Answers
The length of line EF is proved to be parallel to the length of line EF.
What is the prove that EF// BD?To prove that EF is parallel to BD, we need to show that the opposite interior angles are equal.
Let's denote the center of the circle as O, and the intersection point of BD and AE as X. Since ABCD is a square, we have:
AD = AB, andBD is a diagonal, so BD passes through the center of the circle O.From the above information, we can deduce that:
∠ABD = 45°, and
∠OBD = 90°.
Since line_AF = line_AE, we can also deduce that:
∠FAE = ∠FEA.
Now, let's consider the triangle AFE. We have:
∠AFE + ∠FAE + ∠FEA = 180° (sum of angles in a triangle)
∠AFE + 2∠FAE = 180° (substituting ∠FEA with ∠FAE)
∠AFE = 180° - 2∠FAE
Also, in triangle AXε, we have:
∠AXε + ∠AEX + ∠XAE = 180° (sum of angles in a triangle)
∠AXε + ∠AEX + ∠FAE = 180° (substituting ∠XAE with ∠FAE)
∠AXε + ∠FAE + ∠FAE = 180° (rearranging terms)
∠AXε + 2∠FAE = 180°
Now, let's consider the quadrilateral ABXE. We have:
∠ABX + ∠AXε + ∠AEB = 360° (sum of angles in a quadrilateral)
∠ABX + ∠AEX + ∠AEB = 360° (rearranging terms)
∠ABX + ∠FAE + ∠AEB = 360° (substituting ∠AEX with ∠FAE)
∠ABX + 2∠FAE = 360° (substituting ∠AEB with ∠FAE)
∠ABX = 360° - 2∠FAE
Finally, let's consider the triangle BDE. We have:
∠BDE + ∠BED + ∠EBD = 180° (sum of angles in a triangle)
∠BDE + ∠AEB + ∠EBD = 180° (substituting ∠BED with ∠AEB)
∠BDE + ∠FAE + ∠EBD = 180° (substituting ∠AEB with ∠FAE)
∠BDE + 2∠FAE = 180° (since ∠FAE = ∠FEA)
∠BDE = 180° - 2∠FAE
From the above equations, we can see that:
∠ABX = ∠BDE (since both are equal to 360° - 2∠FAE)
∠ABD = ∠EBD (since both are equal to 45°)
Therefore, by the angle-angle (AA) criterion for similarity, we have:
triangle ABD is similar to triangle EXD.
This implies that:
BD/AD = XD/ED (by the property of similar triangles)
Since AD = BD (since ABCD is a square), we have:
BD/BD = XD/ED
1 = XD/ED
XD = ED
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Related Questions
Suppose that $10,405 is invested at an interest rate of 6.4% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answers
Therefore, the doubling time is approximately 10.83 years.
a) The exponential function that describes the amount in the account after time t, in years, is given by:
[tex]$A(t) = A_0 e^{rt}$[/tex]
where $A_0$ is the initial investment, $r$ is the annual interest rate as a decimal, and $t$ is the time in years. Since the interest is compounded continuously, we have $r = 0.064$.
Substituting the given values, we get:
[tex]$A(t) = 10,405 e^{0.064t}$[/tex]
b) To find the balance after 1 year, we plug in $t=1$ into the exponential function:
[tex]$A(1) = 10,405 e^{0.064(1)} \approx 11,069.79$[/tex]
Similarly, we can find the balance after 2, 5, and 10 years:
[tex]$A(2) = 10,405 e^{0.064(2)} \approx 11,778.79$[/tex]
[tex]$A(5) = 10,405 e^{0.064(5)} \approx 14,426.77$[/tex]
[tex]$A(10) = 10,405 e^{0.064(10)} \approx 19,682.08$[/tex]
c) The doubling time can be found using the formula:
[tex]$t_{double} = \frac{\ln 2}{r}$[/tex]
Substituting $r = 0.064$, we get:
[tex]$t_{double} = \frac{\ln 2}{0.064} \approx 10.83$ years[/tex]
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Determine the equation of the circle with center (-6, -2 containing the point (-9, -2).
