Answer:
(z+2)(z+3)(x-8)
Step-by-step explanation:
z² + 5z + 6 can be factored into (z+3)(z+2)
zx + 2x − 8z-16 can be factored into (x-8)(z+2)
the LCM would be (z+2)(z+3)(x-8)
if you were to multiply the two expressions together, you would multiply (z+2)^2, which is not necessary for LCM, which is why you factor them first
evaluate this piecewise function at x= -6 and x=2
The values of the piecewise function are f(-6) = 6 and f(2) = 1
How to evaluate the function?The complete question is in the attached image.
The value x = -6 is in the domain: -8 <= x < 1
The function at this domain is:
f(x) = |x|
So, we have:
f(-6) = |-6|
Evaluate
f(-6) = 6
Also, we have:
The value x = 2 is in the domain: x >= 1
The function at this domain is:
f(x) = 3
So, we have:
f(2) = 1
Hence, the values of the piecewise function are f(-6) = 6 and f(2) = 1
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Question 1 of 10
The Quadratic Formula gives which roots for the equation 2x²+x-6=0?
Answer:
x=-3/2 or-2
Step-by-step explanation:
hope this helps
Please solve this❣️
Answer:
f⁻¹(1/5) = 2
Explanation:
If f(x) = (2x -3)/5
To find inverse of f(x), make x the subject.
[tex]f(x) = \dfrac{2x - 3}{5}[/tex]
[tex]5 f(x) = 2x - 3[/tex]
[tex]2x = 5 f(x) + 3[/tex]
[tex]x = \dfrac{5 f(x) + 3}{2}[/tex]
Then,
[tex]f^{-1}(x) = \dfrac{5x+3}{2}[/tex]
To find f⁻¹(1/5), simplify insert [x = 1/5 or 0.2]
[tex]f^{-1}(0.2) = \dfrac{5(0.2)+3}{2}[/tex]
which yields
[tex]f^{-1}(0.2) = 2[/tex]
Which of the following shows the simplified form of sin x/1+cos x
O sin x- tan x
O sin x-cot x
O csc x-cot x
01
Answer:
csc x - cot x
Step-by-step explanation:
(sinx)/(1+cos x)
Multiplying the numerator and denominator by (1-cos x),
((sinx)(1-cos x))/(1-cos² x)
((sinx)(1-cosx))(sin²x)
(1-cosx)/(sinx)
cscx - cot x
Write the number in numerical form-twenty-six thousandths
What is the equation of the graph below?
Answer:
A
Step-by-step explanation:
what is the reminder when X³ +4X² - 2X + I is divided by X + 1 what is the reminder when X³ + 4X² - 2X + I is divided by X + 1
Answer:
6
Step-by-step explanation:
Simplify the following.
7² =
4⁰ =
6-¹=
Answer:
49
1
1/6
Step-by-step explanation:
7^2 is just 7 * 7 = 49
4^0 = 1, since anything to the power of 0, is 1.
[tex]6^{-1}[/tex] is equal to [tex]\frac{1}{6}[/tex] since [tex](\frac{a}{b})^{-x}=(\frac{b}{a})^x=\frac{b^x}{a^x}[/tex]. Whenever you have a negative exponent, you flip the fraction, in this case the fraction is 6/1 so it becomes 1/6. then distribute the exponent across the division and you get 1^1/6^1 which is just 1/6
Answer:
491Step-by-step explanation:
hey
please like my question
Shania owns a gym for women clients. She advertises that women can lose 1/2 pound per week by visiting her gym 3 times a week. If this is the case, how many pounds can women lose in a month?
(4 wks/mo)(1/2 lb/wk) = 2 lb/mo
(4_1/3 wks/mo)(1/2 lb/wk) = 2.17 lb/mo
Women who visit Shania's gym three times per week have the ability to drop two pounds in a month.
If women visit Shania's gym three times a week and can lose 1/2 pound per week, we can calculate how many pounds they can lose in a month (assuming a month has four weeks on average).
The rate of weight loss is 1/2 pound per week. So in one month, which is four weeks, the weight loss would be:
Weight loss per week × Number of weeks in a month = (1/2) × 4 = 2 pounds
Therefore, women visiting Shania's gym three times a week can potentially lose 2 pounds in a month.
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do synethtic wig curls only come out if you put heat on it Answer Asap for brainlist
Answer:
. It will curl without heat. You Never attempt to use hot tools, like a curling iron, on a synthetic wig – unless the label specifically says that the wig can tolerate heat. If not, you can use foam rollers to curl the wig using the method below.
