C. Find the equation of the line perpendicular to
y = 14x-5 and passing through (2,-3).
Answers
Answer:
[tex]y = -4x + 5[/tex]
Step-by-step explanation:
We want to find the equation of the line that is perpendicular to:
[tex]\displaystyle y = \frac{1}{4} x - 5[/tex]
And which passes through the point (2, -3).
Recall that the slopes of perpendicular lines are negative reciprocals of each other.
In other words, since the slope of the original line is 1/4, the slope of the perpendicular line will be -4.
We are also given that it passes through the point (2, -3). Hence, we can consider using the point-slope form:
[tex]\displaystyle y - y_1 = m(x- x_1)[/tex]
Substitute:
[tex]\displaystyle y - (-3) = -4 (x - (2))[/tex]
Simplify:
[tex]y + 3 = -4(x - 2)[/tex][tex]y = -4x + 5[/tex]
Distribute:
[tex]y + 3 = -4x +8[/tex]
And subtract:
[tex]y = -4x + 5[/tex]
In conclusion, our equation is:
[tex]y = -4x + 5[/tex]
Related Questions
a point, ray, line, segment or plane which divides a segment into 2 congruent parts
Answers
Answer:
This is called a bisector.
solve this problem show work. -5/6 + 1/3
Answers
-5/6 + 1/3 = -5/6 + 2/6
To add fractions, add the numerators:
-5 + 2 = -3
So, -5/6 + 2/6 = -3/6
This can reduce, since 3 and 6 are divisible by 3.
-3/6 = -1/2
Please help with steps, will give brainliest. Simplify
Answers
Answer:
=53*(54 ×^9 y^12 z^15)^1/2
=53*y^6 *z^(15/2) * x^( 9/2)* (54)^1/2
Answer:
[tex] {3x}^{4} {y}^{6} {z}^{7} \sqrt{6xz} [/tex]
Step-by-step explanation:
[tex] \sqrt{54 {x}^{9} {y}^{12} {z}^{15} } [/tex]
➡️ [tex] \sqrt{ {3}^{2} \times 6 {x}^{8 + 1} {y}^{12} {z}^{14 + 1} } [/tex]
➡️ [tex] \sqrt{ {3}^{2} \times 6 {x}^{8 } \times {x}^{1} {y}^{12} {z}^{14} \times {z}^{1} } [/tex]
➡️ [tex] \sqrt{ {3}^{2} \times 6 {x}^{8} \times {xy}^{12} {z}^{14} \times z } [/tex]
➡️ [tex] \sqrt{ {3}^{2} } \sqrt{ {x}^{8} } \sqrt {y}^{12} \sqrt{ {z}^{14} \sqrt{6xz} } [/tex]
➡️ [tex] {3x}^{4} {y}^{6} {z}^{7} \sqrt{6xz} [/tex] ✅
Find all values of $x$ such that
\[\frac{2x}{x + 2} = -\frac{6}{x + 4}.\]
Answers
Answer:x_1= -1 or x_2= -6
Step-by-step explanation:
In the pictures
By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.
What is factorization?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number.
These numbers are broken down into factors or divisors.
For an integer, factorization is decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number and these composing integers are called factors of that considered integers.
Given
[tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex]
Cross multiplication;
2x(x + 4) = 6(x + 2)
[tex]2x^{2} + 8x = 6x + 12\\\\2x^{2} + 8x - 6x - 12 = 0\\\\2x^{2} + 2x - 12 = 0\\\\x^{2} + x - 6 = 0[/tex]
Divide above equation by 2, we get
[tex]x^{2} + x - 6 = 0[/tex]
(x +2) (x-3)
x = -2, 3
Therefore, By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.
Find out more information about factorization here;
brainly.com/question/1863222
#SPJ2
explain what a ratio is in the easiest way possible
Answers
Step-by-step explanation:
A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.
A segment has endpoints (14,-8) and (4, 12). What are the coordinates of
its midpoint?
