Answers
Answer: A - one solution, B - Infinite solutions, C - no solutions
Step-by-step explanation:
Solutions of linear equations are any points at which both lines intersect. The point of intersection provides a point that lies on both lines and satisfies both equations - hence why it is called a "solution" to the system of equations.
In the first diagram, the lines intersect once. There is only one solution to this system of equations at (2, 4).
In the second diagram, the lines are identical. They intersect for any possible value, meaning it has infinite solutions.
In the third diagram, the lines are parallel. They will stretch to infinity without ever intersecting each other, so this system has no solution.
Related Questions
I don’t know how to find this out
Answers
Answer:
C many solutions
Have a good day !what is the slope of the line passing through (13,-2) and (3,-2)
Answers
Answer:
Slope (m) =0
Slope (m) =
ΔY
ΔX
= 0
θ =
arctan( ΔY )
ΔX
= 0°
ΔX = 3 – 13 = -10
ΔY = -2 – -2 = 0
Distance (d) = √ΔX2 + ΔY2 = √100 = 10
What is the solution to the linear equation? 2/4x - 1/2 = 1/3 + 5/6x
Answers
Answer:
x=-60/24 or -5/2
Step-by-step explanation:
u have to find X
2/4x - 1/2 = 1/3 + 5/6x
subtract 2/4x from both sides
to do that u need to have common denominator
2/4= 6/12
5/6=10/12
-1/2=1/3+4/12x
subtract 1/3 on both sides and u need common denominator
-1/2=-3/6
1/3=2/6
-5/6=4/12x
multiply 12/4 on both sides
x=-60/24
Answer:
x=-5/2
Step-by-step explanation:
2/4x-1/2=1/3+5/6x
-5/6x -5/6x
2/4x-5/6x-1/2 =1/3
+1/2 +1/2
6/12x-10/12x=2/6+3/6
-4/12x=5/6
x=5/6:(-4/12)=5/6*(-12/4)=-5/2
x=-5/2
Express 27 1/3 in simplest radical form
Answers
Answer:
this answer is attached to the picture
Radical function or values are values inside the square root. This shows that the cube root of the given value is 3
Radical functionRadical function or values are values inside the square root. For instance;
√a is a radical function.
According to the law of indices
a^1/3 = ∛a
Given the expression
27^1/3 = ∛27
∛27 = 3
This shows that the cube root of the given value is 3
Learn more on radical function here:https://brainly.com/question/13430746
In the problem 8^3 - 10 × 5 - 4
Answers
Answer: 458
Simplify
8³=8×8×8
Multiply
8×8×8=512
10×5=50
Subtract
512-50=462
462-4=458
Answer:
458
Step-by-step explanation:
8×8×8=512
10×5=50
512- 50 = 462
462-4= 458
factorise x square - 7 x minus 42
Answers
Answer:
x =(7-√217)/2=-3.865
x =(7+√217)/2=10.865 mark brainliest please
Step-by-step explanation:
Factoring x2-7x-42
The first term is, x2 its coefficient is 1 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -42
Step-1 : Multiply the coefficient of the first term by the constant 1 • -42 = -42
Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is -7 .
-42 + 1 = -41
-21 + 2 = -19
-14 + 3 = -11
-7 + 6 = -1
-6 + 7 = 1
-3 + 14 = 11
-2 + 21 = 19
-1 + 42 = 41
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 7x - 42 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-7x-42
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.5000
Plugging into the parabola formula 3.5000 for x we can calculate the y -coordinate :
y = 1.0 * 3.50 * 3.50 - 7.0 * 3.50 - 42.0
or y = -54.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-7x-42
Axis of Symmetry (dashed) {x}={ 3.50}
Vertex at {x,y} = { 3.50,-54.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-3.87, 0.00}
Root 2 at {x,y} = {10.87, 0.00}
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-7x-42 = 0 by Completing The Square .
