago

Solve by using substitution 2x-5=-y x+3y=0

Mathematics

1 answer:

kirill115 [55]4 years ago

5 0

Answer:

(3,-1)

Step-by-step explanation:

1) Solve equation for y

2) Plug into other equation

3) Solve for x

4) Plug in the value found for x

5) Solve for y

You might be interested in

To find the average of some quantities , add them together and then divide the total by the number of

Alexxandr [17]

Answer:

quantities or total number of observations

Step-by-step explanation:

Average also known as mean is a measure of central tendency. It is determined by adding the numbers together and dividing it by the total number

Average = sum of the numbers / total number

For example, there are 3 numbers 3 , 6, 9

Average = ( 3 + 6 + 9) / 3 = 18 / 3 = 6

8 0

3 years ago

I forgot how to do these, could somebody explain. 30 points for both

Aleonysh [2.5K]

Answer:

11) A

12) B

Step-by-step explanation:

11) 10x² + 1 = 0

Subtract 1 from both sides:

10x² = -1

Divide both sides by 10:

x² = -1/10

Take the square root of both sides:

x = ±√(-1) / √(10)

Remember that the square root of -1 is i:

x = ±i / √(10)

To rationalize the denominator, multiply top and bottom by √10.

x = ±i√(10) / 10

Answer is A.

12) 2v² + 8v + 6 = 0

Divide both sides by 2:

v² + 4v + 3 = 0

Use AC method or quadratic formula to factor:

(v + 1) (v + 3) = 0

Set each expression to 0:

v + 1 = 0 or v + 3 = 0

Solve:

v = -1 or v = -3

Answer is B.

7 0

3 years ago

How do I verify this identity? I know you should write sin2a as sin(a+a).

Kisachek [45]

SOLUTION

Given the question in the image, the following are the solution steps to verify the identity

STEP 1: Write the given identity

$\sin 2\alpha=2\sin \alpha\cos \alpha$

STEP 2: Verify the identity

$\begin{gathered} \sin 2\alpha=2\sin \alpha\cos \alpha \\ \text{Consider the left hand side of the above trigonometry identity.} \\ \text{That is, }\sin 2\alpha\text{.} \\ \text{ Rewrite }\sin 2\alpha\text{ as }\sin (\alpha+a) \\ \text{ It is known that }\sin (a+b)=\sin (a)\cos b+\cos (a)\sin (b) \\ U\sin g\text{ this statement above, we have;} \\ \sin (\alpha+a)=\sin a\cos \alpha+\cos a\sin \alpha \\ \text{It is known that }xy+yx=xy+xy=2\times xy=2xy \\ U\sin g\text{ this statement above, we have;} \\ \sin a\cos \alpha+\cos a\sin \alpha=\sin a\cos \alpha+\sin \alpha\cos \alpha=2\times\sin \alpha\cos \alpha=2\sin \alpha\cos \alpha \\ \text{Hence, }\sin 2\alpha=2\sin \alpha\cos \alpha \end{gathered}$

The verification of the identity is as seen above.

7 0

1 year ago

tom had a platter of chocolate wafers. he ate 5 of them and then gave his brother 3 he then moved on to his baseball team of 8 m

Aloiza [94]

Tom started with total 72 chocolate wafers.

Explanation

The number of chocolate wafers taken by 8 members of the baseball team are in the sequence : $1, 3,5,7,9,11,13,15$

The above sequence is arithmetic sequence with first term(a₁)= 1 and common difference (d) = 2

Formula for Sum of first $n$ terms in arithmetic sequence is....

$S_{n}= \frac{n}{2}[2a_{1}+(n-1)d]$

So, the Sum of 8 terms in that sequence....

$S_{8}= \frac{8}{2}[2(1)+(8-1)(2)]\\ \\ S_{8}= 4[2+7(2)]\\ \\ S_{8}=4(2+14)\\ \\ S_{8}=4(16)=64$

That means, the total number of chocolate wafers taken by the baseball team members is 64. Tom ate 5 and then gave his brother 3 chocolate wafers at first.

So, the total number of chocolate wafers at starting $=64+5+3=72$

6 0

3 years ago

Megan is checking her tax bill for the last year.

Tanya [424]

Given that Megan's tax rates were as follows:
No tax one the first £11000 of earnings
Earnings in excess of £11000 and up to £43000 taxed at a rate of 20%
Earning in excess of 43000 and up to £150000 taxed at a rate of 40%
Earnings over £150000 taxed at a rate of 45%
If Megan earned £158900 before tax last year, the amount of tax she paid in total is given as follows:
First £11000 = £0 tax
Balance after first £11000 = £158900 - £11000 = £147900

Next (£43000 - £11000 = £32000) = 20% of £32000 = 0.2 x £32000 = £6400 tax
Balance after next £32000 = £147900 - £32000 = £115000 

Next (£150000 - £43000 = £107000) = 40% of £107000 = 0.4 x £107000 = £42800 tax
Balance after next £107000 = £115000 - £107000 = £8000

Remaiming £8000 = 45% of £8000 = 0.45 x £8000 = £3600 tax

Total tax = £6400 + £42800 + £3600 = £52800

Therefore, she paid a total of £52800 in tax last year.

8 0

3 years ago