[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 2x^2+8y^2=16\implies \cfrac{2x^2+8y^2}{16}=1\implies \cfrac{2x^2}{16}+\cfrac{8y^2}{16}=1\implies \cfrac{x^2}{8}+\cfrac{y^2}{2}=1 \\\\\\ \cfrac{(x-0)^2}{(\sqrt{8})^2}+\cfrac{(y-0)^2}{(\sqrt{2})^2}=1\qquad \begin{cases} a=\sqrt{8}\\ b=\sqrt{2}\\ c=\sqrt{a^2-b^2}\\ \qquad \sqrt{6} \end{cases}~\hfill \begin{array}{llll} \stackrel{\textit{vertices}}{(\pm \sqrt{8},0)}\qquad \stackrel{\textit{foci}}{(\pm \sqrt{6},0)}\\\\ ~\hfill \stackrel{\textit{center}}{(0,0)}~\hfill \end{array}[/tex]
Answer:
Step-by-step explanation:
2x² + 8y² = 16
divide both sides of equation by the constant
2x²/16 + 8y²/16 = 16/16
x²/8 + y²/2 = 1
x² has a larger denominator than y², so the ellipse is horizontal.
General equation for a horizontal ellipse:
(x-h)²/a² + (y-k)²/b² = 1
with
a² ≥ b²
center (h,k)
vertices (h±a, k)
co-vertices (h, k±b)
foci (h±c, k), c² = a²-b²
Plug in your equation, x²/8 + y²/2 = 1.
(x-0)²/(2√2)² + (y-0)²/(√2)² = 1
h = k = 0
a = 2√2
b = √2
c² = a²-b² = 6
c = √6
center (0,0)
vertices (0±2√2,0) = (-2√2, 0) and (2√2, 0)
co-vertices (0, 0±√2) = (0, -√2) and (0, √2)
foci (0±√6, 0) = (-√6, 0) and (√6, 0)
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The daily lowest temperature, in degrees Fahrenheit, for a certain week are -2, -3, x, 2x, 4, 8. For the week, the sum of the temperatures was -7°F.What is the value of x?
Answer:
-14/9
Step-by-step explanation:
Combine -2, -3, x, 2x, 4, 8. We get -5 + 3x + 12. This sum is -7.
Solve this equation for x: 3x + 7 = -7, so 3x = -14/3.
Then x is -14/9.
Answer:
-4.7
Step-by-step explanation:
-2 + (-3) + x + 2x + 4 + 8 = -7
-5 + 3x +12 = -7
3x + 7 = -7
3x = -14
x = -14/3 = -4.7 °F
The value of x is -4.7.
Check:
-2 + (-3) + (-4.7) + 2(-4.7) + 4 + 8 = -7
-5 - 4.7 - 9.3 + 12 = -7
-7 = -7
OK
The following chart represents the record high temperatures recorded in Phoenix for April - November. Select the answer below that best describes the mean and median of the data set ( round answers to the nearest tenth)
A. The mean is 114.5F and the median is 111.9F.
B. The mean is 121F and the median is 118.5F.
C. The mean is 111.9F and the median is 114.5F.
D. The mean is 118.5F and the median is 121F
Answer:
C. The mean is 111.9F and the median is 114.5F.
Step-by-step explanation:
The mean is 111.9 given that (105 + 113 + 122 + 121 + 116 + 118 + 107 + 93)/8 = 111.875 which can be rounded to 111.9 F.
Organizing the values we have:
[93, 105, 107, 113, 116, 118, 121, 122]
We find that the median is going to be between 113 and 116. Therefore:
(113 + 116) / 2 = 114,5
Therefore, the correct answer is option C.
The answer would be "C"
mean = 111.9F
median = 114.5F
For the mean, we would add up all the numbers in the data. In this case, we would add...
