The line goes through the point and has a slope of 4, a y-intercept of -6, and a slope of 4. (0, 6).
What is a good example of a line's slope?The proportion of the increase in the y-value to the change inside the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) and Q := (4,1) on the line.
What does slope mean?A line's slope is how steeply it slopes form LEFT to RIGHT. Divide the rise, or vertically increase, by the run, or horizontally start changing, to get the line's gradient.
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The complete question is:
X in graphs the equation y = 4x - 6.
Select all statements about Xin's graph that are true.
a. The graph is a curved line.
b. The line passes through the origin.
c. The line passes through the point (0, 6).
d. The slope of the line is 4.
e. The y-intercept of the line is -6.
could you help with these questions pls?
a. The critical points are (0,0), (0,k), (k,0), and (k,k).
b. x³ and y³ are always non-negative, it can see that this critical point is a local minimum.
c. The function has a local minimum for all k > 0
What is the function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
(a) To find the critical points of f(x, y) = x³ + y³ - 3xy, we need to find where the partial derivatives with respect to x and y are equal to zero:
∂f/∂x = 3x² - 3ky = 0
∂f/∂y = 3y² - 3kx = 0
Solving these equations simultaneously, we get:
x = y
3x² - 3kx = 0
Substituting the first equation into the second, we get:
3x² - 3kx = 0
3x(x - k) = 0
So x = 0 or x = k. Since x = y, we also have y = 0 or y = k.
Therefore, the critical points are:
(0,0), (0,k), (k,0), and (k,k).
To determine the nature of these critical points, we need to compute the second partial derivatives of f(x):
∂²f/∂y² = 6y
∂²f/∂x∂y = -3k
At the point (0,0), we have:
∂²f/∂x² = 0
∂²f/∂y² = 0
∂²f/∂x∂y = 0
So we cannot use the second derivative test to determine the nature of this point.
At the point (0,k), we have:
∂²f/∂x² = 0
∂²f/∂y² = 6k
∂²f/∂x∂y = -3k
The determinant of the Hessian matrix is:
∂²f/∂x² × ∂²f/∂y² - (∂²f/∂x∂y)² = 0 - (-3k)² = 9k² > 0
Since ∂²f/∂y² is positive, we have a local minimum at the point (0,k).
Similarly, we can show that the points (k,0) and (k,k) are also local minima when k > 0.
(b) When k = 0, the partial derivatives are:
∂f/∂x = 3x² = 0
∂f/∂y = 3y² = 0
So x = y = 0 is the only critical point.
The second partial derivatives are:
∂²f/∂x² = 6x = 0
∂²f/∂y² = 6y = 0
∂²f/∂x∂y = 0
So we cannot use the second derivative test to determine the nature of this point. However, since the function is symmetric about the x and y axes, and x³ and y³ are always non-negative, we can see that this critical point is a local minimum.
(c) To find the values of k for which f(x) has a local minimum or maximum, we need to consider the discriminant of the Hessian matrix at each critical point:
For the point (0,k):
∂²f/∂x² × ∂²f/∂y² - (∂²f/∂x∂y)² = 0 - (-3k)² = 9k² > 0
So function has a local minimum for all k > 0
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Create an equivalent expression for 1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six.
The equivalent expression of "1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six" is found as. 1.2²/1.4³
Explain about the rule of exponents?A product where the same integer is used repeatedly as a factor is represented by a number raised to a power. The exponent provides the power, and the integer is referred to as the base.Given expression:
" 1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six."
This, becomes.
(1.4³/1.2⁴)⁻⁶
Using rule of exponents for multiplication:
x² × x³ = x² ⁺ ³ = x⁵
Apply in equation.
(1.4³/1.2⁴)⁻⁶ = (1.4³ ⁻ ⁶)/(1.2⁴ ⁻ ⁶)
1.4⁻³/1.2⁻²
Further solving:
x⁻¹ = 1/x
x⁻² = 1/x²
Now,
1.4⁻³/1.2⁻² = (1/1.4³)/(1/1.2²)
1.2²/1.4³
The equivalent expression of "1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six" is found as. 1.2²/1.4³
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I need help understanding this (For 20 points)
Using equations, we can find that the total cards sold on Mother's Day = 1100.
What are equations?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. It is demonstrated that the expressions on the left and right are equivalent to one another.
In all mathematical equations, LHS = RHS (left hand side = right hand side) is a constant. The value of an unknown variable, or unknown quantity, can be determined through solving equations.
