Answer:
Option C
Step-by-step explanation:
Suppose that we have a given proposition p
We define the complement as:
"NOT p" or ¬p
So, if p is:
the dog is red
the complement is
the dog is NOT red.
The principal rule to work with this is:
if p is true, then ¬p is false
if p is false, then ¬p is true.
Here the proposition is:
p = "When 100 engines are shipped, all of them are free of defects."
When this is this is true, ¬p must be false.
when this is false, ¬p must be true.
Let's analyze the given options, first the incorrect ones:
A: "At most one of the engines is defective."
here if we have for example, two defective engines, then this proposition and the original proposition are false.
B: " All of the engines are defective."
Here if there is one defective engine, then this is false, and also is the original proposition.
D: "None of the engines are defective"
When the original proposition is true "When 100 engines are shipped, all of them are free of defects.", this proposition is also true (because none of the engines are defective)
Finally, the corrrect one
C "At least one of the engines is defective"
When the original proposition is true, there are no defective engines, so this is false.
While, if this is true, there is at least one defective engine, so the original proposition is false.
Then this is the correct option:
¬p = "At least one of the engines is defective"
nit 4 Topic 3 HW Sets Applications e Sunday by 11:59pm Points 100 Submitting an external tool Question How many subsets and proper subsets does the set M = {1,2,3} have? Select the correct answer below:
Answer:
ghthtf
Step-by-step explanation:
tygtgg
(-3,-7) is it a solution
Answer:
It could be a solution
Step-by-step explanation:
This depends on what equation you are solving. It could be a solution for a quadratic or even a transformation problem.
rotation 180 degrees about the origin.
Answer:
Take the picture you uploaded.
Click the rotate button twice.
Done
from an observer o, the angles of elevation of the bottom and the top of a flagpole are 40° and 45° respectively.find the height of the flagpole?
Answer:
Take a look of the image below, we can think on this problem as a problem of two triangle rectangles.
We can see that both triangles share the adjacent cathetus, then the height of the flagpole is just the difference between the opposite cathetus.
Remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus)
So, if we define H as the height of the cliff
X as the distance between the observer and the cliff
and h as the height of the flagopole
we can write:
tan(40°) = H/X
tan(45°) = (H + h)/X
Notice that we have two equations and 3 variables (we should have the same number of equations than variables) then here is missing information, and we can't get an exact solution for the height of the flagpole.
But we can write it in terms of the height of the cliff H, or in terms of the distance between the observer and the cliff.
We want to find the value of h.
If we take the quotient between both equations, we get:
Tan(45°)/Tan(40°) = (H + h)/H
1.192 = (H + h)/H
1.192*H = H + h
1.192*H - H = h
0.192*H = h
So the height of the flagpole is 0.192 times the height of the cliff.
30 POINTS
Help on Part B pleaseeee
In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:
4x-5
Answer:
Solution given:
B.g(x)=[tex]\frac{x+5}{4}[/tex]
let
g(x)=y
y=[tex]\frac{x+5}{4}[/tex]
Interchanging role of x and y
we get:
x=[tex]\frac{y+5}{4}[/tex]
doing crisscrossed multiplication
4x=y+5
y=4x-5
So
g-¹(x)=4x-5
Given that,
→ g(x) = x+5/4
Then g(x)=y,
→ y = x+5/4
Now we can interchange role of x and y,
→ x = y+5/4
Then use the cross multiplication,
→ 4x = y+5
→ y = 4x-5
Hence, g-¹(x) = 4x-5 is the solution.
Simplify the radical expression below square root of 5/64
A square root 5/8
B 5/64
C square root 5/64
D 5/8
Answer:
a
Step-by-step explanation:
square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8
through: (-2, 2), parallel to y=-x-5
Answer:
y = -x.
Step-by-step explanation:
The slope of the line (m) = -1. ( because of the -x in y = -x - 5)
y - y1 = m (x - x1) where (x1, y1) is a point on the line, so we get;
y - 2 = -1(x - (-2))
y - 2 = -x + -1 * +2
y - 2 = -x - 2
y = -x.