105 + 113 + 122 + 121 + 116 + 118 + 107 + 93 = 895
Next, we would divide the sum by the number of bars we have in the graph. There are 8 bars in the graph with 8 different temperatures so we would divide 895 by 8 and we will get a quotient of 111.875. 111.875 rounded to the nearest tenths place is 111.9F
For the median, we would first place all the numbers in order from least to greatest.
least to greatest- 93,105,107,113,116,118,121,122
next, we need to find the two middle numbers because there is no middle number in an even set of data.
The two middle numbers in the data set are 113 and 116. The halfway point between 113 and 116 is 114.5 so our median would be 114.5
I know that these answers are correct, but I don't understand how to get it using the De Moivere Theorem. Can someone please explain in detail? Thank you so much!
Step-by-step explanation:
10.
First, convert 1+i from Cartesian to polar.
r = √(1² + 1²)
r = √2
θ = atan(1/1), θ in first quadrant
θ = 45°
Therefore:
(1+i)²⁰ = (√2 (cos 45° + i sin 45°))²⁰
(1+i)²⁰ = 1024 (cos 45° + i sin 45°)²⁰
Now applying the De Moivre theorem:
1024 (cos (20×45°) + i sin (20×45°))
1024 (cos (900°) + i sin (900°))
1024 (-1 + 0)
-1024
11.
Repeat the same steps from Question 10. First, convert to polar:
r = √(1² + (-1)²)
r = √2
θ = atan(-1/1), θ in fourth quadrant
θ = 315°
Therefore:
(1−i)¹⁰ = (√2 (cos 315° + i sin 315°))¹⁰
(1−i)¹⁰ = 32 (cos 315° + i sin 315°)¹⁰
Now applying the De Moivre theorem:
32 (cos (10×315°) + i sin (10×315°))
32 (cos (3150°) + i sin (3150°))
32 (0 − i)
-32i
Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E={2, 4}.
Answer:
0.2
Step-by-step explanation:
we have given sample space = {1,2,3,4,5,6,7,8,9,10}
favorable outcomes E={2,4}
we know that probability is defined as the ratio of favorable otcomes to the sample space
probability [tex]P=\frac{favorable\ outcomes}{ sample\ space }[/tex]
we have favorable outcomes E={2,4} that is favorable outcomes=2
and sample sapce = {1,2,3,4,5,6,7,8,9,10}
so the probability [tex]p=\frac{2}{10}=0.2[/tex]
The probability of event E={2,4} from the sample space S={1,2,3,4,5,6,7,8,9,10} is 1/5 or 20%, calculated by dividing the number of favorable outcomes (2) by the total number of outcomes (10).
Explanation:The student asked to compute the probability of event E={2,4} from a sample space S={1,2,3,4,5,6,7,8,9,10}. Since the outcomes are equally likely, we use the formula for theoretical probability, which is the number of favorable outcomes divided by the total number of possible outcomes in the sample space.
To find P(E), first count the number of outcomes in event E, which includes just 2 and 4. There are two favorable outcomes. The total number of outcomes in the sample space S is 10. Therefore, P(E) equals 2/10 or 1/5 when simplified. This means the probability of event E occurring is 0.20 or 20%.
Determine whether the polygons are similar. If so, identify the correct similarity ratio and the similarity statement. HELP ASAP!!
Answer:
No, the triangles are not similar
Step-by-step explanation:
The (reduced) side length ratios, shortest to longest, are ...
12 : 18 : 20 = 6 : 9 : 10
and
5 : 12 : 13
These are not the same, so the triangles are not similar.
Answer:
The last answer is correct.
Also known as E
Step-by-step explanation:
What polynomial has roots of −6, −4, and 1?