Here,
Let the total no. of cards sold be = x
Now 2% of cards sold = 22
We can say, 2% of x = 22
⇒ 2/100 × x = 22
⇒ x = (22 × 100)/2
⇒ x = 1100
Therefore, the total number of cards sold on Mother's Day = 1100.
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Hello! Ik it’s annoying to do work so just enjoy a picture of my dog and the question is 1+1
Answer is 2
(Nice dog btw)
The sum of 1+1 is equal to 2. When we add 1 to another 1, we are combining or grouping the two quantities, resulting in a total of two. This is a fundamental concept in mathematics, and the process of addition is used to solve a wide range of problems.
f two fair dice are rolled, find the probability that the sum of the dice is 8, given that the sum is greater than 7.
P(sum of 8 | sum > 7) = 2/36 = 1/18
So the probability of rolling a sum of 8 given that the sum is greater than 7 is 1/18 or approximately 0.056.
How is probability determined?We must first ascertain the total number of outcomes where the sum is larger than 7 in order to calculate the likelihood that the sum of two fair dice will be 8.
A sum larger than 7 can only result in the following outcomes: (2,6), (3,5), (4,4), (5,3), and (6,2). As there are six alternative outcomes for each die roll, there are 36 permutations in which these five events can occur.
We must now count the number of these 36 outcomes that have a sum of 8. There are just two outcomes that could satisfy this requirement: (2,6) and (3,5). Hence, provided that the sum is more than 7, the following is the likelihood of rolling an 8:
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muscle has a force of 100LBS and is pulling on a bone at an angle of 15 degrees. muscle B has a force of 150 lbs and is pulling on the same bone at the same spot but at an angle of 30. muscle c has a force of 75Ibs and is pulling at the same spot with an angle of 10. what is the resultant force of the muscles in the terms of the amount of force and direction? draw a diagram, label and show your work
Answer:
To solve this problem, we need to use vector addition. We can start by breaking down each force into its x and y components.
For muscle A:
Force = 100 lbs
Angle = 15 degrees
X-component = 100 * cos(15) = 96.93 lbs
Y-component = 100 * sin(15) = 25.04 lbs
For muscle B:
Force = 150 lbs
Angle = 30 degrees
X-component = 150 * cos(30) = 129.90 lbs
Y-component = 150 * sin(30) = 75.00 lbs
For muscle C:
Force = 75 lbs
Angle = 10 degrees
X-component = 75 * cos(10) = 73.83 lbs
Y-component = 75 * sin(10) = 13.03 lbs
Next, we can add up the x and y components separately:
X-component = 96.93 + 129.90 + 73.83 = 300.66 lbs
Y-component = 25.04 + 75.00 + 13.03 = 113.07 lbs
We can use these components to find the magnitude and direction of the resultant force:
Magnitude = sqrt(X^2 + Y^2) = sqrt((300.66)^2 + (113.07)^2) = 321.23 lbs
Direction = tan^-1(Y/X) = tan^-1(113.07/300.66) = 21.65 degrees (measured counterclockwise from the positive x-axis)
Therefore, the resultant force of the muscles is 321.23 lbs at an angle of 21.65 degrees. Here is a diagram to illustrate the vectors:
Step-by-step explanation:
25.04 lbs 73.83 lbs 129.90 lbs
/\ /\ /\
/ \ / \ / \
/ \ / \ / \
100 lbs 15° 75 lbs 10° 150 lbs 30°
\ / \ / \ /
\ / \ / \ /
\ / \ / \ /
96.93 lbs 13.03 lbs 75.00 lbs
Consider point M.
If point M is the largest integer less than √ 28, what is the value of point M?
If point M is the largest integer less than √ 28, the value of point M is found as 5.
Explain about the term integer?A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Integers include things like -5, 10, 1, 45, 8, 97, and 3,43.
Positive Integers: If an integer is bigger than zero, it is considered positive. Cases 1, 2, and 3..When an integer is less than zero, it is said to be negative. Examples 1, 2, and 3.Point M is the largest integer less than √ 28.
√ 28 = 5.29
largest integer which is less than 5.92 is 5.
Thus, if point M is the largest integer less than √ 28, the value of point M is found as 5.
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Find the time it takes for $930,000 to double when invested at an annual interest rate of 20%, compounded continuously.
Using Algebraic expression, It will take approximately 3.47 years for an investment of $930,000 to double at an annual interest rate of 20%, compounded continuously.
Algebraic expression can be defined as combination of variables and constants.
