(1,-8); x = 3
Slope intercept form
Answers
An equation of the line in slope-intercept form include the following: y = 3x - 11.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (1, -8) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-8) = 3(x - (1))
y + 8 = 3(x - 1)
y = 3x - 3 - 8
y = 3x - 11
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Related Questions
2) Susan measures the amount of water in a measuring cup. She is pouring water into it at
a rate of 10 mL per second.
Write a function rule that models the height of the water in the cup over time.
b. State the dependent and independent variables.
Dependent
Independent
c. If the cup has a capacity of 100 mL, state an appropriate domain for this function and explain why you
chose it.
Domain:
Reason:
d. Susan tried to evaluate the function and wrote "f(5)." Explain what the number 5 represents in this
situation. Be specific!
e. What was Susan trying to find when she wrote f(5)? . Be specific!
f. Susan wrote f(7) = 70. Explain what these numbers mean in the context of the problem.
46
Answers
Answer:
a. f(t) = h = 10·t/(π·r²)
b. The dependent and independent variables are ;
Dependent = The height of the water in the cup over time, h
Independent = The time of measurement of the water height in the cup
c. The domain is 0 < t < 10
d. The 5 in f(5), represents 5 seconds
e. Susan was trying to find out what the height of the water in the cup will be after 5 seconds
f. The numbers mean that at 7 seconds the water in the cup is 70 units high
Step-by-step explanation:
a. The rate at which water is added to the cup in the question = 10 mL per second
The volume of water in the cup is V = π × r² × h
dV/dt = 10
dV = 10 × dt
V = ∫10 × dt = 10·t
The height of the water in the cup, h = V/(π × r²) = 10·t/(π·r²)
Therefore, we have the function that models the height of the water in the cup over time given as follows;
f(t) = h = 10·t/(π·r²)
b. The dependent and independent variables are given as follows;
Dependent variable = The height of the water in the cup over time, h
Independent variable = The time of measurement of the water height in the cup
c. The domain is 0 < t < 10
Given that the cup has a capacity of 100 mL, we have;
The maximum volume the up can hold = 100 mL
The time it will take to fill the 100 mL cup given that the rate of at which she is pouring water into the cup at 10 mL per second = 100 mL/(10 mL/s) = 10 s
Therefore, a reasonable domain for the independent variable, t is 0 < t < 10
d. We have that the function f(t) = h = 10·t/(π·r²)
Therefore, the 5 in f(5), represents the time in seconds at which the function was being evaluated, which is 5 seconds
e. Given that Susan wrote f(5), Susan was trying to find the height of the water in the cup after 5 seconds
f. Given that Susan wrote f(7) = 70, we have that at 7 seconds the height of the water in the cup is 70 units, where one unit is 1/(π·r²)
Which gives;
f(7) = h = 10 × 7/(π·r²) 70/(π·r²)
f(7) = 70/(π·r²)
Mr. Chen purchased a board game for $14 and 6 puzzles. Each puzzle cost the same amount. The total cost was $86. How much did each puzzle cost?
Answers
Answer:
$12
Step-by-step explanation:
$86-$14 = $72 that you have left for the 6 puzzles
72÷6 = 12
Which of the following statement(s) about multiple regression analysis is FALSE?A. Multiple regression analysis allows you to analyze more than one dependent (Y) variable at a time.B. Multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression.C. Multicollinearity occurs when two or more of the X variables are highly correlated with one another.D. Both A and B are false statements.E. All of the statements above are false.
Answers
Multiple regression analysis analyze more than one dependent variable at a time and multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression are false. Correct option is D.
The statement (A) that "Multiple regression analysis allows you to analyze more than one dependent (Y) variable at a time" is false. In multiple regression, there is only one dependent variable (Y) that is being predicted by a combination of independent variables (X).
The statement (B) that "Multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression" is also false.
Multicollinearity occurs when two or more independent variables (X) are highly correlated with each other, which can cause problems in accurately estimating the effect of each independent variable on the dependent variable.
The statement (C) that "Multicollinearity occurs when two or more of the X variables are highly correlated with one another" is true.
Therefore, the correct answer is (D) "Both A and B are false statements."
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Blake and Jordan bought the same type of candy bar. Blake ate 3/4 of his candy bar and Jordan ate 5/8 of his. How much more of a candy bar did Blake eat than Jordan?
Answers
Answer:
The answer would be 3/4 > 5/8
Help me pleaseeee!
Complete the following statement.
Percent is a fraction where_____parts make one whole.
