How many solutions will each system of linear equations have? Match the systems with the correct number of
solutions.
y=x+6 and 3x-3y = -18
y=-4x+11 and -6x + y = 11
y=-2x+5 and 2x + y = -7
infinitely many solutions
one solution
no solution
Answers
The correct answer is System 1: Infinitely many solutionsSystem 2: One solutionSystem 3: No solution
Let's analyze each system of linear equations and determine the number of solutions they have.
y = x + 6 and 3x - 3y = -18
In this system, the first equation is a linear equation in slope-intercept form, and the second equation is a linear equation in standard form. The two equations represent the same line. Since they are the same line, they intersect at infinitely many points. Therefore, this system has infinitely many solutions.
y = -4x + 11 and -6x + y = 11
Both equations in this system are in slope-intercept form. The slopes of the two lines are different (-4 and -6), indicating that the lines are not parallel. Since the lines are not parallel and have different slopes, they intersect at a single point. Therefore, this system has one solution.
y = -2x + 5 and 2x + y = -7
Both equations in this system are in slope-intercept form. The slopes of the two lines are equal (-2 and 2), but their y-intercepts are different. When the slopes are equal and the y-intercepts are different, the lines are parallel and do not intersect. Therefore, this system has no solution.
Matching the systems with the correct number of solutions:
System 1: Infinitely many solutions
System 2: One solution
System 3: No solution
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Related Questions
Candace bought 14 sacks of dog food to share equally among three dog shelters. How much dog food does each shelter get?
Answers
Answer:
4 sacks
Step-by-step explanation:
Felipe rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 86 cents for each mile driven. Felipe had to pay $270.79 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
421.4 miles
Step-by-step explanation:
Numner of miles= ($270.79-$17.95)/86 cents
= $252.84/$0.60
=421.4 miles
(b) With which club did Bruce hit the shortest distance? What was the distance in feet?(c) With which club did Bruce hit the greatest distance? What was the distance in feet?
Answers
Answer:
(b)
The shortest distance hit by Bruce was 99 yards.
This distance was hit by the 9 Iron Golf Club.
The distance in feet =33 feet.
The distance in yards = 99 yards.
(c)
The greatest distance hit by Bruce was 192 yards.
This distance was hit by the Driver Golf Club.
The distance in feet =64 feet.
The distance in yards = 192 yards.
One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 3 units wide.
Answers
The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.
To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.
Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.
The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units
Area of the inner rectangle = length × width= 6 × 4 = 24 square units
Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units
Therefore, the area of the shaded region is 264 square units.
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Fatheya and Fatema, along with 30 other people, sign up to audition for a talent show. Contestants are called at random to perform for the judges. What is the probability that Fatheya will be called to perform first and Fatema will be called second?
Answers
So there's 30 people or slots. The odds that Fatheya will be chosen to perform first is 1/30. But now there's one less slot.
Now with Fatema, there's 29 slots, so there's a 1/29 chance. Then combine these values by multiplying them:
1/30 * 1/29 = 1/870
All done!
art sculpture composed of 3,880 craft sticks and 960 pieces of balsa wood. What is the ratio of craft sticks to balsa wood?
Answers
Answer:
3880 ÷ 960 = 4.041
ratio = 4:1
Optimal Chapter-Flight Fare If exactly 212 people sign up for a charter flight, Leisure World Travel Agency charges $292/person. However, if
more than 212 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how
many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 212. Show that the
revenue function R is given by R(x) = (212+x)(292-x).
passengers
What is the maximum revenue?
$
What would be the fare per passenger in this case?
dollars per passenger
Answers
Answer:
Dollars per passenger would be $252.
The maximum revenue is $63,404.
Step-by-step explanation:
Let's define the number of passengers above 212 as x.
The revenue function is given by R(x) = (212 + x)(292 - x).
We can expand and simplify the revenue function:
\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)
= \(61804 - 212x + 292x - x^2\)
= \(-x^2 + 80x + 61804\)
The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.
To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).
\(x=\frac{-80}{2*(-1)}\)
\(= \frac{80}{2}\)
\(= 40\)
Therefore, the number of passengers above 212 for maximum revenue is 40.
Substitute x = 40 into the revenue function to find the maximum revenue:
\(R(x) = -(40)^2 + 80(40) + 61804\)
\(= -1600 + 3200 + 61804\)
\(= 61804 + 1600\)
\(= 63404\)
Hence, the maximum revenue is $63,404.
To determine the fare per passenger, subtract x from the base fare of $292:
Fare per passenger = Base fare - x
\(= 292 - 40\)
\(= 252\) Dollars per passenger.
What is the value of |24|
Answers
The absolute value is the distance between a number and zero. The distance between 0 and 24 is 24.
In right triangle ABC, altitude CD with length h is drawn to its hypotenuse. We also know AD = 12 and DB = 3. The scale factor of triangle ADC (pre-image) to triangle CDB (image) is . Express answer in the form of a simplified fraction.
