Final answer:
The two lines have different slopes, with the first line having a slope of -2 and the second line having a slope of 2. Since the slopes are different, the two lines intersect at exactly one point, indicating that there is one solution.
Explanation:
To determine if two lines have no solution, one solution, or an infinite number of solutions, we need to find the slopes of each line. If the slopes are different, the lines intersect at one point, indicating one solution. If the slopes are the same, but they have different y-intercepts, the lines are parallel and there is no solution. If the slopes and y-intercepts are the same, the lines coincide and there are an infinite number of solutions.
For the first line through (-1,3) and (0,1), the slope can be calculated using the formula slope (m) = (y2 - y1) / (x2 - x1). Plugging in the values, we get:
m = (1 - 3) / (0 + 1) = -2
The second line passes through (1,4) and (0,2). Using the same formula:
m = (2 - 4) / (0 - 1) = 2
Since the slopes of the two lines are different, they will intersect at exactly one point, indicating one solution.
The system of equations has one solution since the lines intersect at a single point, confirming a unique solution.
To determine if the system of equations has no solution, one solution, or an infinite number of solutions, we need to analyze the slopes and y-intercepts of the two lines.
Step 1:
Calculate the slope of each line using the formula [tex]\(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\).[/tex]
For the first line passing through (-1,3) and (0,1):
[tex]\[ m_1 = \frac{{1 - 3}}{{0 - (-1)}} = \frac{{-2}}{{1}} = -2 \][/tex]
For the second line passing through (1,4) and (0,2):
[tex]\[ m_2 = \frac{{2 - 4}}{{0 - 1}} = \frac{{-2}}{{-1}} = 2 \][/tex]
Step 2:
Calculate the y-intercept for each line using the slope-intercept form [tex]\(y = mx + b\)[/tex], where (b) is the y-intercept.
For the first line:
[tex]\[ 1 = -2 \cdot 0 + b_1 \][/tex]
[tex]\[ b_1 = 1 \][/tex]
For the second line:
[tex]\[ 2 = 2 \cdot 0 + b_2 \][/tex]
[tex]\[ b_2 = 2 \][/tex]
Step 3: Compare the slopes and y-intercepts.
Since the slopes are different (-2 for the first line and 2 for the second line), the lines are not parallel. Therefore, they will intersect at exactly one point, resulting in one solution for the system of equations.
Conclusion:
The system of equations has one solution.
P (2, 3) and Q (6, 10) are two points on the Cartesian plane.
Find the length of PQ
Find the coordinates of the midpoint of PQ
Find the equation of PQ
Step-by-step explanation:
Given:
[tex] (x_1, \: y_1 ) =(2, \:3)\:\:\&\:\: (x_2, \: y_2) =(6, \:10)[/tex]
[tex]l(PQ) = \sqrt{ {(x_1 - x_2)}^{2} + {(y_1 - y_2)}^{2}} \\ \\ = \sqrt{ {(2 - 6)}^{2} + {(3 - 10)}^{2}} \\ \\ = \sqrt{ {( - 4)}^{2} + {( - 7)}^{2}} \\ \\ = \sqrt{16 + 49} \\ \\ = \sqrt{65} \\ \\ \therefore \purple{ \boxed{ l(PQ) = 8.06 \: units}}\\\\[/tex]
Let S be the mid-point of PQ.
