[tex]\begin{cases} x+y=1\\\\ 3y=-3x+3 \end{cases}\hspace{5em}\stackrel{\textit{using the 1st equation}}{x+y=1\implies y=1-x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3\stackrel{y}{(1-x)}~~ = ~~-3x+3\implies 3-3x=-3x+3}\implies 0~~ = ~~0[/tex]
now... the result could have been 3 = 3, or hmmm something like so, which is a bit of a flag hmmm let's take a closer look at the 2nd equation
[tex]\begin{cases} \boxed{x+y=1}\\\\ 3y=-3x+3 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 3y=-3x+3\implies 3y=3(-x+1)\implies \cfrac{3y}{3}=-x+1 \\\\\\ y=-x+1\implies \boxed{x+y=1}[/tex]
let's notice, the 2nd equation is really the 1st one in disguise, so both equations are exactly equal. So what's the solution to that? well, there isn't one solution per se, if we were to graph both lines, it'll be the graph on one line pancaked on top of the other, and where they touch each other is the solution, well, hell they touch each other everywhere, and since both lines go to infinity, then they have infinitely many solutions.
5. Find the equation of the line that is perpendicular to the given line and passes through the given point. y = 5x-1; (-1, 1)
Answer:
y = -0.2x+ 0.8
Step-by-step explanation:
If a line is perpendicular to another line then the slope of the line = the negative reciprocal of the other line
Here Line AB has the equation y = 5x - 1. Here slope = 5
This comes from the fact that if a line has the equation y= mx + c then the slope = m and the y intercept = c
If XY is the line perpendicular to AB then its slope = -1/5. Let the y intercept of XY be c
Then equation of line XY is: y = (-1/5)x + c = -0.2x + c (1)
Since it passes through (-1, 1) ie through x = -1, y=1, substitution these values into the above equation (1), we get
1 = (-0.2)(-1) + c or
1 = 0.2 + c or
c = 0.8
pls help, urgently!!!
Answer:
Yes, no is correct
Step-by-step explanation:
This is because you only add up the outside sides of the polygon to find the perimeter. None of the inside sides. Hope this makes sense and hope it helps.
Answer:
No, because the friend counted a length that is inside of the polygon, which you don't need for finding the perimeter, since the perimeter is the sum of the outside lengths of the polygon.
Find the area of EFGH
The area of triangle FGH that is similar to triangle ABC is: 8 square feet.
What is the Area of Similar Figures?If two shapes are similar, the ratio of their areas equals the ratio of the square of their corresponding sides.
Therefore:
area of triangle EFG / area of triangle ABC = FG²/BC²
Plug in the values
area of triangle EFG / 18 = 2²/3²
area of triangle EFG / 18 = 4/9
area of triangle EFG = (18×4)/9
area of triangle EFG = 8 sq. ft.
Learn more about the area of similar figures on:
https://brainly.com/question/11899908
#SPJ1
can anyone help me with this? 10th grade geometry
Answer:
In romania I was doing this in the 6th grade
Step-by-step explanation:
5.
A B and D C are parallel lines.
"slope" means inclination. and as you can imagine, parallel lines must have the same inclination, or they would not be parallel.
so, the slope of D C must be also 2/7.
4.
same thing as with 5.
both lines are parallel and must therefore have the same slope.
so, the slope of D C is also 3/4. and the first answer is correct.
Sorry it is hard to read, I’m using an iPhone 6 lol
Giving brainliest
Answer:
Domain: [tex]\displaystyle (-\infty,-3)\cup(-3,6)\cup(6,\infty)[/tex]
Range: [tex](-\infty,0)\cup(0,\frac{1}{9})\cup(\frac{1}{9},\infty)[/tex]
Step-by-step explanation:
Factor the numerator and denominator
[tex]\displaystyle f(x)=\frac{x-6}{x^2-3x-18}\\ \\f(x)=\frac{x-6}{(x-6)(x+3)}\\\\f(x)=\frac{1}{x+3}[/tex]
Because the factor [tex]x-6[/tex] exists in both the numerator and denominator, then there is a hole at [tex]x=6[/tex] because the function is not continuous there. Additionally, because the denominator cannot be 0, [tex]x\neq-3[/tex], and there will be a vertical asymptote at the line [tex]x=-3[/tex].
