Answer:
4.382 cubiti
Step-by-step explanation:
That's a simple exercise of cross-multiplication:
[tex]\frac{x}{1.95} = \frac{1}{0.445}[/tex]
x being the measure in cubitus we're looking for. We can isolate it:
x = (1.95 m * 1 ) / (0.445 m/cubitus) = 4.382 cubiti
1.95 m = 4.382 cubiti
Which totally makes sense... since a cubitus is roughly half a meter long... and the basketball is 2 meters high... so there are roughly 4 cubiti in 2 meters.
The height of the basketball forward in cubiti is approximately 4.38.
To convert the height from meters to cubiti, we use the conversion factor provided in the question:
1 cubitus = 0.445 m
Given the height of the basketball forward is 1.95 m, we divide this value by the conversion factor to find the height in cubiti:
Height in cubiti = Height in meters / Conversion factor
Height in cubiti = 1.95 m / 0.445 m/cubitus
Now, we perform the division:
Height in cubiti ≈ 4.38 cubiti
Since the value of 1 cubitus is considered to be exact, the number of significant figures in the answer is determined by the height in meters, which is 1.95 m (three significant figures). Therefore, the answer is rounded to three significant figures as well.
please help
must show work
number 6
and
number8
Answer:
6 is -3
8 is -5
Step-by-step explanation:
This problem has been solved!See the answerVerify that the line intergral and the surface integral of Stokes Theorem are equal for the following vector field, surface S and closed curve C. Assume that C has counterclockwise orientation and S has a consistent orientation.F= < x,y,z>; S is the paraboloid z = 13 - x^2 - y^2, for 0 less than or equal z less than or equal 13 and C is the circle x^2 + y^2 = 13 in the xy plane.
Line integral: Parameterize [tex]C[/tex] by
[tex]\vec r(t)=\langle\sqrt{13}\cos t,\sqrt{13}\sin t,0\rangle[/tex]
with [tex]0\le t\le2\pi[/tex]. Then
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle\sqrt{13}\cos t,\sqrt{13}\sin t,0\rangle\cdot\langle-\sqrt{13}\sin t,\sqrt{13}\cos t,0\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}0\,\mathrm dt=\boxed 0[/tex]
Surface integral: By Stokes' theorem, the line integral of [tex]\vec F[/tex] over [tex]C[/tex] is equivalent to the surface integral of the curl of [tex]\vec F[/tex] over [tex]S[/tex]:
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S[/tex]
The curl of [tex]\langle x,y,z\rangle[/tex] is 0, so the value of the surface integral is 0, as expected.
A magazine has a total readership of 750,000; 65 percent of readers report seeing a company's advertisement in one issue. The cost of the ad was $97,500. Calculate the cost per customer.
Answer:
$0.20
Step-by-step explanation:
Cost per customer is cost divided by the number of customers:
cost/customer = $97,500/(0.65·750000) = $0.20
The cost per customer is 20¢.
"Find four numbers proportional to the numbers 2, 4, 5, and 6 if the difference between the sum of the two last numbers and the sum of the first two numbers is equal to 4.8."
Answer:
1.92, 3.84, 4.8, 5.76
Step-by-step explanation:
In the given set, the sum of the last two numbers is 5+6 = 11; the sum of the first two numbers is 2+4 = 6. The difference between these sums is 11-6 = 5.
You want to scale all the numbers by a factor of 4.8/5 = 0.96 so that the difference computed the same way is 4.8 instead of 5.
Then the numbers are ...
0.96{2, 4, 5, 6} = {1.92, 3.84, 4.8, 5.76}
Answer:
[tex]\boxed{\text{1.92, 3.84, 4.80, and 5.76}}[/tex]
Step-by-step explanation:
The numbers must be in the ratio 2:4:5:6.
Let's call them 2x, 4x, 5x, and 6x. Then
5x + 6x = 11x = sum of last two numbers
2x + 4x = 6x = sum of first two numbers
According to the condition,
11x – 6x = 4.8
5x = 4.8
x = 0.96
2x = 1.92; 4x = 3.84; 5x = 4.80; 6x = 5.76
The numbers are [tex]\boxed{\textbf{1.92, 3.84, 4.80, and 5.76}}[/tex]
Check:
(4.80 + 5.76) – (1.92 + 3.84) = 4.8
10.56 – 5.76 = 4.8
4.8 = 4.8
OK.
