Answers
The point of intersection of lines represents the common solution of the system of linear equations. The solution of linear equations given in the graph is (0,2).
Linear equation represents a line on the graph. The system of linear equations represents couple/s of linear equations or lines.
The solution of system of linear equations means the common point satisfying the different linear equations.
Graphically, the point of intersection of two lines represents the common solution of these two lines or simply the solution of the system of linear equations.
So, the point of intersection from the given graph is (0,2).
Therefore, the solution of linear equations given in the graph is (0,2).
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Related Questions
An amusement park is installing a new roller coaster. The park intends to charge $5 per adult and $4 per child for each ride. It hopes to earn back more than the $650,000 cost of construction in four years. With the best of weather, the park can provide 125,000 adult rides and 50,000 child rides in one season
Answers
Answer:
Step-by-step explanation:
5x+ 4y greater than or equal to 650,000
500,000
y greater than or equal to 200,00
Answer is : 5x+4y greater than or equal to 650,000
X less than or equal to 500,000
Y is less than or equal to 200,000
Can someone solve #4 and explain it? I really appreciate it on this problem! Thank you :)
Answers
The table below shows the velocity y, in miles per minute, of a toy car at different times x, in minutes: Time (x) (minutes) 10 20 30 40 Velocity (y) (miles) 0.2 0.8 0.1 0.4 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and velocity of the toy car. (4 points) [Choose the value of correlation coefficient from −1, 1, −0.04, 0.99] Part B: What is the value of the slope of the graph of velocity versus time between 10 minutes and 20 minutes, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation?
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B. The slope of the graph is equal to y2-y1/x2-x1, In this case, it would specifically be v2-v1/t2-t1
Slope = 0.8-0.2/20-10 = 0.06 miles/s^2
The slope represents the acceleration at time 10 to 20 minutes.
C. The table in the graph shows causation rather than correlation. The points in the data occur in a sequential manner.
Use the arc length formula to find the length of the curve y = 5x − 4, −1 ≤ x ≤ 3. check your answer by noting that the curve is a line segment and calculating its length by the distance formula
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The length of the arc is computed from the formula
[tex]S= \int_{-1}^{3} \,\sqrt{1+ (\frac{dy}{dx} )^{2}} \, dx[/tex]
The derivative is
y' = 5
Therefore
[tex]S = \int_{-1}^{3} \sqrt{1+25} \, dx =\sqrt{26}*(3-(-1))=20.396[/tex]
Note that
x = -1 +> y = 5(-1) - 4 = -9
x = 3 => y = 5(3) - 4 = 11
The distance between the points (-1, -9) and (3, 11) from the distance formula is
D = √[(3-(-1))² + (11-(-9))²] = √(16+400) = 20.396
This answer agrees with that obtained by integration.
Answer: 20.396
Obtained by integration and verified by the distance formula.
The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.
To find the length of the curve y = 5x − 4 over the interval −1 ≤ x ≤ 3, we can use the arc length formula for a function y = f(x). The formula for the arc length L is given as:
L = ∫ab√(1 + (dy/dx)2) dx, where dy/dx is the derivative of y with respect to x.
1. Calculate the derivative dy/dx:
y = 5x − 4, so dy/dx = 5.
2. Substitute the derivative into the arc length formula:
L = ∫-13√(1 + 5²) dx = ∫-13√26 dx.
3. Integrate the function:
L = √26 ∫-13 dx = √26 [x]-13 = √26 (3 − (-1)) = 4√26 ≈ 20.396.
To verify this using the distance formula (since the curve is a straight line), we take the points (−1,−9) and (3,11) from the given curve:
4. Apply the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) = (-1, -9) and (x2, y2) = (3, 11).
Therefore,
Distance = √((3 - (-1))² + (11 - (-9))²) = √((4)² + (20)²) = √(16 + 400) = √416 = 4√26 ≈ 20.396.
Thus, the arc length calculated using the formula and the distance formula are consistent.
The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.
3 to the 2 over 3 power inches squared
3 to the 8 over 3 power inches squared
9 inches squared
9 to the 2 over 3 power inches squared
Question 4(Multiple Choice Worth 2 points)
(MC)
Rewrite the rational exponent as a radical.
