Answer:
Slope of the line that is parallel: -1
Slope of the line that is perpendicular: 1
Step-by-step explanation:
For the parallel line:
Rewrite your equation to slope-intercept form: y = mx + b
y = mx + b
m = slopeb = y-intercept (when x = 0)-4x - 4y = -2 <== add 4x to both sides
+4x +4x
-4y = 4x - 2 <== divide both sides by -4
/-4 /-4
y = -x + 1/2
The slope of the line that is parallel to this line is -1 (invisible 1 in front of x).
For the perpendicular line:
*Perpendicular lines have negative reciprocals*
Steps:
1. Take your original slope (-1)
2. Flip it (-1/1)
3. Change the sign (1)
For a slope of -1, the reciprocal would be: 1
Hope this helps!
Answer:
Parallel line:
-1
Perpendicular line:
1
Step-by-step explanation:
Let's simplify first!
-4x-4y=-2
-4x=-2+4y
4y=-4x+2
y=-x+0.5
For a parallel line, the slope should be the same
Therefore...
Slope=1
For a perpendicular line, the slope should be the negative reciprocal of the original.
Therefore...
Slope=-(-[tex]\frac{1}{1}[/tex])
=1
Hope this helps! :D
Determine the equation of a circle with its centre at the origin in the Cartesian plane and with a radius of 2√3 units
Answer:
x^2 + y^2 = 12
Step-by-step explanation:
For a circle with the center at the origin [(h,k) is (0,0)]
use the formula:
x^2 + y^2 = r^2
In this case r is 2sqroot3.
(2sqroot3)^2 is 12.
2•2•sqrt3•sqrt3
= 4•3
= 12
So we get,
x^2 + y^2 = 12
Which graph represents the solution to the given system? Y=5x+4 and 5=5x-3
y = 5(x) + 4
for this function,
y-intercept: 4x-intercept:-0.85=5(x)-3
for this function,
y-intercept: nonex-intercept: 1.6If f ( 1 ) = 2 f(1)=2 and f ( n ) = f ( n − 1 ) 2 − 5 f(n)=f(n−1) 2 −5 then find the value of f ( 4 ) f(4).
[tex]f(1) = 2\\f(2)=f(2-1)^2-5=(f(1))^2-5 = 2^2-5 = -1\\f(3) = f(3-1)^2 - 5=f(2)^2-5=(-1)^2-5=-4\\f(4) = f(4-1)^2-5 = f(3)^2-5 = (-4)^2-5 = 11[/tex]
so f(4) = 11
Hope that helps!
Answer:
f(4) = 11
Step-by-step explanation:
Given :
base function ⇒ f(n) = f(n - 1)² - 5f(1) = 2Solving :
f(2) = f(1)² - 5f(2) = 2² - 5 = 4 - 5 = -1f(3) = f(2)² - 5f(3) = (-1)² - 5 = 1 - 5 = -4
f(4) = f(3)² - 5f(4) = (-4)² - 5f(4) = 16 - 5 = 11
What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most $1000?
Using the normal distribution and the central limit theorem, it is found that there is a 0.5934 = 59.34% probability that there is an error of at most $1000.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Researching the problem on the internet, it is found that the population has mean and standard deviation given, respectively, by [tex]\mu = 57300, \sigma = 9600[/tex].
For samples of 64, the standard error is given by:
[tex]s = \frac{9600}{\sqrt{64}} = 1200[/tex]
The probability of an error of at most $1000 is the probability of a sample mean between $56,300 and $58,300, which is the p-value of Z when X = 58300 subtracted by the p-value of Z when X = 56300, hence:
X = 58300:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{58300 - 57300}{1200}[/tex]
Z = 0.83
Z = 0.83 has a p-value of 0.7967.
X = 56300:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56300 - 57300}{1200}[/tex]
Z = -0.83
Z = -0.83 has a p-value of 0.2033.
0.7967 - 0.2033 = 0.5934.