The math problem is 3x - 7 > 5 = 4 so is x greater than 4?
Answer:
yes, x > 4
Step-by-step explanation:
Add 7 to your inequality to get ...
3x > 12
Then divide by 3, and you have ...
x > 4
_____
We're not understanding the meaning of your " = 4" in the problem statement. It appears to have no place, either in the problem or in the solution.
Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. The area of the reduced photo is 64 square inches. In the equation (x – 3)2 = 64, x represents the side measure of the original photo.
What were the dimensions of the original photo?
11 inches by 11 inches
5 inches by 5 inches
3 + inches by 3 + inches
3 inches by 3 inches
Answer:
11 inches by 11 inches
Step-by-step explanation:
The dimensions of the original photo were 11 inches by 11 inches.
We are informed that the area of the reduced photo is 64 square inches and that In the equation (x – 3)^2 = 64, x represents the side measure of the original photo.
In order to solve for x, we shall first take square roots on both sides of the equation;
The square root of (x – 3)^2 is simply (x - 3).
The square root of 64 is ±8 but we ignore -8 since the dimensions of any figure must be positive.
Therefore, we have the following equation;
x - 3 = 8
x = 8 + 3
x = 11
Answer:
Option 1: 11 inches by 11 inches
Step-by-step explanation:
(a) What is a sequence? A sequence is an unordered list of numbers. A sequence is the sum of an ordered list of numbers. A sequence is an ordered list of numbers. A sequence is the sum of an unordered list of numbers. A sequence is the product of an ordered list of numbers. (b) What does it mean to say that lim n → ∞ an = 8? The terms an approach 8 as n becomes large. The terms an approach 8 as n becomes small. The terms an approach infinity as n become large. The terms an approach -infinity as 8 approaches n. The terms an approach infinity as 8 approaches n. (c) What does it mean to say that lim n → ∞ an = ∞? The terms an become large as n becomes large. The terms an become large as n becomes small. The terms an approach zero as n becomes large. The terms an become small as n becomes small. The terms an become small as n becomes large.
Step-by-step explanation:
A sequence is an ordered list of numbers.
lim n → ∞ an = 8 means that as n approaches infinity (becomes large), an approaches 8.
lim n → ∞ an = ∞ means that as n approaches infinity (becomes large), an approaches infinity (becomes large).
A sequence is an ordered list of numbers, and when lim n → ∞ an = 8, it means the sequence's terms approach 8 as n becomes large. Saying lim n → ∞ an = ∞ indicates that the sequence's terms grow without bound as n increases.
Explanation:Answering your questions on sequences and limits:
(a) What is a sequence?
A sequence is an ordered list of numbers. Unlike a set where the order of elements does not matter, in a sequence, every number has a distinct place. For instance, the sequence of natural numbers is an ordered list starting from 1 and proceeding indefinitely in the order 1, 2, 3, 4, ... etc.
(b) What does it mean to say that lim n → ∞ an = 8?
This statement means that the terms an approach 8 as n becomes large. In other words, as you progress further along in the sequence, the values of the terms get closer and closer to 8, virtually reaching 8 as the sequence goes towards infinity. This is a fundamental concept in understanding sequences' behavior at their extremities.
(c) What does it mean to say that lim n → ∞ an = ∞?
This implies that the terms an become large as n becomes large. As the n value increases, the sequence's terms grow unlimitedly, indicating the sequence's divergence rather than converging to a definite number.
Determine which equation is belongs to the graph of the limacon curve below.
[-5,5] by [-5,5]
a. r= 4 + cose
b. r= 2 + 3 cose
c. r= 3 + 2 cose
d. r= 2 + 2 cose
Answer:
c. 3 + 2 cosθ
Step-by-step explanation:
a = 3, b = 2
Since a > b, 1 < [tex]\frac{3}{2}[/tex] <2
we get a dimpled limacon.