[tex]\therefore S = \{\frac{x_1+x_2}{2}, \:\:\frac{y_1+y_2}{2}\} \\\\
= \{\frac{2 +6}{2}, \:\:\frac{3+10}{2}\} \\\\
= \{\frac{8}{2}, \:\:\frac{13}{2}\} \\\\
\therefore S= \{4, \:\:6.5\} \\\\[/tex]
Equation of line PQ is given as:
[tex] \frac{y-y_1}{y_1 - y_2}=\frac{x-x_1}{x_1 - x_2} \\\\
\therefore \frac{y-3}{3 - 10}=\frac{x-2}{2 - 6} \\\\
\therefore \frac{y-3}{-7}=\frac{x-2}{-4} \\\\
\therefore \frac{y-3}{7}=\frac{x-2}{4} \\\\
\therefore 4(y-3)=7(x-2)\\\\
\therefore 4y-12=7x-14\\\\
\therefore 7x-14 - 4y + 12=0\\\\
\red{\boxed {\therefore 7x-4y - 2 =0}} [/tex]
Answer:
length = square root of ((2-6)^2)+((3-10)^2) = square root (of) 16+49
square root of 65 = 8.062257748 = approx 8.1
midpoint = (x1+x2)/2 , (y1+y2)/2
= 2+6 /2 , 3+10 /2
=8/2 , 13/2
= 4, 6.5 (midpoint)
equation= y=mx+c
m(gradient) = (y2-y1)/(x2-x1) or (y1-y2)/(x1-x2)
= so, (3-10)/(2-6) (y1-y2)/(x1-x2)- i normally use this one
= -7/-4 = 1.75
so y=1.75x+c
plug in the values from any one of them (2,3) or (6,10)
to get
for example: 3=1.75*2+c
3=3.5+c
-0.5=c
now we get the equation y=1.75x+(-0.5)
you always have to have a plus( +(-0.5)) since the equation is y=mx+c
A delivery truck drove 203 miles in 3.5 hours. After unloading and loading new cargo, it traveled on another 243 miles for 4.5 hours.
What was the average speed of the truck over its entire route?
Round to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
203 miles in 3.5 hrs....and 243 miles in 4.5 hrs
totaling : (203 + 243) miles in (3.5 + 4.5) hrs = 446 miles in 8 hrs
speed = distance / time
speed = 446 / 8
speed = 55.75 mph <==
NO CAP 45 PTS I NEED A 100
Which situation is best modeled by an exponential function?
A.the cost to rent a bicycle from a company that charges a flat rate plus x dollars per day
B.the amount of a substance remaining after x years if it is decreasing at a rate of 25% annually
C.the number of gas stations in a town that had 4 stations in 2010 and x new stations have opened each year since
D.the distance a car is from a fixed point if the car was originally 200 feet from that point and traveled at a speed of x miles per hour
The best scenario for an exponential function is Option B, as it describes a consistent percentage decrease annually, which is characteristic of exponential decay.
The situation that is best modeled by an exponential function is Option B, which describes the amount of a substance remaining after x years if it is decreasing at a rate of 25% annually. This exemplifies an exponential decay scenario where the rate of change of a quantity is directly proportional to its current value. Over time, the substance decreases by a consistent percentage, which is characteristic of exponential decay functions.
A key feature of exponential relationships is that they describe processes where the change at any given point is proportional to the current amount, which fits the description of a substance decreasing by a consistent percentage each year.
Explain the difference between lateral and surface area below. If you are given the total surface area, then how could you determine the lateral surface area?
Lateral surface area is given as the area of all sides of a figure excluding the area of the base where as surface area is the sum of the areas of all faces of the solid.
Step-by-step explanation:
Lateral surface area is given as the area of all sides of a figure excluding the area of the base where as surface area is the sum of the areas of all faces of the solid.
If given total surface area, you can find lateral surface area by subtracting the area of the base from the surface area of the solid.
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Lateral surface area refers to the area of the sides only, while total surface area includes the area of all faces. To compute the lateral surface area from the total surface area, subtract the areas of the bases. This process isolates the lateral surface area.
The difference between lateral and surface area is critical in understanding geometric shapes. In contrast, the total surface area includes the area of all the faces, including the bases. For example, in a cylinder, the lateral surface area is the area of the side rolled out into a rectangle, while the total surface area includes the areas of the upper and lower two circular bases.
