What is the equation in point-slope form of the line that passes through the points (-3, -1) and (2, 9)?
y-1 = 2(x+3)
y-9=2(x-2)
y+9=2(x-2)
y-1= 2(x-3)
Answers
Answer:
\(\textsf{B)} \quad y-9=2(x-2)\)
Step-by-step explanation:
\(\boxed{\begin{minipage}{9cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}\)
Given points:
(-3, -1)(2, 9)Substitute the given points into the slope formula to find the slope of the line:
\(\implies m=\dfrac{9-(-1)}{2-(-3)}=\dfrac{10}{5}=2\)
\(\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}\)
Substitute the found slope and point (-3, -1) into the point-slope formula:
\(\implies y-(-1)=2(x-(-3))\)
\(\implies y+1=2(x+3)\)
Substitute the found slope and point (2, 9) into the point-slope formula:
\(\implies y-9=2(x-2)\)
Therefore, the correct answer option is:
\(\textsf{B)} \quad y-9=2(x-2)\)
Related Questions
Which line represents a horizontal asymptote of f (x) = StartFraction 5 x squared minus 3 x + 2 Over 10 x squared minus 1 EndFraction y = –2 y = –0.5 y = 0.5 y = 2
ANSWER: B
Answers
Answer:
Answer is B
Step-by-step explanation:
Got it right on the quiz
The horizontal asymptote is y=-0.5.
How to find horizontal asymptote?
If the degree of the polynomial in the numerator and the denominator is same then the horizontal asymptote is given by \(y=\frac{\text{leading coefficient of the numerator}}{\text{ leading coefficient of the denominator}}\)
What will the horizontal asymptote of given function?
In the given function, the degree of the polynomial of the numerator is 2 and of the denominator is also 2.
The leading coefficient in the numerator is -5 and in the denominator it is 10.
Divide -5 by 10 and equate the result to y to get the horizontal asymptote .
\(y=\frac{-5}{10}\)
y=-0.5
Therefore, the correct option is b.
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How can i solve algeba equations
Answers
Answer:
what kind?
Step-by-step explanation:
and if its not a specific kind of algebra just use an algebra calculator
Answer:
Use PEMDAS
Step-by-step explanation:
First, solve inside the (P)arentheses. Next, calculate all (E)xponents. Then check to see which comes first in the equation: multiplication or division? Complete these in the order that they appear in the equation. Now, repeat the previous step with addition and (S)ubtraction. If all else fails, use MathPapa.
The figure shows a net of a cube. Which expression can be used to find the total surface area of the cube?
Answers
Answer:
Option C: 6(7 * 7)
Step-by-step explanation:
There are six faces of the cube. Since each face is 7 by 7 units, there are 6(7 *7) units total.
A sphere and its dimension are shown in the diagram 15 inches
Answers
The measurement that is closest to the volume of the sphere is given as follows:
1,767.1 in³.
What is the volume of an sphere?The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:
\(V = \frac{4\pi r^3}{3}\)
From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:
r = 0.5 x 15
r = 7.5 units.
Then the volume of the sphere is given as follows:
V = 4/3 x π x 7.5³
V = 1,767.1 in³.
Missing InformationThe sphere is given by the image presented at the end of the answer.
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Each student at Riverside Elementary has a student ID number made up of six numbers between 1 and 9. How many possible student ID's can be made? A. 60,480 B. 117,649 C. 531,441 D. 1,000,000. Please put a good explanation, I need to figure this out soon!
Answers
Answer:
C. 531,441
Step-by-step explanation:
You take the largest possible value and put it to the power of how many numbers there are. In this case 9^6. Hope this helps.
9. 16 is 40% of what number? If necessary, round to the nearest tenth. A 40.0 B 0.4 C 640.0 D 6.4
Answers
Answer:
A
Step-by-step explanation:
16 x 100 = 1600
1600 / 40 = 40.0
Answer:
A. 40.0
Step-by-step explanation:
Which values are solutions to the inequality below?
