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3 years ago

5x + 7y = -29 y = x + 1

Mathematics

1 answer:

o-na [289]3 years ago

6 0

Answer:

(x, y) = (-3, -2)

Step-by-step explanation:

Perhaps this is a system of equations you want the solution for.

Since you have an expression for y, substitution is a viable approach.

5x +7(x+1) = -29 . . . . . . substitute for y

12x = -36 . . . . . . subtract 7 and simplify

x = -3 . . . . . . . . . divide by 12

y = (-3) +1 = -2 . . . use the expression for y

The solution is (x, y) = (-3, -2).

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Determine the sum of the areas of the three triangles shown above.

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How do I simplify this expression?

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A certain brand of dinnerware set comes in three colors: red, white, and blue. Twenty percent of customers order the red set, 45

denis23 [38]

Answer:

a) 0.20

b) 0.45

c) 0.65

d) Yes

e) Yes

f) Z = X + Y (except when X = 1 and Y = 1)

This is because the successes of X and Y are mutually exclusive events but their failures aren't. X and Y cannot both be 1.

Step-by-step explanation:

Probability of a red set = 20% = 0.20

Probability of a white set = 45% = 0.45

Probability of a blue set = 35% = 0.35

Probability of the single set being a red or white set = 20% + 45% = 65% = 0.65

P(X=1) = 0.20, P(X=0) = 1 - 0.2 = 0.80

P(Y=1) = 0.45, P(Y=0) = 1 - 0.45 = 0.55

P(Z=1) = 0.65, P(Z=0) = 1 - 0.65 = 0.35

a) pX = P(X=1) = 0.20

b) pY = P(Y=1) = 0.45

c) pZ = P(Z=1) = 0.65

d) Since only one order is being considered at a time, it isn't possible to order red & white set in a single set, hence, both X and Y cannot both be successes (equal to 1) at the same time. But they can both be failures (both equal to 0) if a blue set is ordered. The successes of X and Y are mutually exclusive events but their failures aren't

e) Is pZ = pX + pY

pX = 0.2, pY = 0.45, pZ = 0.65

Hence, this statement is correct!

f) Z = X + Y

Let's check all the probabilities

when X = 1 and Y = 1, Z = 1

1 ≠ 1 + 1

when X = 0 and Y = 1, Z = 1

1 = 0 + 1

when X = 1 and Y = 0, Z = 1

1 = 1 + 0

when X = 0 and Y = 0, Z = 0

0 = 0 + 0

Hence, Z = X + Y (except when X = 1 and Y = 1)

This is because the success of X and Y are mutually exclusive events but their failures aren't.

8 0

3 years ago

Please help |3r -6| =21

julsineya [31]

3r-6=-21

3r-6+6=-21+6 (Add 6 to both sides...)

3r=-15

r=-5

3r-6=21

3r-6+6=21+6 (Add 6 to both sides...)

3r=27

r=9

r=-5 or r=9

8 0

3 years ago

Read 2 more answers

Which exponential equation is equivalent to the logarithmic equation below?

julsineya [31]

Answer:

$\implies\boxed{ 10^a = 300 }$

Step-by-step explanation:

We are provided logarithmic equation , which is ,

$\implies log_{10}^{300}= a$

Here we took the base as 10 , since nothing is mentioned about that in Question .

Say if we have a expoteintial equation ,

$\implies a^m = n$

In logarithmic form it is ,

$\implies log_a^n = m$

Similarly our required answer will be ,

$\implies\boxed{ 10^a = 300 }$

3 0

3 years ago