Answers
Answer:
x = 53
Step-by-step explanation:
BCDE is a trapezoid
Therefore diagonals are equal
BD = EC
8x-27 = 2x+33
8x-2x = 33+27
6x = 60
x = 10
DB = 8x-27
= 8*10 - 27
= 80 - 27
= 53
Related Questions
Which function has a greater maximum?
�
(
�
)
=
−
2
(
�
+
4
)
2
+
1
f(x)=−2(x+4)
2
+1f, left parenthesis, x, right parenthesis, equals, minus, 2, left parenthesis, x, plus, 4, right parenthesis, squared, plus, 1
A coordinate plane. The x- and y-axes both scale by one. The graph is the function y equals g of x which is a parabola that opens down. The function increases through negative four, negative five and negative three, negative two. It has a maximum at negative two, one, then the function decreases through negative one, negative two and zero, negative five.
Answers
The function f(x) = [tex]-2(x+4)^2[/tex] + 1 has a greater maximum.
1. The given function is f(x) = [tex]-2(x+4)^2[/tex] + 1.
2. To find the maximum of the function, we need to determine the vertex of the parabola.
3. The vertex form of a quadratic function is given by f(x) = [tex]a(x-h)^2[/tex] + k, where (h, k) represents the vertex.
4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.
5. The x-coordinate of the vertex is given by h = -4.
6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = [tex]-2(-4+4)^2[/tex] + 1 = [tex]-2(0)^2[/tex] + 1 = 1.
7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.
8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = [tex]-2(x+4)^2[/tex] + 1 is greater than the maximum of g(x).
9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.
10. Hence, the function f(x) =[tex]-2(x+4)^2[/tex] + 1 has a greater maximum.
For more such questions on maximum, click on:
https://brainly.com/question/29795588
#SPJ8
You are given that z > 2. Write an inequality for each expression.
a) 2z+ 9
b) 3(z - 4)
c) 4+2z
d) 5(3z-2)
Answers
a) The inequality for the expression 2z + 9 is 2z + 9 > 13.
b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.
c) The inequality for the expression 4 + 2z is 4 + 2z > 8.
d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.
a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:
2z > 2 * 2
2z > 4
Adding 9 to both sides:
2z + 9 > 4 + 9
2z + 9 > 13
Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.
b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:
3z - 3 * 4
3z - 12
Since we are given that z > 2, we can substitute z > 2 into the expression:
3z - 12 > 3 * 2 - 12
3z - 12 > 6 - 12
3z - 12 > -6
Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.
c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:
4 + 2z > 4 + 2 * 2
4 + 2z > 4 + 4
4 + 2z > 8
Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.
d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):
5 * 3z - 5 * 2
15z - 10
Considering the given inequality z > 2, we can substitute z > 2 into the expression:
15z - 10 > 15 * 2 - 10
15z - 10 > 30 - 10
15z - 10 > 20
Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.
for such more question on inequality
https://brainly.com/question/17448505
#SPJ8
A fancy restaurant put dishes of butter at each table. They divided 4/5 of a kilogram of butter evenly to put 1/5 of a kilogram in each dish. How many butter dishes did they fill?
Answers
Answer: 4
This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.
4/5 ÷ 1/5
Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:
4/5 x 5
To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.
You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.
Hope this helps!
$22,954 is invested part at 7% and the rest at 5%
Answers
To calculate the amounts invested at 7% and 5%, let's assume the amount invested at 7% is x dollars. Then the amount invested at 5% would be (22,954 - x) dollars since the total investment is $22,954.
The interest earned from the investment at 7% would be 7% of x, which is 0.07x dollars. Similarly, the interest earned from the investment at 5% would be 5% of (22,954 - x), which is 0.05(22,954 - x) dollars.
The total interest earned is the sum of the interest earned from both investments. Therefore, we can write the equation:
0.07x + 0.05(22,954 - x) = Total Interest
To find the amounts invested at each rate, we can solve this equation.
0.07x + 0.05(22,954 - x) = Total Interest
0.07x + 0.05 * 22,954 - 0.05x = Total Interest
0.07x + 1,147.7 - 0.05x = Total Interest
0.02x = Total Interest - 1,147.7
x = (Total Interest - 1,147.7) / 0.02
Given the specific values of the total interest, you can substitute them into the equation and solve for x. This will give you the amount invested at 7%. Subtracting this amount from $22,954 will give you the amount invested at 5%.