Answers
Answer:
Percent is a fraction where the denominator is represented by 100 or 100 parts make one whole
Step-by-step explanation:
yesterday 270 tickets were sold today 216 were sold
A find the percent of change in the number of tickets sold from yesterday to today
B use the percent of change from part A to predict the number of tickets sold tomorrow round to the nearest ticket
C find the predicted percent of change in the number of tickets sold from yesterday to tomorrow round to the nearest tenth of a percent if necessary
Answers
Therefore , the solution of the given problem of percentage comes out to be The number of tickets sold fell by 20% , tomorrow ticket sold is 173 ticket and 35.92% percentage fall.
Define percentage.Any quantity that is expressed as a ratio of 100 is referred to as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." But it is commonly indicated by the "%" symbol. The percentage amount is flat with no dimensions. Percentages actually function as fractions because their numerator is 100. The percent symbol (%) should be used in front of a number to indicate that it is a percentage. If you correctly answered 75 of the total test questions, for example, you would score 75%.
Here,
Given:
Yesterday was 270, and today is 216.
Part A :The % change is calculated using the number of tickets that were sold the day before. Thus, 270 represents 100%.
the difference in ticket sales is 54 * (270 - 216).
54/270 is 0.20 x 100%, which is 20% * percent of change.
The number of tickets sold fell by 20%.
Part B:
20/100 * 216 = 43.2 or 43
So,
Tomorrow ticket sold are = 216 -43 = 173 ticket
Part C:
=> 270 - 173 = 97
=> 97 /270 * 100
=> 35.92%
Therefore , the solution of the given problem of percentage comes out to be The number of tickets sold fell by 20% , tomorrow ticket sold is 173 ticket and 35.92% percentage fall.
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How to solve for j -10=║j-7║
Answers
Answer:
No solutions.
Step-by-step explanation:
-10 = 7
No solutions
Can anybody help me out with this
Answers
The final coordinates of the figure, following the reflection and translation are;
A''(-2, -1)
B''(-3, 1)
C''(2, 2)
What is a translation transformation?A translation transformation is a geometric transformation that moves every point of a shape or object by the same distance in the same direction.
The coordinates of the vertices of the triangle are;
(-5, -1), (-6, -3), and (-1, -4)
1) The first transformation is a reflection across the x-axis
The coordinate of the point (x, y) following a reflection across the x-axis = The point (x, -y)
Therefore, the coordinate of the image of the triangle following the reflection across the x-axis are the points;
(-5, -1) ⇒ (-5, 1)
(-6, -3) ⇒ (-6, 3)
(-1, -4) ⇒ (-1, 4)
The coordinates of the image following the reflection are therefore;
A'(-5, 1), B'(-6, 3), C'(-1, 4)
b. The coordinates of the image of the reflected triangle following a translation of <3, -2> are;
A'(-5, 1) ⇒ A''(-5 + 3, 1 - 2) = A''(-2, -1)
B'(-6, 3) ⇒ B''(-6 + 3, 3 - 2) = B''(-3, 1)
C'(-1, 4) ⇒ C''(-1 + 3, 4 - 2) = C''(2, 2)
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A square-shaped park has an area of 400 yd? What are the dimensions of the park? Write and solve an equation.
Answers
We know that a square has sides that are the same length
We know to find the area, we multiply the length of one side by the length of another
A = x*x or x^2
T
complete the identitysin 2x - cot x
Answers
Let's complete the identity:
\(\begin{gathered} \sin 2x-\cot x=2\sin x\cos x-\frac{\cos x}{\sin x} \\ =\frac{2\sin^2x\cos x-\cos x}{\sin x} \\ =\frac{\cos x(2\sin^2x-1)}{\sin x} \\ =\frac{\cos x}{\sin x}(2\sin ^2x-1) \\ =\frac{\cos x}{\sin x}(2(1-\cos ^2x)-1) \\ =\frac{\cos x}{\sin x}(2-2\cos ^2x-1) \\ =\frac{\cos x}{\sin x}(1-2\cos ^2x) \\ =\frac{\cos x}{\sin x}(-\cos 2x) \\ =-\cot x\cos 2x \end{gathered}\)For the sequence −9, −3, 3, 9, 15, ... write the recursive formula. a(1) = __, a(n) = a(n-1) + d *
Answers
Answer:
the answer to the question is online if you
Find the derivatives of the following using increment method.1.y = 6x² +10x - 3
Answers
Given
\(y=6x²+10x-3\)Find
derivatives using increment method.
