The slopes of perpendicular lines are negative reciprocals is proved.
What is Equation of a Straight Line ?An equation of a straight line is given by
y = mx +c
It is given that
Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular.
Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).
The slopes of lines PQ and P’Q’ can be determined using the formula
[tex]\rm m = \dfrac{ v _2 - v _1 }{ x _2 -x _1 }[/tex]
The product of these slopes is -1 .
This product shows that the slopes are negative reciprocals
Therefore , The slopes of perpendicular lines are negative reciprocals is proved,
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which choice is equivalent to the expression below? square root of -64
Step-by-step explanation:
[tex] \sqrt{ - 64 } = - 8[/tex]
so the answer you got pls mark branlist
Seven times the twice of a number and 6 equals 4
Answer:
7(2a+6) = 4
and the answer is:
19/7
Step-by-step explanation:
7(2a+6) = 4
7*2a + 7*6 = 4
14a + 42 = 4
14a = 4 - 42
14a = -38
a = -38/14
a = -19/7
A line contains points M(1, 3) and N(5, 0). What is the slope of MN?
negative StartFraction 4 Over 3 EndFraction
negative StartFraction 3 Over 4 EndFraction
StartFraction 3 Over 4 EndFraction
StartFraction 4 Over 3 EndFraction
Answer:
-¾
Step-by-step explanation:
gradient = delta y over delta x
gradient = 0 - 3 / 5 - 1
gradient = -3 / 4
PLEASE HELP TIMED!!!
Which of the following describes the growth rate of the exponential function in the graph below?
a) For each x increase of 1, the y increases by a common difference of 3.
b) For each x increase of 1, the y increases by a common factor of 3.
c) For each x increase of 1, the y increases by 4 more than the previous increase.
d) For each c increase of 2, the y increases by doubling and then adding one.
Answer:
B
Step-by-step explanation:
let me know if you want an explanation :))
For which temperature will the model most accurately predict the time spent cooling? 0 100 300 400
The temperature that accurately describes the time that would have spent cooling is 300.
How to solve for the cooling time.We have the function as f(t) = 349.2(0.98)t
We have to solve for all of the values in the option
When t = 0
This would give us an infinite value for t hence it is not the answer.
When t = 100
we have 61.6
When t = 300
we have f(t) = 7.5
WHen t = 400
f(t) = -6.7
From the solved values the accurate one that has to talk about the time spent cooling is 300 at 7.5
Complete questionThe function f(t) = 349.2(0.98)t models the relationship between t, the time an oven spends cooling and the temperature of the oven. For which temperature will the model most accurately predict the time spent cooling? 0 100 300 400
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If f(x) is a linear function, which statement must be true?
O f(x) has no constant term.
O f(x) has no x²-term.
Of(x) has no terms with a coefficient other than 1.
Of(x) has no x-term.
Answer:
has no x^2 term
Step-by-step explanation:
Has no x^2 term <====== that would make it an exponential function, not linear
find the missing value. 2 + blank = -13
Answer:
-15
Step-by-step explanation:
-13-2= -15
(to check:2+ -15= -13)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2 + [blank] = -13}[/tex]
[tex]\large\textbf{CONVERT TO: }[/tex]
[tex]\mathsf{2 + b = -13}[/tex]
[tex]\mathsf{b + 2 = -13}[/tex]
[tex]\large\textbf{SUBTRACT 2 to BOTH SIDES: }[/tex]
[tex]\mathsf{b + 2 - 2 = -13 - 2}[/tex]
[tex]\large\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{b = -13 - 2}[/tex]
[tex]\mathsf{b = -15}[/tex]
[tex]\huge\text{Therefore, the mystery number is: \boxed{\mathsf{-15}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
If x + y = 2 and x - y = 6, solve for x and y.
