Use the slope formula to find the slope of the line through the points P1 and P2.P1= (8,-9)P2 = (-3,4)
Answers
To answer this question we will use the following formula for the slope of a line that passes through (x₁,y₁) and (x₂,y₂):
\(m=\frac{y_2-y_1}{x_2-x_1}\text{.}\)Substituting (x₁,y₁)=(8,-9) and (x₂,y₂)=(-3,4) in the above formula, we get:
\(m=\frac{4-(-9)}{-3-8}\text{.}\)Simplifying the above result we get:
\(m=\frac{4+9}{-11}=\frac{13}{-11}=-\frac{13}{11}\text{.}\)Answer:
\(-\frac{13}{11}\text{.}\)Related Questions
A library contains 60000 books. 14,000 are on the subject of business and 22000 are on health care and 12000 on psychology and Law. What percentage of the librarys is on the if the computing books are two-thirds of the reminder
Answers
Answer: The percentage of computing books is 13.33%.
Step-by-step explanation:
The library consist of books on different subjects:
S = {Business, Healthcare, Computing, Psychology, Law,...}
There are a total of N = 60,000 books in the library.
Business (B) = 14,000
Healthcare (H) = 22,000
Psychology and Law (P&L) = 12,000
Remaining = N - B - H - P&L
= 60000 - 14000 - 22000 - 12000
= 12000
It is provided that computing books make up two thirds of the remainder
Compute the number of computing books as follows:
C = 12000 × (2/3) = 8000
Compute the percentage of computing books as follows:
\(C\)%=\(\frac{8000}{60000}*100=13.33\)\(%\)%
Thus, the percentage of computing books is 13.33%.
what is the value of the underlined digit in the number 27,416,385. 4 is the underlined number.
Answers
The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.
How can the digits be known?The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23. however amount is represented by a number.
It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.
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Someone help me with this
Answers
a. Category with the greatest frequency is 20 - 24
b. 14 students
c. The percentage is 7%
What is frequency?Frequency is simply described as the number of times an event or observation happened in a given study or experiment that is carried out.
From the information given, we have that;
a. The category with the greatest frequency is the one with most words spelt, we have;
20 - 24
b. The number of students that spelt 35 - 39 words is traceable to
14 students
c. If the total number of students is 200
Then, the percent of students in the 35 - 39 category is;
14/200 × 100/1
Multiply the values
7%
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Need the answer and steps please
Answers
use the error formula to determine a value of n so that the maclaurin polynomial of degree n of f(x) = E^X Approximates F(2)=e2 with error less than. 001
Answers
Answer:
less than 0.001.
Step-by-step explanation:
The formula for the error in approximating a function using a Maclaurin polynomial is given by:
|F(x) - Pn(x)| = |Rn(x)| <= M * |x - a|^(n+1) / (n+1)!,
where F(x) is the actual function, Pn(x) is the Maclaurin polynomial of degree n, Rn(x) is the remainder term, a is the center of the approximation (a = 0 for Maclaurin polynomials), x is the point at which the approximation is being made, and M is an upper bound on the absolute value of the function's n+1 derivative on the interval [0, x].
To determine the value of n that satisfies the error condition |F(2) - Pn(2)| <= 0.001, we can rearrange the formula as follows:
n >= log(M * |2 - 0|^(n+1) / 0.001) / log(n + 1)
Unfortunately, without knowing the value of M, it is difficult to determine the exact value of n that satisfies the error condition. However, a common approach is to use numerical methods to estimate M and iteratively calculate the value of n until the error is less than 0.001.
What is the surface area of a sphere with diameter 8 cm?
Answers
Answer:
As = 256\(\pi\) or 804.25cm
Step-by-step explanation:
By formula As = \(4\pi r^{2}\)
As = 256\(\pi\) or 804.25cm
4
D
C
Which choices correctly describe reflections in the diagram? Check all that apply.
