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3 years ago

How many solutions does the system have?

Mathematics

1 answer:

marishachu [46]3 years ago

3 0

Answer:

{x,y} = {-2,2}

Step-by-step explanation:

Solve equation [2] for the variable y

7y = 7x + 28

y = x + 4

Plug this in for variable y in equation [1]

-8x + 4•(x +4) = 24

-4x = 8

Solve equation [1] for the variable x

4x = - 8

x = - 2

By now we know this much :

x = -2

y = x+4

Use the x value to solve for y

y = (-2)+4 = 2

Solution :

{x,y} = {-2,2}

and this intersects at only one point so your answer is A

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Mr. Tally inherited $200,000. He used a portion of the inheritance to build a house. He invested the rest of the money for one y

Ivan

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Amount inherited = $200,000

Portion used to build house = h

Invested amount = 200,000 - h

1/3 of (200,000 - h) was invested at 12%

2/3 of 200,000 - h was invested at 15%

Interest from both investment = 8400

Cost of building =?

Using the simple interest formula :

Principal(P) * rate(r) * time

If the investment was for a year:

1st investment :

(200,000 - h)/3 * 0.12 * 1 = (24000 - 0.12h) / 3 = (8000 - 0.04h)

2nd :

(200,000 - h)*2/3* 0.15 * 1 = (20,000 - 0.1h)

Summing both :

8000 - 0.04h + 20,000 - 0.1h = 8400

28000 - 0.14h = 8400

-0.14h = 8400 - 28000

-0.14h = - 19600

= 140,000

3 0

3 years ago

The school’s guidance department compares the grade-point averages and standardized state test scores for 10 students in each gr

horrorfan [7]

10th grade and 12th grade data sets
This is because both have a negative correlation coefficient, meaning they are showing regression, or decrease.

7 0

3 years ago

Read 2 more answers

Meldie made a cube whose side is (3x - 2) inches. Find its volume in cubic inches.

irinina [24]

Answer:

x^2(3x-2) cubic inches OR in^3

3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3

I AM UNAWARE IF YOU ASKED THAT ONE SIDE IS (3X-2) OR ALL. I WILL ANSWER BOTH PARTS

-

NOTE: '^' MEANS TO THE POWER OF..

-

Volume = v, abc = 3 sides of cube (height, width, length)

Using the formula for volume in a cube,

$v = abc$

We can solve this.

If one side is (3x-2)in,

(3x-2)(x)(x) = v.... x are the other two sides
x^2(3x-2) = v

x^2(3x-2) cubic inches OR in^3

If all sides are (3x-2)in,

Use the formula,

$(a - b) ^{3} = {a}^{3} + 3ab(b - a) - {b}^{3}$

We can solve this.

(3x-2)(3x-2)(3x-2) = v
(3x-2)^3 = v.... 3x = a and -2 = b
(3x)^3 + [(3)(3x)(2)][2-3x] - (2)^3 = v
27x^3 + 18x(2-3x) -8 = v
(27x^3 + 36x - 54x^2) - 8 = v.. Terms inside brackets - take 3x as common and leave out 8
3x(9x^2 -18x +12) = v... Take 3 as common again in the brackets
3x [ 3 ([3x^2 -6x] + 4) -8 = v....Take 3x common in the terms in square brackets
3x [ 3 [ 3x (x-2) + 4 ]] - 8 = v
3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 = v

3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3

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If you have any questions regarding formulas or anything, comment and I will get back to you asap.

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5 0

1 year ago

Which equation demonstrates the additive identity property?

Blababa [14]

Answer:

first you have to add

Step-by-step explanation:

6 0

3 years ago

Please! Due soon

Ivenika [448]

Answer:So, the least squares regression equation is : y= mx+b ⇒ y= 6.33x +38.71

b. When x= 8, then y= (6.33×8)+38.71 = 50.64 + 38.71 =89.35

The approximate test score of a student who sleeps an average of 8 h a night is 89.35%

Step-by-step explanation:

hey someone else has already answered this!

a. To find the least squares regression equation for a group of (x,y) points:

Step 1: For each point(x,y), we need to calculate x² and xy first.

Step 2: Sum all x, y, x² and xy, which gives us Σx, Σy, Σx² and Σxy

Step 3: Calculate Slope m: m = (NΣxy − Σx Σy)/ N(Σx²) − (Σx)² , here N is the number of data.

Step 4: Calculate Intercept b: b = Σy − m(Σx)/ N

Step 5: Assemble the equation as y= mx+b

Here, we have ∑x = 120, ∑y= 1379, ∑x²= 919.5, ∑xy= 10466 and N= 16

So, m= (NΣxy − Σx Σy)/ N(Σx²) − (Σx)²

= 6.33

and b = Σy − m(Σx)/ N

= 38.71

So, the least squares regression equation is : y= mx+b ⇒ y= 6.33x +38.71

b. When x= 8, then y= (6.33×8)+38.71 = 50.64 + 38.71 =89.35

The approximate test score of a student who sleeps an average of 8 h a night is 89.35%

EVERYTHING IS FROM sicista on brainly!

4 0

3 years ago