Answers
Answer:
(9,2)
Step-by-step explanation:
To find the x coordinate of the midpoint, average the x coordinates of the endpoints
(14+4)/2 = 18/2 = 9
To find the y coordinate of the midpoint, average the y coordinates of the endpoints
(-8+12)/2 = 4/2 = 2
(9, 2)
Step-by-step explanation:
Find the distance of the line, then find the slope of the line using the following coordinates (-7,2) and (-4,6)?
Answers
Answer:
Distance = 5 units
Slope = [tex]\displaystyle\frac{4}{3}[/tex]
Step-by-step explanation:
Hi there!
1) Finding the distance of the line
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two endpoints of a line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the points (-7,2) and (-4,6):
[tex]d=\sqrt{(-4-(-7))^2+(6-2)^2}\\d=\sqrt{(-4+7)^2+(6-2)^2}\\d=\sqrt{(3)^2+(4)^2}\\d=\sqrt{9+16}\\d=\sqrt{25}\\d=5[/tex]
Therefore, the length of the line/distance of the line is 5 units.
2) Finding the slope of the line
[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the points (-7,2) and (-4,6):
[tex]m=\displaystyle\frac{6-2}{-4-(-7)}\\\\m=\displaystyle\frac{6-2}{-4+7}\\\\m=\displaystyle\frac{4}{3}[/tex]
Therefore, the slope of the line is [tex]\displaystyle\frac{4}{3}[/tex].
I hope this helps!
9/8(4-1/2a)=3(1/4a+5/2)
Answers
Answer:A=2 2/7
Step-by-step explanation:
Correct me if I am wrong
(1.2E-3) x (4.6E-1) =
Answers
Answer:
0.0012*x*0.46
Step-by-step explanation:
My question is in the picture attached below, thank you.
Ps: I need full explanations of the answers as said by the instructions. Thanks
Answers
The volume of a rectangular prism is the product of the prism's dimension (i.e. length, width and height). The dimension of the rectangular prism are:
[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]
Given that:
[tex]Volume = (18x^4 + 15x^3 - 12x^2)[/tex]
First, we factor out [tex]3x^2[/tex]
[tex]Volume = 3x^2 \times (6x^2 + 5x - 4)[/tex]
Expand
[tex]Volume = 3x^2 \times (6x^2 + 8x-3x - 4)[/tex]
Factorize
[tex]Volume = 3x^2 \times (2x(3x + 4) -1(3x + 4))[/tex]
Factor out [tex]3x + 4[/tex]
[tex]Volume = 3x^2 \times ((2x -1) (3x + 4))[/tex]
Rewrite as:
[tex]Volume = 3x^2 \times (2x -1) \times (3x + 4)[/tex]
The volume of a rectangular prism is:
[tex]Volume = Length \times Width \times Height[/tex]
So; by comparison:
[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]
Read more about polynomials and volumes at:
https://brainly.com/question/2141804
Rectangle ABCD translates 4 units down and 2 units to the right to form rectangle A'B'C'D'. The vertices of rectangle ABCD are labeled in alphabetical order going clockwise around the figure. If AB = 3 units and AD = 5 units, what is the length of B'C'? A. 5 units B. 9 units C. 11 units D. 3 units
Answers
Answer:5 units
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Distance between (-2,-2) and (8,-6)
Answers
Answer:
Distance btw (-2, -2) and (8, -6) is (10, -4)
Step-by-step explanation:
I. Give (-2, -2) is A and (8, -6) is B
B - A = 8 - (-2) in x
= -6 - (-2) in y
So B - A = 10, -4
II. You can prove the answer by A.value + (10, -4) = B.value
Hope that help :D
Hi ;-)
[tex]\text{A}=(-2,-2) \ \text{and} \ \text{B}=(8,-6)\\\\|AB|=\sqrt{(8-(-2))^2+(-6-(-2))^2}\\\\|AB|=\sqrt{(8+2)^2+(-6+2)^2}\\\\|AB|=\sqrt{10^2+(-4)^2}\\\\|AB|=\sqrt{100+16}\\\\|AB|=\sqrt{116}\rightarrow\boxed{|AB|=2\sqrt{29}} \ (\text{because} \ 116=4\cdot29)[/tex]
How many of the 320 million Americans would you predict wear contacts lenses?