Answer:
Correct option is C ) [tex]r=3+2\,cos\theta[/tex]
Step-by-step explanation:
Limacons are polar functions of the type:
[tex]r=a\pm\,b\,cos\theta[/tex]
[tex]r=a\pm\,b\,sin\theta[/tex]
Where [tex]|\frac{a}{b}|<1\,or\,1<|\frac{a}{b}|<2\,or\,|\frac{a}{b}|$\geq$2[/tex]
In provided options part (a) and (d) constants 'a' and 'b' does not satisfied the condition,
in part (b) and (c) both satisfies the condition but in part (b) we get loop inside the sketch.
so, [tex]r=3+2\,cos\theta[/tex] satisfies the condition of graph.
hence correct option is c ) [tex]r=3+2\,cos\theta[/tex] .
The greater of two consecutive integers is 7 less than one-third the smaller integer. Find the integers and show your work.
Answer:
{-12, -11}
Step-by-step explanation:
Let x represent the smaller of the two integers. The problem statement tells us ...
x +1 = (1/3)x -7
(2/3)x = -8 . . . . . . subtract 1/3x +1
x = -12 . . . . . . . . . multiply by 3/2
The integers are -12 and -11.
Final answer:
To find two consecutive integers where the greater is 7 less than one-third the smaller, we defined the smaller integer as x and set up an equation: x + 1 = (x/3) - 7. Solving through algebraic operations, we found the integers to be -12 and -11.
Explanation:
To solve for two consecutive integers where the greater is 7 less than one-third the smaller integer, let us denote the smaller integer as x and the greater as x + 1. According to the problem, the greater integer (x + 1) is 7 less than one-third the smaller integer (x/3). Thus, we can set up the equation:
x + 1 = (x/3) - 7
To solve for x, we perform the following steps:
Multiply all terms by 3 to eliminate the fraction: 3(x + 1) = x - 21.
Distribute the 3: 3x + 3 = x - 21.
Combine like terms: 2x = -24.
Divide both sides by 2: x = -12.
Now that we have found the smaller integer to be -12, the greater integer is just one more, so it is -11.
Therefore, the two consecutive integers are -12 and -11.
Show that if X ∼ Geom(p) then P(X = n + k|X > n) = P(X = k), for every n, k ≥ 1. This one of the ways to define the memoryless property of the geometric distribution. It states the following: given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.
Since [tex]X\sim\mathrm{Geom}(p)[/tex], [tex]X[/tex] has PMF
[tex]P(X=x)=\begin{cases}(1-p)^{x-1}p&\text{for }x\in\{1,2,3,\ldots\}\\0&\text{otherwise}\end{cases}[/tex]
By definition of conditional probability,
[tex]P(X=n+k\mid X>n)=\dfrac{P(X=n+k\text{ and }X>n)}{P(X>n)}[/tex]
[tex]X[/tex] has CDF
[tex]P(X\le x)=\begin{cases}0&\text{for }x<1\\1-(1-p)^x&\text{for }x\ge1\end{cases}[/tex]
which is useful for immediately computing the probability in the denominator:
[tex]P(X>n)=1-P(X\le n)=(1-p)^n[/tex]
Meanwhile, if [tex]X=n+k[/tex] and [tex]k\ge1[/tex], then it's always true that [tex]X>n[/tex], so
[tex]P(X=n+k\text{ and }X>n)=P(X=n+k)=(1-p)^{n+k-1}p[/tex]
Then
[tex]P(X=n+k\mid X>n)=\dfrac{(1-p)^{n+k-1}p}{(1-p)^n}=(1-p)^{k-1}p[/tex]
which is exactly [tex]P(X=k)[/tex] according to the PMF.
The memoryless property states that given there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.
Explanation:To show that if X ∼ Geom(p) then P(X = n + k|X > n) = P(X = k), for every n, k ≥ 1, we use the memoryless property of the geometric distribution. The memoryless property states that given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k. So, we have P(X = n + k|X > n) = P(X = k).
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Simplify by using factoring: (2a+6b)(6b−2a)−(2a+6b)^2
Answer:
-8a(a+3b)
Step-by-step explanation:
(2a+6b)(6b−2a)−(2a+6b)^2
(2a+6b) {(6b−2a)−(2a+6b)(2a+6b)}
2(a+3b) (6b-2a-2a-6b)
2(a+3b) (-4a)
-2(a+3b) x 4a
-2 x 4a (a+3b)
-8a(a+3b)
The simplified expression is -8a² - 24ab.
