Answer:
The two lines do not intersect, and are parallel to one another on a graph.
Step-by-step explanation:
A system of equations consists of two or more equations with two or more variables. The solution to these variables must satisfy all of the variables in the equations in the system at the same time. Usually, all the equations in the system are considered and solved simultaneously. A linear equation might have a unique solution, an infinite solution, or no solution at all.
A system with exactly one solution is called a consistent system, and it is said to be independent, and the graph of its lines intersects at the point that is the solution to the equations. A system with an infinite number of solution is said to be dependent and the lines are coincident on a graph.
If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, and the lines are parallel to one another on the graph.
For two lines of linear equations to have no solution, they must be parallel to each other i.e they must have the same slope.
The standard form of writing linear equation is expressed as y = mx + b
m is the slope of the line
b is the y-intercept
For two lines of linear equations to have no solution, they must be parallel to each other i.e they must have the same slope.
For instance, the system of equations y = 2x + 7 and y = 2x - 3 have no solutions because they have the same slope.
Learn more on system of equation here: https://brainly.com/question/12526075
what must be added to 2/3 of 5.25 to make it 7.00
Answer:
3.5
Step-by-step explanation:
Well you have to find first 2/3 of 5.25. This means multiplication, which is 3.5. so to find how much to add to this to get 7, we have to subtract 3.5 from 7. 7-3.5=3.5. so we must add 3.5 to get 7. Hope this helps :D
Find the particular solution of the differential equation that satisfies the initial condition(s). (Remember to use absolute values where appropriate.) f ''(x) = 4 x2 , f '(1) = 2, f(1) = 5
Looks like either [tex]f''(x)=4x^2[/tex] or [tex]f''(x)=\frac4{x^2}[/tex]...
In the first case, integrate both sides twice to get
[tex]f''(x)=4x^2\implies f'(x)=\dfrac43x^3+C_1\implies f(x)=\dfrac13x^4+C_1x+C_2[/tex]
Then the initial conditions give
[tex]f'(1)=2\implies 2=\dfrac43\cdot1^3+C_1\implies C_1=\dfrac23[/tex]
[tex]f(1)=5\implies 5=\dfrac13\cdot1^4+C_1\cdot1+C_2\implies C_2=4[/tex]
so that the particular solution is
[tex]f(x)=\dfrac{x^4}3+\dfrac{2x}3+4[/tex]
If instead [tex]f''(x)=\frac4{x^2}[/tex], we have
[tex]f''(x)=\dfrac4{x^2}\implies f'(x)=-\dfrac4x+C_1\implies f(x)=-4\ln|x|+C_1x+C_2[/tex]
[tex]f'(1)=2\implies 2=-\dfrac41+C_1\implies C_1=6[/tex]
[tex]f(1)=5\implies 5=-4\ln|1|+C_1\cdot1+C_2\implies C_2=-1[/tex]
[tex]\implies f(x)=-4\ln|x|+6x-1[/tex]
3
2
Vx
1
1
2 3 4 5 6 7 8 9 10 11 12 X
Magnets
Using equivalent ratios, which statements are true about the cost per magnet? Check all that apply.
The cost of 2 magnets is $1.
The cost of 9 magnets is $3.
The cost of 10 magnets is $3.
The cost of 4 magnets is $2.
The cost of 6 magnets is $2.
The cost of 3 magnets is $1.
Next
Submit
Save and Exit
Mark this and retum
Answer:
The cost of 3 magnets is $1
The cost of 9 magnets is $3
The cost of 6 magnets is $2
Step-by-step explanation:
The cost of magnets is calculated using the equivalent ratio. If 3 magnets cost $ then the multiple used for the calculations of more magnets is 3. The ratio for every magnet price is 1 : 3 which means every dollar will be equal to 3 magnets. The cost of 3 magnets is $1, the cost of 6 magnets is $2 and cost of 9 magnets is $3.
