Three students each examine the system of linear equations shown.
8x+4y=16
8x+2y=8
Caleb says there is exactly one solution. Jeremy says there is no solution. Kim says there are infinitely many solutions.
Answers
Linear equation
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Given the equation:
8x + 4y = 16 (1)
8x + 2y = 8 (2)
Solving equation 1 and 2 simultaneously gives:
x = 0, y = 4
Caleb is right because there is exactly one solution at (0, 4).
Answer:
The solution is (0, 4), and there is only one solution
Step-by-step explanation:
Let's actually solve the system if that's possible. Solving the second equation for 8x, we get 8x = 8 - 2y. Substituting this result into the first equation eliminates y:
8 - 2y + 4y = 16,
which simplifies to 2y = 8 and then y = 4.
Substituting 4 for y in the second equation yields 8x + 2(4) = 8, so we can quickly deduce that x = 0.
The solution is (0, 4), and there is only one solution
Related Questions
Carlos drove 65 miles to a friend's house in another town. The graph below shows the relationship between the distance he drove and the amount of time it took to drive that distance. Which point represents the unit rate of the number of hours Carlos drives and the distance in miles he traveled?
Answers
Answer: distance = rate x time d
Step-by-step explanation:
can somebody help out ill give brainlest
What is the mode of this data set? {15, 15, 15, 16, 16, 17, 18}
Enter your answer in the box.
Answers
Answer:
15
Step-by-step explanation:
15 because the mode is the one that occurs the most and 15 has 3 numbers.
Answer:
15 is the mode of this data
Step-by-step explanation:
because 15 accurs 3 times
16 accurs 2 times
17 aaccurs1 times
18 accurs 1 times
so 15 has more quantities
that this is mode
Find the 88th term of the arithmetic sequence 21, 15, 9
and step by step how you solved it
Answers
Answer:
-501Step-by-step explanation:
The given sequence is :
21, 15, 9, ...
Finding the common difference (d)
d = Term - previous term d = 15 - 21d = -6Formula for the nth term of a sequence
aₙ = a + (n - 1)da = first term = 21 (in this case)n = number of termsd = common difference = -6Taking n = 88 as we are asked to find the 88th term :
a₈₈ = 21 + (88 - 1)(-6)a₈₈ = 21 + 87(-6)a₈₈ = 21 - 522a₈₈ = -501The difference of three times a number and a second number is two. The sum of the two numbers is fourteen. What are the two numbers?
Answers
Answer:
x=4
y=10
Step-by-step explanation:
3x-y=2
x+y=14 are the 2 equations
you do the elimination process to get 4x=16
which x=4
then you plu 4 into either equation to get y=10
please answer and include step by step explanation
no bots
unrelated answer/comment = report
Answers
Identify the vertex and axis of symmetry.
f(x) = 3(x+7)²-5
Answers
Answer:
haiii i can only solve for the vertex...
Step-by-step explanation:
so to find the vertex you have to make it to
y - h = a(x - k)^2
i think
(you could also just make it y = a(x - k)^2 + h but i like the second one better)
soo
y + 5 = 3(x + 7)^2
the vertex is
(-7, -5)
and ummm i think the axis for the axis of symmetry .ss
x = 2a/b but im not sure
Which describes the cross section of the rectangular prism that passes through vertices A, B, C, and D? A rectangular prism with measurements 3 centimeters, 10 centimeters, 6 centimeters. a rectangle with two 10-cm sides and two 6-cm sides a rectangle with two 10-cm sides and two sides that are longer than 6 cm a nonrectangular parallelogram with two 10-cm sides and two 6-cm sides a nonrectangular parallelogram with two 10-cm sides and two sides that are longer than 6 cm
Answers
how do you find the fist step to solving the system of equations x+y=8 and 3x-2y=-6
Answers
Answer:
The first stpe in solving this system of equations is finding either X or Y in terms of the other variable. Ex: x = 8 - y or y = 8 - x
Step-by-step explanation:
When faced with a system of equations problem, you need to find one variable at a time. To do this, you need to eliminate one of the variables from one of the equations. I used x + y = 8 because that was simplier to find one of the variables from. From there, you can substitute that in for the variabel in the secone equation.