Answers
The Scale factor of ΔADC to ΔCDB is 2 .
In the question ,
a right triangle ABC is given (the figure is shown below )
h is the length of the altitude , AD = 12 , DB = 3 ,
to find the scale factor , we first need to find the value of h ,
since triangles ADC is similar to triangle CDB ,
we have , CD / AD = DB / CD
on cross multiplication , we get
CD² = AD × DB
CD² = 12 × 3 = 36
CD = 6
For the scale factor we divide the length of the original triangle ADC with the length of the image triangle CDB .
we get
Scale factor = AD / CD
= 12/6
= 2
Therefore , The Scale factor of triangle ADC to triangle CDB is 2 .
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Convert 1.4394 to a percent
Answers
Answer: = 143.94%
Step-by-step explanation:
Multiply 1.4394 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.
1.43941×100100=143.94100
143.94/100 is 143.94 over 100 and means 143.94 per 100. 143.94 "per 100" means 143.94 "percent" or 143.94%
Therefore, we have shown that
1.4394 = 143.94%
Answer:
143.94%
It is a whole number so it is 100% plus the 43 so it is 143.94
5x-y=54 x=10 what is the answer
Answers
Answer:
Y = 4
Step-by-step explanation:
5x-y=54
50-y=54
circle y and subtract 50 from itself then subtract 50 from 54.
after subtracting you should have y=4
What is the area of the square that measures 3.1 m on each side
Answers
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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Keisha, Miguel, and Ryan sent a total of 103 text messages during the weekend. Ryan sent 3 times as many messages as Miguel. Keisha sent 8 more
messages than Miguel. How many messages did they each send?
Number of text messages Keisha sent:
Number of text messages Miguel sent:
Number of text messages Ryan sent:
Answers
Answer:
only god knows
Step-by-step explanation:
because they didn't give us an answer on how many text messages anyone sent
Consider two data sets. Set A: n = 5; x = 10 Set B: n = 50; x = 10 (a) Suppose the number 26 is included as an additional data value in Set A. Compute x for the new data set. Hint: x = nx. To compute x for the new data set, add 26 to x of the original data set and divide by 6. (Round your answer to two decimal places.) (b) Suppose the number 20 is included as an additional data value in Set B. Compute x for the new data set. (Round your answer to two decimal places.) (c) Why does the addition of the number 20 to each data set change the mean for Set A more than it does for Set B? 1) Set B has a smaller number of data values than set A, so to find the mean of B we divide the sum of the values by a larger value than for A. 2) Set B has a larger number of data values than set A, so to find the mean of B we divide the sum of the values by a smaller value than for A. 3) Set B has a smaller number of data values than set A, so to find the mean of B we divide the sum of the values by a smaller value than for A. 4) Set B has a larger number of data values than set A, so to find the mean of B we divide the sum of the values by a larger value than for A.
Answers
(a) The new x for Set A is 12.00.
(b) The new x for Set B is 10.04.
(c) The addition of the number 26 to each data set changes the mean for Set A more than it does for Set B because Set A has a smaller sample size than Set B.
So the Correct answer is option 4.
When a new value is added to a smaller data set, it has a larger impact on the mean than when added to a larger data set, because the new value represents a larger proportion of the overall data set. This means that adding 26 to Set A had a more significant effect on its mean than adding 26 to Set B.
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Which of the following graphs is a function
Answers
Answer:
D
Step-by-step explanation:
Hope this helps:)
Answer:
Graph B is a function
Step-by-step explanation:
Hope this helps
Plz mark brainliest
Consider a cookie recipe in which 1½ cups of chocolate chips are needed to make 25 cookies. Lara wants to double the number of cookies. How many cups of chocolate chips should she use?
Answers
The number of cups of chocolate chips she should use is 3 cups.
How to find the cups of chocolate chips that should be used?Consider a cookie recipe in which 1½ cups of chocolate chips are needed to make 25 cookies.
She decided to double the number of cookies.
Therefore,
Remember she wants to double the size of cookies,
25 cookies = 1½ cups of chocolate chips
2(25 cookies) = ?
cross multiply
number of cups of chocolate chips required = 50 × 1.5 / 25
number of cups of chocolate chips required = 75 / 25
number of cups of chocolate chips required = 3 cups
Therefore, the number of cups of chocolate chips she should use is 3 cups.
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2(3a - 12) = 3(2a - 8)
One solution
Infinitely many solutions
No solutions
Answers
Infinitely many solutions
Step-by-step explanation:
2(3a - 12) = 3(2a - 8)
6a - 24 = 6a - 24
Infinitely many solutions
(Because both expressions end up with the same distribution)
Answer: Infinitely many solutions
Step-by-step explanation:
Given expression
2 (3a - 12) = 3 (2a - 8)
Expand parentheses and apply the distributive property
2 · 3a - 2 · 12 = 3 · 2a - 3 · 8
6a - 24 = 6a - 24
Subtract 6a on both sides
6a - 24 - 6a = 6a - 24 - 6a
-24 = -24
Add 24 on both sides
-24 + 24 = -24 + 24
0 = 0
Therefore, it has infinitely many solutions since both sides are identical which means any terms will make the equation true.