Step-by-step explanation:
Answer:
Yes, it is possible to curl a synthetic wig. But you should never attempt to use hot tools, like a curling iron, on a synthetic wig, unless the label specifically says that the wig can tolerate heat. If not, you can use foam rollers to curl the wig.
A 4-sided dice is rolled. The set of equally likely outcomes is {1,2,3,4}. Find the probability of rolling a number less than 14
The probability of rolling a number less than 14 is?
The probability of rolling a number less than 14 among {1,2,3,4} is 1.
Given The dice is 4 sided. Likely outcomes is {1,2,3,4} and we have to find the probability of rolling a number less than 4.
Probability is the likeliness of happening an event among all the events possible. The value of probability cannot be negative or greater than 1. It lies between 0 to 1. The formula of calculating probability is:
Probability= number of events/ total number of events.
Total likely outcomes=4 {1,2,3,4}
Numbers less than 14 = 4
Probability of rolling a number less than 14=1/4
=0.25 because all number less than 14 is present.
1,2,3,4 are all less than 14.
and because all numbers are included that's why the value of probability is 1.
Hence the probability of rolling a number less than 14 is 1.
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In a country 55% of the male population has houses in cities while 30% have houses both in cities and in villages . Find the percentage of the population that has houses only in villages.
15%
{100-(55+30)}%
={100-(85)}%
=15%
The actual length of the ship is 575 feet. The scale of the model is 1 inch: 25 feet. What will be the length of the model?
The length of the model as described in the task content would be; 23 inches.
What is the length of the model?According to the task content, it follows that for every 25 feet measure of the actual ship length, the representation is 1 inch on the model.
On this note, for 575 feet length of the actual ship, the length of the model is; 575/25 = 23 inch.
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A body of mass 50 kg explodes and splits into three pieces. The first piece has a mass of 10 kg and a velocity of [-3,2] m/s, the second piece has a mass of 18 kg and a velocity of [5,-4]m/s. What is the velocity of the third piece?
Step-by-step explanation:
From the conversation of angular momentum
Initial momentum=final momentum
Here,
Since body is initially resting, it's momentum must be zero.
Let v be velocity of third piece. Then
0= 10(-3i+2j) + 18(5i-4j) + 22v
Solving this we get,
v= 4/22(15i+13j).
The velocity of third piece is 2/11(13 j - 15i)
What is velocity?Velocity defines the direction of the movement of the body or the object.
Given:
As the body is at rest so the initial momentum is zero.
Let v be velocity of third piece.
so,
0= 10(-3i+2j) + 18(5i-4j) + 22v
0= -30i + 20j + 90i -72j + 22 v
0= 60i - 52j + 22 v
-60i +52j = 22v
v= 2/11( 13j - 15 i)
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Write the equation of a sine or cosine function to describe the graph.
Answer:
y = cos(3/2x)
Step-by-step explanation:
A general sine or cosine function will have parameters of amplitude, vertical and horizontal offset, and period. The values of these parameters can be determined from the given graph.
y = A·cos(2π(x -B)/P) +C
where A is the amplitude, B and C are the horizontal and vertical offsets, and P is the period.
AmplitudeFor sine and cosine functions, the amplitude of the function is half the difference between the maximum and minimum:
A = (3 -1)/2 = 1
Horizontal offsetA sine function has its first rising zero-crossing at x=0. A cosine has its first peak at x=0. The given graph has its first peak at x=0, so it is a cosine function with no horizontal offset.
B = 0
Vertical offsetFor sine and cosine functions, the vertical offset is the average of the maximum and minimum values:
C = (3 +1)/2 = 2
PeriodThe period is the difference in x-values between points where the function starts to repeat itself. Here, we can use the peaks to identify the period as 4π/3.
P = 4π/3
Function equationUsing the parameter values we determined, the function can be written as ...
y = cos(3/2x) +2
__
Additional comment
The argument of the cosine function is ...
[tex]\dfrac{2\pi(x-B)}{P}=\dfrac{2\pi(x-0)}{\dfrac{4\pi}{3}}=\dfrac{3(2\pi)}{4\pi}x=\dfrac{3}{2}x[/tex]
Halfway through the season, a soccer player has made 12 penalty kicks in 18 attempts.
Based on her performance to date, what is the relative frequency probability that she will miss
her next penalty kick?
