use the graph to estimate the solution 8. y = x + 4 y = 3x - 1
Answers
The Slope-Intercept form of the equation of a line is:
\(y=mx+b\)Where "m" is the slope of the line and "b" is the y-intercept.
1. In this case, you have the first equation of the line in Slope-Intercept form:
\(y=x+4\)You can identify that:
\(\begin{gathered} m=1 \\ b=4 \end{gathered}\)The line intersects the x-axis when the value of "y" is:
\(y=0\)Substituting this value into the equation and solving for "x", you get that the x-intercept is:
\(\begin{gathered} 0=x+4 \\ x=-4 \end{gathered}\)Now you graph the first line.
2. The second line is:
\(y=3x-1\)You can see that:
\(\begin{gathered} m=3 \\ b=-1 \end{gathered}\)Find the x-intercept applying the same procedure used for the first line:
\(\begin{gathered} 0=3x-1 \\ 1=3x \\ \\ x=\frac{1}{3} \\ \\ x\approx0.33 \end{gathered}\)Now you can graph the second line.
See the graph below:
The point of intersection between the lines is the solution of the System of equations. Then, you can estimate that the solution is:
\(\begin{gathered} x=2.5 \\ y=6.5 \end{gathered}\)
Related Questions
Use synthetic division to find the result when 2x^4-8x³ - 27x² + 14x + 24 is divided by x-6
Answers
First, write the coefficients of the polynomial in order of decreasing degree and include a placeholder for missing terms:
2 -8 -27 14 24
6
Bring down the leading coefficient:
2 -8 -27 14 24
6
2
Multiply the divisor by the result of the previous step and subtract from the corresponding coefficients:
2 -8 -27 14 24
6
2 -12
48
2 -12 21
-42
2 -12 21 -28
168
2 -12 21 -28 192
The result of the division is 2x³ - 12x² + 21x - 28 with a remainder of 192.
according to data given in this table find percentage of absentees on friday
plz solve it CORRECTLY step by step
Answers
Answer:
\(\%Absent = 80.20\%\)
Step-by-step explanation:
Given
The attached data
Required
%Absentee on Friday
First, calculate the total present
\(Present = 42 + 36 + 40 + 36 + 38\)
\(Present = 192\)
Calculate the %Present on Friday
\(\%Present = \frac{Friday}{Present} * 100\%\)
\(\%Present = \frac{38}{192} * 100\%\)
\(\%Present = \frac{3800}{192}\%\)
\(\%Present = 19.80\%\)
Using complement rule:
\(\%Absent = 100\% - \%Present\)
\(\%Absent = 100\% - 19.80\%\)
\(\%Absent = 80.20\%\)
John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Answers
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
Obtain the required confidence interval for the difference between two population proportions. Assume that independent simple random samples have been selected from the two populations. A survey found that 37 of 74 randomly selected women and 47 of 74 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program. Group of answer choices
Answers
Answer:
The 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program = ( -0.293, 0.023)
Step-by-step explanation:
The formula for confidence interval for the difference between the proportions is given as:
p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2
From the question
We have two groups.
Group 1 = For women
A survey found that 37 of 74 randomly selected women
p1 = x/n1
n1 = 74
x1 = 37
p1 = 37/74
p1 = 0.5
Group 2 = For Men
A survey found out that 47 of 74 randomly selected men follow a regular exercise program
p2 = x/n1
n2= 74
x2 = 47
p2 = 47/74
p2 = 0.6351351351 ≈ 0.635
z = z score for 95% Confidence Interval = 1.96
The confidence interval for the difference between the proportions is given as:
p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2
0.5 - 0.635 ± 1.96 × √0.5 (1 - 0.5)/74 + 0.635(1 - 0.635)/74
-0.135 ± 1.96 × √(0.5 × 0.5)/74 + (0.635× 0.365)/74
-0.135 ± 1.96 × 0.08068750209663572
-0.135 ± 0.158147504109406
Hence:
= -0.135 - 0.158147504109406
= -0.2931475041
Approximately = -0.293
= -0.135 + 0.158147504109406
= 0.0231475041
Approximately = 0.023
Therefore, the 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program = ( -0.293, 0.023)
Every week at the Cougar Scouts meeting, Rosanne is in charge of the craft activity. This week, she decides to make pinecone bird feeders. At the meeting, Rosanne divides a bag of 1/3 birdseed evenly among 15 Cougar Scouts, and each scout gets of a cup of birdseed.
