3. Consider the linear equation 2y - 3x = 5.
a. The pair (-1, 1) is a solution to the equation. Find another (x, y) pair that is
a solution to the equation.
b. Are (-1, 1) and (4, 1) solutions to the inequality 2y – 3x < 5? Explain how
you know
c. Explain how to use the answers to the previous questions to graph the
solution set to the inequality 2y - 3x < 5.
-
Answers
Answer:
Step-by-step explanation:
a.
2y - 3x = 5
2(-2) - 3x = 5
-4 - 3x = 5
-3x = 9
x = -3
(-3,-2) is another solution
b.
(-1,1)
2y - 3x = 5
2(1) - 3(-1) = 5
2 + 3 = 5
5 = 5
true, the point is a solution to the equation because the equation is true after substituting x and y with the point (-1,1)
(4,1)
2y - 3x = 5
2(1) - 3(4) = 5
2 - 12 = 5
-10 = 5
not true, the point is not a solution to the equation because the equation is not true after substituting x and y with the point (4,1)
c. You can use the points from the given (-1,1) and (-3,-2) to form a line. You then shade whichever half solves the solution using points on the graph.
Related Questions
ralph records the time it takes for each of his classmates to run around the track one time. as he analyzes the data on the graph, he locates the mean and median time. which component of data analysis is ralph utilizing?
Answers
The component of data analysis that Ralph is utilizing is the overall spread of the data. That is option D.
What is data analysis?Data analysis is defined as the method a researcher uses to collect, clean, sort, and process raw data in a way that it's representation can be understood by the reader.
The mean of a data set is defined as the addition of all the data set which is then divided by the number of the data set.
The median of a data set is the number that falls at the middle of the set after being arranged in an ascending or descending order.
Therefore, to find the mean and median of a data set will depend on the spread out of the data.
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Complete question:
Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on the graph, he notices very little variation between his classmates' times.
Which component of data analysis is Ralph observing?
A. An outlier in the data set
B. The overall shape of the data
C. The center of the data set
D. The overall spread of the data
Answer:
The overall spread of the data.
Step-by-step explanation:
Got it right on the test.
sketch the solution to each system of inequalities
Answers
The solution to the system of inequalities y ≤ 2x + 2 and y < -2x - 3 can be represented by a graph. The inequality y ≤ 2x + 2 represents a line with a slope of 2 and y-intercept of 2. The inequality y < -2x - 3 represents a line with a slope of -2 and y-intercept of -3. ( The graph attached)
SYSTEM OF INEQUALITIESThe inequality y ≤ 2x + 2 represents a line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2 and the y-intercept is 2. To graph this inequality, we can first plot the line by using the y-intercept, which is the point (0,2) on the graph. Then, we can use the slope to find additional points that fall on the line, such as (1,4) or (-1,0). Once we have plotted several points, we can connect them to form the line.
The inequality y < -2x - 3 represents a similar line, but with a different slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. To graph this inequality, we can use the same process as before by first plotting the y-intercept (0,-3), and then using the slope to find additional points that fall on the line.
The solution to the system of inequalities is the area that lies on one side of the first line and the opposite side of the second line, which is the area between the two lines. This area can be represented by shading the region below the first line and above the second line on the graph. It is important to note that the solution region is not including the lines themselves, because the inequalities are strict inequalities.
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pls help, it is due now. Thank You so much to whoever helps!
Answers
Answer:
(7, -1)
Step-by-step explanation:
3x + 7y = 14
y = x - 8
3x + 7(x - 8) = 14
3x + 7x - 56 = 14
10x - 56 = 14
Add 56 to both sides.
10x = 70
Divide both sides by 10.
x = 7
3(7) + 7y = 14
21 + 7y = 14
Subtract 21 from both sides.
7y = -7
Divide both sides by 7.
y = -1
(7, -1)
Plsss help I’ll give u brainlest and 10 points
Answers
It is known that X has a uniform distribution with μ=0.5 minutes and σ=0.29 minutes. Suppose a random sample of 64 people is selected. The shape of the sampling distribution of X
ˉ is: Uniform Approximately Normal Normal not enough information to determine
Answers
In this scenario, the shape of the sampling distribution of X-bar is approximately normal.