Thus, the domain of the function is [tex]\displaystyle (-\infty,-3)\cup(-3,6)\cup(6,\infty)[/tex].
Also, notice that because [tex]x\neq6[/tex], as the function gets closer to [tex]x=6[/tex], the function gets closer to [tex]\displaystyle f(6)=\frac{1}{6+3}=\frac{1}{9}[/tex], so [tex]\displaystyle y=\frac{1}{9}[/tex] is not included in the range.
Thus, the range is [tex](-\infty,0)\cup(0,\frac{1}{9})\cup(\frac{1}{9},\infty)[/tex].
Starting time: Elapsed time: 50 minute Ending time: 9:05 A.M.
[tex]help[/tex]
Answer:
8:15 am.
Step-by-step explanation:
So the starting time will be 50 minites before 9:05 am.
That will be 9:05 - 50
= 9:00 - 45
= 8:15 am.
Two buildings are 96 ft apart . The first building is 164ft tall. The second building is 92ft tall. If a string is stretched between the top of the two buildings so that it forms a straight line from the top of one to the top of the other, how long would the string be
Answer:
120ft
Step-by-step explanation:
How many three digit numbers can you make by arranging the numbers 5, 4, and 9.
okay,here is about a formula.
n=2x
where x is the numbers.
n=2×3
n=6.
therefore the three digit numbers which can be obtained is 6.
-1/2(x+5)=-10 I WONT BREATHE UNTIL U ANSWER ME!!
Step-by-step explanation:
well don't breath just collect like terms and booom
If an astronaut has a mass of 90 kg, and visits Jupiter which has a gravitational field of 25.3 N/kg, how much will he weigh there?
A. 115.3N
B. 64.7 N
C. 3.55 N
D. 2,277 N
Answer: 2277 Newtons
Step-by-step explanation:
I will show you how to do this the Physics way, so first we must write down our given values.
gravitational field = gravity = 25.3 N/kg
Mass of the astronaut = 90kg
Fun fact: know that if you convert the Newtons to a different unit, Newtons = kg (m/s^2) so we can say that instead of N/kg, we can write it as m/s^2 because if we divide kg(m/s^2) with kg, you’ll end with m/s^2
If you’re in physics, we always work with m/s^2 for every acceleration that exists. So we basically have 25.3 m/s^2 for gravity.
To find the weight, we can use the F=ma formula but rewritten as Weight = mass * gravity
Weight = (90kg)(25.3 m/s^2) = Option D = 2277 Newtons
higher level thinking cell phone plan is shown on the right. Prices, which include an unlimited data plan, are the same every month for 7 months. The total cost for all seven months is $180.39. Let m be the average number of minutes exceeding 700 minutes each month. 700 minutes talked: $19.70 per month Every minute over 700 minutes: $0.05 per minute A. Write an equation to represent the given situation
Equation to represent the given situation :
7(19.70 + 1.97 + m X 0.05) = 180.39,
What is Linear Equation?
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given that:
Total cost for 7 month =$180.39
Let m be the average number of minutes that exceeds 700 minutes each month.
Equation :
7(19.70 + 1.97 + m X 0.05) = 180.39,
or, 7(19.70 + 1.97 + m X 0.05) = 180.39,
or, 21.67 + 0.05m = 180.39/ 7,
or, 0.05m = 25.77 – 21.67,
0.05m = 4.1
m= 82
Hence, equation to represent the given situation : 7(19.70 + 1.97 + m X 0.05) = 180.39.
Learn more about this concept here:
https://brainly.com/question/15101949
#SPJ1
Which set of graphs can be used to find the solution set to 3e^x> -1/2x?
Step-by-step explanation:
all the pink area above the blue line (above means ">", and the blue line is -1/2 x), and not including the line.