5 to the 3 over 4 power, to the 2 over 3 power
the cube root of 5 squared
the twelfth root of 5
the square root of 5
the cube root of 5 the fourth power
Question 5(Multiple Choice Worth 2 points)
(MC)
Rewrite the radical as a rational exponent.
the cube root of 2 to the seventh power
2 to the 3 over 7 power
2 to the 7 over 3 power
2 to the power of 21
2 to the power of 4
Answers
[tex]A= \sqrt[3]{81}*3^{ \frac{2}{3} }= \sqrt[3]{3^4}*3^{ \frac{2}{3} } = 3^{ \frac{4}{3} }*3^{ \frac{2}{3} }=3^{ \frac{4}{3} + \frac{2}{3} }=3^2=9[/tex]
9 inches squared
#2
[tex]\left( 5^{ \frac{3}{4} } \right)^{ \frac{2}{3} }=5^{ \frac{3}{4} *\frac{2}{3} }=5^{ \frac{1}{2} }= \sqrt{5} [/tex]
C. the square root of 5
#3
[tex] \sqrt[3]{2^7}=2^{ \frac{7}{3} } [/tex]
2 to the 7 over 3 power
A jar has 4 balls lettered A, E, D, and G. One ball is drawn from the jar and it's letter is noted. A second ball is also drawn without replacing the first ball and it's letter is noted. List all the possible outcomes and find the probability that the letters on the 2 balls drawn consist of at least 1 vowel, no vowels, and the same letter.
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EA DA GA DE GE GD
P( at least one vowel) = 10/12 = 5/6
P( no vowels) = 2/12 = 1/6
P(same letter) = 0
What is the circumference of a circular disc with a diameter of 10 centimeters? (Round your answer to the nearest tenth.)
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C = Pi • d
C = (3.14)(10 cm)
C = 31.41 cm or 31.4 cm, rounded to the nearest tenth.
The circumference of the circle is 31.4 cm
What is Circumference of circle?The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.
Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.
Center: The center of the circle is a point that is at a fixed distance from any other point from the circumference.Diameter: The diameter is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center.Radius: The radius of a circle is the distance from the center of a circle to any point on the circumference of the circle.The formula for the circumference of a circle is expressed using the radius 'r' of the circle and the value of 'pi'. It is expressed as, Circumference of a circle formula = 2πr.
Given:
diameter= 10 cm
So,
Circumference of circle is = πd
=3.14* 10
=31.4 cm
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What is the approximate distance between the points (-5, 1) and (-2, 3) on a coordinate grid ?
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[tex]d= \sqrt{(x_{2} -x_{1})^{2} + (y_{2}-y_{1})^{2}} [/tex]
Therefore the distance between (-5,1) and (-2, 3) is
[tex] \sqrt{(-2+5)^{2} + (3-1)^{2}} =3.6056[/tex]
Answer: 3.61 (nearest hundredth)
The function h(x) = x2 + 14x + 41 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)
Part C: Determine the axis of symmetry for h(x). (2 points)
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[tex]h(x)= x^{2} +14x+41[/tex]
The first step of completing the square is writing the expression [tex] x^{2} +14x[/tex] as [tex] (x+7)^{2} [/tex] which expands to [tex] x^{2} +14x+49[/tex].
We have the first two terms exactly the same with the function we start with: [tex] x^{2} [/tex] and [tex]14x[/tex] but we need to add/subtract from the last term, 49, to obtain 41.
So the second step is to subtract -8 from the expression [tex] x^{2} +14x+49[/tex]
The function in completing the square form is
[tex]h(x)= (x+7)^{2}-8 [/tex]
Part B:
The vertex is obtained by equating the expression in the bracket from part A to zero
[tex]x+7=0[/tex]
[tex]x=-7[/tex]
It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a U-shape.
A quadratic function [tex]a x^{2} +bx+c[/tex] can either make U-shape or ∩-shape depends on the value of the constant [tex]a[/tex] that goes with [tex] x^{2} [/tex]. When [tex]a[/tex] is (+), the curve is U-shape. When [tex]a[/tex] (-), the curve is ∩-shape
Part C:
The symmetry line of the curve will pass through the vertex, hence the symmetry line is [tex]x=-7[/tex]
This function is shown in the diagram below
to anyone who may be a lil' sus, the previous answer is correct.
