keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]-9x + y = 3\implies y = \stackrel{\stackrel{m}{\downarrow }}{9} x +3 \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so then
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {9\implies \stackrel{slope}{\cfrac{9}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{9}}}[/tex]
so we're really looking for the equation of a line whose slope is -1/9 and passes through (-9 , -1)
[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-1})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{9} \\\\\\ \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-\stackrel{y_1}{(-1)}=\stackrel{m}{-\cfrac{1}{9}}(x-\stackrel{x_1}{(-9)}) \\\\\\ y+1=-\cfrac{1}{9}(x+9)\implies y+1=-\cfrac{1}{9}x-1\implies y=-\cfrac{1}{9}x-2[/tex]
What happens to the area of a triangle after you translate it 2 units to the left and 1
unit up?
Answer:
nothing
Step-by-step explanation:
If you are translating entire triangle, then translating doesn't influence the area. It's just going to change where the triangle is located not its size
i)
Find the first term of a G.P. whose fifth term is 243 and the
common ratio 3.
Answer:
first term = 3
Step-by-step explanation:
The n th term of a GP is
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here r = 3 and a₅ = 243 , thus
a₁ × [tex]3^{4}[/tex] = 243
a₁ × 81 = 243 ( divide both sides by 81 )
a₁ = 3
Jane ran 8 fewer miles this week than last week. This week, she ran 10 times
as far as John. John ran 3 miles. How many miles did Jane run last week?
Step-by-step explanation:
John ran 3 miles this week.
Jane ran 10 times as far as John this week :
10×3 = 30 miles
but she ran this week 8 fewer miles than last week. in other words, last week she ran 8 miles more than this week :
30 + 8 = 38 miles.
so, last week she ran 38 miles.
Help help help ASAP math math
Answer:
x=-15
y= 65
Step-by-step explanation:
I explain the answer of the question in the photo
Can anybody solve this please?
Answer:
1/3 X 15 = 5
Step-by-step explanation: Hope this helps
what is a commonly accepted set of assumptions
Find the equation of a line that has the same slope as y = 6 - 2x and the same y-intercept as y= -10x – 4.
Step-by-step explanation:
I hope this will help....
Simplify these expressions:
a) 5x+3x+2y+4y
b) 6x - 2x + 8y - 6y
Answer:
a)8x+6y
b)4x+2y
Step-by-step explanation:
a)5x+3x+2y+4y
5x+3x=8x
2y+4y=6y
=8x+6y
b)6x-2x+8y-6y
6x-2x=4x
8y-6y=2y
=4x+2y
Answer:
a) x = -0.75y
b) x = -0.5y
Step-by-step explanation:
Simplifying
5x + 3x + 2y + 4y = 0
Combine like terms: 5x + 3x = 8x
8x + 2y + 4y = 0
Combine like terms: 2y + 4y = 6y
8x + 6y = 0
Solving
8x + 6y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6y' to each side of the equation.
8x + 6y + -6y = 0 + -6y
Combine like terms: 6y + -6y = 0
8x + 0 = 0 + -6y
8x = 0 + -6y
Remove the zero:
8x = -6y
Divide each side by '8'.
x = -0.75y
Simplifying
x = -0.75y
Simplifying
6x + -2x + 8y + -6y = 0
Combine like terms: 6x + -2x = 4x
4x + 8y + -6y = 0
Combine like terms: 8y + -6y = 2y
4x + 2y = 0
Solving
4x + 2y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2y' to each side of the equation.
4x + 2y + -2y = 0 + -2y
Combine like terms: 2y + -2y = 0
4x + 0 = 0 + -2y
4x = 0 + -2y
Remove the zero:
4x = -2y
Divide each side by '4'.
x = -0.5y
Simplifying
x = -0.5y
write a statement that correctly describes the relationship between these two sequences; 2,4,6,8,10 and 1,2,3,4,5
Answer: Any number in the first sequence is two times the second.
Step-by-step explanation: Mark me as brainiest!
elisa was going to sell all of her stamp collection to buy a videos game then she changes her mind then she bought 8 more how many did she start with if she now has 36
Answer:
24 (not sure)
Step-by-step explanation:
36 - 8 = 24
im not sure if this is what the question is asking for.
Find the length of . Round answer to nearest tenth. PLS HELP ASAP
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =75 \end{cases}\implies s=\cfrac{(75)\pi (7)}{180}\implies s=\cfrac{35\pi }{12}\implies s\approx 9.2[/tex]
If the angle of an isosceles triangle at the top of the triangle is 70 degrees, then what is the measure of the other two angles if they must be equal.
Answer:
55
Step-by-step explanation:
What is the remainder when
8
x
3
+
6
x
2
−
7
x
−
2
is divided by
x
+
2
?
Which of the following cosine functions has a period of 3Pi
Answer:
C
Step-by-step explanation:
Hello!
In the equation y=a cos bx, we can learn alot about the cosine graph.
a is the amplitude, or how 'long' the cosine graph is.
b is the period, which is how 'wide' one cycle of a cosine period can be. The higher the period, the wider the cycle is.
