Answer:
Option (4)
Step-by-step explanation:
The given system of equations is,
y = -2x + 4 ------ (1)
6x + 3y = a --------(2)
We have to find the value of a for which the system of equations will have infinitely many solutions.
Option (1). If a = -12
6x + 3y = -12
2x + y = -4
y = -2x - 4
Both the equations have same slope, therefore, they are parallel and will have no solutions.
Option (2). If a = -4
6x + 3y = -4
3y = -6x - 4
[tex]y=-2x-\frac{4}{3}[/tex]
Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.
Option (3). If a = 4
6x + 3y = 4
3y = -6x + 4
y = -2x + [tex]\frac{4}{3}[/tex]
Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.
Option (4). If a = 12
6x + 3y = 12
3y = -6x + 12
y = -2x + 4
Therefore, both the equations (1) and (2) are same for a = 12 and they will have infinitely many solutions.
This question is based on system of linear equation .Thus, for a=12 will have infinitely many solution.
Given:
y = -2x + 4 ------ (a)
6x + 3y = a ------(b)
We need to determined the value of a for which the system gives infinitely many solution.
Now check all the options as given below:
Option(1) a = -12 and put it in (b) we get,
6x + 3y = -12
2x + y = -4
y = -2x - 4
Both the equations have same slope, therefore, they are parallel to each other and have no solutions.
Option(2) a= -4 and put it in (b) we get,
6x + 3y = -4
3y = -6x - 4
[tex]y=-2x-\dfrac{4}{3}[/tex]
Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.
Option(3) a= 4
6x + 3y = 4
3y = -6x + 4
[tex]y=-2x+\dfrac{4}{3}[/tex]
Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.
Option(4) a= 12
6x + 3y = 12
3y = -6x + 12
y = -2x + 4
Both the equation are same for a= 12.
Thus, for a=12 will have infinitely many solution.
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Which event is most likely to occur? *
A. Flipping a fair coin, with sides labeled heads and tails, and the coin landing on tails.
B. Choosing a marble out of a bag, with nine blue marbles and one red marble, and the marble being red.
C. Rolling a fair number cube, with faces labeled one to six, and the cube landing a number less than six.
D. Spinning the arrow on a spinner, with four equal sectors labeled one to four, and the arrow landing on a number greater than one.
Answer:
C. Rolling a fair cube, with faces labeled one to six, ans the cube landing a number less than six.
Step-by-step explanation:
A. flipping a fair coin, and the coin landing on tails, has only got a 50% chance
B. Picking a red marble has only got 10% chance
C. Rolling the cube and getting a number less than 6 has got 5/6 chance, as, from one to six, 5 numbers are less than six.
D. the spinning an arrow similation has only got a 75% chance.
since 5/6 is greater than 3/4, Simulation C is more likely to occur
The event which is most likely to occur is Rolling a fair number cube, with faces labeled one to six, and the cube landing a number less than six, correct option is C.
What is the probability?
Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes.
We are given that;
A coin flip, bag of marbles, A fair number cube, an arrow spinner
Now,
The probability of an event is defined as the number of ways the event can occur divided by the total number of possible outcomes.
A. The probability of flipping a fair coin and getting tails is 1/2.
B. The probability of choosing a red marble out of a bag with nine blue marbles and one red marble is 1/10.
C. The probability of rolling a number less than six on a fair number cube is 5/6.
D. The probability of spinning the arrow on a spinner and landing on a number greater than one is 3/4.
Comparing the probabilities, we see that option C has the highest probability, with a probability of 5/6.
Therefore, by probability answer will be rolling a fair number cube and getting a number less than six is the most likely event to occur.
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solution of the system of equations.
4x + 5y = 13
W
8x + 7y = 11
Answer:
so the answer is y=5,x=-3
A long-distance delivery truck averages 8 miles per gallon when the truck is full. The miles per gallon improves by 20% when the truck is empty. Which expression represents the amount of gasoline used (g) in terms of the number of miles driven when full (mf) and the number of miles driven when empty (me)?