Oh Plz help - I can't handle this one :)
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b: 4*0.5*1.5 = 3, 6*4 = 24, 6*2.5 = 15.5, 15.5*2 + 3*2 + 24 = 61m^2
c: 5.2*3.5 = 18.2, 2.4*3.5 = 8.4, 2.4*5.2 = 12.48, 12.48*2 + 8.4*2 + 18.2*2 = 78.16ft^2
A bit late but hope it helps
A = 2 *pi * r^2 + 2 * pi * r * h
A = 2 * pi * 5^2 + 2 * pi * 5 * 10
A = 50 pi + 100 pi
A = 150 * pi cm^2 (Exact Answer)
A = 471 cm^2 (Decimal Approximation)
b. A(triangles)
A = (1/2) * b * h * 2
A = (1/2) * 4 * 1.5 * 2
A = 6 m^2
A(rectangles)
A = L * W
A = 4 * 6 + 2.5 * 6 * 2
A = 24 + 30
A = 54 m^2
Total area = 6 + 54 = 60 m^2
c. A(rectangular prism)
A = 2LW + 2LH + 2WH
A = 2 * 5.2*2.4 + 2 * 5.2 * 3.5 + 2 * 2.4 * 3.5
A = 78.16 ft^2
d. A(rectangular prism)
A = 2LW + 2LH + 2WH
A = 2 *12 * 6 + 2 * 12 * 4.5 + 2 * 6 * 4.5
A = 306 ft^2
e. You have a large box to wrap and need to know how much wrapping paper will be needed to wrap the box.
The dimensions of the box are L = 10 in., W = 4 in., H = 6 in.
You have a cone with a radius of 4 ft and a height of 12 ft. What is the height of the triangle formed by a perpendicular cross-section through the cone’s center?
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ABC is the triangle formed by a perpendicular cross-section through the cone's center.
The height OC of this triangle, is the height of the cone.
So the height is equal to 12 ft.
Answer: 12 ft.
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e) Isabel’s competition,who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. (5 points)
f) Graph the function in part e. (10 points)
g) Is your graph discrete or continuous? Explain. (5 points)
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Answer:
Isabel’s competition,who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. (5 points)
The price of the shipping ( f(x)) is equal to the cost of the fixed fee per order (3) plus the product of the number of books ordered (x) and the cost of the fee per book (1.99).
f(x)= 1.99x +3
for f(0) = 1.99(0)+3
f(0) =3
For F(0) there is a order of 0 books. The price is only for the shippping.
Step-by-step explanation:thats it buddy
A function that expresses f(x) is f(x) = 1.99x + 3. Graph is continuous.
What is continuous function?A continuous function is a function that does not have discontinuities that means any unexpected changes in value. A function is continuous if we can ensure arbitrarily small changes by restricting enough minor changes in its input.
For this case we have the following data:
A shipping fee of $ 1.99 is charged for each book sold.
There is a fixed fee of 3 dollars per order.
We must express the total cost by a function of the form .
If x represents the number of books sold, we have an expression of the form:
f(x) = 1.99x + 3
That is, according to the number of books sold, represented by x, a different value will be obtained for the total cost given by function f (x). For example:
If 3 books are sold, we have:
f(x) = 1.99x + 3
f(0) = 1.99(0) + 3
f(0) = 3
Thus, the value of f(x) for x = 0 is f(0) = 3.
The graph is continuous. Continuous is something that can and must be able to be broken down into fractions and decimals. Discrete means something that cannot be broken down into fractions or decimals.
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The graph shows the number of paintballs a machine launches, y, in x seconds::
A graph titled Rate of Launch is shown. The x axis label is Time in seconds, and the x axis values are from 0 to 20 in increments of 4 for each grid line. The y axis label is Number of Balls, and the y axis values from 0 to 80 in increments of 16 for each grid line. A line is shown connecting points on ordered pair 4, 16 and 8, 32 and 12, 48 and 16, 64.
