Answers
Answer:
1. a. 2
b. -½
c. y - 3 = -½(x - 8) => point-slope form
y = -½x + 7 => slope-intercept form
2. a. -1
b. 1
c. y - 5 = 1(x - 3) => point-slope form
y = x + 2 => slope-intercept form
Step-by-step explanation:
1. (8, 3) and (10, 7):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (8, 3) = (x_1, y_1) [/tex]
[tex] (10, 7) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{7 - 3}{10 - 8} [/tex]
Gradient = [tex] \frac{4}{2} [/tex]
Gradient = 2
b. The gradient of the line perpendicular to this line = the negative reciprocal of 2
Negative reciprocal of 2 = -½
c. The equation of perpendicular line if it passes through the first point, (8, 3):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (8, 3)
Slope (m) = -½
Substitute (a, b) = (8, 3), and m = -½ into the point-slope equation, y - b = m(x - a).
Thus:
y - 3 = -½(x - 8) => point-slope form
We cam also express the equation of the perpendicular line in slope-intercept form by rewriting y - 3 = -½(x - 8) in the form of y = mx + b:
Thus:
y - 3 = -½(x - 8)
y - 3 = -½x + 4
y - 3 + 3 = -½x + 4 + 3
y = -½x + 7
2. (3, 5) and (4, 4):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (3, 5) = (x_1, y_1) [/tex]
[tex] (4, 4) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{4 - 5}{4 - 3} [/tex]
Gradient = [tex] \frac{-1}{1} [/tex]
Gradient = -1
b. The gradient of the line perpendicular to this line = the negative reciprocal of -1
Negative reciprocal of -1 = 1
c. The equation of perpendicular line if it passes through the first point, (3, 5):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (3, 5)
Slope (m) = 1
Substitute (a, b) = (3, 5), and m = 1 into the point-slope equation, y - b = m(x - a).
Thus:
y - 5 = 1(x - 3) => point-slope form
We can also express the equation of the perpendicular line in slope-intercept form by rewriting y - 5 = 1(x - 3) in the form of y = mx + b:
Thus:
y - 5 = 1(x - 3)
y - 5 = x - 3
y - 5 + 5 = x - 3 + 5
y = x + 2
Related Questions
the table of values below represents a liner function and show the amount of money in the savings account since she began her part-time job what is her monthly rate of savings
Answers
Answer:
she saves $24 dollars every month. 36 + 24 =60 +24 =84 +24 =108 +24 =132 :)
Yet another calculus question :)
Given [tex]y = x^3 - 2x[/tex] for [tex]x \geq 0[/tex], find the equation of the tangent line to y where the absolute value of the slope is minimized.
I have tried taking both the first and second derivatives and setting them equal to 0 and using that as the answer, but they're incorrect. Could somebody please explain how to complete the question correctly? Thank you so much!
Answers
Answer: y = (-4/3)*sqrt(2/3)
This is the same as writing [tex]y = -\frac{4}{3}\sqrt{\frac{2}{3}}[/tex]
============================================================
Explanation:
The phrasing "where the absolute value of the slope is minimized" is an interesting way of saying "the tangent slope is 0". This is because absolute values are never negative, so the smallest it can get is 0.
Your teacher has given you
y = x^3 - 2x
which differentiates into
dy/dx = 3x^2 - 2
after using the power rule
The derivative function lets us determine the slope of the tangent. The slope is the dy/dx value. Since we want a slope of 0, we'll set 3x^2-2 equal to zero and solve for x. So you have the correct idea, but you won't involve the second derivative.
dy/dx = 0
3x^2 - 2 = 0
3x^2 = 2
x^2 = 2/3
x = sqrt(2/3)
Notice how I'm ignoring the negative version of this root. This is due to the fact that [tex]x \ge 0[/tex]
-------------------------
Now plug this x value back into the original equation to find its corresponding y coordinate.
y = x^3 - 2x
y = x(x^2 - 2)
y = sqrt(2/3)*( 2/3 - 2 )
y = sqrt(2/3)*( -4/3 )
y = (-4/3)*sqrt(2/3)
Note that x = sqrt(2/3) leads to x^2 = 2/3 after squaring both sides.