Check all that apply.
x2 < 81
A. 6
B. 9
C. 10
D. -4
E. -9
F. -12
Answers
Answer:
Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.
Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.
Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.
Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.
It took Alfonzo 25 minutes to shop for a shirt. If he left the store at 2:25 P.M. after buying the shirt, what time did he start shopping?
Answers
The time he start shopping is 2 : 00 PM
How to determine the time he start shopping?From the question, we have the following parameters that can be used in our computation:
Time spent = 25 minutes
Time he left the store = 2 : 25PM
Using the above as a guide, we have the following:
Time he started = Time he left the store - Time spent
substitute the known values in the above equation, so, we have the following representation
Time he started = 2 : 25PM - 25 minutes
Evaluate
Time he started = 2 : 00 PM
Hence, the time he start shopping is 2 : 00 PM
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Solve for z. Round to the nearest tenth of a degree, if necessary.
3.9
M
5-3
to/
L
Answers
L is then equal to 36.7 degrees (rounded to the nearest decimal point). in this right angle triangle
Define right angle triangle?A right triangle, also known as a right-angled triangle, is a triangle with two perpendicular sides and one angle that is a right angle (90 degrees). The hypotenuse is the side that forms the right angle; the other two sides are referred to as the legs. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
This describing the right triangle LMN, where M is at a 90-degree angle and ML is parallel to MN.
We can use the tangent function to determine the angle L if MN is 3.9 and ML is 5.3.
An angle's tangent is equal to the adjacent side divided by the angle's opposing side.
The opposing side in this instance is MN, and the side next to it is ML.
Tan(L) = MN/ML = 3.9/5.3 = 0.7358 as a result.
We can use a calculator or a table to get L by taking the inverse tangent of both sides of the equation.
L is then equal to 36.7 degrees (rounded to the nearest decimal point). Therefore, L is almost 36.7 degrees.
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Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. Select one:
-1.6; unusual
-17.6; unusual
-1.6; not unusua
l 1.6; not unusual
Answers
The z-score of -1.6 is less than 2.00 but greater than -2.00.
Hence, we can conclude that the value is not unusual.
The correct answer is: -1.6; not unusual.
When we are given a test score of 48.4 on a test that has a mean of 66 and a standard deviation of 11,
we need to find the corresponding z-score and determine whether the value is unusual or not.
The formula for calculating z-score is:
z = (x - μ) / σ
Where, z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the given values in the formula, we get: z = (48.4 - 66) / 11z = -1.6
Therefore, the z-score corresponding to the given value is -1.6.
Now, we need to determine whether this value is unusual or not.
A score is considered unusual if its z-score is less than -2.00 or greater than 2.00.
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what will be the 40th term in the sequence defined by an=-12+4(n-2)
Answers
Answer:
140
Explanation:
an=-12+4(n-2)
an=-12+4([40]-2)
an=-12+4(38)
an=-152-12
an=140
The 40th term in the sequence defined by aₙ= -12+4(n-2) is 140
using AP formula,
aₙ = a + (n - 1)d
where
a = first term
d = common difference
n = number of terms
Therefore,
aₙ = -12 + 4(n-2)
n = 40
a₄₀ = -12 + 4(40 - 2)
a₄₀ = -12 + 4(38)
a₄₀ = -12 + 152
a₄₀ = 140
The 40th term of the sequence is 140.
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A basketball player scores
126
points in
9
games. At this rate how many points will he score in
17
games?
Answers
I got 126 points and that divided by the 9 games got 14 points and multiple that by 17 games and got 238 points
I hope this helps
4. Chelsea determined that the value of x in the triangle at the right was 5.
a. Find the value of each angle by substituting 5 for x.
b. Was Chelsea's solution, x = 5, correct? How do you know?