The sampling distribution of the sample mean, X-bar, can be determined by the Central Limit Theorem. In this case, since the sample size is large (n = 64) and the underlying distribution (X) is approximately normal, the sampling distribution of X-bar will also be approximately normal. The Central Limit Theorem states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of X-bar tends to become more and more normal. Therefore, in this scenario, the shape of the sampling distribution of X-bar is approximately normal.
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given that ac is perpendicular to ab and equation of bc is y=-5x+47 find coordinates of c if a(3,6) and b(7,12)
Answers
y - 6 = (1/5)(x - 3)
Simplifying, we get:
y = (1/5)x + 27/5
To find the coordinates of point C, we need to find where BC and AC intersect. We can do this by setting the equations of BC and AC equal to each other and solving for x:
-5x + 47 = (1/5)x + 27/5
Multiplying both sides by 5, we get:
-25x + 235 = x + 27
Simplifying, we get:
26x = 208
x = 8
Now that we know x = 8, we can plug it into either equation to find y:
y = -5(8) + 47 = 7
Therefore, point C has coordinates (8, 7).
PLEASE HELP, NEED IT BY TODAY
Write three equations. Each equation must include the numbers 3 and 30.3 and must be easy to solve by inspection. Solve your equations.
Answers
The three equations are:
3x = 30.3
30.3 - x = 27.3
3x + 30.3 = 63.6
We have,
Equation 1:
3x = 30.3
Solving for x, we can divide both sides by 3:
x = 10.1
Equation 2:
30.3 - x = 27.3
Solving for x, we can subtract 27.3 from both sides:
x = 3
Equation 3:
3x + 30.3 = 63.6
Solving for x, we can first subtract 30.3 from both sides:
3x = 33.3
Then, we can divide both sides by 3:
x = 11.1
Thus,
The three equations are:
3x = 30.3
30.3 - x = 27.3
3x + 30.3 = 63.6
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A(n) _____ leader is an individual who grows into the leadership role, often out of necessity.
a. appointed
b. autocratic
c. democratic
d. emergent
e. laissez-faire
Answers
The correct answer is d. emergent.
An emergent leader is an individual who grows into the leadership role naturally, often due to circumstances or necessity. They are not appointed or assigned to the position of leadership but rather emerge from the group or organization based on their skills, qualities, or actions.
Emergent leaders may possess certain qualities or demonstrate their competence and ability to guide and influence others. They gain recognition and respect from their peers, leading to their emergence as leaders within the group or organization.
This type of leadership often occurs in situations where formal leadership structures may be absent or ineffective, and individuals step up to take charge based on their capabilities and the needs of the group.
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is Pi/2 rational or irational explain your thinking
Answers
Answer:
irrational
Step-by-step explanation:
pi itself is an irrational number, pi/2 will also be an irrational number
Answer:
irrational
Step-by-step explanation:
it's an irrational number divided by a rational so therefore it is irrational
create a flowchart using the bisection method when a=2 and b=5 and y=(x-3)3-1
Answers
1. Set the initial values of a = 2 and b = 5.
2. Calculate f(a) and f(b) and check if they have different signs.
3. Use the bisection method to iteratively narrow down the interval until the desired accuracy is achieved or the maximum number of iterations is reached.
Here's a step-by-step guide using the given values:
1. Set the initial values of a = 2 and b = 5.
2. Calculate the value of f(a) = (a - 3)^3 - 1 and f(b) = (b - 3)^3 - 1.
3. Check if f(a) and f(b) have different signs.
4. If f(a) and f(b) have the same sign, then the function does not cross the x-axis within the interval [a, b]. Exit the program.
5. Otherwise, proceed to the next step.
6. Calculate the midpoint c = (a + b) / 2.
7. Calculate the value of f(c) = (c - 3)^3 - 1.
8. Check if f(c) is approximately equal to zero within a desired tolerance. If yes, then c is the approximate root. Exit the program.
