What is the point-slope equation of the line with a slope 4/3 that goes through the point (-4,6)?
Answers
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})~\hspace{10em}slope = m\implies \cfrac{4}{3}\\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-6=\cfrac{4}{3}[x-(-4)]\implies y-6=\cfrac{4}{3}(x+4)[/tex]
Answer:
The point-slope form of the equation is y - 6 = 4/3(x + 4), which is answer B.
Step-by-step explanation:
In order to find the point-slope form of any equation, start with the base form of the equation.
y - y1 = m(x - x1)
Now input the slope given as m, and the point in for x1 and y1.
y - y1 = m(x - x1)
y - 6 = 4/3(x - -4)
y - 6 = 4/3(x + 4)
Related Questions
The recursive rule for a sequence is shown. an=an−1+7 a1=17 what is the explicit rule for this sequence?
Answers
an=a(n-1)+7; a1=17
to get the explicit formula we proceed as follows:
common difference=7
a1=17
but the explicit formula for arithmetic sequence is:
an=a+(n-1)d
where:
a=fist term
n=number of terms
d=common difference
plugging the values in the formula we get:
an=17+(n-1)7
simplifying we get
an=17+7n-7
an=7n+10
Answer: an=7n+10
The explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
The recursive rule is given as:
[tex]a_n=a_{n-1}+7[/tex]
[tex]a_1 = 17[/tex]
The above shows that the sequence is an arithmetic sequence.
Start by calculating a2
We have:
[tex]a_n=a_{n-1}+7[/tex]
Substitute 2 for n
[tex]a_2=a_1+7[/tex]
This gives
[tex]a_2 = 17 + 7[/tex]
[tex]a_2 = 24[/tex]
So, we have:
a1=17
a2 = 24
The common difference (d) is:
d =a2 - a1
d = 24 - 17
d = 7
The explicit rule is then calculated as:
[tex]a_n = a_1 + (n - 1)d[/tex]
This gives
[tex]a_n = 17 + (n - 1) * 7[/tex]
Expand
[tex]a_n = 17 - 7 + 7n[/tex]
[tex]a_n = 10 + 7n[/tex]
Hence, the explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
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Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura. How long would Tammy take to do the job alone?
3 hrs.
4 hrs.
6 hrs.
Answers
Time = x hr/job ; Rate = 1/x job/hr
Jeri DATA
Time = x+2 hr/job ; Rate = 1/(x+2) job/hr
Tammy DATA:
Time = (x+2)/2 hr/job ; Rate = 2/(x+2) job/hr.
Together DATA:
time = 4/3 hr/job ; Rate = 3/4 job/hr
EQUATION:
rate + rate + rate = together rate
1/x + 1/(x+2) + 2/(x+2) = 3/4
Multiply thru by 4x(x+2) to get:
4(x+2) + 4x + 8x = 3x(x+2)
16x + 8 = 3x^2+6x
3x^2-10x-8 = 0
3x^2-12x+2x-8 = 0
3x(x-4)+2(x-4) = 0
(x-4)(3x+2) = 0
Positive answer:
x = 4 hrs. time for Laura to do the job
x+2=6 hrs. time for Jeri to do the job
(x+2)/2 = 3 hrs. time for Tammy to do the job
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura.
The equations are given as,
T + J + L = 1 + 20/60
T + J + L = 1.333 ....1
J = 2T ....2
J = 2 + L ....3
The rate for Laura, Tammy, and Jeri will be given as,
Laura DATA:
Time = x hr/job ; Rate = 1/x job/hr
Jeri DATA:
Time = x+2 hr/job ; Rate = 1/(x+2) job/hr
Tammy DATA:
Time = (x+2)/2 hr/job ; Rate = 2/(x+2) job/hr.
Together DATA:
Time = 4/3 hr/job ; Rate = 3/4 job/hr
The equation is given as,
Rate + Rate + Rate = Together rate
1/x + 1/(x+2) + 2/(x+2) = 3/4
Multiply the equation by 4x(x+2) to get:
4(x+2) + 4x + 8x = 3x(x+2)
16x + 8 = 3x^2+6x
3x^2-10x-8 = 0
3x^2-12x+2x-8 = 0
3x(x-4)+2(x-4) = 0
(x-4)(3x+2) = 0
x = 4, - 2/3
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
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In how many ways can 4 blue flags 3 green flags and 2 flags be arranged
Answers
[tex]\text {Number of ways } = \dfrac{9!}{4!3!2!} = 1260[/tex]
--------------------------------
Answer: 1260 ways
--------------------------------
You can calculate the number of ways to arrange the flags using the formula for permutations of multi-sets. We substitute the quantities of each flag color into the formula, which yields our answer of 1260 ways to arrange the flags.
