A system of equations is graphed on the coordinate plane. y=−x+5y=2x−1 What is the solution to the system of equations? Enter the coordinates of the solution in the boxes.
Answers
Answer:
[tex](2;3)[/tex]
Step-by-step explanation:
We can find the solution directly on the graph. The solution of a system of equations is the intersections between the two lines. Remember that each equation in this case represent a line, where the common points are always shown as an intersection.
To prove this result, we can apply other methods. Using the substitution method, we have to isolate one variable from one equation and then replace it in the other equation, like this:
[tex]\left \{ {{y=-x+52'} \atop {y=2x-1}} \right.[/tex]
The variable y is already isolated, now we just replace the first equation in the second:
[tex]-x+5=2x-1\\5+1-2x+x\\6=3x\\x=\frac{6}{3}=2[/tex]
Then, we replace the x-value in one equation, no matter which one:
[tex]y=2x-1\\y=2(2)-1\\y=4-1=3[/tex]
Therefore, we found that the solution is[tex](2;3)[/tex]
Related Questions
helppppppppppppppppppppppppppppppppppppppp
Answers
the answer is √2^5
FOURTH TIME POSTING! EXTRA POINTS!
Complete each function. ( y = -x )
Answers
-2 = 2
-1 = 1
0 = 0
1 = -1
2 = -2
so
x y
-2 2
-1 1
0 0
1 -1
2 -2
a fund drive announces that it has raised 4376 which is 20% of its goal. How much more must be raised?
Answers
It must raise an additional 17504
Explanation:
Assume that the amount to be raised is x.
Now, we are given that 20% of x is 4376, therefore:
0.2x = 4376
x = 4376/0.2
x = 21880
It has raised 4376, therefore:
amount left to raise = 21880 - 4376 = 17504
Hope this helps :)
1. Let's call the amount: "y".
2. The exercise says that 4376 which is 20% of its goal, so we have:
y=4376
20% of its goal=4376
3. Then, we have the equation below:
20y/100=4376
0.20y=4376
4. When we clear the variable "y", we obtain:
y=4376/0.20
y=21880
5. Finally, we will have:
21880-4376=17504
6. How much more must be raised?
The anwer is: 17504
A florist sold 15 arrangements in its first month of business. The number of arrangements sold doubled each month.
What was the total number of arrangements the florist sold during the first 9 months?
Answers
Answer:
total number of arrangements the florist sold during the first 9 months = 7665 arragements
Explanation:
Florist start a business.
In his 1st month Florist sold 15 arrangement.
He grow his business, he sold twice arrangements as compare to the previous month.
First month = 15
Second month = 2*15 = 30
Third month = 2*30 = 60
15, 30, 60 .....
we need to find the total number of arrangements in first nine months
This sequence is geometric series.
A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,
r = [tex] \frac{30}{15} = \frac{60}{30} = 2 [/tex]
Sum of Terms in a Geometric Progression ([tex] S_{n} [/tex])= [tex] \frac{a_{1} (r^{n} -1)}{r-1} [/tex]
where [tex] a_{1} [/tex] is first term = 15
n is the number of terms = 9
r is common ratio = 2
[tex] S_{9} =\frac{15(2^{9}-1)}{2-1} [/tex]
[tex] S_{9} =\frac{15*(512-1)}{1} [/tex]
[tex] S_{9} = 7665 [/tex]
total number of arrangements the florist sold during the first 9 months = 7665.
Answer:7665
Step-by-step explanation:
Help me in this plz plz
Answers
3b. You can tell the system of linear equations has no solution if the equations result in a contradiction, such as 0 = 1. They will have infinite solutions if the result is a tautology, such as x = x or 0 = 0.
