Kuta Software In Systems of Two Solve each system by graphing. 2) y=x+2 1) y=-3x +41 y= 3x - 2
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ok
Equations : 4x + y = 2 x - y = 3
Equation 1 4x + y = 2 x - y = 3
x y x y
-2 10 -2 -5
-1 6 -1 -4
0 2 0 -3
1 -2 1 -2
2 -6 2 -1
The point where both lines cross is (1, -2) so it is the solution.
Related Questions
Can you help me pls with the answers
Answers
The remainder when 14 is divided by 3 is 2
What is remainder?
When we divide a number by another number if at the end if we have a number less than quotient and we can not divide further we say that the remaining number is remainder.
We are given a number as 14 and we divide 14 by 3
And on dividing 14 by 3 we get the quotient as 4 and remainder as 2.
Hence the remainder we get on dividing 14 by 3 is 2.
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an airplane, flying horizontally at 200 mph at an altitude of 3 miles, passes over a radar station. what is the rate of change of the angle of elevation between the radar station and the plane 3 minutes after the plane passes over the radar station? (the angle of elevation is the angle between the horizontal and a line between the radar station and the airplane.)
Answers
The rate of change of angle of elevation between the radar station and airplane is
[tex]\displaystyle \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]
The airplane is flying at the speed of 200 mph
The airplane is at an altitude of 3 miles over the radar station
The distance travelled by the airplane after 3 mins
distance = speed x time
= 200 mi/hr x 3 min
Since the speed is hour let us convert it to mins
= 200 x 3 x 1/60
= 600 / 60
= 10 miles
So , let us assume that the airplane is exactly at the top of the radar station at an altitude of 3 miles
Then the elevation angle of the between radar station and airplane can be find by
tan θ = O / A
where O is the opposite side to the angle of elevation
A is the adjacent side to the angle of elevation.
But we need the find the rate of change of angle of elevation , so let us differentiate on both side with respect to time
[tex]\displaystyle sec^{2}\theta\frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{A^{2}}[/tex]
[tex]\displaystyle \frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{sec^{2}\theta A^{2}}[/tex]
[tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{sec^{2}(10)^{2}}[/tex]
The altitude is gonna be a constant , thus the derivative of altitude will be zero whereas , the the distance travelled by airplane is changing with respect to time.
[tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{\frac{109}{100}(10)^{2}}[/tex]
We had found the value of sec²θ = (hyp/adj)²
[tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \frac{rad}{hr}[/tex]
Now , let us convert in terms of rad/min
[tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \left(\frac{1}{60}\right)[/tex]
[tex]\displaystyle \frac{d\theta}{dt} = \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]
Therefore , the rate of change of angle of elevation is -10/109 (rad/min)
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Jenna bought a new car for $29,000. She paid a 10% down payment and financed
the remaining balance for 48 months with an APR of 4.5%. Determine the monthly
payment that Jenna pays.
Answers
If the remaining balance for 48 months with an APR of 4.5%. the monthly payment that Jenna pays is: $595.17.
How to find the monthly payment?Using this formula to determine the monthly payment
P = A ×r × ( 1 +r)^n ÷( 1+ r)^n -1
Where:
P = Principal = ?
A = Amount = $29,000 × ( 1- .10) = 26,100
r = Interest rate = 4.5% / 12 = 0.00375
n = number of months = 48 months
Let plug in the formula
P = 26,100 × 0.00375 × ( 1+ 0.00375)^ 48 ÷ ( 1+ 0.00375)^ 48 -1
P = 26,100 × 0.00375 × ( 1.00375)^ 48 ÷ ( 1.00375)^ 48 -1
P = 26,100 × 0.00375 × 1.196814377 ÷ 1.196814377 -1
P = 26,100 × 0.00375 × 1.196814377 ÷ 0.196814377
P = $117.1382456 ÷ 0.196814377
P = $595.17
Therefore $595.17 is the monthly payment.