The length of the segment between the points $(2a, a-4)$ and $(4, -1)$ is $2\sqrt{10}$ units. What is the product of all possible values for $a$? LOTS OF POINTS AND BRAINLIEST TO CORRECT ANSWER!
Answer:
-3
Step-by-step explanation:
The length of a segment is
sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)
sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)
sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)
Combine like terms
sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)
Square each side
( a-3)^2 + (2a -4) ^2) = 4 *(10)
FOIL the left side
a^2 -6a +9 + 4a^2 -16a +16 = 40
Combine like terms
5a^2 -22a +25 = 40
Subtract 40 from each side
5a^2 -22a -15 =0
Factor
(a - 5) (5 a + 3) = 0
Using the zero product property
a-5 =0 5a +3 = 0
a = 5 5a = -3
a=5 a = -3/5
The product of the terms is
5 * -3/5 = -3
BRAINLEST , If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.
Answer:
Question 18: B. 104
Question 19: [tex] x = \frac{3}{2} [/tex]
Step-by-step Explanation:
Question 18:
Step 1: express the inverse relationship with an equation
[tex] y = \frac{k}{x^2} [/tex] ,
where k is constant
y = 26 when x = 4,
Constant, k, = [tex] y*x^2 = k [/tex]
[tex] k = 26*4^2 = 416 [/tex]
The equation would be [tex] y*x^2 = 416 [/tex]
Step 2: use the equation to find y when X = 2.
[tex] y*x^2 = 416 [/tex]
[tex] y*2^2 = 416 [/tex]
[tex] y*4 = 416 [/tex]
Divide both sides by 4
[tex] \frac{y*4}{4} = \frac{416}{4} [/tex]
[tex] y = 104 [/tex]
Question 19:
[tex] \frac{x}{3} = \frac{x + 2}{7} [/tex]
Cross multiply
[tex] x(7) = 3(x + 2) [/tex]
[tex] 7x = 3x + 6 [/tex]
Subtract 3x from both sides
[tex] 7x - 3x = 3x + 6 - 3x [/tex]
[tex] 4x = 6 [/tex]
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{6}{4} [/tex]
[tex] x = \frac{3}{2} [/tex]
Answer: D.) 52
Explanation: I guessed and got it right lol
I dont understand how to do this
Answer:
Put 25 in the box.
Step-by-step explanation:
Apply the exponent rule: (ax)^n = a^n × x^n
So we have:
(5x)^2 = 5^2 × x^2
= 25x^2
Best Regards!
Frank and Gregory leave Centreville traveling in opposite directions on a straight road. Gregory drives 22 miles per hour faster than Frank. After 2.25 hours, they are 216 miles apart. Find Frank's speed and Gregory's speed.
Answer:
Frank speed = 37mi/hGregory speed = 59mi/hrStep-by-step explanation:
Let the speed of Frank be x and speed of Gregory be y. If Gregory drives 22 miles per hour faster than Frank, then y = 22+x. SInce they they are 216miles apart after 2.25 hours,
Speed = Distance/Time
Total time travelled by them = 2.25hours
Total distance = 216 hours
Total speed = x+y = x+22+x
Substituting this parameters into the formula given to get x we will have;
x+22+x = 216/2.25
2x+22 = 96
2x = 96-22
2x = 74
x = 74/2
x = 37
Hence the speed of Frank is 37miles per hour while that of gregory is 37+22 = 59miles/hour
In order to earn an A in her math course,
Bernadette must have an average of at
least 90 on her exam scores. She has
grades of 83, 97, 89, and 82 on her first 4
exams. What is the minimum she can
score on the final exam to earn an A in the
course?
Step-by-step explanation:
Let minimum score on the final exam to earn an A be X
[tex]mean \: = \frac{sum \: of \: observation}{number \: of \: observation} [/tex]
[tex]90 = \frac{83 + 97 + 89 + 82 + x}{5} [/tex]
Further solving :
X = 99 marks
How do i do this equation
-3(-2y-4)-5y-2=
Answer:
Step-by-step explanation: distribute -3 to the parenthesis (-2y-4) to eliminate the parenthesis. you’ll be left with 6y +12 -5y-2. From there you combine like terms. do 6y-5y= 1y or just y and 12-2 = 10. your answer would be 10
A box is 1 m high, 2.5 m long, and 1.5 m wide, what is its volume?