15x
x
11x
(8x+5)
Z
Answers
Step-by-step explanation:
a) 11*5=55
15*5=75
8*5+5=45
b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°
PLEASE HELP 50 POINTS
The total leaf mass of a certain species of young plant saplings is approximately normally distributed with a mean of 14.2 grams and a standard deviation of 0.5 grams.
a. What is the probability of obtaining a randomly chosen plant sapling with a total leaf mass of more
than 15 grams?
b. Identify the leaf mass that would represent the 99th percentile.
Answers
Answer:
THE ANSWER IS A
Step-by-step explanation:
CORRECT IF I WRONG
It took a motorboat 1 hour longer to travel 63 miles against the current than travel the same distance with the current. The speed of the current is 2 mph. What is the speed of the motorboat in still water?
Answers
Answer:
Step-by-step explanation:
I just need help on the second one , I’m not too sure if the others are correct but I hope , so please help me on the second one
Answers
A country's population in 1991 was 103 million, in 1999 it was 108 million. estimate the total population in 2013
Answers
Answer:
117
Step-by-step explanation:
The total population is 117 million
The expression 120 + 15m gives the volume of water in Miguel's pool (in liters) after he spends m minutes filling his pool.
What is the volume of water in Miguel's pool after he fills it for 6.5 minutes?
Answers
Answer:
217.5 liters
Step-by-step explanation:
15 x 6.5 = 97.5. 97.5 + 120 = 217.5 liters
write a rational number between root2 and root3
Answers
Answer:
prational number between root2
pls say hard
very hard
Answers
Answer:
3
Step-by-step explanation:
Joe has £1. He buys a can of pop
for 62p.
How much change does he get?
Answers
Answer:
that's a pound which is made of 100 pence... so 100-62= 38
his change should be 38 pence
Tom read 3/4 of a book. Sarah read 2/3 of the same book. Which student read more?
A) Tom
B) Sarah
C) Both students read the same amount.
Answers
1. determine grams of agarose required to make 60 ml of a 0.8% (w/v) agarose solution in 1x tae (tris base-acetic-acid-edta): express answer with two decimals.
Answers
The grams of agarose required to prepare a 0.8% (w/v) agarose solution is 0.48 grams.
To make a 0.8% (w/v) agarose solution in 1x TAE, you will need to calculate the grams of agarose required using the formula:
Grams of agarose = (volume of solution in ml) x (percentage of agarose solution)
In this case, the volume of solution is 60 ml and the percentage of agarose solution is 0.8%.
Grams of agarose = (60 ml) x (0.8%)
Grams of agarose = (60 ml) x (0.008)
Grams of agarose = 0.48 g
In conclusion, you will need 0.48 grams of agarose to make 60 ml of a 0.8% (w/v) agarose solution in 1x TAE.
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What is the area of trapezoid ABCD?
Enter your answer as a decimal or whole number in the box. Do not round at any steps.
_____units
Answers
Answer:
answer on the picture.....
In triangle FGH, m∠F=59°
and m∠H=77
Complete the equation to determine m∠G
Answers
Answer: 44 degrees
Step-by-step explanation: 59+77+x=180
x=44
In the month of March, the temperature at the South Pole varies over the day in a periodic way that can be modeled approximately by a trigonometric function.
The highest temperature is about -50°C, and it is
reached around 2 p.m. The lowest temperature is
about -54°C and it is reached half a day apart
from the highest temperature, at 2 a.m.
Find the formula of the trigonometric function that models the temperature T in the South Pole in March t hours after midnight. Define the function using radians.
Answers
The trigonometric function that models the temperature T in the South Pole in March t hours after midnight is given as follows:
T(t) = 2cos(π/12(t - 14)) - 52.
How to define the cosine function?The cosine function is defined as follows:
g(x) = acos(bx+c)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2pi/B.c: phase shift.d: vertical shift.The lowest temperature is of -54ºC, while the highest is of -50ºC, with a difference of 4ºC, hence the amplitude is given as follows:
2a = 4
a = 2.
A function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -54 and -50, hence the vertical shift is given as follows:
d = -50.
The period is of 24 hours, hence:
2π/B = 24
24B = 2π
B = π/12.
