Hence, in response to the provided question, we can say that As a result, exponents [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].
what are exponents?Exponentiation, sometimes known as "raising b to the nth power," is a substitution cipher that includes two numbers: a base quantity, b, and an argument, meaning power, n. Exponents represent the number of times a value has been increased by itself. As an example, 2-3 (represented as 23) represents: 2 x 2 x 2 = 8. 2 + 3 = 6 does not equal 23. Remember that an integer multiplied by one equals itself. Exponents are a method for expressing large numbers as powers. The amount that represents however many times a statistic has already been amplified by itself is called the exponent. As an example, multiplying 6 by 4 yields 6 x 6 x 6.
Using exponent principles and the square root of perfect squares, we may simplify sqrt(196y8) as follows:
[tex]\sqrt(196y8) = \sqrt((142*(y4)2) [since 196 = 142 and (y4)2 = y8]\\\sqrt(142) * \sqrt((y4)2) [using the \sqrt(ab) = \sqrt(a) * \sqrt(b) rule]\\= 14y^4[/tex]
As a result, [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].
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Find the area of the figure. (Sides meet at right angles.)
Answer:
Step-by-step explanation:
The area of the figure is 1120
The ordered pair ( 3 , 2 7 ) is on the graph of a proportional relationship. 2 5 10
a. Show how to find the constant of proportionality. b. Write an equation for this relationship.
a) The constant of proportionality is solved to be 9
b) The equation of the relationship is y = 9x
How to find the constant of proportionalitya. To find the constant of proportionality, we can use the formula:
K = y/x
where
k is the constant of proportionality,
y is the dependent variable (output), and
x is the independent variable (input).
In this case, The ordered pair (3, 27) will be used them to solve for k.
where
x = 3
y = 27
k = y/x = 27/3
k = 9
b. The equation for this relationship is written using the formula
K = y/x
rewriting in terms of y
y = kx
y = 9x
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Rodolfo has two checks that he needs to deposit into his checking account.
One check is for $108.93, and the second check is for $372.47. He wants to receive $75 cash back from his deposit. What is Rodolfo's net deposit?
Answer:
Rodolfo has two checks, one for $108.93 and the other for $372.47. Let's add the amounts of the checks to get the total amount of the deposit:
$108.93 + $372.47 = $481.40
Next, Rodolfo wants to receive $75 cash back from his deposit. We need to subtract $75 from the total amount of the deposit to get the net deposit:
$481.40 - $75 = $406.40
Therefore, Rodolfo's net deposit is $406.40.
Step-by-step explanation:
Answer:
Step-by-step explanation:
To find Rodolfo's net deposit, we need to add the values of his two checks and subtract the amount of cash he wants to receive back:
Net deposit = (Value of Check 1) + (Value of Check 2) - (Amount of Cash Back)
Net deposit = $108.93 + $372.47 - $75
Net deposit = $406.40 - $75
Net deposit = $331.40
Therefore, Rodolfo's net deposit is $331.40.
Chapter 8 test geometry
Does anyone know how to do this? Pls help
a. The sketch is attached
b. The vertical height is 18.13 feet
c. The given angle 65° is the angle of elevation.
d. The foot of the ladder is 8.45 feet away from the wall.
7. The angle of elevation is congruent to angle of depression because they are on the alternate sides of two parallel lines.
8.
a. Diagram of triangle CDE is attached
b. The formula that can be used to solve triangle CDE is the Law of Sines
c.
∠ e = 11
c = 75.47
d = 8.77
How to vertical height of the ladderb. To find the vertical height of the ladder that is touching the wall, we use the trigonometric function
sin 65 = vertical height / height of ladder
sin 65 = vertical height / 20
vertical height = sin 65 * 20
vertical height = 18.13 feet
c. The given angle 65° is the angle of elevation.
d. To find how far the foot of the ladder is from the wall, we can use the trigonometric function cosine.
cos 65° = x / 20
x = 20 cos 65°
x ≈ 8.45 feet
7. The statement is true. The angle of elevation is the angle between the horizontal line and the line of sight from the observer to the object above the horizontal line.
The angle of depression is the angle between the horizontal line and the line of sight from the observer to the object below the horizontal line.
If the two objects are on parallel lines (e.g., the ground and a bridge above it), then the angle of elevation from one object is congruent to the angle of depression from the other object.