At a store, Eva bought two shirts and five hats for $154.00. Nicole bought
three same shirts and four same hats for $168.00. What is the price of each
shirt? _____
Simplify radical expression
√10z^5 - z^2 √10z
Answer:
√10z^3(z - 1)(z + 1).
Step-by-step explanation:
The GCF is √10z* z^2
= √10z^3
So factoring we get
√10z^3(z^2 - 1) The expression in brackets is difference of 2 squares so:
= √10z^3(z - 1)(z + 1)
Picture is attached! Select the reason that nest supports Statement 3 on the given proof
The reason that best supports statement 3 in the given proof is the substitution property of equality. The correct option is - D. Substitution
Substitution propertyThe substitution property of equality states that, if m = n, then m can be substituted in for n in any equation, and vice versa.
From the question, we are to determine the reason that best supports Statement 3
In the diagram, statement 3 is
m∠A ÷ 5 = 20°
From the given expressions,
m∠A ÷ 5 = m∠B and m∠B = 20°
By the substitution property, we can substitute 20° for m∠B in the first expression
That is,
m∠A ÷ 5 = m∠B becomes
m∠A ÷ 5 = 20°
Hence, the reason that best supports statement 3 in the given proof is the substitution property of equality. The correct option is - D. Substitution
Learn more on Substitution property here: https://brainly.com/question/10905255
#SPJ1
What is the square root of 9
may someone help me please?
Step-by-step explanation:
Radio=
Normal Price = K48.
Discount 20%
Selling Price
The dot plot below shows the hourly rate of some babysitters in a city:
A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark. The horizontal axis label is Dollar per hour. There are 4 dots above 4 dollars, 2 dots above 5 dollars, 3 dots above 6 dollars, and 1 dot above 7 dollars. The title of the line plot is Babysitting Rates.
Which statement best describes the shape of the data?
It is a cluster from $1.00 to $7.00 and has no gaps.
It is a cluster from $1.00 to $7.00 and has gaps.
It is not symmetric and has a peak at $4.00.
It is symmetric and has a peak at $7.00.
*will mark brainliest*
Answer:
A dot plot is like a histogram but it uses dots instead of bars. Like histogram, a dot plot also presents the frequency of data points. The dot plot as described by the problem is shown in the picture. A bell shape is drawn for a symmetrical data. From the choices, the answer is: It is symmetric and has no gaps. The other statements are wrong because the peak is at $5 or $6.
Answer:
A dot plot is like a histogram but it uses dots instead of bars. Like histogram, a dot plot also presents the frequency of data points. The dot plot as described by the problem is shown in the picture. A bell shape is drawn for a symmetrical data. From the choices, the answer is: It is symmetric and has no gaps. The other statements are wrong because the peak is at $5 or $6.
Step-by-step explanation:
A dot plot is like a histogram but it uses dots instead of bars. Like histogram, a dot plot also presents the frequency of data points. The dot plot as described by the problem is shown in the picture. A bell shape is drawn for a symmetrical data. From the choices, the answer is: It is symmetric and has no gaps. The other statements are wrong because the peak is at $5 or $6.
Round 82585 to the nearest ten thousand. Enter your answer in the box
below.
Which expression is equivalent to 6^4 • 6^3?
(6•6•6•6)+(6•6•6)
(6+6+6+6)•(6+6+6)
(6•6•6•6)•(6•6•6)
(6•6•6•6•6)•(6•6•6•6)
Answer: C)
Step-by-step explanation:
A Ferris wheel has a diameter of 60 m, with a minimum height of 9 m above the
ground. It takes 20 seconds for the Ferris wheel to complete one rotation. If a rider
boards a car when it is at its lowest point
O: What is the minimum height of the rider?
A: Minimum height of the rider is __ meters.
No Links Or I’ll Report You
By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.