Answers
The equatiοn οf the circle is (x + 6)(x+6) + (y + 2)(y+2) = 9.
What is circle ?A circle is a twο-dimensiοnal geοmetric figure that cοnsists οf all pοints that are equidistant frοm a single fixed pοint called the center. A circle can alsο be defined as the lοcus οf a pοint that mοves in a plane in such a way that its distance frοm a fixed pοint is always cοnstant.
Tο find the equatiοn οf a circle, we need the cοοrdinates οf the center and the radius.
The center οf the circle is given as (-6, -2), sο the cοοrdinates οf the center are (h, k) = (-6, -2).
The pοint (-9, -2) is οn the circle, sο its distance frοm the centre is equal tο the radius. We can use the distance fοrmula tο find the radius:
[tex]\rm r = \sqrt{((x_2 - x_1)\times (x_2 - x1) + (y_2 - y_1)\times(y_2 - y_1))}[/tex]
[tex]= \sqrt{((-3)^2 + 0^2)[/tex]
= 3
Therefοre, the radius οf the circle is 3.
Nοw we can use the standard fοrm οf the equatiοn οf a circle, which is:
(x - h)(x-h)+ (y - k)(y-k)= r*r
Substituting the values we fοund, we get:
Simplifying:
(x + 6)(x+6) + (y + 2)(y+2) = 9
Therefοre, The equatiοn οf the circle is [tex](x + 6)(x+6) + (y + 2)(y+2) = 9[/tex].
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3x-4>2
solve the inequality
Answers
Answer:
x > 2
Hope this helps!
Step-by-step explanation:
3x - 4 > 2
3x - 4 ( + 4 ) > 2 ( + 4 )
3x > 6
3x ( ÷ 3 ) > 6 ( ÷ 3 )
x > 2
What is the answer to? -15∣x−7∣+4=10∣x−7∣+4
50 points for anybody that answers
Answers
Answer: Only x=7
Step-by-step explanation:
Victor is using the distributive property on the expression 9-4(5x-6) Here is his work:
9-4(5x-6)
9+(4)(5x+-6)
9+-20x+-6
3-20x
a. Find the step where victor made an error and explain what he did wrong
b. Correct victor's work
Answers
Answer:
33 - 24x
Step-by-step explanation:
a. He made mistake here
9+(4)(5x+-6)
b.
9 - 4(5x - 6)
= 9 + (- 4)(5x - 6)
= 9 + (- 4)(5x) - (- 4)(6)
= 9 + (- 20x) - (- 24)
= 9 - 20x + 24
= 9 + 24 - 24x
= 33 - 24x
Consider f(x)= 4 cos x (1 – 3 cos 2x +3 cos² 2x − cos³ 2x).
Show that for f(x) dx = 3/2 sin7 m, where m is a positive real constant.
Answers
Answer:
We can start by simplifying the expression inside the parentheses using the identity:
cos 2x = 2 cos² x - 1
Substituting this in, we get:
1 – 3 cos 2x + 3 cos² 2x − cos³ 2x
= 1 – 3(2 cos² x - 1) + 3(2 cos² x - 1)² − (2 cos² x - 1)³
= 1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x
Therefore, we can rewrite f(x) as:
f(x) = 4 cos x (1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x)
Next, we can use the trigonometric identity:
sin 2x = 2 cos x sin x
to express cos x in terms of sin x:
cos x = √(1 - sin² x)
Substituting this in, we get:
f(x) = 4 sin x cos³ x (1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x)
= 4 sin x (√(1 - sin² x))³ (1 – 6 (2 sin² x - 1) + 9 (2 sin² x - 1)² - 4 (2 sin² x - 1)³)
= 4 sin x (1 - sin² x)^(3/2) (16 sin⁶ x - 48 sin⁴ x + 36 sin² x - 8)
Next, we can use the substitution u = 1 - sin² x, du = -2 sin x cos x dx, to obtain:
f(x) dx = -2 du (u^(3/2)) (16 - 48u + 36u² - 8u³)
Integrating, we get:
f(x) dx = 2/3 (1 - sin² x)^(5/2) (8 - 36(1 - sin² x) + 36(1 - sin² x)² - 8(1 - sin² x)³) + C
Now, we can use the trigonometric identity:
sin² x = (1 - cos 2x)/2
to simplify the expression inside the parentheses. After some algebra, we obtain:
f(x) dx = 3/2 sin 7x + C
where C is the constant of integration. Since m is a positive real constant, we can set:
7x = m
and solve for x:
x = m/7
Substituting this in, we get:
f(x) dx = 3/2 sin(7m/7) = 3/2 sin m
Therefore, we have shown that:
f(x) dx = 3/2 sin m, where m is a positive real constant.