Given expression: (2a + 6b)(6b - 2a) - (2a + 6b)^2
First, let's expand the squared term (2a + 6b)^2:
(2a + 6b)(6b - 2a) - (2a + 6b)(2a + 6b)
Now, we have a common factor of (2a + 6b) in both terms, so let's factor it out:
(2a + 6b)[(6b - 2a) - (2a + 6b)]
Now, simplify the expression inside the brackets:
(2a + 6b)[6b - 2a - 2a - 6b]
Combining like terms within the brackets:
(2a + 6b)[-4a]
Now, multiply the remaining terms:
-4a(2a + 6b)
-8a² - 24ab
Therefore, the simplified expression is -8a² - 24ab.
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Please help ASAP and help me find what the value of x is
Answer:
x=44
Step-by-step explanation:
33+103+x=180
136+x=180
x=44
The sum of all the angles of a triangle is 180 degrees.
Add all the angles together and set it equal to 180, then solve for x
33 + 103 + x = 180
(136 - 136) + x = 180 - 136
x = 44
Hope this helped!
Please help last question
Answer:
The total is 8.
And the total of not green is 6
so the probability is 6/8 or you can write as
3/4
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Which inequality best represents that ice cream at −5°C is cooler than ice cream at 4°C?
-5°C < 4°C
An object that is cooler, or colder, than a second object means that the first object has a lower, or lesser, temperature than the second object. So, we write the inequality that states that -5°C is less than 4°C.
Answer:
The answer for this question would be 4°C > −5°C
sin C =
Whats the answer ?!?
The answer would b "C" 15/17 because Sin is Opposite over Hypotenuse
Step-by-step explanation:
The measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse option third is correct.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have a right angle triangle with dimensions shown in the picture:
From the sin ratio in the right angle triangle:
sin∠C = 15/17
Thus, the measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse.
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Four research teams each used a different method to collect data on how fast a new iron skillet rusts. Assume that they all agree on the sample size and the sample mean (in days). Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation.
A. Confidence Level: 99.7%; Confidence Interval: 40 to 40
B. Confidence Level: 95%; Confidence Interval: 40 to 50
C. Confidence Level: 68%; Confidence Interval: 43 to 47
D. Confidence Level: 95%; Confidence Interval: 42 to 48
Answer:
D. Confidence Level: 95%; Confidence Interval: 42 to 48
Step-by-step explanation:
48-42=6
6/2=3
3 is smallest
I tested A and got it incorrect so D is the awnser
Confidence Level: 95%; Confidence Interval: 42 to 48. Then the correct option is D.
How to interpret the confidence interval?Suppose the confidence interval at P% for some parameter's values is given by x ± y.
That means that the parameter's estimated value is P% probable to lie in the interval
[x - y, x + y]
Four research teams each used a different method to collect data on how fast a new iron skillet rusts.
Assume that they all agree on the sample size and the sample mean (in days).
Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation.
Then we have
48 - 42 = 6
Then we have
6/2=3
3 is smallest
Then the correct option is D.
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Look at the table of values below. x y 1 -1 2 -3 3 -5 4 -7 Which equation is represented by the table? A. y = 1 − 2x B. y = -x − 1 C. y = x − 2 D. y = 2x − 1
Answer:
A. y=1-2x
Step-by-step explanation:
if to substitute the values of 'x'=1; 2; 3; 4 into the equations, only the 'A' is correct.
Answer:
A. y=1-2x
Step-by-step explanation:
if to substitute the values of 'x'=1; 2; 3; 4 into the equations, only the 'A' is correct.
Step-by-step explanation:
ruben is making a display that includes dinosaurs in their habitat. the dinosaurs will need to be decreased in size to fit the display.
What's the question?
Answer:
80%
Step-by-step explanation:
"He will start with the Brachiosaurus which has an estimated height of 15 meters and make the model 3 meters on height. by what percent will Ruben decrease the size of the Brachiosaurus in order to fit it into the display"
The percent decrease is the difference in heights divided by the original height.
(15 - 3) / 15
12/15
0.8
So Ruben will decrease the size by 80%.