The formula for continuous compound interest is given by:
[tex]A = Pe^{(rt)}[/tex]
where A is the amount after time t, P is the initial principal, r is the annual interest rate (as a decimal), and e is the constant 2.71828... (also known as Euler's number).
To find the time it takes for an investment to double at a 20% annual interest rate, we need to solve for t in the equation:
[tex]2P = Pe^{(rt)}[/tex]
Dividing both sides by P, we get:
[tex]2 = e^{(rt)}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(2) = rt ln(e)[/tex]
Since ln(e) = 1, we can simplify to:
ln(2) = rt
Solving for t, we get:
[tex]t = ln(2) / r[/tex]
Substituting P = $930,000 and r = 0.20, we get:
[tex]t = ln(2) / 0.20t = 3.47 years[/tex]
Therefore, it will take approximately 3.47 years for an investment of $930,000 to double at an annual interest rate of 20%, compounded continuously.
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Find x if 144x+288y=1440 and 28x+84y=280
Therefore , the solution of the given problem of equation comes out to be the system of equations has an answer of x = -20 and y = 10.
What is an equation?The same letter is frequently used in mathematical formulas to attempt to enforce variable uniformity among two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Using the outcome y + 6 = 12 as an example, the normalise divides the numbers 12 and b + 6 into 2 parts. The relationship between each symbol component and the amount of lines can be found. A symbol's meaning typically runs counter to itself.
Here,
The set of linear equations can be used to find the values of x and y:
144x + 288y = 1440 \s28x + 84y = 280
By dividing both parts of the second equation by 28, we can begin by making it simpler:
x + 3y = 10
Then, by separating x, we can use this equation to solve for x in terms of y:
x = 10 - 3y
In order to simplify the first problem, we can use this expression in place of x:
=> 144(10 - 3y) + 288y = 1440
=> 1440 - 432y + 288y = 1440
=> -144y = -1440
=> y = 10
Given that y = 10, we can solve for x by substituting this number into the equation x + 3y = 10:
=> x + 3(10) = 10
=> x + 30 = 10
=> x = -20
As a result, the system of equations has an answer of x = -20 and y = 10.
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Purchased 1400 units of product at a cost of $40 per unit. Terms of the sale are 5/10, n/60; the invoice is dated November 5
Answer
November 5 - Purchase = 1100Unit cost = $40Payable = (1,100*40) 44000 November 7Returns - 25 defective units = 25*40 =1000Terms of sale = 5/10 , n/60If invoices are paid within 10 days , a discount of 5% is given.Therefore payment on November 15 attracts a discount of 5% of the net purchase Journal entries
Step-by-step explanation:
PLEASE HELP ASAP, WILL GIVE FIRST ANSWER BRAINLIEST!!!!
Triangle XYZ is drawn with vertices X(1, 2), Y(2, 5), Z(3, 4). Determine the translation direction and number of units if Z′(9, 4).
6 units down
6 units up
6 units to the right
6 units to the left
Answer:
6 units to the right
Step-by-step explanation:
Z(3,4) → Z'(9,4)
d = √(9-3)² + (4-4)² = √6²+0² = 6 to the right
The translation of point Z of triangle XYZ from (3, 4) to Z′(9, 4) is a move of 6 units to the right.
Explanation:In Mathematics, particularly geometry, the translation of a point is the process of moving the point a specific number of units either up, down, left or right. In the case of your triangle XYZ, the original position of point Z is at (3, 4) and Z′ is positioned at (9, 4). The y-coordinate hasn't changed; it remains at 4. This tells us that the translation is not up or down. However, if we observe the x-coordinate, you’ll see that it went from 3 to 9. Changing the x-coordinate moves the point horizontally, so we know our translation is left or right. Lastly, the difference between 3 and 9 is 6. We can therefore determine that the point moved 6 units to the right.
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jill has 4 granola bars.each bar weighs2/3oz.write the weight of jill's granola bars as an improper fraction and as a mixed number
Answer:
8/3 improper fraction
2 2/3 mixed
Step-by-step explanation
The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters.
Answer:
No triangles can be constructed
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so
In this problem
4+5>9 ------> is not true / is wrong
therefore
No triangles can be constructed with the given side lengths
Hope this helped !
During your chemistry lab, you fill a cone-shaped beaker that has a 1-inch diameter and a 2- inch height with lead, which weigh 0.41 pounds per cubic inch. Find the weight of the lead in the beaker.
The weight of the lead in the beaker is 0.21 pounds.