Explanation:The question is asking about permutations of different objects— in this case, flags of multiple colors. For such problem, you can use the formula for permutations of multiset:
P(n1, n2, ..., nk) = (n1 + n2 + ... + nk)! / (n1! * n2! * ... * nk!)
Where n1, n2, ..., nk represent the counts of each distinct item (in this case, flag colors).
For our flags, you would substitute n1=4 (blue flags), n2=3 (green flags), and n3=2 (red flags). Applying the formula gives us (4+3+2)! / (4!*3!*2!) = 9! / (4!*3!*2!) = 1260.
So, "there are 1260 ways to arrange 4 blue flags, 3 green flags and 2 red flags that the student has".
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A circle has a radius of 7.2 feet and a central angle aob that measures 112°. what is the area of sector aob? use 3.14 for pi and round your answer to the nearest tenth.
Answers
A=θ/360πr²
but
θ=112°, r=7.2 ft, π=3.14
hence
A=112/360×3.14×7.2²
A=50.64192 ft²
A~50.6 ft²
what is the classification for this polynomial u^2v^3w?
A.) monomial
B.)binomial
C.)trinomial
Answers
The polynomial u^2v^3w is classified as a monomial because it consists of a single algebraic term. Monomials are polynomials with exactly one term, unlike binomials or trinomials which have two or three terms, respectively.
Explanation:The classification for the polynomial u^2v^3w is a monomial. A monomial is a single term algebraic expression with one or more variables raised to a non-negative integer power. Since u^2v^3w consists of a single term without a plus (+) or minus (-) sign connecting it to other terms, it is considered a monomial.
The classification of polynomials is based on the number of terms they contain:
Monomial: A polynomial with one term, such as 3x or -a^4b^2.Binomial: A polynomial with two terms, such as x + y or 3a - 7b.Trinomial: A polynomial with three terms, such as x^2 + 2x + 1 or a^3 - 3a^2b + 2ab^2.Knowing the classification of polynomials helps in understanding how to perform operations such as addition, subtraction, multiplication, and division with them.
Which table represents a direct variation function?
x y x y x y
-3 -4.5 -5.5 -3 -3 -7.5
-1 -3.0 -5.5 -1 -1 -2.5
2 -1.5 -5.5 2 2 5.0
5 0.0 -5.5 5 5 12.5
10 1.5 -5.5 10 10 25.0
x y
-5.5 10
-4.5 8
-3.5 6
-2.5 4
-1.5 2
Answers
The answer to this question is B Ed
The table that represents a direct variation function is
x y
-3 -7.5
-1 -2.5
2 5.0
5 12.5
10 25.0
How to determine the table?For a table to represents a direct variation, the following must be true
k = y/x
Where k represents the constant of variation
In table 3, we have:
k = 25.0/10 = 12.5/5 = 5.0/2 = -2.5/-1 = -7.5/-3
This gives
k = 2.5
The value of k is the same for all input and output values
Hence, the table that represents a direct variation function is the table 3
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The antarctic peninsula is less than 700 miles from what continent
Answers
Find the equation of the line that passes through (-2,5) and is parallel toy= -1/3x+2
Answers
If lines are parallel, then their slopes are equal, so m=-1/3.
So we can write
y=(-1/3)x+b
To find be, we need substitute value's of x and y using point (-2,5).
5=(-1/3)*(-2)+b
5=2/3+b
b= 5-2/3=15/3-2/3=13/3
The equation of the line is
y=(-1/3)x+13/3
Tracy can wallpaper 7 rooms in a new house in 21 hours. together with her trainee they can wallpaper the 7 rooms in 12 hours. how long would it take the trainee working by herself to do the job? round to the nearest tenth.
Answers
We have then:
x: time it takes the trainee to do the work alone.
For this case we have the following equation:
7/21 + 7 / x = 7/12
Solving for x we have:
x = 28 hours
Answer:
it would take the trainee working by herself about:
x = 28 hours
Simplify the equation 7.5+N+9.63
Answers
Add 7.5+9.63 which would be 17.13
17.13+N
Please pretty please help me fast
Answers
Ordered pair -- (0, 50)
Explanation: The red region represents solutions to the red line inequality that are not solutions to the blue line.
Region 2:
Ordered pair -- (50, 0)
Explanation: The purple region represents solutions to both the red line and blue line.
Region 3:
Ordered pair -- (20, - 10)
Explanation: The blue region represents solutions to the blue line inequality that are not solutions to the red line.