Use an equation to find the amount of birdseed in the bag.
Answers
The bag contains 4 cups of bird seeds for the Cougar Scouts.
What is a fraction ?
A fraction is the value of a given number after the decimal point.
There are two types of fraction they are proper fraction and improper fraction in proper fraction numerator is less than the denominator and in improper fraction numerator is greater than the denominator.
According to the given question
The bag of bird seeds are evenly distributed among 16 cougar scouts.
Each scout gets 1/4th cup of bird seeds.
Assuming bird seeds to be x cups
∴ x = (1/4) × 16
x = 4 cups
So, the amount of birdseed present in the bag is 4 cups.
Answer: 5 cups
Step-by-step explanation:
15 x (1/3)
Determine the turning points and distinguish between them when necessary y=x³ - 3x - 9x + 4
Answers
The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).
To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.
1. Find the derivative of the function:
y' = 3x² - 6x - 9
2. Set the derivative equal to zero and solve for x:
3x² - 6x - 9 = 0
3. Factorize the quadratic equation:
3(x² - 2x - 3) = 0
4. Solve the quadratic equation by factoring or using the quadratic formula:
(x - 3)(x + 1) = 0
This gives us two possible values for x: x = 3 and x = -1.
5. Substitute these critical points back into the original function to find the corresponding y-values:
For x = 3:
y = (3)³ - 3(3)² - 9(3) + 4
= 27 - 27 - 27 + 4
= -23
For x = -1:
y = (-1)³ - 3(-1)² - 9(-1) + 4
= -1 - 3 + 9 + 4
= 9
6. Therefore, the turning points are (3, -23) and (-1, 9).
Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.
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What would the height need to be for this curve to be a density curve?
1/5
1/4
1/2
1
Answers
For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.
Let's see how the height would need to be for this curve to be a density curve.A density curve is a statistical representation of the distribution of a dataset or population. Density curves are used to describe the distribution of continuous data and provide a visual representation of the likelihood of an event occurring within a specific range of values. It helps to determine the proportion of data that falls within a given range of values. A density curve is used to provide a graphical representation of data without showing the individual data points.To be a density curve, a curve must have the following properties:The curve should be non-negative.The area under the curve should be equal to 1.The curve should be smooth and continuous.There should be no values outside the range of the data.From the above properties, we can conclude that the height required for a curve to be a density curve depends on the data that the curve represents. As long as the curve meets the above conditions, it can be considered a density curve. So, there is no specific height required for a curve to be a density curve. The height of the curve can vary depending on the range of the data and the distribution of the data.For such more question on properties
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what is the value of x^2 - 6x + 9 when x = 2 + i?
Answers
The Expression x^2 - 6x + 9 when x = 2 + i is -2i
To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:
(2 + i)^2 - 6(2 + i) + 9
Simplifying the first term, we get:
(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2
Since i^2 = -1, we can substitute that in and simplify further:
(2 + i)^2 = 4 + 4i - 1 = 3 + 4i
Now we substitute this into the original expression:
(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9
Simplifying further, we get:
= 3 + 4i - 12 - 6i + 9
= 0 - 2i
= -2i
Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.
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If u guys help
Me this should be easy depending on who’s doing it ok what are the answers to this u guys have to figure it out This is 3rd grade homework I trying to help my friend and he doesn’t know what the rest are can u help please asap
Name
wrap
sign
wrote
gnaws
wring
knee
wreath
knit
knife
knight
knock
write
gnome
wrists
wreck
A. Write the spelling words that match the clues below.
1. street marker
S
4. a sharp tool
ínite
MA
2. tap on a door
5. cover a gift with paper
3. a ring of plants used for
decoration
B. Write the spelling word that best completes each sentence.
6. The doctor checked both her
after she fell.
P
7. He
a letter to the mayor about the park.
8. I am learning to
a wool scarf.
9. A beaver
trees into logs.
10. My friend likes to
silly poems about animals.
11. My little sisters
my room when they come in.
12. My story is about a brave
- who fights dragons.
13. I scraped my left
when I fell off my bike.
14. A
is small and usually wears a pointed hat.
15. We will
out the wet towels.
Answers
Answer: look at explanation
Step-by-step explanation:
number 3. wreath
number 8. knit
number 9. gnaws
number 10. write
number 11. wreck
number 12: knight
number 14: gnome
number 15: wring
write an equation in slope intercept form for the line that has a slope of 1/3 and passes through the point (3, -20)
Answers
y = 1/3x - 21 is the equation of the line in slope-intercept form.