For more such questions on investment
https://brainly.com/question/25893158
#SPJ8
What needs to be corrected in this construction of a line parallel to line AB passing through C?
A
DA.
B.
C.
D.
C
E
D
The first arc should pass through C.
The first arc should be centered at C.
The second arc should be centered at C.
The second arc should cross the first arc.
E. The second arc should be centered at F.
second arc (centered at E)
first arc (centered at D)
F
B
Answers
The step that should be corrected in the construction of a line parallel to the line AB passing through C is the option;
C. The second arc should be centered at C
The steps to construct a line parallel to another line are;
Place the compass at the point D and draw an arc with radius DE
Place the compass at the point C and with the same radius DE, draw an arc to intersect the line EC at a point above the point C at G
Open the compass to the radius EF, place the compass at the point G and draw an arc to intersect the arc drawn at C at the point H
Join CH and extend the line to complete the construction of a line parallel to the line AB at C
The correct option is therefore, option C
Learn more on geometric constructions here: https://brainly.com/question/4062148
#SPJ1
Two diagonals of a parallelogram have lengths 6 and 8. What is the largest possible length of the shortest side of the parallelogram?
Answers
Answer:
5 units----------------------
The intersecting diagonals form a triangle with sides 3, 4 and shorter side x of the parallelogram.
Possible angle measure between diagonals, opposite to shorter side is maximum 90°.
Find the largest possible length of x using the law of cosines:
[tex]x=\sqrt{3^3+4^2-3*4*cos\ 90} =\sqrt{25}=5\ units[/tex]3. Show that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.
Answers
Answer:
Step-by-step explanation:
To check whether the given credit card number is valid or not, we need to apply the Luhn algorithm or the mod-10 algorithm. The Luhn algorithm works by adding up all the digits in the credit card number and checking if the sum is divisible by 10 or not. If it is, then the credit card number is considered valid, otherwise, it is invalid.
Let's apply the Luhn algorithm to the given credit card number:
Step 1: Starting from the rightmost digit, double every second digit
| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| | 8 | | 8 | | 16| | 6 | | 14| | 0 | | 0 | | 10|
Step 2: If the doubled value is greater than 9, add the digits of the result
| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| | 8 | | 8 | | 7 | | 6 | | 5 | | 0 | | 0 | | 1 |
Step 3: Add up all the digits in the credit card number, including the check digit
5 + 4 + 2 + 4 + 9 + 8 + 1 + 3 + 2 + 7 + 2 + 0 + 0 + 0 + 8 + 5 + 1 = 61
Step 4: If the sum is divisible by 10, then the credit card number is valid, otherwise, it is invalid.
61 is not divisible by 10, therefore the given credit card number is invalid.
Hence, it can be concluded that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.
What is the interval solution?
0.35 x - 4.8 ∠ 5.2 -0.9x
a). (-∞, -8) b). (-∞, 8) c). (-8, ∞) d). (8,∞)
Answers
The interval solution for the inequality 0.35x - 4.8 ≤ 5.2 - 0.9x is b) (-∞, 8].
To find the interval solution of the expression 0.35x - 4.8 ≤ 5.2 - 0.9x, we need to solve the inequality for x.
First, let's simplify the expression by combining like terms:
0.35x + 0.9x ≤ 5.2 + 4.8
Simplifying further:
1.25x ≤ 10
To isolate x, divide both sides of the inequality by 1.25:
x ≤ 10 / 1.25
x ≤ 8
The solution to the inequality is x ≤ 8. This means that any value of x that is less than or equal to 8 satisfies the inequality.
To represent this solution as an interval, we use square brackets for inclusive values and parentheses for exclusive values. Since the inequality includes the value of 8, the interval is:
(-∞, 8]
The left endpoint of the interval is negative infinity (-∞), indicating that x can take any value less than 8. The right endpoint is 8, indicating that x can be equal to 8 but cannot exceed it.
The correct option from the given choices is b). (-∞, 8).
