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Leni [432]
3 years ago
13

Find the value of x in each case:

Mathematics
1 answer:
Soloha48 [4]3 years ago
4 0

Answer:

x = 36

Step-by-step explanation:

To obtain the value of x, we must first obtain the value of y and z as shown in the attached photo.

i. Determination of y

2x + y = 180 (angle on a straight line)

Rearrange

y = 180 – 2x

ii. Determination of z.

z + 4x = 180 (angle on a straight line)

Rearrange

z = 180 – 4x

iii. Determination of x

x + y + z = 180 (sum of angles in a triangle)

But:

y = 180 – 2x

z = 180 – 4x

Therefore,

x + y + z = 180

x + 180 – 2x + 180 – 4x = 180

Collect like terms

x – 2x – 4x = 180 – 180 –180

– 5x = – 180

Divide both side by – 5

x = – 180 / – 5

x = 36

Therefore, the value of x is 36.

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What are the coordinates of the fourth point that could be connected with (–8, 0), (1, 0), and (1, –5) to form a rectangle?
sergey [27]
(-8, -5)

To form a rectangle, all the lines must be perpendicular and parallel. If you draw out the points on a coordinate plane then you can find the answer pretty easily. 

Also, this one is easy because all the lines are vertical or horizontal, and when that is the case then you can just see which number in the set hasn't appeared twice (1 appeared twice as an <em>x</em> value, 0 appeared twice as a <em>y </em>value, but -8 has only appeared once as an <em>x</em> and -5 has only appeared once as a <em>y </em>value)
6 0
3 years ago
Determine whether the statement is true or false. Justify your answers.
marusya05 [52]

Answer:

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis. ⇒ False

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis. ⇒ False

Step-by-step explanation:

<em>Let us explain the reflection about the axes</em>

  • If a graph is reflected about the x-axis, then the y-coordinates of all points on it will opposite in sign

Ex: if a point (2, -3) is on the graph of f(x), and f(x) is reflected about the x-axis, then the point will change to (2, 3)

  • That means reflection about the x-axis change the sign of y
  • y = f(x) → reflection about x-axis → y = -f(x)

  • If a graph is reflected about the y-axis, then the x-coordinates of all points on it will opposite in sign

Ex: if a point (-2, -5) is on the graph of f(x), and f(x) is reflected about the y-axis, then the point will change to (2, -5)

  • That means reflection about the y-axis change the sign of x
  • y = f(x) → reflection about y-axis → y = f(-x)

<em>Now let us answer our question</em>

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis.

It is False because reflection about x-axis change sign of y

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the x-axis

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis.

It is False because reflection about y-axis change sign of x

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the y-axis

7 0
3 years ago
Are the fractions 1/5 , 5/5 , and 5/1 equivalent?Explain.
Debora [2.8K]
No, these equations are not equivalent. 

1/5, or one fifth, is part of a whole. Imagine you have a pie, cut into five pieces, and your friend comes over and eats four pieces, so now you have one of the five original pieces. That's what you have here. 

5/5, or five fifths, is a whole. any number divided by itself is automatically one, so it is like making another pie and cutting it into five pieces, only this time no one eats any of it because it's burned or something. At the end, you have five pieces of pie

5/1 is actually just another way of writing plain old 5. To keep the pie example rolling, you have five pies, and no one eats any of these either, so they are all yours. You have 5 pies divided between one person, so at the end of the day you have 5 whole pies. 

Hope that helped!
7 0
3 years ago
Read 2 more answers
A field that is 3/4 acres must be planted with seed. If 28 people will split the job equally, how many acres must each person pl
zlopas [31]

Answer:

3/112

Step-by-step explanation:

you take 3/4 and divide it between how many workers you have so that equals 3/112

5 0
3 years ago
The phone company NextFell has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of mon
zaharov [31]

The equation in the form y = mx + b is y = 0.35x + 36.

<h3>How to represent a linear equation?</h3>

The equation formed from the expression is a linear equation and should be expressed in the slope intercept form.

y = mx + b

where

  • m = slope
  • b = y-intercept

Therefore,

y = mx + b

where

  • x = the number of monthly minutes used
  • y = the total monthly of the Next fell plan

using the coordinates, let's find m

(470, 200.5)(590, 242.5)

Hence,

m = 242.5 - 200.5 / 590 - 470

m = 42 / 120

m = 0.35

Therefore,

y = 0.35x + b

200.5 = 0.35(470) + b

200.5  - 164.5 = b

b = 36

Finally, the equation in the form y = mx + b is y = 0.35x + 36.

learn more on linear equation here: brainly.com/question/24223023

#SPJ1

7 0
1 year ago
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