x3 − 9x2 − 22x + 24
x3 − x2 − 26x − 24
x3 + x2 − 26x + 24
x3 + 9x2 + 14x − 24
Answer:
x^3+9x^2+14x-24 has roots of -6,-4 and 1
Option D is correct
Step-by-step explanation:
If the polynomial has roots of -6 -4 and 1
then x=-6, x=-4, x=1
Which can be written as:
(x+6)(x+4)(x-1)
Multiplying we get,
(x+6)(x(x-1)+4(x-1))
(x+6)(x^2-x+4x-4)
(x+6)(x^2+3x-4)
x(x^2+3x-4)+6(x^2+3x-4)
x^3+3x^2-4x+6x^2+18x-24
x^3+3x^2+6x^2-4x+18x-24
x^3+9x^2+14x-24
So, x^3+9x^2+14x-24 has roots of -6,-4 and 1
Option D is correct
Find the distance between the points given
(0, -6) and (9, 6)
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[9-0]^2+[6-(-6)]^2}\implies d=\sqrt{(9-0)^2+(6+6)^2} \\\\\\ d=\sqrt{9^2+12^2}\implies d=\sqrt{225}\implies d=15[/tex]
Which expression is equivalent to (10x)–3?
The given expression evaluates to 1/(1000x^3).
Option (C) is correct.
What are exponents?The exponent of a number of says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.
As per the given data:
The given expression is (10x)^(–3)?
We can write the expression as:
= [tex]\frac{1}{(10x)^3}[/tex]
= [tex]\frac{1}{10^3x^3}[/tex]
= [tex]\frac{1}{1000x^3}[/tex]
= 1/(1000x^3)
Hence, the given expression evaluates to 1/(1000x^3).
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(The given question is incomplete, the complete question is given below)
Which expression is equivalent to (10x)^-3?
a. 10/x^3
b. 1000/x^3
c. 1/(1000x^3)
d. 1/10x^3
Find the value of x that makes a || b
Answer:
15
Step-by-step explanation:
So angle 2 and angle 4 have a relationship that is called same-side interior or consecutive interior angles. The name there depends what class you are in but they mean the same thing.
If you have the transversal goes through parallel lines, then same-side interior angles will add up to 180 degrees.
So you are trying to solve the following equation for x:
angle2+angle4=180
2x+10+4x+80=180
Combine like terms:
6x+90=180
Subtract 90 on both sides:
6x =90
Divide both sides by 6:
x =90/6
Simplify:
x =15
15 is x so that the lines are parallel
Answer:
x = 15°
Step-by-step explanation:
Notice that if A is // to B, then ∠2 and ∠4 are supplementary angles, i.e they add up to 180°. We can write this as:
∠2 + ∠4 = 180
(2x + 10) + (4x + 80) = 180
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 180 - 90
6x = 90
x = 15°
In a given week, it is estimated that the probability of at least one student becoming sick is 17/23. Students become sick independently from one week to the next. Find the probability that there are at least 3 weeks of no sick students before the 2nd week of at least one sick student.
Answer:
0.614
Step-by-step explanation:
Let the time be given by = t
and P(S ) = probability that a person is sick
P(s) = probability that a person is not sick
P(s) = [tex](\frac{17}{23})^{23}* (1-\frac{17}{23})\\[/tex]
Then the probability for that there are at least 3 weeks of no sick students before the 2nd week of at least one sick student is given by:
[tex](\frac{17}{23})(\frac{17}{23})(\frac{17}{23})(\frac{17}{23}) + \frac{6}{23} + 3(\frac{17}{23})^{3}\\ = 0.614[/tex]
HELP!!!!
Select the correct answer.
What is the volume of this cone in terms of ?
Answer:
168.75π cm^3 is your answer.
Volume of a cone is 1/3 πr^2h.
Here, radius is given 7.5cm and height is given 9cm. So by using the formula we get the above answer.
For this case we have that by definition, the volume of a cone is given by:
[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]
Where:
h: It's the height
r: It is the cone radius
According to the data we have:
[tex]h = 9cm\\r = 7.5cm[/tex]
Substituting:
[tex]V = \frac {\pi * (7.5) ^ 2 * 9} {3}\\V = \frac {\pi * 56.25 * 9} {3}\\V = 168.75\pi[/tex]
Thus, the volume of the cone is [tex]168.75 \pi \ cm ^ 3[/tex]
Answer:
Option C
whats the absolute vaule of -1 1/3
Answer:
1 1/3
Step-by-step explanation:
Absolute values are how far away it is from 0, so it is always positive. It is always the positive number of itself, so absolute values of negative numbers are the opposite, and the absolute value of positive numbers and just the same numbers.