Assume that the price of a combo meal is the same price as purchasing each item separately. Find the price of a pizza, a coke, and a bag of chips.
Answer:
pizza: $4, coke: $3, chips: $2
Step-by-step explanation:
Lets make the price of a pizza=p a coke= k and a bag of chips=c
then we have the following equations
p+k+c=9
p+2k=10
2p+2c=12
Because p is common in all the equations we shall make it the subject of each equation.
p=9-(k+c)...........i
p=10-2k..............ii
p=6-c...................iii
We then equate i and iii
9-(k+c)=6-c
9-k-c=6-c
putting like terms together we get:
9-6=-c+c+k
1 coke, k=$3
replacing this value in equation ii
we get p=10-2(3)
p=10-6= 4
1 pizza, p=$4
replacing this value in equation iii
4=6-c
c=6-4
=2
a bag of chips, c=$2
Thus, a pizza, a coke and a bag of chips= pizza: $4, coke: $3, chips: $2
What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below?
logarithmic graph passing through point 1, negative 2.
f(x − 2)
f(x + 2)
f(x) − 2
f(x) + 2
Answer: Third option
[tex]f(x) - 2[/tex]
Step-by-step explanation:
The function [tex]y=log_3 (x)[/tex] passes through the point (1,0) since the function [tex]y=log_a (x)[/tex] always cuts the x-axis at [tex]x = 1[/tex].
Then, if the transformed function passes through point (1,-2) then this means that the graph of [tex]y=log_3(x)[/tex] was moved vertically 2 units down.
The transformation that displaces the graphically of a function k units downwards is:
[tex]y = f (x) + k[/tex]
Where k is a negative number. In this case [tex]k = -2[/tex]
Then the transformation is:
[tex]f(x) -2[/tex]
and the transformed function is:
[tex]y = log_3 (x) -2[/tex]
a 47-foot-long piece of pipe is to be cut into three pieces. The second piece is three times as long as the first piece, and the third piece is two feet more than five times the length of the first piece. What is the length of the longest piece?
A. 5 feet
B. 15 feet
C. 27 feet
D. 32 feet
Answer:
27 ft
Step-by-step explanation:
I hope I helped
Answer:
C
Step-by-step explanation:
We need to write this in an algebraic form.
Let's name x the first piece of pipe. If the second piece is three times as long as the first piece, this would be represented as 3x.The third piece is two feet more than five times the first piece, this would be represented as 5x + 2Lastly, the three pieces sum up 47 foot.Therefore, the equation we would have is: [tex]x+3x+5x+2=47\\9x+2=47\\9x=45\\x=45/9\\x=5[/tex]
Therefore, the first piece is 5 feet long.The second piece is 5(3) = 15 feet long.The third piece is 5(5) + 2 = 27 feet long.Thus, the longest piece is 27 feet long.
Write the equation 8y = x – 0.8 in standard form. Identify A, B, and C.
480x + 5y = –48 where A = 480, B = 5, and C = 96
480x – 1y = –48 where A = 480, B = –5, and C = 96
5x – 480y = 48 where A = 5, B = –480, and C = 96
1x + 96y = 9.6 where A = 1, B = –96, and C = 0.8
Answer:
[tex]5x-40y=4[/tex]
Step-by-step explanation:
we know that
The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers
In this problem we have
[tex]8y=x-0.8[/tex]
Multiply by 5 both sides
[tex]40y=5x-4[/tex]
Adds both sides 4
[tex]40y+4=5x[/tex]
Subtract 40y both sides
[tex]4=5x-40y[/tex]
Rewrite
[tex]5x-40y=4[/tex] ----> equation of the line into standard form
A=5
B=-40
C=4
Part A
the beginning of a hiking trail is exactly at sea level. There are three rest stops along the trail. The elevation of the first rest stop is -15 feet. The elevation of the second rest stop is -20 feet. The elevation of the third rest stop is 7 feet. John compares the elevations, in feet, of the first two rest stops by writing the inequality -15 < -20. John states that the inequality he wrote is correct because 15 is less than 20.
