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4 years ago

Solve the system of equations: y=x^2+3x-6 y=2x-6

Mathematics

2 answers:

alexira [117]4 years ago

5 0

here's your answer in the given attachment

san4es73 [151]4 years ago

5 0

Answer:

Solution: {(-1,-8), (0,-6)}

Step-by-step explanation:

y=x^2+3x-6 ............(1)

y=2x-6 ....................(2)

Solution:

by comparison, the right-hand sides of both equations are equal (to y)

x^2+3x-6 = 2x - 6

Transpose and simplify

x^2 -x = 0

x = -1 or x=0

Substitute x = -1 in (2)

y = 2(-1) -6 = -8 ..............(-1,-8)

substitute x = 0 in (2)

y = 2(0) -6 = -6 ...............(0,-6)

So there are two solutions, corresponding to the intersection of the quadratic and the straight line.

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The ratio of the same side interior angles of two parallel lines is 1:14. Find the measures of all eight angles formed by the pa

Andrew [12]

Answer:

At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.

At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.

Step-by-step explanation:

At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.

At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.

Step-by-step explanation:

Let a be the first interior angle. Since they are in 1:14, the second same side interior angle is b = 14a.

We know that the sum of interior angles equals 180°.

So, a + b = 180°

a + 14a = 180°

15a = 180°

a = 180/15

a = 12°

At alternate angle to the other interior angle, b adjacent to a is c = b = 14a = 14 × 12 = 168°

The angle vertically opposite to a is d = a = 12°

The angle vertically opposite to a is b = e = 168°

At the intersection of the second parallel line and the transversal, the angle alternate to a is f = a = 12°

the angle vertically opposite to angle b is g = b = 168°

the angle vertically opposite to f is h = 12°

6 0

3 years ago

You plan on buying new flooring for your bedroom. Your bedroom is a rectangle that is 12.7 ft. by 14.25 ft. How many square feet

joja [24]

Answer:

180.975 square feet

Step-by-step explanation:

est: 181 square feet

4 0

3 years ago

-5.2 - (-3.1) + 5.2 =

aleksley [76]

Answer:

the answer is 31/10

Step-by-step explanation:

5 0

3 years ago

What is the volume of this figure?

Oksi-84 [34.3K]

Answer:

88 ft^3

Step-by-step explanation:

First find the volume of the rectangular prism on the left

V = l*w*h = 2*(4)*8 = 2*4*8= 64 ft^3

Then find the volume of the rectangular prism on the bottom

The base is not 5 but 5-2 since we used 2 on the left side

V = l*w*h = (5-2) *4*2 = 3*4*2 = 24 ft^3

Add them together

64+24=88

3 0

3 years ago

A hippopotamus can stay under water for 15 minutes. A sea cow can stay under water y minutes.This is 11 minutes longer than one-

egoroff_w [7]

Answer:

<em>The sea cow can stay under water for 16 minutes.</em>

Step-by-step explanation:

A hippopotamus can stay under water for 15 minutes.

A sea cow can stay under water $y$ minutes and this is 11 minutes longer than one-third the time a hippopotamus can.

So, "11 minutes longer than one-third the time a hippopotamus can" means: $[\frac{1}{3}(15)+11] minutes$

Thus, the equation will be: $y= \frac{1}{3}(15)+11$

Now, solving the above equation, we will get.........

$y= \frac{1}{3}(15)+11 \\ \\ y=5+11= 16$

So, the sea cow can stay under water for 16 minutes.

8 0

3 years ago