The triangles shown are similar. Which side of triangle PQR corresponds to side LN in triangle MNL? Triangle L N P. Side L N is 12, N M is 10, M L is 14. Triangle P R Q. Side P R is 28, R Q is 24, Q P is 20. RQ PQ PR LM
Answers
Answer:
The side on triangle PQR that corresponds to side LN in triangle MNL is side QR.
Step-by-step explanation:
Triangle PQR is a dilated version of triangle LMN, specifically a dilation of 2, since LN = 12, the corresponding side to it on triangle PQR is side QR because it is twice as big as side LN, which is the dilation value for converting triangle LMN to triangle PQR.
The side of triangle PQR corresponds to side LN in triangle MNL will be QR.
What are similar triangles?Similar triangle are those which have two pairs of interior corresponding angles are equal or two pairs of corresponding sides are in proportion.
We have,
Two triangles as shown in the given figure,
Now,
Using triangle similarity rule,
i.e.
Sides are in equal proportion,
i.e.
[tex]\frac{LM}{PR} =\frac{MN}{PQ} =\frac{LN}{QR}[/tex]
So,
Put values of sides ,
[tex]\frac{14}{28} =\frac{10}{20} =\frac{12}{24}[/tex]
i.e.
[tex]\frac{1}{2} =\frac{1}{2} =\frac{1}{2}[/tex]
So,
All sides in proportion according to the question,
Now,
The side which is in proportion to side LN is QR.
Hence, we can say that the side of triangle PQR corresponds to side LN in triangle MNL will be QR.
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Related Questions
Which of the following statements is TRUE about rectangle ABDC.
Answers
The statement that is TRUE of the rectangle is AB + BD > AD. Option A
Facts about the rectangleWE have that a diagonal divides the rectangle into two equal triangles
line AD is the length of the diagonal
With the diagonal drawn, we have
AD = hypotenuse
AB and BD are the two other sides
From the Pythagorean theorem, we have that the square root of the square sum of the other two sides fives the hypotenuse. This mean that their sum is greater than the hypotenuse
Thus, the statement that is TRUE is AB + BD > AD. Option A
The complete question is;
Which of the following statements is TRUE about rectangle ABDC.
a. AB + BD > AD
b. AB + BD < AD
c. AB + BD = AD
d. (AB) (BD) = AD
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a green grocer has 180 mangoes to sell. she has to arrange them in piles of 9,10,and 12 mangoes. in which ways would she arrangfe them without a reminder?
Answers
It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.
What are the different ways the mangoes can be arranged?The conditions for mangoes to be arranged are that the piles should have either 9, 10 or 12 mangoes and reminders are not allowed. This means you need to fit all the mangoes and no mangoes can be left.
Based on the conditions and the total number of mangoes (180 mangoes), here are the possibilities that you can determine using division:
9 mangoes piles: 180/ 9 = 20 piles (9 x 20 = 180 with no remainders)10 mangoes piles: 180/10 = 18 piles (10 x 18 = 180 with no remainders)12 mangoes piles: 180/12 = 15 piles (12 x 15 = 180 with no remainders)Learn more about division in https://brainly.com/question/369266
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You are training to compete in a 10-kilometer race, and you know the circular running trail at your park is one mile long. How many times will you need to run this trail in order to run 10 kilometers?
Answers
Answer:
6.2 rounds
Step-by-step explanation:
since 1 kilometer is 0.62 miles
10 kilometers is 6.2 miles
so about 6 and 1/5 rounds
1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find 1) number of student that applaid for all the university
Answers
Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.
We're given the cardinalities of several sets:
• total number of students: [tex]n(U) = 60[/tex]
• A applicants: [tex]n(A) = 30[/tex]
• B applicants: [tex]n(B) = 25[/tex]
• W applicants: [tex]n(W) = 24[/tex]
• A and B applicants: [tex]n(A\cap B) = 11[/tex]
• A and W applicants: [tex]n(A \cap W) = 6[/tex]
• B and W applicants: [tex]n(B\cap W) = 9[/tex]
• non-applicants: [tex]n(U \setminus (A\cup B\cup W)) = 4[/tex]
The last cardinality tells us [tex]n(A\cup B\cup W) = 60-4 = 56[/tex] students applied anywhere at all.
