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3 years ago

Is (-1,7) a solution for the system of linear equations below? x + 2y = 13 and 3x - y

Mathematics

1 answer:

juin [17]3 years ago

6 0

Answer:

x = -9/7, y = 50/7.

Step-by-step explanation:

x + 2y = 13 ---------(eqn 1)

3x - y = -11 -----------(eqn 2)

Let's solve simultaneously using elimination method by multiplying eqn 2 by 2 so as to eliminate y.

3x - y = - 11 -------( × 2)

It gives

6x - 2y = - 22 ---------- ( new eqn 2)

x + 2y = 13 -----------( eqn 1)

Now add eqn 1 and new eqn 2

6x + x -2y + 2y = -22 + 13

7x = -9

Divide both sides by 7

7x/7 = -9/7

x = -9/7

Put x = -9/7 into eqn 1

x + 2y = 13

-9/7 + 2y = 13

Add 9/7 to both sides

-9/7+9/7 + 2y = 13+9/7

2y = 100/7

Divide both sides by 2

2y/2 = 100/7 ÷ 2

y = 100/7 × 1/2

y = (100÷2)/7

y = 50/7

Therefore

x = -9/7, y = 50/7

(-9/7, 50/7)

Therefore (-1,7) is not the solution for both equations , it is not a solution for NEITHER equation.

I hope this was helpful, please rate as brainliest

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On which triangle can the law of cosines be applied once to find an unknown angle measure? Law of cosines: a2 = b2 + c2 – 2bccos

Maksim231197 [3]

Answer:

C) Angle X Y W is 76 degrees. The length of X Y is 5, the length of W Y is 10, and the length of W X is y.

Step-by-step explanation:

On which triangle can the law of cosines be applied once to find an unknown angle measure?

The Law of cosines is given as:

a² = b² + c² - 2bccos(A)

From the options given above, the correct option is Option C

C) Angle X Y W is 76 degrees. The length of X Y is 5, the length of W Y is 10, and the length of W X is y.

This is because:

Law of Cosines helps us to find an unknown side of a triangle when we are given 2 known sides and 1 angle.

In the above question, we are given angle 76 degree, and the length of two sides: The length of X Y is 5, the length of W Y is 10

The unknown side is the length of W X which is represented as y.

Hence, Option C is the correct option.

3 0

3 years ago

Read 2 more answers

A scientist has started a bacteria culture with 1,000 cells. The cells will double every hour. 1. Write the sequence that repres

babymother [125]

Answer:

See below in bold.

Step-by-step explanation:

1. The sequence is 1000, 2000, 4000, 8000.

2. The common ratio is 2000/1000 = 2.

3. Number of bacteria after 7 hours is 1000(2)^(7- 1)

= 64,000.

4. 1000(2)^(x-1) > 1,000,000

2^x-1 > 1000

x- 1 log 2 > log 10

x- 1 > 9.96

x > 10.96

During the 11th hour.

8 0

3 years ago

A rug is to be centered in a room so that the border around it is of a consistent width on all four sides. If the room is 10 ft

aleksley [76]

Answer:

The width of the border can be 9 feet or 3.5 feet.

Step-by-step explanation:

Let the width be x

Length of room = 10 feet

Breadth of room = 15 feet

Length of rug = 10-2x

Breadth of rug = 15-2x

Area of rug = $(10-2x)(15-2x)$

We are given that the area of the rug is 24 square feet.

So, $(10-2x)(15-2x)=24$ ---A

$150-20x-30x+4x^2=24$

$150-24-50x+4x^2=0$

$126-50x+4x^2=0$

$2(x-9)(2x-7)=0$

$x=9,\frac{7}{2}$

$x=9,3.5$

Substitute x =9 in A

$(10-2(9))(15-2(9))=24$

$24=24$

LHS = RHS

Substitute x = 3.5

$(10-2(3.5))(15-2(3.5))=24$

$24=24$

LHS = RHS

So, The width of the border can be 9 feet or 3.5 feet.

7 0

3 years ago

A suncatcher has 6 sections. Each section is in the shape of a parallelogram witha base of 12 cm and a height of 8 cm. What is t

jonny [76]

Answer:

576 cm²

Step-by-step explanation:

Given:

Number of sections in a suncatcher (n) = 6

Each section is in the shape of a parallelogram.

Base of parallelogram = 12 cm

Height of parallelogram = 8 cm

Now, area of a parallelogram is given as:

Area of parallelogram = Base × Height

Area of 1 parallelogram = 12 cm × 8 cm = 96 cm²

Now, there are 6 parallelogram shaped sections.

So, area of the sections = area of 1 section × total number of sections

∴ Area of 6 sections = 96 cm² × 6 = 576 cm²

Therefore, the total area of the sections of a suncatcher is 576 cm².

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2 years ago

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fgiga [73]

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3 years ago