One fifth of the sum of a number and -3 is twice the number

12y=17-9x and -4y-3x=31 solve by elimination

vodka [1.7K]

Answer:

0 ≠ 110

No solution

Step-by-step explanation:

Solve by Addition/Elimination

12y = 17 − 9x and −4y − 3x = 31

Reorder 17 and −9x. 12y = −9x + 17

−4y − 3x = 31

Add 9x to both sides of the equation.

12y + 9x = 17

−4y − 3x = 31

Reorder the polynomial.

9x + 12y = 17

−4y − 3x = 31

Reorder the polynomial.

9x + 12y = 17

−3x − 4y = 31 9x + 12y = 17

Multiply each equation by the value that makes the coefficients of x opposite.

9x + 12y = 17

(3) ⋅ (−3x − 4y) = (3) (31)

Simplify (3) ⋅ (−3x − 4y).

Apply the distributive property.

9x + 12y = 17

3 (−3x) + 3 (−4y) = (3) (31)

Multiply −3 by 3. 9x + 12y = 17

−9x + 3 (−4y) = (3) (31)

Multiply −4 by 3. 9x + 12y = 17

−9x − 12y = (3) (31)

Multiply 3 by 31. 9x + 12y = 17

−9x − 12y = 93

Add the two equations together to eliminate x from the system.

9x+12y=17

+−9x−12y=93

0=110

Since 0 ≠ 110, there are no solutions. No solution

7 0

3 years ago

Caitlin plays on her school basketball team and scored 1/4 of the total points during the first three games. Her team scored 38

horsena [70]

Answer:

33 Points

Step-by-step explanation:

We can figure out that the total number of points scored by the team is 38+45+49=132. Since we know that Caitlin scored 1/4 of these total points, and 1/4 of 132=33, then she scored 33 points during the first three games.

5 0

3 years ago

$3,250 is withdrawn at the end of every month from an account paying 4.1% compounded monthly. Determine the previous value of th

kirill [66]

The amount needed such that when it comes time for retirement is $2,296,305. This problem solved using the future value of an annuity formula by calculating the sum of a series payment through a specific amount of time. The formula of the future value of an annuity is FV = C*(((1+i)^n - 1)/i), where FV is the future value, C is the payment for each period, n is the period of time, and i is the interest rate. The interest rate used in the calculation is 4.1%/12 and the period of time used in the calculation is 30*12 because the basis of the return is a monthly payment.

FV = $3,250*(((1+(4.1%/12)^(30*12)-1)/(4.1%/12))

4 0

3 years ago

Diane purchased a prepaid phone card for $15. Long distance calls cost 17 cents a minute using this card. Diane used her card on

tester [92]

Answer:

22 minutes

Step-by-step explanation:

15-11.26=3.74

3.74 divided by .17 eqauls 22

8 0

3 years ago

A five-digit number starts with a number between 4-9 in the first position, with no restrictions on the remaining 4 digits. a

Maurinko [17]

Answer:

(a) $Pr = 0.3024$

(b) $Pr = 0.6976$

(c) $Pr = \frac{^9P_{n-1}}{10^{n-1}}$

Step-by-step explanation:

Given

$Start = \{5,6,7,8\}$ i.e. between 4 and 9

$n(Start) =4$

$Digits = 5$

Solving (a): Probability that each of the 5 digit are different

Since there is no restriction;

The total possible selection is as follows:

$First\ digit = 4$ (i.e. any of the 4 start digits)

$Second\ digit = 10\\$ (i.e. any of the 10 digits 0 - 9)

$Third\ digit = 10$ (i.e. any of the 10 digits 0 - 9)

$Fourth\ digit = 10$ (i.e. any of the 10 digits 0 - 9)

$Fifth\ digit = 10$ (i.e. any of the 10 digits 0 - 9)

So, the total is:

$Total = 4 * 10 * 10 * 10 * 10$

$Total = 40000$

For selection that all digits are different, the selection is:

$First\ digit = 4$ (i.e. any of the 4 start digits)

$Second\ digit = 9$ (i.e. any of the remaining 9)

$Third\ digit = 8$ (i.e. any of the remaining 8)

$Fourth\ digit = 7$ (i.e. any of the remaining 7)

$Fifth\ digit = 6$ (i.e. any of the remaining 6)

So:

$Selection =4 * 9 * 8 * 7 * 6$

$Selection =12096$

So, the probability is:

$Pr = \frac{Selection}{Total}$

$Pr = \frac{12096}{40000}$

$Pr = 0.3024$

Solving (b): At least 1 repeated digit

The probability calculated in (a) is the all digits are different i.e. P(None)

So, using laws of complement

We have:

$P(At\ least\ 1) = 1 - P(None)$

So, we have:

$Pr= 1 - 0.3024$

$Pr = 0.6976$

Solving (c): An expression to model the probability.

<em>Using (a) as a point of reference, we have;</em>

$Pr = \frac{Selection}{Total}$

Where

$Selection =4 * 9 * 8 * 7 * 6$ ---- for selection of 5 i.e. n = 5

$Total = 4 * 10 * 10 * 10 * 10$

$Selection =4 * 9 * 8 * 7 * 6$

This can be rewritten as:

$Selection = 4 * ^9P_4$

4 can be expressed as: 5 - 1

So, we have:

$Selection = (5-1) *^9P_{5-1}$

Substitute n for 5

$Selection = (n-1) *^9P_{n-1}$

$Selection = (n-1)^9P_{n-1}$

$Total = 4 * 10 * 10 * 10 * 10$

This can be rewritten as:

$Total = 4 * 10^4$

$Total = (5-1) * 10^{5-1}$

$Total = (n-1) * 10^{n-1}$

$Total = (n-1) 10^{n-1}$

So, the expression is:

$Pr = \frac{(n-1)^9P_{n-1}}{(n-1)10^{n-1}}$

$Pr = \frac{^9P_{n-1}}{10^{n-1}}$

<em>Where n represents the digit number</em>

5 0

3 years ago