The two lines, P and Q, are graphed below: Line P is drawn by joining ordered pairs negative 8,15 and 6, negative 12. Line Q is drawn by joining ordered pairs 4,16 and negative 9,10 Determine the solution and the reasoning that justifies the solution to the systems of equations
Answers
Answer:
[tex]\text{Solution: }\left(-\dfrac{2654}{435},\dfrac{1644}{145}\right)[/tex]
Step-by-step explanation:
Line P is drawn by joining ordered pairs (-8,15) and (6,-12)
Using two point formula of line. Find equation of line P
[tex]\dfrac{y-15}{x-(-8)}=\dfrac{-12-15}{6-(-8)}[/tex]
[tex]\dfrac{y-15}{x+8}=\dfrac{-27}{6+8)}[/tex]
[tex]\dfrac{y-15}{x+8}=\dfrac{-27}{14}[/tex]
[tex]y=\dfrac{-27}{14}(x+8)+15[/tex]
[tex]y=\dfrac{-27}{14}x+\dfrac{-27}{14}\times 8 + 15[/tex]
[tex]y=\dfrac{-27}{14}x-\dfrac{3}{7}[/tex]
[tex]\text{Equation of line P:}y=\dfrac{-27}{14}x-\dfrac{3}{7}[/tex]
Line Q is drawn by joining ordered pairs (4,16) and (-9,10)
Using two point formula of line. Find equation of line Q
[tex]\dfrac{y-16}{x-4}=\dfrac{10-16}{-9-4}[/tex]
[tex]\dfrac{y-16}{x-4}=\dfrac{-6}{-13}[/tex]
[tex]\dfrac{y-16}{x-4}=\dfrac{6}{13}[/tex]
[tex]y=\dfrac{6}{13}(x-4)+16[/tex]
[tex]y=\dfrac{6}{13}x-\dfrac{6}{13}\times 4 + 16[/tex]
[tex]y=\dfrac{6}{13}x+\dfrac{184}{13}[/tex]
[tex]\text{Equation of line Q:}y=\dfrac{6}{13}x+\dfrac{184}{13}[/tex]
Using graphing find solution of system of equation.
We draw the line on graph and see the intersection point.
Please see the attachment of the line.
Answer:
(−2, 4), because it is the point of intersection of the two graphs
Step-by-step explanation:
BECAUSE
Related Questions
The sum of two numbers is 0.25. their quotient is 0.25. find the numbers.
Answers
[tex]n,\ m-the\ numbers\\\\n+m=0.25\qquad(*)\\\\n:m=0.25\to\dfrac{n}{m}=0.25\to n=0.25m\qquad(**)\\\\\text{Substitute}\ (**)\ \text{to}\ (*):\\\\0.25m+m=0.25\\\\1.25m=0.25\qquad\text{divide both sides by 1.25}\\\\\boxed{m=0.2}\\\\\text{Put the value of }\ m\ \text{to}\ (**):\\\\n=0.25(0.2)\\\\\boxed{n=0.05}\\\\Answer:\ \boxed{0.05\ and\ 0.2}[/tex]
If area of a circle measures 16/25 pi cm square, what is the circumference of the circle in terms of pi
Answers
(16/25)*pi = pi*r^2
16/25 = r^2
rt(16/25) = r
r = 4/5
C = 2pi*r
C = 2pi*(4/5)
C = (8/5) pi cm
Which equation can be used to find the volume of this solid?(Please see attached picture)
V=3*5*4
V-3+5+4
V=5*4
V=3*5
Answers
Hope that helps
Maria is traveling for business. She starts by traveling from Mexico City to Singapore which is about 1.26 x 104 miles. She then travels from Singapore to New York which is approximately 9.53 x 103 miles. What is the total distance that Maria traveled?
Answers
1.26 x 104 = 131.04
9.53 x 103 = 981.59
131.04 + 981.59 = 1112.63
Hope this helps :)
Answer:
D
2.213 x 10^4 miles
Step-by-step explanation:
Took the test
how do i answer this question
[tex]7 - 3x = 2x + 7 - 5x[/tex]
Answers
7 - 3x = - 3x + 7
You can rearrange the right side to be:
7 - 3x = 7 - 3x
Because are the same thing, your answer ends up being all real numbers or infinitely many solutions. This means whatever number you plug in for the x-variable, the two sides will always be equal to each other.
The product of some negative number and 10 less than three times that number is 25. find the number.
