The point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1), where the slope m= -0.5 was calculated using the formula m = (y2 - y1) / (x2 - x1).
Explanation:To complete the point-slope equation of the line through points (1,3) and (5,1), we first need to find the slope of the line, which can be calculated using the formula: m = (y2 - y1) / (x2 - x1), here (x1,y1) and (x2,y2) are the coordinates of two points on the line.
Substituting in the given coordinate values gives us m = (1 - 3) / (5 - 1), which simplifies to m = -0.5, indicating a downward slope.
The point-slope form of the equation of a line is y - y1 = m(x - x1). So, substituting one of the given points (1, 3) and the calculated slope into the point-slope form gives us y - 3 = -0.5(x - 1).
Therefore, the point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1).
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help please
Find the volume of a pyramid with a square base, where the perimeter of the base is 5.5 m and the height of the pyramid is 2.9 m. Round your answer to the nearest tenth of a cubic meter.
Jacqui has grades of 79 and 76 on her first two algebra tests. if she wants an average of at least 71, what possible scores can she make on her third test?
Triangle LMN is located at L(2,3), M(1,2), and N(4,4). The triangle is then transformed using the rule (x+5, y+2) to form the image L’M’N. What are the new coordinates of L’,M’, and N’?
Given:- L (2, 3), M (1, 2), and N make up the triangle known as LMN (4, 4). The image L'M'N' is created by first transforming the triangle according to the rule
To Locate:
What are L's, M's, and N's new coordinates?Solution:-
Rule for Points = (x + 2) on the x-axis.
Thus, the new x-points axis's are as follows:
L' = 2 + 5 = 7
M' = 1 + 5 = 6
N' = 4 + 5 = 9 .
and, Rule for y - axis Points = (y + 2) .
Therefore, New y - axis points of new ∆ are :-
L' = 3 + 2 = 5
M' = 2 + 2 = 4
N' = 4 + 2 = 6 .
Hence, New coordinates of L', M', and N' :-
L' = (7 , 5)
M' = (6, 4)
N' = (9, 6)
Find out more:
show that the point of trisection for the line connecting the points (-5,12) and (-1,12) is the midpoint of the line connecting the...
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Sean used 3/4 cup of sugar to make a dozen brownies. How much sugar is in each brownie
Sean used 3/4 cups of sugar to make 12 brownies. By dividing 3/4 by 12, we find that there is 1/16 cup of sugar in each brownie.
Explanation:The subject of this problem is mathematics, specifically, it's about division in the context of fractions. In this scenario, Sean used 3/4 cups of sugar to make a dozen (12) brownies. To determine the amount of sugar in each brownie, we can divide the total amount of sugar by the total number of brownies.
So, 3/4 divided by 12 is 1/16. This means that there is 1/16 cup of sugar in each brownie.
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Item 15 A square wrestling mat has a perimeter of (12x−32)(12x−32) feet. Write an expression in simplest form that represents the side length (in feet) of the mat.
Choose the biconditional that is equivalent to the definition, "A skyscraper is a very tall building."
A skyscraper is a very tall building. The biconditional equivalent to this definition is 'A building is a skyscraper if and only if it is very tall.'
Explanation:The biconditional equivalent to the definition 'A skyscraper is a very tall building' is:
A building is a skyscraper if and only if it is very tall.
This biconditional statement means that for a building to be classified as a skyscraper, it must satisfy the condition of being very tall. Conversely, if a building is very tall, it can be classified as a skyscraper. This definition establishes a two-way relationship between being a skyscraper and being very tall.
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In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 189.7 pounds in the summer, including clothing and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 41.4 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 27 passengers.
What is the approximate probability (±0.0001) that the total weight of the passengers exceeds 5511 pounds?
The only way I can think of to solve this problem is to assume normal distribution.
Since the total weight excess 5511, hence the weight per passenger is at least:
x = 5511 / 27 = 204.1 pounds
Solve for the z score:
z = (x – u) / s
z = (204.1 – 189.7) / 41.4
z = 0.35
From the standard probability tables, the P value using right tailed test is:
P = 0.3632
Which ordered pair is a solution to this equation?
2x+6y=10
A (12, 2)
B (4, 1)
C (3, 1)
D (2, 1)
A line has a slope of 5 and a y-intercept of 4 what is the equation in slope intercept form
Write your answer using integers proper fraction and improper fractions in simplest form
Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of the quantity 2 times x to the 4th power plus 8 times x and 4 times x to the 3rd power plus 4, dx. Your work must include the use of substitution and the antiderivative.
Answer:
-162
Step-by-step explanation:
Integration by substitution is a technique in calculus where a change of variables is made to simplify the integral by expressing it in terms of a new variable, making the integration easier to manage.
