Two lines, C and D, are represented by the equations given below:Line C: y = x + 12
Line D: y = 3x + 2

Which of the following shows the solution to the system of equations and explains why?

(4, 14), because one of the lines passes through this point
(4, 14), because the point lies between the two axes
(5, 17), because both lines pass through this point
(5, 17), because the point does not lie on any axis

Answers

Answer 1

Answer: If you would like to know what is the solution to the system of equations, you can calculate this using the following steps:

y = x + 12
y = 3x + 2
______________
y = y
x + 12 = 3x + 2
12 - 2 = 3x - x
2x = 10
x = 5

y = x + 12 = 5 + 12 = 17

The correct result would be (x, y) = (5, 17); because both lines pass through this point.

Answer 2

Answer:

Answer:

The correct answer is C.

Step-by-step explanation:

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Answers

Answer:

h=9cm

P=(x+5)cm

b=(x-3)cm

by the Pythagoras theorem,

h^2=p^2+b^2

9^2=(x+5)^2+(x-3)^2

81=x^2+10x+25+x^2-6x+9

81=2x^2+4x+34

If the x- intercept is 2 and the y- intercept is -5 and the slope is 1/3. Write in equation in slope intercept form and standard form.

Answers

Answer:

The equation in slope-intercept form is

$y=(5)/(2)x-5$

The equation in the standard form will be:

$(5)/(2)x-y=5$

Step-by-step explanation:

The x-intercept is obtained when we set the value y=0

As the x-intercept is 2, therefore the point representing

the x-intercept will be: (2, 0)

The y-intercept is obtained when we set the value x=0

As the y-intercept is -5, therefore the point representing

the y-intercept will be: (0, -5)

So we get the two points

(2, 0)

(0, -5)

Finding the slope between (2, 0) and (0, -5)

$\left(x_1,\:y_1\right)=\left(2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:-5\right)$

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)$

$m=(-5-0)/(0-2)$

$m=(5)/(2)$

Using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

Here m is the slope

substituting the values m = 5/2 and the point (2, 0)

$y-0=(5)/(2)\left(x-2\right)$

so writing the equation in slope-intercept form

As we know that the slope-intercept form is

$y=mx+b$

here

m = gradient or slop

b = y-intercept

$y=(5)/(2)\left(x-2\right)$

$y=(5)/(2)x-5$

Hence, the equation in slope-intercept form is

$y=(5)/(2)x-5$

Writing the equation in the standard form form

As we know that the equation in the standard form is

$Ax+By=C$

where x and y are variables and A, B and C are constants

As we already know the equation in slope-intercept form

$y=(5)/(2)x-5$

so the equation in the standard form will be:

$(5)/(2)x-y=5$

What is the name of the relationship between ∠1 and ∠8 ?A. adjacent angles

B. alternate interior angles

C. alternate exterior angles

D. corresponding angles

Answers

Answer:

∠1 and ∠8 are alternate exterior angles.

Step-by-step explanation:

We are given two parallel lines and one transversal line which cuts both parallel line and makes two 8 angles.

We need to find the relation between them

As we know total 8 angles form when two parallel line cut by one line.

Name of angles (relation of angles)

Alternate interior angles
Adjacent angles
Corresponding angles
Alternate exterior angles

Alternate Exterior Angles are a pair of angles on the inside of each of those two parallel lines but on opposite sides of the transversal.

Alternate Exterior Angles are a pair of angles on the outer side of each of those two parallel lines but on opposite sides of the transversal.

Adjacent angles are a pair of angles whose a common side and a common vertex.

Corresponding angles are a pair of angles whose one out side and one inside of those parallel lines but on same side of the transversal.

Here, ∠1=∠8 because ∠1 and ∠8 are alternate exterior angles.

Thus, ∠1 and ∠8 are alternate exterior angles.

Answer:

Alternate exterior angles

Given the geometric sequence where a1 = 5 and the common ratio is −3, what is the domain for n?All integers where n ≥ 0

All integers where n ≥ 1

All integers where n ≥ 5

All integers where ≤ 5