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a survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. a sample 20 employees is selected and the data is given below. education (no. of years) length of tenure in current employment (no. of years) age (no. of years) annual income ($) 17 8 40 124,000 12 12 41 30,000 20 9 44 193,000 14 4 42 88,000 12 1 19 27,000 14 9 28 43,000 12 8 43 96,000 18 10 37 110,000 16 12 36 88,000 11 7 39 36,000 16 14 36 81,000 12 4 22 38,000 16 17 45 140,000 13 7 42 11,000 11 6 18 21,000 20 4 40 151,000 19 7 35 124,000 16 12 38 48,000 12 2 19 26,000 10 6 44 124,000 for two people a and b with the same years of education and age, suppose a's length of tenure is 2 more years than b, what would the salary difference between a and b? group of answer choices -4387.76 2193.88 2689.24 10011.92 none of the choices
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The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model.
What is linear regression model?The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model. The response variable is another name for the dependent variable. Explanatory or predictive variables are other names for independent variables. Models with a single predictor are known as simple linear regression. Multiple predictor models are known as multiple linear regression. Models for numerous response variables using multivariate linear regression. Finding the weights (namely, W0 and W1) that result in the best-fitting line for the input data (i.e., the X characteristics) that we have is how linear regression functions. The line with the lowest price is chosen to be the greatest fit.Using an online multiple regression calculator, the estimated multiple linear regression equation that can be used to forecast the annual income using the number of school years completed (Education), length of tenure in the current employment, and age is as follows:
y = - 143481.1924 + 10011.9212x1 - 2193.8838x2 + 2689.2405x3
According to the general form of a multiple linear regression model:
-143481.1924 = intercept(c) ; where regression line crosses the origin
10011.9212x1 - 2193.8838x2 + 2689.2405x3 are weight coefficients of the three predictor variables ; x1, x2, and x3
y = predicted variable
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Solve 0.005x - 0.03 = 0.01
Answers
Given the equation:
[tex]0.005x-0.03=0.01[/tex]You need to solve for "x" in order to find its value:
1. Apply the Addition Property of Equality by adding 0.03 to both sides of the equation:
[tex]\begin{gathered} 0.005x-0.03+(0.03)=0.01+(0.03) \\ 0.005x=0.04 \end{gathered}[/tex]2. Apply the Division Property of Equality by dividing both sides of the equation by 0.005:
[tex]\begin{gathered} \frac{0.005x}{0.005}=\frac{0.04}{0.005} \\ \\ x=8 \end{gathered}[/tex]Hence, the answer is:
[tex]x=8[/tex]
In the accompanying diagram, points A, E, and B are collinear, measure of angle A= 30, measure of angle DEB= 130, and segment AB is perpendicular to segment BC. Find the measure of angle C and the measure of angle D.
Answers
Step-by-step explanation:
I assume the points D, E and C are also collinear (are on the same straight line).
that is something your teacher forgot to mention. but it is essential.
we have to remember :
1. the sum of all angles in a triangle is always 180°.
2. the sum of all angles around a single point on one side of a line is also always 180°.
3. the angles at the intersection point of 2 lines are the same on both sides of any of the intersecting lines, but they are left-right mirrored.
so,
angle A = 30°
angle DEB = 130°, so,
angle AED = 180 - DEB = 180 - 130 = 50°.
therefore, angle BEC = AED = 50°
therefore, angle D = 180 - 30 - 50 = 100°.
we know, angle B = 90° (AB is perpendicular to BC).
therefore,
angle C = 180 - 90 - 50 = 40°
What is the equation to this graph? pls help
Answers
Answer is y=1/2x+2 because the slope is 1/2 and the starting point is +2
A 46 gram sample of a substance that's a by product of fireworks has a k-value of 0.1394. Find the substance's half-life in days. Round your answer to the nearest tenth.
N=N0e^-kt
Answers
The half life obtained to the nearest tenth is 5.0 days.
What is the half life?The half life is the time taken for only half of the initial amount of the radioactive substance to remain. We know that we have to use the formula;
N=N0e^-kt
N = amount present at time t
No = Amount initially present
k = The constant
t = The half life
We now have that;
HALF LIFE = O.693/k
We have to recall that the term k is the decay constant for the process as shown.
Half life = O.693/0.1394
Half life = 5.0 days
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the dial on a combination lock contains markings which represent the numbers from 0 to 39. how many 3- number combinations are possible if the first and the second must be different odd numbers, while the third number must not be an odd number?