9. Check if f(a) and f(c) have different signs.
10. If f(a) and f(c) have different signs, set b = c and go to step 2.
11. Otherwise, f(a) and f(c) have the same sign. Set a = c and go to step 2.
Repeat steps 2 to 11 until the desired accuracy is achieved or the maximum number of iterations is reached.
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This is confusing! Help me show my work and explain:( Its only for number 15
Answers
Answer:
it is too hard and we didn't learn it
What is 5^2 + 45 - 67 + 15x, when x is 7?
Answers
Answer:
108
Step-by-step explanation:
5^2 + 45 - 67 + 15x when x = 7
= 5^2 + 45 - 67 + 15(7)
= 25 + 45 - 67 + 105
= 70 - 67 + 105
= 3 + 105
= 108
So, the answer is 108
1) Find the solution set of the quadratic inequality -x²+x+6≥0 on the set of all i) N = natural numbers. ii) Z = integers. (5pts) iii) R = real numbers.
2) Someone bought 16 two types of books in birr 1560. He bought one mathematics book in birr 120 and one biology book in birr 80. How many mathematics and biology books did he buy?
3) Show the following relations f≤ NX N and g = R XR are functions or not. a) f = {(ab, a + b): a,b € N} b) g = {(labl, a + b): a, b = R} x
4) Let f(x) = 2 and g(x)=be functions. The find x²-5x+6 a) Dom (f) and Dom (g) b) Dom (f±g) and Dom (fg) c) Dom() d) Dom (fog) e) Dom(gof)
5) Find all roots (zeros) of the polynomial x4 -x³-5x² - x - 6.
Answers
i) N: The quadratic inequality -x²+x+6≥0 can be factored as -(x-3)(x+2)≥0. Thus, the solution set is {1,2,3,4,5,...}. ii) Z: The quadratic inequality can be factored as -(x-3)(x+2)≥0.
The values of x that satisfy the inequality are x ≤ -2 and x ≥ 3. Thus, the solution set is {...,-3,-2,-1,0,1,2,3,...}. iii) R: The quadratic inequality can be factored as -(x-3)(x+2)≥0. The values of x that satisfy the inequality are x ≤ -2 and x ≥ 3. Thus, the solution set is (-∞,-2] ∪ [3,∞).
Let the number of mathematics books be x and the number of biology books be y. Then, x+y=16 and 120x + 80y = 1560. Solving for x and y, we get x=9 and y=7. Thus, the person bought 9 mathematics books and 7 biology books.
a) f is a function because for each value of a and b in N, there is a unique value of a+b. b) g is not a function because for a given value of |ab|, there can be multiple values of a+b, since a and b can take on any real values.
a) Dom(f) = R and Dom(g) = R. b) Dom(f+g) = R and Dom(fg) = R. c) Dom(1/f) = {x | x ≠ 0} and Dom(√f) = {x | x ≥ 0}. d) Dom(fog) = Dom(g) = R. e) Dom(gof) = Dom(f) = R.
To find the roots of the polynomial x^4 - x^3 - 5x^2 - x - 6, we can use the rational root theorem to test possible rational roots. The possible rational roots are ±1, ±2, ±3, ±6. Testing these values, we find that x=-1 and x=2 are roots of the polynomial.
Using long division, we can factor the polynomial as (x-2)(x+1)(x^2-3x-2), which has additional roots of x=3+√11 and x=3-√11. Thus, the roots of the polynomial are x=-1, x=2, x=3+√11, and x=3-√11.