We want to find [tex]n(A\cap B\cap W)[/tex], the number of students that applied to each of the three universities.
By the inclusion/exclusion principle,
[tex]n(A\cup B\cup W) = n(A) + n(B) + n(W) \\\\~~~~~~~~~~~~~~~~~~~~~~~~ - n(A\cap B) - n(A\cap W) - n(B\cap W)\\ \\~~~~~~~~~~~~~~~~~~~~~~~~ + n(A\cap B\cap W)[/tex]
That is, we count up all the students in the sets A, B, and W, then subtract the number of students in each pairwise intersection to not double-count, then add back the number of students in the intersection of all three sets since it was removed in the previous step.
Now solve.
[tex]56 = 30 + 25 + 24 - 11 - 6 - 9 + n(A\cap B\cap W)[/tex]
[tex]\implies n(A\cap B\cap W) = \boxed{3}[/tex]
Plug in different values of h and k to answer the following questions. What happens when h is positive? What happens when h is negative? What happens when k is positive? What happens when k is negative?
Answers
A logarithmic function is the inverse of an exponential function.
What is a logarithmic function?A logarithmic function is the inverse of an exponential function.
Now we have the function;
f(x) = log(x) and the translated function f(x) = log (x-h) + k.
When h is positive, the asymptote moves upwards by the stated amountWhen h is negative , the asymptote moves downwards by the stated amountSimilarly;
When k is positive, the entirety of the graph moves upwardsWhen k is negative , the entirety of the graph moves downwardsLearn more about logarithmic function:https://brainly.com/question/3181916
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Missing parts;
Use the graphing calculator to graph the parent function.
f(x) = log(x)
Add the translated function.
f(x) = log (x-h) + k
Plug in different values of h and k to answer the following questions.
What happens when h is positive?
What happens when h is negative?
What happens when k is positive?
What happens when k is negative?
Answer:
When h is positive: horizontal shift to the right
When h is negative: horizontal shift to the left
When k is positive: vertical shift up
When k is negative: vertical shift down
Step-by-step explanation:
got it right on Edge
Suppose that X is a Bernoulli random variable with success probability 0.8. (Note: If this number is not already rounded to two decimal places, round it to two decimal places before proceeding.)
Calculate the mean of X. Round your answer to two decimal places.
Answers
Reminder I don't know if I'm right, if I'm wrong please tell me. <3
For the piecewise function, find the values g(-1), g(2), and g(5). g(x)= x+4, for x≤2 9-x, for x>2
Answers
Answer:
g(-1) = 3, g(2) = 6, g(5) = 4
Step-by-step explanation:
Please refer to attached photo. (Apologies for the terrible handwriting.)
From here we can see,
g(x) = x + 4 applies for values x less than or equal to 2.
g(x) = 9 - x applies for values x more than 2 (which does not include 2.)
g(-1):
Since -1 < 2,
g(-1) = -1 + 4 = 3
g(2) = 2 + 4 = 6
g(5):
Since 5 > 2,
g(5) = 9 - 5 = 4
The exchange rate in some prehistoric village was 6 jagged rocks for every 2 smooth pebbles. Also, one shiny rock could be traded for 3 smooth pebbles. If Joaquin has 30 jagged rocks, what is the maximum number of shiny rocks he could trade for?
A. 6
B. 4
C. 5
D. 3
Answers
30 Jagged rocks are the same 3 shiny rocks using the exchange rates provided(i.e. option D)
What is an exchange rate?
Exchange rate means the rate at which one item exchanges hands with another, for instance, in this case, 6 jagged rocks are equivalent to 2 smooth pebbles.
