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2 years ago

Which of the following systems of equations has infinitely many solutions?

Mathematics

2 answers:

Sonja [21]2 years ago

3 0

Answer:

C. y = x + 4, 2y = 2x + 8

Step-by-step explanation:

The system has infinitely many solutions if the two equations are equivalent.

We can analyze the given systems to see:

2x + 7x + y = 6 ⇒ 9x + y = 6 ⇒ y = - 9x + 6
y = 9x + 6

Different slopes, there is one solution

y = 5x + 7
y = 2x + 8

Different slopes, there is one solution

y = x + 4
2y = 2x + 8 ⇒ y = x + 4

Same lines, infinitely many solutions

7x - y = 10 ⇒ y = 7x - 10
y = 6x + 8

Different slopes, there is one solution

Ainat [17]2 years ago

3 0

Solution:

When two equations are equivalent, it is infinitely many solutions because the two lines overlap each other.

Option A - 2x + 7x + y = 6 and y = 9x + 6

=> (9x + y = 6) = (y = 9x + 6)
=> (y = -9x + 6) ≠ (y = 9x + 6)

Option B - y = 5x + 7 and y = 2x + 8

=> (y = 5x + 7) ≠ (y = 2x + 8)

Option C - y = x + 4 and 2y = 2x + 8

=> (y = x + 4) = (2y = 2x + 8)
=> (y = x + 4) = (y = 2x/2 + 8/2)
=> (y = x + 4) = (y = x + 4)

Option D - 7x - y = 10 and y = 6x + 8

=> (7x - y = 10) = (y = 6x + 8)
=> (-y = -7x + 10) = (y = 6x + 8)
=> (y = 7x - 10) ≠ (y = -6x - 8)

Hence, Option C is correct.

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3 years ago

Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for e

bekas [8.4K]

Answer:

The water she need is $7\frac{7}{8} \ cups.$ and strawberry syrup $11\frac{13}{16}\ cups$ .

Step-by-step explanation:

Given:

Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for every 3/4 cup of syrup.

Now, to find the quantity of water and syrup she need to use.

As given in question ratio so:

Strawberry syrup = 2 1/4 = 9/4.

Water = 3/4.

Total cups of strawberry drink = 15 3/4 = 63/4.

Let the strawberry syrup be $\frac{9}{4} x$ .

And let the water be $\frac{3}{4} x$ .

According to question:

$\frac{9x}{4} + \frac{3x}{4}=\frac{63}{4}$ .

On adding the fractions:

⇒ $\frac{9x+3x}{4} =\frac{63}{4}$

⇒ $\frac{12x}{4} =\frac{63}{4}$

Multiplying both sides by 4 we get:

⇒ $12x=63$

Dividing both sides by 12 we get:

⇒ $x=\frac{63}{12}$

Dividing numerator and denominator by 3 on R.H.S we get:

⇒ $x=\frac{21}{4}$

Now, putting the value of $x$ on ratios:

Strawberry syrup = $\frac{9}{4}\times x=\frac{9}{4}\times\frac{21}{4}$

= $\frac{189}{16}$

= $11\frac{13}{16}\ cups$

Water = $\frac{3}{4}\times x =\frac{3}{4} \times\frac{21}{4}$

= $\frac{63}{8}$

= $7\frac{7}{8} \ cups.$

Therefore, the water she need is $7\frac{7}{8} \ cups.$ and strawberry syrup $11\frac{13}{16}\ cups$ .

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3 years ago

SOMEONE PUT AN ANSWER SO IT DOESNT GET DELETED!!!

Nadusha1986 [10]

Answer:

The height of the cylinder is 4x units.

Step-by-step explanation:

volume of a cylinder = nr^2h

n = 22/7

r = radius = x/2

Let illustrate with an example. If the diameter of a cylinder is 6 and the volume is 6^3 = 216. The radius = 6/2 = 3

n3^2 x h = 216

h = 216/9 = 24

so the height is 4 times the diameter

Area of the base = nr^2

1/2^2 x x = 1/4 pi x^2

3 0

2 years ago