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Answer:
Step-by-step explanation:
c (3,5)
Help I’ll give Brainly est
Answers
Answer:i think a
Step-by-step explanation:
The first, second and third terms of a geometric progression are the first, fourth and tenth terms, respectively,
of an arithmetic progression. Given that the first term in each progression is 12 and the common ratio of the geometric progression is r, where r # 1, find:
a) the value of r
b) the sixth term of each progression
Answers
Answer:
a) r = 2
b)
GP a₆ = 384
AP a₆ = 32
Step-by-step explanation:
First term a₁ = 12 for both progressions
r = common ratio, d = common difference
nth term of geometric progression = a₁ x rⁿ⁻¹
nth term of arithmetic progression = a₁ + (n - 1)d
Second term of GP = Fourth term of AP
=> 12r¹ = 12 + 3d
==> 12r = 12+ 3d (1)
Third term of GP = 10th term of AP
=> 12r² = 12 + 9d (2)
3 x (1) => 3(12r = 12 + 3d) => 36r = 36 + 9d (3)
(2) - (3) gives12r² -36r = 12 - 36
12r² - 36r = 12 + 9d - (36 + 9d)
12r² -36r = -24
12r² -36r + 24 = 0
Dividing by 12 gives
r² - 3r + 2= 0
We can factor r² - 3r + 2 as (r - 1)(r-2)
r² - 3r + 2= 0
=> (r - 1)(r-2) = 0
=> r = 1 or r = 2
r cannot be 1 since all terms of the GP will be equal with a common ratio of 1
Therefore r = 2 (Part a)
Using equation (1) we get:
12r = 12+ 3d
12 x 2 = 12 + 3d
24 = 12 + 3d
3d = 24 - 12 = 12
d = 12/3 = 4
So the common ratio, r, is 2. Common difference d = 4
6th term of GP =12 x r⁵ = 12 x 2⁵ = 12 x 32 = 384
6th term of Ap = 12 + 5d = 12 + 5(4) = 12 + 20 = 32
After its Saturday competition, a swim team ordered three orders of pizza rolls and five orders of fried pickles for a total cost of $22. After its Tuesday night competition, the team ordered six orders of pizza rolls and two orders of fried pickles for a total cost of $28. what is the price of each appetizer? show your work.
Please help
Answers
Answer:
pizza rolls = $4
fried pickles = $2
Step-by-step explanation:
3 x 4 = 12
5 x 2 = 10
BRAINLY TO WHOEVER HELPS AND GET IT RIGHT
~no links pls~
Answers
Answer:
4 yards saved
Step-by-step explanation:
two adjacent sides: 6 + 8 = 14
diagonal: √(6² + 8²) = √100 = 10
14 - 10 = 4
Suppose you have two similar rectangular prisms. The volume of the smaller rectangular prism is 64 in³ and the volume of the larger rectangular prism is 1,331 in³. What is the scale factor of the smaller figure to the larger figure?
4:11
1:21
3:10
9:25
Answers
Answer: A 4:11
Step-by-step explanation:
The scale factor for volume is:
64:1331 > you are working with volume, you need to take
the cube root of the ratio because the dimensions are
cubed
∛64 : ∛1331
4:11
A
a lump sum of $2000 is invested at 4.2% compounded continuously. (a) write the function for the model that gives the future value of the investment in dollars after t years. f(t)
Answers
The function for the model that gives the future value of the investment in dollars after t years is: f(t) = 2000.e⁰·°⁴²t
Give, a lump sum of $2000 is invested at 4.2% compounded continuously.
Hence we have:
P = $2000
rate of interest = 4.2%
years = t
we know that A = Pe^rt
Substitute the above values in the formula.
Amount = f(t)
f(t) = 2000.e⁰·°⁴²t
hence we get the function for the model that gives the future value of the investment is f(t) = 2000.e⁰·°⁴²t
Therefore we get the required function.
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1/6(x+6)=11 Solve the equation.
Answers
1/6(x+6)=11
distribute
1/6x+1=11
-1 on both sides
1/6x=10
×6 on both sides
1x=60
x=60
PLEASE HELP FOR BRAINLEST!!!
Answers
Answer:
oh this isnt math but im learning about this
electrical ; thermal
Step-by-step explanation:
because the computer turns on with electricity then it gets hot which is thermal
What is the equation in slope-intercept form of a line that passes through the point (4, 5) and has a slope of 12?
Y=_x+_
Answers
Answer:
y= 12x -43
Step-by-step explanation:
y-5 = 12(x-4)
y-5= 12x-48
+5 +5
y= 12x- 43
Which expression is equivalent to (m−5n−3)−3?