what is p(divisor of 6) write your answer as a percentage rounded to the nearest tenth
Answers
The probability of selecting a divisor of 6 is 66.7%.
What is probability?It is expressed as a number between 0 and 1, where 0 represents an impossible event (it will never occur) and 1 represents a certain event (it will always occur).
According to question:1, 2, 3, and 6 can be divided by 6.
To find the probability (p) of selecting a divisor of 6, we need to divide the number of divisors of 6 by the total number of possible outcomes, which is also 6 (since there are 6 positive integers from 1 to 6).
So, p(divisor of 6) = number of divisors of 6 / total number of outcomes
= 4 / 6
= 2 / 3
We can multiply this fraction by 100 to get the percentage:
p(divisor of 6) = 2 / 3 * 100
= 66.7%
Rounded to the nearest tenth, the answer is 66.7%. Therefore, the probability of selecting a divisor of 6 is 66.7%.
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What is the range of the function represented by the graph?
A.
all real numbers
B.
y ≤ 1
C.
1 ≤ y ≤ 6
D.
y ≥ 1
Answers
Name: 7. A line segment has endpoints (4.25, 6.25) and (22, 6.25). What is the length of the line segment?
Answers
Answer:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.
In this case, (x1, y1) = (4.25, 6.25) and (x2, y2) = (22, 6.25).
Plugging these values into the distance formula, we get:
distance = sqrt((22 - 4.25)^2 + (6.25 - 6.25)^2)
= sqrt(17.75^2 + 0^2)
= sqrt(315.0625)
= 17.75
Therefore, the length of the line segment is 17.75 units.
Please help me with this math work
Answers
Answer:
{0, 1, 2}
Step-by-step explanation:
4x<8x+2
-4x<2
x<-1/2
Only {0, 1, 2} meets the critera.
Prove that,
If I = A then I U{—A} is not satisfiable.
Answers
Our assumption that I U{—A} is satisfiable must be false. Hence, I U{—A} is not satisfiable if I = A.
What is concept of satisfiability?A set of propositional formulae, sometimes referred to as a propositional theory, can be satisfiable in terms of propositional logic by having the quality of being true or untrue according to a certain interpretation or model. If there is at least one interpretation that makes all of a set of formulae true, the set is said to be satisfiable.
Using the proof by contradiction we have:
Assume that I U{—A} is satisfiable.
Then, by definition of satisfiability, every formula in the set I U{—A} is true in M.
Since I = A, every formula in I is also in A. Therefore, every formula in I is true in M, since A is true in M.
Consider the formula —A, which is in {—A}. Since M satisfies {—A}, —A is true in M.
But this contradicts the fact that A is true in M, since —A is the negation of A.
Therefore, our assumption that I U{—A} is satisfiable must be false. Hence, I U{—A} is not satisfiable if I = A.
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Moussa and Anand own competing taxicab companies. Both cab companies charge a
one-time pickup fee for every ride, as well as a charge for each mile traveled. Moussa
charges a $3 pickup fee and $2.20 per mile. The table below represents what Anand's
company charges.
Anand's Taxicab Company
Miles (2) Total Cost (y)
10
$25
20
$48
30
$71
40
$94
Use the dropdown menu and answer-blank below to form a
true statement.