Part B Explain whether the inequality Jack writes is correct or incorrect. In your explanation, include a description of each value in the inequality in terms of what it represents. The beginning of a hiking trail is exactly at sea level. There are three rest stops along the trail. The elevation of the first rest stop is -15 feet. The elevation of the second rest stop is -20 feet. The elevation of the third rest stop is 7 feet. John compares the elevations, in feet, of the first two rest stops by writing the inequality -15 < -20. John states that the inequality he wrote is correct because 15 is less than 20. The change in elevation is greatest between the beginning of the trail and which rest stop? Explain your reasoning.
please help ,need help now
Part A is incorrect because for negative numbers, the greater the magnitude the smaller the number. -2 is smaller than -1, for example, and -20 is smaller than -15.
An elevation of -15ft means 15 ft below sea level, an elevation of -20ft means 20 ft below sea level, and an elevation of (+) 7ft means 7 ft above sea level.
If John started the trail at sea level (0ft elevation), then the greatest change in elevation would be between that and the second rest stop. Take the absolute value of all the numbers and see which one is the largest.
Suppose at one point along the Nile River a ferryboat must travel straight across a 1.40-mile stretch from west to east. At this location, the river flows from south to north with a speed of 2.35 m/s. The ferryboat has a motor that can move the boat forward at a constant speed of 21.8 mph in still water. In what direction should the ferry captain direct the boat so as to travel directly across the river?
Answer:
about 14° south of east
Step-by-step explanation:
The river speed is about ...
(2.35 m/s)×(1 mi/(1609.344 m))×(3600 s)/(1 h) ≈ 5.2568 mi/h
The angle of interest is such that its sine is the ratio of river speed to boat speed:
sin(α) = (5.2568 mi/h)/(21.8 mi/h) = 0.241138
α = arcsin(0.241138) = 13.9537°
Since the river is flowing north, the boat should be directed south of its intended course by this angle.
The boat should be directed 14° south of east.
To counteract the effect of the river current, the boat should be directed slightly upstream. The specific direction can be calculated using trigonometric relationships between the boat's velocity and the river's velocity.
Explanation:In order to answer this question, one must understand the basic concepts of vectors and relative velocity in physics. These concepts are essential in determining the correct direction for the ferry captain to steer the boat.
To make the journey directly across the river, the captain needs to counteract the effect of the south-to-north current. This essentially means that the boat should be directed slightly upstream. Applying basic physics concepts, the velocity of the boat relative to the ground (or the river bank) is the sum of the boat's velocity relative to the river (21.8 mph toward the east) and the river's velocity (2.35 m/s to the north).
The direction to aim can be obtained by using trigonometric relationships. The direction is tan^-1((2.35 m/s)/(21.8 mph in m/s)) to the north of east. Note that you need to convert 21.8 mph to m/s before solving.
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Given: MNOK is a trapezoid, MN=OK, m∠M=60°, NK⊥MN, MK=16cm
Find: The midsegment of MNOK
Answer:
the length of the midsegment is 12 cm
Step-by-step explanation:
ΔMNK is a 30°-60°-90° triangle, so side MK is twice the length of side MN. That makes MN = (16 cm)/2 = 8 cm.
Dropping an altitude from N to intersect MK at X, we have ΔMXN is also a 30°-60°-90° triangle with side MN twice the length of side MX. That makes MX = (8 cm)/2 = 4 cm.
The length of the midsegment of this isosceles trapezoid is the same as the length XK, so is (16 -4) cm = 12 cm.
Answer:
12 cm.
Step-by-step explanation:
1. Consider right triangle MNK. In this triangle, angle N is right and m∠M=60°, then m∠K=30°. Thus, this triangle is a special 30°-60°-90° right triangle with legs MN and NK and hypotenuse MK=16 cm. The leg MN is opposite to the angle with a measure of 30°. This means that this leg is half of the hypotenuse, MN=8 cm.
2. Consider right triangle MNH, where NH is the height of trapezoid drawn from the point N. In this triangle m∠M=60°, angle H is right, then m∠N=30°. Similarly, the leg MH is half of the hypotenuse MN, MH=4 cm.
