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3 years ago

Translate and solve: five less than z is 4

Mathematics

1 answer:

vazorg [7]3 years ago

8 0

z -5 =4

neutralize the left -5 by adding 5 on both sides

z -5 (+5) = 4 (+5)

z = 9

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3 years ago

← How many solutions does this linear system have y = x+2 6x - 4y = -10

defon

Answer:

This linear system has one solution.

Step-by-step explanation:

First equation: y = x + 2

Second equation: 6x - 4y = -10

Let's change the second equation in slope-intercept form y = mx + b.

Slope-intercept form

y = mx + b

m ... slope

b ... y-intercept

$6x - 4y = -10$

$6x + 10 = 4y$

$\frac{6}{4}x + \frac{10}{4} = y$

$\frac{3}{2}x + \frac{5}{2} = y$

If two lines have the same slope but different y-intercept, they are parallel - system has no solutions.

If two lines have the same slope and the same y-intercept, they are the same line and are intersecting in infinite many points - system has infinite many solutions.

If two lines have different slopes then they intersect in one point - system has one solution.

We see that lines have different slopes. First line has slope 1 and the other line has slope $\frac{3}{2}$ . So the system has one solution.

You can also check this by solving the system.

Substitute y in second equation with y from first.

6x - 4y = -10

6x - 4(x + 2) = -10

Solve for x.

6x - 4x - 8 = -10

2x = -2

x = -1

y = x + 2

y = -1 + 2

y = 1

The lines intersect in point (-1, 1). <-- one solution

8 0

2 years ago

PLEASE HELP I AM DESPERATE!!!

Vilka [71]

Answer:

Statements:

m<b = 180 - m<a

m<c = 180 - m<d

m<b = m<c

180 - m<a = 180 - m<d

Reasons:

The measure of m<b is the angle of a straight line subtracted with m<a. The measure of m<c is the angle of a straight line subtracted with m<d. If m<a and m<d are equal, m<b and m<c are equal.

Step-by-step explanation:

We know, m<a = m<d

So, we need to prove m< b = m<c

Let's start by defining what b and c is

m<b + m<a = 180 This is because a straight line is 180 degrees

m<b = 180 - m<a

m<c + m<d = 180

m<c = 180 - m<d

With this, we can substitute in proof

m<b = m< c

180 - m<a = 180 - m<d

180 - m<a = 180 - m<a

Your welcome for the answer. Tell me if you have any questions in the comments section of this answer! If you could mark this answer as the brainliest, I would greatly appreciate it!

4 0

3 years ago