Add 42 to both side of the equation :
x2-7x = 42
Now the clever bit: Take the coefficient of x , which is 7 , divide by two, giving 7/2 , and finally square it giving 49/4
Add 49/4 to both sides of the equation :
On the right hand side we have :
42 + 49/4 or, (42/1)+(49/4)
The common denominator of the two fractions is 4 Adding (168/4)+(49/4) gives 217/4
So adding to both sides we finally get :
x2-7x+(49/4) = 217/4
Adding 49/4 has completed the left hand side into a perfect square :
x2-7x+(49/4) =
(x-(7/2)) • (x-(7/2)) =
(x-(7/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-7x+(49/4) = 217/4 and
x2-7x+(49/4) = (x-(7/2))2
then, according to the law of transitivity,
(x-(7/2))2 = 217/4
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(7/2))2 is
(x-(7/2))2/2 =
(x-(7/2))1 =
x-(7/2)
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-(7/2) = √ 217/4
Add 7/2 to both sides to obtain:
x = 7/2 + √ 217/4
Since a square root has two values, one positive and the other negative
x2 - 7x - 42 = 0
has two solutions:
x = 7/2 + √ 217/4
or
x = 7/2 - √ 217/4
Note that √ 217/4 can be written as
√ 217 / √ 4 which is √ 217 / 2
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-7x-42 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -7
C = -42
Accordingly, B2 - 4AC =
49 - (-168) =
217
Applying the quadratic formula :
7 ± √ 217
x = —————
2
√ 217 , rounded to 4 decimal digits, is 14.7309
So now we are looking at:
x = ( 7 ± 14.731 ) / 2
Two real solutions:
x =(7+√217)/2=10.865
or:
x =(7-√217)/2=-3.865
Answer:
x^2 - 7x - 42
x^2 - x (21 - 14 ) - 42
x^2 - 21x + 14x -42
7x ( x - 3) + 14 ( x- 3)
(x -3) (7x + 14)
hope this helps you
When Mr. Shelton preheated his oven, the oven's temperature rose 3 degrees in 1/6
of a minute. At that rate, how much will the oven heat up in 1 minute?
Answers
Answer:
Step-by-step explanation:
18 degrees
Is 8/6 equivalent to 16/12 as a ratio
Answers
Answer:
they are equivalent
Step-by-step explanation:
8/6
Divide the top and bottom by 2
4/3
16/12
Divide the top and bottom by 4
4/3
They are the same so they are equivalent
You can simply 16/12 to either 8/6 or 4/3.
^ You can divide by 2 or multiply by 2.
8x2= 16
6x2=12
8/6 = 16/12
Maren used the table shown to find a ratio which is equivalent to 2:6.
A multiplication table.
Which ratio is equivalent to 2:6?
8:18
8:24
10:36
10:42
Answers
8:24
Step by step:
2:6 = 8:24 because 2•4=8 and 6•4=24, so the reason they are equivalent to each other is because they are both multiplied by 4.
Answer:
8:24
Step-by-step explanation:
dont ask me
Which of the following is always true of the vertical angles formed by
perpendicular lines? Check all that apply.
A. They are congruent.
B. They are right angles.
C. They are acute.
D. They are obtuse.
Answers
Answer:
A
Step-by-step explanation:
This is because vertical angles are always congruent, they cross diagonally which makes them equal to each other.
When two perpendiculars line intersect the angles formed must be a right angle. Hence option b is correct.
What is angle?The angle can be defined as the one line inclined over other line.
Here, When perpendicular lines intersect each other the angle formed between them is 90 degree. So the angles are right angles.
Thus, when two perpendiculars line intersect the angles formed must be a right angle.
Learn more about angles here:
https://brainly.com/question/13954458
#SPJ2
Please help! Correct answer only!
I've been on this question for more than an hour...
You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking a 3 and then picking a 3?
Simplify your answer and write it as a fraction or whole number.
Answers
Answer:
You have three card : 3, 4, 5 and 6.
You first pick one card randomly, the probability of picking a 3 is:
P = 1/4
You then pick a second card without putting the first card back, the probability of picking a 3 is:
P = 1/3
=> The probability of picking a 3 and then picking a 3:
P = (1/4) x (1/3) = 1/12
Hope this helps!