Explanation
Given
\(y=6x²+10x-3\)replace x and y by
\(\begin{gathered} x+\Delta x \\ y+\Delta y \end{gathered}\)so ,
\(\begin{gathered} y+\Delta y-y=6(x+\Delta x)^2+10(x+\Delta x)-3-(6x^2+10x-3) \\ \Delta y=6x^2+6\Delta^2x^2+12\Delta x^2+10x+10\Delta x-3-6x^2-10x+3 \\ \Delta y=12\Delta x^2+6\Delta^2x^2+10\Delta x \\ \end{gathered}\)now divide by
\(\Delta x\)so ,
\(\begin{gathered} y^{\prime}=\frac{12\Delta x^2+10\Delta x+6\Delta^2x^2}{\Delta x} \\ \\ y^{\prime}=12x+10+6\Delta x \end{gathered}\)now taking limit
\(\begin{gathered} \lim_{\Delta x\to0}y^{\prime}=\lim_{\Delta x\to0}(12x+10+6\Delta x) \\ \\ y^{\prime}=12x+10 \end{gathered}\)Final Answer
Therefore , the derivative of the function using increment method is 12x + 10
A monopoly player claims that the probability of getting a when rolling a six-sided die is because the die is equally likely to land on any of the six sides. Is this an example of a theoretical probability or an empirical probability? explain.
Answers
It is an illustration of theoretical probability.
Theoretical probability establishes the probability of certain events occurring.
The ratio of the entire number of conceivable possibilities to the intended outcome is known as theoretical probability.
In this case, the intended consequence is earning a 2, which is only one of the six potential possibilities. The possibility of receiving a 2 is.
Observance determines empirical probability. Nothing about the observing of the specified episode is indicated in the question, hence it is not an empirical probability.
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6 cm
63 cm
the area of the rectangle
Answers
Answer:
Area of a rectangle is length *width
Therefore the area is 378cm square
What is the simplified form of 1 over x squared all over 3 over x cubed
Answers
The simplified expression is x/3.
An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
(1/x)² / (3/x³)
This can be written as,
= (1/x²) x (x³/3)
= x³ / 3x²
= x/3
Thus,
The simplified expression is x/3.
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Using the graph determine the equation of the axis of symmetry
Answers
wherever the vertex is, is the line of symmetry
a survey timeline indicates the date for activation of the measurement instrument. true/false
Answers
A survey timeline does not indicate the date for activation of the measurement instrument and this date is typically determined by the project team.
False. A survey timeline does not indicate the date for activation of the measurement instrument. A survey timeline typically provides a timeline for the duration of a survey, which includes the start date, the end date, and any other important milestones such as when data collection begins, when the data is analyzed, and when the results are reported. The date for activation of the measurement instrument is typically determined by the project team and will depend on the type of instrument used and the purpose of the survey. For example, if the survey is designed to measure customer satisfaction, the instrument might be activated on a certain date in order to ensure that the survey is conducted in a timely manner.
A survey timeline does not indicate the date for activation of the measurement instrument and this date is typically determined by the project team.
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The table lists the government ministers of the legendary kingdom of Neverland.
Nqverland.
Sum
Can the government offices be represented as a function of the ministers' names?
please help me i Just need 2 more to finish please
Answers
Answer:
No
Step-by-step explanation:
You cannot compare the ministers’ name because it has no correlation to their government office, so it cannot be represented as a function.
No, the government offices can not be represented as a function of the ministers' names.
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Given that, names of offices and their presidents,
Since,
You cannot compare the ministers’ name because it has no correlation to their government office, so it cannot be represented as a function.
Hence, the government offices can not be represented as a function of the ministers' names.
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Suppose you work for a company that manufactures cylindrical cans. Which will cost more to manufacture, a can with a radius of 4 inches and a height of 5 inches, or a can with a radius of 5 inches and a height of 4 inches? Assume that the cost of material for the tops and bottoms is per $1.40 square inch and the cost of material for curved surfaces is $0.90 per square inch.
Answers
Answer:
the can with the 5-inch radius will cost more
Step-by-step explanation:
The cost will be given by the formula ...
cost = 1.40 × (top & bottom area) + 0.90 × (lateral area)
In terms of radius and height the areas are ...
top & bottom area = 2πr²
lateral area = 2πrh
So, the total cost of a can with radius r and height h is ...
c(r, h) = 1.40·2πr² +0.90·2πrh
Filling in the given values and doing the arithmetic, we find the costs to be ...
c(4, 5) = $253.84
c(5, 4) = $333.01
The cost of the can with the 5-inch radius is the greatest.