Which expression can be used to calculate the rate per second at which the machine launches the balls?
fraction 64 over 4
fraction 4 over 64
fraction 16 over 4
fraction 4 over 16
Answers
a fraction should be number of balls over time per second
so it should be 16/4 which is 4 balls per second
Answer: fraction 16 over 4
Step-by-step explanation:
The given graph shows the number of paintballs a machine launches, y, in x seconds.
We know that the rate of change of a line is given by :-
[tex]k=\frac{y_2-y_1}{x_2-x_1}[/tex]
The ordered pairs on the line in graph are (4, 16) and (8, 32) and (12, 48) and (16, 64).
Thus, the rate per second at which the machine launches the balls is given by :-
[tex]k=\frac{32-16}{8-4}=\frac{16}{4}
Sara is 33 years younger than Rolando. The Sum of their ages is 105. Select the system of equations if Sara's age is represented by S and Rolando's age is represented by R.
A. s+r=33
s=r-105
B. s+r=105
r=s-33
C. s+r=105
s=r-105
D. s+r=105
s=r-33
E. None of these
Answers
So that is answer D.
Sara is 33 years yonder than Rolando: i.e. S<R specifically S=R-33.
They are 105 years old together: i.e. S+R=105
The only answer that has both is D.
(Be careful here, B is almost right but says that Sara is OLDER by 33 years.)
2x+3y=-2 4x+7y=-6 solve for the system of equations
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multiply first equation by -2 and add to 2nd equation
-4x-6y=4
4x+7y=-6 +
0x+1y=-2
y=-2
sub back
2x+3y=-2
2x+3(-2)=-2
2x-6=-2
2x=4
x=2
(x,y)
(2,-2)
A low bal will always cause a hangover
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Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth
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9.678937... (never ending)...it is irrational because it cannot be made into a fraction because it is infinite.
the decimal approximation to the nearest hundredth is : 9.68
how would you solve it. I know the answer already. my problem working it out.
4b/2 + 3 = 11 + b.
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4b/2 = 8 +b
multiply both sides by two
(4b/2 = 8 + b) X2 = 4b = 16+2b
subtract 2b from both sides
2b = 16
divide both sides by 2
b=8
1. Simplify any parentheses using the distributive property if needed.
2. Combine like terms if needed.
3. Use the addition principle of equality if needed.
4. Use the multiplication or division principle of equality if needed.
[tex]\frac{4b}{2} + 3 = 11 + b[/tex]
2b + 3 = 11 + b
b + 3 = 11 <-- Subtract b from each side
b = 8 <-- Subtract 3 from each side
So, b is equal to 8.
graph the line with the slope 1/3 and y-intercept -2
Answers
The graph of the line y = (1/3)x - 2 can be plotted on a graph paper by choosing some arbitrary values of x.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The given line in terms of the slope-intercept method can be written as,
y = (1/3)x - 2.
Now to plot the graph on graph paper or any digital tool we have to choose some arbitrary values of x that corresponds to some values of y.
Like at x = 0 y = -2 So, the coordinates are (0, -2).
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Kaveri has a total rs 590 as currency notes is the denominations ofrs50 , rs 20 , and rs 10 . the ratio of the number of rs 50 note and rs 2o is 3:5. if she has a total of 25 notes , how many notes of each denomination she has?
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x = number of rs 50
y = number of rs 20
z = number of rs 10
Because there are 25 total notes,
x + y + z = 25 (1)
The ratio of rs 50 to rs 20 is 3:5, therefore
x = 0.6y (2)
The total amount is rs 590, therefore
50x + 20y + 10z = 590
or
5x + 2y + z = 59 (3)
Subtract (1) from (3).
4x + y = 34 (4)
Substitute (2) into (4).
4*(0.6y) + y = 34
3.4y = 34
y = 10
From (2), obtain
x = 6
From (1), obtain
z = 25 - 6 - 10 = 9
Answer:
Kaveri has
6 rs 50 notes,
10 rs 20 notes,
9 rs 10 notes.