Answer:
When the truck is full: [tex]g_{mf} = \frac{m}{8}[/tex]
When the truck is empty: [tex]g_{me} = \frac{m}{9.6}[/tex]
Step-by-step explanation:
When the truck is full for every eight miles traveled by the vehicle, there is a cost of one gallon of fuel, therefore for every mile the cost is one eight of a gallon, with this information we can create the following expression:
[tex]g_{mf} = \frac{m}{8}[/tex]
Where m is the number of miles traveled by the truck.
When the vehicle is empty, it's performance improves by 20 %, which means that for the same amount of fuel it'll travel a distance 120% of the previous one. Therefore we need to multiply 1.2 on the denominator of the last expression:
[tex]g_{me} = \frac{m}{8*1.2}\\\\g_{me} = \frac{m}{9.6}[/tex]
The expression represents the amount of gasoline used (g) is,
When the truck is full (mf) is represented as [tex]m_f = \dfrac{m}{8}[/tex],
And when the truck is empty (me) is represented as, [tex]m_e = \dfrac{m}{9.6}[/tex]
Given that,
A long-distance delivery truck averages 8 miles per gallon when the truck is full.
The miles per gallon improve by 20% when the truck is empty.
We have to determine,
Which expression represents the amount of gasoline used (g) in terms of the number of miles driven when full (mf) and the number of miles driven when empty (me).
According to the question,
The amount of gasoline used (g) in terms of the number of miles driven when full (mf),
And The distance delivery truck averages 8 miles per gallon when the truck is full.
The amount of gasoline when the truck is full is represented as,
[tex]m_f = \dfrac{m}{8}[/tex]
Then,
The miles per gallon improve by 20% when the truck is empty.
The number of miles driven when empty is represented as,
[tex]m_e = \dfrac{m}{8 + 8 \times 0.20}\\\\m_e = \dfrac{m}{8+ 1.6}\\\\m_e = \dfrac{m}{9.6}[/tex]
Hence, The expression represents the amount of gasoline used (g) is,
When the truck is full (mf) is represented as [tex]m_f = \dfrac{m}{8}[/tex],
And when the truck is empty (me) is represented as, [tex]m_e = \dfrac{m}{9.6}[/tex].
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The number of viewers for a new television show are modeled by the following function, where V(t) represents the number of
viewers, in tens of thousands, and t represents the number of months since the show's debut.
V(t) = -8\n(t + 1) + 50
What does the y-intercept of V(t) represent?
Answer: 10000.23
Step-by-step explanation:
Solve for q.
0.48 + 5.7q = 6.3q
q =
Answer:
[tex] \boxed{q = 0.8} [/tex]
Step-by-step explanation:
[tex] = > 0.48 + 5.7q = 6.3q \\ \\ = > 6.3q = 5.7q + 0.48 \\ \\ = > 6.3q - 5.7q = 0.48 \\ \\ = > 0.6q = 0.48 \\ \\ = > q = \frac{0.48}{0.6} \\ \\ = > q = 0.8[/tex]
Answer:
q = 0.8
Step-by-step explanation:
isolate the variable and solve
In pentagon $MATHS$, $\angle M \cong \angle T \cong \angle H$ and $\angle A$ is supplementary to $\angle S$. How many degrees are in the measure of $\angle H$?
Answer:
H = 120°
Step-by-step explanation:
The sum of the internal angles of a polygon with n sides is given by the formula:
S = (n-2)*180
So, for a pentagon, we have n = 5, then:
S = (5-2)*180 = 540°
So we have that:
M + A + T + H + S = 540° (eq1)
M = T = H (eq2)
A + S = 180° (eq3)
Using the second and third equation in the first one, we have:
H + H + H + 180 = 540
3H = 360
H = 120°
put the fractions in order smallest to largest
7/10, 2/3 , 4/5, 11/15
Answer:
Step-by-step explanation:
2/3, 7/10, 11/15, 4/5
These tables of values represent continuous functions. For whichfunction
will the y-values be the greatest for very large values of x?
PLEASE HELP!!!
I think it's B because it contains the highest numbers
Answer:
D
Step-by-step explanation:
The answer is D because every time x increase by 1, the y is tripling. Making it so that as x gets larger and larger, the y will become the larger than the other choices.
