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3 years ago

In a system of equations, two different lines intersect. How many solutions does the

Mathematics

1 answer:

romanna [79]3 years ago

3 0

A) One
If the line is intersecting and is parallel then the line will only intersect once at one point

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What is the vertex of y=-3x^2+6x+15? Help is much appreciated.

DENIUS [597]

Answer:

(1, 18)

Step-by-step explanation:

Rewrite the equation in vertex form by completing the square for -3x^2 + 6x + 15. This = -3(x - 1)^2 + 18.

Set y equal to the new right side.

y = -3(x - 1)

Use the vertex form, y = a(x - h)^2 + k, to determine the values of a, h, and k.

a = -3

h = 1

k = 18

Vertex = (h, k) / (1, 18)

5 0

3 years ago

Y=4x-6 and passes through point 8,12

umka2103 [35]

Answer:

Slope of required line if both lines are parallel: y=4x-20

Slope of required line if both lines are perpendicular: y=-1/4x+14

Step-by-step explanation:

We need to find equation of line while we are given another line having equation y=4x-6 and passes through point (8,12)

Note: Since it is not given if the required line is parallel or perpendicular to the given line. I will solve for both cases.

If Both lines are parallel the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are parallel there slopes are same

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=4

Now finding y-intercept

Using slope m=4 and point (8,12) we can find y-intercept

$y=mx+b\\12=4(8)+b\\12=32+b\\b=12-32\\b=-20$

y-intercept of new line is: b=-20

Equation of required line having slope m=4 and y-intercept b=-20 is

$y=mx+b\\y=4x-20$

If Both lines are perpendicular the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are perpendicular there slopes are opposite of each other

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=-1/4

Now finding y-intercept

Using slope m=-1/4 and point (8,12) we can find y-intercept

$y=mx+b\\12=-\frac{1}{4} (8)+b\\12=-2+b\\b=12+2\\b=14$

y-intercept of new line is: b=14

Equation of required line having slope m=-1/4 and y-intercept b=14 is

$y=mx+b\\y=-\frac{1}{4} x+14$

8 0

3 years ago

Number 2 i need help

daser333 [38]

The table you drew under the question is exactly the right way to start.

-- Make a second column, next to the 6 and 7. This column will be
the actual number of each thing.

-- You know that there are 42 marbles, so write '42' in the box
next to the 6, on the 'Marbles' line.
Now you need to figure out what to write in the 'Stones' line, next to the 7.

-- Look at the 'Marbles' line. There's a 6 and then a 42.
Ask yourself: " Self ! What does the 6 have to be multiplied with to get 42 ?"

-- Whatever the answer is, drop down to the 'Stones' line,
and multiply the 7 by the same number.
The product is the total number of stones, and it goes in the box.
.
.
.
(The mystery number is 7. There are 49 stones.)

6 0

3 years ago

Use the net to find the lateral area of the prism. 15 m 3 m 6 m 3 m 6 m

postnew [5]

Answer:

270 m²

Step-by-step explanation:

LA = (3+6+3+6)×15

= 18×15 = 270 m²

5 0

3 years ago

I need help on this question as soon as possible

Dennis_Churaev [7]

Answer:

2.5, 5, 7, 8

Step-by-step explanation:

6 0

3 years ago