Region 4:
Ordered pair -- (0, 0)
Explanation: The white region represents all points/ordered pairs that are not solutions to either inequality.
In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. to avoid confusion between "o" and zero and between "i" and one, the letters "o" and "i" are not used. how many distinct license plates can be formed in this state?
Answers
The length of a rectangle is 5 yd less than three times the width, and the area of the rectangle is 28 yd2 . find the dimensions of the rectangle.
Answers
The formula for the area of a rectangle is A = lw. Substitute, so then it's 28 = (3x-5) * x, and you evaluate.
Hope this helps you! And rate so I can see if I did well!
The dimensions of the rectangle are width = 4 yds and length = 7 yds.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that the length of a rectangle is 5 yds less than three times the width,
The area of the rectangle is 28 yds square.
Let the width of the rectangle is x
So the length of the rectangle = 3x - 5
The area of a rectangle = x × (3x - 5)
28 = 3x² - 5x
3x² - 5x - 28 = 0
(3x + 7)(x - 4) = 0
3x + 7 = 0 and and x - 4 = 0
x = -7/3 and x = 4
Take x = 4 as the width
So the length of the rectangle = 3(4) - 5 = 12 - 5 = 7
Therefore, the dimensions of the rectangle are width = 4 yds and length = 7 yds.
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Simplify: (3 + 4i) + (2 - 3i) - (5 - 6i)
Answers
= 0 + 7i
________________________________________________________
Explanation:
________________________________________________________
(3 + 4i) + (2 - 3i) - (5 - 6i) =
(3 + 4i) + 1(2 - 3i) - 1(5 - 6i) ; ← Note that the coefficient, "1" is implied;
since any value, multiplied by "1" , results in that same value.
_____________________________________________________________
Note the "distributive property" of multiplication:
_____________________________________________________________
a(b + c) = ab + ac ;
a(b – c) = ab – ac .
_____________________________________________________________
We have:
(3 + 4i) + 1(2 - 3i) - 1(5 - 6i) ;
Start with:
" + 1(2 - 3i) " = (1*2) - (1*3i) = 2 - 3i ;
Then, we examine:
" - 1(5 - 6i) " = (-1*5) + (-1 * -6i) = -5 + (+6i) = -5 + 6i ;
______________________________________________________________
And we rewrite the entire expression:
______________________________________________________________
3 + 4i + 2 - 3i - 5 + 6i ;
Combine the "like terms" ; as follows:
3 + 2 - 5 = 5 - 5 = 0 ;
4i - 3i + 6i = 1 i + 6i = 7 i ;
0 + 7i = 7i .
_______________________________________________________
The answer is: " 7 i " .
_______________________________________________________
what is the volume of the cylinder?
radius=7 height=18
A.126
B.252
C.2268
D.882
Answers
Answer:
Option D. [tex]882\pi\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
In this problem we have
[tex]r=7\ units[/tex]
[tex]h=18\ units[/tex]
substitute
[tex]V=\pi (7^{2})(18)=882\pi\ units^{3}[/tex] -----> exact value of the volume
PLEASE HELP: Question above ☝☝☝
Answers
I'm actually pretty sure it's B
What is the probability that a randomly selected house with 2 bathrooms has 3 bedrooms?
0.2
0.4
0.6
0.8
Answers
there is a total of 30 houses with 2 bathrooms
the probability is 24 /30 = 0.8
[tex] |\Omega|=30\\
|A|=24\\\\
P(A)=\dfrac{24}{30}=\dfrac{4}{5}=0.8 [/tex]
The Tran Family drove 1,246 miles during a vacation that lasted 14 days. How many miles on average did they drive each day? :3
Answers
1246 / 14 = 89
The Tran Family drove an average of 89 miles every day.
To solve this problem, divide the numbers 1,246 and 14 . . .
1,246 ÷ 14 = 89 ←
Once you divide the miles and days, you will find your answer (89).
The correct answer is 89.
They drove 89 miles each day on average.
I hope this helps you.
Have a great day! :)
Phil is offered a 3-year contract with a law firm. His first year earnings would be $81,000 with an annual raise of 15%.
What would Phil's total earnings be over the term of the contract?
Enter your answer, rounded to two decimal places, in the box.
Answers
Second year: 1.15($81000) = $93150
Third year: 1.15($93150) = $107122.50
Add these three together to get Phil's total salary over the 3 years of his contract.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%. Phil's total earnings would be over the term of the contract is $281272.5.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%.