Word Problem
(a) There is actually no problem stated. If we assume the problem is to determine the length and width that meet the described conditions, then it would be appropriate to let variables represent the length (L) and width (W). The system of equations restates what the words state:
.. L - W = 2 . . . . . . length and width differ by 2 units
.. 2(L + W) = 40 . . the perimeter is 40 units
(b) You can solve this many ways. One way is to divide the second equation by 2, so you have a "sum and difference" problem
.. L - W = 2
.. L + W = 20
This is easily solved by adding the two equations to get
.. 2L = 22
.. L = 11
.. W = L -2 = 9
The solution is (L, W) = (11, 9). This is interpreted to mean the length of the rectangle is 11 units; the width is 9 units.
an angle with measure between 90 and 180 is called
Answers
An angle with measure between 90° and 180° is called obtuse angle.
The definition of an obtuse angle in geometry states that an angle whose measure is greater than 90° and less than 180° is called an obtuse angle.
So, if the angle measure between 90 degree and 180 degree is obtuse angle.
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What is the value of x in the figure?
Enter your answer in the box.
x =
Answers
Answer:
The value of x in the given figure is, [tex]34^{\circ}[/tex]
Step-by-step explanation:
Complementary angle states that the two angles sum up to 90 degree.
From the given figure
[tex]x^{\circ}[/tex] and [tex]56^{\circ}[/tex] are complementary angles.
by definition of complementary angles;
[tex]x^{\circ} +56^{\circ} = 90^{\circ}[/tex]
Subtract [tex]56^{\circ}[/tex] from both sides we get;
[tex]x^{\circ} = 90^{\circ} -56^{\circ}[/tex]
Simplify:
[tex]x = 34^{\circ}[/tex]
therefore, the value of x in the given figure is, [tex]34^{\circ}[/tex]
A rectangular auditorium seats 1344 people. The number of seats in each rows exceeds the number of rows by 20. Find the number of seats in each row
Answers
rows = x
seats in each row = x + 20
total seats = 1344
x (x + 20) = 1344
x^2 + 20x - 1344 = 0
(x + 48)(x - 28) = 0
x = -48 (rejected, answer cannot be negative) or x = 28
Therefore,
x = 28
x + 20 = 48
Check:
Row = 28
Numbers of seat per row = 28 + 20 = 48
28 x 48 = 1344 (Correct)
Ans:There are 48 seats per row
To solve this problem, we must first set up an equation. We are told that the total number of seats in the auditorium is 1344. We are also told that the number of seats in each row exceeds the number of rows by 20.
Let's denote the number of rows as x. Therefore, the number of seats per row is x + 20 (as it exceeds the number of rows by 20). Setting up an equation would be as follows:
x * (x + 20) = 1344
This equation states that the number of rows times the number of seats per row equals the total number of seats.
Solving this equation requires finding the roots of a quadratic equation. We set it up as a quadratic equation ax² + bx + c = 0. Here, a = 1, b = 20, and c = -1344.
Solving a quadratic equation gives us two possible solutions, but in our case, we disregard the negative value, as the number of rows cannot be negative. So, we take the maximum of the two roots.
Solving this equation gives us x = 28.0, which represents the number of rows.
Finally, to find the number of seats in each row, we remember that it exceeds the number of rows by 20. So, we add 20 to the number of rows.
28.0 + 20 = 48.0
So, there are 48 seats in each row.
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If a couple has three children, let x represent the number of girls. what is the probability that the couple does not have boys for all three children?
Answers
Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x^2 − 6x + 1 square feet, what is the length of one side of the room?