-------------------------
Therefore, the equation of this tangent line is y = (-4/3)*sqrt(2/3)
All horizontal lines are of the form y = k, for some constant k. This constant value is basically what number you want the horizontal line to go through on the y axis. That number would be (-4/3)*sqrt(2/3).
Someone help plsssss
Answers
Correct answer gets brainliest and 5 star
Answers
Answer:
d
Step-by-step explanation:
Answer:
option D
Step-by-step explanation:
the formula for slope is: y = mx + b
where m = slope & b = y intercept
so in y = -2x + 1,
m (slope) = -2 & b (y-int) = (0,1)
so i need help with this pls i suck at algebra
Answers
Answer:
The 5x^2 vs -5x^2 will reflect over "X" axis
the +1 vs -2 will shift the graph down three units
the first answer is the correct answer
Step-by-step explanation:
What number line shows Point A at -4, Point B at 2.5, Point C at -2 1/2, and Point D, which is the opposite of Point A.
Answers
Answer: Choice A
Explanation:
Since -3/5 > -0.8, this means -3/5 is to the right of -0.8
Larger stuff is to the right of smaller stuff. Another example would be 10 > 7, meaning we have 10 to the right of 7 since 10 is larger.
Any negative value is always to the left of 0, so -3/5 is to the left of 0.
That's why the answer is choice A.
Does 8in to 1ft reduce it or enlarge it
Answers
Answer:
enlarge it
Step-by-step explanation:
I ft = 12 inches
Thus 8 in → 12 in makes the transformation larger.
Thus going from 8 in to 12 in is an enlargement
"A parabola has the equation = ^ + − . What are the coordinates of the vertex? (You must solve by factoring)!!!!!" I NEED THE ANSWER TO THIS FAST WITH STEPS I'm a grade 10 academic student by the way
Answers
Answer:
1
Step-by-step explanation:
1
what is the answer for 7 to the negitive second power.
Answers
Answer:
the negative just tell you you put a one over the number. Once that's done, the power will be positive, and you can square like normal
Are you asking about [tex]7^{-2}[/tex] ?
If so:
A negative in the exponent tells us that we must take the reciprocal of the number, in this case, 7, and then use the exponent like normal:
[tex]7^{-2}[/tex] =
[tex](\frac{1}{7})^{2}[/tex] =
[tex]\frac{1}{49}[/tex],
So our answer is 1/49.
1. Three products from renewable resources are
Answers
Answer:
biomass energy (such as ethanol), hydropower, geothermal power, wind energy, and solar energy.
31. Which choice describes the value of m when -5(m + 1) = 23?
А
B.
m 2-3
ms-
6 m2
D.ms-
Answers
Answer:
The correct choice is Option A. m ≥ -28/5
Step-by-step explanation:
Can anyone help me with this?
Answers
I thing it lies on the negativity side of the number line between -2,24
Have fun all !!! This is my trash account. You all can have my points.
Answers
Answer:
Step-by-step explanation:
OK
Answer:
rshjgdlf
FGshjfgsfds
Step-by-step explanation:
GIMME'
What is the value of g?
Answers
Answer:
56 degrees
Step-by-step explanation:
1. Notice how g is part of a right angle, which equals 90 degrees.
2. Notice how the 34 degree angle on the other side is also part of a 90 angle.
3. Notice how the 2 right angles are vertical to each other, meaning they are the same.
4. Subtract 34 from 90.
5. g=56 degrees
Hope this helps!
-Stella
I think it would be 90 degrees. The g marking looks like it's taking up 2 angles. One of the angles is 34 degrees, because it's opposite to the one marked. Together they look like they form a 90 degree angle.
*It's kind of of hard to see if g is referring to both angle degrees or not.
What is 4,327 rounded to the nearest thousand?