Answers
n=2+1/3√111 or n=2+-1/3√111
F(x)=5x^3-2x^2-3x Polynomial factoring
Answers
Make t the subject of the formula
Answers
[tex]t= \frac{4p+3}{p-2} [/tex]
Hopefully i helped, i suppose ill go answer the other one too hehe well mark brainly if possible ^.^
What are the solutions of the inequality? 12x – 3x + 11 > 4x – (17 – 9x) a. x > –7 b.x > −1411 c. x < −1411 d.x < 7
Answers
Explanation:
1) given: 12x – 3x + 11 > 4x – (17 – 9x)
2) expand the parenthesis: 12x - 3x + 11 > 4x - 17 + 9x
3) combine like terms on each side: 9x + 11 > 13x - 17
4) subtract 9x and add 17 to both sides:9x - 9x + 11 + 17 > 13x - 9x - 17 + 17
5) combine like terms: 28 > 4x
6) divide both sides by 4: 7 > x
That is x < 7 which is the option d.
The circle graph shows the portions of the time that Ralph spent playing different games.
Which two types of games did Ralph spend a total of 9/10 of his time playing?
Choose exactly two answers that are correct. exactly two plz!!
A.
Truck Rider
B.
Space Cadet
C.
Trivia Tasks
D.
Wizard Maze
Answers
Which linear equation has a slope of 3 and a y-intercept of –2?
Answers
Y=3x-2, or B.
Answer:
I believe the answer is A.
Step-by-step explanation:
If you flip 3 coins, what is the probability of landing on heads only 2 times? list your answer as a fraction in simplest form.
Answers
No. of outcomes with only 2 heads = 3
S0 the Probability of just 2 heads = 3/8
The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions of the rectangle.
Answers
Answer:
length = 9 kilometres
Width = 12 kilometres
Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.
Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.
The area of a rectangle can be found by using the formula:
A = width × length
Plug in the data from the formula
A = x (2x - 6).
Simplify using rainbow technique.
[tex]x(2x - 6) = 2 {x}^{2} - 6x[/tex]
Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.
[tex]2 {x}^{2} - 6x = 108[/tex]
Subtract 108
[tex]2 {x}^{2} - 6x - 108 = 0[/tex]
Divide by 2.
[tex] {x}^{2} - 3x - 54[/tex]
[tex](x - 9)(x + 6) = 0[/tex]
Rule AB = 0, gives A is 0 or B is 0.
[tex]x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6[/tex]
The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).
Length
[tex]x = 9[/tex]
Width
[tex]2x - 6 = 2 \times 9- 6 = 18 - 6 = 12[/tex]
Answer:
length = 9 kilometres
Width = 12 kilometres
~ Hope this helps you!
A lion’s heart beats 12 times in 16 seconds.how many heartbeats will it have in 60 seconds?
Answers
Here is your answer:
The proper answer to this question is "44 times".
Reason:
You have to solve it this way:
12 heartbeats=16 seconds
16+16=32
36+16=48
48+16=64
16-12=4
12+12=36+8=44
Therefore lions heart beats 44 times every 60 seconds.
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Marie is buying an ice-cream sundae. There are 3 sizes of sundaes, 15 different ice-cream flavors, and 5 different toppings. How many ways can Marie choose a sundae?
Answers
[tex]3 \times 15 \times 5 = 225[/tex]
Multiplying them out, you can see that there are 225 different combinations of sundaes
A computer salesperson's monthly income depends on the amount of his sales. his monthly income is a salary of $1575 plus 9% of his monthly sales. write a linear equation for his monthly income for sales of x dollars. ( i=mx+b ).
Answers
Commission = 9% = 0.09
Monthly Sales = x
Monthly income = 1575 + 0.9x
Answer: Monthly income = 1575 + 0.9x
The solution is, 1575 + 0.9x, is a linear equation for his monthly income for sales of x dollars.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
given that,
A computer salesperson's monthly income depends on the amount of his sales.
his monthly income is a salary of $1575 plus 9% of his monthly sales.
Fixed salary = $1575
Commission = 9% = 0.09
Monthly Sales = x
Monthly income = 1575 + 0.9x
Answer: Monthly income = 1575 + 0.9x
Hence, The solution is, 1575 + 0.9x, is a linear equation for his monthly income for sales of x dollars.
To learn more on percentage click:
brainly.com/question/13450942
#SPJ2
If you are examining a triangle with given measurements for one leg and the hypotenuse, how will you determine the measure of the unknown leg? Explain.
Answers
By using Pythagoras theorem, length of one leg of triangle can be determined.
Given:
A triangle with length of one leg and the hypotenuse
According to question,
Let the length of one leg of triangle which can be base [tex](b)[/tex] or perpendicular [tex](p)[/tex] and hypotenuse represented by [tex](h)[/tex].