3x - 2y = -6
3x - 2(8 - x) = -6
3x - 16 + 2x = -6
5x - 16 = -6
5x = 10
x = 2
Than you can use that and plug it back into one of the original equations to find the other variable.
x + y = 8
2 + y = 8
y = 6
Given: KLMN is a trapezoid, KL=MN, angle 1 = angle 2, LM/KN = 8/9, Perimeter = 132. Find the length of the legs
Answers
Answer:The length of midsegment is 34 units.
Given data:
The trapezoid KLMN, Such that KL = MN.
And , LM/KN = 8/9
Also, perimeter of KLMN = 132 units.
To find:
The length of midsegment (KM).
In the given problem, we can observe that KM is a transversal relative to parallel lines LM and KN. Which means,
Clearly, two base angles are equal. So, the triangles KLM and KMN are isosceles.
Taking the ratios of sides of two triangles as,
= KL : LM : MN : KN
= 8 : 8 : 8 : 9
The sum of ratio units is, 8 + 8 +8 +9 = 33. Then, the value of each ratio is,
Then the length of segment LM is,
And, length of segment KN is,
Then, the length of midsegment KM is obtained by taking the average of LM and KN as,
Thus, the length of midsegment is 34 units
Step-by-step explanation:
which equation is equialent to 60% of 25? choose all that apply
Answers
Because 60% of 25 is 15 and they equal 15
Four students were given dot to create. Sketch the dot plots in questions 1-4. Then use the clues in A-D to determine each student's data set.
Answers
Answer:
Step-by-step explanation:
please help me with this i dont really knwo how to calculate it
thank you :D
Answers
Answer:
p = (4 × 2401) × 121 = ( 9604 × 121) = 1162084
q = (9 × 125) × 14641 = (1125 × 14641) = 16471125
LCM of 1162084 = 2324168 , 3486252 , 4648336 , 5810420 , 6972504
LCM of 16471125 = 32942250 , 49413375 , 65884500
Step-by-step explanation:
please help me on this because I'm stressed right now
Answers
500 * 1/8 =
500/8=
62.5 or 63
Answer:
D. 63
Step-by-step explanation:
500 * 1/8 = 62.5
62.5 lightsbulbs do not exist soo we round up to 63
Figure B has a total area of 75 in squared.
Answers
Answer: and what do I answer
Step-by-step explanation:
Answer:
[tex]
\begin{gathered}A=\underbrace{\begin{pmatrix}1&2\\4&3\end{pmatrix}}_{M_1}\underbrace{\begin{pmatrix}6&1&5\\7&3&4\end{pmatrix}}_{M_2}\end{gathered}[/tex]
Just Trying out this latex
18 divided by 3600 28pts
Answers
Step-by-step explanation:
The answer would be 200!
Answer:
200
Step-by-step explanation:
Please help! First right answer gets 20+
Answers
Answer:
276 3/8
Step-by-step explanation:
You might be able to simplify a little more but this is the answer
hope this helps
-8 1/3 + 3 2/5
lol i need a refresh when you multiply the fraction to get it to be added with the other one do you multiply the whole number too?
Answers
Answer:
-81/3+32/5
-81×5+32×3/15
-243+96/15
-147/15
-49/5 Ans
To answer your question ("do you multiply the whole number too?"): Yes, you have to multiply the whole number as well. You can't just separate 1/3 from -8 and multiply it with 2/5, because the whole number is part of the mixed #. Whenever you multiply, add, divide, subtract, or do anything to two mixed numbers, you must include the whole term.
- - - - - - - - - -
Now your question is addition. Like I said, when you add them together, the whole number and the fractions count as one term.
So basically, -8 1/3 + 3 2/5...
- - - - - - - - - -
1) Find the LCM (least common multiple) of the denominators
The LCM of 3 and 5 is 15. To get from 3 to 15, you have to multiply 3 by 5. Now multiply the numbers of the fraction part only by 5.
1/3 --> 5/15 (as you can see, 1x5 = 5, 3x5 = 15)
Now for 2/5: To get from 5 to 15, multiply 5 by 3. Do the same thing to the numbers in the fraction
2/5 --> 6/15 (2x3 = 6, 5x3 = 15)
***TO CLARIFY, DO NOT MULTIPLY THE WHOLE TERM BY THE NUMBER***
Right: 2x3 = 6, 5x3 = 15, 6/15
Wrong: 2/5 x 5 = 2
- - - - - - - - - -
2) So now that we found a common denominator, change the two terms to -8 5/15 + 3 6/15 (because we had to find the LCM to make life a lot easier)
- - - - - - - - - -
3) We just add them together. Even though they are a term together, you can split them apart and add them together separately thanks to the commutative property of addition*.