Anand's company charges
per mile than Moussa's
options are more/less
Answers
Anand's business charges $25 for a 10-mile ride, which is less than Moussa's overall expenses.
How to calculate Anand's expense per mile?In comparison to Moussa, Anand's business costs less per mile.
Let's examine why by contrasting the costs charged by the two businesses for a 10-mile trip:
With a $3 pick-up fee and $2.20 per mile,
Moussa's business costs a total of $3 + $2.20*10 = $25.
Less than Moussa's overall expense,
Anand's business charges $25 for a 10-mile ride.
For all other distances mentioned in the table, we can verify that Anand's business charges less per mile than Moussa's. Thus, it is accurate that
"Anand's company charges less per mile than Moussa's."
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Sixty-nine percent of U.S. college graduates expect stay at their first employer for three or more years. You randomly select 18 U.S. college graduates and ask them whether they expect to stay at their first employer for three or more years. Find the probability that the number who expect to stay at their first employer for three or more years is (a) than at least 15. Identify any unusual events. Explain
Answers
P(X >= 15) ≈ 0.271 is an unusual event would be one that has a very low probability of occurring (e.g., less than 5%).
What is probability?
Probability is a numerical measurement that represents the likelihood or chance of an event happening. The value of probability always lies between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.
a) To find the probability that at least 15 out of 18 U.S. college graduates expect to stay at their first employer for three or more years, we can also use the CDF of the binomial distribution:
P(X >= 15) = 1 - P(X < 15)
Using a calculator or statistical software, we find:
P(X >= 15) ≈ 0.271
An unusual event would be one that has a very low probability of occurring (e.g., less than 5%). Therefore, these outcomes could be considered unusual.
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A system of inequalities is shown. The graph shows a dashed upward opening parabola with a vertex at negative 2 comma negative 6, with shading inside the parabola. It also shows a dashed line passing through the points negative 3 comma negative 5 and 0 comma 4, with shading below the line. Which system is represented in the graph? y < x2 + 4x – 2 y > 3x + 4 y > x2 + 4x – 2 y < 3x + 4 y ≤ x2 + 4x – 2 y ≥ 3x + 4 y > x2 + 4x – 2 y > 3x + 4
Answers
Answer:
y > x² – 2x – 3
y > 3x + 4
Step-by-step explanation:
I took the test;. hoped this help.
98+x=154
x-4=20
x+25=-10
Answers
Answer:
98+x=154
x=154-98
x=56
x-4=20
x=20+4
x=24
x+25=-10
x=-10-25
x=-35
In a large population, 58 % of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Answers
Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693
If 58% = 58÷100 of the people have been vaccinated, then;
1 - (58/100) = 42% = 42÷100 of the people who have not been vaccinated.
Now:
Probability, P( > 1 ), that at least one of the selected four has been vaccinated is given by;
P( > 1 ) = 1 - P(0) -----------(1)
Where;
P(0) = probability that all of the four have not been vaccinated.
P(0) = P(1) x P(2) x P(3) x P(4)×p(5)
Where;
P(1) = Probability that the first out of the four has not been vaccinated
P(2) = Probability that the second out of the four has not been vaccinated
P(3) = Probability that the third out of the four has not been vaccinated
P(4) = Probability that the fourth out of the four has not been vaccinated
P(5)=Probability that the fifth out of the five has not been vaccinated
Remember that 42÷100 of the population has not been vaccinated. Therefore,
P(1) = 42÷100
P(2) = 42÷100
P(3) = 42÷100
P(4) = 42÷100
P(5)=42÷100
P(0) = (42÷100) x (42÷100) x (42÷100) x (42÷100)×(42÷100)
P(0) = (42÷100)⁵
P(0) = (0.42)⁵
P(0) = 0.013067
Therefore, from equation (1);
P( > 1 ) = 1 -0.013067
P( > 1 ) = 0.98693
Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693
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You leave your house to go the mall. You drive due north 8 miles, due east 7.5 miles, and due north again 2 miles. Answer b and c.