A quadratic equation is shown below: 3x2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 3x2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
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Answer:
[tex]\text{The roots of }3x^2+5x-8=0\text{ are }x=1,\frac{-8}{3}[/tex]
Step-by-step explanation:
[tex]\text{Part A: Given a quadratic equation }3x^2-15x+20=0[/tex]
[tex]\text{Comparing above equation with }ax^2+bx+c=0[/tex]
a=3, b=-15, c=20
Discriminant can be calculated as
[tex]D=b^2-4ac[/tex]
[tex]D=(-15)^2-4(3)(20)=225-240=-15<[/tex]
The roots are imaginary
The solution is
[tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
[tex]x=\frac{-(-15)\pm \sqrt{-15}}{2(3)}=\frac{15\pm\sqrt{15}i}{6}[/tex]
The roots are not real i.e these are imaginary
[tex]\text{Part B: Given a quadratic equation }3x^2+5x-8=0[/tex]
[tex]\text{Comparing above equation with }ax^2+bx+c=0[/tex]
a=3, b=5, c=-8
Discriminant can be calculated as
[tex]D=b^2-4ac[/tex]
[tex]D=(5)^2-4(3)(-8)=25+96=121>0[/tex]
The roots are real
By quadratic formula method
The solution is
[tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
[tex]x=\frac{-5)\pm \sqrt{121}}{2(3)}=\frac{-5\pm 11}{6}[/tex]
[tex]x=1,\frac{-8}{3}[/tex]
which are required roots.
I choose this method because I can get the solutions directly by substituting the values in formula, and I don't have to guess the possible solutions.
A textile corporation buys equivalent with an initial purchase price of $750000. It is estimated its useful life will be 3 years and at that time it's value will be$75000. The total depreciation is depreciation is divided equally among the three years. What is the total amount of depreciation declared each year?
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Enter the slope-intercept equation of the line shown below.
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Find the length of a to the nearest tenth.
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212 tens divided by 10 =
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212×10/10
2120/10
212
did u mean this?
hope this helps u...
In a store 60 cans of soup are arranged to be this play into equal rows why does the fraction 10 over 60 not represent the situation explain
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This is given by the fraction 60 over 10.
The fraction 10 over 60 is not used to represent this situation because the fraction 10 over 60 gives the number of rows which is needed for 1 can. That is number of rows per can. But there is nothing like a fraction of a row. Hence the fraction 10 over 60 cannot be used to represent the situation.
(03.01) Is the following relation a function? y equals the sine of 3 x
Answers
Answer:
Yes. This is a function.
Step-by-step explanation:
Given is a function as
[tex]y = sin 3x[/tex]
We find that for every x in the domain of real numbers there is a unique image for every x as sin 3x.
Thus this relation given satisfies the requirements of a function.
Also we find that this function is periodic with amplitude 1 and period = 2pi/3
So vertical line test if done will find that there is only one intersection for every vertical line throughout the domain
Hence this relation is definitely a function
A pet store has 7 tanks of fish. Each tank has k fish. Using k, write an expression for the total number of fish in the store.
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The expression which represents the total number of fish in the store is 7k.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given,
Number of tank = 7
Number of fish in each tank = k
The total number of fish = number of tanks x number of fish in each tank
The total number of fish = 7 x k = 7k
Hence "The expression which represents the total number of fish in the store is 7k".
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3tan3x=3
solve please
Answers
[tex]3 tan(3x)=3[/tex] ⇒ divide both sides by 3
[tex]tan(3x)= \frac{3}{3} [/tex]
[tex]tan(3x)=1[/tex] ⇒ then take arctan of 1
[tex]3x= tan^{-1}(1) [/tex]
[tex]3x=45[/tex]°
From here we can read the solution on tan(x) graph between a certain interval.
Say the interval is 0°<x<360°, the graph of tan(x) is given below, there are two solutions between this interval
3x = 45° and 225° ⇒ dividing each answer by 3
x = 15°, 75° ⇒ these are the answer to the equation for the equation between 0° and 360°
(48.9, -53.3) (84.6, -19.9) (-62.6, 81.7) (-14.4 ,-42.6) (71.2, -84.1) (71.2, 76.8 ) state the domain