Solve the following systems of equations to find the point of intersection.
a) y = 3x + 5
y = -2x + 30
b) x+y=-3
2y = -2x+8
Answers
Given:
The system of equations are:
(a) [tex]y=3x+5[/tex]
[tex]y=-2x+30[/tex]
(b) [tex]x+y=-3[/tex]
[tex]2y=-2x+8[/tex]
To find:
The intersection points of the given system of equations.
Solution:
(a)
We have,
[tex]y=3x+5[/tex] ...(i)
[tex]y=-2x+30[/tex] ...(ii)
From (i) and (ii), we get
[tex]3x+5=-2x+30[/tex]
[tex]3x+2x=30-5[/tex]
[tex]5x=25[/tex]
[tex]x=5[/tex]
Putting x=5 in (i), we get
[tex]y=3(5)+5[/tex]
[tex]y=15+5[/tex]
[tex]y=20[/tex]
Therefore, the point of intersection is (5,20).
(b)
The given system of equations is:
[tex]x+y=-3[/tex]
[tex]2y=-2x+8[/tex]
Write these equation in slope intercept form [tex](y=mx+b)[/tex], where m is slope and b is y-intercept.
[tex]y=-x-3[/tex] ...(iii)
[tex]y=-x+4[/tex] ...(iv)
From the equation (iii) and (iv), it is clear that the slopes of both equations are same, i.e., -1 but the y-intercepts are different, -3 and 4 respectively.
It means the lines are parallel and parallel lines never intersect each other.
Therefore, the point of intersect does not exist because the lines are parallel.
Related Questions
I need serious help
Answers
Answer:
a. 3
b. 12
c. 4
Step-by-step explanation:
the equation is y= -3x+ 12, so the slope says you will lose 3 gallons of gas every hour
Please help what is 15 2/3
Answers
Answer:
its
47/3 i can show u more steps how did i do it
Answer:
47/3
Step-by-step explanation:
Decimal form = 15.667
Find this by multiplying 3 by 15, then adding it by 2. That is now your numerator.
PLEASE HELP!!! Find the values of x and y for which the lines are parallel.
Answers
Answer:
x = 68
y = 72
Step-by-step explanation:
if the lines are parallel, then x-3 = 65
x = 68
(68 - 3) + 46 + y - 3 = 180
y = 72
6. What is the center and the radius ( x + 1)^2 + (y - 5)^2 = 2^2
Center (-1,-5) radius= 2
Center (1,-5) radius= 2
Center (-1, 5) radius= 4
Center (-1, 5) radius= 2
Answers
Answer:
The equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where h, k, is the center and r is the radius.
So, in this case: the center is (-1, 5) and the radius is 2.
Let me know if this helps!
Select the polynomials that are a difference of squares. Thank you so much for helping me!
y^4−2
25m^2n^4−1
p^8−q^4
16x^2−24
Answers
Answer:
a
Step-by-step explanation:
Select the polynomials that are a difference of squares. Thank you so much for helping me!
Please help me out with this. It's due soon and I'm really really struggling.
Answers
Answer:
Yes, the bat fitsStep-by-step explanation:
The measure of the diagonal is:
d = [tex]\sqrt{27^2+16^2+16^2}[/tex] = 35.22 in > 34 inYes, the bat fits in the box diagonally
A church is packing Thanksgiving baskets. Each basket weighs 30 pounds. Here are two situations. For each situation, write an equation to represent the situation. If you get stuck, consider drawing a diagram. Each basket contains 3 identical bags of stuffing and a 6-pound bag of rice. Each basket contains 3 boxes. Each box contains a 6-pound bag of rice and a bag of stuffing. The bags of stuffing are all identical.
Answers
Answer:
3x + 6 = 30
Step-by-step explanation:
We’re getting married bro
Answers
Answer:
It's not that hard so lets get a divorce bro
Step-by-step explanation:
Solve the whole problem i give brainliest please help me.