Here is the general information about the Learn by Doing discussion board exercises (directions, grading, feedback). Prompt
1) Give an example of a research question that involves estimating a characteristic about the population of part-time students at your college.
2) Improve this poorly stated research question: Do students work a lot of hours
Answer:
Step-by-step explanation:
Answer to question 1:
On average do part-time students spend less than 20 hours per work on academic work and assignments ?
Answer to question 2:
On average do students work greater than 50 hours a week ?
Identify the sampling techniques used, and discuss potential sources of bias (if any). Assume the population of interest is the student body at a university. Questioning students as they leave an academic building, a researcher asks 341 students about their eating habits.
1. What type of sampling is used?
a. Systematic sampling is used, because students are selected from a list, with a fixed interval between students on the list.
b. Cluster sampling is used because students are divided into groups, groups are chosen at random, and every student in one of those groups is sampled.
c. Simple random sampling is used because students are chosen at random.
d. Stratified sampling is used because students are divided into groups, and students are chosen at random from these groups.
e. Convenience sampling is used because students are chosen due to convenience of location.
2. What potential sources of bias are present if any. Select all that apply.
a. University students may not be representative of all people in their age group.
b. The sample only consists of members of the population that are easy to get. These members may not be representative of the population.
c. Because of the personal nature of the question, students may not answer honestly.
d. There are no potential sources of bias.
Answer:
1. e. Convenience sampling is used because students are chosen due to convenience of location.
2. a. University students may not be representative of all people in their age group.
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
Questioning students as they leave an academic building, a researcher asks 341 students about their eating habits.
Students sampled as they leave the build, which is convenience, in this case convenience of location, which means that the correct answer to question 1 is given by option e.
2. What potential sources of bias are present if any. Select all that apply.
Only members of one group are asked(university students), and this may not be representative of the rest of the population, which means that the correct answer to question 2 is given by option a.
Please help with problem
9514 1404 393
Answer:
∠CAE ≈ 16.7°DF ≈ 5.3Step-by-step explanation:
a) Angle CAE can be found using the tangent relation.
tan(∠CAE) = CE/AE
tan(∠CAE) = 6/20
∠CAE = arctan(6/20) ≈ 16.7°
__
b. The length of DF can be found using the law of cosines.
DF² = FA² +DA² -2·FA·DA·cos(A)
DF² = 14² +10² -2·14·10·cos(16.7°) ≈ 27.8086
DF ≈ √27.8086
DF = 5.3
the complement of guessing 5 correct answers on a 5 question true or false examination is
Answer:
Guessing at least one incorrect answer
Step-by-step explanation:
The complement of guessing 5 correct answers on a 5-question true/false exam is-
Guessing at least one incorrect answer because, when 1 or more questions are incorrectly guessed, the event of 5 correct answers can not occur.
A humanities professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 60% C: Scores below the top 40% and above the bottom 23% D: Scores below the top 77% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 70 and a standard deviation of 9.6. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary
Answer:
81
Step-by-step explanation:
Given data:
mean μ = 70.
standard deviation σ, 9.6.
P(Z < 1.123) = 0.13
z = 1.13
Use the z-score formula,
x = z×σ +μ
Substitute the values in the above equation.
x = 1.13 9.6 + 70 = 81
The minimum score required for an A grade is = 81
How many flowers spaced every 4 inches are needed to surround a circular garden with a 15-foot radius? Round all circumference and area calculations to the nearest whole number.
Answer:
283 flowers
Step-by-step explanation:
c=2pi*r
c = 1130.973 =1131
1131/4
282.75 = 283
You buy a six pack of Gatorade for $9.00. What is the unit price or the price per bottle?
Answer:
Price per bottle is 1.5 or $1.50
Step-by-step explanation:
To get price per unit, you just divide the amount of money spent by the items purchased. 9/6 = 1.5
math help plz
how to solve literal equations, how to understand and step by step with an example provided please
9514 1404 393
Explanation:
Your question covers a good bit of the material in an algebra course. The short answer is, "the same way you solve a numerical equation." The point of algebra is that literals can stand for numbers, and so be manipulated the same way numbers are.