How to analyze a Ferris wheel
The model of the height of a Ferris wheel is represented by a sinusoidal model, which is presented below:
h = A + B · sin ωt (1)
Where:
A - Midpoint height, in meters. B - Amplitude, in metersω - Angular frequency, in radians per second.t - Time, in secondsSinusoidal functions are bounded functions, the minimum height of the Ferris wheel represents the lower bound of the function and the maximum height is the upper bound. Therefore, the minimum height of the rider is:
[tex]h_{min} = 39\,m - 30 \,m[/tex]
[tex]h_{min} = 9\,m[/tex]
By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.
To learn more on Ferris wheel: https://brainly.com/question/16396069
#SPJ1
Melissa Doubet's home is insured for 90% of its replacement value of $94,000, or
$84,600. Use the chart below to determine the amount of coverage for her personal
property.
Insurance Coverage Chart
Coverage
Percent of Coverage
Garage and other structures
15%
Loss of use
30%
Personal property
60%
O $51,276
O $47,328
$50,760
$49,970
Based on the percentage coverage for personal property, the amount of coverage for Melissa's personal property is $50,760.
What is Melissa's personal property coverage?This can be found by the formula:
= Replacement value x Percentage of personal property coverage
Solving gives:
= 84,600 x 60%
= $50,760
In conclusion, Melissa's personal property coverage is $50,760.
Find out more on insurance coverage at https://brainly.com/question/2501031.
#SPJ1
Find the amount accumulated after investing m principal P for t and an internet rate compounded annually P=40500 r=3.8% t=20 k=12
The amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
What is an interest in banking?Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.
The formula for calculating compound interest is expressed as;
A = P(1 + r/k)^(k*t)
Where A is final amount, P is initial principal balance, r is interest rate, k is number of times interest applied per time period and t is number of time periods elapsed.
Given that;
Initial principal balance P = $40500Interest rate r = 3.8= 3.8/100 = 0.038Time t = 20 yearsNumber of times interest applied per time period = 12 (annually) = 12/12 = 1 Amount accumulated A = ?A = P(1 + r/k)^(k*t)
A = 40500(1 + 0.038/1)¹ˣ²⁰
A = 40500 × (1.038)²⁰
A = 40500 × 2.10837
A = $85389
Therefore, the amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
Learn more about compound interest here: brainly.com/question/27128740
#SPJ1
A company rents storage sheds shaped like rectangular prisms. Each shed is 11 feet long, 7 feet wide, and 12 feat tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
Answer:
308
Step-by-step explanation:
so to find how much a rectangular prisim is by
length * with* height
11* 7 * 12
= 924 cubic feet
and then we just divid by 3
=308
What is the slope of the line that passes through the points (-6, 1) and (-6,-4)?
Write your answer in simplest form.
Answer:
horizontal line
Step-by-step explanation:
The slope formula is m=(y2-y1)/(x2-x1)
-6+6/-4-1
y2-y1 = 0
Please help? I need to please it will give you a lot of rewards
Answer:
<HAD
Step-by-step explanation:
HELP PLEASE!!! Which shows how to find the value of this expression when x=-2 and y=5?
What is the area of the circle below if the area of the square is 36?
If the area of the square is 36 square units. Then the area of the circle will be 28.26 square units.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The area of the square will be given as 36 square units.
Then the side length of the square will be
36 = a²
a = 6 units
Then the diameter of the circle and side length of the square are equal. Then we have
a = d = 6 units
Then the radius of the circle will be
2r = d
2r = 6
r = 3 units
Then the area of the circle will be
Area of circle = πr²
Area of circle = 3.14 x 3²
Area of circle = 28.26 square units.
More about the geometry link is given below.
https://brainly.com/question/7558603
#SPJ1
find the domain and range
Answer:
Domain: all real numbers (all reals)
Range: y> OR EQUAL TO -2
Step-by-step explanation:
Hope this helps! ;-)
Please help, thank you! Image below
Answer:
The diameter divides a circle into fourths. (False)
The diameter is twice the length of the radius. (True)
The diameter is the distance around the circle. (True)
The diameter is a chord. (True)
The diameter passes through the center of a circle. (True)
The diameter is about three times larger that the circumference. (I don't really know this from the top of my head. Sorry!
Step-by-step explanation:
Hope this helps!
From your neighborhood softie. :)