Answers
Answer:
The inequality will be $75x + $25 ≤ $340
and the amount of days that she can afford the vehicle is 4.2
Step-by-step explanation:
if you subtract 25 from both sides, you'll get
75x ≤ 315
and when you divide both sides by 75, you'll get 4.2, or 4 days
Find the volume of a cylinder either enter an exact number in the terms of pi areU3.14 for pie 5 and 2
Answers
Answer:
[tex]V=384\pi \ \text{unit}^3[/tex]
Step-by-step explanation:
The attached figure shows a cylinder of radius 8 units and height 6 units. We need to find the volume of the cylinder. The formula is as follows :
[tex]V=\pi r^2h\\\\V=\pi (8)^2\times 6\\\\V=384\pi[/tex]
So, the required volume of the cylinder is [tex]384\pi \ \text{unit}^3[/tex].
HELP ME PLEASE ILL MSRK YOU A BRAINLIEST IF YOU GET THIS RIGHT !!!NO SPAM!!!
Answers
Answer:
B I'm pretty sure its been a while if I wrong in sorry
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
24 min : 56 min
Answers
Answer:
6/13
the simplest form of
24 / 56 is
6/13
hope it helps
Figure B is a scale image of Figure A, as shown.
Please help
Answers
Answer:
Scale factor: 2
Step-by-step explanation:
In figure A the parralellagram his sides of 4 and 7. Figure B has sides of 8 and 14, which are double the sides of figure A.
14/7 = 2
8/4 = 2
Therefore the scale factor is 2
I need this done right now and can you help me with other question. question in picture
Answers
Answer:
1 4/5
Step-by-step explanation:
x + 4 / 10 - x and it has given you that x = 5. Basically plug 5 in the x place and solve.
x + 4 / 10 - x
5 + 4 / 10 - 5
9 / 5
1 4/5 (Option D)
Hope this helps, thank you :) !!
What type of graph would have the title, "Favorite TV Show"?
bar graph
line graph
line plot
stem-and-leaf plot
Answers
Answer:
line graph
Step-by-step explanation:
line graph
Answer:
bar graph
Step-by-step explanation:
thats what i'm guessing because a bar graphs compares categories
Help me with this pleaseeeee
Answers
Answer:
i notice that she only has $30 to spend for a month. and she has to pay $21 every month including $3 for every download so she can only download 3 1GB of data
Step-by-step explanation:
HELP PLEASE!!!
3g >12
Answers
Answer:
2 : g<4
Step-by-step explanation:
light blue
Find the value of x so that the ratios are equivalent 9:x and 54:8
i cant seem to get it i tried 48 but it said it was wrong
Answers
Answer:
The answer is 48
Step-by-step explanation:
Please help show work I beg
A 50
B 13
C 12
D 51
Answers
An event that is made up of two or more outcomes is called_______
Answers
Answer:
Compound Events
Step-by-step explanation:
What is the sum of 7 3/16+3 3/4
Answers
Answer:
10.9375
Step-by-step explanation:
Answer:
10.9375
Step-by-step explanation:
what is the inverse relation of f(x) = x^2 - 9
Answers
Answer: 400.3
Step-by-step explanation:
Answer:
To find the inverse, interchange the variables and solve for
y.
f-1(x)=x+9,-x+9
Step-by-step explanation:
Mrs.Diya and her mother-in-law are both school teachers and earn Rs.16,800 and Rs. 10,500 per month respectively. Ratio of distance to the school from their home, to the distance to the school from their colleague John’s home is 2 : 1.
1) If the distance to John’s home from the school is 12 km, what is the distance from school to Mrs. Deewan’s home?
2)If John’s earning twice the income of that of the mother in law, what is the ratio of their wages?
3)Who lives nearer to the school?
i need the correct answer and a proper answer with WORKING or else i will report
Answers
Answer:
1. the distance from the school to Mrs Deewan's home = 24km
2. John's wage to the mother-in-law's wage = 2:1
Mother-in-law's wage to John's = 1:2
3. John lives nearer the school
Step-by-step explanation:
1. The ratio of the distance between Mrs Diya's (Deewan's) home and John's home to school = 2:1.
This means that the distance of Mrs Diya's home is twice that of John's home to school. Therefore if John's home from school is 12km;
Mrs Diya's home = 12 × 2 = 24km
2. If john earns twice the income of the mother-in-law, the ratio of the wages is as follows:
John's wage to the mother-in-law's wage = 2:1
Mother-in-law's wage to John's = 1:2
3. John lives nearer the school. From the calculation we've done in 1 above, you can see that the distance between John's home and the school = 12km, while the distance between Mrs Diya's home and the school is 24km, therefore, John lives nearer the school.
plsss help i’ll give brainly...but pls give a correct answer
Answers
Answer:
3
Step-by-step explanation:
Terms are separated by symbols for operations (like plus, minus, multiply, divide.)
