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10 months ago

Y=−2x+4y, equals, minus, 2, x, plus, 4

Mathematics

1 answer:

vlabodo [156]10 months ago

3 0

The missing value of the solution to the equation y = −2x + 4, is: 3.

<h3>What is the Solution to an Equation?</h3>

The solution to a given equation, is the x and y values of an ordered pair that would make the equation true, if we substitute their values into the equation.

Given the equation, y = -2x + 4, and we have (x, -2) as the solution where the value of x is the missing value in the solution, to find the value of x, substitute y = -2 into the equation and solve for x:

-2 = -2x + 4

Subtract 4 from both sides

-2 - 4 = -2x + 4 - 4 (subtraction property of equality)

-6 = -2x

Divide both sides by -2

-6/-2 = -2x/-2

3 = x

x = 3

Therefore, the missing value is: 3.

Learn more about the solution to an equation on:

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On a long hike Keiko drank 5 pints of water. How much did she drink in quarts

Artemon [7]

She drank about 0.60 quarts
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4 0

2 years ago

Let Y1 and Y2 have the joint probability density function given by:

Ann [662]

Answer:

a) k=6

b) P(Y1 ≤ 3/4, Y2 ≥ 1/2) = 9/16

Step-by-step explanation:

a) if

f (y1, y2) = k(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere

for f to be a probability density function , has to comply with the requirement that the sum of the probability of all the posible states is 1 , then

P(all possible values) = ∫∫f (y1, y2) dy1*dy2 = 1

then integrated between

y1 ≤ y2 ≤ 1 and 0 ≤ y1 ≤ 1

∫∫f (y1, y2) dy1*dy2 = ∫∫k(1 − y2) dy1*dy2 = k ∫ [(1-1²/2)- (y1-y1²/2)] dy1 = k ∫ (1/2-y1+y1²/2) dy1) = k[ (1/2* 1 - 1²/2 +1/2*1³/3)- (1/2* 0 - 0²/2 +1/2*0³/3)] = k*(1/6)

then

k/6 = 1 → k=6

P(Y1 ≤ 3/4, Y2 ≥ 1/2) = P (0 ≤Y1 ≤ 3/4, 1/2 ≤Y2 ≤ 1) = p

then

p = ∫∫f (y1, y2) dy1*dy2 = 6*∫∫(1 − y2) dy1*dy2 = 6*∫(1 − y2) *dy2 ∫dy1 =

6*[(1-1²/2)-((1/2) - (1/2)²/2)]*[3/4-0] = 6*(1/8)*(3/4)= 9/16

therefore

P(Y1 ≤ 3/4, Y2 ≥ 1/2) = 9/16

8 0

3 years ago

Find the values of X and Y that makes these triangles congruent by the HL theorem

muminat

Answer:

C. x = 3, y = 2

Step-by-step explanation:

If both triangles are congruent by the HL Theorem, then their hypotenuse and a corresponding leg would be equal to each other.

Thus:

x + 3 = 3y (eqn. 1) => equal hypotenuse

Also,

x = y + 1 (eqn. 2) => equal legs

✔️Substitute x = y + 1 into eqn. 1 to find y.

x + 3 = 3y (eqn. 1)

(y + 1) + 3 = 3y

y + 1 + 3 = 3y

y + 4 = 3y

y + 4 - y = 3y - y

4 = 2y

Divide both sides by 2

4/2 = 2y/2

2 = y

y = 2

✔️ Substitute y = 2 into eqn. 2 to find x.

x = y + 1 (eqn. 2)

x = 2 + 1

x = 3

8 0

3 years ago

Does 2 and 12 have a least common multiple of 24

vova2212 [387]

Answer:

Least common multiple (LCM) of 12 and 24 is 24.

Step-by-step explanation:

6 0

2 years ago

He mean potassium content of a popular sports drink is listed as 140 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sa

mezya [45]

Answer: (A) H0: μ = 140 mg vs. H1: μ ≠ 140 mg

Step-by-step explanation:

Usually null hypothesis represents the claim that the values associated to the groups being tested have no statistical difference but alternative hypothesis supports the claim that there is statistical difference.

Let $\mu$ be the population mean .

We are given that the mean potassium content of a popular sports drink is listed as 140 mg in a 32-oz bottle.

i.e. Null hypothesis : $H_0:\mu=140$

Alternative hypothesis for two tail hypothesis has sign (≠).

i.e. Alternative hypothesis : $H_1 : \mu\neq140$

∴ The hypotheses for a two-tailed test of the claimed potassium content:

H0: μ = 140 mg vs. H1: μ ≠ 140 mg

3 0

3 years ago