Answer:
3.75
Step-by-step explanation:
[tex]v = lbh \\ 2.5 \times 1.5 \times 1 \\ = 3.75[/tex]
The volume of the rectangular prism will be 3.75 cubic meters.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
A box is 1 m high, 2.5 m long, and 1.5 m wide.
Then the volume of the rectangular prism will be
V = L x W x H
V = 1 x 2.5 x 1.5
V = 3.75 cubic meters
Thus, the volume of the rectangular prism will be 3.75 cubic meters.
More about the volume of the rectangular prism link is given below.
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PLEASE PLEASE PLEASE HELP ME ANSWER THIS QUESTION QUICK!! The picture of the question is down below.
Answer:
Step-by-step explanation:
You must multiply the first two equation which is 5x+1 and x this will give you
5x^2 + x. The bold goes in the first box.
Then do the same thing for 2x+1 and x+1 which will give you 2x^2+2x+x+1 or 2x^2+3x+1. This goes in the second box.
In the last box you will add 5x^2 +x and 2x^2 +3x +1, which gives you 7x^2 +4x +1.
Goes in the last box.
Hope this helps you.
The upper-left coordinates on a rectangle are (-1,4), and the upper-right coordinates are (3,4). The rectangle
has a perimeter of 24 units.
Draw the rectangle on the coordinate plane below.
Answer:
Step-by-step explanation:
Note that the perimeter of a rectangle P = 2(Length + Breadth)
The distance between the upper-left coordinates on a rectangle and the upper-right coordinates is the breadth of the rectangle. To get the breadth of the rectangle, we will use tgw formula for calculating the distance between two points as shown.
D = √(y2-y1)²+(x2-x1)²
Given the coordinates (-1,4) and (3,4), the distance between the coordinates where x1 = -1, y1 = 4, x2 = 3 and y2 = 4 will be expressed as.
B = √(4-4)²+(3-(-1))²
B = √0+4²
B = √16
B = 4
Hence the breadth of the rectangle is 4 units.
Substituting the breadth into the formula for calculating the perimeter will give;
P = 2(L+B)
24 = 2(L+4)
L+4 = 24/2
L+4 =12
L = 12-4
L = 8
Hence the length of the rectangle is 8 units.
The diagram of the rectangle on a coordinate is as given in the attachment below.
Which line is parallel to the line 8x + 2y = 12? On a coordinate plane, a line goes through (negative 2, negative 4) and (0, 4). On a coordinate plane, a line goes through (negative 1, 1) and (3, 0). On a coordinate plane, a line goes through (negative 2, 2) and (negative 1, negative 2). On a coordinate plane, a line goes through (negative 3, 2) and (1, 3).
Answer:
C.
On a coordinate plane, a line goes through (negative 2, 2) and (negative 1, negative 2).
The line parallel to the line 8x + 2y = 12 will be a line that goes through (-2, 2) and (-1, -2). The correct option is C.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
Given that the equation of the line is 8x + 2y =12. First, calculate the slope of the line if the slope of the line is the same as the equation of the given line then the two lines will be parallel.
8x + 2y = 12
2y = -8x + 12
y =-4x + 6
Take points (-2, 2) and (-1, -2) and find the slope of the line.
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -2 - 2 ) / ( -1 + 2 )
Slope = -4
Therefore, the line parallel to the line 8x + 2y = 12 will be a line that goes through (-2, 2) and (-1, -2). The correct option is C.
To know more about an equation of the line follow
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Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = 1/sqrt(n)
This sequence converges to 0.