8. a. Diagram of triangle CDE is attached
b. The formula that can be used to solve triangle CDE is the Law of Sines
∠ e = 180 - 52 - 17 = 111
sin E / 28 = sin C / c = sin D / d
c = 28 sin 52 / sin 111 = 23.63
d = 28 sin 17 / sin 111 = 8.77
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.2. The International calls tariffs of Telkom are given in the following table.
Number of minutes
3
5
9
Y
Costs
R4.95
R8.25
X
R28.05
The following table lists Telkom's rates for international calls. Number minutes needed for [tex]x[/tex] to be [tex]17[/tex]and [tex]y[/tex] to be [tex]14.85[/tex].
Do numbers have any symbolic significance?Many numbers have deeper symbolic connotations in addition to their spiritual significance, and it is crucial to grasp these meanings in order to comprehend how they influence other cultures' perceptions of the physical world.
What may seeing 333 represent for you personally?According to Wilder, any sequence of consecutive threes is probably a sign of good fortune or a shift in your job, achievement, aspirations, or emphasis. According to Wilder, the number 333 is frequently a signal that you should have faith in your ability to make the next move.
Let[tex]y=k*b[/tex]
When [tex]x=3, y=4.95, x=5, y=8.25[/tex]
[tex]4.95=3k+b[/tex]
[tex]8.25=5k+b[/tex]
[tex]k=1.65[/tex]
[tex]b=0[/tex]
[tex]y=1.65x[/tex]
when [tex]x=9[/tex]
[tex]y=1.65*9 = 14.85[/tex]
when [tex]y=28.05[/tex]
[tex]x=y/1.65=28.05/1.65=17[/tex]
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The complete and the correct form of question is:
The International calls tariffs of Telkom are given in the following table:
Number of minutes 3 5 9 y
Cost R4.95 R8.25 X R28.05
Determine the cost of 9 minute call
Tickets for The Phantom of the Opera cost $6 for children and $12 for adults. A local school group paid $252 for 36 tickets. How many of each did they purchase?
HELP ASAP WILL GIVE BRAINLIEST
When rolling a 6-sided die twice, determine P(sum of 4).
3
36
5
36
8
36
2/6
The probability of the sum of 4 is 3/36
How to determine the probability of the sum of 4From the question, we have the following parameters that can be used in our computation:
rolling a 6-sided die twice
So, the sample space are
S1 = {1, 2, 3, 4, 5, 6}
S2 = {1, 2, 3, 4, 5, 6}
For the sum of 4, we have]
(1, 3), (2, 2) and (3, 1): Count of 3
The sample size of the event is
Size = 6 * 6
Size = 4
Using the above as a guide, we have the following:
P = Count/Size
So, we have
P = 3/36
Evaluate
P = 1/12
Hence, the probability is 1/9
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Which expression is equivalent to 9(2x+5y)
Answer: 18x + 45y.
Step-by-step explanation:
Expanding the brackets, we get:
9(2x+5y) = 92x + 95y
Simplifying the products, we get:
9(2x+5y) = 18x + 45y
Therefore, the expression equivalent to 9(2x+5y) is 18x + 45y.
Answer:
18x+45y
Step-by-step explanation:
9(2x+5y) = 18x + 45y
Therefore, the expression equivalent to 9(2x+5y) is 18x + 45y.
Question 6 of 10
Fill in the blank to complete the following sentence.
If a polynomial has one root in the form a- √5, it has a second root in the
form of a√5.
Considering the complex-conjugate root theorem, the statement is given as follows:
If a polynomial has one root in the form a - √5, it has a second root in the
form of a + √5.
What is the complex-conjugate theorem?The complex conjugate theorem for rational roots states that if a polynomial with real coefficients has a complex root of the form a + bi (where a and b are real numbers and i is the imaginary unit), then its complex conjugate a - bi is also a root of the polynomial.
In the case of a rational root, we have that:
If [tex]a + \sqrt{b}[/tex] is a root, then the number [tex]a - \sqrt{b}[/tex] is also a root, which justifies the answer for this problem.
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A cylindrical tank is lying horizontally on the ground.
Diameter - 20ft
Length - 22ft
Depth of water in tank is 6ft.
1 gallon = 231 cubic inches.