What is volume of a cone?A cone is a three dimensional shape with slant sides and a circular surface. Its volume can be defined as the amount of substance that it can contain.
volume of a cone = 1/3 [tex]\pi[/tex]r^2*h
where r is the radius of its circular surface, and h is its height.
In the given question, we have;
r = d/2 = 1/2
= 0.5 inches
h = 2 inches
Thus,
volume of the cone-shaped beaker = 1/3 [tex]\pi[/tex]r^2*h
= 1/3 *22/7*(0.5)^2*2
= 0.524
The volume of the lead in the cone-shaped beaker is 0.524 cubic inch.
Weight of the lead in the beaker = 0.524*0.41
= 0.2148
The weight of the lead in the beaker is 0.21 pounds.
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what is the greatest common factor of 4x^3 y^2 and 12x^2 y?
The greatest common factor of 4x³y² and 12x²y is: 4x²y.
What do you mean by greatest common factor?The GCF is a term used to refer to the largest common factor between any two or more numbers (Greatest Common Factor). The GCF of two natural integers, x and y, is the largest possible number that equally and completely divides both x and y. GCF is typically calculated using the following three techniques: division, multiplication, and prime factorization.
Now in the given question,
4x³y² can be written as = 2×2×x×x×x×y×y
12x²y can be written as = 2×2×3×x×x×y
The common factors among them are:
2×2×x×x×y = 4x²y.
Therefore, the greatest common factor of 4x³y² and 12x²y is: 4x²y.
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Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $47.96 and costs an additional $0.19 per mile driven. The second plan has an initial fee of $53.96 and costs an additional $0.15 per mile driven. How many miles would Debra need to drive for the two plans to cost the same?
The number of miles Debra need to drive for the two plans to cost the same is 150miles
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Initial fee of first plan=$47.96
Additional fee of first plan=$0.19 per mile
Initial fee of second plan=$53.96
Additional fee of second plan=$0.15 per mile
Now,
Let's call the number of miles Debra drives "m". Then the cost of the first plan would be:
47.96 + 0.19m
And the cost of the second plan would be:
53.96 + 0.15m
To find the number of miles at which the two plans cost the same, we can set these expressions equal to each other and solve for "m":
47.96 + 0.19m = 53.96 + 0.15m
0.04m = 6
m = 6 / 0.04
m = 150
Therefore, by the unitary method answer will be 150 miles.
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Juan ran 2.3 miles on Monday. he ran 5.6 miles on Wednesday.his goal is to run 12 miles by Saturday. how many more miles does juan need to run to meet his goal of 12 miles.
please show work and help me
Answer:Juan has already run a total of 2.3 + 5.6 = 7.9 miles on Monday and Wednesday.
To reach his goal of running 12 miles by Saturday, he still needs to run an additional 12 - 7.9 = 4.1 miles.
Therefore, Juan needs to run 4.1 more miles to meet his goal of running 12 miles by Saturday.
Step-by-step explanation:
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The estimate for the value of 5^(3/2) using the tangent line approximation of the function y = x^(3/2) at x = 4 is 11.
What is the estimated value of 5^3/2 using the equation for the tangent line at x = 4To estimate the value of 5^(3/2), we can use the tangent line approximation of the function y = x^(3/2) at x = 4.
First, we need to find the slope of the tangent line at x = 4. To do this, we take the derivative of the function y = x^(3/2):
y = x^(3/2)
y' = (3/2)x^(1/2)
y'(4) = (3/2)(4)^(1/2) = 3
So the slope of the tangent line at x = 4 is 3.
Next, we need to find the equation of the tangent line at x = 4. To do this, we use the point-slope form of the equation of a line, using the point (4, 8):
y - 8 = 3(x - 4)
y = 3x - 4
Now we can estimate the value of 5^(3/2) by substituting x = 5 into the equation of the tangent line:
y = 3x - 4
y = 3(5) - 4
y = 11
Therefore, an estimate for the value of 5^(3/2) using the tangent line approximation of the function y = x^(3/2) at x = 4 is 11.
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What fraction is greater than 1/9, is less than 1/3, and has a denominator of 18?
Maricopa's Success scholarship fund receives a gift of $ 190000. The money is invested in stocks, bonds, and CDs. CDs pay 2.75 % interest, bonds pay 3.7 % interest, and stocks pay 11.1 % interest. Maricopa Success invests $ 50000 more in bonds than in CDs. The annual income from the investments is $ 11877.5
Maricopa Success invested $ in stocks.
Maricopa Success invested $ in bonds.
Maricopa Success invested $ in CDs.