0.5934 = 59.34% probability that there is an error of at most $1000.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
Find the measure of the angle given
Step-by-step explanation:
This is a cyclic quadrilateral, so angles E and P are supplementary.
Since angle P is 100 degrees, angle E is 180-100=80 degrees.
someone help me please
The equation x² - 6x = 8 is equivalent to the equation (x - 3)² = 17. Then the correct option is A.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
x² - 6x = 8
Add 9 on both sides, then we have
x² - 6x + 9 = 8 + 9
(x - 3)² = 17
The equation x² - 6x = 8 is equivalent to the equation (x - 3)² = 17. Then the correct option is A.
More about the equivalent link is given below.
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Write a rational expression with denominator (x - 3)(x + 2) that is equivalent to 3x-1/x+2
Answer:
(x-3)(3x-1)/((x-3)(x+2))
Step-by-step explanation:
An equivalent fraction is formed by multiplying or dividing numerator and denominator by the same factor.
__
To get the desired denominator, the given denominator must be multiplied by (x-3). To get the desired numerator of the equivalent fraction, the numerator must also be multiplied by (x-3).
[tex]\dfrac{3x-1}{x+2}=\boxed{\dfrac{(x-3)(3x-1)}{(x-3)(x+2)}=\dfrac{3x^2-10x+3}{x^2-x-6}}[/tex]
In circle H with m∠GHJ=66 and GH=10 units, find the length of arc GJ. Round to the nearest hundredth
Answer:
Step-by-step explanation:
arc length= central length/360 (circumference)
GJ=90/360 (2π20)
GJ= 31.42
31.42
The length of arc GJ is 11.5133 unit.
What is Arc length?In geometry, the arc length refers to the length of a portion of a curve or an arc of a circle. It is the distance along the curve between two endpoints of the arc.
We have,
m <GHJ = 66 and GH = 10 unit
Now, using arc length formula
= nπr / 180
= 66 x 3.14 x 10/ 180
= 11.5133 unit
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Find the zeros using the quadratic formula x^2-5x+4=y.
Answer:
(x-4) (x-1)
Step-by-step explanation:
X-4=0
x=4
X-1=0
X=1
If £2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after two years
Answer:
£2121.8
Step-by-step explanation:
2000 X 1.03 X 1.03 = 2121.8
Please help!!
Sorry for the bad quality
Answer:
For the table I got 18 for the 5, 36 for the ten and not sure on the last one for the table and for the last one I got approx 5 mins but I’m not too sure
Step-by-step explanation:
Answer:
A.
5 mins = $5.20
10 = $7.20
M - i can't calculate that without having more info but the equation would be (M × 0.40) + 3.20 = Total amount in dollars.
B. 42 minutes
Step-by-step explanation:
Use the equation I listed before for A.
For B. 20.00 - 3.20 = 16.80. 16.80/0.40 = 42.
you should give me brainliest if im right
Paulina is driving 25 miles per hour. Which equation can be used to determine d, the distance Paulina traveled in miles after h hours?
Applying the relation between speed, distance and time, we made distance subject of formula hence the expression for distance is
d = 25*h
Speed, Distance and TimeGiven Data
Speed = 25 miles per hoursDistance = d milesTime traveled = h oursWe know that the expression showing the relationship between speed, distance and time is given as
Speed = Distance/Time
Substituting our given data we have
25 = d/h
Making distance subject of formula we have
25*h = d
d = 25*h
Learn more about speed here:
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someone please help
Answer:
[tex]g(g(x)) = {x}^{4} + 14 {x}^{2} + 56 [/tex]
[tex]h(h(x)) = x[/tex]
Step-by-step explanation:
[tex]g(x) = {x}^{2} + 7[/tex]
[tex]g(g(x)) = {( {x}^{2} + 7)}^{2} + 7 [/tex]
[tex]g(g(x)) = {x}^{4} + 14 {x}^{2} + 49 + 7 = {x}^{4} + 14 {x}^{2} + 56 [/tex]
[tex]h(x) = \frac{5}{9x} [/tex]
[tex]h(h(x)) = h( \frac{5}{9x} )[/tex]
[tex]h(h(x)) = \frac{5}{9( \frac{5}{9x} )} = \frac{5}{ \frac{5}{x} } = 5( \frac{x}{5}) = x [/tex]
Simplify the expression: 4a+8−2a−4+7b
Expression:__
Answer:
2a+7b+4
Step-by-step explanation:
collect like terms:
4a-2a=2a
8-4=4
then put the equation back together
 Find the length of the third side. If necessary, write in simplest radical form.
