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2 years ago

What is the solution to the system of equationsY=4x+11 and y =-2x-1

Mathematics

1 answer:

pav-90 [236]2 years ago

5 0

For this case we must solve a system of two equations with two unknowns, given by "x" and "y".

We have:

$y = 4x + 11\ (1)\\y = -2x-1\ (2)$

We multiply (2) by -1:

$-y = 2x + 1\ (3)$

We add (1) and (3):

$y-y = 4x + 2x + 11 + 1\\0 = 6x + 12$

Clearing x:

$-12 = 6x\\x = \frac {-12} {6}\\x = -2$

We substitute $x = -2$ in (2)

$y = -2 (-2) -1\\y = 4-1\\y = 3$

Thus, the solution of the system is $(x, y) = (- 2,3)$

Answer:

The solution of the system is $(x, y) = (- 2,3)$

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Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?

timama [110]

The Mean Value Theorem:
If a function is continuous on [ a, b ] and differentiable on ( a , b ) than there is a point c in ( a, b ) such that:
f ` ( c )= ( f ( b ) - f ( a ) ) / ( b - a )
f ` ( c ) = ( f ( 2 ) - f ( 0 ) ) / ( 2 - 0 )
f `( x ) = 10 x - 3
f ` ( c ) = 10 c - 3
2 f ` ( c ) = 16 - 2
f ` ( c ) = 7
7 = 10 c - 3
c = 1
Answer:
Yes, the function is continuous on [ 0, 2 ] and differentiable on ( 0, 2 ).

4 0

3 years ago

Finding the area of a regular polygon

ddd [48]

<h2>Solution:</h2>

360° ÷ 10 ÷ 2 = 18°

So the length of the decagon side is:

10 × tan18° × 2 = 20 × tan18°

The area is: ½ × 20 × tan18° × 10 × 10 = 1000 × tan18°

≈ 324.9

.: 324.9 is the final answer.

I hope this helps. 

5 0

1 year ago

M 1 = 30°, m 2 = 45°, m 3 = 30 75 105 150

Serggg [28]

105 :)))))))))))))))))

4 0

3 years ago

Read 2 more answers

A swimming pool is filled with water. Find .. 15m 1.2 3.7m 1.89

Andreyy89

Answer:

Step-by-step explanation:

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2 years ago

Read 2 more answers

Imagine an experiment having three conditions and 20 subjects within each condition. The mean and variances of each condition ar

xxTIMURxx [149]

Answer:

1. Mean square B= 5.32

2. Mean square E= 16.067

3. F= 0.33

4. p-value: 0.28

Step-by-step explanation:

Hello!

You have the information of 3 groups of people.

Group 1

n₁= 20

X[bar]₁= 3.2

S₁²= 14.3

Group 2

n₂= 20

X[bar]₂= 4.2

S₂²= 17.2

Group 3

n₃= 20

X[bar]₃= 7.6

S₃²= 16.7

1. To manually calculate the mean square between the groups you have to calculate the sum of square between conditions and divide it by the degrees of freedom.

Df B= k-1 = 3-1= 2

Sum Square B is:

∑ni(Ÿi - Ÿ..)²

Ÿi= sample mean of sample i ∀ i= 1,2,3

Ÿ..= general mean is the mean that results of all the groups together.

General mean:

Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (3.2+4.2+7.6)/3 = 5

Sum Square B (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (3.2 - 5)² + (4.2 - 5)² + (7.6 - 5)²= 10.64

Mean square B= Sum Square B/Df B= 10.64/2= 5.32

2. The mean square error (MSE) is the estimation of the variance error (σ $_{e}^2$ → $S_{e} ^{2}$ ), you have to use the following formula:

Se²= (n₁-1)S₁² + -(n₂-1)S₂² + (n₃-1)S₃²

n₁+n₂+n₃-k

Se²= 19*14.3 + 19*17.2 + 19*16.7 = 915.8 = 16.067

20+20+20-3 57

DfE= N-k = 60-3= 57

3. To calculate the value of the statistic you have to divide the MSB by MSE

$F= \frac{Mean square B}{Mean square E} = \frac{5.32}{16.067} = 0.33$

4. P(F $_{2; 57}$ ≤ F) = P(F $_{2; 57}$ ≤ 0.33) = 0.28

I hope you have a SUPER day!

3 0

3 years ago