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Solve the system of linear equations below. <br><br> X+y=4<br> 2x+3y=0

deff fn [24]

X + y = 4...x = 4 - y

2x + 3y = 0
2(4-y) + 3y = 0
8 - 2y + 3y = 0
-2y + 3y = 0 - 8
y = -8

x + y = 4
x - 8 = 4
x = 4 + 8
x = 12

solution is : (12,-8)

7 0

3 years ago

Read 2 more answers

Express 35.4% as a decimal

jekas [21]

Answer:

0.354

Step-by-step explanation:

7 0

3 years ago

1) What is the solution of the given system?

m_a_m_a [10]

Answer:

1 x=-2.5 y = -5.5

2. x=5 y=1

Step-by-step explanation:

1) What is the solution of the given system?

5x-y=-7

3x-y=-2

Multiply the second equation by -1

-1*(3x-y)=-1(-2)

-3x +y = 2

Now add the first equation to the modified second equation

5x-y=-7

-3x +y = 2

------------------

2x = -5

Divide each side by 2

2x/2 = -5/2

x = -2.5

Now we need to find y

-3x+y =2

-3(-2.5) +y =2

7.5 +y =2

Subtract 7.5 from each side

7.5 -7.5 +y =2-7.5

y = -5.5

2) what is the solution of the given system?

5x+7y=32

8x+6y=46

Divide the second equation by 2

8x/2+6y/2=46/2

4x+3y =23

Multiply the first equation by 4

4 (5x+7y)=32*4

20x+28y = 128

Now multiply the modified 2nd equation by -5

-5(4x+3y )=-5(23 )

-20x -15y = -115

Lets add the new equations together to eliminate x

20x+28y = 128

-20x -15y = -115

---------------------

13y = 13

Divide each side by 13

13y/13 =13/13

y=1

Now substitute back in to find x

5x+7y=32

5x +7(1) =32

5x +7 =32

Subtract 7 from each side

5x+7-7 =32-7

5x =25

Divide by 5

5x/5 =25/5

x=5

3 0

3 years ago

A student union cafeteria worker checked the weight of ten half-pound bags of whole bean coffee and recorded the following weigh

Likurg_2 [28]

Answer: σ = 0.0154

Step-by-step explanation:

1. Calculate the mean for the recorded data.

(0.48 + 0.51 + 0.47 + 0.49 + 0.49 + 0.50 + 0.52 + 0.48 + 0.49 + 0.51)/10 =

4.94 / 10 = 0.49

The mean is represented with the greek letter μ, so μ = 0.49

2. For each element in the serie, subtract the mean (0.49) and square the result

(0.48 - 0.49)^2 = (-0.01)^2 = 0.0001

(0.51 - 0.49)^2 = (0.02)^2 = 0.0004

(0.47 - 0.49)^2 = (-0.02)^2 = 0.0004

(0.49 - 0.49)^2 = 0

(0.50 - 0.49)^2 = (0.01)^2 = 0.0001

(0.52 - 0.49)^2 = (0.03)^2 = 0.0009

(0.48 - 0.49)^2 = (-0.01)^2 = 0.0001

(0.49 - 0.49)^2 = 0

(0.51 - 0.49)^2 = (0.02)^2 = 0.0004

So we get these results: 0.0001, 0.0004, 0.0004, 0, 0, 0.0001, 0.0009, 0.0001, 0, 0.0004

3. Now, we calculate the mean of these squared differences

(0.0001 + 0.0004 + 0.0004 + 0 + 0 + 0.0001 + 0.0009 + 0.0001 + 0 + 0.0004) / 10 =

(0.0024) / 10 = 0.00024

4. Now to get the standard deviation, we need to get the root of this last value (0.00024).

√(0.00024) = 0.0154

5. So that will be our standard deviation value:

σ = 0.0154

DONE!

7 0

3 years ago

A rose garden Is formed by jolning a rectangle and a semicircle, as shown below. The rectangle Is 23 ft long and 14 ft wide.Find

Ratling [72]

Answer:

Area of the garden:

$\begin{equation*} 398.93\text{ ft}^2 \end{equation*}$

Explanation:

Given the below parameters;

Length of the rectangle(l) = 23 ft

Width of the rectangle(w) = 14 ft

Value of pi = 3.14

Since the width of the rectangle is 14 ft, so the diameter(d) of the semicircle is also 14 ft.

The radius(r) of the semicircle will now be;

$r=\frac{d}{2}=\frac{14}{2}=7\text{ ft}$

Let's now go ahead and determine the area of the semicircle using the below formula;

$A_{sc}=\frac{\pi r^2}{2}=\frac{3.14*\left(7\right)^2}{2}=\frac{3.14*49}{2}=\frac{153.86}{2}=76.93\text{ ft}^2$

Let's also determine the area of the rectangle;

$A_r=l*w=23*14=322\text{ ft}^2$

We can now determine the area of the garden by adding the area of the semicircle and that of the rectangle together;

$\begin{gathered} Area\text{ of the garden = Area of semi circle + Area of rectangle } \\ =76.93+322 \\ =398.93\text{ ft}^2 \end{gathered}$

Therefore, the area of the garden is 398.93 ft^2

8 0

1 year ago