If you are given the total surface area of a cylinder and need to determine the lateral surface area, you can use the following steps:
Identify and compute the area of the two bases. A cylinder's base is a circle with an area of πr², where r is its radius.Subtract the combined base area from the total surface area.The result will be the lateral surface area.The price of gasoline rose from $2.45 in May to $2.89 in August. Find the percent of increase. Round your answer to the nearest whole percent.
Answer:
The percent in increase is 18%.
Step-by-step explanation:
Given:
The price of gasoline rose from $2.45 in May to $2.89 in August.
Now, to find the percent of increase.
The price of gasoline in May = $2.45.
The price of gasoline in August = $2.89.
So, we get the price of increase:
[tex]2.89-2.45=\$0.44.[/tex]
Now, to get the percent increase:
[tex]\frac{0.44}{2.45} \times 100[/tex]
[tex]=0.179\times 100[/tex]
[tex]=17.9\%.[/tex]
The increase in percent nearest to whole = 18%.
Therefore, the percent in increase is 18%.
To find the percent increase in gasoline prices, you subtract the initial price from the final price, divide this difference by the initial price, and then multiply by 100 to get a percentage. In this case, the increase in price was about 18%.
Explanation:The first step to finding the percent of increase in the price is to subtract the initial price from the final price. So, $2.89 - $2.45 equals $0.44. This is the amount of the increase in price. Then, to find the percentage of this increase, we divide the increase by the initial price, and multiply by 100 to convert it into a percentage. So, ($0.44 / $2.45) * 100 equals about 18%. So the percent of increase in the price of gas from May to August is 18%.
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1. Greg Forrester's charge account statement showed a previous balance 20 points
of $152.35, a finance charge of $1.78, new purchases of $45.23 and $15.67,
a payment of $50.00, and a credit of $12.84. What is the new balance? *
O
O
$152.19
$152.51
$227.87
O
$277.87
Answer:
Option $152.19
Step-by-step explanation:
Data provided in the question:
Previous balance = $152.35
Finance charge = $1.78
New purchases of $45.23 and $15.67
Payment = $50.00
Credit = $12.84
Now,
New Balance
= [Previous balance + Finance charge + New purchases ] - [ Payments + Credits ]
= [ $152.35 + $1.78 + ($45.23 + $15.67) ] - [$50.00 + $12.84 ]
= $215.03 - $62.84
= $152.19
Hence,
Option $152.19
What is the graph for the above relationship?
A. 1st Graph
B. 2nd Graph
C. 3rd Graph
D. 4th Graph
Second graph.
Explanation:Hello! You haven't provided any relationship, but I found it on the internet and it is the table attached below. The point-slope form of the equation of a line is given by:
[tex]y=mx+b[/tex]
So:
[tex]y-Intercept: \\ \\ (0,b) \\ \\ \\ From \ the \ table: \\ \\ (0,b)=(0,46) \\ \\ So: \\ \\ b=46[/tex]
Finding the slope:
[tex]m=\frac{39-46}{1-0} \\ \\ m=-7[/tex]
So the equation of the line is:
[tex]y=-7x+46[/tex]
From the graphs, only option 2 and 4 have negative slope and only option 2 passes through [tex](0,46)[/tex]
Conclusion: Correct option is second graph.
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936 + 97281= x? what is x?
Answer:
x=98,217
Step-by-step explanation:
936 + 97281 = x
x=98217
Answer:
936 + 97281 = 98,217
x = 98,217
You just need to add to find x
look at the images please help
I WILL MARKTHE BRAINLEST PLEASE HELP
Answer:
not too sure sorry :(
Step-by-step explanation:
The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark, get ready, start.
Graph if f (x) =2x^-10 for find f(5)
Answer:
[tex]f(5)=2.048*10^{-7}[/tex]
Step-by-step explanation:
We have that [tex]f(x)=2x^{-10}[/tex], we want to find [tex]f(5)[/tex].