Answers
Answer:
CD = 1.5 milesAE = 12.5 milesStep-by-step explanation:
Given the figure with triangle ABC similar to triangle EDC and AB=8 mi, ED=2 mi, BD = 7.5 mi, you want the measures of CD and AE.
b. CDSimilar triangles will have corresponding sides proportional. That means ...
ED/CD = AB/CB
2/CD = 8/(7.5 -CD)
Inverting the ratios and multiplying by 8 gives ...
4·CD = 7.5 -CD
5·CD = 7.5 . . . . . . . add CD
CD = 1.5 . . . . . . . . . divide by 5
c. AEThe distance AE is the hypotenuse of a right triangle with side lengths 7.5 and (8+2) = 10. The Pythagorean theorem can be used to find AE:
AE² = 7.5² +10² = 56.25 +100 = 156.25
AE = √156.25 = 12.5
AE = 12.5 miles, the distance to the mall.
__
Additional comment
You may recognize these triangles are 3-4-5 triangles. ABC has a scale factor of 2, so has side lengths 6-8-10. EDC has a scale factor of 1/2, so has side lengths 1.5, 2, 2.5. The triangle with AE as its hypotenuse is the sum of these, so has a scale factor of 2.5 (miles).
AE = (2.5 miles) · 5 = 12.5 miles
a pilot of an airplane flying at 12000 feet sights a water tower. the angle of depression to the base of the tower is 22 degrees. what is the length of the line of sight from the plane to tower
Answers
The length of the line of sight from the plane to the base of the water tower is approximately 19298 feet.
The length of the line of sight from the plane to the base of the water tower can be determined using trigonometry. We can use the tangent function, which relates the opposite side of a right triangle (in this case, the height of the water tower) to the adjacent side (the length of the line of sight), to find the length of the line of sight.
First, we can draw a diagram and label the relevant angles and sides:
|\
| \
12000 ft| \ height of tower
| \
|22°\
-----
Let x be the length of the line of sight. Then, we can use the tangent function:
tan(22°) = height of tower / x
We know the height of the tower is not given, but we can set up a right triangle with the height of the tower as one of the legs and the distance from the tower to the point directly below the plane as the other leg. Since the angle of depression is 22 degrees, the angle between the two legs of the triangle is 90 - 22 = 68 degrees.
Using the trigonometric ratio for the tangent of 68 degrees, we get:
tan(68°) = height of tower/distance from the tower to point below the plane
Solving for the height of the tower, we get:
height of tower = distance from tower to point below the plane x tan(68°)
Substituting this into the first equation, we get:
x = height of tower / tan(22°) = (distance from tower to point below the plane x tan(68°)) / tan(22°)
We don't have any values for the distance or the height of the tower, but we can simplify the expression by noting that the distance from the tower to the point directly below the plane is equal to the length of the line of sight plus the height of the plane above the ground. Assuming the height of the plane is negligible compared to the distance from the tower, we can approximate the distance as just the length of the line of sight:
distance from the tower to the point below the plane ≈ x
Substituting this approximation into the expression for x, we get:
x = x tan(68°) / tan(22°)
Solving for x, we get:
x ≈ 19298 ft
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Kevin and Randy Muise have a jar containing 28 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $3.80. How many of each type of coin do they have?
Answers
Answer:
The answer is 15 nickels and 13 quarters\
Step-by-step explanation:
. Mateo and Haley both collect coins. Mateo has 8 more (+) coins in his
collection than Haley. Which expression represents the total number of
coins (c) in both collections?
Answers
Answer:
Let Haley be represented as x
Now Mateo has 8 more coins than haley
Mateo = 8 + x
total number of coins is Mateo coins and Haley coins.
x + 8 + x
2x + 8
Choose the intervals where the graph has a decreasing average rate of change.
Answers
When the x-values rise while the y-values fall, this is known as a declining pattern. So, as x increases from 3 to 6, the graph declines. When the point on the graph at the interval's left end is higher than the interval's right end, the average rate of change will be declining.