Answers
The dial for the standard combination lock is fastened to a spindle. The spindle travels through many wheels and a drive cam inside the lock. Every number has one wheel, hence the number of wheels in a wheel pack depends on how many numbers are in the combination.
The lock uses the numbers 0 to 39 and has 64,000 distinct combinations.
How many possible three-number combinations are there?
You have 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit, giving you 10x9x8 = 720 if you want all three possible numbers with no duplication of the digits.
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X 2 4 6 8 10
Y 1, 3, 5 , 7, 9
(a) Is it a function?
(b) Domain:
(c) Range:
Answers
Answer:B
Step-by-step explanation:
If three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c. Write an absolute value equation to represent the definition of betweenness.
Answers
The absolute value equation to represent the definition of betweenness is
AB + BC = AC ↔ B ∈ A,C
Absolute value equation:
An absolute value equation is a function that contains an algebraic expression within absolute value symbols.
Given,
Here we have the statement "If three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.".
Here we need to find the absolute value function for this statement.
In order to find the absolute value equation,
First we have to identify the symbols for the terms mentioned in the statement they are,
between = ∈
if and only if = ↔
sum = +
Now, we have to divide the statement as two parts.
First one is, "c lie on the same line, then b is between a and c"
It can be written as,
B ∈ A,C
Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."
Which can be written as
AB + BC = AC
When we combine it, the we get the absolute value equation as,
B ∈ A,C ↔ AB +BC = AC
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Sandra saves 12% of her salary for retirement. This year her salary was $1,000 more than in the previous
year, and she saved $4,920. What was her salary in the previous year?
Answers
Answer:
$32,000
Step-by-step explanation:
Create a system of equations and use algebra to write a quadratic equation with points (-3,-4), (3,14), and (0,-4). Equations 1: -4=9a-3b+c Equation 2: 14=9a+3b+c Equation 3: -4=c
what is the resultiNg of b?
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In the system of equations, the value of the variable 'b' will be 3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of the equations is given below.
Equations 1: - 4 = 9a - 3b + c
Equation 2: 14 = 9a + 3b + c
Equation 3: - 4 = c
Put the value of c in equations 1 and 2, then we have
- 4 = 9a - 3b - 4
9a - 3b = 0 ...4
14 = 9a + 3b - 4
9a + 3b = 18 ...5
Subtract equation 4 from 5,
9a + 3b - 9a + 3b = 18 - 0
6b = 18
b = 3
In the system of equations, the value of the variable 'b' will be 3.
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help pls it's so hard (that's what she said) but fr
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If we draw a vertical line and it crosses the figure more than once, then it is not a function.
So, the only graph that a vertical line will intersect the line once is graph A:
B, C and D are intersected more than 1 time, so they are not functions.
Answer: A
A family buys a studio apartment for 200,000 . They pay a down payment of 50000
Answers
Answer:
A 20% B. 45%
Step-by-step explanation:
A 40,000/200000=.2 0r 20%
b. 90,000/200000=.45 or 45%
A package contains 11 resistors, 2of which are defective. If 4 are selected find the probability of getting the following results.P(1 defective)=
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From the given values, we know there are 2 defective resistors and 9 not defective. then, we have
[tex]P(1\text{ defective)=}\frac{C^9_3\times C^2_1}{C^{11}_4}[/tex]where
[tex]C^9_3[/tex]denote the combinations of 9 elements taking in 3, that is 3 good resistor from the 9 which are not defective. Similarly,
[tex]C^2_1[/tex]denotes the combinations of 2 elements taking in 1, that is, 1 defective resistor form the 2 defective resistors.
Then, we have
[tex]P(1\text{ defective)=}\frac{84\times2}{330}[/tex]then, the answer is
[tex]P(1\text{ defective) =}0.509[/tex]5. For which values of x and y is line p parallel to line q? (1 point)
R
(26y)⁰
Ox= 5, y = 3
Ox= 1, y = 5
Ox=3, y=5
Ox=3, y=6
(16x + 2)°
(45x-51
Answers
Answer:
x = 3 and y = 5
Step-by-step explanation:
1st: The sum of the same side interior angles equal 180°. Use this to solve for x.