Now, using Pythagoras theorem which states that if a triangle is right-angled ([tex]90[/tex] degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
From the figure,
In [tex]\Delta AOB, \;\angle O=90^\circ[/tex]
[tex]\rm{H^2=P^2+B^2}\\\rm{AB^2=AO^2+OB^2[/tex]
[tex]h^2=p^2+b^2[/tex]
[tex]b=\sqrt{h^2-p^2}\\[/tex]
or
[tex]p=\sqrt{h^2-b^2}\\[/tex]
Therefore, length of one leg of the triangle is determined by using Pythagoras theorem.
Learn more about Pythagoras theorem here:
https://brainly.com/question/15138986
Graph y ≥ (x + 2)2 Click on the graph until the correct graph appears.
Answers
The graph shows a parabola with a solid line and shading above or on the curve to represent the inequality [tex]y\geq (x+2)^{2}[/tex] This graph visually illustrates the solution set for the given inequality.
To graph the inequality [tex]y\geq (x+2)^{2}[/tex] we first need to plot the parabola [tex]y=(x+2)^{2}[/tex] with a solid line. The vertex of the parabola is at [tex](-2,0)[/tex] and it opens upwards.
Next, we shade all the regions above or on the parabola to represent the inequality [tex]y\geq (x+2)^{2}[/tex] Since the inequality includes "or equal to" [tex](\geq )[/tex] we use a solid line for the graph of the parabola.
By following these steps, we create a graph where the area above or on the parabola is shaded, indicating the solutions to the inequality [tex]y\geq (x+2)^{2}[/tex] his shading represents all the points.
where the y-values are greater than or equal to the corresponding y-values on the parabola. The solid line ensures that points on the parabola itself are included in the solution set.
In summary, the graph shows a parabola with a solid line and shading above or on the curve to represent the inequality [tex]y \geq (x+2)^{2}[/tex] This graph visually illustrates the solution set for the given inequality.
I have a question about the application of definite integrals. I came up with the following integral:
[tex] \int\limits^5_0 {62.5 * 6 * 2 * x} \, dx [/tex]
This is equal to 9780. Unfortunately, 9780 ft-lb is not an answer, but 9375.0 ft-lb is! Can someone tell me what is wrong with my integral and if 9375.0 ft-lb is the answer to my question?
Answers
The volume of each slice is 6*2*DeltaX cubic feet. So the force pulling down on each slice is 62.5*6*2*DeltaX pounds as this is the weight of the slice.
The work done to move that slice x feet upward is 62.5*6*2*DeltaX*x or 62.5*6*2x*DeltaX as you wrote for your integrand.
Integrating with respect to x will effectively add up all the horizontal slices to get the total work done
See the attached image for the integral and steps leading to the answer of 9375
Roll a 5 win 6 dollars roll a 6 win 12 dollars if you play one time what is your expected reward
Answers
Which of the following sets of possible side lengths forms a right triangle? 12, 35, and 38 11, 60, and 61 9, 40, and 45 6, 12, and 13
Answers
11, 60, and 61
Let's check it using the Pythagorean theorem.
We have then:
ROOT ((a) ^ 2 + (b) ^ 2) = c
Where,
a = 11
b = 60
ROOT ((11) ^ 2 + (60) ^ 2) = 61
Answer:
11, 60, and 61
Answer:
11,60, and 61
Step-by-step explanation:
The measure of a squares side is 1.2 feet. What is the perimeter of the square in inches?
Answers
perimeter = 4 * 14.4 = 57.6 inches.
What is the probability of drawing five face cards?
Answers
Total number of face cards = 12
P( 5 face cards) = (12/52)(11/51)(10/50)(9/49)(8/48) = 33/108290
Answer: 33/108290
A climber is standing at the top of Mount Kazbek, approximately 3.1 miles above sea level. The radius of the Earth is 3959 miles. What is the climber's distance to the horizon?
Answers
The radius of the earth = OC = OB = 3959 miles
Peak of the Mount Kazbek = A = 3.1 miles
OA = OC + CA
OA = 3959 + 3.1 = 3962.1 miles
As OBA is a right triangle,
[tex] OA^{2} [/tex] = [tex] OB^{2} [/tex] + [tex] AB^{2} [/tex]
[tex] 3962.1^{2} [/tex] = [tex] 3959^{2} [/tex] + [tex] AB^{2} [/tex]
15698236.41 = 15673681 + [tex] AB^{2} [/tex]
[tex] AB^{2} [/tex] = 15698236.41 - 15673681
[tex] AB^{2} [/tex] =24555.41
AB = 156.701659
climber's distance to the horizon is 156.7 miles
Based on the information marked in the diagram, ABC and XYZ must be congruent.
Can somebody help ??
A. True
B. False
Answers
There isn't enough info. We have a pair of hypotenuses that are congruent (AB and XY) based on the single tickmarks they share together. Other than that, we don't know anything about any other pairs of sides. We know that angle C = angle Z because of the square angle markers (they're both 90 degrees), but we don't know anything else about the other angles. The triangles could be congruent, or they may not be. There's no way to tell without more information.