To evaluate the following integral, use the method of substitution:
[tex]\displaystyle \int_{-1}^0 (2x^4 + 8x)^3 (4x^3 + 4) \;\text{d}x[/tex]
Let u = 2x⁴ + 8x.
Differentiate u with respect to x using the power rule for differentiation by multiplying each term by its exponent and then subtracting 1 from the exponent:
[tex]\dfrac{\text{d}u}{\text{d}x}=4 \cdot 2x^{4-1}+1\cdot 8 x^{1-1}[/tex]
[tex]\dfrac{\text{d}u}{\text{d}x}=8x^{3}+8[/tex]
Rewrite it so that dx is on its own:
[tex]\text{d}u=8x^{3}+8\;\text{d}x[/tex]
[tex]\text{d}x=\dfrac{1}{8x^{3}+8}\;\text{d}u[/tex]
Change the limits of integration from x to u:
[tex]\begin{aligned}x=-1 \implies u&=2(-1)^4 + 8(-1)\\&=2(1)-8\\&=2-8\\&=-6\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies u&=2(0)^4 + 8(0)\\&=2(0)-0\\&=0-0\\&=0\end{aligned}[/tex]
Rewrite the integral in terms of u:
[tex]\begin{aligned}\displaystyle \int_{-1}^0 (2x^4 + 8x)^3 (4x^3 + 4) \;\text{d}x&=\int_{-6}^0 u^3 (4x^3 + 4) \cdot \dfrac{1}{8x^{3}+8}\;\text{d}u\\\\&=\int_{-6}^0 u^3 (4x^3 + 4) \cdot \dfrac{1}{2(4x^{3}+4)}\;\text{d}u\\\\&=\int_{-6}^0\dfrac{u^3}{2} \;\text{d}u\end{aligned}[/tex]
Integrate with respect to u using the power rule for integration by adding 1 to the exponent of each term and then dividing by the new exponent:
[tex]\begin{aligned}\displaystyle \int_{-6}^0\dfrac{u^3}{2} &=\left[\dfrac{u^{3+1}}{2 \cdot (3+1)}\right]^0_{-6}\\\\&=\left[\dfrac{u^{4}}{8}\right]^0_{-6}\\\\&=\dfrac{(0)^4}{8}-\dfrac{(-6)^4}{8}\\\\&=0-\dfrac{1296}{8}\\\\&=-162\end{aligned}[/tex]
Therefore, the value of the given integral is -162.
What is the value of n in the numerical sentence below?
√16 ÷ 4³ = 4ⁿ
n = ?
Need help quickly ???????!?
Let x1, . . . , xn be independent exponential random variables having a common parameter λ. determine the distribution of min(x1, . . . , xn)
Given fx (x) = λe^λx
Fx (x) = 1 – e^-λx x…0
To find distribution of Min (X1,….Xn)
By applying the equation
fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)
For minimum j = 1
[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx
= ne^[(n-1) λx] λe^(λx)
= nλe^(-λx[1+n-1])
= nλe^(-nλx)
The distribution of min(x1, . . . , xn) for independent exponential random variables with common parameter λ is given by the exponential distribution with parameter λ*n.
Explanation:The distribution of min(x1, . . . , xn) for independent exponential random variables with common parameter λ is given by the exponential distribution with parameter λ*n.
To determine this, we can use the fact that the minimum of a set of random variables is less than or equal to a given value if and only if each of the individual random variables is less than or equal to that value. So, we can find the cumulative distribution function (CDF) of the minimum by raising the CDF of each individual exponential random variable to the power of the number of variables in the minimum. The resulting distribution is an exponential distribution with parameter λ*n.
You have 6 pints of glaze. It takes 7/8 of a pint to glaze a bowl and 9/16 of a pint to glaze a plate. You want to glaze 5 bowls, and then use the rest for plates. How many plates can you glaze? How much glaze will be left over?
2 plates can be glazed and 0.50 glaze will be left over.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total bowls= 5
fraction of pint to glaze bowl= 7/8
So, pint to glaze 5 bowls
= 5 bowls x 7/8 of a pint
= 4.375 pints
and, left over after glazing the bowls.
= 6 pints - 4.375pints
= 1.625
Now, we know to glaze plate pint used= 9/16
So, number of plates will be = 1.625 x 16/9
= 2.88 plates
Thus, we can only glaze 2 plates.
Also, glaze left over
= 1.625 - 1.125
= 0.50 glaze left over.
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The same amount of principal is invested in different accounts earning the same interest rate. Which of the following accounts would have the greatest accumulated value at the end of one year?
a.
An account earning no interest
b.
An account earning simple interest
c.
An account earning interest compounded annually
d.