A. m−15n−9
B. m15n9
C. m−8n−6
D. 1 over the quantity m raised to the eighth power times n raised to the sixth power end quantity
Answers
Answer:
m - 5n - 6
Step-by-step explanation:
See the attached picture
researchers conducted a randomized comparative experiment to test a new drug to help balding men keep their hair. forty-two percent of the placebo group kept or increased their hair compared to 86% of the men getting the new drug. what can we conclude?
Answers
The correct option is A, we can conclude the placebo effect partially explains the results seen in the men taking the new drug.
The placebo effect is a phenomenon where a person experiences an improvement in their condition after receiving a treatment that is inactive or has no therapeutic effect. This can occur when a person believes that they are receiving an effective treatment, and their expectations and beliefs about the treatment can influence their experience of the treatment's benefits. The placebo effect can be observed in a range of conditions, including pain relief, depression, anxiety, and even in some cases, more objective measures such as blood pressure and heart rate.
Placebo treatments can come in many forms, including sugar pills, saline injections, or sham surgeries, among others. While the mechanism behind the placebo effect is not fully understood, it is thought to involve a complex interplay between psychological and physiological factors.
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Complete Question: -
Researchers conducted a randomized comparative experiment to test a new drug for helping balding men keep their hair. 42% of the placebo group kept or increased their hair compared to 86% of the men getting
the new drug. What can we conclude?
A. The placebo effect partially explains the results seen in the men taking the new drug.
B. The placebo effect is not present in this experiment because the men are randomly assigned to treatments.
C. The results of this experiment cannot be trusted because of the placebo effect.
How much more does the 5-year loan cost overall than the 4-year loan?
Answers
Answer:
$600 overall
Step-by-step explanation:
Answer:
$600 more overall
Step-by-step explanation:
i'm great at math
A shopper bought the following items at the farmer’s market: 15 tomatoes for $9.30 What was the cost per tomato?
Answers
Answer:
The answer is 3.12
Step-by-step explanation:
Answer:
the answer is 62 cents per tomato.
Step-by-step explanation:
PLEASE HELPPP!!!!!!!!!!!!!!
Answers
Hey there!
The answer you're looking for is C.
Answer:
c
Step-by-step explanation:
A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?
2y = 16x +14
y = 8x – 7
y = –8x + 7
2y = −16x − 14
Answers
Step-by-step explanation:
the answer is 2y=16x+14
The equations that could be the other equation are y = 8x - 7 and y = -8x + 7.
If the system of equations has no solution, then the other equation must not have the same slope-intercept form as the first equation.
The slope-intercept form of the equation y = 8x + 7 is y = mx + b, where m is the slope and b is the y-intercept. Thus, the slope of the first equation is 8 and the y-intercept is 7.
Now let's check each of the given equations to see which one could be the other equation.
2y = 16x + 14
Rewriting this equation in slope-intercept form, we get y = 8x + 7, which is the same as the first equation. Therefore, this equation cannot be the other equation.
y = 8x – 7
This equation has the same slope as the first equation but a different y-intercept. Therefore, it represents a different line and could be the other equation.
y = –8x + 7
This equation has a slope that is the negative of the slope of the first equation, so it represents a different line. Therefore, it could be the other equation.
2y = −16x − 14
Rewriting this equation in slope-intercept form, we get y = -8x - 7, which has the same slope as the first equation but a different y-intercept. Therefore, it represents a different line and could be the other equation.
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If x = 2 and y = 5, evaluate the following expression:
100 – 3(3y – 4x)
Answers
Answer:
Step-by-step explanation:
100-3(3(5)-4(2)
100-3(15-8)
100-3(7)
100-21
79
how many participants would be needed for a within-subjects experiment comparing four different treatment conditions with a total of 20 scores in each treatment?
Answers
The number of participants that would be needed for a within-subjects experiment is 80.
What is an experiment?An experiment simply means a research that's conducted in order to get information about a particular thing.
In this case, we want to know the number of participants that will be neeed within-subjects experiment comparing four different treatment conditions with a total of 20 scores in each treatment.
This will be:
= Number of scores × Number of treatment
= 20 × 4
= 80
The participants needed are 80.
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