(3x + 1) feet
(9x − 1) feet
(3x − 1) feet
(9x + 1) feet
Answers
helpppppppppppppppppppppppppppp
Answers
x = -7 +/- √(-64)
x = -7 +/- 8*√-1
x = -7 +/- 8i
We have then:
x ^ 2 + 14x + 17 = -96
Rewriting:
x ^ 2 + 14x + 113 = 0
Applying resolver we have
x = (- b +/- root (b ^ 2 - 4ac)) / (2a)
Substituting values:
x = (- (14) +/- root ((14) ^ 2 - 4 (1) (113))) / (2 (1))
x = (- (14) +/- root ((196 - 452)) / (2 (1))
x = (- 14 +/- root (-256))) / (2)
x = (- 14 +/- i * 16)) / (2)
x = (- 7 +/- i * 8)
Answer:
x = (- 7 +/- i * 8)
(option 2)
PLEASE HELP
Three times the number of blue marbles exceeds twice the number of red marbles by 18 also five times the number of blue marbles is two less than six times the number of red marbles how much of each are there
Answers
x----------> number of blue marbles
y----------> number of red marbles
we know that
3x=2y+18----------> y=(3x-18)/2------> equation 1
and
5x=6y-2-----------> y=(5x+2)/6----------> equation 2
(1)=(2)
(3x-18)/2=(5x+2)/6----> 3*(3x-18)=5x+2
9x-54=5x+2
9x-5x=2+54-------> 4x=56---------> x=14
y=(3x-18)/2-------> y=(3*14-18)/2=24/2-------> y=12
the answer is
14 blue marbles
12 red marbles
If point P is at the center of the circle, and the length of equals 12 inches, which is the length of AP?
a)4.5 inches
b)6 inches
c)9 inches
d)12 inches
Answers
you divide by 2
I need help please with these two questions.
1. What is the volume of this sphere? (First Picture)
8π cm³
16π cm³
27π cm³
36π cm³
2. What is the volume of this sphere? (Second Picture)
Use 3.14 for pi and round to the nearest hundredth when necessary.
615.44 cm³
2461.76 cm³
11,488.21 cm³
91,905.71 cm³
Answers
Answer:
(1) Volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .
(2)volume of the sphere is 11488.21 cm³ .
Step-by-step explanation:
Formula
[tex]Volume\ of\ a\ sphere = \frac{4}{3} \pi r^{3}[/tex]
Where r is the radius of the sphere .
Part First
As given the radius of the circle is 3cm .
Putting values in the formula
[tex]Volume\ of\ a\ sphere = \frac{4\times 3\times 3\times 3}{3} \pi[/tex]
[tex]Volume\ of\ a\ sphere = \frac{108}{3} \pi[/tex]
[tex]Volume\ of\ a\ sphere = 36 \pi\ cm^{3}[/tex]
Therefore the volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .
Second Part
As given
Diameter of the sphere is 28 cm .
[tex]Radius (r) = \frac{Diameter}{2}[/tex]
[tex]Radius (r) = \frac{28}{2}[/tex]
[tex]Radius (r) = 14\ cm[/tex]
[tex]\pi = 3.14[/tex]
Putting all the values in the formula
[tex]Volume\ of\ a\ sphere = \frac{4}{3}\times 3.14\times 14\times 14\times 14[/tex]
[tex]Volume\ of\ a\ sphere = \frac{4\times 3.14\times 14\times 14\times 14}{3}[/tex]
[tex]Volume\ of\ a\ sphere = \frac{34464.64}{3}[/tex]
[tex]Volume\ of\ a\ sphere =11488.21\ cm^{3}[/tex]
Therefore the volume of the sphere is 11488.21 cm³ .
1. The volume of the sphere is 16π cubic centimeters, which matches option B.
2. The correct answer for the volume of the second sphere is:
C. 11,488.21 [tex]cm^3[/tex]
1. For the sphere shown in the image with a diameter of 3 cm, the correct choice for its volume is:
B. 16π cm³
To calculate the volume of a sphere, we use the formula:
V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3
Where r is the radius of the sphere.
Given:
- Diameter of the sphere = 3 cm
- Therefore, radius (r) = 3/2 = 1.5 cm
Substituting in the formula:
V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] (1.5)^3
V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] 3.375
V = 4 [tex]\times[/tex] π [tex]\times[/tex] 3.375/3
V = 16π cm³
So the volume of the sphere is 16π cubic centimeters, which matches option B.