6
-7-6-6-4-3-2-1₁
Active
5
4
3-
2
1
& COM
2
4
A
2 3 4 5 6 7 X
B
7
1
00
2
3
The red triangle A is reflected across the x-axis onto triangle B.
Mark this and return
5
Save and Exit
Next
8
9 10
Submit
Answers
The correct conclusions about the triangle reflections are -
The red triangle is the reflection of the triangle across the{y} - axis.
The green triangle is the reflection of the triangle across the{x} - axis.
What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.
Given is a triangle along with their reflections.
We can conclude the following points regarding the reflected triangles -
The red triangle is the reflection of the triangle across the{y} - axis.
The green triangle is the reflection of the triangle across the{x} - axis.
Therefore, the correct conclusions about the triangle reflections are -
The red triangle is the reflection of the triangle across the{y} - axis.
The green triangle is the reflection of the triangle across the{x} - axis.
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Can someone Help me ASAP plss!!
Answers
a machinist is making a gear that will pull a chain at 60 ft/min when rotating at 40 rev/min. What should the radius of the gear be? Answer in inches.
Answers
The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.
To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:
chain speed = 2 x pi x radius x rotational speed
where pi is a mathematical constant approximately equal to 3.14.
We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:
60 = 2 x 3.14 x radius x 40
Simplifying the equation, we get:
radius = 60 / (2 x 3.14 x 40)
radius = 0.2387 ft
To convert feet to inches, we can multiply the answer by 12:
radius = 0.2387 x 12 = 2.8644 inches.
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Solve using elimination. Write your answer as an ordered pair (x,y).
3x - 4y = -29
and
6x + 5y = -32
Answers
Answer:
x=-7,y=2
Step-by-step explanation:
3x - 4y = - 29
and 6x + 5y = - 32
3x - 4y = - 29 (1)
6x + 5y = -32 (2)
equation (1) x 2
6x-8y = -58
equation (2) × 1
6x + 5y = - 32
Substracting → - 13y = -26
13y = 26.
26/ 13 ⇒ y =
⇒ yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy = 2
Putting y = 2 in equation (1), we have
3x - 4(2) = - 20
→ 3x = -29 +8
→3x = -21
→ X = -7
x = - 7
Heather is putting together a square
bulletin board for her new room, and
the area of the bulletin board is
196cm squared. What is the total
distance around the bulletin board?
(perimeter)
Answers
Answer:
392 cm
Step-by-step explanation:
Since your trying to find the perimeter of the bulletin board by using the area, you should:
Divide the area by 2. 196 divided by 2 = 98 (which is the length of one side)Now add 98 four times to get your answer. 392.A down payment of $195 is made on a television that costs $1300. What percent of the
cost is the down payment?
Answers
Answer:
15%
Step-by-step explanation:
Add 195 to 1300, which gives you, 1495.
Use the formula for percent change: Difference = % * original price.
So what is the difference between 1495 and 1300? It’s 195.
Now we have 195 as the difference.
Do we know the original price of the TV? Yes we do. What is it? Its 1300 because the question states the TV costs $1300.
Now we have the equation 195 = % * 1300
We don’t know the percentage, right? So now we have to solve for %. To do that, you have to do 195 divided by 1300, which gives you 0.15. Lastly, you have to turn 0.15 into a percentage, to do that, multiply 0.15 by 100, and it should give you 15%.
Therefore, 15% is the down payment. Hope this helps!
Ravi has two and one-fourth meters of rope. He gives ninety-three centimeters of the rope to his brother. How many centimeters of rope does Ravi have left?
Answers
If he gives ninety-three centimeters of the rope to his brother, Ravi has 132 centimeters of rope left.
Two and one-fourth meters of rope can be written as 2.25 meters. Since 1 meter is equal to 100 centimeters, we can convert 2.25 meters to centimeters by multiplying it by 100, giving us 225 centimeters.
If Ravi gives 93 centimeters of the rope to his brother, we can subtract it from the original length to find how much rope he has left.