First year
= $81000
Second year
1.15 x ($81000)
= $93150
Third year
1.15 x ($93150)
= $107122.50
Phil's total earnings would be over the term of the contract
= $81000 + $93150 + $107122.50
= 281272.5
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The range of y=1x−2+3 is y=0.
true
false
Answers
Help! WHAT IS THE VALUE OF X, and can you show how you got it please?
Answers
in the right triangle ABD
applying the Pythagoras theorem
8²=AD²+(x+4)²-----> AD²=64-(x+4)²------> equation 1
in the right triangle ADC
applying the Pythagoras theorem
12²=AD²+(2x+1)²-----> AD²=144-(2x+1)²------> equation 2
equate equation 1 and equation 2
64-(x+4)²=144-(2x+1)²-------> 64-[x²+8x+16]=144-[4x²+4x+1]
64-x²-8x-16=144-4x²-4x-1
4x²-x²-8x+4x=144-1-64+16
3x²-4x=95
3x²-4x-95=0
using a graph tool----> to resolve the second order equation
see the attached figure N 2
the solution is
x=6.33
the answer is
x=6.33 units
If cosine x is approximately.9511 what is the measurement of x to the nearest degree? Approximately what is the sine of the angle that is complementary to x
Answers
Sin(x) = .2588 Given
ARCSin (x) = x = ARCSin(.2588) Using the calculator = 14.9988 degrees ( ~ 15 degrees)
COMPLIMENTARY angle is the angle which added to 'x' will equal 90 so the COMPLIMENTARY Angle is 75 degrees
Using the calculator again cos (75) = .2588 The same as the complimentary angle's SIN !!!
Morgan uses 1/4 of her supply of raisins to make a trail mix and 3/8 of her supply of raisins to make cookies.If Morgan uses 5 pounds of raisins, how many pounds of raisins are in her supply.
Answers
3/8=37.5%
37.5%+25%=62.5%
62.5%=0.625
5/0.625=8
Morgan has 8 pounds of raisins in her supply.
What are three consecutive odd integers that have a sum of 39?
Answers
x + x + 2 + x + 4 = 39
3x + 6 = 39
3x = 33
x = 11
The three consecutive odd integers are 11, 13, and 15
Select the equations that are equivalent to the equation y – 2 = 3(x + 6). Select all that apply.
y = 3x + 20
y = 3x + 6
2x - y = -3
3x - y = -20
Answers
y = 3x + 20
3x - y = -20
The explanation is shown below:
1. You have the folllowing expression given in the problem above:
y-2=3(x+6)
2. If you solve it for y, you have:
y-2=3x+18
y=3x+18+2
y=3x+20
3. And if you move the variables to the left member, you have:
3x-y=-20
Therefore, as you can see, the correct answer are the options mentioned above.
Lines that are not in the same plane are called _____ lines. A.perpendicular B.transversal C.skew D.parallel
Answers
Skew is a line that does not have a same plane.
Hope it helped you.
-Charlie
Thanks!
Lines that are not in the same plane are called skew lines.
What is a line?"A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely."
Given, two lines are not in the same plane.
Here, perpendicular lines, transversal lines, and parallel lines should be in the same plane.
Two lines are called skew lines are two lines if they do not intersect and are not parallel.
Therefore, skew lines are not in the same plane.
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x(t) = t^3 - 12t^2 + 36t
Velocity = x'(t) = 3y^3 - 24t + 36 = 0
x'(t) = t^2 - 8t + 12 = 0
x'(t) = t^2 - 6t - 2t + 12 = 0
x'(t) = t(t - 6) - 2(t - 6) = 0
x'(t) = (t - 2)(t - 6) = 0
t = 2 and t = 6 must be the roots.
Is my answer of D "2 and 6" correct based on this work?
Answers
The only flaw I see is that you wrote
x'(t) = 3y^3 - 24t + 36
on line 2 when it should be
x'(t) = 3t^2 - 24t + 36
Other than that it looks perfect.
How would I write #3
Answers
Someone please help me?
Answers
You are looking at two different houses. house #1 would have a daily 5-mile commute to work, while house #2 would have a daily 20-mile commute. how much more co2 would you produce annually if you buy house #2? (hint: driving 1 mile produces 1.1 lb of co2 and you work 240 days/year.)
Answers
5 (miles a day) x 240 (work days a year) = 1,200 miles
total co2 produced = 1.1 x 1200 = 1,320 lbs of CO2 a year
Annual Commute from house 2:
20 (miles a day) x 240 (work days a year) = 4,800 miles
Total CO2 produced = 1.1 x 4800 = 5,280 lbs of CO2 a year
Difference = 5,280 - 1,320 = 3,960 more if you buy house 2.
Answer:
B: 3960 lb
Step-by-step explanation:
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