6 jagged rocks=2 smooth pebbles
divide both sides by 2
6/2 jagged rocks=2/2 smooth pebbles
3 jagged rocks=1 smooth pebble
We can rewrite as below:
1 jagged rock=1/3 smooth pebble
30jagged rocks=1/3*30 smooth pebbles
30 jagged rocks=10 smooth pebbles
Now we need to convert 10 smooth pebbles to shiny rock equivalence
3 smooth pebbles=1 shiny rock
1 smooth pebble=1/3 shiny rock
10 smooth pebbles=1/3*10 shiny rocks
10 smooth pebbles=3 shiny rocks( even though it is 3.33, but the final answer should be rounded to a whole number)
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Please help. Attached as an image
Answers
Distance formula ds = v(dx² + dy²) s = ? v(1 + (dy/dx)²) dx ......... s = the arc length y = 171 - x²/45
chegg
someone solved it on this
https://youtu.be/UGjXlMVdZvc
2x-y+52=16
X-6у +2z=-9
3x+4y- z=32
Answers
The solution to the given system of equation is (3, 3, 3)
Solving system of equationsGiven the following system of equation expressed as:
2x-y+5z=16
X-6у +2z=-9
3x+4y- z=32
Multiply equation 2 by 2 to have:
2x-y+5z=16
2X-12у +4z=-18
Subtract
10y+z = 34 .........4
Similarly
3X-18у +6z=-27
3x+4y- z=32
Subtract
-22y+7z = -59 ........... 5
Equate 4 and 5
10y+z = 34 .........4 * 7
-22y+7z = -59 ........... 5 * 1
_______________________
70y+7z = 238
-22y+7z = -59
Subtract
92y = 297
y = 3
Recall that
10y+z = 34
10(3) + z = 34
z = 3
Since x - 6y +2z = -9
x-6(3)+2(3) = -9
x - 18 + 6 = -9
x = 3
Hence the solution to the given system of equation is (3, 3, 3)
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find p + q
someone pls help
Answers
Answer:
70
Step-by-step explanation:
45+90=135
180-45=45
q=45
45+65=110
180-110=70
70-45=25
p=25
45+25=70
Answer: 70°
Step-by-step explanation:
We know that the sum of all 3 angles in a triangle is 180°. Hence, we can just set all measures to be equal to 180° and solve for the variables.
Left Triangle[tex]p+65+90=180\\p+155=180\\p=25[/tex]
Right Triangle[tex]45+90+q=180\\135+q=180\\q=45[/tex]
Sum[tex]p+q=25+45=70[/tex]
The sum of p and q is 70°.
A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t3 + 8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 4 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit?
1 thousand
2 thousand
3 thousand
5 thousand
Answers
The quantity of product that would result in the same profit is 1 thousand. Option A
How to determine the function
Given the polynomial function as;
P(t) = –2t³ + 8t² + 2t
Where;
P(t) is the company's profit = $8 milliont is the number of skincare profitLet's equate the values
–2t³ + 8t² + 2t = 8
–2t³ + 8t² + 2t - 8 = 0
Factorize the expression
(-2t³ + 8t²) + ( 2t -8) = 0
- t² ( 2t - 8) + (2t -8) = 0
We take the similar factor
2t - 8 = 0
2t = 8
t = 8/2
t = 4
But we have that the company produced 4 thousand products for $8 million profit, so we have
= 4/ 4
= 1 thousand
Thus, the quantity of product that would result in the same profit is 1 thousand. Option A
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Need help, please.
Quick answer is okay
Answers
Answer:
The answer is choice C from the given alternatives.
You can solve by plugging in values for x and checking their corresponding values of y
The total square footage of your house is 1200 square feet. You want to put new carpet in every room, hallway, and closet, except for the kitchen, dining room and bathroom. If the kitchen is 10 ft by 12 ft and the dining room is 11 ft by 13 ft and the bathroom is 6 ft by 8 ft, how many square feet of carpet do you need for the house?
Answers
The number of square feet of carpet needed for the rooms is 889 ft².
How to find the area of a figure?The total square footage of your house is 1200 square feet.
He wants to put new carpet in all rooms except for the kitchen, dining room and bathroom.
Therefore,
total area = 1200 ft²
Area of the other rooms with no carpet = (10 × 12) + (11 × 13) + (6 × 8)
Area of the other rooms with no carpet = 120 + 143 + 48
Area of the other rooms with no carpet = 311 ft²
Hence, the number of square feet for the house = 1200 - 311 = 889 ft²
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NO LINKS!! Please help me with this problem.
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Information : The given ellipse is a horizontal ellipse, and it's centre lies on origin, as the foci are given on x - axis.