Expressions are evaluated according to the Order of Operations. For equations involving a single variable, the equation specifies what operations are being performed on that variable. To find the vale of the variable (solve for that literal), you need to "undo" the operations that are performed on it. As with many problems that have layers, you work down through the layers from the outside in. Generally, that means working through the list of operations "backwards," undoing the last one first.
Simple example
y = mx + b . . . . . . solve for x
In this equation, the operations performed on x are ...
multiplication by maddition of b to the productIn accordance with the above, the first thing we do is "undo" the addition of b. (Note that this could be a number or literal--or even a complicated expression--and the process would be exactly the same.) To "undo" addition, we add the opposite.
y -b = mx +b -b ⇒ y -b = mx
Next, we "undo" the multiplication by m. That is, we divide by m, or multiply by the reciprocal of m. Either is the same as the other.
(y -b)(1/m) = (mx)(1/m) ⇒ (y -b)/m = x
Now, we have solved this literal equation for x.
_____
Throughout this process you must adhere strictly to the properties of equality. That is, anything you do to one side of the equation must also be done to the other side.
The reason you study inverses and identity elements is so you understand that addition of an additive inverse produces the additive identity element:
x + (-x) = 0
Similarly, multiplication by the multiplicative inverse (reciprocal) produces the multiplicative identity element.
x · (1/x) = 1
When other operations are involved, such as raising to a power, trig functions, roots, logs, exponentiation, each of these has an associated inverse function that produces an identity:
(x^a)^(1/a) = x^1 = x
arcsin(sin(x)) = x
(√x)^2 = x
10^(log(x)) = x or log(10^x) = x
Some of these inverse functions have restricted domains, so care must be used when solving equations involving them.
When a variable of interest appears on both sides of the equal sign, then you must figure a way to rearrange the equation so the terms with the variable can be combined.
Example:
ax + b = cx +d . . . . . solve for x
ax -cx = d -b . . . . . . subtract (cx+b). (Of course, this is subtracted from both sides of the equation.)
x(a -c) = d -b . . . . . combine x-terms
x = (d -b)/(a -c) . . . . divide by the coefficient of x
Note that we had to divide the entire right-side expression by the x-coefficient, so had to enclose it in parentheses.
More Complicated Example:
A recent Brainly problem asked for the solution to ...
T = 2π√(L/g) . . . . solve for L
Here, L is divided by g, a root taken, and that multiplied by 2π. Undoing these in reverse order, we first divide by 2π, square both sides to undo the root, then multiply by g to undo the division:
[tex]T=2\pi\sqrt{\dfrac{L}{g}}\\\\\dfrac{T}{2\pi}=\sqrt{\dfrac{L}{g}}\\\\\left(\dfrac{T}{2\pi}\right)^2=\dfrac{L}{g}\\\\\boxed{L=g\left(\dfrac{T}{2\pi}\right)^2}[/tex]
The problem posted on Brainly had numbers where some of these variables are. That does not affect the solution method, except that sometimes numerical values can be combined where literal values cannot.
_____
Key Points
The equal sign is sacred, and its truth must be preserved at every step.Literal equations are solved the same way numerical equations are solved.Inverse operations and functions are used to "undo" operations and functions.The Order of Operations can be helpful when considering what to do first.A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15.875, 16.595) ounces. What is the sample mean weight of grapes, and what is the margin of error?
O The sample mean weight is 15.875 ounces, and the margin of error is 16.595 ounces.
O The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces.
O The sample mean weight is 16.235 ounces, and the margin of error is 0.720 ounces.
O The sample mean weight is 16 ounces, and the margin of error is 0.720 ounces.
Answer:
The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces
Step-by-step explanation:
To find the sample mean, we can find the mean of the confidence interval.
(15.875 + 16.595)/2 = 16.235
To find the margin of error, that is the difference between the mean and one of the edges of the confidence interval. 16.595 - 16.235 = 0.36
The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces
Answer:
C. We are 90% confident that the interval from 15.875 ounces to 16.595 ounces captures the true mean weight of bags of grapes.