Answer:
Step-by-step explanation:
Givens
x + y = 2
x - y = 6
Solution
Just add the two equations together. The y's will drop out.
x + y = 2
x - y = 6 Add
2x = 8 Divide by 2
2x/2 = 8/2 Combine
x = 4 Substitute x = 4 into the top equation
x + y = 2
4 + y = 2 Subtract 4 from both sides
4-4+y=2-4 Combine
y = - 2
Answer
x = 4
y = -2
please help me guys its math
Can someone explain to me #2 I only need #2
Answer:
in a rectangle, opposite sides are equal in length
Step-by-step explanation:
now in this question, Pythagoras theorem is being used to find the length
we know both sides by using Pythagoras theorem find third side and get the sum to find ac+bd
Step-by-step explanation:
So it tells you that AB = 21 and AD = 28
and you to find what BD + AC is and since BD is the same length as AC
you only need to find one of them, then double it
There is a formula you use called the Pythagorean theorem
The Pythagorean theorem is A²+B²=C²
In this problem A = 21 B = 28 and C = the length of BD
so it'll look like 21²+28²=Length of BD² or BD²=21²+28² now you find BD
first do 21²+28² --> 441+784 --> 1225 Now you know that 21²+28²=1225
so BD²=1225 Then to find BD, you find √1225(square root of 1225)
Which is 35 So BD=35 and you want to know what BD+AC is
so 35+35=70
ab (2a²b² - 4b) = what is the answer
Answer:
2ab(a2b−2)
Step-by-step explanation:
A boat travels 333 km in 7 hours with a constant speed how far can it travel in 6 hours with the same speed
Answer:
258 km
Step-by-step explanation:
We can calculate the speed of the boat with (333km/7 hours) = 47.57 km/hr.
Assuming the same speed, the boat would travel (47.57 km/hr)*(6 hr) = 258 km
convert the following numbers into scientific notation
3,400=
0.000023=
4.50=
1,000,000=
0.00671=
The Scientific notation of given numbers are [tex]3400=3.4 \times 10^{-3}[/tex], [tex]0.000023=2.3 \times 10^{5}[/tex], 4.50, [tex]1,000,000=1 \times 10^{6}[/tex] and [tex]0.00671=6.71 \times 10^{-3}[/tex].
The given numbers are 3400, 0.000023, 4.50, 1,000,000 and 0.00671.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
Now, [tex]3400=3.4 \times 10^{-3}[/tex], [tex]0.000023=2.3 \times 10^{5}[/tex], 4.50, [tex]1,000,000=1 \times 10^{6}[/tex] and [tex]0.00671=6.71 \times 10^{-3}[/tex].
Therefore, the Scientific notation of given numbers are [tex]3400=3.4 \times 10^{-3}[/tex], [tex]0.000023=2.3 \times 10^{5}[/tex], 4.50, [tex]1,000,000=1 \times 10^{6}[/tex] and [tex]0.00671=6.71 \times 10^{-3}[/tex].
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Which shows all the exact solutions of 2sec^2 (x)-tan^4 (x)=-1? Give your answer in radians.
a) pi/3 + kpi and 2pi/3 + kpi
b) pi/3 +2kpi and 5pi/3 +2kpi
c) pi/4 +2kpi, 3pi/4 + 2kpi, 5pi/4 +2kpi, and 7pi/4 +2kpi
d) pi/3 + kpi, 2pi/3 +kpi, 4pi/3 +kpi, and 5pi/3 +kpi
Answer:
a. 1/3pi+kpi and 2/3pi+kpi
Step-by-step explanation:
2Sec²x
=2+2tan²x-(tan²x)²=-1
Let tan²x=u
-u²+2u+2=-1
-u²+2u+3=0
u²-2u-3=0
(u+1)(u-3)=0
u=-1,u=3
(tan x)²=-1(No solution)
(tan x)²=3
>>tan x=±sqrt(3)
I) tan x=sqrt(3)
>>tan(pi/3)=sqrt 3
Tan(pi+A) =tanA
Tan(pi+pi/3)=tan(pi/3)
>>tan(4/3pi)=sqrt(3)
>>x=4/3pi and 1/3pi
General solution: 1/3pi+kpi
ii) tan x=-sqrt(3)
x=2/3pi(At 2nd quadrant)
x=5/3pi(at 4th quadrant)
General solution: 2/3pi+kpi
1. (08.01 MC)
The graph shows two lines. A and B
Answer:
Part A:
A pair of linear equations can only have one solution or infinitely many solutions. In this case, there would only be one solution as they intersection at only one point.