What is the graph's average rate?An indicator of how much the function changed on average per unit throughout that time is the graph's average rate. In the graph of the function, it is calculated from the slope of the straight line joining the interval's ends. So, by applying the average rate of change formula, the slope of a graphed function is calculated.
Hence divide the y-value change by the x-value change in order to determine the average rate of change. When analyzing changes in observable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.
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The complete question is:
Choose the intervals where the graph has a decreasing average rate of change. The graph is attached below:
x = 0 to x = 13
x = 3 to x = 6
x = 4 to x = 8
x = 6 to x = 10
39÷63=? in simplest form as proper fraction
Answers
Answer:
[tex]\frac{13}{21}[/tex]
Hope this helps!
Step-by-step explanation:
[tex]\frac{39}{63}[/tex] ( Simplify both numerator and denominator by 3 )
39 ÷ 3 / 63 ÷ 3
[tex]\frac{13}{21}[/tex]
i need help please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
Answers
(A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
What is the rate of change?
The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.
A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.
Using the formula for an annual rate of change (r):
final value = initial value * [tex](1 - r)^t[/tex]
where t is the number of years and r is the annual rate of change expressed as a decimal.
Substituting the given values, we get:
$15,000 = $44,000 * (1 - r)¹⁴
Solving for r, we get:
r = 0.0804
So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.
B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:
r = 0.0804 * 100% = 8.04%
C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.
Substituting the known values, we get:
value in 2009 = $15,000 * (1 - 0.0804)³
value in 2009 = $11,628.40
Rounding to the nearest $50, we get:
value in 2009 = $11,650
Hence, (A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
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what is the quotient? x^2-9 / x+3
Answers
Answer:
x-3
Step-by-step explanation:
can you always divide by e^x? and what example can you give to prove this statement
Answers
Answer: No, you cannot always divide by e^x. When e^x equals zero, dividing by it would result in an undefined value or division by zero error.
For example, consider the function f(x) = e^x. We know that e^x is never equal to zero for any value of x. Therefore, we can always divide by e^x for any value of x, and the resulting quotient will be well-defined.
However, if we consider the function g(x) = 1 / e^x, we cannot always divide by e^x. When e^x equals zero, g(x) will be undefined. In fact, there is no value of x for which e^x is equal to zero, so the function g(x) is well-defined for all values of x.
In summary, dividing by e^x is allowed for most cases, except when e^x equals zero.
Step-by-step explanation:
Construct a labeled diagram of the circular fountain in the public park and Find the map location in coordinates of the centerand Find the distance from the center of the fountain to its circumference.
Answers
Answer:
I'm sorry, I cannot create a labeled diagram of the circular fountain in the public park or find its map location in coordinates without more specific information about the park and fountain. However, I can provide some general information about circular fountains.
To find the map location in coordinates of the center of a circular fountain, you would need to know the specific location of the park and fountain. Once you have the location, you can use a mapping tool or website to find the coordinates of the center of the fountain.
To find the distance from the center of the fountain to its circumference, you would need to know the radius of the fountain. Once you have the radius, you can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. The distance from the center of the fountain to its circumference is equal to the radius of the fountain.
I hope this information helps. If you have more specific information about the circular fountain in the public park, please let me know and I can try to provide more detailed information.
Match each exercise with the first step needed to perform the operation. Do not actually perform the operation.
Choose the correct answer below.