The foci of the ellipse can be written in form :
[tex]\qquad \sf \dashrightarrow \: ( \pm ae , 0)[/tex]
So,
[tex]\qquad \sf \dashrightarrow \: ae = 5[/tex]
and Vertex of the ellipse can be written as
[tex]\qquad \sf \dashrightarrow \: (\pm a,0)[/tex]
so, we get a = 11Now, plug the value in first equation ~
[tex]\qquad \sf \dashrightarrow \: ae = 5[/tex]
[tex]\qquad \sf \dashrightarrow \: 11e = 5[/tex]
[tex]\qquad \sf \dashrightarrow \: e = \cfrac{5}{11} [/tex]
Now, we have to find b (length of semi minor axis)
we can use the formula ~
[tex]\qquad \sf \dashrightarrow \: b {}^{2} = {a}^{2} (1 - {e}^{2} )[/tex]
[tex]\qquad \sf \dashrightarrow \: b {}^{2} = 121(1 - \frac{25}{121} )[/tex]
[tex]\qquad \sf \dashrightarrow \: b {}^{2} = 121( \frac{121 - 25}{121} )[/tex]
[tex]\qquad \sf \dashrightarrow \: b {}^{2} = 96[/tex]
Now, we can write the equation of ellipse as :
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
[ plug the values ]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {121}^{} } + \cfrac{ {y}^{2} }{ {96}^{} } = 1[/tex]
Answer:
[tex]\dfrac{x^2}{121}+\dfrac{y^2}{96}=1[/tex]
Step-by-step explanation:
General equation of an ellipse:
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
where:
center = (h, k)Vertices = (h±a, k) and (h, k±b)Foci = (h±c, k) and (k, h±c) where c²=a²−b²Major Axis: longest diameter of an ellipseMinor Axis: shortest diameter of an ellipseMajor radius: one half of the major axisMinor radius: one half of the minor axisIf a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.
If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.
Given:
foci = (-5, 0) and (5, 0)vertices = (-11, 0) and (11, 0)Therefore, the ellipse is horizontal with its center at (0, 0):
⇒ h = 0 and k = 0
⇒ a = 11
⇒ c = 5
To find b², use c² = a² − b²:
⇒ 5² = 11² − b²
⇒ b² = 11² − 5²
⇒ b² = 96
Therefore, the standard form of the equation of the ellipse is:
[tex]\implies \dfrac{(x-0)^2}{11^2}+\dfrac{(y-0)^2}{96}=1[/tex]
[tex]\implies \dfrac{x^2}{121}+\dfrac{y^2}{96}=1[/tex]
If m4 = 108°, what is the measure of 26?
Answers
Answer:
108
Step-by-step explanation:
When the lines cut through by a transversal are parallel, alternate interior angles are congruent. angle 4 = angle 6 = 108
Carol and Janis decide to sew fancy masks to sell on Etsy. Carol can cut, pin, sew and pack a mask in 30 minutes. Working together they can complete a package in 16 minutes. How long does it take Janis to complete a package alone?
Answers
it would take Janis 14 minutes to complete a package alone
How to determine the valueFrom the information given,
Let's say that
Carol working time = x = 30 minutes
Janis working time = y
x + y = 16 minutes
Let's make 'y' the subject
30 - 16 = y
y= 14 minutes
Thus, it would take Janis 14 minutes to complete a package alone
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Miranda works 25 hours a week at a wage rate of $10. Thus, her total weekly income is $250. On this income, she pays total taxes of $12.50. However, she calculates that on the last hour that she works, she pays $2.50. Miranda average take rate is ___% Miranda marginal tax rate is ___%
Answers
Step-by-step explanation:
Ig by dividing 12.50 and 250
In a stock of 12 blouses, 90 are sleeveless. How many percent of the stock are sleeveless?
Answers
75 percent of the stock are sleeveless
How to determine the percentage?The given parameters are:
Blouse = 120
Sleeveless = 90
The percentage is calculated as:
Percentage = Sleeveless/Blouse * 100%
So, we have:
Percentage = 90/120* 100%
Evaluate the expression
Percentage = 75%
Hence, 75 percent of the stock are sleeveless
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50 POINTS!!! Answer the question well and I will also give Brainliest.