We can rewrite this function with positive index to get:
[tex]f(x)=\frac{2}{x^{10}}[/tex]
We need to substitute [tex]x=5[/tex] into the given function to get:
[tex]f(5)=\frac{2}{5^{10}}[/tex]
This implies that:
[tex]f(5)=\frac{2}{9765625}[/tex]
In scientific notation:
[tex]f(5)=2.048*10^{-7}[/tex]
What k/8-1=-3 what is the answer for k
Give line XY with coordinates X(3,1) and Y(3,-3), find the length of line XY
Answer:
4 units
Step-by-step explanation:
Distance formula:
[tex] \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]
[tex]length \: of \: line \: xy \\ = \sqrt{(3 - 3 )^{2} + (1 - ( - 3))^{2} } \\ = \sqrt{(1 + 3)^{2} } \\ \ = \sqrt{4^{2} } \\ = 4 \: units[/tex]
Or since both coordinates lie at x=3, the line is a vertical line so you can simply count the increase in y to find the distance of the line.
1-(-3)= 4 units
GHI = JKL. Which statement is FALSE.!?
URGENT 15 POINTS
What is the greatest possible probability in any experiment?
A. 9/10
B. 1
C. 10
D. 100
Answer:
B) GREATEST POSSIBLE PROBABILITY in any experiment is 1.
Step-by-step explanation:
The probability of any event E is given as:
[tex]\textrm{Probability of any event E} = \frac{\textrm{Number of favorable events}}{\textrm{Total Number of outcomes}}[/tex]
Let us assume the the number of TOTAL OUTCOMES of any event E = n
Now, if the event is a SURE EVENT, then all outcomes are favorable events.
So, the total number of maximum favorable events = n
[tex]\textrm{Probability of event E} = \frac{\textrm{Number of favorable events}}{\textrm{Total Number of outcomes}} = \frac{n}{n} = 1[/tex]
Hence, the GREATEST POSSIBLE PROBABILITY in any experiment is 1.
. Marcus has 50 tokens to spend at the school
carnival. The Ferris wheel costs 7 tokens and
the carousel costs 5 tokens. The inequality
7x + 5y = 50 represents the possible ways
Marcus could use his tokens on the two rides.
Is the ordered pair (6, 3) a solution for the
problem situation?
Answer:
The ordered pair (6,3) can not be a solution for the problem situation.
Step-by-step explanation:
Marcus has total 50 tokens to spend at the carnival.
Now, given that the Ferris wheel costs 7 tokens and the carousel costs 5 tokens.
So, if Marcus play the Ferris wheel for x times and the carousel for y times, the total expenditure will be given by
7x + 5y = 50 ............ (1)
Now, the ordered pair (6,3) i.e. x = 6 and y = 3 does not satisfy the above relation equation (1).
So, the ordered pair (6,3) can not be a solution for the problem situation. (Answer)
HELP ME!!! IM STUCK
Answer:help with mine ples
Step-by-step explanation: beause i need it orther wise i fail
ameson downloaded one digital song for $1.45, two digital songs for $2.90, and 5 digital songs for $7.25. Enter and solve an equation to find the cost to download 25 digital songsUse n for your independent variable and c for your dependent variable. The equation is Total cost of 25 songs is .
The equation is c = 1.45 n
Total cost of 25 songs is $36.25
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
m is the rate of changeb is the initial value (value y at x = 0)∵ The cost of downloaded one digital song is $1.45
∵ The cost of downloaded two digital song is $2.90
∵ The cost of downloaded five digital song is $7.25
- There is a linear relation between the cost of downloading
the songs and the number of songs
∵ 2.90 = 2 × 1.45
∵ 7.25 = 5 × 1.45
∴ The total cost of downloaded songs is the product of the number
of songs and the cost per song
∵ The cost per song is 1.45
∵ n is the independent variable
∴ n represents the number of songs
∵ c is the dependent variable
∴ c represents the total cost of n songs
- Now we can write the linear equation
∴ c = 1.45 n
The equation is c = 1.45 n
∵ 25 digital songs downloaded
∴ n = 25
∵ c = 1.45 n
∴ c = 1.45(25)
∴ c = 36.26
Total cost of 25 songs is $36.25
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PLEASE HELP (answer only if you now)
Answer:
y = 30
Step-by-step explanation:
If y varies directly with x, then you can make a ratio:
24/8
Simplify the ratio:
3/1
Y is always the first number/ on top in a ratio, that's where I get 24 over 8
3/1 means that y is triple x
so 10 * 3 is 30
PLS HELP!!!