Answer: The answer i false
Step-by-step explanation:
A family took a trip. They spent $90.71 for gasoline, $153.00 on meals, $197.00 on amusements, and $73.38 on miscellaneous expenses. How much did the trip cost?
Answers
Theoretically, the actual TRIP cost $90.71, because the extra money spent was on other things other than the transportation, which is the main part of the trip.
but in total, DURING that trip, they spent $514.09
I hope this helps, and have a nice day!
The Bright Star Video Club offers the two membership plans described below.
Plan A: $50 yearly membership fee and $2 for each video rental
Plan B: $10 yearly membership fee and $4 for each video rental
Greg is planning to enroll in one of these plans. For how many video rentals would the total cost of Plan A be equal to the total cost of Plan B?
A. 50
B. 20
C. 30
D. 40
Answers
Plan A: y = 2x + 50
Plan B: y = 4x + 10
2x + 50 = 4x + 10
Now solve the combined equation.
2x + 50 = 4x + 10
- 10 - 10
2x + 40 = 4x
-2x -2x
40 = 2x
x = 20
Plan A: y=2x+50
Plan B: y=4x+10
and see where they intersect, and that will give you the answer.
OR
You can substitute each answer for x, like this,
A. 50
Plan A:
y=2(50)+50
y=100+50
y=150
Plan B:
y=4x+10
y=4(50)+10
y=200+10
y=210
So, therefore, A.50 is not the answer.
B.20
Plan A:
y=2x+50
y=2(20)+50
y=40+50
y=90
Plan B:
y=4x+10
y=4(20)+10
y=80+10
y=90
So, B.20 is correct but always check the rest of the answers. Just in case
C.30
Plan A:
y=2x+50
y=2(30)+50
y=60+50
y=110
Plan B:
y=4x+10
y=4(30)+10
y=120+10
y=130
So, C.30 is incorrect.
D.40
Plan A:
y=2x+50
y=2(40)+50
y=80+50
y=130
Plan B:
y=4x+10
y=4(40)+10
y=160+10
y=170
So, in conclusion the correct answer is B.20.
a bag contains 7 red marbles 6 green marbles 5 yellow marbles and 2 orange. marbles are drawn twice with a replacement. what is p {yellow and green?
a coin is tossed and a number cube is rolled. what is p{h, then prime number?
letter tiles that spell the word happiness are replaced in a bag. a tile is drawn and then a second tile is drawn. find p then vowel p?
Answers
[tex]226[/tex]
Question 1:
We have been given that a bag contains 7 red marbles, 6 green marbles, 5 yellow marbles, and 2 orange. Further we are given that marbles are drawn twice with a replacement. We need to figure out the probability P(Yellow and Green).
Basically, we need to determine the probability that first marble drawn is yellow and second marble drawn is green.
Probability of first marble drawn being yellow is [tex]\frac{5}{20}=\frac{1}{4}[/tex] and probability of second marble drawn being green is [tex]\frac{6}{20}=\frac{3}{10}[/tex].
Therefore, the probability P(Yellow and Green) = [tex]\frac{1}{4}\cdot \frac{3}{10}=\frac{3}{40}[/tex].
Question 2:
We have been given that a coin is tossed and a number cube is rolled and we need to find the probability P(H, prime number).
Probability of getting head on the coin is [tex]\frac{1}{2}[/tex].
Probability of getting a prime number on the cube is [tex]\frac{3}{6}=\frac{1}{2}[/tex].
Therefore, probability P(H, prime number) = [tex]\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}[/tex]
K(x)=10x+5 inverse function
Answers
The inverse of the function is k(x) = [tex] \frac{x - 5}{10} [/tex]
You can find the inverse of any function by switching the k(x) value and the x value. After that, solve for the new k(x). The result will be your inverse function. The step-by-step process is below.
k(x) = 10x + 5 ----> Switch the x and k(x)
x = 10k(x) + 5 ----> Subtract 5 from both sides
x - 5 = 10k(x) ----> Divide both sides by 10.
[tex] \frac{x - 5}{10} [/tex] = k(x) ----> Now switch the order for formatting
k(x) = [tex] \frac{x - 5}{10} [/tex]
And this is your new inverse function.
A principal of $3900 is invested at 6.5% interest, compounded annually. How much will the investment be worth after 5 years? Use the calculator provided and round your answer to the nearest dollar.
Answers
[tex]3900 \times 0.065 \times 5 = 1267.5 \\ 1267.5 + 3900 = 5167.5[/tex]
Answer:
The answer would to be able to multiply the answers together. For example, the answer for this question would be 5,343 dollars rounded to the nearest tenth.
Step-by-step explanation: