The graph of a linear equation contains the points (4,1) and (-2,-11). Which point also lies on the graph?
A. (1,1)
B.(1,-5)
C.(1,-2)
D.(1,-7)
Answer:
Option B is correct.
(1 , -5) lies on the graph.
Step-by-step explanation:
Given the points (4,1) and (-2 , -11)
First find the linear equation for the given points.
Equation of line for two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
is given by: [tex]y-y_1 = (\frac{y_2-y_1}{x_2 - x_1}) (x-x_1)[/tex]
Substitute the given points (4,1) and (-2 , -11) in above equation to find the equation of line:
[tex]y-1=(\frac{-11-1}{-2-4})(x-4)[/tex]
or
[tex]y-1=(\frac{-12}{-6})(x-4)[/tex]
or
[tex]y-1=2(x-4)[/tex]
Using distributive property on RHS ( i.e, [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex] )
we have;
y -1 = 2x-8
Add 1 to both sides of an equation;
y-1+1 = 2x-8+1
Simplify:
y = 2x -7
Therefore, the equation of line for the given point is: y =2x - 7 ....[1]
To find which points lies on the graph ( i.e, Line)
Substituting the given options in equation [1] we have;
A . (1,1)
Put x =1 and y =1
[tex]1 = 2\cdot 1 -7 = 2-7[/tex]
1 = -5 which is not true.
Similarly
B. for (1, -5)
[tex]-5= 2\cdot 1 -7 = 2-7[/tex]
-5 = -5 which is true.
C. for (1, 2)
[tex]2= 2\cdot 1 -7 = 2-7[/tex]
2 = -5 which is not true.
And
D. For (1 , -7)
[tex]-7= 2\cdot 1 -7 = 2-7[/tex]
-7 = -5 which is also not true.
Therefore, the only point which lies on the line graph [1] is; (1 ,-5)
A system of two equations is shown below: equation
c.a = 3b + 6 equation
d.a = 7b − 1 what value of a can be substituted into equation d to solve the system of equations? 3b 7b 3b + 6 7b − 1
What is 5.75% of $6,000? (Express answer as dollars as cents.)
Answer:
The answers are:
345 dollars
34500 cents
Step-by-step explanation:
In order to determine the answers, we have to know about the percentage notation. For any "x" value that is expressed as x%, it is the same that:
x%=[tex]\frac{x}{100}[/tex]
So, first we determine the value in dollars and then we determine the value in cents, where:
1 dollar=100 cents
In dollars $:
=5.75%*$6000
=[tex]\frac{5.75}{100}[/tex]*$6000
=$345.00
In cents c:
=5.75%*6000*100
=[tex]\frac{5.75}{100}[/tex]*6000*100
=34500.00 cents
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: ∠F ∠ F is supplementary to ∠G ∠ G and ∠G ∠ G is supplementary to ∠H ∠ H . Conjecture: ∠F ∠ F is supplementary to ∠H ∠ H .
A fantasy board game makes use of four dice. The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each. If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?
Answer:
2400
Step-by-step explanation:
Given : The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each.
To Find: If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?
Solution:
No. of faces of first die = 6
No. of faces of second die = 4
No. of faces of third die = 10
No. of faces of fourth die = 10
Now we are supposed to find the the number of possible outcomes exist.
So, Number of possible outcomes if all the dice are thrown together :
= [tex]6 \times 4 \times 10 \times 10[/tex]
=[tex]2400[/tex]
Hence there are 2400 possible outcomes if all the dice are thrown together and their combination dictates a certain outcome of the game.
Use the functions f(x) = 2x + 7 and g(x) = 6x − 5 to complete the function operations listed below.
Part A: Find (f + g)(x). Show your work. (3 points)
Part B: Find (f ⋅ g)(x). Show your work. (3 points)
Part C: Find f[g(x)]. Show your work. (4 points)
We are given the two functions:
f(x) = 2x + 7
g(x) = 6x – 5
Part A. Find (f + g)(x)
(f + g)(x) = f(x) + g(x)
(f + g)(x) = 2 x + 7 + 6 x – 5
(f + g)(x) = 8 x + 2
Part B. Find (f ⋅ g)(x)
(f ⋅ g)(x) = f(x) ⋅ g(x)
(f ⋅ g)(x) = (2 x + 7) (6 x – 5)
(f ⋅ g)(x) = 12 x^2 – 10 x + 42 x – 35
(f ⋅ g)(x) = 12 x^2 + 32 x – 35
Part C. Find f[g(x)]
f[g(x)] = 2 (6 x – 5) + 7
f[g(x)] = 12 x – 10 + 7
f[g(x)] = 12 x - 3
Kwamee created a coffee blend for his cafe by mixing Kona beans and Fuji beans.Kona beans cost $11 per pound and Fuji beans cost $7.50 per pound.He bought a total of 23 pounds of coffee beans and it cost $197. Write a system of equations that can be used to determine how many pounds of Kona and Fuji beans Kwamee bought.
What is the measure of (arc) BC?
A. 55
B. 110
C. 48
D. 96
Answer:
(D)[tex]96^{\circ}=(arc)BC[/tex]
Step-by-step explanation:
It is given from the figure that m∠BAC=48° and arcAC=110°.
The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.
Now, using the above property, we have
[tex]m{\angle}BAC={\frac{1}{2}}(arc)BC[/tex]
Substituting the given values, we get
[tex]48^{\circ}=\frac{1}{2}(arc)BC[/tex]
[tex]96^{\circ}=(arc)BC[/tex]
Thus, the measure of the arc BC is 96 degrees.
Hence, option D is correct.
josianne had two difference offers (1) 12000 cash and (2) 8000 semiannually for 5 years. assuming 10% compounded semiannualy determine the better offer and find the difference between them
The table shows the outputs y for different inputs x:
Input
(x) 2 4 6 8
Output
(y) 1 2 3 4
Part A: Do the data in this table represent a function? Justify your answer.
Part B: Compare the data in the table with the relation f(x) = 3x – 10. Which relation has a greater value when x = 8?
Part C: Using the relation in Part B, what is the value of x if f(x) = 80?
Suppose that some country had an adult population of about 50 million, a labor-force participation rate of 60 percent, and an unemployment rate of 5 percent. how many people were unemployed?
Based on the labor force participation rate, the number of unemployed people is 1.5 million people.
The unemployed rate is based on the labor force participation rate and not the adult population.
The labor force is 60% and in absolute value this is:
= 60% x 50 million people
= 30 million people
The unemployment rate is 5% of this:
= 5% x 30 million
= 1.5 million people
In conclusion, there are 1.5 million unemployed people
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LeRon draws an orange counter from one bag and a red counter from another bag. Which statement is true?
Collinear points are not necessarily coplanar.. true or false
The given statement is a false statement.
Step-by-step explanation:Collinear Points--
Two or more points are said to be collinear if they lie on a straight line.
Coplanar--
Set of points are said to be coplanar if they lie on the same plane.
If the set of points are collinear then we may get a line such that it will contain all these points and as we know that line always lie in a plane also there may be infinite number of planes which may contain the same line.
So, all the points on the line will also lie in the same plane.
Yes, collinear points are necessarily coplanar.
Consider the system of linear equations.
7x+16y=-2
9x-4y=22
To use the linear combination method and addition to eliminate the y-terms, by which number should the second equation be multiplied?
A. -4
B. -1/4
C. 1/4
D. 4
To use the linear combination method and addition to eliminate the y-terms, the second equation should be multiplied by 4.
What is equation?An equation is like a relationship between two or more variables. It is expressed in equal to form. Equation of two variables looks like: ax+ by=c.
It is solved to find the value of variables.
How to solve equation?The given equations are 7x+16y= -2 and 9x-4y=22 and we have to solve using linear combination method.
First we have to change -4y to -16y because after we have to do addition so we will multiply the second equation by 4 which makes the equation as under:
36x-16y=88
Adding equation 1 and 2
7x+16y+36x-16y=-2+22
42x=20
x=20/42
x=10/21
Put the value of x in 7x+16y=-2
7(10/21)+16y=-2
10/3+16y=-2
16y=-2-10/3
16y=-16/3
y=-1/3
Hence to solve the equations we need to first multiply second equation by 4 which is option D.
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How do I simplify this?
The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown. (Figure is not drawn to scale.) A picture of a right triangle ABC with right angle at B is shown. The length of the side AC is labeled as 9 miles. The length BC of the triangle is labeled as 6 miles. This length BC is also the length of an irregular gray shaded shape. Which of the following options is closest to the distance (in miles) between points A and B? 6.71 miles 7.35 miles 8.66 miles 10.82 miles.
Answer:
6^2 + x^2 = 9^2
36 + x^2 = 81
81-36= 45
square root of 45 is approximately 6.71 miles
Step-by-step explanation:
Using the theram theroy is very important to know the fulma and steps
What does exclamation point mean in math?
In mathematics, an exclamation point represents a factorial, meaning the product of an integer and all the positive integers below it. For example, 5 factorial, or 5!, is 5 x 4 x 3 x 2 x 1 = 120. Unlike exponentials, factorials involve consecutive multiplication of integers.
Explanation:In mathematics, the exclamation point is used to represent a factorial. Factorial indicates the product of an integer and all the positive integers below it. For instance, 5! would be 5 x 4 x 3 x 2 x 1 = 120. This calculation method is a significant concept especially in exponential arithmetic.
Contrary to exponential notation, factorials do not deal with the concept of powers or repeated multiplication of the same number. Instead, they focus on consecutive multiplication of descending positive integers. For example, 3! is evaluated as 3 x 2 x 1 = 6, instead of 3 x 3.
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PLZ HELP NEED ANSWER ASAP! A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low represents the fewest points scored and High represents the highest points scored by a single team member. Team Low High Range Mean Median IQR σ Team A 22 58 36 42.1 44 18.25 10.35 Team B 38 49 11 43.9 44.5 3.5 2.97 Team C 27 36 9 31.8 32 3.75 2.55 Part A: If the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? Justify your answer mathematically. (5 points) Part B: If the club wants to award the team with the highest average score, which team should it choose and why? Justify your answer mathematically. (5 points)
How to factor:
x^3-216=0
Jessica deposits $2000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first 2 years?
Please help! Thanks (:
Which of the following represents the set of possible rational roots for the polynomial shown below 2x^3+5x^2-8x-20=0
The possible rational roots are given by the ratio of the constant term to the leading coefficient. That is [tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2, [tex]\pm[/tex]1/5, [tex]\pm[/tex]1/10, [tex]\pm[/tex]1/20, and so on and this can be determined by using the arithmetic operations.
Given :
Polynomial Equation -- [tex]2x^3+5x^2-8x-20=0[/tex]
The following steps can be used in order to determine the rational roots of the given polynomial equation:
Step 1 - Write the given polynomial equation.
[tex]2x^3+5x^2-8x-20=0[/tex]
Step 2 - The coefficient of [tex]x^3[/tex] is 2. So the factors of 2 are [tex]\pm[/tex]1, [tex]\pm[/tex]2.
Step 3 - The constant term of the given polynomial is -20 and the factors of the constant term are [tex]\pm[/tex]1, [tex]\pm[/tex]2, [tex]\pm[/tex]5, [tex]\pm[/tex]10, [tex]\pm[/tex]20.
Step 4 - The rational roots are given by the ratio of the constant term to the leading coefficient. That is,
[tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2, [tex]\pm[/tex]1/5, [tex]\pm[/tex]1/10, [tex]\pm[/tex]1/20, and so on.
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The Hamilton Brush Company issued 2500 shares of common stock worth 100,000,000 total.What is the par value of each share
Shamus can paint the barn in 6 hours, and ishmael can paint the barn in 7 hours. how long will it take them to paint the barn together?
how do you write 710,000 in scientific notation with answers
The scientific notation for 710,000 is [tex]7.1 \times 10^5[/tex].
Identify the significant digits:
In 710,000, the significant digits are “7.1”.
Determine the power of 10:
To convert 710,000 into a number between 1 and 10 times a power of 10, you notice that moving the decimal point 5 places to the left gives “7.1”.
This is because:
[tex]710,000 = 7.1 \times 100,000 = 7.1 \times 10^5[/tex]
Write the number in scientific notation:
Combine the significant digits with the power of 10.
[tex]7.1 \times 10^5[/tex].
Thirty pounds of a salt-water solution contains fifteen percent salt. How much salt is in the water?
1.5 lb
3 lb
4.5 lb
(I came up with 2 answers and I need someone with the same answer, the two options that I came up with is 1.5 lb. or 4.5lb.
What information can be used to compare linear relationships?
Sample Response:
Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.
determine whether the sequence converges or diverges. if it converges give the limit.
48, 12, 3, 3/4, ...
Final answer:
The provided sequence is a geometric sequence that converges to 0 because its common ratio's absolute value is less than 1.
Explanation:
The sequence provided is 48, 12, 3, 3/4, suggesting a pattern where each term is divided by 4 to get the next term (this is a common ratio r = 1/4). This type of sequence is known as a geometric sequence, and to determine if it converges, we can apply the ratio test.
In a geometric sequence, successive terms approach zero if |r| < 1. Since the absolute value of the common ratio here is less than 1, the terms of the sequence will get progressively smaller and approach zero. Therefore, we can conclude that this geometric sequence converges, and the limit is 0.
Two angles are supplementary one angle measure 12 more than the other find the measures
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
a.
What is the area of the pool cover?
b.
What is the length of the rope?
Answer:
Given the data, the pool has a diameter of 20 feet, so, R=10ft.
The pool cover expands 12 inches beyond the pool, so, 12in.= 1 foot
Therefore, the radius of the pool cover will then be: 10+1= 11ft.
ANSWER A (pool cover)) r² π = 11² π = 121 π ft²
A.)= 121 π ft²
ANSWER B (rope)) l = 2 r π = 2 · 11 π = 22 π ft.
B.)= 22 π ft
Step-by-step explanation:
I got a 100% on it on founders edtell