A. Multiply the numerators and multiply the denominators.
B. Multiply the first rational expression by the reciprocal of the second rational expression.
C. Subtract the numerators. Place the difference over a common denominator.
D. Subtract the denominators. Place the difference below a common numerator.
Answers
Find the sum of the first 25 terms of the following arithmetic sequence. Rather that write out each term use a Fourmula
a1=5,d=3
Answers
Answer:
1025
Step-by-step explanation
The formula to find the sum of the first n terms of an arithmetic sequence is
Sn = n/2 * [2a1 + (n-1)d]
Where
a1 = the first term of the sequence
d = the common difference between consecutive terms
n = the number of terms we want to sum
Substituting the given values, we get
a1 = 5
d = 3
n = 25
S25 = 25/2 * [2(5) + (25-1)3]
= 25/2 * [10 + 72]
= 25/2 * 82
= 25 * 41
= 1025
A report on consumer financial literacy summarized data from a representative sample of 1,669 adult Americans. When asked if they typically carry credit card debt from month to month, 587 of these people responded "yes." Estimate p, the proportion of adult Americans who carry credit card debt from month to month. (Round your answer to three decimal places.)
Answers
The answer is 0.351
To estimate the proportion p of American adults with monthly credit card debt, the sample proportion can be used as an estimate. The sample ratio is simply the number of people in the sample with monthly credit card debt divided by the total number of people in the sample.
p hat = 587/1669
p-hat = 0.3511 (rounded to four decimal places)
Therefore, based on this sample, the percentage of adult Americans with monthly credit card debt is estimated to be approximately 0.351. After rounding to three decimal places, its estimate is 0.351.
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Tell whether the three side measure will make a triangle or not.
1. 6 cm, 5 cm, 3 cm
2. 5 cm, 12 cm, 13 cm
3. 2 in, 3 in, 2 in
4. 2 cm, 4 cm, 1 cm
5. 6 cm, 8 cm, 10 cm
6. 1 in, 2 in, 1 in
7. 5 cm, 7 cm, 4 cm
8. 2 in, 2 in, 2 in
9. 1 in, 5 in, 3 in
10. 3 cm, 4 cm, 5 cm
Please explain why, also this is due for me tomorrow and I’ll mark you brainlist if you can help me pls
Answers
1) Not a triangle as According to the triangle inequality theorem ,2)Triangle. as According to the triangle inequality theorem , 3)Not a triangle. , 4)Not a triangle., 5)Triangle. , 6)Not a triangle., 7) Not a triangle., 8)Equilateral triangle. 9)Not a triangle 10) Triangle.
what is triangle ?
A triangle is a two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry, and it is formed by connecting three non-collinear points. The sum of the angles in a triangle is always 180 degrees.
In the given question,
Not a triangle. (6 + 5 = 11 > 3)
Explanation: According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side. However, in this case, 6 + 5 is equal to 11, which is not greater than the third side of length 3.
Triangle. (5 + 12 > 13)
Explanation: The sum of the two smaller sides (5 and 12) is greater than the largest side (13), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.
Not a triangle. (2 + 2 = 4 > 3)
Explanation: Similar to the first case, the sum of the two smaller sides (2 and 2) is equal to 4, which is not greater than the third side of length 3.
Not a triangle. (1 + 2 = 3 > 4)
Explanation: Again, the sum of the two smaller sides (1 and 2) is equal to 3, which is not greater than the third side of length 4.
Triangle. (6 + 8 > 10)
Explanation: The sum of the two smaller sides (6 and 8) is greater than the largest side (10), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.
Not a triangle. (1 + 1 = 2 > 2)
Explanation: Similar to cases 1 and 3, the sum of the two smaller sides (1 and 1) is equal to 2, which is not greater than the third side of length 2.
Not a triangle. (4 + 5 = 9 > 7)
Explanation: In this case, the sum of the two smaller sides (4 and 5) is greater than 7, but the difference between the two larger sides (7 - 5) is smaller than the smallest side (4), violating the triangle inequality theorem.
Equilateral triangle. (All sides are equal)
Explanation: All sides are equal, satisfying the criteria for an equilateral triangle.
Not a triangle. (1 + 3 = 4 > 5)
Explanation: The sum of the two smaller sides (1 and 3) is greater than the largest side (5), but the difference between the two larger sides (5 - 3) is smaller than the smallest side (1), violating the triangle inequality theorem.
Triangle. (3 + 4 > 5)
Explanation: The sum of the two smaller sides (3 and 4) is greater than the largest side (5), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.
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