Answer:
21
Step-by-step explanation:
18÷6=3 attemps
13÷6=2 makes
she will probably missed I next 3rd pe alty kick
21st attempts
In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 73.5 grams.
I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.
Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?
%
The sum of two numbers is 32. One number is 3 times the other. Find the numbers.
The numbers whose sum is 32 in which one number is 3 times the other is 8 and 24 respectively.
Equation of the unknownLet
x = one of the unknowns3x = second unknownx + 3x = 32
4x = 32
x = 32/4
x = 8
So,
3x = second unknown
= 3(8)
= 24
Check:
x + 3x = 32
8 + 24 = 32
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Solution
We are given two endpoints here
Point 1: (−1, Answer
)
Point 2: ( Answer
,4)
We know our rise between the two points is 1. So
12= Answer
And our run between the two points is 4. So
42= Answer
We now have rise2+run2=distance2, so we have
1+16=distance2
Answer
=distance2
So once we take the square root of both sides we have
distance=√ Answer
We could also use the actual distance formula we developed to get the same answer.
d=(4−3)2+(−5−(−1)2)−−−−−−−−−−−−−−−−−−−√
d=(12+(−4)2)−−−−−−−−−−√
d=(1+16)−−−−−−−√
d=√ Answer
The distance between the two points on the plane is √17
Distance between two pointsThe formula for calculating the distance between two points is expressed as;
D = √(x2-x1)²+(y2-y1)²
From the given plane, we have the following coordinates
(-5, 4) and (-1, 3)
Substitute
D = √(3-4)²+(-1-(-5))²
D = √(-1)²+(4)²
D= √1+16
D=√17
Hence the distance between the two points on the plane is √17
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Mr. Parks begins to fill a large container with water for the dunk tank at the school
fair before asking Brian to finish the job. The container has 25 gallons of water in it
before Brian uses a hose to finish filling it up. The container fills at a rate of 10
gallons per minute. Suppose that y is the amount of water in the tank after x
minutes. Which equation could be graphed to help Brian find out how much water is
in the tank at any time?
y = 25x + 10
y= 10x + 25
y= 10x - 25
y = 10x
Answer:
The answer is B / y= 10x+25
Step-by-step explanation:
your welcome
A Bus begins its trip with R occupants (including the driver).At each of the 20 stops three people get on and no one leaves if there are three times as many boss occupants at the end of the 20th stop as there are at the end of the fourth stop how many occupants did the bus have immediately after the 10th stop?Pls explain for brainlest
A.12
B.24
C.30
D.42
Answer
D.42
Step-by-step explanation:
It's pretty easy and hard at the same time just do not overthink it. Obviously, the bus leaves with R occupants including the driver but that still means that there are occupants, to begin with. Now remembering that 3 people get on each stop you can take it to multiply 3*10 (3 people, ten stops) you would get thirty. Would this be the answer? NO! Remember that you began with R occupants to begin with and either using the process of elimination or common sense you can conclude that 12,24 are improbable answers because they are lower than thirty, and what about thirty? No, because you had thirty people in addition to the original occupants so that eliminates thirty. What's left?
42
There Is Your Answer
Answer:
D. 42================
GivenThe bus has initially R occupants,At each stop the occupants increase by 3,After 20 stops there are 3 times more occupants than after 4 stops.To findThe number of occupants after 10 stopsSolutionLet's find out the how many occupants are there after 20 and 4 stops, then compare:
After 20 stops:
R + 3*20 = R + 60After 4 stops:
R + 3*4 = R + 12Compare and solve for R:
R + 60 = 3(R + 12)R + 60 = 3R + 363R - R = 60 - 362R = 24R = 12We found the number of initial occupants.
Use this to find the number of occupants after 10 stops:
12 + 3*10 = 12 + 30 = 42Correct answer choice is D.
Whats the correct answer answer asap for brainlist
Answer:
option C: Asian
explanation:
Asian countries, such as China, produce goods like the European products, but for much cheaper prices.
9. The measure of each exterior angle of a regular pentagon is
the measure of each exterior
angle of a regular nonagon.
Answer:
55,55
Step-by-step explanation:
hereakaigdidjuwjapwwjshd
The cleaning service requires $39 in variable costs for cleaning materials. The fixed costs of labor, the company's truck, and administrative support are $349,200 per year. Chimneysweep averages 200 service calls per month. What is the average cost per cleaning service call?