Time to split it apart to make life a whole lot easier. -8 5/15 can be split apart into the two terms -8 and 5/15. For 3 6/15, it can be split into 3 and 5/15.
Two options from here on:
Set up a single equation: Put all the terms into one equation. -8 + 3 + 5/15 + 6/15. Solve by adding all the terms together in whichever order you prefer (again, thanks to the commutative property of addition)
It would result in the answer -4 4/15
Or...
Set up two separate equations: Set up an equation for whole numbers, and another one for fractions.
Equation 1: -8 + 3 = -5
Equation 2: 5/15 + 6/15 = 11/15
(6 + 5 = 11)
And we add the sums together. -5 + 11/15 = -4 4/15
And that's it!
- - - - - - - - - -
*Commutative Property of Addition: The sum of the numbers will NOT change even if you change the order of the addends
Was an hour late, but I hope this still helped you! If there are any questions, just comment below this
Triangle
ABC with vertices A(-6, -8), B(0, 4), and C (-6, 10) is dilated so that A’ is
now (-15, -20). What was the
dilation, and where are B’ and C’?
Answers
Answer:
scale factor = 2.5 and b` is now (0,10) and c` is (-15, 25)
Step-by-step explanation:
You first want to divide -15 and -6, the x values of a and a`. this will give you the scale factor. then multiply every other number by the scale factor to get the points for b` and c`.
(not sure if this is right but this is how i learned)
Approximate square root 18 to the nearest hundredth. Be sure to show all of your work.
Answers
Answer:
The square root of 18 with one digit decimal accuracy is 4.2.
Step-by-step explanation:
Answer:
4.24 (nearest hundredth)
Step-by-step explanation:
Step 1
Square numbers: 1, 4, 9, 16, 25, 36, ...
Find the perfect squares either side of 18:
16 and 25As [tex]\sf \sqrt{16}=4[/tex] and [tex]\sf \sqrt{25}=5[/tex] then [tex]\sf 4 < \sqrt{18} < 5[/tex]
Step 2
Divide 18 by one of the two square roots in step 1 (4 or 5):
⇒ 18 ÷ 4 = 4.5
Step 3
Find the average of the root (4) and the result (4.5):
[tex]\sf \implies \dfrac{4+4.5}{2}=4.25[/tex]
Repeat steps 2 and 3:
Divide 18 by the solution of step 3. Then find the average of this and the solution of step 3:
⇒ 18 ÷ 4.25 = 72/17
[tex]\sf \implies \dfrac{4.25+\frac{72}{17}}{2}=\dfrac{577}{136}=4.242647059[/tex]
Repeat:
⇒ 18 ÷ 577/136 = 2448/577
[tex]\sf \implies \dfrac{\frac{577}{136}+\frac{2448}{577}}{2}=4.242640687[/tex]
As the approximate square root needs to be to the nearest hundredth, we do not need to keep repeating the steps.
Therefore, √18 ≈ 4.24 (nearest hundredth)
helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
the Answer is 4
Step-by-step explanation:
Draw a open circle on 4 and a straight line 5-10
At noon, a team bus left City College for their opponent's school. Soon thereafter, City's first-line player Brett Starr arrived at the gym. A loyal day-student parent volunteered to overtake the bus and deliver Brett. The two left at 12:15 pm. The parent drove at 54 mph, while ahead of them the yellow bus poked along at 48 mph. Did the car catch the bus before it reached the game, which is 110 miles from City college? If so, where and when?
Answers
Answer:
No, the car didn't catch the bus, as their time and distance traveled doesn't intersect when portrayed on a graph.