Hope this helps!! :)
Please let me know if you have any questions
Determine the center of the ellipse whose equation is.
Answers
Answer:
It is reported as an equation but it has no equal sign.
Care to explain?
Step-by-step explanation:
Answer:
(4, -3) is the center
Step-by-step explanation:
The equation ...
16x^2 +25y^2 -128x +150y +81 = 0
can be rearranged by completing the square(s) to ...
(4x -16)^2 +(5y +15)^2 = 400
Dividing by 400 gives ...
(x -4)^2/5^2 +(y +3)^2/4^2 = 1
This is the equation of an ellipse centered at (4, -3) with major axis 10 and minor axis 8.
Find all of square roots of 36i and write the answers in rectangular (standard) form
Answers
r = √(0^2 + 36^2) = 36
θ = tan^-1(0/36) + kπ = kπ (where k is an integer)
Since 36i lies on the positive imaginary axis, we can choose k = 1/2 so that θ = π/2.
Thus, 36i in polar form is 36(cos(π/2) + i sin(π/2)).
Now we can find the square roots of 36i by taking the square root of the magnitude and dividing the angle by 2:
√36(cos(π/4) + i sin(π/4)) = ± 3(cos(π/8) + i sin(π/8))
√36(cos(9π/4) + i sin(9π/4)) = ± 3(cos(9π/8) + i sin(9π/8))
Therefore, the square roots of 36i in rectangular form are:
±3(cos(π/8) + i sin(π/8)) and ±3(cos(9π/8) + i sin(9π/8))
Which is the value of t = 1
Answers
7 ( option C)
please see the attached picture for full solution
Hope it helps..
Good luck on your assignment...
whats the GCF for 1248
Answers
Answer:
None or 12 depending on what the question is. See explanation below.
Step-by-step explanation:
If the number is 1248:
A single number cannot have a GCF. The GCF has be for at least two numbers.
If the numbers are 12 and 48, then the GCF can be calculated.
Since 12 is a factor of 48, then the GCF of 12 and 48 is 12.
In general, to calculate the GCF do this:
To calculate it, find the prime factors of 12 and 48.
12 = 2^2 * 3
48 = 2^4 * 3
GCF is the product of common factors with lower exponent.
GCF = 2^2 * 3 = 12
Help help please please
Answers
✽ Hello there! ✽
4x+9<21
Move all the constants (numbers) to the right, using the opposite operation:
4x<21-9
4x<12
Divide both sides by 4 to isolate x:
x<3
Therefore, x<3 ✔︎Hope this helps!
~Just a felicitous girlie
#HaveASplendidDay
\(SilentNature\)
A scooter travels 30 feet in 2 seconds what is the spend of the scooter in feet per second
Answers
Answer:
15 feet per second
Step-by-step explanation:
30÷2=15
Answer:
15 feet per second.
Step-by-step explanation:
30 feet in 2 seconds.
30 = 2x
Divide both sides by 2 so u can leave the x alone, and it gives you 15 = x.
Please Solve, Thank you!
Answers
Answer:
1711
Step-by-step explanation:
\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)
Make sure to follow order of operations!
Lisa and Susan are driving to college together. They look at a map to find out how far they have to drive. On the map, Lisa measures the distance to be 4.5 inches. How many miles do they have to drive if the map scale is 1 in. = 35 mi?
Answers
Answer:157.5
Step-by-step explanation:becuase mutilpy 4.5x35 that equals 157.5
please help! i'm unsure what the answer is
Answers
Answer:
option 2
Step-by-step explanation:
The graphs intersect at x=-4 and x=0.
how to get the area of the base ?
Answers
Answer:
LxWxH
Step-by-step explanation:
Bases
The area of a rectangle is equal to its length, l, multiplied by its width, w: A = l x w.
example: Given a pyramid whose base is 10 inches long and 15 inches wide, find area as follows: A = 10 inches x 15 inches = 150 square inches.
Using the spinner above, what is the probability of landing on blue then red if the spinner is spun twice?
Answers
Запиши числа в виде суммы разрядных слагаемых двумя способами 1) 4915 2) 6083 3) 15009 4) 25467 5) 10803 6) 206030
Answers
Answer:
4912
given that,
Step-by-step explanation:
you should add and
you should
Which number line correctly shows the graphing of point A,2 1/2 point b -2.75 and point c -0.25
Answers
Answer:
C
Step-by-step explanation:
There are two negative numbers must be before zero and one positive number must be after zero
A = 2 1/2 = 2.5 between 2 and 3
B = -2.75 between -2.5 and -3
C = -0.25 between 0 and -0.5