45x - 5 + 16x + 2 = 180
61x - 3 = 180
61x - 3 + 3 = 180 + 3
61x/61 = 183/61
x = 3
2nd: find the measure of angle 16x + 2
16x + 2
16(3) + 2
48 + 2
50°
3rd: the sum of the 50° angle and the angle 26y° is 180 since they make a straight angle. Make an equation and solve for y.
50 + 26y = 180
50 - 50 + 26y = 180 - 50
26y = 130
26y/26 =130/26
y = 5
Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36. His work is shown below.
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
66 + 36 = 3 (22 + 12)
What statement best describes Gary’s error?
Gary did not use correct factors for 66 in the equation.
Gary did not use correct factors for 36 in the equation.
Gary did not use two equivalent expressions in the equation.
Gary did not use the greatest common factor in the equation. pls hurry 10 mins left
Answers
A statement which best describes Gary’s error is that: Gary did not use correct factors for 66 in the equation.
What is the distribution property of multiplication?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.
Mathematically, the distributive property of multiplication is given by this expression:
a(b + c) = ab + ac.
Also, the correct greatest common factor of 66 and 36 is given by:
Greatest common factor (GCF) = 6
By applying the distributive property of multiplication, we have:
66 + 36 = 6(11 + 6)
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Two cars are initially 10 miles parat on the same straight road and are moving towards each other. One car is going 30 miles per hour and the other car is going 36 miles per hour. How far apart are the two cars 2 minutes later?
Answers
Answer:
Let's break down the given information.
Car A
Speed - 30 mph
Hence the distance traveled per minute would 30/60 mph which is 0.5 Miles every minute.
Car B
Speed - 36 mph
The distance traveled per minute would 36/60 mph which is 0.6 Miles every minute.
Initial distance between the cars is 10 Miles
Car A travels 1 miles in 2 minutes and Car B travels 1.2 miles in 2 minutes.
Hence to calculate the distance between the 2 cars we need to calculate
Initial distance - Distance travelled by Car A - Distance traveled by Car B
Which is
10 - 1 - 1.2
7.8 Miles distance between the 2 cars
A fair coin is flipped 10 times. Each flip is independent.
What is the probability of getting exactly eight heads?
Answers
Answer:
8 out of 10.
Step-by-step explanation:
if you flip a coin independent then it doesn't matter what the other outcomes are. So if it's a one out of two chance every time then it's 8 /10.
-5/2 can be simplified?
If it can be simplified, would the answer be a fraction or a decimal?
Answers
Answer: -2 1/2 or -2.5
Step-by-step explanation:
Yes, it can be simplified.
-5/2 can be simplified to -2 1/2 which can be as a decimal as -2.5
I need this answered please
Answers
The rate of the slowest car is 86 km/hr using the concept of relative velocity.
What is Relative velocity?Relative speed is the rate at which one moving body moves in relation to another. The differential between two moving bodies determines their relative speed while they are traveling in the same direction. However, when two bodies are traveling in opposition to one another, the relative speed is determined by averaging their respective speed.
Let the speed of 1st car is v₁.
Let the speed of 2nd car is v₂.
v₁- v₂ = 18 km/hr --- (1)
And using the concept of relativity.
S(rel) = D(rel)/time
S(rel) = 360 / 2
S(rel) = 190
v₁ + v₂ = 190 --- (2)
Adding equations 1 and 2 we get
v₁ = 104 km/hr
v₂ = 86 km/hr
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1 billion, 1 million compare and give the factor
Answers
Answer:
1000000
Step-by-step explanation:
100000000: 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5
100000: 2 2 2 2 2 5 5 5 5 5
GCF: 2 2 2 2 2 5 5 5 5 5
The Greates Common Factor (GCF) is: 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 = 100000
5. Estimation What is the greatest possible integer solution of the inequality
3.806x< 19.902?
Answers
The greatest possible integer of the inequality is 19.902.
What is the inequality?
In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equal. But various inequalities are used to compare the values, as to if it is less than or greater than. The different inequality symbols, properties, and methods for resolving linear inequalities inside one variable and two variables will all be covered in this article along with examples.
Given that,
3.806< 19.902
In which, less than inequality is used.