Step-by-step explanation:
Hannah would like to make an investment that will turn 8000 dollars into 33000 dollars in 7 years. What quarterly rate of interest, compounded four times per year, must she receive to reach her goal?
Answer:
20.76%
Step-by-step explanation:
[tex]33000=8000(1+\frac{i}{4})^{4*7}\\4.125=(1+\frac{i}{4})^{28}\\\sqrt[28]{4.125}=1+\frac{i}{4} \\i= .207648169[/tex]
which rounds to 20.76%
Answer:
About 0.2076 or 20.76%.
Step-by-step explanation:
Recall that compound interest is given by the formula:
[tex]\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is applied per year, and t is the number of years.
Since Hannah wants to turn an $8,000 investment into $33,000 in seven years compounded quarterly, we want to solve for r given that P = 8000, A = 33000, n = 4, and t = 7. Substitute:
[tex]\displaystyle \left(33000\right)=\left(8000\right)\left(1+\frac{r}{4}\right)^{(4)(7)}[/tex]
Simplify and divide both sides by 8000:
[tex]\displaystyle \frac{33}{8}=\left(1+\frac{r}{4}\right)^{28}[/tex]
Raise both sides to the 1/28th power:
[tex]\displaystyle \left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}= 1+\frac{r}{4}[/tex]
Solve for r. Hence:
[tex]\displaystyle r= 4\left(\left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}-1\right)[/tex]
Use a calculator. Hence:
[tex]r=0.2076...\approx 0.2076[/tex]
So, the quarterly rate of interest must be 0.2076, or about 20.76%.
find the LCM of ;
(1+4x+4x2-16x) and (1+2x-8x3-16x4)
Answer:
16x4−4x2+4x−116x4−4x2+4x−1
=16x4−(4x2−4x+1)=16x4−(4x2−4x+1)
=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2
=(4x2−2x+1)(4x2+2x−1)∵a2−b2=(a−b)(a+b
Step-by-step explanation:
How would you write 8^5 as a multiplication expression?
Answer:
8 * 8 * 8 * 8 * 8
Step-by-step explanation:
8^5 is basically 8 times itself five times.
True or false: If you are changing a larger unit into a smaller unit, like cm into mm, the decimal is moved to the right because you are multiplying by a power of ten
Answer:true
Step-by-step explanation:
i dont know
Two balls are drawn with replacement from a bag containing 12 red,3 white and 1 blue balls.what is the probability that both are red?
The probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]
What is probability?"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
What is the formula of combination?"[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]"
For given question,
a bag contains 12 red, 3 white and 1 blue balls.
Total balls = 12 + 3 + 1
Total = 16
Two balls are drawn from a bag.
The number of possible ways of drawing 2 balls from the bag are:
Using combination formula,
[tex]^{16}C_2\\\\=\frac{16!}{2!(16-2)!}\\\\ =\frac{16!}{2!\times 12!}\\\\ =120[/tex]
So, n(S) = 120
Two balls are drawn with replacement from a bag.
We need to find the probability that both are red.
Let event A: both the balls are red
[tex]\Rightarrow n(A)=^{12}C_2[/tex]
Using combination formula,
[tex]^{12}C_2\\\\=\frac{12!}{2!\times (12-2)!}\\\\= \frac{12!}{2!\times 10!}\\\\ =66[/tex]
Using probability formula,
[tex]\Rightarrow P(A)=\frac{n(A)}{n(S)}\\\\\Rightarrow P(A)=\frac{66}{120}\\\\\Rightarrow P(A)=\frac{11}{20}[/tex]
Therefore, the probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]
Learn more about probability here:
brainly.com/question/11234923
#SPJ2
CHECK MY ANSWERS PLEASE
____
The sequence is geometric:
3, 13, 23, 33,...
True
False***
_____________________
The sequence is geometric:
5, -25, 125, -625,...
True***
False
Answer:
1. False 2. True
Step-by-step explanation:
For a geometric sequence,
[tex]\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}[/tex]
1. The sequence is :
3, 13, 23, 33,...