Proof: Recall that
[tex]\displaystyle\lim_{n\to\infty}\frac1{\sqrt n}=0[/tex]
is to say that for any given [tex]\varepsilon>0[/tex], there is some [tex]N[/tex] for which [tex]\left|\frac1{\sqrt n}-0\right|=\frac1{\sqrt n}<\varepsilon[/tex] for all [tex]n>N[/tex].
Let [tex]N=\left\lceil\frac1{\varepsilon^2}\right\rceil[/tex]. Then
[tex]n>\left\lceil\dfrac1{\varepsilon^2}\right\rceil\ge\dfrac1{\varepsilon^2}[/tex]
[tex]\implies\dfrac1n<\varepsilon^2[/tex]
[tex]\implies\dfrac1{\sqrt n}<\varepsilon[/tex]
as required.
Reduce 24/64 to its lowest terms.
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
To simplify the fraction [tex]\frac{24}{64}[/tex], we need to find its greatest common factor.
Both 24 and 64 are divisible by 2, but that's not the biggest.
Both 24 and 64 are divisible by 4, but that's not the biggest either.
Both 24 and 64 are divisible by 8, and that's the highest we can go.
So:
[tex]\frac{24\div8}{64\div8} = \frac{3}{8}[/tex].
Hope this helped!
Use the order of operations to simplify this expression 1.2x3.5x4.1= What
[tex] 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)[/tex]
$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$
$=(3+0.5+0.6+0.1)(4+0.1)$
$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$
$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$
$=16+0.4+0.8+0.02=17.22$
Given: x - 5 > -2. Choose the solution set.
Answer: x>3
Step-by-step explanation:
x-5>2
x>+5-2
x>3
jana has 3 banana muffins, 3 poppy seed muffins, 3 spice muffins and 3 blurry muffins she put 1/2 of the muffins on a late how many muffins did janna put on the plate
Answer:
6
Step-by-step explanation:
Jana had a total of 3+3+3+3 = 12 muffins. Half that number is 3+3 = 6 muffins.
Jana put 6 muffins on the plate.
What is the difference in their elevations?
An airplane flies at an altitude of 26,000 feet. A submarine dives to a depth of 700 feet below sea level
Answer:
their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster
A cubical sandbox has a volume of 91.125 cubic inches. What is the side length of the
sandbox?
Hey there! I'm happy to help!
To find the volume of a cube, you simply cube the side length (multiply it by itself three times). This is because all of the sides of a cube are the same and if you multiply the length by the width by the height it is the same number multiplied by itself three times.
We already know that the volume is 91.125 cubic inches. To find the side length, we simply do the cube root on our calculator, which tells us what number we cube to get 91.125.
∛91.125=4.5
Therefore, the side length of the sandbox is 4.5 inches.
I hope that this helps! Have a wonderful day! :D
please help me guys please find the value of 3x°
Answer:
finding the value of x first
2x + 3x + 10 = 180 (linear pair)
5x = 180 - 10
x = 170 / 5
x = 34
3x = 102
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 30 31 64 59 57 33 54 77 56 41 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
30 31 64 59 58 33 54 77 56 41 (arrange it)
30 31 33 41 54 56 58 59 64 77 (done!)
Mean: Find the number in the middle (54+56)/2= 110/2 = 55
Mode: None
Mean: (30+31+33+41+54+56+58+59+64+77)/10=503/10= 50,3
PLEASE HELP ASAP WILL GIVE BRAINLIEST
The weight of an object on moon is 1/6 of its weight on Earth. If an object weighs 1535 kg on Earth. How much would it weigh on the moon?
Answer:
255.8
Step-by-step explanation:
first
1/6*1535
=255.8
which function represents the area of the triangle h(x)=1/2f(x)g(x)
Answer:
h=1/2fg
Step-by-step explanation:
Solve for x, h=1/2fg
It is true for all x; h=1/2fg
h=1/2fg
Both sides are equal
It is true for all x; h=1/2fg
PLEASE FAST 40 POINTS
A box contains four tiles, numbered 1,4.5, and 8 as shown.
Kelly randomly chooses one tile, places it back in the box, then chooses a second tile.