A). How many gallons of water are in the tank?
B). How many more gallons of water will it take to fill the tank?
Answer:
I don't know
Step-by-step explanation:
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A manufacturer of lighting fixtures has daily production costs of C 800 - 50x+ 0.25x2, where C is the total cost (in dollars) and x is the number of units produced. What daily production number
yields a minimum cost?
x fixtures
Submit Answer
what is the debt to equity ratio for 2024
Answer:
75.6%
Step-by-step explanation:
Reducing Debt: 2024's debt to equity ratio has increased from 67.6% to 75.6% over the past 5 years. Debt Coverage: 2024's operating cash flow is negative, therefore debt is not well covered.
DEDUCTION AND APPLICATION Do not use a calculator when answering Part 3. 3.1 Apply the compound angle expansion sin(x + y) = sin x cos y + cos x sin y to expa sin 2x and simplify your answer: sin 2x = sin(x+x) 3.2 Expand each of the following, using your answer from 3.1: 3.2.1 sin 100° = ..... 3.2.2 sin 46° = .... 3.2.3 sin 40° =. Write the following expressions as a single trigonometric ratio: 3.3.1 2 sin 19° cos 19° = 3.3.2 2 cos 40° sin 40° - 3.3.3 sin 25° cos155° .........
Answer:
Step-by-step explanation:
3.1:
Using the compound angle expansion, we have:
sin 2x = sin(x + x) = sin x cos x + cos x sin x
sin 2x = 2 sin x cos x
Therefore, sin 2x = 2 sin x cos x.
3.2:
Using the result from 3.1:
3.2.1: sin 100° = 2 sin 50° cos 50° = sin 100° = 0.766
3.2.2: sin 46° = 2 sin 23° cos 23° = sin 46° = 0.719
3.2.3: sin 40° = 2 sin 20° cos 20° = sin 40° = 0.642
3.3:
Using the identity sin(a ± b) = sin a cos b ± cos a sin b:
3.3.1: 2 sin 19° cos 19° = sin 38° = sin (45° - 7°) = sin 45° cos 7° - cos 45° sin 7° = (1/√2)cos 7° - (1/√2)sin 7° = -sin (7° - 45°) = -sin 38°
Therefore, 2 sin 19° cos 19° = -sin 38°.
3.3.2: 2 cos 40° sin 40° = sin 80° = sin (45° + 35°) = sin 45° cos 35° + cos 45° sin 35° = (1/√2)cos 35° + (1/√2)sin 35° = sin (35° + 45°) = sin 80°
Therefore, 2 cos 40° sin 40° = sin 80°.
3.3.3: sin 25° cos 155° = (1/2)(sin 180°) = 0
Therefore, sin 25° cos 155° = 0.
Which expression is equivalent to 1/3b+2/3b-5/6(b+1)
the answer is (a) [tex]\frac{1}{6}b-\frac{5}{6}[/tex]
In order to combine the two terms that have a 3b common denominator, we can first do so to simplify the statement 1/3b + 2/3b - 5/6(b+1):
1/3b + 2/3b = 3/3b = 1/b
what are expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
from the question:
In order to combine the two terms that have a 3b common denominator, we can first do so to simplify the statement 1/3b + 2/3b - 5/6(b+1):
1/3b + 2/3b = 3/3b = 1/b
We can now reintroduce this value into the first expression:
1/b - 5/6(b+1)
We can distribute the 5/6 term in order to further simplify this:
1/b - 5/6b - 5/6
Now that the first two terms share a common denominator of 6b, we may combine them:
6/6b - 5/6b - 5/6
Simplifying this gives us:
1/6b - 5/6
Therefore, the answer is (a) 1/6b - 5/6.
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Solve the equation 4tan+5=0 on the interval[0,360 )
answer
306.87 degrees and 666.87 degrees.
steps
4tanθ+5=0.
Subtract 5 from both sides to get 4tanθ=-5.
Divide both sides by 4 to obtain tanθ=-5/4.
θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:
θ = -53.13 + 360 = 306.87 degrees
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
Equation with tangent function.
Title: Solving an equation involving tangent function
Synopsis: We will solve the equation 4tanθ+5=0 on the interval [0,360).