3. Trapezoid MNOK is isosceles because of MN=OK=8 cm. This means that NO=MK-2MH=16-8=8 cm.
4. The midsegment of the trapezoid is:
[tex]\frac{MK+NO}{2}=\frac{16+8}{2}=12cm[/tex]
1. Solve. r -7> 10 (1 point)
Ox>3
Or>7
O.x>17
Or> 70
Answer:
r > 17
Step-by-step explanation:
r -7> 10
Add 7 to each side
r-7+7 > 10+7
r > 17
A regular octagon can be concave.
True or False? Please explain.
Thanks!
a regular polygon has all equal angles, interior and exterior, as well as all equal sides.
Check the picture below.
the one on the left is a regular octagon, as well as a convex one.
the one on the right is also an octagon, but is concave, the issue is that, though all sides remain equal, the angles do not, and so is not a regular octagon.
Which statement about the solution of the inequality k<-3 1/4 is true?
The number 7.1 is not a solution to the inequality because -3 1/4 is located to the right of 7.1 on the number line.
The number 0.9 is not a solution to the inequality because -3 1/4 is located to the right of 0.9 on the number line.
The number –3 is a solution to the inequality because –3 is located to the left of -3 1/4 on the number line.
The number -8.4 is a solution to the inequality because -3/14 is located to the left of -3 1/4 on the number line.
Answer: Last option
The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.
Step-by-step explanation:
Note that: [tex]-3\frac{1}{4} =-3-\frac{1}{4} =-3.25[/tex]
The inequality is:
[tex]k<-3 \frac{1}{4}[/tex]
The inequality is:
This means that the inequality includes all values of the number line that are less than -3.25 or that are to the left of -3.25
__-8.4_________-3.25_-3____0___0.9____________7.1__
Note that the number -8.4 is less than -3.25, because it is to its left on the number line.
Then the correct statement is:
The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.
Answer:
the last option!!!
Step-by-step explanation:
i took the unit test
f(x)=e^2x-4
Determine inverse of given function
Answer:
[tex]f^{-1}(x)=\frac{1}{2}ln(x)+2[/tex]
Step-by-step explanation:
Start by changing the f(x) into a y. Then switch the x and the y. Then solve for the new y. Like this:
[tex]y=e^{2x-4}[/tex] becomes
[tex]x=e^{2y-4}[/tex]
To solve for the new y, we need to get it out of its current exponential position which requires us to take the natural log of both sides. Since a natural log has a base of e, natural logs and e's "undo" each other, just like taking the square root of a squared number.
[tex]ln(x)=ln(e)^{2y-4}[/tex]
When the ln and the e cancel out we are left with
ln(x) = 2y - 4. Add 4 to both sides to get
ln(x) + 4 = 2y. Divide both sides by 2 to get
[tex]\frac{1}{2}ln(x) + 4 = y[/tex].
Since that is the inverse of y, we can change the y into inverse function notation:
[tex]f^{-1}(x)=\frac{1}{2}ln(x)+4[/tex]
Final answer:
To find the inverse function of f(x) = e²ˣ - 4, you switch x and y, solve for the new y, and arrive at the inverse function f^-1(x) = (1/2) * ln(x + 4).
Explanation:
To find the inverse function of f(x) = e²ˣ - 4, we first need to switch the roles of x and f(x), and then solve for the new x. Here are the steps:
Replace f(x) with y to get y = e²ˣ - 4.Switch x and y to get x = [tex]e^{(2y)} - 4[/tex].Add 4 to both sides to isolate the exponential on one side: x + 4 = [tex]e^{(2y)[/tex].Take the natural logarithm of both sides to get ln(x + 4) = 2y.Divide both sides by 2 to solve for y: y = (1/2) * ln(x + 4).So, the inverse function of f(x) = e²ˣ - 4 is f-1(x) = (1/2) * ln(x + 4).
Leif took out a payday loan with an effective interest rate of 26,600%. If he has $180 to invest for a year at this interest rate, how much would he make in interest?
Answer: $47,880
Step-by-step explanation:
APEX
Answer:
Leif makes $47880 in interest.
Step-by-step explanation:
Given: Interest rate (r) = 26,100%
r = [tex]\frac{26600}{100} = 266[/tex]
Principle (p) = $180
time (t) = 1
Now we have to find the simple interest. The simple interest formula is I=prt
Plugging in the given values, we get
I = 180×266×1
I = $47880
So Leif makes $47880 in interest.