Answer:
Step-by-step explanation:
/ -1 1/3/ = -(-11/3) = 11/3
Select the correct answer.
Which table shows a proportional relationship between x and y?
Answer: The answer would be choice C because there is a constant rate of change of 3 :)
Step-by-step explanation:
Answer:
C.Step-by-step explanation:
If x and y are proportional then the ratio y/x is constant.
[tex]A.\\\\\dfrac{4}{2}=2,\ \dfrac{6}{3}=2,\ \dfrac{9}{4}\neq2\\\\B.\\\\\dfrac{4}{3},\ \dfrac{16}{9}\neq\dfrac{4}{3}\\\\C.\\\\\dfrac{12}{4}=3,\ \dfrac{15}{5}=3,\ \dfrac{18}{6}=3\ \qquad\bold{CORRECT}\\\\D.\\\\\dfrac{4}{1}=4,\ \dfrac{8}{2}=4,\ \dfrac{15}{3}=5\neq4[/tex]
A regional soccer tournament has 64 participating teams. In the first round of the tournament, 32 games are played. In each successive round, the number of games played decreases by 1/2. Find a rule for the number of games played in the nth round, then find the total number of games played in the regional soccer tournament.
Answer:
A regional soccer tournament has 64 participating teams.
In the first round of the tournament, 32 games are played.
In each successive round, the number of games played decreases by 1/2.
Part A:
We know;
[tex]a_n=a_1\times r^{n-1}[/tex]
[tex]a_1=32[/tex]
[tex]r=\frac{-1}{2}[/tex]
So, we get;
The rule for the number of games played in the nth round is given by:
[tex]a_n=32(\frac{1}{2})^{n-1}[/tex]
where [tex]1\leq n\leq 6[/tex]
Part B:
As in each successive round the rounds are decreasing by 1/2 we have.
round 1 = 32
round 2 = 16
round 3 = 8
round 4 = 4
round 5 = 2
round 6 = 1
So, the total number of games played in the regional soccer tournament are: [tex]32+16+8+4+2+1=63[/tex]
Answer:
63 games total
Step-by-step explanation:
edge 2021
Find the 6th term in the expansion of (x + 2)9.
Answer:
[tex]4032x^4[/tex]
Step-by-step explanation:
Use the 10th row of Pascal's Triangle to get you where you need to be. You need 10 rows because any polynomial raised to the 9th power has 10 terms. Those 10 terms are, in order:
1, 9, 36, 84, 126, 126, 84, 36, 9, 1
Setting up for the first 6 terms:
[tex]1(x^9)(2^0)+9(x^8)(2^1)+36(x^7)(2^2)+84(x^6)(2^3)+126(x^5)(2^4)+126(x^4)(2^5)+...[/tex]
The 6th term is the last one. It goes on from there, but I stopped at the 6th term, since that is what you need.
Simplifying gives us:
[tex]126(x^4)(32)[/tex]
and multiplying gives us:
[tex]4032x^4[/tex]
The 6th term in the expansion of (x + 2)^9 is calculated using the binomial theorem, with the result being 4032x^4.
Explanation:The 6th term in the expansion of the binomial expression (x + 2)9 is found using Binomial Theorem. The general formula for any term in the expansion of (a + b)^n, where n is a positive integer, is C(n, k) * (a^(n-k)) * (b^k), where C(n, k) is the combination of n items taken k at a time, and k is the term number minus 1.
For the 6th term, k equals 5 (since k = term number -1). By substituting these values into formula, you get: C(9, 5) * (x^(9-5)) * (2^5), which equals 126 * x^4 * 32, or 4032x^4.
So, the 6th term in the expansion of (x + 2)9 is 4032x^4.
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Find the hypotenuse of the triangle. Round your result to two decimal places. Can anybody help me with this??