225 cm - 93 cm = 132 cm
In general, to convert between meters and centimeters, you can multiply the number of meters by 100 to get the length in centimeters. To convert between centimeters and meters, you can divide the number of centimeters by 100 to get the length in meters.
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Aris and Josiah are reading a 50-page book for their ELA class. Aris wants to know what page Josiah is reading. Josiah gives her two hints: 1. The product of the two page numbers he can see is 930. 2. The page he is reading is an odd numbered page.
Answers
Answer:
31
Step-by-step explanation:
Let x and (x + 1) be the page numbers Josiah can see
Hint 1: x(x + 1) = 930
⇒ x² + x = 930
⇒ x² + x - 930 = 0
Using quadratic formula,
\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)
a = 1, b = 1 and c = -930
\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)
\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)
Sice x is a page number, it cannot be negative
⇒ x = 30 and
x + 1 = 31
The two pages Josiah can see are pg.30 and pg.31
Hint 2: The page he is reading is an odd number
Out of the pages 30 and 31, 31 is an odd number
Thereofre, Josiah is reading page 31
What is the answer for this question?
Answers
The percentage of having a probability of a non-vowel letter is 44%
What is ProbabilityProbability is the measure of the likelihood that an event will occur in a given set of circumstances. It is a quantifiable measure of the chance of something happening. Probability is expressed as a number between 0 and 1 (or 0% to 100%) where the higher the number, the more likely the event is to occur.
The probability to select a vowel letter is = 15 + 22 + 11 + 6 + 2 = 56%
The probability of selecting any vowel is 56%
In the English alphabet, we have 26 letters and 5 vowel letters.
The probability of not having a vowel letter is calculated as;
26 - 5 = 21
P = 21 / 28
In percentage, we can simply say the probability of having a non-vowel is 100 - 56 = 44
The percentage of having a non-vowel is 44%
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List all the subsets of the given set.
{e, n, t}
Answers
The subsets of the set {e, n, t} are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
How to obtain the number of subsets in a set?Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:
\(2^n\)
The set for this problem is given as follows:
{e, n, t}
The cardinality is given as follows:
n = 3.
Hence the number of subsets is given as follows:
2³ = 8.
The subsets are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
In which {} is the empty set.
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10. Higher Order Thinking Each of 5 friends has x action figures in
his or her collection. Each friend buys 11 more action figures. Now
the 5 friends have a total of 120 action figures.
a. Write an equation that models the problem.
b. Solve the equation to find the number of action figures, x, that
each friend had originally.
Answers
Each friend had originally 13 action figures before buying 11 more.
Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.
a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.
Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.
The total number of action figures will be 5(x + 11) = 5x + 55.
Now, according to the problem,5x + 55 = 120
This is our equation that models the problem.
b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.
5x + 55 = 120
5x = 120 - 55 (subtract 55 from both sides)
5x = 65x = 13
Therefore, each friend had originally 13 action figures before buying 11 more.
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The radius of the base of a cylinder is expanding at a constant rate of 3 mm/min. If the height of
the cylinder is a constant 20 mm, find the rate at which the VOLUME of the cylinder is changing at the
moment when the radius of the base of the cylinder is 10 mm. Also find the rate at which the SURFACE
AREA of the cylinder is changing at this same moment.
(V = r²h, SA=2лrh+2rr²)
I’m getting 1800pi mm^3/min for volume and 360pi mm^2/min for surface area but I’m not sure if it’s correct
Answers
The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.
To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.
Given:
Radius rate of change: dr/dt = 3 mm/min
Height: h = 20 mm
Radius: r = 10 mm
Volume of the cylinder (V) = \(r^2h\)
Differentiating with respect to time (t), we have:
dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)
Since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dV/dt = 2(10)(20)(3) + (10^2)(0)
dV/dt = 600 + 0
dV/dt = 600 mm^3/min
Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.
Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)
Differentiating with respect to time (t), we have:
dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)
Again, since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)
dSA/dt = 0 + 120π + 120π
dSA/dt = 240π mm^2/min
Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.