Abstract: To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation. We start by subtracting 5 from both sides, giving us 4tanθ=-5. Then we divide both sides by 4, obtaining tanθ=-5/4. Finally, we take the arctangent (or inverse tangent) of both sides to find θ, remembering to specify the interval [0,360).
Numbered list:
Start with the equation 4tanθ+5=0.
Subtract 5 from both sides to get 4tanθ=-5.
Divide both sides by 4 to obtain tanθ=-5/4.
Take the arctangent (or inverse tangent) of both sides to find θ.
Specify the interval [0,360) when giving the solution.
Analogy: Solving this equation is like solving a puzzle where you need to rearrange the pieces to get the right picture.
One-sentence summary: We solve the equation 4tanθ+5=0 by subtracting 5, dividing by 4, taking the arctangent, and specifying the interval [0,360).
To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation.
Subtracting 5 from both sides gives us: 4tanθ = -5
Dividing both sides by 4: tanθ = -5/4
Taking the arctangent (or inverse tangent) of both sides, we get: θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
However, we need to specify the interval [0,360), which means we need to add 360 degrees to the negative solution, giving us 306.87+360 = 666.87 degrees (which is equivalent to 306.87-360 = -53.13 degrees in this interval).
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
Sure, here's just the math:
4tanθ + 5 = 0
Subtracting 5 from both sides:
4tanθ = -5
Dividing both sides by 4:
tanθ = -5/4
Taking the arctangent (or inverse tangent) of both sides:
θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:
θ = -53.13 + 360 = 306.87 degrees
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
ChatGPT
Jose measures the diameter of a ball as 15 inches. How many cubic inches of air can the ball hold, to the nearest tenth?
Answer:
Assuming the ball is a perfect sphere, we can use the formula for the volume of a sphere to calculate the amount of air it can hold.
The formula for the volume of a sphere is:
V = (4/3)πr^3
where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.
To calculate the radius of the ball from its diameter of 15 inches, we divide by 2:
r = d/2 = 15/2 = 7.5 inches
Substituting this value into the formula, we get:
V = (4/3)π(7.5)^3 ≈ 1767.15 cubic inches
Therefore, the ball can hold approximately 1767.15 cubic inches of air to the nearest tenth.
Step-by-step explanation:
A serving of Cereal A contains 4 more grams of carbohydrates than a serving of Cereal B. If you eat a serving of each cereal, you will consume 66 g of carbohydrates. Find the amount of carbohydrates in each cereal.
Answer:
Let's assume that a serving of Cereal B contains x grams of carbohydrates.
According to the problem, a serving of Cereal A contains 4 more grams of carbohydrates than Cereal B. So, the amount of carbohydrates in Cereal A is (x + 4) grams.
The total amount of carbohydrates consumed from both cereals is 66 grams:
x + (x + 4) = 66
Simplifying the equation:
2x + 4 = 66
Subtracting 4 from both sides:
2x = 62
Dividing by 2:
x = 31
So a serving of Cereal B contains 31 grams of carbohydrates.
And a serving of Cereal A contains 4 more grams:
31 + 4 = 35
Therefore, a serving of Cereal A contains 35 grams of carbohydrates.
If two adjacent angles (x+18) and x are inside a 90° angle, what is the equation for the two adjacent angles?
Answer:
Step-by-step explanation:
For a right angle triangle we use Pythagoras theorem
hypotenuse²=x²+(x+18)²
=x²+x²+36x+324
=2x²+36x+324
If the total amount of wealth in the world is $418.3 Trillion, and the wealth of the top 1% combined is worth more than $190 Trillion, what percent of global wealth is concentrated in the hands of the top 1%
?
Answer: The top 1% of the world's population holds more than 45% of global wealth.
Step-by-step explanation:
To find the percentage of global wealth concentrated in the hands of the top 1%, we need to divide the wealth of the top 1% by the total amount of global wealth, and then multiply by 100 to get the percentage.
Percentage of global wealth held by top 1% = (Wealth of top 1% / Total global wealth) x 100
We are given that the total amount of global wealth is $418.3 trillion, and the wealth of the top 1% is more than $190 trillion.
So, the percentage of global wealth held by the top 1% is:
(190 trillion / 418.3 trillion) x 100 = 45.38%
Therefore, the top 1% of the world's population holds more than 45% of global wealth.