[tex]\dfrac{13}{3}\ne \dfrac{23}{13}[/tex]
It is not geometric. It is false
2. The sequence is :
5, -25, 125, -625
[tex]\dfrac{-25}{5}=\dfrac{125}{-25}\\\\-5=-5[/tex]
So, the sequence is geometric as the common ratio is same. It is true.
Assisted-Living Facility Rent. Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486. Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is .
Complete Question
Assisted-Living Facility Rent.Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486 (the Wall Street Journal, October 27, 2012). Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is s = $650. a. Develop a 90% confidence interval estimate of the population mean monthly rent.
Answer:
[tex]CI: 3388.39<X<3583.61[/tex]
Step-by-step explanation:
Sample Size n=120
Mean \=x =3486
Standard Deviation \sigma=650
Confidence interval CI=0.9
Therefore
Level of sig [tex]\alpha=0.1[/tex]
Therfore
The Critical Value from table is
Z_c=1.645
Generally the equation for Standard error is mathematically given by
[tex]S.E=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]S.E=\frac{650}{\sqrt{120}}[/tex]
[tex]S.E=59.3366[/tex]
Generally the equation for Margin error is mathematically given by
[tex]M.E= = Z_c * SE[/tex]
[tex]M.E=1.65 * 59.34[/tex]
[tex]M.E= 97.61[/tex]
Therefore
[tex]CI= \=x \pm M.E[/tex]
[tex]CI= 3486 \pm 97.61[/tex]
Lower limit
[tex]LL= \=x-M.E=3486-97.6087[/tex]
[tex]LL= 3388.39[/tex]
Upper limit:
[tex]UL= \=x+E=3486+97.6087[/tex]
[tex]UL= 3583.61[/tex]
Therefore The 90% confidence interval estimate of the population mean monthly rent.
[tex]CI: 3388.39<X<3583.61[/tex]
Mr johnson sells erasers for $3 each. He sold 96 erasers last week and he sold 204 erasers this week.
A. $300 B $600 C $100 D $900
I believe your answer is D.) $900
204 + 96 = 300
300 x 3 = 900
I hope this is correct and helps!
Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.)
f(x) = x² + 5x – 2
relative maximum
(x, y) = DNE
relativo minimum
(x, y) =
Answer:
Relative minimum: [tex]\left(-\frac{5}{2}, -\frac{33}{4}\right)[/tex], Relative maximum: [tex]DNE[/tex]
Step-by-step explanation:
First, we obtain the First and Second Derivatives of the polynomic function:
First Derivative
[tex]f'(x) = 2\cdot x + 5[/tex] (1)
Second Derivative
[tex]f''(x) = 2[/tex] (2)
Now, we proceed with the First Derivative Test on (1):
[tex]2\cdot x + 5 = 0[/tex]
[tex]x = -\frac{5}{2}[/tex]
The critical point is [tex]-\frac{5}{2}[/tex].
As the second derivative is a constant function, we know that critical point leads to a minimum by Second Derivative Test, since [tex]f\left(-\frac{5}{2}\right) > 0[/tex].
Lastly, we find the remaining component associated with the critical point by direct evaluation of the function:
[tex]f\left(-\frac{5}{2} \right) = \left(-\frac{5}{2} \right)^{2} + 5\cdot \left(-\frac{5}{2} \right) - 2[/tex]
[tex]f\left(-\frac{5}{2} \right) = -\frac{33}{4}[/tex]
There are relative maxima.