Answers
Answer: 4,000
Step-by-step explanation: To round 4,327 to the nearest thousand, we first find the digit in the rounding place, which in this case is the 4 in the thousands place. Next, we look at the digit to the right of the 4, which is 3.
According to the rules of rounding, since the digit to
the right of the rounding place is less than 5, we round down.
So the 4 in the rounding place stays the same
and all digits to the right of the 4 become 0.
So 4,327 rounded to the nearest thousand is 4,000.
In an input/output table, all outputs are 0, regardless of the input. What could the function equation be? Select all that apply.
y = 0 x
y = x
y = x/0
y = 0/x
Answers
Answers:
choice A) y = 0x
choice D) y = 0/x
========================================================
Explanation:
Choice A is the same as y = 0 because 0x turns into 0. Multiplying 0 with any number always leads to 0.
Similarly, choice D is the same as y = 0 as well. Dividing 0 over any nonzero value leads to 0. Note the key term "nonzero" here. We cannot have 0 in the denominator. So x = 0 is not allowed for choice D.
So for any nonzero x, we have 0x and 0/x result in the same thing.
-----------
Extra info:
Choice B can be ruled out because something like x = 2 leads to y = 2.
Choice C is ruled out because we can never have 0 in the denominator.
REALICE LOS SIGUIENTES PROBLEMAS DE ECUACIÓN DE LA RECTA CORRECTAMENTe
1.- Encuentre la ecuación vectorial de la recta si tenemos A(4, -2) y el vector V=(2, 5) paralelo a la recta y que pasa por A
2.- Encuentre la ecuación general de una recta conociendo un punto P(-2 ; 4) y su pendiente m= - 5 y grafique la recta.
Answers
Answer:
1. La ecuación vectorial de la línea es [tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]
2. La ecuación de la recta es, y = -5·x - 6
Step-by-step explanation:
1. El punto dado en la línea es A (4, -2), el vector paralelo a la línea es (2, 5)
Por tanto, la ecuación vectorial de la línea es;
[tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]
Donde;
t = Cualquier número
2. El punto por el que pasa la recta es P (-2; 4)
La pendiente de la recta, m = -5
Por lo tanto, la ecuación de la línea en forma de punto y pendiente se presenta de la siguiente manera;
y - 4 = (-5) · (x - (-2)) = -5 · x - 10
∴ y - 4 = -5 · x - 10 + 4 = -5 · x - 6
La ecuación de la recta es, y = -5·x - 6
Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial
function.
f(x) = 2^(5x-6)
h(x) = 3x^5 - 2x^3 - 4x + 7
x=4
x=7
x = 6
x=5
Answers
Answer: ¿Hablas español porque no entiendo esto? Si lo haces, ¿puedes decirme en español?
Step-by-step explanation:
what is the external angle of a polygon where the corresponding interior angle equals 105 degrees
Answers
Answer:
75 degrees maybe.......
Answer:
75 degrees
Step-by-step explanation:
the external angle is between the outside of one of the sides of the angle and the continued line of the second side of the angle.
and because it is measured against a line, where we have a total of 180 degrees for angles, we have
exterior angle = 180 - interval angle = 180-105 = 75
Write 128 as a product of its prime factors
Answers
Answer:
The prime factorization of 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2.
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Find the missing side lengths
Answers
Answer:
u is 17√2 and v is 17
Step-by-step explanation:
To find u:
[tex]{ \bf{ \sin( \theta) = \frac{opposite}{hypotenuse} }}[/tex]
feed in the terms:
[tex] \sin(45 \degree) = \frac{17}{u} \\ \\ u = \frac{17}{ \sin(45 \degree) } \\ \\ u = 17 \sqrt{2} [/tex]
To find v:
[tex] \cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]
feed in the terms:
[tex] \cos(45) = \frac{v}{u} \\ \\ v = u. \cos(45) \\ v = (17 \sqrt{2} )÷( \sqrt{2} ) \\ v = 17[/tex]
John earns $6 per hour for mowing the lawn. If t represents John's total earnings for h hours of mowing, which equations can be used to model the situation
Answers
Answer:
h=6
Step-by-step explanation:
Determine el radio vector del punto medio del segmento que se forma al unir los puntos (-8, 7) y (6, 3).