The given numbers are in decimal form.
comparison be between the given numbers and check which one is greater.
3.806< 19.902
19.902 is the greater than 3.806
Hence, the greatest possible integer is 19.902.
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I need this answered please
Answers
Answer:
76 child tickets were sold
Step-by-step explanation:
let a represent number of adults and c number of child tickets sold, then
a + c = 165 → (1)
5.8a + 8.9c = 1192.6 → (2)
multiplying (1) by - 5.8 and adding to (2) will eliminate a
- 5.8a - 5.8c = - 957 → (3)
add (2) and (3) term by term to eliminate a
0 + 3.1c = 235.6
3.1c = 235.6 ( divide both sides by 3.1 )
c = 76
that is 76 child tickets were sold that day
Jamie has 8/10 of a
candy bar leftover. He
wants to split it into 4
pieces. How big will
each piece be?
Answers
Answer: 1/5
Step-by-step explanation: It might be first easier to put it in decimal form so 8/10 is 0.8 and 0.8 divided by 4 is 0.2. 0.2 as a fraction is 1/5.
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
convert element to fraction: 4 = [tex]\frac{4}{1}[/tex]
= [tex]\frac{8}{12}[/tex] ÷[tex]\frac{4}{1}[/tex]
The fraction rule: a/b ÷ c/d = a/b x d/c
= [tex]\frac{8}{12}[/tex] × [tex]\frac{1}{4}[/tex]
Cross - cancel common factor: 4
= [tex]\frac{2}{12}[/tex]
Cancel the common factor: 2
= [tex]\frac{1}{6}[/tex]
A laptop computer originally priced at $1,700 now sells for $1,800. What is the percent of increase?%.The percent of increase is(Type an integer or decimal rounded to one decimal place as needed.)
Answers
EXPLANATION:
We are given the original price of a laptop computer at $1,700.
Now the price has been increased to $1,800.
Note that there is a $100 increase over the original price.
For us to calculate the percent increase we shall use the ratio of the increase over the original price and calculate as a percentage.
[tex]\begin{gathered} Original\text{ price}=1700 \\ Increase=100 \\ Percent=x \end{gathered}[/tex]We can now set up the following equation;
[tex]\frac{100}{1700}=\frac{x}{100}[/tex]We now cross multiply;
[tex]\frac{100\times100}{1700}=x[/tex][tex]\frac{10000}{1700}=x[/tex][tex]x=5.8823...[/tex]Rounded to one decimal place, the percent increase is;
ANSWER:
[tex]Increase=5.9\%[/tex]are the figures similar why or why not?
Answers
Answer: Yes
Step-by-step explanation:
because their overall shape it the same, their size is the only thing that sets them apart, so they're not identical
Can anyone do these
Answers
Answer: 1. Complementary
2. Supplementary
3. 116
4. 17
5. A- 28 B-152 C-118
4.7.4 Modeling Pumpkin launch, we were covering graphs of quadratic functions please help! Thank you
Answers
Using a quadratic function, it is found that:
a) The coordinates of the second x-intercept are: (50,0).
b) The vertex shows the maximum flight of the projectile.
c) The coordinates of the vertex are (25, 62).
3) The graph of the equation y = -0.0992(x² - 50x) is given at the end of the answer.
Quadratic functionA quadratic function has two x-intercepts, x' and x'', and is defined as follows:
y = a(x - x')(x - x'').
The intercepts are given as follows:
First x-intercept: coordinates (0,0), as the fruit is thrown from the ground.Second x-intercept: coordinates (50,0), as the fruit travels a distance of 50 feet to hit the ground.The vertex is found as follows:
x-coordinate of 25, which is the mean of the two intercepts.y-coordinate of 62, which is the maximum height.Hence the coordinates are: (25, 62).
The equation can be defined as follows:
y = ax(x - 50)
y = a(x² - 50x).
When x = 25, y = 62, hence the leading coefficient is found as follows:
62 = a(25² - 50(25))
-625a = 62
a = -62/625
a = -0.0992.
Hence the equation is:
y = -0.0992(x² - 50x).
The domain of the function is between the roots, hence 0 ≤ x ≤ 50, and the graph is sketched at the end of the answer.
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