So your terms would be
8y
+z
-6
Colleen earns $5 for each hour of yard work. Write an equation that shows the relationship between the time spent x and the amount earned y.
Write your answer as an equation with y first, followed by an equals sign
Answers
Answer:
Easy
Step-by-step explanation:
Y=5x
I hope this helps
Please answer the following question for 85 points.
Answers
Answer:
188.4 cm²
Step-by-step explanation:
Surface area of rectangles :-
A = 15cm * 5 cm * 2 A = 150 cm²Surface area of triangles :-
A = 2 * 1/2 * 4cm * 4.6 cm A = 18.4 cm²Surface area of middle rectangle :-
A = 4cm * 5cm A = 20 cm²Total Area :-
A = ( 150 + 18.4 + 20 ) cm²A = 188.4 cm²Answer:
Solution given:
Total surface area of triangular prism=
area of two triangle +2*area of rectangle+area of base
=2*½*4*4.6+2*15*5+15*4
=228.4cm²
The area of triangular prism=228.4cm²
HELP ME PLS WILL MARK BRAINLISTT!!!!
Answers
Answer:
4,4
Step-by-step explanation:
Answer:
(5,3)
Step-by-step explanation:
visualize it on a graph
Segment AB and segment CD intersect at point E. Segment AC and segment DB are parallel. If m∠A=41m∠A=41o and m∠D=56m∠D=56o, find the m∠AECm∠AEC.
Answers
Answer:
m∠AEC = 83°
Step-by-step explanation:
∠C and ∠D are alternate angles and are congruent because segment AC is parallel to DB
Therefore, m∠C = 56°
Sum of measures of angles of a triangle is 180.
So, m∠A + m∠C + m∠AEC = 180
41 + 56 + m∠AEC = 180
m∠AEC + 97 = 180
m∠AEC = 83°
Five years ago, Charlie was twice older than Priya. What are their ages now if in 3 years the um of their ages will be 76?
Answers
Answer:
Charlie is 45 and Priya is 25
Step-by-step explanation:
Answer:
present age of charlie is 45 years
present age of priya is 25 years
Step-by-step explanation:
Let start from five years ago
Let at that age of Priya was x years
given that
Charlie was twice older than Priya
age of Charlie = 2x
_____________________________________________
present age of charlie = age 5 years ago + 5 years = 2x + 5
present age of priya = age of priya 5 years ago + 5 years x + 5 = x + 5
_________________________________________________
age of charlie 3 years from now = present age of charlie + 3 years
age of charlie 3 years from now =2x + 5 + 3 = 2x + 8
age of priya 3 years from now = present age of priya + 3 years
age of priya 3 years from now =x + 5 + 3 = x + 8
Given that
in 3 years the sum of their ages will be 76
thus
sum of their ages in 3 years from now = x + 8 + 2x + 8 = 76
=> 3x + 16 = 76
=> 3x = 76-16 = 60
=> x = 60/3 = 20
Thus,
present age of charlie = 2x + 5 = 2*20 + 5 = 45 years
present age of priya = x + 5 = 20 + 5 = 25 years
Ethan has 12 coins. There are three 10p coins and nine 20p coins 20p coins. Ethan chooses 3 coins at random. Work out the probability that he takes exactly 50p.
Answers
Answer:
3/220.
Step-by-step explanation:
To get exactly 50p he must take 2 20p coins and 1 10p coin.
There are 3! /2! = 3 ways of getting this.
Total number of ways of getting any 3 coins form 12 is 12!/9!3!
= 12*11*10 / 3!
= 220.
So the answer is 3/220.