The average cost per cleaning service call charge by the company is $184.5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the total cost for x number of service calls in a year. Hence:
y = 39x + 349200
For 200 service call, in a year, x = 200 * 12 = 2400
y = 39(2400) + 349200 = $442800
Average cost = $442800 / 2400 = 184.5
The average cost per cleaning service call charge by the company is $184.5.
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The average student loan debt for college graduates is $25,150.
Suppose that that distribution is normal and that the standard deviation
is $12,050. Let X = the student loan debt of a randomly selected college
graduate. Round all probabilities to 4 decimal places and all dollar
answers to the nearest dollar.
a. What is the distribution of X? X - N
b Find the probability that the college graduate has between $14,200
and $33,950 in student loan debt.
c. The middle 10% of college graduates' loan debt lies between what
two numbers?
Low: $
High: $
Using the normal distribution, it is found that:
a) [tex]X \approx N(25150, 12050)[/tex]
b) There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.
c) Low: $23,519.65, High: $26,580.35.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 25150, \sigma = 12050[/tex].
Hence the distribution of X can be described as follows:
[tex]X \approx N(25150, 12050)[/tex]
The probability that the college graduate has between $14,200 and $33,950 in student loan debt is the p-value of Z when X = 33950 subtracted by the p-value of Z when X = 14200, hence:
X = 33950:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33950 - 25150}{12050}[/tex]
Z = 0.73
Z = 0.73 has a p-value of 0.7673.
X = 14200:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14200 - 25150}{12050}[/tex]
Z = -0.91
Z = -0.91 has a p-value of 0.1814.
0.7673 - 0.1814 = 0.5859.
There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.
Considering the symmetry of the normal distribution, the middle 10% is between the 45th percentile(X when Z = -0.127) and the 55th percentile(X when Z = 0.127), hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.127 = \frac{X - 25150}{12050}[/tex]
X - 25150 = -0.127(12050)
X = $23,519.65.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.127 = \frac{X - 25150}{12050}[/tex]
X - 25150 = 0.127(12050)
X = $26,580.35.
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ch circle shows AB that measures 60°?
O
60⁰ -0
A
60°
B
60°
.0
Mark this and return
B
B
Save and Exit
Next
Submit
Step-by-step explanation:
there are a lot of typos and missing info in your problem and answer option definition.
based on what I understood the answer should be
"the second answer option".
this is where A and B have an arc angle (or inner angle at the center of the circle) of 60°.
one could see the 3rd answer to be right too, as the angle between A and B at Y is also 60°.
but I don't think this is really the meaning of this question here.
A group of friends was working on a student film that had a budget of $700. They used $658 of their budget on costumes. What percentage of their total budget did they spend on costumes?
[tex]\huge\boxed{94\%}[/tex]
Simply use division to solve this problem.
[tex]\dfrac{\$658}{\$700}=0.94[/tex]
Now, multiply this by 100 to get a percentage.
[tex]0.94=\large\boxed{94\%}[/tex]
Calculus help please 10 points for 18&19
thanks!
First function - The function is not continous on [0, 5] because h(5) is not defined.
Second function - There are no discontinuities.
How to determine the continuity of a function
In this problem we have two functions, whose continuity has to be checked. The first equation is a rational function and the second one is a polynomic function. There is a discontinuity in a function f at a given point if and only if the function evaluated at such point does not exist.
The discontinuities of rational functions are those x-values such that the denominator equals zero. The first function is defined for the interval [0, 5] and it is continuous if the function exists for all value of the interval. Thus:
5 - x = 0
x = 5
The rational function has a discontinuity at x = 5. The function is not continous on [0, 5] because h(5) is not defined. (Correct choice: C)
In accordance to algebra, polynomic functions are continuous as there exist a result for all value of x. There are no discontinuities.
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Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H=60 and from a second position L=30 farther along this path it is B=50 What is the height of the tree?
The height of the tree based on the information is 229.23.
How to calculate the height?Based on the information given,
tan 50 = h/x + 60
h = (x + 60)tan 50°
x tan 60 = (x + 60)tan 50°
x(tan 60° - ta 50°) = 60 ta 60
x = 132.34
Therefore, the height will be:
= x tan60°
= 132.34 × tan 60
= 229.23
Therefore, the height is 229.23.
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Which of these is an exponential parent function? OA. f(x)=2x-2 OB. f(x) = 2x C. f(x) = 2x + 3 OD. f(x) = 24x
The answer to this question is choice B