What is a slope?
Slope is a measure of the steepness or incline of a line. It describes how much the dependent variable (usually y) changes for a given change in the independent variable (usually x).
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
We are given that the slope is 1/3 and that the line passes through the point (3, -20). We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is the point through which the line passes, and m is the slope. Plugging in the values we have:
y - (-20) = 1/3(x - 3)
Simplifying this equation:
y + 20 = 1/3x - 1
Subtracting 20 from both sides:
y = 1/3x - 21
This is the equation of the line in slope-intercept form.
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100 Points. Use the given features to sketch a linear graph. Only looking for an answer to A. Photo attached. Thank you!
Answers
Step-by-step explanation:
Linear graphs are straight line graphs to represent the relationship between two quantities. This graph helps in depicting a result in single straight lines. There is no use of curves, dots, bars, etc., and a straight line is denoted by the term linear.
Enter the number that belongs in the green box
Answers
The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:
\(c^2 = a^2 + b^2 - 2ab*cos(C)\)
In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:
\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)
49 = 16 + 25 - 40*cos(C)
49 = 41 - 40*cos(C)
40*cos(C) = 41 - 49
40*cos(C) = -8
cos(C) = -8/40
cos(C) = -0.2
To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:
C = arccos(-0.2)
Using a calculator, we find that C ≈ 101.54 degrees.
Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
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Hurry - Fill in the blanks
Answers
Answer:
The first value of a relation is an input value and the second value is the output value. A function is a specific type of relation in which each input value has one and only one output value.
An input is an independent value, and the output value is the dependent value, as it depends on the value of the input.
Use the triangle shown on the right to complete the statement:
_____ (75*)=14.1/x
Answer: cos
2nd part: Use the equation shown to solve for the value of x. Round to the nearest tenth.
cos(75*)=14.1/x x=14.1/cos(75*)
Answer: 54.5 in
Answers
Answer:
Step-by-step explanation:
The answer is 54.5 on edg
For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
What is right angle triangle property?In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.
\(\rm \cos=\dfrac{ adjacent}{hypotenuse}\)
Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.
The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.
Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,
\(\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}\)
Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.
For the second part, we need to find the value of x. Thus solve the above equation further as,
\(\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o\)
Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
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PLS HELP
Select the correct answer.
A museum curator estimates that 85% of people who attend the museum would return a second time. She randomly surveys
50 people and finds that only 75% indicate that they would return a second time. So she decides to randomly survey an additional
100 people.
if her model is valld, what could she expect from the 150 total survey results?
The difference between the data and the model will get larger.
The difference between the data and the model will stay the same.
O it is impossible to predict how the difference between the data and the model will change
The difference between the data and the model will get smaller.
O
Submit
Answers
The difference between the model and the data will get smaller.
What is the sample size?A sample is a percentage of the total population in statistics. You can use the data from a sample to make inferences about a population as a whole.
Given here, she 50 people and finds that only 75% and additional 100 people hence changing the sample size
As our sample size increases, the confidence in our estimate increases, our uncertainty decreases and we have greater precision. Thus with the increase in sample size, the data would move closer to the estimated probability.
Hence The difference between the model and the data will get smaller.
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Answer:
The difference between the data and the model will get smaller.
Step-by-step explanation:
Plato/Edmentum
express the following into standard form
\( \frac{1}{3500000000} \)
Answers
Answer:
350000
P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6
what is the nth term in a cube number sequence
Answers
Answer:
cube numbers: 1, 8, 27, 64, 125, ... - the nth term is. triangular numbers: 1, 3, 6, 10, 15, ... (these numbers can be represented as a triangle of dots).Step-by-step explanation:
IF IT HELPED UH PLEASE MARK ME A BRAINLIEST :-)Which word best describes the degree of overlap between the two data sets?
Responses
high
high
moderate
moderate
low
low
none
Answers
If 15 people can fit comfortably in a 5 ftby 5 squarewhat is the ratio of the people to the rectangle's area ?
Answers
Answer: 15:25
Step-by-step explanation: the number of people is 15 and the area would be 25
please help PLEASE HELP!!!!!!!!!!!!!!!