An ice cream truck sells ice cream between 2 p.m. and 10 p.m. each night in the summer. At the end of the night, the driver calculates his profits and makes a graph to analyze the data. What is the average rate of change for the data from the 5th hour to the 8th hour? Be sure to include the correct units of measurement.
7 hours
−7 dollars per hour per hour
21 dollars
−21 dollars per hour per hour
Answer:
[tex]\large\boxed{-7\text{ }dollars\text{ }per\text{ }hour}[/tex]
Explanation:
The average rate of change is the ratio of the change in the dependent variable (Money Earned) to the change in the independent variable (Hour).
Thus, the average rate of change for the data from the 5th hour to the 8th hour is calculated using the points (5, 96) and (8, 75) from the graph. This is, what happens in the middle does not affect the average rate of change.
[tex]Rate\text{ }of\text{ }change=(\$75-\$96)/(8hour-5hour)[/tex]
[tex]Rate\text{ }of\text{ }change=(-\$21)/(3hour)=-7\text{ }dollars\text{ }per\text{ }hour[/tex]
Answer:
−7 dollars per hour per hour
Step-by-step explanation:
took test
Rectangle URST undergoes a dilation centered at the origin. The result is rectangle U'R'ST. Which rule describes
the dilation?
Plsssss help
Answer:
The rule depends on the scale factor.
Step-by-step explanation:
Hi there,
1) Many, I'd say mostly, dilations is centered at the origin (0,0) of the cartesian plane. Like the picture below.
2) So now, what's left to do is what is the scale factor? What coefficient that multiplies the original rectangle URST, will result the U'R'S'T'?
3) Since no coordinates, no options or any numerical value were given, then I've made one example.
Check below
If you do have the coordinates of each point then divide each coordinate this way
[tex]\frac{U'(x,y)}{U(x,y)}=\frac{R'(x,y)}{R(x,y)}=\frac{S'(x,y)}{S(x,y)}=\frac{T'(x,y)}{T(x,y)}=scale \:factor\\\frac{U'(-4,4)}{U(2,2)}\Rightarrow U'=2U\\(x,y)=D2(x,y)[/tex]
Answer:
you didn't put a picture
Step-by-step explanation:
tommy is buying used books for school. the price of the books is $180. he uses the 30%-off student discount and there is a 4% sales tax.
Answer:
131.04
Step-by-step explanation:
I did it and got it right.
Tommy have to pay $133.2
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Price of book = $180
Discount= 30% off
and, tax = 4%
So, the total discount will be = 30- 4= 26%
Then, price after 26% discount
= 180 - 26% of 180
= 180 - 46.8
= 133.2
Hence, Tommy have to pay $133.2
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1
-
-x+y=-5
9x-y=-11
Answer:
look at the picture shown
A savings account of $5,000 for 12 years, compounded at an annual interest rate of 6%
Answer: 3600
Step-by-step explanation:
What is 10m-3(2m-9)=9(m-1)+1
Answer:
a linear equation with a solution of m = 7
Step-by-step explanation:
The equation is a linear equation in m.
Perhaps you want the value of m that is the solution to the equation.