Answer:
45.42%
Step-by-step explanation:
To find:-
What percent of global wealth is concentrated in the hands of the top 1% .Answer:-
We are here given that, the total global wealth is 418.3T dollars and more than 190T dollars is in hands of top 1% of the people. We are interested in finding out the percentage of global wealth in the hands of top 1% . We can find the percentage as ,
[tex]:\sf\implies \pink{ \% =\dfrac{Wealth\ owned\ by \ 1\% }{Total\ wealth}\times 100}\\[/tex]
On substituting the respective values, we have;
[tex]:\sf\implies \% =\dfrac{\$ 190T}{\$ 418.3T}\times 100\\[/tex]
[tex]:\sf\implies \pink{\% = 45.42\% } \\[/tex]
Hence the required percentage is 45.42% .
Which is the factor for all numbers ?
Answer: 1
Step-by-step explanation: From the above data, we observe that 1 is the greatest factor of itself and the smallest factor of any other number. Therefore, 1 is the factor of every number.
Kremena took out a $500 discounted loan for a period of 3 months. The amount she actually received into her bank account was $460. Assuming simple interest rates, what is effective interest rate re?
The effective interest rate on the loan is also 32%.
What is effective interest rate ?
Effective interest rate is the actual interest rate that is paid or earned on an investment, loan, or other financial product. It takes into account not only the nominal interest rate, which is the stated rate of interest, but also the frequency of compounding or other factors that affect the overall return.
According to the question:
To find the effective interest rate, we first need to calculate the amount of interest Kremena paid on the loan. We can do this by subtracting the amount she received from the amount of the loan:
Interest = Loan amount - Amount received
Interest = $500 - $460
Interest = $40
Next, we can use the formula for simple interest to calculate the interest rate:
I = P * r * t
where I is the interest, P is the principal (loan amount), r is the interest rate, and t is the time in years.
Since Kremena took out the loan for 3 months, which is a quarter of a year, we have:
I = P * r * t
$40 = $500 * r * (3/12)
$40 = $500 * r * 0.25
r = $40 / ($500 * 0.25)
r = 0.32 or 32%
So the interest rate on the loan is 32%. However, this is the nominal interest rate, which does not take into account the effects of compounding. To find the effective interest rate, we need to take into account the fact that Kremena only received $460, which means that she effectively paid more interest than she would have if she had received the full $500.
To calculate the effective interest rate, we can use the formula:
[tex]re = (1 + r/n)^n - 1[/tex]
where re is the effective interest rate, r is the nominal interest rate, and n is the number of compounding periods per year. Since the problem specifies simple interest, there is no compounding, so we can take n = 1. Plugging in the values, we get:
[tex]re = (1 + 0.32/1)^1 - 1[/tex]
re = 0.32 or 32%
So the effective interest rate on the loan is also 32%.
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Which of the following statements are true about the diagram
The statements that are true about the diagram given above = Line JL is an angle bisector and L is the midpoint of a segment in the diagram. That is option B and F.
What is an angle bisector?An angle bisector is defined as the lone the
at is drawn through an angle such that it divides the angle into two equal parts.
From the diagram above, line JL divided the angle < J into two equal angles while diving the line segment KI into two equal parts such as KL and LI.
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PLEASE HELP WILL GIVE BRAINLISET AND 60 PTS I APPRECIATE IT !!:)
Answer:
Step-by-step explanation:
domain is negative infinity, positive infinity
range is -3, positive infinity
Answer:
F(x) is all values that x can be. so the answer is the domain is (-∞,4)
Step-by-step explanation:
PLEASE HELP ME!!!!!!!!!!
Reflect △ABC across the y-axis
PLEASE LOOK AT THE PICTURE!!!!!!!
A: (4,-2)
B: (1,-1)
C: (1,-4)
Hope this helps! Just graph it.
Solving Square Root Equations
Solve the following equations. Be sure to label any extraneous solutions.
The solution of each equation are;
1) x = 6, x = 0
2) x = 3, x = 2
3) x= 4 ±√6
4) x = 6 ± √24/2
What is an extraneous solution?An extraneous solution is a solution obtained in a mathematical equation that does not satisfy the original equation, even though it appears to be a valid solution when plugged into the equation.