Maricopa Success invested $140022.5 in stocks, $64000 in bonds, and $36000 in CDs. The total annual income from the investments was $11877.5.
What is income?Income is the money that an individual receives in exchange for work, investments, or other activities. It can be earned from employment, from investments such as stocks and bonds, from business activities, and from government programs. Income can also be earned from other sources such as rents, scholarships, tips, and inheritances. Income is an important source of financial security and can be used to pay for basic needs, to save for future expenses, and to invest in other potential income sources.
To calculate the amount of money Maricopa Success invested in each asset type, we can use the following equation:
Stocks + Bonds + CDs = $190000
To solve for Stocks, we can subtract the amounts invested in Bonds and CDs from the $190000:
Stocks = $190000 - $50000 - $ (11877.5/3.7)
Stocks = $140022.5
To solve for Bonds, we can subtract the amounts invested in Stocks and CDs from the $190000:
Bonds = $190000 - $140022.5 - $ (11877.5/2.75)
Bonds = $64000
To solve for CDs, we can subtract the amounts invested in Stocks and Bonds from the $190000:
CDs = $190000 - $140022.5 - $64000
CDs = $36000
Therefore, Maricopa Success invested $140022.5 in stocks, $64000 in bonds, and $36000 in CDs. The total annual income from the investments was $11877.5.
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A person is parasailing. The length of the chord connecting the person to the boat is 400 feet long and the
person looks down at angle of depression of 36° to see the boat. How high up is the parasailer?
The answer to this question is that the parasailer is 600 feet high. To solve this problem, we can use the tangent of the angle of depression to calculate the height of the parasailer.
What is angle of depression?Angle of depression is the angle between the horizontal line of sight and the line of sight to an object below the horizontal line. It is used to measure the height of an object from the observer's point of view. It is used to measure the angle between the observer and an object located below the observer. It is sometimes referred to as the inverse of the angle of elevation.
The formula for the tangent of an angle is opposite/adjacent. In this case, the opposite side is the height of the parasailer, and the adjacent side is the length of the chord. Therefore, the equation becomes height/400 = tangent (36°).
Solving for the height, we get height = 400 * tangent (36°). Plugging in the value of the tangent (1.732050808) gives us a height of 692.82 feet.
However, since the question specifies that the length of the chord is 400 feet, the answer should be rounded off to the nearest whole number, which is 600 feet. Therefore, the parasailer is 600 feet high.
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At a restaurant, the bill comes to $76. If you decide to leave a 20% tip, how much total do you need to pay? Give your answer to the nearest dollar.
Answer: To calculate the tip amount, we need to multiply the bill amount by the percentage tip as a decimal:
Tip amount = 0.20 x $76 = $15.20
To find the total amount to pay, we add the bill amount and the tip amount:
Total amount = $76 + $15.20 = $91.20
Rounding this to the nearest dollar gives:
Total amount = $91
Therefore, you need to pay $91 in total if you leave a 20% tip on a $76 bill.
Step-by-step explanation:
RectangleA′B′C′D′ is the image of rectangleABCD after a dilation.
What is the scale factor of the dilation?
Enter your answer in the box.
The scale factor of the dilation for the rectangle ABCD is found as 3.
Explain about the scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a varying design is known as a scale factor (bigger or smaller).
The rectangle A'B'C'D' is created by dilation of rectangle ABCD.
We shall calculate the ratio of the rectangle's lengths in order to get the scale factor.
A:(1,5) and B:(4,5).
Length of side AB = 4 - 1 = 3
And,
A':(3,15) and B': (12,15).
Length of the side A'B' = 12-3 = 9
Ratio of the sides
AB : A'B' = 3 : 9
AB : A'B' = 1 : 3.
Thus, the scale factor of the dilation for the rectangle ABCD is found as 3.
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A set of 2-inch-wide by 5/8-inch-thick carbon brushes fits the brush holders too tightly. It is necessary to take 5/1000 inch off the width and 0.015 inch off the thickness by sanding. Give in decimal form the thickness dimension of the carbon brushes after sanding.
In answering the question above, the solution is Hence, after sanding, expressions the thickness of the carbon brushes is 0.61 inches, or 0.61 decimal inches.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
The carbon brushes were originally 5/8 inches thick, however during the sanding process, 0.015 inches were removed, resulting in the following new thickness:
0.625 - 0.015 Equals 0.61 inches for 5/8.
We divide this by 1 inch to get the decimal equivalent:
1 inch / 0.61 inches equals 0.61
Hence, after sanding, the thickness of the carbon brushes is 0.61 inches, or 0.61 decimal inches.