What is the probability that the sum of the two chosen tiles is greater than 7?
A. 1/4
B. 5/16
C. 2/3
D. 11/16
Answer:
[tex]\bold{\dfrac{11}{16}}[/tex]
Step-by-step explanation:
Given four tiles with numbers:
1, 4, 5 and 8
Tile chosen once and then replaced, after that another tile chosen:
All possibilities are:
{(1, 1) ,(1, 4) ,(1, 5) ,(1, 8)
(4, 1) ,(4, 4) ,(4, 5) ,(4, 8)
(5, 1) ,(5, 4) ,(5, 5) ,(5, 8)
(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }
Total number of possibilities = 16
When the sum is greater than 7, the possibilities are:
{(1, 8)
(4, 4) ,(4, 5) ,(4, 8)
(5, 4) ,(5, 5) ,(5, 8)
(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }
Number of favorable cases = 11
Formula for probability of an event E is:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Hence, the required probability is:
[tex]\Rightarrow \bold{\dfrac{11}{16}}[/tex]
Answer:11/16
Step-by-step explanation:i took the test
arthur walks 5/8 mi to school jonathan rides a bus 8 times that far> How far does Jonathan ride to school
Answer:
Step-by-step explanation:
Distance walked by Arthur = 5/8 miles
Distance ride by Jonathan = 8 times that of Arthur
it means that Distance rode on bus by Jonathan is 8 multiplied by Distance walked by Arthur
Distance rode on bus by Jonathan = 8 * Distance walked by Arthur
Distance rode on bus by Jonathan = 8 * 5/8 = 5 Miles Answer
Which of the following describes a situation in which the total distance a ball travels is zero meters from its starting point? (5 points)
a
b
The ball first bounces up to a height of 4 meters, and then falls 2 meters towards the ground.
The ball first bounces up to a height of 2 meters, and then falls 2 meters towards the ground.
The ball first bounces up to a height of 2 meters, and then falls 4 meters towards the ground.
The ball first bounces up to a height of 4 meters, and then falls 0 meters towards the ground.
С
d
Answer:
The ball first bounces up to a height of 2 meters, and then falls 2 meters towards the ground
Step-by-step explanation:
Need Help
*Please Show Work*
Hi there! :)
Answer:
y = -2x + 3
Step-by-step explanation:
We can write an equation in slope-intercept form. Use the slope formula to find the rate of change in the table:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in values from the table:
[tex]m = \frac{5 - 7}{-1 - (-2)}[/tex]
Simplify:
m = -2 (rate of change)
Use a point from the table (-2, 7) and the slope to solve for the equation for the linear function:
7 = -2(-2) + b
7 = 4 + b
7 -4 = b
b = 3
Rewrite:
y = -2x + 3 is the equation for the linear function.
Find the total area the regular pyramid. T.A=
Answer:
18√91 +54√3
Step-by-step explanation:
Name the point at the top of the pyramid "A", the point at the left front corner "B", and the one in the center of the hexagonal base "C". Then right triangle ABC is shown. The "base" BC of that triangle is the same measure as the front edge (6), because the diameter of a regular hexagon is equal to twice the side length.
Using the Pythagorean theorem, we can find the face edge length to be ...
AB^2 = BC^2 +AC^2
AB^2 = 6^2 +8^2 = 100
AB = √100 = 10
If we call the midpoint of the front edge "D", then we need to find the length of AD in order to determine the face area. Again, we can use the Pythagorean theorem.
AB^2 = BD^2 +AD^2
AD^2 = AB^2 -BD^2 = 10^2 -3^2 = 91
AD = √91
The area of one of the 6 lateral faces is ...
A = (1/2)bh = (1/2)(6)√91 = 3√91
The area of one of the 6 equilateral triangles that make up the base is ...
A = (√3)/4·s^2 = (√3)/4(6^2) = 9√3
Then the total area of the pyramid is ...
total area = 6 × (face area + partial base area)
= 6(3√91 +9√3)
total area = 18√91 +54√3