2.For the second sphere shown with a diameter of 28 cm, to calculate its volume using π = 3.14 and rounding to the nearest hundredth, we follow these steps:
1) Find the radius by dividing the diameter by 2:
Radius = 28 cm / 2 = 14 cm
2) Use the formula for sphere volume: V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3
Substituting the values:
V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] (14 cm)^3
V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] 2744
V = 11,488.53 cm^3
3) Rounding to the nearest hundredth as instructed:
V = 11,488.53 cm^3 rounds to 11,488.21 cm^3
Therefore, the correct answer for the volume of the second sphere is:
C. 11,488.21 [tex]cm^3[/tex]
The correct question is:
1. What is the volume of this sphere? (First Picture)
A. 8π cm³
B. 16π cm³
C. 27π cm³
D. 36π cm³
2. What is the volume of this sphere? (Second Picture)
Use 3.14 for pi and round to the nearest hundredth when necessary.
A. 615.44 cm³
B. 2461.76 cm³
C. 11,488.21 cm³
D. 91,905.71 cm³
The combined average weight of an okapi and a llama is 450450450 kilograms. The average weight of 333 llamas is 190190190 kilograms more than the average weight of one okapi. On average, how much does an okapi weigh, and how much does a llama weigh?
Answers
x= Okapi weight
y= Llama weight
EQUATIONS:
There are 2 equations to be written:
1) 450kg is equal to the weight of one Okapi and one Llama
450kg= x + y
2) The weight of 3 llamas is equal to the weight of one Okapi plus 190kg.
3y=190kg + x
STEP 1:
Solve for one variable in one equation and substitute the answer in the other equation.
450kg= x + y
Subtract y from both sides
450-y =x
STEP 2:
Substitute (450-y) in second equation in place of x to solve for y.
3y=190kg + x
3y=190 + (450-y)
3y=640 -y
add y to both sides
4y=640
divide both sides by 4
y=160kg Llama weight
STEP 3:
Substitute 160kg in either equation to solve for x.
3y=190kg + x
3(160)=190 + x
480=190 + x
Subtract both sides by 190
290= x
x= 290kg Okapi weight
CHECK:
3y=190kg + x
3(160)=190 + 290
480=480
Hope this helps! :)
Llama's weight will be 160kg and Okami's weight will be 290kg.
What is an average?An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
The weight for both will be calculated as below:-
x= Okapi weight
y= Llama weight
There are 2 equations to be written:
1) 450kg is equal to the weight of one Okapi and one Llama.
450kg= x + y
2) The weight of 3 llamas is equal to the weight of one Okapi plus 190kg.
3y=190kg + x
Solve for one variable in one equation and substitute the answer in the other equation.
450kg= x + y
Subtract y from both sides.
450-y =x
Substitute (450-y) in the second equation in place of x to solve for y.
3y=190kg + x
3y=190 + (450-y)
3y=640 -y
Add y to both sides.
4y=640
Divide both sides by 4.
y=160kg Llama weight
Substitute 160kg in either equation to solve for x.
3y=190kg + x
3(160)=190 + x
480=190 + x
Subtract both sides by 190.
290= x
x= 290kg Okapi weight
Therefore, Llama's weight will be 160kg and Okami's weight will be 290kg.
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Robby and Tony both took a 25 question test. Robby completed 25 questions and Tony completed 14 questions. Can we conclude that Robby will make a higher grade than Tony? Explain why or why not. -
Answers
What transformations change the graph F(x) to the graph g(x)
f(x) = 3x^2
G(x) = 9x^2-4
A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units
B. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated UP 4 units
C. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated up 4 units
Answers
Final answer:
The transformation from f(x) = 3x^2 to g(x) = 9x^2 - 4 includes a vertical stretch by a factor of 3 followed by a vertical translation down by 4 units.
Explanation:
The transformations that change the graph f(x) = 3x2 to the graph g(x) = 9x2 - 4 involve two steps:
A vertical stretch by a factor of 3, which is achieved by multiplying the original function f(x) by 3, yielding 9x2. This transformation changes the original coefficient (3) in front of x2 to a new coefficient (9).
A vertical translation down by 4 units, which is represented by subtracting 4 from the result of the stretch transformation.
Therefore, the correct answer to the student's question is:
A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units.
Mr burn's class is taking
a. field trip to the planetarium. The trip will cost $27 for each student. There are 18 students in his class.Use compatible numbers to estimate the total cost of field trip
Answers
Answer:
600
Step-by-step explanation:
The answer is 600
How would you solve this?