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Please help with this worksheet
real numbers
Answers
I DO NOT KNOW JUST GIVE ME A SECOND.
Write a function in vertex form that is translated 3 units down and 3 units to the right of f (x) = x^2
f (x) =
Answers
Answer:
f(x)= (x-3)^2-3
Step-by-step explanation:
Vertex Form: y= a(x-h)^2+k
a is the reflection
h and k are the vertex so in an ordered pair (x,y) = (h,k)
Since it is translating 3 units down it is going to be a negative 3. If it was translating up it would be positive 3. This represents the "k" because it is moving on the y-axis.
Since it is translating 3 units to the right it is going to be positive 3. If it was translating left it would be negative 3. This represents the "h" because it is moving on the x-axis.
After plugging it into the vertex form formula: f(x)= (x-3)^2-3
*notice when I plugged the "h" in it became negative because x-(3)= x-3*
please help me answer this
Answers
The prompt that examines linear functions and ordered pairs are given below.
What is the explanation for the above response?1) Here are the ordered pairs for each point:
Point A: (4, 9)
Point B: (6, 3)
Point C: (1, 3)
Point D: (8, 7)
Point E: (8, 9)
See the attached graph.
2) Part A: The completed table and graph for Derek is given as attached.
Part B: Derek makes 10 bracelets in 5 hours.
3) The ordered pairs are given in the labelled graph accordingly.
4) Deanna's coordinates plane is labelled and attached accordingly. The correct answer is Option B (5,8)
5) The other ordered pairs that could be the vertext are Options A - E. See the attached image (Miguel's Squre
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Felipe rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 86 cents for each mile driven. Felipe had to pay $270.79 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
421.4 miles
Step-by-step explanation:
Numner of miles= ($270.79-$17.95)/86 cents
= $252.84/$0.60
=421.4 miles
Find the restricted values of x for the following rational expression.
Simplify the following union and/or intersection.
(−∞,−12]∩[−12,18)
Answers
The restricted values of x for the given rational expression are all real numbers except for x = −12.
Find the restricted values of x for the following rational expression?The restricted values of x for the rational expression are x ≠ -12.The simplified union and/or intersection is (−∞,−12).The simplified union and/or intersection is (−12, 18). This is called an open interval because it does not include the endpoints.The restricted values of x for the given rational expression are all x-values that make the expression undefined.This includes any values of x that make the denominator of the expression equal to 0, as this would result in a division by 0.The given union and intersection is (−∞,−12]∩[−12,18).This is known as the intersection of two intervals, and the result of this expression is (−12,18).This means that the set of values that satisfy the expression are all real numbers greater than -12 and less than 18.To learn more about intersection of two intervals refer to:
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6. Rewrite y = √√4x+16 +5 to make it easy to graph using a translation. Describe the graph.
Answers
Answer:
~
Step-by-step explanation:
To make it easier to graph using a translation, we can rewrite the given equation as:
y - 5 = √√4x + 16
This is obtained by subtracting 5 from both sides of the equation.
The graph of the original equation y = √√4x+16 +5 can be obtained by taking the graph of y = √√4x + 16 and shifting it upwards by 5 units. The graph of y = √√4x + 16 is a square root function that has a vertical stretch of 2, a horizontal compression of 4, and a vertical translation of 16 units upwards. So the graph of the given equation y = √√4x+16 +5 will be the same as the graph of y = √√4x + 16, but shifted upwards by 5 units.
A cooler contains 12 bottles of apple juice and 18 bottles of orange juice. You reach into the cooler without looking and pull out one bottle of apple juice. Then you reach into cooler and pull out another bottle of juice. What is the probability of pulling apple juice and then pulling another apple juice?
Answers
Answer:
P = 0.232
Step-by-step explanation:
In the cooler, we have 12 bottles of apple juice and 18 bottles of orange juice.
This adds up to a total of 30 bottles.
Now we want to find the probability of pulling a bottle of apple juice after you pulled one bottle of apple juice.