Es para hoy
Answers
Answer:
The radius vector is (-8, 7) and (-1 , 5).
Step-by-step explanation:
Determine the radius vector of the midpoint of the segment that is formed by joining the points (-8, 7) and (6, 3).
The end points are (- 8, 7) and (6, 3) .
The mid point is given by
[tex]x = \frac{x' + x''}{2}\\\\y = \frac{y' +y''}{2}\\\\x =\frac{- 8 + 6}{2}=-1\\\\y = \frac{7+3}{2} = 5[/tex]
So, the radius vector is (-8, 7) and (-1 , 5).
3. If bº = 110°, what is the value of gº?
Answers
Answer:
hello mate <3
u see here its a quadrialteral
with 4 angles b , d , 70 , g
so b + d + 70 + g = 360
now u see 60 + d = 180 (straight line)
d = 120 and b = 110 ( given)
so
110 + 120 + 70 + g = 360
g + 300 = 360
g = 360 - 300 = 60 degrees option c
brainliest?
please help with number 9!!!
Answers
Answer:
2 + sqrt(3)
Step-by-step explanation:
Roots that contain square roots come in pairs
If there is a root that is a- sqrt(b), there is a root that is a+ sqrt(b)
2 -sqrt(3) means there is a root 2 + sqrt(3)
factorize. xy^2-y(x-z) -z
Answers
Answer:
The equation x The equation x 2The equation x 2 +xy+xz+yz can be factorised as follows:The equation x 2 +xy+xz+yz can be factorised as follows:x The equation x 2 +xy+xz+yz can be factorised as follows:x 2The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)Hence, x The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)Hence, x 2The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)Hence, x 2 +xy+xz+yz=(x+z)(x+y)Answer:
= (y-1) (xy-z)
Step-by-step explanation:
First we expand them -
= xy^2 - xy - yz - z
= xy(y-1)-z(y-1)
= (y-1) (xy-z)
Hope this helped
The width of a rectangle measures (2h-6) centimeters, and its length measures (7h+8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
Answer:
18h +4
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w) where l is the length and w is the width
=2( 7h+8 + 2h-6)
Combine like terms
= 2( 9h+2)
Distribute
= 18h +4
if a = 6 b=5, then find the value (a+b)
Answers
Step-by-step explanation:
Put the numbers as the value is given
So,
(6+5)= 11 Answer
11
Step-by-step explanation:
(a + b) where a = 6 and b = 5
Step 1. Substitute a for 6 and b for 5
(6 + 5)
Step 2. Add
11
If i work in a week 2 days cleaning and i will work 4 hours in a day and in 1 hour is 8$ how much will it be in a year
Answers
Answer:
$3072
Step-by-step explanation:
It is given that :
I work for 4 hours everyday, working 2 days a week.
And in 1 hour , I get $8.
Therefore,
1 hour = $8
4 hours = 4 x 8
= $32
So, in 1 day working for 4 hours, I get $32.
∴ Working 2 days = 32 x 2
= $64
In 1 month, there are 4 weeks
So, in 4 weeks (or 1 month), I work for = 4 x 2
= 8 days
Therefore, in 8 days, I get = 8 x 32
= $256
Now there are 12 months in a year.
So, in 12 months , I will get = 12 x 256
= $3072
Therefore, in 1 year , I will get $3072.
Setting y = 0 allows you to determine the what
of a graph
Answers
[tex]y=0[/tex] allows you to determine the x-intercept of a graph.
x-intercept and y-intercept:The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept. Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.When y is 0, the x-intercept is reached. The graph's intersection with the y-axis, or (0, b), is known as the y-intercept. When x is 0, the y-intercept is reached. When y is 0, the x-intercept is reached.Therefore, [tex]y=0[/tex] allows you to determine the x-intercept of a graph.
Know more about x-intercept and y-intercept here:
https://brainly.com/question/24363347
#SPJ2