:)
Find 3 rational numbers between ¼ and ½
Answers
Answer:
5/16 and 3/8 are two
Step-by-step explanation:
idk a third
Your Monthly Net Pay
If your gross monthly income will be $3,750, you need
to determine the net pay for your monthly budget.
Your monthly net pay is
Monthly gross pay
$3,750
Federal withholding
$238.00
Social Security
$232.50
Medicare
$54.38
State tax
$236.00
Net pay
$?
Answers
Answer:
2989.12
Step-by-step explanation:
238.00+232.50+54.88+236.00= 760.88
3750-760.88=2989.12
In how many ways can a
recorder, facilitator, and
questioner be chosen in a club
containing 14 members?
Answers
Answer:
The answer is 364. There are 364 ways of choosing a recorder, a facilitator and a questioner froma club containing 14 members.
This is a Combination problem.
Combination is a branch of mathematics that deals with the problem relating to the number of iterations which allows one to select a sample of elements which we can term "r" from a collection or a group of distinct objects which we can name "n". The rules here are that replacements are not allowed and sample elements may be chosen in any order.
Step-by-step explanation:
Step I
The formula is given as
[tex]C (n,r) = \frac{n}{r} = \frac{n!}{(r!(n-r)!)}[/tex]
n (objects) = 14
r (sample) = 3
Step 2 - Insert Figures
C (14, 3) = [tex](\frac{14}{3})[/tex] = [tex]\frac{14!}{(3!(14-3)!)}[/tex]
= [tex]\frac{87178291200}{(6 X 39916800)}[/tex]
= [tex]\frac{87178291200}{239500800}[/tex]
= 364
Step 3
The total number of ways a recorder, a facilitator and a questioner can be chosen in a club containing 14 members therefore is 364.
Cheers!
hey everyone! can u guys please help i really struggle in math and i just need some help
i will follow and mark u as brainleist even if u know a friend or google that could help me
thanks everyone and have a great corona time day
Answers
Answer:
d= 5.2
[][][]-[][][]
P = √5.2 ^3
P = √5.2 × 5.2 × 5.2
P = √140.608 (plug into calculator)
P = 11.857824421
P = 11.86
The orbital period of Jupiter is 11.86 Earth years.
Can someone please help me with this question
Answers
Answer:
u = -4w+9
Step-by-step explanation:
u - 5 = -4(w-1)
Distribute
u - 5 = -4w +4
Add 5 to each side
u -5+5 = -4w +4+5
u = -4w+9
Find the volume of the given
shape.
2 points
5cm
3.5cm
6cm
Answers
Answer:
to find volume you multiply length x width x height
Step-by-step explanation:
5 x 3.5 x 6= 105
Answer:
5 x 3.5 x 6= 105
Step-by-step explanation:
PLZZZ give me brainliest
Pleaseee helpp i will let you brainlest
Answers
Answer:
13
Step-by-step explanation:
use Pythagorean
it is usually, 5, 12, 13
Explanation:-
2 2
Hypotenuse (x) = 12 + 5
= 144 + 25
= 169 route is
= 13
Use the Distributive Property to determine which of the following statements is equivalent to 5(6 – 1).
A. 6 - 1
B. 5 • 5
C. 30 - 5
D. 11 - 5
Answers
[tex]\text{You would use the distributive property to get your answer} \\\\\text{This means that you would distribute the 5 to the numbers inside the}\\\text{parenthesis}\\\\\text{When you distribute, you would multiply}\\\\\text{Distribute:}\\\\5(6-1)\\\\5(6)-5(1)\\\\30-5\\\\\text{You would see that this is equal to answer choice C, therefore making}\\\text{C your answer}\\\\\boxed{\text{C). 30 - 5}}[/tex]
When 18 is subtracted from six times a certain number, the result is − 42.
What is the number?
Answers
Answer:
18-6×10=-42
Step-by-step explanation:
all i did was put it in my calculator
Some help please? I’m lost
Answers
Answer:
1/2
Step-by-step explanation:
When you find the sine of an angle, it is the opposite side / hypotenuse. This means that the hypotenuse of this triangle is 2 and the side opposite to 60° is √3. This means that the side adjacent to 60° is 1 (Pythagorean Theorem). When you find the cosine of an angle, it is the adjacent side / hypotenuse, which in this case will be 1 / 2. Hope this helps!