Answer:
x = 16.49
Step-by-step explanation:
By Pythagorean Formula
8.34² + 14.22² = x²
x² = 69.556 + 202.208
x² = 271.764.
x = √271.764
x = 16.4852
x = 16.49 (rounded to 2 dec. pl)
An vulture is perched 40 ft up in a tree and looks down at an angle of depression of a 35? angle and spots roadkill. How far is the roadkill from the vulture? Round to the nearest tenth
Answer:
69.7 ft
Step-by-step explanation:
we know that
The function sine of angle of 35 degrees is equal to divide the opposite side to the angle of 35 degrees (the height of the vulture in a tree) by the hypotenuse ( the distance from the vulture to the roadkill)
Let
z -----> the distance from the vulture to the roadkill
sin(35°)=40/z
z=40/sin(35°)=69.7 ft
Answer:
69.7 feet.
Step-by-step explanation:
Let x represent the distance between vulture and roadkill.
We have been given that a vulture is perched 40 ft up in a tree and looks down at an angle of depression of a 35 and spots roadkill.
We can see from the attachment that vulture, roadkill and angle of depression forms a right triangle with respect to ground, where, x is hypotenuse and 40 ft is opposite side.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(35^{\circ})=\frac{40}{x}[/tex]
[tex]x=\frac{40}{\text{sin}(35^{\circ})}[/tex]
[tex]x=\frac{40}{0.573576436351}[/tex]
[tex]x=69.7378718[/tex]
[tex]x\approx 69.7[/tex]
Therefore, the roadkill is 69.7 feet away from the vulture.
Sue graphed the formula for converting temperatures from Fahrenheit to Celsius. If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius? 5 degrees Celsius 10 degrees Celsius 15 degrees Celsius 20 degrees Celsius
Answer:
Second Option (10° Celsius)
Step-by-step explanation:
There is a formula to convert the temperature which is in degree Celsius into degree Fahrenheit and vice versa. The formula to convert the temperature in degree Fahrenheit into degree Celsius is:
C° = (F° - 32) * 5/9.
It is given that the temperature is 50° Fahrenheit. Therefore, F° = 50°. Substituting F° = 50° in the formula gives:
C° = (50° - 32) * 5/9.
Further simplification results in:
C° = 18 * 5/9. Therefore, C° = 10°.
So the correct answer is 10° Celsius!!!
Proportions in Triangles
Tom crossed the finish line 3.8 seconds after Steve. Steve finished the race in 45.1 seconds. If t represents Tom's race time, which of the following equations is true?
A. 45.1 – t = 3.8
B. 45.1 + t = 3.8
C. t – 3.8 = 45.1
D. t + 3.8 = 45.1
Answer:
C. t – 3.8 = 45.1
Step-by-step explanation:
Steve's time = 45.1 seconds
Tom finished 3.8 seconds later
So add 3.8 to steve's time to find tom's time (t)
t =s+3.8
t = 45.1 + 3.8
Subtract 3.8 from each side
t -3.8 =45.1 +3.8-3.8
t -3.8 = 45.1
Answer:
Its C.
Step-by-step explanation:
You better give the guy above me brainliest. I got the answer from the king above me
Find the equation for the horizontal line and the vertical line passing through ( − 10 , 7 )
Answer:
Step-by-step explanation:
Horizontal lines have the form " y = " where vertical lines have the form " x = ".
Horizontal lines run parallel to the y = 0 line, the x-axis, so horizontal lines are found in the y coordinate of the point. Therefore, the horizontal line at that point is y = 7.
The vertical lines run parallel to the y-axis, which is the line x = 0. The vertical lines are found then in the x coordinate of the point. Therefore, the vertical line at that point is x = -10
PLEASE HELP ME WITH THIS MATH QUESTION PLEASE FILL ALL BLANKS
Answer:
1/3y-axis(1, -2)Step-by-step explanation:
The length AC is 3, but the corresponding length FD is 1, so the dilation factor is FD/AC = 1/3.