The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. Which conclusion can be made from the given information?
A) The volume of the prism is half the volume of the cylinder.
B) The volume of the prism is twice the volume of the cylinder.
C) The volume of the prism is equal to the volume of the cylinder.
D) The volume of the prism is not equal to the volume of the cylinder.
Answers
Answer:
C) The volume of the prism is equal to the volume of the cylinder.
Step-by-step explanation:
volume of triangular prism = area of base × height
volume of cylinder = area of base × height
The cross sectional area are equal, so the bases have the same area.
The heights are also equal.
The volumes must be equal.
Answer: C) The volume of the prism is equal to the volume of the cylinder.
Answer:
C) The volume of the prism is equal to the volume of the cylinder.
Step-by-step explanation:
If the cross-sectional areas of the triangular prism and the right cylinder are congruent, it means that when you look at their shapes from the top or bottom, they have the same size and shape.
Since both the triangular prism and the right cylinder have a height of 5 units, and their cross-sectional areas are the same, it implies that they have the same volume as well. So, the volume of the triangular prism is equal to the volume of the cylinder.
Please mark me as Brainliest if you're satisfied with this answer
What effect will replacing x with (x - 4)have on the
graph of the equation y = (x - 3)²?
A. slides the graph 4 units up
B. slides the graph 7 units down
OC. slides the graph 4 units right
D. slides the graph 1 unit right
Answers
Answer: D. slides the graph 1 unit right
Step-by-step explanation:
See attached image.
Simplify the expression.
(8+20)÷4+3
Answers
The answer to this problem is 10 because by using order of operations/PEMDAS, we can start the evaluation by solving P, which stands for Parenthesis.
Since 8 + 20 is inside parenthesis, we can start by solving this portion.
8 + 20 = 28
Now, for the next step, we can simplify by plugging 28 into the expression.
28 / 4 + 3
The E in PEMDAS stands for Exponents, but we can skip this step since there are none.
The M in PEMDAS stands for Multiplication, but we can skip this step since there is nothing to multiply.
The D in PEMDAS stands for Division, and there does happen to be division in this expression!
28 / 4 = 7
Now that we have our division portion solved, we can simplify the problem again by plugging 7 into the expression.
7 + 3
Now that we have our final simplification, we can add to get our answer.
7 + 3 = 10
Therefore, your answer is 10.
Your final answer: 10 is your final answer. If you need help, let me know and I will gladly assist you.
4+3=7
28/7= 4
Pls help me i'm stuck
Answers
Answer: [tex]m\angle BAM=30^{\circ}[/tex]
Step-by-step explanation:
[tex]AD=x\sqrt{3}[/tex] (Pythagorean theorem)
[tex]m\angle ACD=60^{\circ}[/tex] (30-60-90 triangle)
[tex]m\angle MCA=30^{\circ}[/tex] (angle subtraction)
[tex]m\angle MAC=30^{\circ}[/tex] (base angles theorem)
[tex]m\angle CAD=30^{\circ}[/tex] (30-60-90 triangle)
[tex]m\angle BAM=30^{\circ}[/tex] (angle subtraction)
Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 17 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.40 gram.
(a)
Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)
lower limit
upper limit
margin of error
(b)
What conditions are necessary for your calculations? (Select all that apply.)
normal distribution of weights
is unknown
uniform distribution of weights
is known
n is large
Correct: Your answer is correct.
(c)
Interpret your results in the context of this problem.
The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.
We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.
We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.
The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.
Correct: Your answer is correct.
(d)
Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.13 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
Incorrect: Your answer is incorrect.
hummingbirds
Answers
a)
E =0.124Lower limit =3.026Upper limit = 3.274b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights
c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on
d) sample size [tex]n \approx 27[/tex].