Part B:
The solution would be (3, 4) because it is the point of intersection between the two linear lines.
Solve the equation.
8-2x = -8x + 14
O x=-1
3
0x = - 1²/20
5
0x = ²/3
O x = 1
Answer:
D. x=1
Step-by-step explanation:
8-2x = -8x + 14
First, add 8x to both sides.
8+6x=14
Next, subtract 8 from both sides.
6x=6
Lasty, divide 6 from both sides.
x=1
Hope this helps!
If not, I am sorry.
It takes two points to define a plane.
Answer:
In a Euclidean space of any number of dimensions, a plane is uniquely determined by any of the following: Three non-collinear points (points not on a single line). A line and a point not on that line. Two distinct but intersecting lines.
Step-by-step explanation:
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Vanessa has 16 songs on a Classic Rock CD. Six of the songs are by the Beatles, 4 are by the Rolling Stones, 4 are by the Who, and 2 are by the Doors. Vanessa plays the CD. She selects a setting that randomly chooses songs to play.
Find the probability of each event:
a) The first 3 songs played are by the Beatles.
b) The first 2 songs played are by the Rolling Stones and the next 2 songs are by the Beatles.
c) The first 2 songs played are by the Doors, and the next song played is either by the Beatles or the Rolling Stones.
Using it's concept, it is found that the probabilities are given as follows:
a) 0.0527 = 5.27%.
b) 0.0088 = 0.88%.
c) 0.0098 = 0.98%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Item a:
6 out of 16 songs are of the Beatles, hence the probability of a single music being from the Beatles is:
[tex]pB = \frac{6}{16} = \frac{3}{8}[/tex]
Of three musics, the probability is:
[tex]p = \left(\frac{3}{8}\right)^3 = 0.0527[/tex]
Item b:
For the Rolling stones, the probability is:
[tex]pR = \frac{4}{16} = \frac{1}{4}[/tex]
For the four musics, the probability is:
[tex]p = \left(\frac{1}{4}\right)^2 \times \left(\frac{3}{8}\right)^2 = 0.0088[/tex]
Item c:
For the doors, the probability is:
[tex]pD = \frac{2}{16} = \frac{1}{8}[/tex].
For Beatles or Rolling stones, the probability is:
[tex]pBR = \frac{10}{16} = \frac{5}{8}[/tex]
For the three musics, the probability is:
[tex]p = \left(\frac{1}{8}\right)^2 \times \frac{5}{8} = 0.0098[/tex]
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Write a quadratic equation, in factored form solution are 0,and 6
Answer: [tex]x(x-6)=0[/tex]
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.
The options that are true of the triangles include:
∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'The complete question is given below:-
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.
△XYZ ~ △X'Y'Z'AngleXZY ≅ AngleY'Z'X'YX ≅ Y'X'XZ = 2X'Z'mAngleYXZ = 2mAngleY'X'Z'What is translation?The process of changing the location of the image on the coordinate system will be known as the translation.
It should be noted that triangle XYZ is reflected over a vertical line. Then, it's dilated by 1/2 to form XYZ.
This implies that the triangles are similar, the angles are congruent and the side length of XYZ is twice that of X'Z.
Therefore the options that are true of the triangles include:
∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'Learn more about translation on:
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What are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)
The value of (x,y) is (1.2 , -4.7) , Option D is the right answer.
The complete question is
On a coordinate plane, a line is drawn from point a to point b. point a is at (7, negative 2) and point b is at (negative 8, negative 9). what are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)
What are Coordinates ?Coordinates are the location of a point in an (x,y) plot.
The given data is
Coordinates of
A = (7,-2)
B = (-8,-9)
m:n = 5:8
The coordinates of partition has to be determined
The formula used is
[tex]\rm (x,y) = \dfrac{1}{m+n} *(nx_1 + mx_2 , ny_1+ny_2)\\\\\\\rm (x,y) = \dfrac{1}{5+8} *(5*-8 + 8*7 , 5*-9+8*-2)[/tex]
(x,y ) = (1.2 , -4.7)
Therefore Option D is the correct answer.