Step-by-step explanation:
It would take the car approximately 2.14 hours to catch up to the bus. Since the car left at 12:15 pm, it should have caught up to the bus at 2:29 pm.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
Yes, the car was able to catch up to the bus before it reached the game. With the car travelling at 54 mph and the bus travelling at 48 mph, the car is travelling 6 mph faster than the bus. In order to calculate how long it would take for the car to catch the bus, we use the formula for average speed:
Average speed = (speed of car + speed of bus) / 2
Average speed = (54 mph + 48 mph) / 2
Average speed = 51 mph
Now, we can use the formula for distance travelled over time to calculate how long it would take the car to travel the 110 miles to the game:
Distance = Rate x Time
110 miles = 51 mph x Time
Time = 110 miles / 51 mph
Time = 2.14 hours
Therefore, it would take the car approximately 2.14 hours to catch up to the bus. Since the car left at 12:15 pm, it should have caught up to the bus at 2:29 pm.
Learn more about the average speed here:
brainly.com/question/9834403.
#SPJ2
Which meal is your favorite: breakfast, lunch, or dinner?
choice question
Answers
Step-by-step explanation:
lunch :DDDDDDDDDDDDDDDD
Answer:
My favorite meal is Breakfast
Step-by-step explanation:
HELP ASAP PLEASE NEED STEP BY STEP
Answers
Answer:
I BELIVE ITS ROUNDED TO SOME LIKE $37.87
Step-by-step explanation:
is ther answer choices
If you roll a fair number cube 30 times, what is the experimental probability of rolling a 2
Answers
Answer:
1/6 chance or 16.667% chance
Step-by-step explanation:
a fair number cube has six sides so if you roll that 30 times that's 180 sides and the probability of rolling a 2 out of a single dice is 1/6 and since 180 * 1/6 is equal to 30 that is 30 out of 180 which is 1/6
please help! unrelated comment/answer = report
Answers
200.96
Explanation:
First you do r squared which is 8x8 to get 64. Then you do 64x3.14 to get 200.96
hope this helps
i did A = 3(8)^2
beinggreat78 answer fast please :')
Answers
Answer:
17662.5 sq. feet
Step-by-step explanation:
We know that the formula for Area of a Circle is [tex]A = \pi (r)^2[/tex].
r = radius; d = diameter, which is r*2
And so, in the question, it gives you that the diameter is 150, first we divide it by 2 to get the radius.
150/2 = 75
The question said to keep [tex]\pi[/tex] =3.14, so then we plug in the equation-
[tex]A = 3.14 * 75^2[/tex]
Then we use PEMDAS [Parenthesis; Exponents; Multiply & Divide; Add & Subtract] which would get us-
[tex]A = 3.14 * 5625[/tex] (first doing the Exponent)
And we continue-
[tex]A = 17662.5[/tex] (then multiple)
So our answer is-
17662.5 sq. feet
I hope this helps!
Please give brainliest!
Have a great day
Please give step by step I’ll give u Brainly or whatever it is
Chantelle deposits $7,500 into the bank. she does not withdraw or deposit money 6 years. She earns 6% interest during that time.
a. How much interest will she have earned at the end of 6 years?
B. What will the balance be when she is finally able to withdraw her money?
Answers
Step-by-step explanation:
p=7500*100=750000
t=6yrs
r=6%
I=p*t*r/100
=750000*6*6/100
=270000
=270000/100
=$2700
Jasmine unfolded a cardboard box. The figure of the unfolded box is shown below:
A long rectangle divided along the length into 4 equal squares is shown. Along the upper edge length of the second square is shown another square, and along the lower edge length of the fourth square is shown another square. The first square from the left has two adjacent sides labeled as 2 inches each.
Which expression can be used to calculate the area of cardboard, in square inches, that was used to make the box?
2 x 6 x 6
6 x 1 x 1
6 x 2 x 2
1 x 6 x 6
Answers
Answer:6x2x2
Step-by-step explanation:
Mona had $20.00. She bought one loaf of bread for $2.25, a gallon of milk for $4.39, and a carton of eggs for $1.19. How much change should she get back?
Answers
Answer:
She should get $12.17 in change.
Step-by-step explanation:
20- 2.25 = 17.75
17.75 - 4.39 = 13.46
13.46 - 1.19 = 12.17
HGD
-ghost
17.75 - 4.39 = 13.36
13.36 - 1.19 = 12.17
She should get back $12.17 worth of change
Write (5x-2)^2 as a trinomial in expanded form.
Answers
Answer:
25x^2 - 20x + 4