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3 years ago

Identify the correct slope and y intercept of the equation 6x – 3y = 12

2 answers:

8 0

Y = mx + b
m = slope
b = y intercept.

6x - 3y = 12
-3y = -6x + 12
-3y/-3 = -6x/-3 + 12/-3
y = 2x - 4
m = slope = 2
b = y intercept = -4

y = -x + 6
m = -1 ; b = 6

(-4,-2)
Since it is perpendicular to y = -x + 6, the slope of (-4,-2) is the opposite reciprocal of the -1.

m = +1

-2 = 1(-4) + b
-2 = -4 + b
b = -2 + 4
b = 2

y = x + 2 is the equation of the line passing through the point (-4,-2)

Zina [86]3 years ago

5 0

Equation of a line is given by y = mx + c; where m is the slope and c is the y-intercept.
For line 6x - 3y = 12
3y = 6x - 12
y = 6/3 x - 12/3
y = 2x - 4

Therefore, slope is 2.

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What is B-CF?

Sholpan [36]

I'm guessing on the make up of the matrices.
First off let's look at [C][F].
[C]=
[F]=
[C][F]=
where each element of [C][F] comes from multiplying a row of [C] with a column of [F].
Example: First element is product of first row and first column.

.
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Now that we have [C][F], we can subtract it from [B], element by element,

[B]-[C][F]=
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If this is not how the matrices look,please re-state the problem and be more specific about the make up of the matrices (rows x columns).
Here's an example.
[A] is a 2x2 matrix. A=[1,2,3,4].
The assumption is that [A] looks like this,
[A]=
[B] is a 3x2 matrix. B=[5,6,7,8,9,10]
[B]=

7 0

3 years ago

Consider f(x) = -(x+7)^2 +4. check all that apply

kirill [66]

-the equation is a quadratic

-the axis of symmetry is x=-7

-the graph has a relative maximum

5 0

3 years ago

Matthew wants to estimate the mean height of students attending his college. He records the heights of 100 randomly selected stu

Mnenie [13.5K]

The correct option that shows the population of the research carried out by Matthew is;

Option D; all the students attending the college

We are told that Matthew wants to estimate the mean height of students attending his college.

Now, let us say the total number of students in his college is x. If he decides to select 100 students randomly to record their height, it means this 100 students is a sample out of the total number of students which is x that is the population.

In conclusion, we can say that the population of this research by Matthew is the total number of students that attend the college.

Read more at; brainly.com/question/6028584

6 0

2 years ago

Can someone please help me on number 16-ABC

melomori [17]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the inequality

-2x < 10

-6 < -2x

Part a) Is x = 0 a solution to both inequalities

FOR -2x < 10

substituting x = 0 in -2x < 10

-2x < 10

-3(0) < 10

0 < 10

TRUE!

Thus, x = 0 satisfies the inequality -2x < 10.

∴ x = 0 is the solution to the inequality -2x < 10.

FOR -6 < -2x

substituting x = 0 in -6 < -2x

-6 < -2x

-6 < -2(0)

-6 < 0

TRUE!

Thus, x = 0 satisfies the inequality -6 < -2x

∴ x = 0 is the solution to the inequality -6 < -2x

Conclusion:

x = 0 is a solution to both inequalites.

Part b) Is x = 4 a solution to both inequalities

FOR -2x < 10

substituting x = 4 in -2x < 10

-2x < 10

-3(4) < 10

-12 < 10

TRUE!

Thus, x = 4 satisfies the inequality -2x < 10.

∴ x = 4 is the solution to the inequality -2x < 10.

FOR -6 < -2x

substituting x = 4 in -6 < -2x

-6 < -2x

-6 < -2(4)

-6 < -8

FALSE!

Thus, x = 4 does not satisfiy the inequality -6 < -2x

∴ x = 4 is the NOT a solution to the inequality -6 < -2x.

Conclusion:

x = 4 is NOT a solution to both inequalites.

Part c) Find another value of x that is a solution to both inequalities.

solving -2x < 10

$-2x\:$

Multiply both sides by -1 (reverses the inequality)

$\left(-2x\right)\left(-1\right)>10\left(-1\right)$

Simplify

$2x>-10$

Divide both sides by 2

$\frac{2x}{2}>\frac{-10}{2}$

$x>-5$

$-2x-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-5,\:\infty \:\right)\end{bmatrix}$

solving -6 < -2x

-6 < -2x

switch sides

$-2x>-6$

Multiply both sides by -1 (reverses the inequality)

$\left(-2x\right)\left(-1\right)$

Simplify

$2x$

Divide both sides by 2

$\frac{2x}{2}$

$x$

$-6$

Thus, the two intervals:

$\left(-\infty \:,\:3\right)$

$\left(-5,\:\infty \:\right)$

The intersection of these two intervals would be the solution to both inequalities.

$\left(-\infty \:,\:3\right)$ and $\left(-5,\:\infty \:\right)$

As x = 1 is included in both intervals.

so x = 1 would be another solution common to both inequalities.

<h3>SUBSTITUTING x = 1</h3>

FOR -2x < 10

substituting x = 1 in -2x < 10

-2x < 10

-3(1) < 10

-3 < 10

TRUE!

Thus, x = 1 satisfies the inequality -2x < 10.

∴ x = 1 is the solution to the inequality -2x < 10.

FOR -6 < -2x

substituting x = 1 in -6 < -2x

-6 < -2x

-6 < -2(1)

-6 < -2

TRUE!

Thus, x = 1 satisfies the inequality -6 < -2x

∴ x = 1 is the solution to the inequality -6 < -2x.

Conclusion:

x = 1 is a solution common to both inequalites.

7 0

3 years ago

There are 96 people consisting of 48 married couples in a room. Assuming that no husband or wife shakes thr others hand but ever

NikAS [45]

Answer:

4512 handshakes

Step-by-step explanation:

We are told in the question, that there are

96 people in the room = 48 couples

Assuming that no husband or wife shakes each others hand but everyone else shakes hands exactly once

This means

48 couples will shake 94 people because they are excluded

This is calculated as

48 × 94 = 4512 handshakes

6 0

3 years ago