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When the sum of a list of integers is divided by the mean of the integers, the result is x. What does x represent?
Answer:
it is the number of intigers in the list
Based on the concept of integer and the options available, x does represent the number of 2 integers in the list.
What is Integers?An integer is a mathematical term that is known as the number zero, a positive natural number, or a negative integer with a minus sign.
Generally, Integers the negative numbers are the additive inverses of the corresponding positive numbers.
In this case, it has been mathematically proven that when the sum of a list of integers is divided by the mean of the integers the result x represents the total number of integers in the list.
Hence, in this case, it is concluded that the correct answer is option H. The numbers if integers in the list.
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Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
I'm pretty sure it is d... .......
Find the equation of the line passing through the points -2x+1 (8,2)
The line that passes through (-2, 1) and (8, 2) is:
y = (1/10)*x + 12/10
How to find the equation of the line?I assume you want to find the equation of the line that passes through (-2, 1) and (8, 2).
A general linear equation is written as:
y = a*x + b
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we know that it passes through (-2, 1) and (8, 2), then:
[tex]a = \frac{2 - 1}{8 - (-2)} = 1/10[/tex]
Then the line is:
y = (1/10)*x + b
To find the value of b, we use one of the given points, for example if we use (8, 2), it means that when x = 8, we must have y = 2.
2 = (1/10)*8 + b
2 - 8/10 = b
20/10 - 8/10 = b
12/10 = b
Then the linear equation is:
y = (1/10)*x + 12/10
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The set of rational numbers include all the following numbers except...
O √120
6²
O 12.9
O1/3
Answer:
[tex] \sqrt{120} [/tex]
Step-by-step explanation:
√120 is irrational.
Please help!!!! ASAP!!!!!!!!!!
Answer:
[tex]\sqrt[]{4+\frac{1}{25}y }[/tex]
Step-by-step explanation:
Transform - y-25^2=-100
divide
simplify
x plus-minus [tex]\sqrt[]{4+\frac{1}{25}y }[/tex]
Please help! I'm not quite understanding this.
Answer:
d.) 21
Explanation:
Rules:
-|a| = -a|-a| = ax = |a| then x = ±aSolve:
[tex]\rightarrow \sf \dfrac{4|a|}{2} + |a-3|[/tex]
[insert a = -6]
[tex]\sf\rightarrow \dfrac{4|-6|}{2} + |-6-3|[/tex]
[simplify the following]
[tex]\sf\rightarrow \dfrac{4(6)}{2} + 9[/tex]
[tex]\sf\rightarrow 12 + 9[/tex]
[tex]\sf\rightarrow 21[/tex]
how to graph y = 2|x + 3| - 4
The x-intercepts and the y-intercepts of the function is that determines the graph is:
x-intercepts = (-5,0) and (-1,0)y-intercepts = (0,2)How do we graph the function y = f(x) of an absolute equation?The function of an absolute equation can be graphed by determining the values of x-intercepts and the y-intercepts of the function.
From the given equation:
y = 2|x+3| - 4
To determine the y-intercepts, we need to set the values of x to zero, and vice versa for x-intercepts.
By doing so, the x-intercepts and the y-intercepts of the function is:
x-intercepts = (-5,0) and (-1,0)y-intercepts = (0,2)Therefore, since we know the x and y-intercepts, the graph of the absolute value can be seen as plotted below.
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A cake decorator is rolling a square of fondant into a rectangle. the area of the rectangle can be represented by the expression 1.5s(2s). simplify the expression representing the area. 3.5s 3s2 3.5s2 3s
Answer:3.5s2
Step-by-step explanation:
because I said so
Answer:
3.5s2
Step-by-step explanation:
because that guy said so and it was right
difference between compounded annually, monthly and daily.
Answer:
With monthly compounding, the bank will calculate interest on your account just once per month. It will not update your balance on a daily basis when it calculates how much interest it owes you. Assuming that the APR is the same, accounts with monthly compounding offer a lower APY than accounts with daily compounding.