Answers
I suppose as we don't see correctely the 2nd image, that it is the first one.
Angles DOY and DKY intersept then same arc are equals.
5x+15=3x+21
==>2x=6
==>x=3 and 5x+15=5*3+15=30°, 3x+21=3*3+21=30°
Angle OYK=15x=15*3=45°
Angle ODK=9x+18=9*3+18=45° =Angle OYK which intersept the same arc.
Help please.....!!!!!
Answers
______________________________________________________
Note:
_______________________________
When x = 0 ;
y = f(x) = 5(2)⁻ˣ = 5* (2)⁻⁰ = 5 * 1 = 5 .
_______________________________
By inspection of the graph, the only given answer choices with graphs that fall on the point "(0, 5)" are:
[A]: "Graph A" (the red graph) ; and:
[B]: "Graph B" (the green graph) .
________________________________________________________
Now, let us look at other points and see if the selected points are true values for the given function/ equation;
Start with "Graph B" (the green graph): Upon inspection, it is clear that "(0.5 , 7)" is a point on the graph; that is, for "Graph B" ,
when "x = 0.5" , y = 7" .
Let us plug these values into the equation: y = 5(2)⁻ˣ ; to see if the equation holds true; that is, when "x = 0.5" , does "y = 7" ?
5* 2^(-0.5) = 5 * 0.7071067811865475 ;
→ 5 * (√2/2) =
3.5355339059327375;
→ 3.5355339059327375 [tex] \neq [/tex] 7 .
________________________________________________
So; we are left with: Choice: [A]: "Graph A" {the red graph}.
________________________________________________
Carlo wants to join gym.the total gym offers three options for the membership. Option1:pay as you go.pay only $6 each time You work out. Option2: Regular Deal. Pay $50 a month and $2 each time you workout.
Answers
1- Carlo thinks he will go to the gym 20 times this month. Calculate how much each of these options will cost Carlo for one month.
a- Pay as you go:
Total cost = 6 * 20 = $120
b- Regular deal:
Total cost = 50 + 2(20) = 50 + 40 = $90
c- All-in-one-price:
Total cost = $100
d- The least expensive for Carlo in this case would be the regular deal.
2- How many visits each month would make the cost of the Regular-Deal and the All-in-one the same?
Assume number of visits is x.
Regular deal = All in one
50 + 2x = 100
2x = 100 - 50
2x = 50
x = 25 visits
3a- It costs $300 to join the new Superfit Gym. You then pay $15 each month and $2 each time you work out. Carlo thinks he will use the gym 20 times each month for a year.
Calculate the cost of the Superfit gym for one year.
Total cost = initial payment + 15*number of month + 2*days of workout
initial payment = $300
15*number of months = 15 * 12 = $180
2*days of workout = 2*20*12 = $480
Total cost = 300 + 180 + 480 = $960
3b- How much will Carlo save during the first year if he uses the Superfit gym rather than the regular deal at the other gym?
First we will calculate the total cost of one year using the regular deal at the other gym as follows:
Total cost at other gym = monthly cost + cost of each workout
Total cost at other gym = 50(12) + 2(12)(20) = $1080
Then, we will calculate the difference to know the amount Carlo would save as follows:
Carlo would save = 1080 - 960 = $120
Hope this helps :)
30 POINTS + BRAINLIEST!
Answers
Put in plane English
YX^2 = YV * YZ
YV = 9
YZ = 9 + 19 = 28
YX^2 = 28 * 9
yX^2 = 252
YX = sqrt(252)
YX = 15.87
The answer is 15.87.
Four sides of a octagon each measure 12 cm. The perimeter of the octagon is 70 cm. What is the length of each remaining side, if each remaining side has the same length?
Answers
4 * 12 = 48
70-48 = 22
so the remaining 4 sides need to = 22 cm
22 / 4 = 5.5
each remaining side = 5.5 cm
Answer:
It would be 5.5 cm
Step-by-step explanation:
Choose the option that correctly completes the statement.