In this equation, we are focused on finding the period; so any choices that contain amplitude is not a correct answer choice for this problem, which leaves out B and C.
To find the period, we can plug b into [tex]\frac{2\pi }{b}[/tex] , which in a way converts the b value to a period.
For B) y= cos3x
[tex]\frac{2\pi }{3}[/tex]= it does not equal 3 [tex]\pi[/tex]
For C) y=cos [tex]\frac{2}{3}[/tex]x
[tex]\frac{2\pi }{\frac{2}{3}}[/tex]= equals 3 [tex]\pi[/tex] when simplified
Since C equals 3 [tex]\pi[/tex] as a period, C is the only logical answer.
Sara buys a bag of candy. In the bag, 1/2 of the candies are red, 1/5 are green, and the
remainder are white. What fraction of the candies are white? ANSWER ASAP???
Answer: 3/10
Step-by-step explanation: You need to make it where all of the denominators match.
1/2 = 5/10
1/5 = 2/10
5/10+2/10=7/10
7/10+3/10=10/10
Find the distance between (7,3) and (-3,-1). Round to the nearest tenth.
Answer:
22 ok i eo
Step-by-step explanation:
ok i will explaim
Triangle XYZ is rotated to create the image triangle X'Y'Z'.
On a coordinate plane, 2 triangles are shown. The first triangle has points X (negative 2, 2), Y (1, 2), Z (0, 4). The second triangle has points X prime (2, negative 2), Y prime (negative 1, negative 1), Z prime (0, negative 4).
Which rules could describe the rotation? Select two options.
R0, 90°
R0, 180°
R0, 270°
(x, y) → (–y, x)
(x, y) → (–x, –y)
Answer:
R0, 180°
(x, y) → (–x, –y)
Step-by-step explanation:
Knowing that:
The coordinates of ΔXYZ is x '(-2, 2), Y(1, 2), Z(0, 4)
The coordinates of ΔX'Y'Z' is x'(2, -2), Y'(-1, -1), Z'(0, -4)
Coordinates of the preimage = (x, y)
Coordinates of the image = (-x, -y)
transformation by rotation 180° about the origin.
Solve:
R0, 180°
(x, y) → (–x, –y)
~Lenvy~
Answer: R0, 180° and (x, y) → (–x, –y)
Step-by-step explanation: On Edge!!
the number can be divided by the least common multiple of 3 and 5
the hundreds digit is 2
the sum of all three digits is 12
9514 1404 393
Answer:
255
Step-by-step explanation:
If the sum of digits is 12, the number is divisible by 3. If the number ends in 0 or 5, it is divisible by 5. So, we're looking for ...
2x0 . . . where x is a digit and 2+x+0 = 12 . . . . . . not possible
2x5 . . . where x is a digit and 2+x+5 = 12 . . . . true for x=5
The number is 255.
Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two cities at the same time so that one is catching up to the other. How long after the trains leave will they be 10 miles apart for the first time? How long after the trains leave will they be 10 miles apart for the second time?
5. A triangle has a 60° angle, a 60° angle and a side 2 centimeters in length. a Select True or False for each statement about this type of triangle.
The triangle must be an equilateral triangle.
- More than one triangle can be made with these measures.
The triangle must contain an angle measuring 75º.
Answer:
Step-by-step explanation:
Choose the algebraic description that maps the image ΔABC onto ΔA′B′C′.
(x,y) → (x + 1,y)
(x,y) → (x,y + 1)
(x,y) → (x – 1,y)
(x,y) → (x,y – 1)
if the function rule is y equals 3x - 4 what is range when the domain is 7?
Eliana opened a savings account and deposited $300.00. The account earns 13% interest, compounded annually. If she wants to use the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike?
Answer:
$432.87Step-by-step explanation:
Use below compound interest formula and the given data.
[tex]F = P*(1 + r)^{nt}[/tex]F- future amount, P- invested amount, r - interest rate, n - number of compounds, t- time
Given:
P = $300r = 13% or 0.13t = 3 yearsn = 1Find the amount after 3 years:
[tex]F = 300(1 + 0.13)^3 = 432.87[/tex]WHAT IS 9+8+9-2+5x5+5-25+5-4+2+-2+4-+2-5+4-2+5-4+2-5+4-1+5-4+-2+4-2+5-4+2-4
+-+
Answer:
34
Step-by-step explanation:
cause you had to doit the simple math problem
are you trying to prank on this problem
the answer is 5 because I got it correct on a quiz
[tex] \rm\frac{13}8 + \sum \limits_{n = 0}^{ \infty } \frac{( - {1)}^{n + 1} (2n + 1)! }{n! (n + 2)! {4}^{2n + 3} } \\ [/tex]
Rewrite the factorial parts of the summand as
[tex]\dfrac{(2n+1)!}{n!(n+2)!} = \dfrac{(2n+1)(2n!)}{(n+2)(n+1)(n!)^2} = \dfrac{2n+1}{(n+2)(n+1)} \dbinom{2n}n[/tex]
where [tex]\binom nk[/tex] is the binomial coefficient, and [tex]\binom{2n}n[/tex] are the so-called central binomial coefficients.