plz g0ive me solution
Answer:
separate the x from the numbers it will make the equation easier
y is inversely proportional to x when y=9, x=24
Answer:
216
Step-by-step explanation:
y=k÷x
k=xy
k=9×24
k=216
Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0 ≤ θ ≤ 2π. Enter your answers as a comma-separated list of ordered pairs.) r = 1 − sin(θ) horizontal tangent
The tangent to the curve at a point P (x, y) has slope dy/dx at that point. By the chain rule,
dy/dx = (dy/dθ) / (dx/dθ)
We're in polar coordinates, so
y (θ) = r (θ) sin(θ) ==> dy/dθ = dr/dθ sin(θ) + r (θ) cos(θ)
x (θ) = r (θ) cos(θ) ==> dx/dθ = dr/dθ cos(θ) - r (θ) sin(θ)
We're given r (θ) = 1 - sin(θ), so that
dr/dθ = -cos(θ)
Then the slope of the tangent to the curve at P is
dy/dx = (dr/dθ sin(θ) + r (θ) cos(θ)) / (dr/dθ cos(θ) - r (θ) sin(θ))
dy/dx = (-cos(θ) sin(θ) + (1 - sin(θ)) cos(θ)) / (-cos²(θ) - (1 - sin(θ)) sin(θ))
dy/dx = - (cos(θ) - sin(2θ)) / (sin(θ) + cos(2θ))
The tangent is horizontal if dy/dx = 0 (or when the numerator vanishes):
cos(θ) - sin(2θ) = 0
cos(θ) - 2 sin(θ) cos(θ) = 0
cos(θ) (1 - 2 sin(θ)) = 0
cos(θ) = 0 or 1 - 2 sin(θ) = 0
cos(θ) = 0 or sin(θ) = 1/2
[θ = π/2 + 2nπ or θ = 3π/2 + 2nπ] or [θ = π/6 + 2nπ or θ = 5π/6 + 2nπ]
where n is any integer.
In the interval 0 ≤ θ ≤ 2π, we get solutions of θ = π/6, θ = 5π/6, and θ = 3π/2. (We omit π/2 because the denominator is zero at that point and makes dy/dx undefined.) So the points where the tangent is horizontal are themselves (√3/4, 1/4), (-√3/4, 1/4), and (0, -2), respectively.
The tangent is vertical if 1/(dy/dx) = 0 (or when the denominator vanishes):
sin(θ) + cos(2θ) = 0
sin(θ) + (1 - 2 sin²(θ)) = 0
2 sin²(θ) - sin(θ) - 1 = 0
(2 sin(θ) + 1) (sin(θ) - 1) = 0
2 sin(θ) + 1 = 0 or sin(θ) - 1 = 0
sin(θ) = -1/2 or sin(θ) = 1
[θ = 7π/6 + 2nπ or θ = 11π/6 + 2nπ] or [θ = π/2 + 2nπ]
Then for 0 ≤ θ ≤ 2π, the tangent will be vertical for θ = 7π/6 and θ = 11π/6, which correspond respectively to the points (-3√3/4, -3/4) and (3√3/4, -3/4). (Again, we omit π/2 because this makes dy/dx non-existent.)
would someone help me out with this question? I got it wrong the first time but I don't understand how.
Answers:
Choice 2) Angle ABC is bisected by ray BD.
Choice 3) BC = 1/2 AC
Choice 5) 2*(angle DBC) = angle ABC
================================================
Explanation:
Since B is the midpoint of AC, this means that AC is cut in half to form the smaller equal pieces AB and BC
We can then say
AB+BC = AC
BC+BC = AC
2BC = AC
BC = (1/2)*AC
which shows why choice 3 is one of the answers
----------------------
Angle ABD is shown to be 90 degrees. Let's say we didn't know angle DBC is also 90. Lets call it x
(angle ABD) + (angle DBC) = 180
90 + x = 180
x = 180 - 90
x = 90
So angle DBC is also 90.
We can see that the 180 degree angle (ABC) is cut in half into two smaller 90 degree angles (ABD and DBC). Therefore, angle ABC has been cut in half and that's why choice 2 is another answer.
------------------------
Using the angle addition postulate, we know that,
(angle ABD) + (angle DBC) = angle ABC
(angle DBC) + (angle DBC) = angle ABC
2*(angle DBC) = angle ABC
Showing why choice 5 is the third answer.
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Choice 1 isn't true since ray BD helps form angle DBC.
Choice 4 isn't true because there isn't a tickmark on segment BD to indicate it's the same length as BC.
What is y=-2(x+3)^2+2
Answer:
y = -2(x + 3)² + 2
y = 2{ -(x + 3)²+ 1}
y = 2{ -(x² + 6x + 9) + 1}
y = 2{ -x² - 6x - 9 + 1}
y = 2{ -x² - 6x - 8 }
y = -2 { x² + 6x + 8}
OR
y = -2{(x + 4)(x + 2)}