Answers
Step-by-step explanation:
you have to have some number for someone to solve it
Part A. Dario purchased a party size sub, and he decides to share it with three of his friends. so he cuts the sub into four equal pieces. however another one of his friends also showed up, and they are now five people in total now that the sun will be shared equally among five people will each person get more or less sub briefly state why do you think so. Part B. Dario decide to take each one of the four pieces and shared equally among the five of them first he divides one piece into five equal parts in shares it then the next one and so on what fraction of the party say sub did each person get after all the parts were shared out explain your reasoning
Answers
Answer: 4/6 = 2/32/3 = 2/3
Step-by-step explanation: hope this help
7x^7+10x^4+4x^3-5x^11-10x^6-6x^7
Answers
The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6
How to determine the valueTo determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.
These algebraic expressions are also identified with the presence of arithmetic operations,
These operations are;
AdditionBracketParenthesesSubtractionMultiplicationDivisionFrom the information given, we have that;
7x^7+10x^4+4x^3-5x^11-10x^6-6x^7
collect the like terms
7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6
add the like terms
x^7+10x^4+4x^3-5x^11-10x^6
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Find m and c for this line
Y+3x=1
Answers
Answer:
m = -3 ; c = 1
Step-by-step explanation:
y = -3x + 1
y = mx + c
m = -3
c = 1
Find the slope of the line that goes
through the points (0,7) and (-3,-5).
Answers
Riley put £450 into a savings account which
gathered simple interest at a rate of 2% per month.
After 6 months, Riley used some of the money in
the account to buy a bike costing £480.
How much money did Riley have left?
Answers
Answer:
£26.77
Step-by-step explanation:
450(100% + 2%)^6
= 450 (1.02)^6
= 506.77.
506.77 - 480 - 26.77.
Riley had £26.77 left.
what is one of the zeros of the function shown in this graph?
Answers
Answer:
x = -3 and x = 1 are the two zeroes of this function. Choose one of them for your answer.
Tina was observing the changing heights of a ball as it bounced over time. She graphed the function on this coordinate grid to show f(x), the height of the dropped ball, in feet, after its xth bounce.
Part A: What does the value of f(3) represent in the given context?
A.
After 4 bounces the height of the ball is 3 feet.
B.
After 3 bounces the height of the ball is 4 feet.
C.
After 4 bounces the height of the ball is 4 feet.
D.
After 3 bounces the height of the ball is 3 feet.
Part B: Tina said that a possible range for the given function is y > 0. Based on the given scenario, do you agree or disagree?
A.
I disagree; because the graph has an asymptote at y = 0, the height cannot be 0.
B.
I disagree; although the graph has an asymptote at y = 0, the ball will stop bouncing and have a height of 0.
C.
I agree; although the graph has an asymptote at y = 0, the ball will stop bouncing and have a height of 0.
D.
I agree; because the graph has an asymptote at y = 0, the height cannot be 0
Answers
Answer:
Step-by-step explanation:
Part A:
The value of f(3) represents the height of the ball after its 3rd bounce.
From the graph, we can see that the point corresponding to the 3rd bounce has a height of 4 feet.
Therefore, the correct answer is B. After 3 bounces, the height of the ball is 4 feet.
Part B:
The given function represents the height of the ball after each bounce. Since the ball is bouncing, its height will always be greater than zero.
The graph shows that the function has an asymptote at y = 0, which means that the height of the ball will approach zero as it bounces. However, this does not mean that the ball will never have a height of zero. The ball will eventually stop bouncing and come to rest on the ground, which corresponds to a height of zero.
Therefore, the correct answer is C. We agree that a possible range for the given function is y > 0.
Somebody please help
Answers
Answer:
Line A slope = 3/2
Line B slope = 2
Step-by-step explanation:
We create the triangles they request for each line, as shown in the attached image, which we use to calculate the vertical change (height of the triangle) and horizontal change (base of the triangle). The height and base of the triangles (depicted in red and blue matching the color of the lines) have been highlighted for easy identification.
We estimate the vertical and horizontal changes, as well as the slope, for each line as shown below:
Line A:
vertical change = (6 - 3 ) = 3
horizontal change = (2 - 0) = 2
slope of line A = 3 / 2
Line B:
vertical change = (6 - 4) = 2
horizontal change = (3 - 2) = 1
slope = 2 / 1 = 2
Write the equation in slope-
intercept form of the line that
passes through (6, -11) and is
parallel to the graph of
y= -2/3 x+12
Answers
Answer:
(y+11)=-2/3(x-6) is the answer
Find the measure of angle 1
Answers
Answer:
112*
Step-by-step explanation:
( 360 - 46 - 90 ) ÷ 2 = 112