10m -6m +27 = 9m -9 +1 . . . . . eliminate parentheses
4m +27 = 9m -8 . . . . . . . . . . . . collect terms
35 = 5m . . . . . . . . . . . . . . . . . . add 8-4m to both sides
7 = m . . . . . . . . . divide by the coefficient of m
The solution is m = 7.
3 hats and 2 scarves costs £12.
5 hats and 4 scarves costs £21.
Find the cost of a hat.
Find the cost of a scarf.
Answer: Hat: £3 Scarf: £1.50
Step-by-step explanation:
hope this helps
The cost of a hat is £2 and the cost of a scarf is £1.5, obtained by solving the system of simultaneous equations representing the cost relationships.
Explanation:To solve this problem, you need to use a method called simultaneous equations. We denote the cost of a hat as 'h' and the cost of a scarf as 's'.
Then, we write down two equations based on the problem:
3h + 2s = 12 (Equation 1) 5h + 4s = 21 (Equation 2)
From Equation 1, we express 'h' as (12 - 2s) / 3. Substituting this into Equation 2 leaves us with a sole variable 's', after calculating this equation, you obtain s = 1.5, Substituting s into the first equation, we get h = 2. So, the cost of a hat is £2 and the cost of a scarf is £1.5.
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How many unique ways are there to arrange the letters in the word TIGER?
Answer:
120
Step-by-step explanation:
Because it is lol
120
What is the method of arranging object?The number of ways of arranging n unlike objects in a line is n! (pronounced ‘n factorial’). n! = n × (n – 1) × (n – 2) ×…× 3 × 2 × 1.
In the words TIGER there are 5 letters T,I,G,E,R.
The number of unique ways are there to arrange the letters in the word TIGER=5!=5*4*3*2*1=120.
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Find the exact values below. if applicable, click on "undefined". cot7pi/6
Yo sup??
cot(7π/6)=cot(π+π/6)
=cot(π/6)
=√3
Hope this helps
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the trigonometric identity
cot x = [tex]\frac{1}{tanx}[/tex]
Consider tan([tex]\frac{7\pi }{6}[/tex] )
[tex]\frac{7\pi }{6}[/tex] is an angle in the third quadrant where tan > 0
Thus tan([tex]\frac{7\pi }{6}[/tex] ) = tan([tex]\frac{7\pi }{6}[/tex] - π ) = tan([tex]\frac{\pi }{6}[/tex] ) = [tex]\frac{1}{\sqrt{3} }[/tex]
Hence
cot([tex]\frac{7\pi }{6}[/tex] ) = [tex]\frac{1}{\frac{1}{\sqrt{3} } }[/tex] = [tex]\sqrt{3}[/tex]
What is the simplified form of
Answer:
A. 2x/3
Step-by-step explanation:
4xsqrt5-2xsqrt5/3sqrt5
4x-2xsqrt5/3sqrt5
2xsqrt5/3sqrt5
2x/3
A Physician orders Amoxicillin 500mg by mouth every 8 hours for a patient to treat Bronchitis. The pharmacy has available 250 mg tablets.
How many tablets will you dispense for a 10-day supply?
Answer:
60
Step-by-step explanation:
2of the 250mg pills 3times a day=6 pills a day for 10 days = 60 pills
Brandus bought 1/3 pound of ground turkey and 1/4 pound of ground beef to make sausages. How many pounds of meat did he buy?
Brandus bought a total of 7/12 pounds of meat by adding together 1/3 pound of ground turkey and 1/4 pound of ground beef.
To find out how much meat Brandus bought, you need to add the weights of the ground turkey and the ground beef. Brandus bought 1/3 pound of ground turkey and 1/4 pound of ground beef.
Convert the fractions to have a common denominator:
1/3 = 4/12 (multiply both the numerator and the denominator by 4)
1/4 = 3/12 (multiply both the numerator and the denominator by 3)
Add the two amounts:
4/12 + 3/12 = 7/12
Hence, Brandus bought 7/12 pounds of meat in total to make sausages.