An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
< 12.5, x > 18.9
12.5 < x < 18.9
x < 6, X > 26
6
26
Answer:
I'm not sure but I think the second one. 12.5 < x < 18.9
Step-by-step explanation:
Answer:
B. 12.5 < x < 18.9
Step-by-step explanation:
on edge
What is 4575 rounded to the nearest thousand
Answer:
5000 because you round up
Answer:
5000
Step-by-step explanation:
you round up since the second number is higher then 4
How to graph inequalities
Answer:
1) Rearrange the equation so "y" is on the left and everything else on the right.
2) Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
3) Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).
Step-by-step explanation:
In the figure above circles with centre o and o' are externally tangent at P. I f OA= 5 is a tangent to circle centre o', the area of rectangle oklm is Brainly
Answer:
give me points pls
Step-by-step explanation:
Kurt's truck uses 12 gallons of gas to travel 156 miles. He has 6 gallons in the tank. How much more gas will he need to drive 351 miles?
Answer:
it will be 27 gallons
Step-by-step explanation:
if we take the gallons number is x
then x=[tex]\frac{351*12}{156}[/tex]
Assigned Media
Skill Builder
X 2.4.75
The telephone company offers two billing plans for local calls. Plan 1 charges $36 per month for unlimited calls and Plan 2 charges $17 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2
b. Explain the meaning of the answer to part a.
Answer: a. 36-17 <0.04x ⇒ 475 < x
b. When the number of calls is higher than 475 , Plan 1 is more economical than Plan 2.
Step-by-step explanation:
Hi, to answer this question we have to write an inequality:
The cost of plan 1 (36) must be less (<) than the cost of plan 2 (fixed charge [17] plus the product of the charge per call [0.04] and the number of calls [x] )
a.36 < 17+ 0.04x
Solving for x
36-17 <0.04x
19 < 0.04x
19 /0.04 <x
475 < x
b. When the number of calls is higher than 475 , Plan 1 is more economical than Plan 2.
In Haley's favorite video game, players stack blocks to create buildings. Haley builds a fort shaped like a cube. Haley's fort has a length, width, and height of 9 meters. What is the volume of Haley's fort?
Answer:
729 cubic meters
Step-by-step explanation:
Volume of cube is given by side^3
where side is length of the side
Given in the problem
side is 9 meters as length, width, and height of fort is 9 meters and it is in cube shape .
Thus,
volume of cube = 9^3 = 9*9*9 = 729
Thus, volume of Haley's fort is 729 cubic meters.
Please answer correctly !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!
Answer:
-10
Step-by-step explanation:
-(x-5) ^2+25
-x+5^2+25
-5 -5
-x^2+20
-2x+20
---- ----
-2 -2
x=-10
// have a great day //
how do you rotate this for it to look the same.
Answer:
90°
Step-by-step explanation:
when u rotate it up to 90° I think it will look the same
What is m∠BCD? A. 82 degrees B 168 degrees C. 192 degrees D. 220 degrees
Answer:
m∠BCD = 82°
Option A
Step-by-step explanation:
The opposite angles of quadrilateral inscribed in a circle are supplementary.
i.e m∠A +m∠C = 180°
or, m∠BAD + m∠BCD= 180°
or, 98° + m∠BCD = 180°
or, m∠BCD = 180°-98°
or,m∠BCD = 82°
Answer: A - 82
Step-by-step explanation:
180 - 98 = 82
took the test and got it right.
This tally below shows the number of times that Jim and rob won games of checkers. What is the experimental probability that rob beats jim in future games? Jim: IIIIIIII ROB: IIIIII
if A=13 and B=10, find C. Pythagorean theorem.
Answer:
C = √269
C ≈ 16.4
Step-by-step explanation:
Use the Pythagorean Theorem to solve for 'c'.
[tex]a^2+b^2=c^2[/tex]
We are given:
'a' = 13
'b' = 10
Replace the variables with the appropriate values and solve for 'c':
[tex]13^2+10^2=c^2\\\rightarrow 13^2=169\\\rightarrow 10^2=100\\169+100=c^2\\269=c^2\\\sqrt{269}=\sqrt{c^2}\\\boxed {16.40122... = c}[/tex]
16.4012195 ≈ 16.4
C is about 16.4.
On any particular Saturday evening, the probability that Hannah will go to the movies and go for a coffee is 1/3. The probability that she will go for a coffee, given that she has gone to the movies, is 4/7.