The highest value of the cosine function should be assumed at t = 0, but it is assumed at t = 14(2 p.m.), hence the phase shift is given as follows:
c = 14.
Thus the function is defined as follows:
T(t) = 2cos(π/12(t - 14)) - 52.
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Simplify this expression.
4^9/4^3
Answers
Answer: \(\frac{4^{9} }{4^{3} }\)=4096
Steps:
\(\frac{4^{9} }{4^{3} }\)
\(\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\)
\(\frac{4^9}{4^3}=4^{9-3}\)
\(=4^{9-3}\)
\(4^{9} -^{3}\)
=4096
The Simplifying the expression 4 ^ 9 / 4 ^ 3 will be 4096.
What is simplifying?Simplification is the process of replacing a mathematical expression with an equivalent one, that is simpler (usually shorter), for example.
Simplification of algebraic expressions, in computer algebra.
Simplification usually involves making the expression simple and easy to use later.
We need to Simplifying the expression
4 ^ 9 / 4 ^ 3 .
Now, 4 ^ 9 / 4 ^ 3
Using exponent formula;
= 4 ^ ( 9 - 3 )
= 4 ^ 6
= 4096
Therefore, the Simplifying the expression 4 ^ 9 / 4 ^ 3 will be 4096.
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Lucy buys baseball cards in packages of 10. List the number
of baseball cards for 0 to 4 packages in the table. Then write
the ordered pairs.
Number of
Packages, x
Number of
Cards, y
Ordered Pair
(x, y)
84238*ASOSO
Baseball Cards
50
45
40
35
30
25
20
15
10
5
0
01
Plot the points in the coordinate plane to the right.
Describe the relationship between the coordinates of the ordered pairs.
(0,0)
2
456
Packages
X
Answers
Here is the table of the number of baseball cards for 0 to 4 packages and their corresponding ordered pairs:
What are the data in the table?Number of Packages, x | Number of Cards, y | Ordered Pair (x, y)
0 | 0 | (0, 0)
1 | 10 | (1, 10)
2 | 20 | (2, 20)
3 | 30 | (3, 30)
4 |40 | (4, 40)
To plot these points in the coordinate plane, we can use the horizontal axis for the number of packages (x) and the vertical axis for the number of cards (y), with each unit representing 1 package or 10 cards. Here is the plot:
|
50 |
45 |
40 ● (4, 40)
35 |
30 ● (3, 30)
25 |
20 ●(2, 20)
15 |
10 ● (1, 10)
5 |
0 ● (0, 0)
--------------
0 1 2 3 4
As we can see from the plot and the table, the relationship between the coordinates of the ordered pairs is linear, with the number of cards increasing by 10 for each additional package.
Specifically, the relationship can be described by the equation y = 10x, where y is the number of cards and x is the number of packages. This means that the slope of the line connecting any two points is always 10, and the y-intercept is 0.
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Mr. Smith and Mr. Stein were driving to a business meeting 140 miles from their office. Mr. Smith drove the first
miles, then Mr. Stein drove the rest of the way.
Write an algebraic expression for how many miles Mr. Stein drove.
Answers
The distance that Mr. Stein drove can be represented by the expression: \(140 - x\)
What is an algebraic expression?A mathematical phrase made up of one or more variables, constants, and arithmetic operations like addition, subtraction, multiplication, and division is known as an algebraic expression. Exponentiation and other mathematical operators could also be present.
Let's assume that Mr. Smith drove "x" miles before Mr. Stein took over the driving.
Then, the total distance they traveled is 140 miles.
So, the distance that Mr. Stein drove can be represented by the expression:
140 - x
Therefore, This is because if Mr. Smith drove "x" miles, then the remaining distance that needed to be covered by Mr. Stein would be the difference between the total distance of 140 miles and the distance already driven by Mr. Smith.
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Please Help With this question!
There are 3 pictures!
Answers
Corresponding Angles postulate is ur answer mate