Answer:
The cylinder with radius of 5 inches and height of 4 inches costs more to manufacture.
Step-by-step explanation:
First Can:
Top and Bottom Surface Area = 2(pi(4)^2) = 2(16pi) = 32 pi = 100.53 square inches
Cost for top and bottom surface area = 1.40 * 100.53 = $140.74
Curved Surface Area = 2pi*r*h = 2*pi*4*5 = 40 pi = 125.66 square inches
Cost for Curved Surface Area = 125.66 * 0.90 = $113.10
Total Cost = $140.74 + $113.10 = $253.84
Second Can
Top and Bottom Surface Area = 2(pi(5)^2) = 2(25pi) = 50 pi = 157.08 square inches
Cost for top and bottom surface area = 1.40 * 157.08 = $219.91
Curved Surface Area = 2pi*r*h = 2*pi*5*4 = 40 pi = 125.66 square inches
Cost for Curved Surface Area = 125.66 * 0.90 = $113.10
Total Cost = $219.91 + $113.10 = $333.01
So, the cylinder with radius of 5 inches and height of 4 inches costs more to manufacture.
Floyd weigh 160 pounds and is gaining 5 pounds per month. John weighs 140 pounds
and is gaining 10 pounds per month. How many months will it take for Floyd and John to
weigh the same amount?
Answers
Kirsten's house is located at a point on the map that is
7 miles west and 2 miles south of the center of town. She drives to a movie
theater, which is 5 miles east and 3 miles north of the center of town. If
the image represents the road she drove, how far did she travel?
Answers
Kirsten had to drive 5 miles north, and then turn to the east for 12 miles where she found a nice parking spot at the Movie Theater :)
If the image represents the road she drove, she did travel 5 + 12 miles, thus she finally travelled 17 miles.
1/2x+y = 3
y = 3x + 10
Solve using substitution
Answers
Answer:
(-2,4)
x = -2 y = 4
I hope this helps
the metric system is a decimalized system of measurement used exclusively in the united states. question 1 options: true false
Answers
False. The metric system is a decimalized system of measurement, but it is not used exclusively in the United States.
In fact, the United States primarily uses the U.S. customary system, while the metric system is widely used in most other countries around the world.
Most nations throughout the world use the metric system, a decimal-based measurement system that is universally recognised. It offers a standardised method for gauging temperature, length, mass, and other physical attributes. The metre (for length), kilogramme (for mass), second (for time), ampere (for electric current), kelvin (for temperature), mole (for amount of material), and candela (for luminous intensity) are the basic units of the metric system. Because the metric system is based on powers of 10, converting between units is simple. Global communication and trade are made easier by its promotion of usability, consistency, and compatibility across scientific, industrial, and everyday uses.
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What type of plot can be used to visualize a one-way contingency table? Select one: O a. Histogram O b. Boxplot c. Side-by-side bar plot O d. Stacked bar plot O e. Bar plot
Answers
The side-by-side bar plot is a type of plot that can be used to visualize a one-way contingency table. So, the correct answer is C.
What is contingency tableA contingency table is a table used to study the relationship between two categorical variables. The frequency or count of each combination of categories is recorded in a contingency table.
Aside from side-by-side bar plots, stacked bar plots can also be used to visualize contingency tables. A stacked bar plot, also known as a stacked column plot or stacked bar chart, displays each category’s frequency as a proportion of the whole.
It is created by stacking each category’s frequency on top of one another and then drawing a bar to represent the total.
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What is the solution to the
system of equations graphed below?
Answers
Answer:
A. (1, 2) (How convenient the answer's right below the graph)
Step-by-step explanation:
To find the solution for a system of equations, points that both lines intersect are solutions for both equations, and the only point in the graph is (1, 2).
The rate of growth of a fish populaton was modeled by the equation G(t)= (1+5e −0.6t
) 2
60,000e −0.6t
where t is measured in years since 2000 and G in kilograms per year Write an incegral to find the change in the population predicted between 2000 and 2020. ∫ 20
20
( (1+5e −0.6t
) 2
60,000e −0.6t
)dt Find a substitution and apply it to rewrite the integrand in the form u 2
1
du. (∫)∫ 1+sec −11
( u 2
1
)du If the biomass was 45,000 kg in the year 2000, what is the predicted biomass (in ko) for the year 20207 (Round your antacer to the neanest whale number) स kg
Answers
The predicted biomass (in kg) for the year 2020 is 45,000 kg.
The given equation is as follows: G(t)= (1+5e−0.6t)2/60,000e−0.6t
The required integral is ∫2020 G(t)dt.