The probability of pulling a bottle of apple juice at the beginning is equal to the quotient between the number of apple juice bottles in the cooler and the total number of bottles in the cooler,
This means that 12 out of 30 are apple juice, then the probability of getting first a bottle of apple juice is:
p = 12/30
Now, we want to find the probability of getting another, we will do the same calculation than above, but now the number of bottles of apple juice is 11 (because we took one) and the total number of bottles is 29.
In this case, the probability is:
q = 11/29
The joint probability (the probability of both events happening) is equal to the product of the individual probabilities.
Then the probability of pulling apple juice and then pulling another apple juice is:
P = p*q = (12/30)*(11/29) = 0.232
3 A system of two linear equations is graphed on a coordinate plane. If the system of
equations has infinitely many solutions, which statement must be true?
a. On the graph, there are no points (x, y) that satisfy both equations.
b. On the graph, there is exactly one point (x, y) that satisfies both equations.
c. On the graph, any point (x, y) that satisfies one of the equations cannot satisfy the
other equation.
d.
On the graph, any point (x, y) that satisfies one of the equations must also satisfy
the other equation.
Answers
Answer:
d. On the graph, any point (x, y) that satisfies one of the equations must also satisfy the other equation.----------------------
If the system of linear equations has infinitely many solutions, it means the two lines overlap.
In other words, each point of one of the lines also belongs to the second line.
Choices a, b, c give us one or no solutions and therefore not the answer.
Choice d is reflecting the infinitely many solutions and hence is the correct one.
Write the solution in interval notation.
Nineteen less than p is no less than 47.
Answers
The solution to interval notation or inequality "Nineteen less than p is no less than 47" is p ≥ 66.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The interval notation is - Nineteen less than p is no less than 47.
The inequality expression is -
p - 19 ≥ 47
Solve the inequality -
p - 19 ≥ 47
p ≥ 47 + 19
p ≥ 66
Therefore, the solution to inequality is p ≥ 66.
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Solve for x.
Question 17 options:
A)
–62∕5 or 10
B)
–10 or 62∕5
C)
No solution
D)
Infinitely many solutions
Answers
Please help ASAP ! Find the expressions for the perimeter of these shapes.
Answers
Answer:
Quest 1. P = 3xat2 + 4yat2 + 11xy
Quest 2. P = 7xat2 + 21x + 5y + 5
Step-by-step explanation:
Note: Perimeter, P is the total sum of the distance round about an object. that at symbol cant be used here.so.am.using at2 for squared
NO LINKS!! URGENT HELP PLEASE!!!
Please help me with Growth rate and Initial Value only
Answers
Answer:
growth rate: 4
y-value: 19
equation: y=4x+19
Step-by-step explanation:
Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.
For the question:
The change in y-values is 11-7=4,
and the change in x-values is +1.
Therefore, the growth rate is 4.
\(\hrulefill\)
Initial Value: The initial value of a linear function is the value of the function when x is 0.
In this case, the initial value is 19.
This can be found by looking at the y-value of the point where x is 0.
In this case, the y-value is 19.
\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.
Using the table you provided, we can find the slope by using two points on the line.
Let’s use (-3, 7) and (1, 23).
The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4
Now,
Taking 1 point (-3,7) and slope 4.
we can find the equation by using formula:
y-y1=m(x-x1)
y-7=4(x+3)
y=4x+12+7
y=4x+19
Therefore, the equation of the given table is y=4x+19\(\hrulefill\)
Answer:
Growth rate: 4
Initial value: 19
Equation: y = 4x + 19
Step-by-step explanation:
The slope of a linear function represents its growth rate.
Therefore, the growth rate of a linear function can be found using the slope formula.
Substitute two (x, y) points from the table into the slope formula, and solve for m. Substituting points (0, 19) and (1, 23):
\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)
Therefore, the growth rate of the linear function is 4.
The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.
From inspection of the given table, y = 19 when x = 0.
Therefore, the initial value of the linear function is 19.
To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.
As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:
\(\boxed{y=4x+19}\)