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ladessa [460]
3 years ago
6

Which of the following (x,y) pairs is the solution for the system of equations x+2y=4 and -2x+y=7

Mathematics
1 answer:
kakasveta [241]3 years ago
3 0

Answer:

(-2 ,3)

Step-by-step explanation:

Step 1: Rewrite first equation

x = 4 - 2y

-2x + y = 7

Step 2: Substitution

-2(4 - 2y) + y = 7

Step 3: Solve <em>y</em>

-8 + 4y + y = 7

-8 + 5y = 7

5y = 15

y = 3

Step 3: Plug in <em>y</em> to find <em>x</em>

x + 2(3) = 4

x + 6 = 4

x = -2

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7x - 20 = 2x - 3(3x + 2)
kirill [66]

Answer:

7x-20=2x-3(3x+2)

We move all terms to the left:

7x-20-(2x-3(3x+2))=0

We calculate terms in parentheses: -(2x-3(3x+2)), so:

2x-3(3x+2)

We multiply parentheses

2x-9x-6

We add all the numbers together, and all the variables

-7x-6

Back to the equation:

-(-7x-6)

We get rid of parentheses

7x+7x+6-20=0

We add all the numbers together, and all the variables

14x-14=0

We move all terms containing x to the left, all other terms to the right

14x=14

x=14/14

x=1

   

   

Step-by-step explanation:

4 0
3 years ago
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The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:
Stels [109]

Answer:

SAS postulate

Step-by-step explanation:

In the figure attached, quadrilateral ABCD is shown.

The Side Angle Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

AB is congruent to DC, and DB is the side common to triangles ABD and BCD. The included angle between sides AB and DB is angle ABD which is congruent with angle BDC, the angle included between sides DB and DC.

7 0
3 years ago
May someone please help me out with this problem? May you also explain it?
gavmur [86]

Answer:

Step-by-step explanation:

Given function is,

f(x) = \sqrt{x}

If the given function is vertically stretched by a scale factor of \frac{3}{2} Or 1.5,

Transformed function will be,

h(x) = \frac{3}{2}[f(x)]

h(x) = \frac{3}{2}(\sqrt{x})

Further function 'h' is shifted 1 units upwards,

g(x) = h(x) + 1

g(x) = \frac{3}{2}(\sqrt{x} )+1

Domain of the function → x ≥ 0 Or [0, ∞)

Range of the function → y ≥ 1 Or [1, ∞)

Transformations done → Parent function f(x) is vertically stretched by a scale factor of \frac{3}{2} then shifted 1 unit upward.

3 0
3 years ago
Y + 2 = -3(x - 4). What is the slope?
VARVARA [1.3K]

Answer:

m=-3

Step-by-step explanation:

6 0
3 years ago
7 in 10 auto accidents involve a single vehicle. Suppose 14 accidents are randomly selected. (Round your answers to five decimal
Tpy6a [65]

Answer:

Step-by-step explanation:

Assuming a binomial distribution for the number of auto accidents. If 7 in 10 auto accidents involve a single vehicle, the probability, p = 7/10 = 0.7

Then the probability that the accident involved multiple vehicles is

q = 1 - p = 1 - 7/10 = 3/10 = 0.3

Since 14 accidents are randomly selected, n = 14

The formula for binomial distribution is expressed as

P(x = r) = nCr × q^(n - r) × p^r

a) we want to determine P(x = 4) =

P(x = 4) = 14C4 × 0.3^(14 - 4) × 0.7^4

P(x = 4) = 0.00142

b) we want to find P(x lesser than or equal to 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P( x = 4)

P(x = 0) = 14C0 × 0.3^(14 - 0) × 0.7^0 = 0.00000004783

P(x = 1) = 14C1 × 0.3^(14 - 1) × 0.7^1 = 0.00011

P(x = 2) = 14C2 × 0.3^(14 - 2) × 0.7^2 = 0.00002

P(x = 3) = 14C3 × 0.3^(14 - 3) × 0.7^3 = 0.00022

P(x = 4) = 0.00142

P(x lesser than or equal to 4) = 0.00000004783 + 0.00011 + 0.00002 + 0.00022 + 0.00142 = 0.00177

c) p = 0.7, q = 0.3

P(x = 5)= 14C5 × 0.7^(14 - 5) × 0.3^5 = 0.19631

6 0
3 years ago
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