Answer:
1/2.
Step-by-step explanation:
Sine = opposite side / hypotenuse.
The side opposite 60 degrees has length√3 and the hypotenuse = 2.
By Pythagoras the side adjacent to the angle 60 = √( 2^2 - 3)
= 1 unit.
So cos 60 = adjacent / hypotenuse = 1/2.
I just started learning about rate and I am stuck on a question.(A watch keeps perfect time but only has an hour hand. If the hour hand is three fifths of the distance between 1and2, determine the actual time in hours and minutes)
Answers
Answer:
36 minutes past 1, or 1:36
Step-by-step explanation:
A watch normally has an hour hand that does one revolution in 12 hours.
It takes 1 hour to go from the 1 o'clock position to the 2 o'clock position.
Since 1 hour equals 60 minutes, it takes 60 minutes to go from the 1 o'clock position to the 2 o'clock position.
The hour hand is 3/5 of the way from 1 to 2, so the number of minutes past 1 o'clock is 3/5 of 60 minutes.
3/5 of 60 minutes =
= 3/5 * 60 minutes
= 3/5 * 60/1 minutes
= 180/5 minutes
= 36 minutes
The time is 36 minutes past 1, or 1:36
What is the purpose of a regression line
Answers
Answer:
B. to show the general tendency of the points in a scatterplot
Step-by-step explanation:
a section in a stadium has 24 seats in the first row, 29seats in the second row. increasing by 5 seats each row for a total of 34 rows. how many seats are in this section of the stadium
Answers
Answer:
The answer is 2,142.
Step-by-step explanation:
Mark me brialianist of its right
Please find attached.
Answers
Answer:
5.83
Step-by-step explanation:
[tex]c=\sqrt{a^2+b^2\\} =\sqrt{3^2+5^2}\\=5.83[/tex]
Answer:
5.83
Step-by-step explanation:
rs²=3²+5²
rs²=9+25
rs²=34
rs=5.83
Yuson must complete 30 hours of community service. She does 2 hours each day. Which linear equation represents the hours Yuson has left after x days?
A.) y= -2x + 30
B.) y= 2x + 30
C.) y= -2x - 30
D.) y= 2x - 30
Answers
Answer:
A
Step-by-step explanation:
Because it's subtracting 2 hours every day, the slope is -2. Also because it's 30 hours, it's 30. Therefore: A.) y=-2x+30 is the answer.
Hopes this Helps!
A stock has a price of $72.31. This is $6.28 less than the price of the stock yesterday. Write and solve an equation to find the price p (in dollars) of the stock yesterday. An equation is =72.31. The price of the stock yesterday was $ .
Answers
Answer: The price of the stock yesterday was $78.59
Step-by-step explanation:
p - 6.28=72.31
+6.28 + 6.28
p= 78.59
Answer:
78.59$
Step-by-step explanation:
p-6.28=72.31
p=72.31+6.28
p=78.59$
a)Work out an estimate for the mean time it took the students.Round your answer to 2 significant figures.
b)What fraction of the students finished in less than 20 minutes?
Answers
3 1/2 divided by 2 3/5
Answers
Step-by-step explanation:
31/2×5/23 (use reciprocal)
31×5=155
155÷46=3.369565217
155/46
3 and 17/46
Find the volume of each cylinder. Which cylinder has the greater volume? Use 3.14 for . For cylinder A , h=5 m &c=3 m, cylinder B, h=3 m & c=5 m.
Answers
Answer:
Cylinder B has a greater volume
Step-by-step explanation:
Volume of a cylinder[tex]=\pi r^2h[/tex]
Cylinder A
h=5m, r=3m
Volume
[tex]=3.14 *3^2*5\\=141.3m^3[/tex]
Cylinder B
h=3m, r=5m
Volume
[tex]=3.14 *5^2*3\\=235.5m^3[/tex]
Cylinder B has a greater volume.