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3 years ago

4x + 3y = 1 x - 3y = -11

Mathematics

2 answers:

Ray Of Light [21]3 years ago

6 0

Answer:

x=-2, y=3

Step-by-step explanation:

4x + 3y = 1.......... Equ 1

x - 3y = -11...........Equ 2

5x=-10

x=-2

From equ 1

4x + 3y =1

4(-2)+3y=1

-8+3y=1

3y=1+8

3y=9

y=3

JulijaS [17]3 years ago

4 0

Answer:

(- 2, 3 )

Step-by-step explanation:

Given the 2 equations

4x + 3y = 1 → (1)

x - 3y = - 11 → (2)

Adding the 2 equations term by term will eliminate the y- term

5x + 0 = - 10

5x = - 10 ( divide both sides by 5 )

x = - 2

Substitute x = - 2 into either of the 2 equations and solve for y

Substituting into (1)

4(- 2) + 3y = 1

- 8 + 3y = 1 ( add 8 to both sides )

3y = 9 ( divide both sides by 3 )

y = 3

solution is (2, - 3 )

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Work Shown:

The 63 should be 6^3. There are 6 choices per slot, and 3 slots, so 6^3 = 216 different outcomes.

Here are all of the ways to add to 11 if we had 3 dice

sum = 1+4+6 = 11
sum = 1+5+5 = 11
sum = 1+6+4 = 11
sum = 2+3+6 = 11
sum = 2+4+5 = 11
sum = 2+5+4 = 11
sum = 2+6+3 = 11
sum = 3+2+6 = 11
sum = 3+3+5 = 11
sum = 3+4+4 = 11
sum = 3+5+3 = 11
sum = 3+6+2 = 11
sum = 4+1+6 = 11
sum = 4+2+5 = 11
sum = 4+3+4 = 11
sum = 4+4+3 = 11
sum = 4+5+2 = 11
sum = 4+6+1 = 11
sum = 5+1+5 = 11
sum = 5+2+4 = 11
sum = 5+3+3 = 11
sum = 5+4+2 = 11
sum = 5+5+1 = 11
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sum = 6+2+3 = 11
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There are 27 ways to add to 11 using 3 dice. This is out of 216 total outcomes of 3 dice being rolled.

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Read 2 more answers

If the expression $3^1 times 9^2 times 27^3 \times 81^4 is simplified to the form 3^n, what is the value of n?

Darina [25.2K]

Answer:

$n=30$

Step-by-step explanation:

Given expression:

$3^1\times 9^2\times 27^3\times 81^4$

The given expression needs to be simplified to the form $3^n$

Applying the exponents rule to simplify.

$3^1\times 9^2\times 27^3\times 81^4$

Writing all numbers as product of 3.

⇒ $3^1\times (3\times3)^2\times (3\times3\times3)^3\times (3\times3\times3\times3)^4$

Writing each in exponents form.

⇒ $3^1\times (3^2)^2\times (3^3)^3\times (3^4)^4$

Using power of a power rule $[\ (a^x)^y=a^{xy}\ ]$

⇒ $3^1\times 3^4\times 3^9\times 3^16$

Using multiplication rule of exponents $[\ a^x\times a^y=a^{x+y}\ ]$

⇒ $3^{1+4+9+16}$

⇒ $3^{30}$

So we have $3^n=3^{30}$

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Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define the converse of a statement

The converse of a statement is formed by switching the hypothesis and the conclusion.

STEP 2: break down the given statements

Hypothesis: If M is the midpoint of line segment PQ,

Conclusion: line segment PM is congruent to line segment QM

STEP 3: Switch the two statements

Hence, the answer is given as:

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