The reflection is a left/right reflection, so it is across a vertical line. We suspect the only vertical line you are interested in is the y-axis. (It could be reflected across x=1/2, and then the only translation would be downward.)
The above transformations will put C' at (1, 0). Since the corresponding point D is at (2, -2), we know it is C' is translated by (1, -2) to get to D.
C' + translation = D
(1, 0) +(1, -2) = (2, -2)
WANT FREE 15 POINTS + BRAINLIEST? ANSWER THIS CORRECTLY AND I GOT YOU
Which statements are true based on the diagram?
Check all that apply.
A. Points A, B, and D are on both planes.
B. Point H is not on plane R.
C. Plane P contains point F.
D. Points C, D, and A are noncollinear.
E. The line containing points F and G is on plane R.
F. The line containing points F and H is on plane R.
Answer:
A. Points A, B, and D are on both planes. B. Point H is not on plane R. D. Points C, D, and A are noncollinear. E. The line containing points F and G is on plane R.Step-by-step explanation:
A. Points A, B, and D are on both planes.
-- true. These points are on the line of intersection of the planes, so are in both planes.
B. Point H is not on plane R.
-- true. Point H is not shown as being on either of the identified planes.
C. Plane P contains point F.
-- false. Point F is shown as being in plane R, not P.
D. Points C, D, and A are noncollinear.
-- true. Point C is not on the line containing points A and D.
E. The line containing points F and G is on plane R.
-- true. F and G are both in plane R, so the line containing them will also be in that plane.
F. The line containing points F and H is on plane R.
-- false. Point H is not in plane R, so will not be on any line in plane R.
The answer to this is a, b, d, e
The graph of f(x) = 2x is shown on the grid.
The graph of g(x) = (1/2)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?
Answer:
see below
Step-by-step explanation:
Oddly enough, it is the one that with f(x) reflected over the y-axis. All points on the graph are mirrored across that axis (x is changed to -x, y is left alone).
When a graph gets reflected over y-axis it means that a horizontal reflection reflects a graph horizontally over the y-axis.
The graph of [tex]f(x) = 2^x[/tex] is shown on the grid.
The graph of [tex]g(x) = (\dfrac{1}{2})^x[/tex] is the graph of f(x) reflected over the y-axis.
For x= 0 , [tex]g(x) = (\dfrac{1}{2})^0=1[/tex]
For x= 1 , [tex]g(x) = (\dfrac{1}{2})^1=\dfrac{1}{2}=0.5[/tex]
For x= 2 , [tex]g(x) = (\dfrac{1}{2})^2=\dfrac{1}{4}=0.25[/tex]
i.e. graph of g(x) passes through (-1,2) , (0,1) , (1,0.5) , (2,0.25)
From all the given graph , the correct graph is shown below .
It is showing the exact mirror-image of the given graph across y-axis and it is passing through the(-1,2) , (0,1) , (1,0.5) , (2,0.25) .
The figures are similar. Find the area.
The area of △ABC is 15 square cm. The height of △ABC is 5 cm and the height of △DEF is 13 cm. Find the area of △DEF. Round to the nearest square cm if necessary.
