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2 years ago

How many solutions exist for the system of equations graphed below?

Mathematics

2 answers:

Zinaida [17]2 years ago

6 0

Answer:

one

Step-by-step explanation:

When a system of equations is graphed, the solution is the coordinate that is plotted at the intersection of the two lines.

If the two lines cross once, there is only one solution.

If the two lines are on top of each other then there are infinitely many solutions.

If the two lines are parallel ( and never touch ) then there are no solutions

By looking at the graph we notice the two lines intersect once. So we can conclude that there is only one solution.

Andreas93 [3]2 years ago

5 0

Answer: b) one

Detailed Explanation:

For the graph of a system of linear equations :-

• If the lines are parallel, then the pair of equations has no solution
• If the lines are coincident, then the pair of equations has infinite solutions
• If the lines are intersecting, then the pair of equations have one solution.

In this graph, the lines formed by the equations are intersecting at a point. Hence it has a unique solution.

You might be interested in

Find sin 0, where is the angle shown. Give an exact value, not a decimal approximation.

Nata [24]

Answer:

$\displaystyle \sin\theta=\frac{12}{13}$

Step-by-step explanation:

Recall that in a right triangle, sine is the ratio of the opposite side to the hypotenuse:

$\displaystyle \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

We are actually not given the opposite side in this case. However, since we know the hypotenuse and the adjacent side, we can use the Pythagorean Theorem to find the opposite side. So:

$a^2+b^2=c^2$

Let a be the adjacent side and b be the opposite side. c will be the hypotenuse.

Substitute:

$(5)^2+b^2=(13)^2$

Solve for b:

$b=\sqrt{169-25}=\sqrt{144}=12$

So, the opposite side measures 12.

Then sine will be:

$\displaystyle \sin\theta=\frac{12}{13}$

3 0

3 years ago

Is 0.4 over 0.8 a rational or irrational number

Rudik [331]

It is a rational number and it equals 0.5 or 1/2

5 0

3 years ago

Find the total surface area of a trapezoidal prism.

Ostrovityanka [42]

Split the trapezium into a rectangle and a triangle and work out the areas of them.
4x6=24
(2x4)/2=4
Area of trapezium= 28
There are 2 trapeziums, which makes 56.
The back of the shape is 4x14=56.
The top of the shape is 6x14=84.
The underside of the shape is 8x14=112.
The front rectangle is 14x4.47= 62.58.

As them all together= 56+56+84+112+62.58=370.58.

Total surface area=370.58.

Hope this helps :)

4 0

3 years ago

Read 2 more answers

Can Someone plz help? Thx

Andreyy89

Answer:

7. 2355 m

8. 1570 km

9. 157 cm

10. 40.82 m

Step-by-step explanation:

The circumference of a circle is pi * diameter or 2 * pi * radius.

If you are given the diameter, just multiply it by pi, 3.14.

If you are given the radius, then multiply the radius by 2 and then by pi, 3.14.

7. d = 750 m

circumference = pi * d = 3.14 * 750 m = 2355 m

8. d = 500 km

circumference = pi * d = 3.14 * 500 km = 1570 km

9. r = 25 cm

circumference = 2(pi)r = 2 * 3.14 * 25 cm = 157 cm

10. r = 6.5 m

circumference = 2(pi)r = 2 * 3.14 * 6.5 m = 40.82 m

8 0

3 years ago

The area of a field shaped like a right triangle is 750yd^2.One leg of the field is fenced with wood costing $5/yd. the remainde

Elenna [48]

Assume that
a and b = the two legs of the right triangle.
c = the hypotenuse.

The area of the right triangle is 750 yd², therefore
(1/2)*a*b = 750
ab = 1500 (1)

The perimeter is 150yd, therefore
a + b + c = 150 (2)

Let the side fenced with wood be a, at $5/yd. Sides b and c are fenced with steel at $10/y. The total cost is $1200, therefore
5a + 10b + 10c = 1200
or
a + 2b + 2c = 240 (3)

From (2), obtain
c = 150 - a - b (4)

Substitute (4) into (3)
a + 2b + 2(150 - a - b) = 240
-a + 300 = 240
a = 60

From (1), obtain
60b = 1500
b = 25

From (4), obtain
c = 150 - 60 - 25 = 65

Answer:
A. The length of the leg fenced with wood is 60 yd.
B. The length of the leg fenced with steel is 25 yd.

5 0

3 years ago