What conditions are necessary for your calculations?Generally,
Here n = 17
T= 3.15
[tex]\sigma=0.40[/tex]
confidence level =c = 0.80
Here we will usethe z critical value.
z critical value for (1+c) /2 = (1+0.80)/2
z critical value for (1+c) /2= 0.9
Zc = 1.28
Critical value = 1.28
a) Margin of error (E) :
[tex]E = Zc*\frac{\sigma}{\sqrt{n}}\\\\\E = 1.28*\frac{0.40}{\sqrt{17}}[/tex]
E =0.124
Margin of error = E =0.124
Lower limit = x-E
L= 3.15 - 0.124
L= 3.026
Lower limit =3.026
Upper limit = x + E
U= 3.15 + 0.124
U= 3.274
Upper limit = 3.274
The following is a confidence interval with a value of 80 percent for the mean weights of Allen's hummingbirds in the area under study: (3.02,3.28)
b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights
c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on.
d) When is already known, the following equation may be used to determine the appropriate number of samples, n:
[tex]n=(\frac{z_c*\sigma }{E})^2[/tex]
Margin of error = 0.13
Sample size (n):
[tex]n= (\frac{z_c*\sigma }{E})^2[/tex]
[tex]n=(\frac{ 1.28*0.36}{0.09})^2[/tex]
n = 26.21
[tex]n \approx 27[/tex]
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What are the solutions to 4x^3 + 16x^2 + 28x = 0
Answers
Step-by-step explanation:
the third option is the answer.
231 ( 40 + 15 ) = 231 x 40 + ------------ x -----------
which property is this
Answers
Answer:
12705
Step-by-step explanation:
The problem could be solved in two different methods:
1:
231×(55)=12705
2.
231×40+231×15=9240+3465=12705
Your car broke down and it's time to get a new one. You've found just the right one to fit your needs but you want to be sure you are making a good financial decision,
so you ask the lender for an amortization table. What key pieces of information will you be able to see in the amortization table to help you make your decision?
Answers
Answer:
what is the monthly payment or ask for the mileage use for the car
You expect to receive $10,000 at graduation in two years. You plan on investing it at 11% until you have $75,000. How long will you wait from now?
Answers
Answer:
about 19.31 years
Step-by-step explanation:
[tex]10000( {1.11}^{x} ) = 75000[/tex]
[tex] {1.11}^{x} = 7.5[/tex]
[tex]x ln(1.11) = ln(7.5) [/tex]
[tex]x = \frac{ ln(7.5) }{ ln(1.11) } = 19.31[/tex]
The real root of the equation x3 – 7x2 + 15x – 25 = 0 is 5. What are the nonreal roots?
–4i, 4i
2 – 4i, 2 + 4i
1 + 2i, 1 – 2i
–16i, 16i
Answers
Answer:
1±2i.
Step-by-step explanation:
1. if to evaluate the expression given, it can be written
(x-5)(x²-2x+5)=0;
2. where the nonreal roots are 1±2i.
Find f−1(x) for f(x)=15+12x.
Answers
Answer:
[tex]\text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]
Step-by-step explanation:
[tex]\text{f}^{-1}(x)[/tex] is the notation for the inverse of a function.
The inverse of a function is a reflection in the line y = x.
Given function:
[tex]\text{f}(x)=15+12x[/tex]
To find the inverse of the given function:
Step 1
Replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=15+12x[/tex]
Step 2
Rearrange the equation to make x the subject:
[tex]\implies y-15=15+12x-15[/tex]
[tex]\implies y-15=12x[/tex]
[tex]\implies \dfrac{y-15}{12}=\dfrac{12x}{12}[/tex]
[tex]\implies x=\dfrac{y-15}{12}[/tex]
Step 3
Replace x with [tex]\text{f}^{-1}(x)[/tex] and y with x → this is the inverse function:
[tex]\implies \text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]
Step 4 (if necessary)
The domain of the function is the range of the inverse function.
The range of the function is the domain of the inverse function.
Therefore, as the domain and range of the given function are unrestricted, so too are the domain and the range of the inverse function:
Domain: (-∞, ∞) → all real numbersRange: (-∞, ∞) → all real numbersLearn more about inverse functions here:
https://brainly.com/question/16071767
[tex]\\ \rm\leadsto y=15+12x[/tex]
Interchange x and y
[tex]\\ \rm\leadsto x=15+12y[/tex]
Solve for y
[tex]\\ \rm\leadsto 12y=x-15[/tex]
[tex]\\ \rm\leadsto y=\dfrac{x-15}{12}[/tex]
That's the inverse