An account earning interest compounded daily
Answer:
D
Step-by-step explanation:
If a triangle is an isosceles triangle, then it has two sides of equal length. If a triangle has two sides of equal length, then it has two angles of equal measure
Conclusion:
If a triangle is an isosceles triangle, then it has two angles of equal measure.
The argument is not valid because the conclusion does not follow from the premises.
The argument is valid by the law of syllogism.
The argument is not valid because the premises are not true.
The argument is valid by the law of detachment.
we know that
The Law of Syllogism says that if the following two statements are true:
(1) If p -------> then q .
(2) If q-------> then r .
Then we can derive a third true statement:
(3) If p--------> then r .
In this problem
(1) If a triangle is an isosceles triangle, then it has two sides of equal length
(2) If a triangle has two sides of equal length, then it has two angles of equal measure
Let
p-------> the statement " an isosceles triangle"
q--------> the statement " has two sides of equal length"
r---------> the statement "has two angles of equal measure"
Then (1) and (2) can be written
1) If p , then q .
2) If q , then r .
So, by the Law of Syllogism, we can deduce
3) If p , then r
or
If a triangle is an isosceles triangle, has two angles of equal measure
therefore
the answer is
The argument is valid by the law of syllogism.
Gary is looking over his receipts from his trip to Europe. When he was in Germany, he exchanged US dollars for euros at a rate of 1:0.7716, and when he was in Poland, he exchanged euros for Polish zloty at a rate of 1:4.0518. To four decimal places, what was the exchange rate of US dollars to Polish zloty?
For anyone who still needs it, the answer is 1:3.1264.
Danielle can spend up to $600 buying small and large jackets for her employees. Small jackets cost $20 each and large jackets cost $25 each. To get a special discount, she needs the number of large jackets to be no more than twice the number of small jackets. Also, she needs to order at least 6 small jackets and 10 large jackets. The graph shows the feasible region, where x represents the number of small jackets and y represents the number of large jackets. Which ordered pairs meet all the constraints and make sense in context of the situation? Select each correct answer. (13, 11) (15, 11) (8, 9) (7, 15) (10,13)
Answer:
10,13 13, 15,11
Step-by-step explanation:
THANK YOU PREVIOUS PERSON YOU SAVED MY WHOLE MATH GRADE! I OWE YOU YOU MADE IT SO I CAN PASS 9TH GRADE.
A cab company charges an initial rate of $2.50 for a ride, plus $0.40 for each mile driven. What is the equation that models the total fee for using this cab company? Write into an equation and then graph it.
Answer:
The equation that models the total fee for using this cab company
[tex]y=\$2.50+\$0.40\times x[/tex]
Step-by-step explanation:
Initial rate charged by company = $2.50
Amount charged for an each mile = $0.40
Let the miles cover during a ride = x
Total cost of ride can given as = y
The equation that models the total fee for using this cab company
[tex]y=\$2.50+\$0.40\times x[/tex]
The graphical interpretation equation in an image.
Parker bought a student discount card for the movies. The card cost $7 and and allows him to buy movie tickets for $5.50. After one month, Parker has spent $89.50 total. How many tickets has he bought since getting the discount card?
A) 12 tickets
B) 14 tickets
C) 15 tickets
D) 16 tickets
PLEASE HELP MATH!!!!!!
A division of a company produces income tax apps for smartphones. each income tax app sells for $9. the monthly fixed costs incurred by the division are $25,000, and the variable cost of producing each income tax app is $4. (a) find the break-even point for the division.
The equation for profit is income – cost:
Profit = Income – Cost
Let us say that x is the number of sold amount
Profit = 9 x – (25,000 + 4 x)
Profit = 5 x – 25,000
Breakeven point occurs when Profit = 0, hence:
5 x = 25,000
x = 5,000
The breakeven is when 5,000 people uses the income tax app
James is writing a coordinate proof involving a parallelogram. Knowing that the opposite sides of a parallelogram are congruent, James places his parallelogram on the coordinate plane such that one vertex is at the origin and one side lies along the x-axis. What coordinates should he assign to the fourth vertex of the parallelogram? (2a, a) (2a, a2) (a2, 0) (2a, 2a)
Answer:-(2a,a) coordinates he should assign to the fourth vertex of the parallelogram.
Explanation:-
Let ABCD be the vertices of the given parallelogram such that A=(0.,0) , B=(a,0) , C(x,y) and D=(a,a)
Construct the diagonals AC and BD of parallelogram ABCD .
We know that diagonals of a parallelogram bisect each other.