IMAGE DOWN BELOW!
SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER
Answer:
7
Step-by-step explanation:
As it is a RIGHT triangle, the formula is a^2+b^2=c^2.
We are given one leg and the hypotenuse. That means 4^2x2+b^2=81.
To find 4 root 2 square, you square them individually then multiply.
4^2=16 times 2 (root 2 squared is 2).
Simplified, that gives 16x2=32,
81-32=49.
The last leg is seven.
What is -1/2+2/3 please answer i need
Answer:
1/6 i think
Step-by-step explanation:
After heating up in a teapot, a cup of hot water is poured at a temperature of
20
8
∘
208
∘
F. The cup sits to cool in a room at a temperature of
6
8
∘
68
∘
F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
T
=
T
a
+
(
T
0
−
T
a
)
e
−
k
t
T=T
a
+(T
0
−T
a
)e
−kt
T
a
=
T
a
= the temperature surrounding the object
T
0
=
T
0
= the initial temperature of the object
t
=
t= the time in minutes
T
=
T= the temperature of the object after
t
t minutes
k
=
k= decay constant
The cup of water reaches the temperature of
18
5
∘
185
∘
F after 3 minutes. Using this information, find the value of
k
k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes.
Enter only the final temperature into the input box.
Answer:
k ≈ 0.060T(4) ≈ 178 °FStep-by-step explanation:
The desired formula parameters for Newton's Law of Cooling can be found from the given data. Then the completed formula can be used to find the temperature at the specified time.
__
Given:[tex]T(t)=T_a+(T_0-T_a)e^{-kt}\\\\T_a=68,\ T_0=208,\ (t,T)=(3,185)[/tex]
Find:k
T(4)
Solution:Filling in the given numbers, we have ...
185 = 68 +(208 -68)e^(-k·3)
117/140 = e^(-3k) . . . . . subtract 68, divide by 140
ln(117/140) = -3k . . . . . . take natural logarithms
k = ln(117/140)/-3 ≈ 0.060
__
The temperature after 4 minutes is about ...
T(4) = 68 +140e^(-0.060·4) ≈ 68 +140·0.787186
T(4) ≈ 178.205
After 4 minutes, the final temperature is about 178 °F.
which equation represents a line which is perpendicular to the line x-5y=-40
Answer:
Final answer -
[tex]equation \: of \: such \: line \dashrightarrow \: y = - 5x + b \\ [/tex]
hope helpful :D
pls help ill kiss u
Write a recursive sequence that represents the sequence defined by the following
explicit formula:
an=-5(3)n+1
Answer:
a1= -45
an= -5 ⋅ 3^n+1
Step-by-step explanation:
Work in groups of 4 to find the areas of these regular polygons.
12
14
What type of triangle is this?
We can classify triangles by their angles and their side lengths.
ANGLES:
---Acute = all angles in the triangle are less than 90 degrees
---Right = one angle in the triangle is equal to 90 degrees
---Obtuse = one angle in the triangle is greater than 90 degrees
SIDE LENGTHS:
---Equilateral = all side lengths of the triangle are the same
---Isosceles = two side lengths of the triangle are the same
---Scalene = no side lengths of the triangle are the same
In the given triangle, it has a right angle, which means that it must be a right triangle. Looking at the side lengths, none of them are the same (presumably), so it is also a scalene triangle.