Answers
Answer:
40,640,000
Step-by-step explanation:
The way I solved this equation was by dividing 320,000,000 by 1,000 (to make smaller numbers). Then, I got 320,000. From here, I was able to multiply 320,000 by 127 (the number found in this specific study group) to get 40,640,000. Or, you could just multiply 320,000,000 by 0.127 (the decimal equivalent to 127/1000) to get the same answer. Please mark Brainliest if this helped :)
Answer:
40,640,000
Step-by-step explanation:
The sample size is 1000 and 127 wear contacts so
127/1000 = x/320000000
(127 * 320000000)/1000 = x
40,640,000 = x
A researcher stands outside a restaurant and asks the youngsters leaving the restaurant if they enjoyed the food there. What type of sampling technique has the researcher employed
Answers
Explanation: He is taking people young and old,tall and short, and asking them if they like the food or not so he doesn’t get biased opinions based on that persons age or any other trait.
find the highest common factor of 36 and 48
Answers
Answer:
12
Step-by-step explanation:
36/12=3
48/12=4
Answer:
highest common factor of 36 and 48 is 12
Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet$ $f(x) 2$ is divisible by $(x 1)^3$. Write your answer in expanded form (that is, do not factor $f(x)$).
Answers
There seems to be one character missing. But I gather that f(x) needs to satisfy
• [tex]x^3[/tex] divides [tex]f(x)[/tex]
• [tex](x-1)^3[/tex] divides [tex]f(x)^2[/tex]
I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or
[tex]f(x) = x^5 + \cdots[/tex]
Since [tex]x^3[/tex] divides [tex]f(x)[/tex], and
[tex]f(x) = x^3 p(x)[/tex]
where [tex]p(x)[/tex] is degree-2, and we can write it as
[tex]f(x)=x^3 (x^2+ax+b)[/tex]
Now, we have
[tex]f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2[/tex]
so if [tex](x - 1)^3[/tex] divides [tex]f(x)^2[/tex], then [tex]p(x)[/tex] is degree-2, so [tex]p(x)^2[/tex] is degree-4, and we can write
[tex]p(x)^2 = (x-1)^3 q(x)[/tex]
where [tex]q(x)[/tex] is degree-1.
Expanding the left side gives
[tex]p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2[/tex]
and dividing by [tex](x-1)^3[/tex] leaves no remainder. If we actually compute the quotient, we wind up with
[tex]\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}[/tex]
If the remainder is supposed to be zero, then
[tex]\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}[/tex]
Adding these equations together and grouping terms, we get
[tex](a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1[/tex]
Then [tex]b=-1-a[/tex], and you can solve for a and b by substituting this into any of the three equations above. For instance,
[tex]2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1[/tex]
So, we end up with
[tex]p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}[/tex]
H. Pete wants a new truck. The sale price is 15% lower than the original price. The sale price is $20,000. Write and evaluate an expression for the original price. Uses for sale price and p for original price.
Answers
100-15=85%=SP
[tex]\\ \sf\longmapsto 85\%\times x=20000[/tex]
[tex]\\ \sf\longmapsto \dfrac{85}{100}x=20000[/tex]
[tex]\\ \sf\longmapsto x=20000\times \dfrac{100}{85}[/tex]
[tex]\\ \sf\longmapsto x=235.2(100)[/tex]
[tex]\\ \sf\longmapsto CP=23520[/tex]
If
f(x) = x^2 + 2x – 4
and
g(x) = 3x + 1
Find
f(g(x)) = 9x^2 + [ ? ]x+ [?]
Answers
Step-by-step explanation:
f(g(x))=(3x+1)^2 +2(3x+1) -4
=9x^2 +6x +1 +6x +2 -4
=9x^2 +12x +(-1)
how r u doing?? 1-10:D? (free pts btw)
Answers
Answer: i am good,how are you?