For more such questions on inequality
https://brainly.com/question/30238989
#SPJ8
prove this question
hurry
Answers
The trigonometric identities for the terms in the left hand side of the equation indicates that we get;
tan(θ)/(1 - tan(θ)) = sin(θ)/(cos(θ) - sin(θ))
-cot(θ)/(1 - cot(θ)) = cos(θ)/(cos(θ) - sin(θ)), therefore;
tan(θ)/(1 - tan(θ)) - cot(θ)/(1 - cot(θ)) = (cos(θ) + sin(θ))/(cos(θ) - sin(θ))What are trigonometric identities?Trigonometric identities are equations involving trigonometric functions that are true for all values in the interval of the input variable.
The specified equation can be expressed as follows;
tan(θ)/(1 - tan(θ)) - cot(θ)/(1 - cot(θ)) = (cos(θ) + sin(θ))/(cos(θ) - sin(θ))
The trigonometric identity indicates that the left hand side of the equation can be presented as follows;
tan(θ) = sin(θ)/cos(θ)
cot(θ) = cos(θ)/sin(θ)
(sin(θ)/cos(θ))/(1 - (sin(θ)/cos(θ))) - (cos(θ)/sin(θ))/(1 - (cos(θ)/sin(θ)))
(sin(θ)/cos(θ))/(1 - (sin(θ)/cos(θ))) = (sin(θ)/cos(θ)) × (cos(θ) - (sin(θ))/cos(θ)))
(sin(θ)/cos(θ)) × (cos(θ) - (sin(θ))/cos(θ))) = -(cos²(θ) - 1 - cos(θ)·sin(θ))/(2·cos²(θ) - 1)
-(cos²(θ) - 1 - cos(θ)·sin(θ))/(2·cos²(θ) - 1) = -(cos²(θ) - 1 - cos(θ)·sin(θ))/(cos²(θ) - 1 + cos²(θ))
= -(-sin²(θ) - cos(θ)·sin(θ))/(cos²(θ) - sin²(θ)) = (sin²(θ) + cos(θ)·sin(θ))/(cos²(θ) - sin²(θ))
(sin²(θ) + cos(θ)·sin(θ)) = sin(θ)·(sin(θ) + cos(θ))
(cos²(θ) - sin²(θ)) = (cos(θ) - sin(θ)) × (cos(θ) + sin(θ))
sin(θ)·(sin(θ) + cos(θ))/((cos(θ) - sin(θ)) × (cos(θ) + sin(θ)))
sin(θ))/(cos(θ) - sin(θ))
Similarly;
-(cos(θ)/sin(θ))/(1 - (cos(θ)/sin(θ))) = cos(x)·(cos(x) + sin(x))/((cos(θ) - sin(θ)) × (cos(θ) + sin(θ)))
cos(x)·(cos(x) + sin(x))/((cos(θ) - sin(θ)) × (cos(θ) + sin(θ))) = cos(x)/((cos(θ) - sin(θ)))
Therefore; (sin(θ)/cos(θ))/(1 - (sin(θ)/cos(θ))) - (cos(θ)/sin(θ))/(1 - (cos(θ)/sin(θ))) = sin(θ)/(cos(θ) - sin(θ)) + cos(x)/((cos(θ) - sin(θ)))
(sin(θ)/cos(θ))/(1 - (sin(θ)/cos(θ))) - (cos(θ)/sin(θ))/(1 - (cos(θ)/sin(θ))) = (sin(θ) + cos(θ))/(cos(θ) - sin(θ)) = (cos(θ) + sin(θ))/(cos(θ) - sin(θ))
Learn more on trigonometric identities here: https://brainly.com/question/25024318
#SPJ1
Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200
Answers
Hello!
The distance, d, is less than 200 miles.
B. d > 200
Solve the following equation. Then place the correct number in the box provided. 3x + 1 = 2x + 12
Answers
Answer:
x = 11
Step-by-step explanation:
3x+1 = 2x+12 (subtract 2x from both sides)
x+1 = 12 (subtract 1 from both sides)
x = 11
So x is equal to 11
27. Which one of the following sentences contains AT LEAST ONE error?
O A Conference attendee's need to check in by 9:00 a.m. or risk forfeiting their reservation.