Answer: right, scalene
Hope this helps!
Factor x2 + 16 completely.
a (x + 4)(x + 4)
b (x + 4)(x − 4)
c Prime
d (x − 4)(x − 4)
Prime
Solution:Let's factor this expression.x^2+16The expression is prime.Let's see why all the other options are wrong.Option A) (x+4)(x+4)x*xx*44*x4*4This makes x^2+8x+16, not x^2+16.Hope it helps.
Do comment if you have any query.
Answer:
prime
Step-by-step explanation:
I tried to delete my answer
A cell phone company charges $20 for a customer to open a new account and $35for each month of phone service.
Write a linear function to represent the total cost,y,a new customer would pay for x months of service
Evaluate the following expression. Round your answer to two decimal places.
logz 11
2.18?
2.40?
0.46?
0.84?
The correct answer would be- A: 2.18
an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. the heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the legnth of the shorter base of each trapezoid is 1.5 centimeters. what is the total area of the face of the watch to the nearest tenth of a square centimemter?
The total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²
Since an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. The heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the length of the shorter base of each trapezoid is 1.5 centimeters, the radii of the hexagon, and the base of the trapezoid form a triangle of
height, h = apothem of the hexagon = 2 cm and base, b = length of shorter base of trapezoid. Area of the triangleSo, the area of this triangle is A = 1/2bh
= 1/2 × 1. 5 cm × 2 cm
= 1.5 cm × 1 cm
= 1.5 cm²
Area of the hexagonSince there are 6 of such triangles in the hexagon, the area of the hexagon, A' = 6A
= 6 × 1.5 cm²
= 9.0 cm²
So, the total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²
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Please help!! thanks!
Answer:
C. (5, 1)
Step-by-step explanation:
Because the slope of F and G is 2, we know that the other points with the same distance are also going to have a slope of ±2. The only answer choice that fits this criteria is C
Hope this helps!
Question below .....
find the unknown measures. round lengths to the nearest hundredth and angle measures to the nearest degree.
Answer:
Angle I = 44
Measure GH=7.64
Measure GI=7.91
Step-by-step explanation:
Angle I:Since we know that m∠H = 46 and m∠G=90, we can find measure angle I by subtracting from 180.
[tex]180=46+90+x\\44=x[/tex]
Measure GH:Since we are given that m∠H = 46, and the triangle is right, we can use trigonometric functions to find the two sides.
First is GH, since it's adjacent to the angle, we will use cosine.
[tex]cos(x)=\frac{adjacent}{hypotenuse} \\cos(46)=\frac{adjacent}{11}\\ 11*cos(46)=adjacent\\7.64=adjacent[/tex]
Measure GI:The same idea as previous, only instead we will use sine since we need to find the opposite.
[tex]sin(x) = \frac{opposite}{hypotenuse}\\ sin(46)=\frac{opposite}{11}\\ 11*sin(46)=opposite\\7.91 = opposite[/tex]
Solve the math problem
Answer:
a no association b non liner c liner d liner
Answer:
A) No association
B) Nonlinear
C) Linear
D) Nonlinear
Step-by-step explanation:
Linear Relationship: A linear relationship is one in which the scatter plot resembles a straight line. When one variable increases, the other variable increases or decreases proportionally.
Nonlinear Relationship: A nonlinear relationship is one in which the scatter plot does not resemble a straight line. It could resemble a curve or it could not resemble anything at all. A proportional increase or decrease in one variable does not result in a proportional rise or decrease in the other variable.
No Association: a graph of data showing discrete (individual) points of data that are not connected.
Using these definitions we can conclude whether the graphs are linear, nonlinear, or no association.
find the measure of angle 8
Answer:
99 degrees.
Step-by-step explanation:
m < 8 = 99 (corresponding angles are congruent).