Thus,∫2020 (1+5e−0.6t)2/60,000e−0.6t dt
Here, the substitution u = e^−0.6t can be used.
Therefore, du/dt=−0.6du/dt=(−0.6)eu
So, dt=−0.6eudu
Using this substitution, the integral becomes:
∫1/e5/e(1+5u2/60,000)du∫(1+5u2/60,000)−1(60,000/5)eudu=12,000∫(1+5u2/60,000)−1du=12,000∫(1+(u/η)2)−1du
[Where, η = 400]
The above integral can be written as:
12,000∫(1+(u/η)2)−1du=12,000η arctan(u/η) + C
[Where, C is the constant of integration]
So, G(t)= 12,000η arctan(u/η) + COn substituting the value of u:
G(t)= 12,000η arctan(e−0.6t/η) + C
[Where, η = 400]
Given, the biomass was 45,000 kg in the year 2000, which is when t = 0.
Therefore, when t = 20 (in 2020):
G(20)= 12,000×400 arctan(e−0.6×20/400) + C
= 12,000×400 (−0.45) + C
= −2,160,000 + C.
Thus, the predicted biomass (in kg) for the year 2020 is approximately:
G(20) = −2,160,000 + C
= 45,000 kg.
Therefore, the predicted biomass (in kg) for the year 2020 is 45,000 kg.
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Which of these numbers lies between 4 and 4.5 on a number line? A √13 B √17 C √22 D √28
Answers
Therefore √17 will lie between 4 and 4.5 on the number line .
In basic mathematics, real numbers are shown as a graphic of a graduated straight line called a number line. Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.
According to one standard, positive numbers always fall on the right side of zero, whereas negative numbers always fall on the left. The line also contains arrowheads at both ends, signifying that it continues in both the positive and negative directions indefinitely.
Let us find the decimal values of the given numbers.
13 lies between 9 and 16 , therefore √13 lies between 3 and 4 on the number line .
17 lies between 16 and 25 , therefore √17 lies between 4 and 5 on the number line .
22 lies between 16 and 25 , therefore √22 lies between 4 and 5 on the number line .
28 lies between 25 and 36 , therefore √28 lies between 5 and 6 on the number line.
Therefore √17 will lie between 4 and 4.5 on the number line as 4.5² = 20.25.
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You ride your bike up a steep mountain road at 5 miles per hour. How far do you go in 3 hours? Student solution: 5\div 3=1.75÷3=1.7. I ride 1.7 miles.
Answers
Answer:
15
Step-by-step explanation:
5x3 = 15 It's Simple Hope it helps
Find all the solutions of the equation
2sin²x+3sinx-2=0
Your answer(s) should be exact.
on the interval [0, 2π).
Answers
The roots of the trigonometric equation 2 · sin² x + 3 · sin x - 2 = 0 are x₁ = 30° and x₂ = 150°.
How to find the solutions from a trigonometric equation
In this problem we find a quadratic-like trigonometric equation, whose solution can be found by means of algebra properties and trigonometric formulas. First, write the trigonometric equation:
2 · sin² x + 3 · sin x - 2 = 0
Second, use the algebraic substitution u = sin x and find the roots of the resulting expression:
2 · [sin² x + (3 / 2) · sin x - 1] = 0
2 · [u² + (3 / 2) · u - 1] = 0
u₁ = 1 / 2 or u₂ = - 2
Third, reverse the algebraic substitution and find the angles associated to the trigonometric function:
sin x = 1 / 2
x₁ = 30° or x₂ = 150°
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HELP!!! Cindy needs to graph the following equation: y = 2x + 5. Which table can help her correctly graph the equation?
Answers
Answer: it is table "a"
explanation:
as the equation is y= 2x + 5 you should substitute each of the x values from -2 to 4 in order to get the y value which will help you decide which table should be used by Cindy to graph the equation.
now, this is how you should substitute the values into the equation and simplify it so that you get the "y" value.
the first x value given is -2 therefore:
you put -2 in the equation instead of putting x, this will allow you to find the y value which you can compare with the choices given.
y= 2x+5 (this is the equation)
y= 2(-2)+5 (here I have replaced the x with -2)
y= -4+5 (you should multiply 2 and -2)
y= 1 (therefore the answer is 1)
you should further continue this way and get the y values which will help you decide which is the correct table to be used. Now you already know that table "a" is the answer.
Answer:
The answer is table A
Step-by-step explanation:
Given:
Form the table of values from x = -2 to x = 4
Hence,
Therefore, the table that can be used for the graph of the equation is;
Table A