Step-by-step explanation:
Answer:1-10 = 9 :D
Step-by-step explanation:
You were looking at your power bill for the month, you pay 12 cents per kilowatt-hour. Your power bill came out to $99.89 how many KWH of energy were used in your house this month?
Answers
Answer:
832.4 KWH of energy
Step-by-step explanation:
Find how many KWH of energy were used by dividing the total cost by 0.12:
99.89/0.12
= 832.4
So, approximately 832.4 KWH of energy were used that month.
What is the distance between points (6,-5) and (2,-2)
Answers
Answer:
ans is 5.
hope it will help you.
If f(x) = -6x and g(x) = -6x + 5, find (fog)
Answers
Answer:
Step-by-step explanation:
(f o g) is the same as f(g(x))
f(x) = -6x, substitute x with g(x) = -6x+5
f(g(x)) = -6g(x) = -6(-6x+5) = 36x -30
(f o g) = 36x -30
Please Help!! I am really stuck on this assignment and i need it done
Answers
Answer:
Step-by-step explanation:
11-B
Uhhhh sorry about everything else I’ll come back when I figure it out
6-D
7-C? Maybe
Answer:
Step-by-step explanation:
The correct answer is b.
27h + 16 = 178 Subtract 16
27h = 178 -16 Combine
27h = 162 Divide by 27
h = 162 / 27
h = 6
Question 6
No they are not the same. They have the same terminal point but they are going in different directions. The answer is D Direction matters.
Question 7
The vectors add if as in arithmetic if they are going in the same direction.
answer C
A train is going at 200/KM per hour
The train tracks is 8482 Miles wide
How long will it take for the train to reach the end
Answers
Answer:
It moved for 152.7 seconds
Step-by-step explanation:
Time taken/ period, T :
[tex]{ \sf{T = \frac{distance}{speed} }}[/tex]
substitute the variables:
[tex]{ \sf{T = \frac{8482}{(200 \times 1000)} }} \\ \\ { \sf{T =0.042 \: hours }}[/tex]
In seconds:
[tex]{ \sf{T = (0.042 \times 3600) \: s}} \\ { \sf{T = 152.7 \: seconds}}[/tex]
Answer: 68.25 hrs.
Step-by-step explanation:
200 Km. to miles = 124.274 miles
8482 mi/124.274 mi =
68.25 hours
A skateboard costs $60 and its got a discount
of 30% and then a sales tax of 10% was
added. What is the final price?
Answers
Answer:
$46.20
Step-by-step explanation:
The discount of 30% brings the price down to $42, and then the sales tax would be $4.20, making the answer $46.20
Help me pls ?? 1. Suppose there is a raffle with numbered tickets 1 - 150. One ticket is randomly
drawn from a hat. Find the following probabilities:
A. Drawing an even number
B. Drawing a number greater than 100
C. Drawing an even prime number
D. Drawing a negative number
Answers
B = less likely / unlikely
C =less likely
D = Impossible
The factorization of a (x + y + z) + b(x + y + z) + c(x + y + z) is
pls answer maheshsinghmeenu sister
Answers
Answer:
(a+b+c) (x+y+z)
Step-by-step explanation:
hope this helps to uh
Step-by-step explanation:
x+y+z+bx+by+bz+cx+cy+cz
Take Like terms
x+bx+cx+y+by+cy+z+bz+cz
x(b+c)+y(b+c)+z(b+c)
(x+y+z)(b+c)
hope it helps
What type of triangle has side lengths 2, 712, and 19?
Answers
Answer:
OPTION B
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
What is A= 2/h (a+b) for h?
Answers
Answer:
h= 2A/a+b
Step-by-step explanation:
you know the gig
Common difference of the arithmetic sequence -6,-13,-20
Answers
Answer:
-7
Step-by-step explanation:
-13 - (-6)
=> -13 + 6
=> -7
So Common Difference = -7