⇒ mid point of AC= mid point of BD...(1)
Mid point of BD[tex]=(\frac{a+a}{2},\frac{0+a}{2})=(\frac{2a}{2},\frac{a}{2})=(a,\frac{a}{2})[/tex]........(2)
Mid point of AC[tex]=(\frac{0+x}{2},\frac{0+y}{2})=(\frac{x}{2},\frac{y}{2})[/tex]......(3)
Substitute (2) and (3) in (1), we get
[tex](\frac{x}{2},\frac{y}{2})=(a,\frac{a}{2})\\\Rightarrow\frac{x}{2}=a;\frac{y}{2}=\frac{a}{2}[/tex]
[tex]\Rightarrow\ x=2a\ and\ y=a[/tex]
⇒C=(2a,a)
⇒ (2a,a) coordinates he should assign to the fourth vertex of the parallelogram.
Explain how to determine if these two are the same function expressed in different ways
Answer:
Sample Answer:
When a linear function is expressed in different forms, its slope and y-intercept remain the same. The slope from the equation is -1, and the y-intercept from the equation is 3. The slope from the table is -1, and the y-intercept from the table is −3. These are not the same functions.
Step-by-step explanation:
Answer:
When a linear function is expressed in different forms, its slope and y-intercept remain the same. The slope from the equation is -1, and the y-intercept from the equation is 3. The slope from the table is -1, and the y-intercept from the table is −3. These are not the same functions.
Step-by-step explanation:
What is the solution set to the equation (2x−4)(4x−5)=0
Answer:
[tex]\left \{ 2,\frac{5}{4} \right \}[/tex]
Step-by-step explanation:
We know that for equation of type [tex](x-a)(x-b)=0[/tex], solutions are [tex]x=a\,,\,x=b[/tex] as both points x = a and x = b satisfy the equation (x-a)(x-b)=0
Given : equation (2x−4)(4x−5)=0
To find : Solution set of this equation .
Solution :
On dividing this equation by 2 and 4, we get
[tex]\left ( \frac{2x-4}{2} \right )\left ( \frac{4x-5}{4} \right )=0\\\left ( x-2 \right )\left ( x-\frac{5}{4} \right )=0[/tex]
On comparing equation [tex]\left ( x-2 \right )\left ( x-\frac{5}{4} \right )=0[/tex] with [tex]\left ( x-a \right )\left ( x-b \right )=0[/tex], we get [tex]a=2\,,\,b=\frac{5}{4}[/tex]
Therefore, solution set is [tex]\left \{ 2,\frac{5}{4} \right \}[/tex]
Final answer:
The solution set to the equation (2x−4)(4x−5) = 0 is {2, 5/4}.
Explanation:
The equation (2x−4)(4x−5) = 0 represents a quadratic equation. To solve this equation, we can set each factor equal to zero and solve for x. So we have:
2x - 4 = 0, which gives x = 2
4x - 5 = 0, which gives x = 5/4
Therefore, the solution set to the equation is {2, 5/4}.
Please Help!
Which is true about the domain and range of a function in the form f(x) = m, where m is a real number greater than 0?
The only value that must be in both the domain and range is 0.
The only values that must be in both the domain and range are 0 and 1.
There are no values that are in the domain and the range.
There is an infinite number of values that are in both the domain and range.
Answer:
infinite number of values in domain and range
Step-by-step explanation:
need points for finals
For a function of the form f(x) = m, the domain is all real numbers and the range is the single real number m. Thus, there are no values that are in both the domain and the range.
Explanation:In a function of the form f(x) = m, where m is a real number greater than 0, the domain encompasses all real numbers since there are no restrictions on any values of x that would make the function undefined. Since the function gives the same result (m) regardless of what x is, f(x) remains constant. Thus, the range only contains one real number, which is m.
The correct option from the ones given, therefore, is: There are no values that are in the domain and the range. This is because the domain contains all real numbers, while the range contains only one number (m), and these sets do not overlap.
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Write what the expressions below best represent within the context of the word problem
How many quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture?
x represents quarts of water to be added to the ____% mixture.
x + 4 represents the total quarts of the mixture at ____%.
first one is 80%
second one is 50%
1st. is 80%
2nd. is 50%
Assume that a randomly selected subject is given a bone density test. those test scores are normally distributed with a mean of 0 and a standard deviation of 1. find the probability that a given score is less than 1.66 and draw a sketch of the region.
The equation c = 6.5h represents the cost, c, of renting a bicycle for h hours. The table below can be used to show the same information.
If Francesca rents a bicycle for 2 hours and Phil rents a bicycle for 6 hours, how much more does Phil pay?
$13
$26
$39
$52
Answer:
26 (I got 100%)
Step-by-step explanation:
39 - 13
Phil payment - Francesca payment = 26
Identify the range of the function shown in the graph
Answer:
Step-by-step explanation: the answer is b for apex