Expand the rational expression into partial fractions:
[tex]\dfrac{2n+1}{(n+2)(n+1)} = \dfrac3{n+2} - \dfrac1{n+1}[/tex]
Pull out a constant factor and collect the exponential terms.
[tex]\dfrac{(-1)^{n+1}}{4^{2n+3}} = -\dfrac1{64} \left(-\dfrac1{16}\right)^n[/tex]
The sum we want is now
[tex]\displaystyle \frac{13}8 - \frac1{64} \sum_{n=0}^\infty \binom{2n}n \left(\frac3{n+2} - \frac1{n+1}\right) \left(-\frac1{16}\right)^n[/tex]
Let f(x) and g(x) be functions with power series expansions
[tex]\displaystyle f(x) = \sum_{n=0}^\infty \binom{2n}n \frac{x^n}{n+1}[/tex]
[tex]\displaystyle g(x) = \sum_{n=0}^\infty \binom{2n}n \frac{x^n}{n+2}[/tex]
and recall the well-known binomial series
[tex]\displaystyle \dfrac1{\sqrt{1-4x}} = \sum_{n=0}^\infty \binom{2n}n x^n[/tex]
which converges for |x| < 1/4.
Integrating both sides yields
[tex]\displaystyle \int \frac{dx}{\sqrt{1-4x}} = \int \sum_{n=0}^\infty \binom{2n}n x^n \, dx[/tex]
[tex]\displaystyle -\frac12 \sqrt{1-4x} = C_1 + \sum_{n=0}^\infty \binom{2n}n \frac{x^{n+1}}{n+1}[/tex]
Taking x = 0 on both sides, it follows that C₁ = -1/2. We then see that
[tex]\displaystyle f(x) = \frac{1-\sqrt{1-4x}}{2x}[/tex]
Step back and multiply both sides of the binomial series identity by x, then integrate. This yields
[tex]\displaystyle \int \frac x{\sqrt{1-4x}} \, dx = \int \sum_{n=0}^\infty \binom{2n}n x^{n+1} \, dx[/tex]
[tex]\displaystyle -\frac1{12} \sqrt{1-4x} (1 + 2x) = C_2 + C_1 x + \sum_{n=0}^\infty \binom{2n}n \frac{x^{n+2}}{n+2}[/tex]
Taking x = 0 again points to C₂ = -1/12. Hence
[tex]\displaystyle g(x) = \frac{1 - \sqrt{1-4x}(1+2x)}{12x^2}[/tex]
Then the value of the sum we want is
[tex]\displaystyle \frac{13}8 - \frac1{64} \left(3g\left(-\frac1{16}\right) - f\left(\frac1{16}\right)\right) = \frac{1+\sqrt5}2 = \boxed{\phi}[/tex]
where ɸ ≈ 1.618 is the golden ratio.
The difference of two supplemtary angles is 58 degrees. Find the measures of the angles
Answer:
The measure of the angles are 61° and 119°
Step-by-step explanation:
Let the first angle = x°
let the second angle = y°
The sum of two supplementary angles = 180°
x° + y° = 180° ----- equation (1)
based on the given question; "the difference of two supplementary angles is 58 degrees."
x° - y° = 58° ------- equation (2)
from equation (2), x° = 58° + y°
Substitute the value of x into equation (1)
(58° + y°) + y° = 180°
58 + 2y = 180
2y = 180 -58
2y = 122
y = 122 / 2
y = 61°
The second angle is given by;
x° = 58° + y°
x = 58° + 61°
x = 119°
Thus, the measure of the angles are 61° and 119°
Find the quotient. 4,216 ÷ 7 with remainder
Answer:
602 r. 2
Step-by-step explanation:
A classroom board is 23 inches wide and 17 inches tall. Juan
is putting ribbon along the outside edge of the board. How
many inches of ribbon will he need?
17 inches
23 inches
40 inches B 43 inches
A
84 inches
D 80 inches
Answer:
80 inches
Step-by-step explanation:
12 x 7=34
23 x 2=46
34+46=80 inches
Use the order of operations to find the value of the following expression 3-4(-2-4)
Answer: 27
Step-by-step explanation:
By the order of operations, we should first calculate the expression in the parentheses:
= 3 - 4 (- 6)
Next, we calculate the expression being multiplied:
= 3 + 24
Lastly, we add the two terms:
= 27
Using the given order operations to solve for the given operation, we have the answer as; 27
How to solve mathematical operations?
We are given the expression;
3 - 4(-2 - 4)
From mathematical operation acronym titled BODMAS, we need to first solve what we have in the bracket and so we get;
3 - 4(-6)
Secondly we multiply out the bracket to get;
3 + 24
We now add to get 27
Read more about Mathematical Operations at; https://brainly.com/question/16788360
Whats the equation given for (5,1) and (4,4)
Answer:
y= -3x+16 I'm pretty sure its right