What is the probability that she will go to the movies on any particular Saturday evening
Answer:
7/20
Step-by-step explanation:
Which linear function has the steepest slope? On a coordinate plane, a line goes through points (0, 3) and (4, 2). y = negative 0.1 x minus 5 A 2-column table with 5 rows. Column 1 is labeled x with entries negative 4, negative 2, 0, 2, 4. Column 2 is labeled y with entries 0, 0.5, 1.0, 1.5, 2.0. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 6, negative 2, 1, 7, 9. Column 2 is labeled y with entries 6.6, 4.2, 2.4, negative 1.2, negative 2.4.
Answer:
Its answer d
Step-by-step explanation:
I took the quiz
A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, negative 28.
A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, and 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, and negative 28.
The answer is option D.
What is the slope of a linear function?Slope measures the rate of change in the dependent variable as the independent variable changes. The greater the slope the steeper the line. Consider the linear function: y = a + bx. b is the slope of the line.
What does a steeper slope mean?A steeper slope in a graph means that the rate of change is faster.
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Yumi conducted a survey at her school in which she asked her fellow students several questions about their interests and preferences. One of the questions in her survey was, “what is your favorite sport?” Yumi displayed the responses to this question in the circle graph shown.
Answer:
70
Step-by-step explanation:
15% said hockey and 10% said gymnastics which together is 25% of the students.
25% of 280 is 70.
What is the mean absolute deviation of this data set?
4, 8 , 3, 8, 7, 10, 9
Answer: Mean Absolute Deviation (MAD): 7
Hope this helps u!
Have a good day and stay safe!
Answer:
7
Step-by-step explanation:
[tex]\frac{3+4+7+8+8+9+10}{7}[/tex]
[tex]\frac{49}{7}[/tex]
49 ÷ 7 = 7
please help quick !!
-0.45 x + 0.33 = -0.66
Adding -0.33 to both sides
-0.45 x = -0.99
Dividing both sides by -0.45
x = -0.99 / -0.45 = 2.2
Answer: x = 2.2, last choice
jenny can walk 0.25 miles in 12 minutes.how far can she walk in an hour
Answer:
1.25 miles
Step-by-step explanation:
hour is 60 minutes
[tex] \frac{60}{12} = 5[/tex]
[tex]0.25 \times 5 = 1.25[/tex]
Find the value of x in the triangle shown below
Find the shadow cast of a 10 foot lamp post when the angle of elevation of the sun is 58°. Find the length of the nearest tenth of a foot. please help
Answer:
Length of the shadow = 6.25 foot
Step-by-step explanation:
Given: A lamp post is of 10 foot
To find: length of the shadow cast of a lamp post when the angle of elevation of the sun is 58°
Solution:
Trigonometric ratios explain the relationship between the angles and sides of the triangle.
For any angle [tex]\theta[/tex],
[tex]tan\theta=[/tex] side opposite to [tex]\theta[/tex]/side adjacent to [tex]\theta[/tex]
In ΔABC,
[tex]tanC=\frac{AB}{BC}[/tex]
Put [tex]AB=10\,\,foot\,,\,\angle C=58^{\circ}[/tex]
[tex]tan58^{\circ}=\frac{10}{BC}\\BC=\frac{10}{tan58^{\circ}}\\=\frac{10}{1.6}\\=6.25\,\,foot[/tex]
So,
length of the shadow = 6.25 foot
Boris eats 1/5 of the cake. Maziy eats one fifth of the cake. Sanjay and Silas eat 1/5 of the cake And jack also has 1/5 of the cake is there any cake left?
Answer:
Yes.
Step-by-step explanation:
We have to first find how much of the whole cake (1) that they all ate.
Boris eats 1/5 of the cake.
Maziy eats 1/5 of the cake.
Sanjay and Silas eat 1/5 of the cake.
Jack also has 1/5 of the cake.
The total fraction of cake eaten was:
1/5 + 1/5 + 1/5 + 1/5 = 4/5
Therefore,the fraction of the cake left is:
1 - 4/5 = 1/5
Yes, there is cake left.
12 less than a number y
Answer: y- 12
Step-by-step explanation:
12 is less than y so is like 12 being subtracted from y.