B. The location for the next conference will not be officially decided for at least another couple of weeks.
dc. The committee planning the next conference has been unable to meet for months.
OD. If attendance at the current conference is used as a barometer of interest, the next conference should be moved to a larger venue.
O Mark to review later...
Answers
The correct version of the sentence would be A Conference attendee's need to check in by 9:00 a.m. or risk forfeiting his or her reservation.
The sentence that contains at least one error is:
O A Conference attendee's need to check in by 9:00 a.m. or risk forfeiting their reservation.
The error in this sentence is the incorrect use of "their" to refer to a singular possessive noun "attendee's."
To maintain subject-verb agreement, it should be "his or her" instead of "their." Therefore, the correct version of the sentence would be:
A Conference attendee's need to check in by 9:00 a.m. or risk forfeiting his or her reservation.
for such more question on Conference
https://brainly.com/question/27746495
#SPJ8
Please explain your answer with each step.
Find the amount of increase and the percent increase if the original amount is 390 and the new amount is 546.
Answers
If the original amount is 390 and the new amount is 546, the amount of increase is 156 and the percent increase is 40%. This indicates that the new amount is 156 units higher than the original amount, representing a 40% increase.
To find the amount of increase and the percent increase between the original amount and the new amount, we can follow these steps:
1. Start with the original amount: 390.
2. Determine the increase by subtracting the original amount from the new amount: 546 - 390 = 156.
3. The amount of increase is 156. This means that the new amount is 156 units greater than the original amount.
4. To calculate the percent increase, divide the amount of increase by the original amount and then multiply by 100: (156 / 390) * 100 = 40.
5. The percent increase is 40%. This means that the new amount is 40% greater than the original amount.
For more such questions on percent
https://brainly.com/question/843074
#SPJ8
Pre - Calculus evaluate exponential derivative at a point !
Answers
Answer:
[tex]\displaystyle[/tex][tex]\displaystyle f'(1)=-\frac{9}{e^3}[/tex]
Step-by-step explanation:
Use Quotient Rule to find f'(x)
[tex]\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}[/tex]
Find f'(1) using f'(x)
[tex]\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}[/tex]
Answer:
[tex]f'(1)=-\dfrac{9}{e^{3}}[/tex]
Step-by-step explanation:
Given rational function:
[tex]f(x)=\dfrac{3x^2+2}{e^{3x}}[/tex]
To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}[/tex]
[tex]\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x[/tex]
[tex]\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}[/tex]
Therefore:
[tex]f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}[/tex]
[tex]f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}[/tex]
[tex]f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}[/tex]
To find f'(1), substitute x = 1 into f'(x):
[tex]f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}[/tex]
[tex]f'(1)=\dfrac{6 -9-6}{e^{3}}[/tex]
[tex]f'(1)=-\dfrac{9}{e^{3}}[/tex]
What is the value of the expression 4 Superscript 4?
Answers
The calculated value of the expression 4 Superscript 4 is 256
How to determine the value of the expressionFrom the question, we have the following parameters that can be used in our computation:
4 Superscript 4
Express properly
So, we have
4⁴
When expanded, we have
4⁴ = 4 * 4 * 4 * 4
Evaluate
4⁴ = 256
Hence, the value of the expression is 256
Read more about expression at
https://brainly.com/question/31819389
#SPJ1
perform the indicated operation and simplifly the result.
Answers
The expression is simplified to x+8/x- 4
How to simply the expressionFirst, we need to know that algebraic expressions are defined as expressions that are made up of terms, variables, constants, factors and coefficients.
These expressions are also made up of arithmetic operations.
From the information given, we have that;
[tex]\frac{x^2 + 2}{x^2 - 9x + 20} - \frac{42 - 3x}{x^2 - 9x + 20}[/tex]
Now, find the lowest common multiple, we have;
x² + 2 - (42 - 3x)/x² - 9x + 20
collect the like term and expand the bracket, we have;
x² + 3x - 40/x² - 9x + 20
x² + 8x - 5x - 40/x² - 5x - 4x + 20
(x-5)(x+8)/(x-5)(x -4)
x+8/x- 4
Learn more about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
Use the Laws of logarithms to rewrite the expression
22 + 18
1o8 483+201468-215
in a form with no logarithm of a product, quotient or power.
After rewriting we have
105 503+20)603-3745 = 1108 (03 + 18) + Blos(° +20) + C108(859-2)
with the constant A =
the constant B =
and the constant C
Answers
Using the laws of logarithm to write 1/2log(x² + 18) - 1/2log(x² + 20) - 15/2log(x³ - 2) in the form Alog(x² + 18) + Blog(x² + 20) + Clog(x³ - 2), we have that
A = 1/2B = - 1/2 and C = -15/2What are laws of logarithm?Laws of logarithm are the laws which govern the operations of logarithms
Given the logarithm expression log√[(x² + 18)/{(x² + 20)(x³ - 2)¹⁵}], we desire to write it in the form Alog(x² + 18) + Blog(x² + 20) + Clog(x³ - 2), we proceed as follows
Since log√[(x² + 18)/{(x² + 20)(x³ - 2)¹⁵}], using the root law of exponents which is [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex], we have that
log√[(x² + 18)/{(x² + 20)(x³ - 2)¹⁵}] = log√[(x² + 18)/√{(x² + 20)(x³ - 2)¹⁵}]
= log[(x² + 18)¹/₂/{(x² + 20)¹/₂(x³ - 2)¹⁵/₂}],
Now using the division law of loagarithm which is log(a/b) = loga - logb, we have that
log[(x² + 18)¹/₂/{(x² + 20)¹/₂(x³ - 2)¹⁵/₂}] = log(x² + 18)¹/₂ - log{(x² + 20)¹/₂(x³ - 2)¹⁵/₂}]
Next using the multiplication law of logarithm which is logab = loga + logb, we have that
log(x² + 18)¹/₂ - log{(x² + 20)¹/₂(x³ - 2)¹⁵/₂}] = log(x² + 18)¹/₂ - log(x² + 20)¹/₂ - log(x³ - 2)¹⁵/₂
Finally, using the power law of logarithm which is logxⁿ = nlogx, we have that
log(x² + 18)¹/₂ - log(x² + 20)¹/₂ - log(x³ - 2)¹⁵/₂}] = 1/2log(x² + 18) - 1/2log(x² + 20) - 15/2log(x³ - 2)
So, log√[(x² + 18)/{(x² + 20)(x³ - 2)¹⁵}] = 1/2log(x² + 18) - 1/2log(x² + 20) - 15/2log(x³ - 2)
Comparing 1/2log(x² + 18) - 1/2log(x² + 20) - 15/2log(x³ - 2) to Alog(x² + 18) + Blog(x² + 20) + Clog(x³ - 2), we have that
A = 1/2B = - 1/2 and C = -15/2Learn more about laws of logarithm here:
https://brainly.com/question/30287532
#SPJ1
an airplane takes 3 hours to travel a distance of 1440 miles with the wind. The return trip takes 4 hours against the wind. Find the speed of the plane in the still air and the speed of the wind.
Answers
Answer:
The speed of the plane in the still air is 420 miles/hour
The speed of the wind 60 miles/hour
Step-by-step explanation:
Let the speed of the plane with the wind be v
Let the speed of the plane against the wind be u
Now, speed = distance/time
With the wind,
v = (1440 miles)/(3 hours) = 480 miles/hour
v = 480 miles/hour
Against the wind,
u = (1440 miles)/(4 hours) = 360 miles/hour
u = 360 miles/hour
Now, let the speed of plane be p, and speed of wind be w,
Now, with the wind, the speed is 480 mph,
so,
speed of plane + speed of wind = 480 mph
p + w = 480 (i)
and against the wind, the speed is 360 mph,
so,
speed of plane - speed of wind = 360mph
p-w = 360 (ii)
adding equations (i) and (ii), we get,
p+w + p-w = 480 + 360
2p = 840
p = 840/2
p = 420 miles/hour
Then, the speed of the wind will be,
p + w = 480,
420 + w = 480
w = 480 - 420
w = 60 miles/hour
The speed of the plane in still air is calculated to be 420 mph, and the speed of the wind is calculated to be 60 mph by solving the two simultaneous equations obtained from the time, rate, and distance relationship.
Explanation:This problem is about the rate, time, and distance relationships. The rate at which the airplane travels in still air is r (unaffected by wind), and the speed of the wind is w. When the plane flies with the wind, it is 'assisted' and therefore travels faster - at a speed of (r + w); against the wind, it travels slower - at a speed of (r - w).
From the problem, we know that:
The trip with the wind covers 1440 miles in 3 hours, so (r + w) * 3 = 1440The return trip against the wind covers the same 1440 miles in 4 hours, so (r - w) * 4 = 1440By solving these two equations, we get the following:
r + w = 480r - w = 360Adding these two gives 2r = 840 => r = 420 mph (the speed of the plane in still air), and subtracting gives 2w = 120 => w = 60 mph (the speed of the wind).
Learn more about Simultaneous Equations here:https://brainly.com/question/31913520
#SPJ2
A survey of 100 high school students provided this frequency table on how students get to school. What is the probability that a randomly selected student is a junior who takes the bus?
Answers
The probability of selecting a junior who takes the bus is P (Junior who takes the bus) = 12/200 = 0.06Hence, the probability that a randomly selected student is a junior who takes the bus is 0.06 or 6/100.
The given frequency table on how students get to school among the high school students is represented in the below table:Transportation Walk Bike BusDriveTotalGrade 9 11 10 14 15 50Grade 10 10 7 13 20 50Grade 11 8 6 12 24 50Grade 12 5 8 8 29 50 Total 34 31 47 88 200Given data from the above frequency table, we are interested in finding the probability of a randomly selected student being a junior who takes the bus.SolutionWe know that the total number of students is 200, and the total number of junior students is 50. Hence the probability of selecting a junior is P (Junior) = 50/200 = 0.25Similarly, the number of students who take the bus is 47 and the number of junior students who take the bus is 12.
for more search question probability
https://brainly.com/question/251701
#SPJ8
Find the equation of the parabola with its focus at (6,2) and its directrix y = 0. Question 18 options: A) y = 1∕4(x – 6)2 + 1 B) y = 4(x – 6)2 + 1 C) y = 1∕4(x – 1)2 + 6 D) y = –1∕4(x – 6)2 + 1
Answers
The equation of the parabola is y = 1/4(x - 6)^2 + 1.
The equation of the parabola with its focus at (6,2) and its directrix y = 0 is y = 1/4(x - 6)^2 + 1. The equation of a parabola is given by the formula y = a(x - h)^2 + k, where(h, k) are the coordinates of the vertex of the parabola and a is a constant called the focus.
The distance between the vertex and the focus is equal to a. Also, the parabola has a directrix, which is a line perpendicular to the axis of symmetry and equidistant from the vertex and the focus.
Step 1: Find the vertex of the parabola. The vertex is halfway between the focus and the directrix, so its y-coordinate is the distance between the focus and the directrix, which is 2. The x-coordinate is the same as the x-coordinate of the focus, which is 6. Therefore, the vertex is (6, 2).
Step 2: Find the distance between the vertex and the focus. The distance between the vertex and the focus is equal to a. The directrix is y = -a, which is y = 0 in this case. Therefore, a = 2.
Step 3: Write the equation of the parabola using the vertex and the focus. Substitute the values of h, k, and a into the formula for the equation of a parabola. The equation of the parabola is y = 1/4(x - 6)^2 + 1. Therefore, the correct answer is (A) y = 1/4(x - 6)^2 + 1.
For more such questions on parabola, click on:
https://brainly.com/question/29635857
#SPJ8
PRE CALCULUS PLEASE HELP ME WITH THESE 2 QUESTIONS
Answers
Answer:
[tex]\dfrac{51}{2}[/tex]
Step-by-step explanation:
The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}[/tex]
The given definite integral is:
[tex]\displaystyle \int^5_{-7} f(x)\; \;\text{d}x[/tex]
This means we need to find the area between the x-axis and the function between the limits x = -7 and x = 4.
Notice that the function is below the x-axis between x = -7 and x = -2.
Therefore, we need to separate the integral into two areas and add them together:
[tex]\displaystyle \int^5_{-7} f(x)\; \;\text{d}x=\int^{-2}_{-7} f(x)\; \;\text{d}x+\int^5_{-2} f(x)\; \;\text{d}x[/tex]
The area between the x-axis and the function between the limits x = -7 and x = -2 is a triangle with base of 5 units and height of 3 units.
The area between the x-axis and the function between the limits x = -2 and x = 5 is a trapezoid with bases of 5 and 7 units, and a height of 3 units.
Using the formulas for the area of a triangle and the area of a trapezoid, the definite integral can be calculated as follows:
[tex]\begin{aligned}\displaystyle \int^5_{-7} f(x)\; \;\text{d}x&=\int^{-2}_{-7} f(x)\; \;\text{d}x+\int^5_{-2} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5)(3)+\dfrac{1}{2}(5+7)(3)\\\\& =\dfrac{15}{2}+18\\\\& =\dfrac{51}{2}\end{aligned}[/tex]
Note: If you integrate a function to find an area that lies below the x-axis, it will give a negative value. So when finding an area like this, you will need to make your answer positive, since area cannot be negative.
Consider the arithmetic sequence 1, 4, 7, 10. Write an expression for the n th term (which is t ) of this arithmetic sequence.
Answers
Answer:
[tex]a_{n}[/tex] = 3n - 2
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 1 and d = a₂ - a₁ = 4 - 1 = 3 , then
[tex]a_{n}[/tex] = 1 + 3(n - 1) = 1 + 3n - 3 = 3n - 2
write an algebraic equation for the followingn problem and then solve for it. Hilltop dormitory just purchased a new soft drink machine on sale for $480. The sale price was 75% of the original price. What was the original price of the soft drink machine?
Answers
Answer:
Step-by-step explanation:480 x o.75=360
and now you add this amount on payed
360 + 480=840 was original price
Find The Quotient. Simplify Completely
(Positive Exponents Only). Polynomials must be in standard form. 26y³ −8y/ 2y . (4y + 1)
Answers
Answer:
Step-by-step explanation:
[tex]\frac{26y^3-8y}{2y} (4y+1)\\ \\=\frac{2y(13y^2-4}){2y} (4y+1)\\\\=(13y^2-4) (4y+1)\\\\= 13(4)y^3 -4(4y) + 13y^2 -4\\\\= 52y^3 -15y + 13y^2 -4\\\\= 52y^3 + 13y^2 -15y -4[/tex]
A bank account gathers compound interest at a rate of 5% each year.
Another bank account gathers the same amount of money in interest by the end of each year, but gathers compound interest each month.
If Haleema puts £3700 into the account which gathers interest each month, how much money would be in her account after 2 years and 11 months?
Give your answer in pounds to the nearest 1 p.
Answers
Haleema would have approximately £3947.46 in her account after 2 years and 11 months, considering the monthly compounding interest of 5%.
To calculate the amount of money in Haleema's account after 2 years and 11 months, we need to consider the monthly compounding interest on the account.
The interest rate is given as 5% per year, which means the monthly interest rate is (5%/12) = 0.4167%.
Let's calculate the final amount using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, P = £3700, r = 0.004167, n = 12 (monthly compounding), and t = 2.917 (2 years and 11 months).
Plugging these values into the formula, we get:
A = £3700(1 + 0.004167/12)^(12*2.917)
A ≈ £3947.46
The amount of money in Haleema's account after 2 years and 11 months would be approximately £3947.46.
For more questions on compound interest
https://brainly.com/question/28020457
#SPJ8
solve the following question
Answers
14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4
15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°
What is a trigonometric equation?A trigonometric equation is an equation that contains a trigonometric ration.
14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows
Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,
We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that
(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°
= 1² + 1² - 4cos²45°
We know that cos45° = 1/√2. So, we have
1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²
= 1 + 1 + 4/2
= 2 + 2
= 4
So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4
15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows
Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1
We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that
2(cos²θ - sin²θ) = 1
2(cos2θ) = 1
cos2θ = 1/2
Taking inverse cosine, we have that
2θ = cos⁻¹(1/2)
2θ = 30°
θ = 30°/2
θ = 15°
So, θ = 15°
Learn more about trigonometric equation here:
https://brainly.com/question/28025415
#SPJ1
Pre calculus homework help
Answers
Answer:
[tex]f'(\frac{1}{3\sqrt{e}})=\frac{1}{2}[/tex]
Step-by-step explanation:
Find f'(x) using Product Rule
[tex]f(x)=x\ln(3x)\\f'(x)=\ln(3x)+3x(\frac{1}{3x})\\f'(x)=\ln(3x)+1\\\\f'(\frac{1}{3\sqrt{e}})=\ln(3\cdot\frac{1}{3\sqrt{e}})+1\\\\f'(\frac{1}{3\sqrt{e}})=\ln(\frac{1}{\sqrt{e}})+1\\\\f'(\frac{1}{3\sqrt{e}})=\ln(e^{-\frac{1}{2}})+1\\\\f'(\frac{1}{3\sqrt{e}})=-\frac{1}{2}\ln(e)+1\\\\f'(\frac{1}{3\sqrt{e}})=-\frac{1}{2}+1\\\\f'(\frac{1}{3\sqrt{e}})=\frac{1}{2}[/tex]
Answer:
[tex]f'\left(\dfrac{1}{3\sqrt{e}}\right)=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x\ln(3x)[/tex]
To find f'(x), differentiate the given function using the product rule.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
[tex]\textsf{Let\;$u=x^2}[/tex][tex]\textsf{Let\;$u=x$}\implies \dfrac{\text{d}u}{\text{d}x}=1[/tex]
[tex]\textsf{Let\;$v=\ln(3x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{3x}\cdot 3=\dfrac{1}{x}[/tex]
Input the values into the product rule to differentiate the function:
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x \cdot \dfrac{1}{x}+\ln(3x) \cdot 1\\\\&=1+\ln(3x)\end{aligned}[/tex]
To find the value of f'(1/(3√e)), substitute x = 1/(3√e) into the differentiated function:
[tex]\begin{aligned}f'\left(\dfrac{1}{3\sqrt{e}}\right)&=1+\ln\left(3\left(\dfrac{1}{3\sqrt{e}}\right)\right)\\\\&=1+\ln\left(\dfrac{1}{\sqrt{e}}\right)\\\\&=1+\ln e^{-\frac{1}{2}}\\\\&=1-\dfrac{1}{2}\ln e\\\\&=1-\dfrac{1}{2}(1)\\\\&=1-\dfrac{1}{2}\\\\&=\dfrac{1}{2}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Differentiation rules used:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{6 cm}\underline{Differentiating $\ln(f(x))$}\\\\If $y=\ln(f(x))$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{f(x)}\cdot f'(x)$\\\end{minipage}}[/tex]
Please help me this is hard
Answers
Shaded Area=11*14 -5*7= 154- 35=119 sqm
A coordinate plane with a straight line passing through the points (negative 6, negative 8) and (2, 8).
Use the formula m =m equals y 2 minus y 1 Over x 2 minus x 1 to calculate the slope of the line.
Answers
he slope of the line passing through the points (-6, -8) and (2, 8) is 2.
The slope of the line passing through two given points can be calculated by using the formula:m = (y₂ - y₁)/(x₂ - x₁)Where m is the slope of the line, (x₁, y₁) and (x₂, y₂) are the two given points on the line. Given a coordinate plane with a straight line passing through the points (negative 6, negative 8) and (2, 8), we can find the slope of the line using the above formula as follows:We have the two points: (x₁, y₁) = (-6, -8) and (x₂, y₂) = (2, 8)Let's substitute these values into the formula to find the slope:m = (y₂ - y₁)/(x₂ - x₁)m = (8 - (-8))/(2 - (-6))m = (8 + 8)/(2 + 6)m = 16/8m = 2
for more search question slope
https://brainly.com/question/1884491
#SPJ8
I need 23 questions answered
Answers
The surface area of a rectangular prism is 48 5/6 mi².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;
Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]
Surface area of rectangular prism = 2[14 + 15/2 + 35/12]
Surface area of rectangular prism = 48 5/6 mi².
Read more on surface area of a rectangular prism here: brainly.com/question/28185251
#SPJ1