1) (√6x)^2 = x^2
6x = x^2
x^2 - 6x = 0
x = 6, x = 0
2) √5x - 6 = x
5x - 6 = x^2
x^2 - 5x + 6 = 0
x = 3, x = 2
3) √2x - 1 = x - 3
2x - 1 = (x - 3)^2
2x - 1 = x^2 - 6x + 9
x^2 - 6x - 2x + 9 + 1 = 0
x^2 -8x + 10 = 0
x= 4 ±√6
4) x = 2 + √2x - 11
x -2 = √2x - 11
x^2 - 4x + 4 = 2x - 11
x^2 -4x -2x + 4 + 11 = 0
x^2 - 6x + 15 = 0
x = 6 ± √24/2
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST PLEASE HELP
The value of f(9), the y-intercept, and the equation will be -3, 15, and f(x) = -2x + 15, respectively.
Given that:
Points, (-1, 17) and (4, 7)
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation of the line passing through (-1, 17) and (4, 7) is given as,
(y - 17) = [(7 - 17)/(4 + 1)](x + 1)
y - 17 = -2x - 2
f(x) = -2x + 15
The value of f(9) is calculated as,
f(9) = -2(9) + 15
f(9) = - 18 + 15
f(9) = - 3
The graph is given below.
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the time taken to fill a tank was 2 hours and 43 minutes. write this time to the nearest 5 minutes
Answer:
To write the time taken to fill a tank to the nearest 5 minutes, we first need to convert 2 hours and 43 minutes to minutes. 2 hours = 2 x 60 = 120 minutes So, the total time taken in minutes is: 120 + 43 = 163 minutes To round this to the nearest 5 minutes, we need to consider the last digit of the number of minutes, which is 3. Since 3 is less than 5, we round down to the nearest multiple of 5, which is 160. Therefore, the time taken to fill the tank to the nearest 5 minutes is: 2 hours and 43 minutes = 160 minutes = 2 hours and 40 minutes
To write the given time to the nearest 5 minutes, round down the minutes value if the last digit is less than 5, and keep the hours value as it is.
Explanation:To write the given time to the nearest 5 minutes, we need to round it to the closest multiple of 5. The given time is 2 hours and 43 minutes. To round to the nearest 5 minutes, we look at the last digit of the number of minutes, which is 3. Since 3 is less than 5, we round down the minutes to 0 and keep the hours as it is. Therefore, the time to the nearest 5 minutes is 2 hours and 40 minutes.
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At her Fourth of July party, Lexi serves her famous grilled chicken. Her secret is to use 6 fluid ounces of lemon-garlic marinade for every pound of chicken. Lexi plans to grill 4 pounds of chicken. How many cups of marinade should she use? cups
Simplify each expression to a single term: 5.5.1 cos² 19⁰-sin² 19° = 5.5.2 cos² 19° + sin² 19⁰ = 5.5.3 2 cos² 50° -1 =.... 5.5.4 1-2 sin² 50° = ........ 5.5.5 6cos² 2 -3= orpress cos169
Answer:
Step-by-step explanation:
5.5.1 cos² 19⁰ - sin² 19° = cos² 19° - (1 - cos² 19°) = 2cos² 19° - 1
5.5.2 cos² 19° + sin² 19⁰ = 1
5.5.3 2 cos² 50° -1 = cos 100° - 1
5.5.4 1-2 sin² 50° = cos² 50°
5.5.5 6cos² 2 -3 = 6cos²(180°-11°) -3 = 6cos²11° -3 = 6cos²(360°-349°) -3 = 6cos²349° - 3
Note: cos(360°-x) = cos x and cos(180°-x) = -cos x, so we can write cos169° = cos(180°-11°) = -cos11°.
Find the measure of line segment JK.
The measure of line segment JK using the Secant Theorem is found as 7 units.
Explain about the Secant Theorems?According to the intersecting secants theorem, the product of one whole secant segment but also its outer segment is equivalent to the product of the other whole secant segment as well as its external segment when two secants cross at an exterior point.
According to the Secant Theorem,
If two secants are drawn from an identical point through a circle, their products, A times their external segment and B times their external segment, are equal.
So, using Secant Theorem:
JK*JL = RM*RL
8* (2x + 7) = 24 * 7
Solving the equation:
x = 7
Thus, the measure of line segment JK using the Secant Theorem is found as 7 units.
know more about the Secant Theorems
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