Answer:
The area of triangle DEF is [tex]101\ cm^{2}[/tex]
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its heights is proportional and this ratio is called the scale factor and the ratio of its areas is equal to the scale factor squared
step 1
Find the scale factor
Let
z ----> the scale factor
[tex]z=\frac{13}{5}[/tex] ----> ratio of its heights
step 2
Find the area of triangle DEF
Let
z ----> the scale factor
x ----> the area of triangle DEF
y ----> the area of triangle ABC
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{13}{5}[/tex]
[tex]y=15\ cm^{2}[/tex]
substitute and solve for x
[tex](\frac{13}{5})^{2}=\frac{x}{15}[/tex]
[tex]x=(\frac{169}{25})(15)[/tex]
[tex]x=101\ cm^{2}[/tex]
Solve: e^2x + 5 = 4
help pls
Answer:
The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex] ⇒ 3rd answer
Step-by-step explanation:
* Lets explain how to solve this problem
- The function f(x) = e^x is called the (natural) exponential function
- The natural logarithm (㏑), or logarithm to base e, is the inverse
function to the natural exponential function
∵ [tex]e^{2x+5}=4[/tex] is an exponential function
∴ We can solve it by using the inverse of e (㏑)
- Remember:
# [tex]ln(e)=1[/tex]
# [tex]ln(e^{m})=m(ln(e))=m[/tex]
- Insert ln in both sides
∴ [tex]ln(e^{2x+5})=ln(4)[/tex]
∵ [tex]ln(e^{2x+5})=(2x+5)ln(e)=2x+5[/tex]
∴ 2x + 5 = ㏑(4)
- Subtract 5 from both sides
∴ 2x = ㏑(4) - 5
- Divide both sides by 2 to find x
∴ [tex]x=\frac{ln(4)-5}{2}[/tex]
* The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex]
Answer:
Answer is C on edge
Step-by-step explanation:
x= (ln 4)- 5/2
Sanjeet paid $32.85 for a file and 3 identical pens.Leon paid $83.50 for 2 such files and 8 such pens.Find the cost of 1 pen.How do you do it?Help pls.
Answer:
Step-by-step explanation:
Let f and p represent the costs of a file and a pen, respectively. The two purchases are ...
f +3p = 32.85
2f +8p = 83.50
Subtracting twice the first equation from the second gives an equation for the cost of pens:
(2f +8p) -2(f +3p) = (83.50) -2(32.85)
2p = 17.80 . . . . simplify
p = 8.90 . . . . . . divide by 2
The cost of one pen is $8.90.
_____
Comment on "how do you do it?"
You are given two purchases related to the costs of two items. Write equations that describe the purchases. (The total cost is sum of the costs of each of the items, which will be the product of the number of items and the cost of each. You have been shopping, so you know this.)
Once you have a "system of equations", there are many ways they can be solved. You are usually instructed on "elimination" and "substitution" as methods of solution. Above, we used "elimination" to eliminate the "f" variable and give an equation only in "p".
The distribution of heights of women for a certain country is approximately Normal, with a mean of 63.6 inches and a standard deviation of 2.8 inches. How tall are the shortest 15% of all women in this country?
Answer: 66.50 inches
Step-by-step explanation:
Given : The distribution of heights of women for a certain country is approximately Normal with ,
[tex]\mu=\text{63.6 inches }\\\\\sigma=\text{2.8 inches}[/tex]
To find the height of the shortest 15% of all women, first we need to find the z-score corresponding to the p-value 0.15 from the standard normal distribution table, we get 1.0364.
Let x be the random variable that represents the height of the randomly selected woman.
Then[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]1.0364=\dfrac{x-63.6}{2.8}\\\\\Rightarrow\ x=2.8\times1.0364+63.6\\\\\Rightarrow\ x=66.50192\approx66.50[/tex]
Hence, the height of the shortest 15% of all women in this country =66.50 inches.
B= [2 8] A= [3 0]
6 3 2 -1
What is the BA
Answer:
[tex]\text{C.}\quad\left[\begin{array}{cc}22&-8\\7.8&-3\end{array}\right][/tex]
Step-by-step explanation:
It is convenient to let a spreadsheet or calculator do the tedious sum of products. Term C22 will be B21·A12 +B22·A22 = 0.6·0 +3·(-1) = -3, for example. Other terms are similarly computed. In general Crc will be the sum of Brx·Axc, where x = 1 or 2.
[tex]BA=\begin{bmatrix}2 & 8 \\0.6 & 3\end{bmatrix}\cdot \begin{bmatrix}3 & 0 \\2 & -1\end{bmatrix}\\BA=\begin{bmatrix}2\cdot3+8\cdot2 & 2\cdot0+8\cdot(-1) \\0.6\cdot3+3\cdot2 & 0.6\cdot 0+3\cdot(-1)\end{bmatrix}\\BA=\begin{bmatrix}22 & -8 \\7.8 & -3\end{bmatrix}[/tex]