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write the standard equation of the circle given the center and radius
Answer:
( x − a ) 2 + ( y − b ) 2 = r 2
Given
f(x) = 4x2 − 1
and
g(x) = −4x + 8,
find the following.
f(2) − g(2)
This means that when function f(x) = 4x²- 1 and g(x) = 4x + 8, f(2) - g(2) = 15, and by using the equation as a substitute.
what is function ?
A function in mathematics is a relationship between a set of inputs (also referred to as the domain) and a set of outputs (also referred to as the range), where each input has a unique outcome. Typically, the variable x stands for the input values, the variable y for the output values, and the variable f for the function itself (x). Tables, graphs, equations, and verbal descriptions can all be used to represent functions. In a wide variety of disciplines, including science, engineering, economics, and social studies, they are employed to model relationships between quantities. Functions are frequently used to explain the relationship between two quantities.
given
We must first determine the values of f(2) and g(2) independently using the provided functions in order to evaluate f(2) - g(2):
f(2) = 4(2)² - 1 = 15
g(2) = -4(2) + 8 = 0
These values can now be added to the expression f(2) - g(2) as a substitute:
f(2) - g(2) = 15 - 0 = 15
This means that when f(x) = 4x²- 1 and g(x) = 4x + 8, f(2) - g(2) = 15, and by using the equation as a substitute.
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Please help!! Worth 50 points
The ball with the greater maximum height is the second ball
The ball with the greater maximum heightFrom the question, we have the following parameters that can be used in our computation:
f(t) - 4t^2 + 16t
g(t) = -16t^2 + 64t + 192
Differentiate and set them to 0
-8t + 16 = 0
-32t + 64 = 0
Solve for t
t = 2 in both cases
So, we have
f(2) = -4(2)^2 + 16(2) = 16
g(2) = -16(2)^2 + 64(2) + 192 = 256
Hence, the ball with the greater maximum height is the second ball
Which ball hits the ground firstTo do this, we set the function to 0 and calculate t
So, we have
f(t) = -4t^2 + 16t = 0
g(t) = -16t^2 + 64t + 192 = 0
Using a graphing tool, we have
t = 4
t = 6
This means that the first ball landed first
How to change the termTo change the term, we set the constant term in g(t) = -16t^2 + 64t + 192 to a negative number > -192
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Need help asap! (50 points)
Answer:
8
Step-by-step explanation:
160×5%
[tex]\frac{160 * 5}{100}[/tex] = 8
The graph shows the relationship between the yards of fabric a costume designer uses, x
, and the number of costumes the designer makes, y
.
Which equation represents the relationship?
Responses
y=16x
y = 1 6 x
y=13x
y = 1 3 x
y=3x
y = 3 x
y=6x
The equation that represents the relationship is y = 1/3x
How to determine the equation that represents the relationship?The missing graph in the complete question is added as an attachment
From the question, we have the following points that can be used in our computation:
(x, y) = (0, 0) and (3, 1)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx
Using the points, we have
1 = 3m
Divide
m = 1/3
Substitute 1/3 for m in y = mx
y = 1/3x
Hence, the function of the relation is y = 1/3x
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A baseball coach uses a scatter plot to compare the number of swings taken before a baseball tournament and the number of hits during the baseball tournament. What can the coach conclude about the relationship between the number of swings and the number of hits? PLEASE HELP !!!!!!
Answer: Without seeing the actual scatter plot, it is difficult to make a definitive conclusion about the relationship between the number of swings and the number of hits. However, there are a few things that the coach can look for in the scatter plot to gain some insights:
Positive correlation: If the scatter plot shows a generally upward trend, with more hits occurring as the number of swings increases, this suggests a positive correlation between the two variables. In other words, players who take more swings tend to have more hits during the tournament.
Negative correlation: On the other hand, if the scatter plot shows a generally downward trend, with fewer hits occurring as the number of swings increases, this suggests a negative correlation between the two variables. In this case, players who take fewer swings tend to have more hits during the tournament.
No correlation: If the scatter plot shows no clear trend or pattern, with hits occurring randomly across different numbers of swings, this suggests no correlation between the two variables. In this case, there is no apparent relationship between the number of swings taken and the number of hits during the tournament.
Overall, the coach can use the scatter plot to gain some insights into the relationship between the number of swings and the number of hits, but more advanced statistical analysis may be necessary to make definitive conclusions.
Step-by-step explanation: