Answer:
1. The correct options are 2 and 4.
2. The measure of angle 6 is 60°.
Step-by-step explanation:
1.
It is given that a∥b , and c is not parallel to a or b. So, we can not establish any relationship among the angles on the line a,b and angles on the line c.
If a traversal line intersect two parallel line, then corresponding angles, alternate exterior angle and alternate interior angles are equal.
![\angle 2=\angle 6=\angle 3=\angle 7](https://tex.z-dn.net/?f=%5Cangle%202%3D%5Cangle%206%3D%5Cangle%203%3D%5Cangle%207)
![\angle 1=\angle 5=\angle 4=\angle 8](https://tex.z-dn.net/?f=%5Cangle%201%3D%5Cangle%205%3D%5Cangle%204%3D%5Cangle%208)
Therefore correct options are 2 and 4.
2.
It is given that AB∥CD and m∠3=120°.
Statements Reasons
m∥nm∠1=120° Given
∠5≅∠1 Corresponding angles are equal
m∠5=m∠1 Angle Congruence Postulate
m∠5=120° Substitution Property of Equality
m∠6+m∠5=180° Supplementary angle property
m∠6+120°=180° Substitution Property of Equality
m∠6=60° Subtraction Property of Equality
Therefore the measure of angle 6 is 60°.
Since we are already given the equation, we can already solve for the given problems above. Let us start with part 2 so we can easily answer part 1.
Part 2: the cost to get started before any books are printed. Using the equation, x = 0. So, y =1250+25(0)
y= 1250
So the cost to get started before any books are printed is 1250.
Now, to part 1, let us say, only 1 book is printed. So x=1
y = 1250 +25(1)
y= 1250 +25
y = 1275
So, for 1 book is 1275, and no book is 1250. This gives us the answer that the change in the total cost for each book printed would be $25. Hope this is the answer that you are looking for.
Answer:
Step-by-step explanation:
We need to first find out how much 400% of 170 is and then add that increase to the original 170 people.
4(170) = 680 and
680 + 170 = 850 people after 3 years.
Answer:
Equation of line perpendicular to given graph is:
![y = -\frac{1}{2}x+4](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%2B4)
Step-by-step explanation:
Given equation of line is:
14x-7y=8
First of all, we have to convert the given equation into slope-intercept form to find the slope of the line
The slope-intercept form is:
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
Now
![14x-7y=8\\14x-8 = 7y\\\frac{7y}{7} = \frac{14x-8}{7}\\y = \frac{14}{7}x - \frac{8}{7}\\y = 2x - \frac{8}{7}](https://tex.z-dn.net/?f=14x-7y%3D8%5C%5C14x-8%20%3D%207y%5C%5C%5Cfrac%7B7y%7D%7B7%7D%20%3D%20%5Cfrac%7B14x-8%7D%7B7%7D%5C%5Cy%20%3D%20%5Cfrac%7B14%7D%7B7%7Dx%20-%20%5Cfrac%7B8%7D%7B7%7D%5C%5Cy%20%3D%202x%20-%20%5Cfrac%7B8%7D%7B7%7D)
The co-efficient of x is 2 so the slope of given line is 2
Let m1 be the slope of line perpendicular to given line
The product of slopes of two perpendicular lines is -1
![m.m_1 = -1\\2.m_1 = -1\\m_1 = -\frac{1}{2}](https://tex.z-dn.net/?f=m.m_1%20%3D%20-1%5C%5C2.m_1%20%3D%20-1%5C%5Cm_1%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
The equation for line perpendicular line to given line will be:
![y = m_1x+b\\y = -\frac{1}{2}x+b](https://tex.z-dn.net/?f=y%20%3D%20m_1x%2Bb%5C%5Cy%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%2Bb)
To find the value of b, putting (-2,5) in the equation
![5 = -\frac{1}{2}(-2) + b\\5 = 1+b\\b = 5-1\\b = 4](https://tex.z-dn.net/?f=5%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%28-2%29%20%2B%20b%5C%5C5%20%3D%201%2Bb%5C%5Cb%20%3D%205-1%5C%5Cb%20%3D%204)
The final equation is:
![y = -\frac{1}{2}x+4](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%2B4)
Hence,
Equation of line perpendicular to given graph is:
![y = -\frac{1}{2}x+4](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%2B4)
ANSWER
![y = 3](https://tex.z-dn.net/?f=y%20%3D%203)
EXPLANATION
The slope is given by the formula,
![m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20)
We now substitute the points to obtain,
![m = \frac{y - 0}{3 - 9}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By%20-%200%7D%7B3%20-%209%7D%20)
We simplify to obtain,
![m = \frac{y }{ - 6}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By%20%7D%7B%20-%206%7D%20)
This must equal
![- \frac{1}{2}](https://tex.z-dn.net/?f=%20-%20%5Cfrac%7B1%7D%7B2%7D%20)
This implies that,
![- \frac{1}{2} = - \frac{y}{6}](https://tex.z-dn.net/?f=%20-%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20-%20%5Cfrac%7By%7D%7B6%7D%20)
We multiply both sides by -6 to obtain,
![- 6 \times - \frac{1}{2} = y](https://tex.z-dn.net/?f=%20-%206%20%5Ctimes%20-%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20y)
![y = 3](https://tex.z-dn.net/?f=y%20%3D%203)
The value of is therefore 3.