The sum of the measures of the interior angles of a quadrilateral is _____ degrees.
270
180
90
360
Answers
Answer:
D. 360 degrees.
Step-by-step explanation:
We have been given an incomplete statement. We are asked to complete the given statement using provided options.
Statement:
The sum of the measures of the interior angles of a quadrilateral is _____ degrees.
We know that a quadrilateral is a polygon with 4 vertices.
We can divide a quadrilateral into two triangles by drawing a diagonal. We know that sum of three angles of a triangle is equal to 180 degrees, so sum of angles of two triangles would be 360 degrees.
Therefore, the sum of the measures of the interior angles of a quadrilateral is 360 degrees and option D is the correct choice.
A dentist had some fish in a fish tank. The dentist added 43 more fish to the fish tank. Now there are 66 fish in the fish tank. How many fish were in the fish tank before the dentist added more?
___fish
Answers
Answer:
The dentist had 23 fish before she added 43
Step-by-step explanation:
Which statement is true about the function f(x)=-√-x
a.The domain of the function is all negative real numbers.
b.The range of the function is all positive real numbers.
c.The domain and range of the function have opposite signs.
d.The domain and range of the function are the same.
Answers
Answer: D.The domain and range of the function are the same.
Step-by-step explanation: Given function f(x)=-√-x.
The given function is a square root function and we have minus sign in front of x inside square root.
A square root always defined for positive values or 0.
In order to get a positive number or 0 inside square root, let us solve the inequality:
[tex]-x\geq 0[/tex]
On dividing both sides by -1, the inequality sign would get flip and we get
Domain: [tex]x \leq 0.[/tex]We can see that we have a negative sign in front of square root. So, the value of f(x) would be always a negative number or 0.
Therefore, range would also be :[tex]x \leq 0.[/tex].Therefore, correct option is D option.Answer:
hi thereee, the answer to this question is
d. the domain and range of the function are the same
hope this helps :)
have a good day!
Step-by-step explanation:
i just took the test
What is the GCF of the terms of 8x3 − 12x2 + 4x?
Answers
MATH HELP!
Kristen's gross annual income is $47,208. She is paid semimonthly and has 6% deducted from her paychecks for her 403(b). Her employer matches her deduction, up to 5%. How much is deposited into Kirsten's 403(b) each payday?
$98.35
$118.02
$196.70
$216.37
Answers
1967 * 0.06 = 118.02
1967 * 0.05 = 98.35
118.02 + 98.35 = 216.37
The amount deposited into Kristen's each payday is is 216.37
Kristen's gross annual income is $47,208.
What is the meaning of semimonthly?Twice a month
semimonthly per year means
12(2)=24
She paid semimonthly,
47,208 / 24 = 1967
6% deducted from her paychecks then,
1967 * 0.06 = 118.02
Her employer matches her deduction, up to 5% then,
1967 * 0.05 = 98.35
The amount deposited into Kristen's each payday is
118.02 + 98.35 = 216.37
Therefore,the amount deposited into Kristen's each payday is is 216.37
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If ΔMNO ≅ ΔPQR, which of the following can you conclude as being true? I'LL MARK BRAINLIEST !!!!
Answers
If the two triangles are congruent, then you can conclude that they have 3 angles in common, or that they are identical or that you could use rigid motions (dilations, translations or reflections) to align them together.
Answer:
NO=QR
Step-by-step explanation:
miss parks wrote 4 statement to the board and asked the class which one was true. Which statement is true?
A)3 and 2/3 x 4/5 is greater than 3 and 2/3
B)1 and 7/8 x 2 and 1/3 is greater than 2 and 1/3
C)1 and 7/8 x 8/8 is less than 2 and 5/6
D)2 and 3/8 x 4 is less than 4
Answers
(1 7/8)(2 1/3) = (15/8)(7/3) = 35/8 = 4 3/8 (true)
(1 7/8) (8/8) = 1 7/8 (true)
(2 3/8)(4) = (19/8)(4) = 19/2 = 9 1/2 (false)
I got two true statements ...