If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
What is 1/7^9 × 1/7^-6
Which of the following sets of points is a direct variation?
(0, 0); (2, 4); (5, 15)
(0, 0); (-1, -2); (1, 2)
(3, 6); (-2, 4); (-1, 2)
(0, 5); (1, 6); (2, 7)
Answer:
(0, 0); (-1, -2); (1, 2) and (0, 5); (1, 6); (2, 7).
Step-by-step explanation:
The set will have a direct variation if each pair is added or subtracted by a common number in each component. You also can see it graphically, if the points form a straight growing line then the set is a direct variation. Then,
In the first set we have
(0,0), (0+2,0+4), (0+2+3, 0+4+11). The behavior is not uniform, then it is not a direct variation.
Second set: (-1, -2); (0,0); (1, 2)
(-1,-2)(-1+1,-2+2), (-1+1+1, -2+2+2). The behavior is uniform and it is increasing, then it is a direct variaton.
Third set:
(-2, 4), (-2+1,4-2), (-2+1+4, 4-2+4). The behavior is not uniform, then it is not a direct variation.
Fourth set:
(0,5), (0+1, 5+1), (0+1+1, 5+1+1). The behavior is uniform and it is increasing, then it is a direct variaton.
If 5+6i is a root of the polynomial function f(x),which of the following must also be a root of f(x)
Answer:
5 - 6i must also be a root of f(x)
Step-by-step explanation:
Complex conjugates states that the two complex numbers are conjugates of each other if they have the same real part and their imaginary parts are negatives of each other i.e, the complex conjugate of a + bi is a - bi where i is imaginary.
Conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a-bi is also a root of that polynomial.
Given: if 5+ 6i is a root of the polynomial function f(x).
then,
by the conjugate root theorem;
5 - 6i is also be a root of the polynomial f(x).
which equation is not true for the solution x = -8
How do you represent any number in an equation?
One card is drawn at random from the deck of cards shown. Which of the following probabilities is equal to one?
P(even or odd)P(even and odd)P(not yellow)
Answer:
P(Even or ODD) ( .Y .)
Step-by-step explanation:
For the expression below, write an equivalent expression that involves x only. assume x is positive.
Write three decimals that have a sum of 27.905. Parts of the needed decimals are listed below! thanks!
14. + 8. + 4. = 27.905
What is the value of log5 125
Answer:
[tex]log_5125=3[/tex]
Step-by-step explanation:
Given : [tex]log_5125[/tex]
We have to find the value of [tex]log_5125[/tex]
Consider the given expression [tex]log_5125[/tex]
Rewrite 125 in power- base form, [tex]125=5^3[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]
[tex]\log _5\left(5^3\right)=3\log _5\left(5\right)[/tex]
[tex]=3\log _5\left(5\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex]
[tex]\log _5\left(5\right)=1[/tex]
[tex]3\log _5\left(5\right)=3[/tex]
Thus, [tex]log_5125=3[/tex]
The value of log_5 125 is 3.
We have,
To find the value of log base 5 of 125, we need to determine the exponent to which we need to raise 5 to obtain 125.
In other words,
What power do we need to raise 5 to in order to get 125.
So,
By evaluating 5³ (5 raised to the power of 3), we find that 5³ = 125.
So, log base 5 of 125 is equal to 3, as log base 5 of 125 = 3.
So,
log base 5 of 125 equals 3 because 5 raised to the power of 3 gives us 125.
Thus,
The value of log_5 125 is 3.
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Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5
(b) how many measurements must be averaged to get a margin of error of ±0.0001 with 98% confidence? (round your answer up to the nearest whole number.)
To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, you can use the formula for the margin of error.
Explanation:To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, we can use the formula for the margin of error:
Margin of Error = Z * (Standard Deviation / √(Sample Size))
Given that we want a margin of error of ±0.0001 and a confidence level of 98%, we can find the corresponding Z-value using a standard normal distribution table.
Once we have the Z-value, we can rearrange the formula to solve for the sample size, which represents the number of measurements that must be averaged.
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Roger can run one mile in 8 minutes. jeff can run one mile in 6 minutes. if jeff gives roger a 1 minute head start, how long will it take before jeff catches up
explain how you could convert a rate of 18000 miles per hour to miles per second
263,148 what is the value of the digit 6 in this number?
show the zero property of multiplication using the number 25
Mary is making some shirts for her school's drama department. The fabric store has 3 1/6 yards of the fabric she wants in stock. But this quantity of fabric can make only 1 1/3 shirts. What length of fabric does Mary need to buy if she wants to sew 2 shirts?
A)1 1/6
B)2 3/8
c)3 5/6
D)4 3/4
HELP ME
On a Saturday, Tyler earned $97.20 waiting tables at a restaurant. He earned $9.25 an hour, and an additional $60.20 in tips. How many hours did he work that day? (Write and solve an equation to solve this problem.)
sorry my writing is messy
A movie rental gives a free popcorn to every 15th customer and a free movie rental to every 4th customer. Which customer was the first to win both prizes?
Carol ate 2/5 of the cake, Dima ate 3/8 of the REMAINING cake, mom ate the rest.
If it was a POUND cake, how many OZ did MOM eat? PLEASE HELP ASAP, GIVING BRAINLIEST.
Her mum ate 31/40 of the cake
Given the weight of the cake to 1 pound
If Carol ate 2/5 of the cake, the remaining fraction of the cake will be 1 - 2/5 = 3/5
If Dima ate 3/8 of the REMAINING cake, then the fraction of cake Dima ate will be:
Dima = 3/8 * 3/5
Dima = 9/40
Fraction of the cake that her mum ate = 1 - 9/40 = 31/40
Hence her mum ate 31/40 of the cake
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jillian bought 1/2 pound of turkey and 1 1/3 pound of cheddar cheese at the deli. both items are on sale for $6 per pound. how much does each turkey cost>
To calculate the cost of the turkey, multiply the weight of the turkey (1/2 pound) by the cost per pound ($6). The total cost for the turkey is $3.
Jillian bought 1/2 pound of turkey and 1 1/3 pounds of cheddar cheese at the deli, with both items on sale for $6 per pound. To find out how much the turkey costs, you need to multiply the weight of the turkey by the cost per pound. Here's how you do it:
Determine the weight of the turkey: 1/2 pound.Multiply the weight of the turkey by the cost per pound: (1/2 pound) x ($6/pound).Calculate the cost: 1/2 x 6 = $3.Therefore, the cost of the turkey is $3.
Theoretically, what would happen if a nation had an unlimited supply of a certain resource?
Which number is a prime number??
111
121
131
141
Final answer:
Among the given options, the number 131 is a prime number, as it only has two divisors: 1 and itself.
Explanation:
The student has asked to identify which number among the given options is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Analyzing the given options:
111 is divisible by 3.
121 is divisible by 11 (11 x 11).
131 is a prime number because it has no divisors other than 1 and itself.
141 is divisible by 3.
Therefore, the correct answer is 131, which is a prime number.
what is 79.4÷8 what is the answer in decimal form
Average speed of Car 1 = 45 mph.
Average speed of Car 2 = 65 mph.
Time elapsed between start of Car 1 and start of Car 2 = 18 minutes.
how long until the cars lapse
It will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.
To find out how long it will take for Car 2 to catch up to Car 1, we first need to determine the distance Car 1 travels during the 18-minute head start.
Convert 18 minutes to hours.
18 minutes ÷ 60 minutes/hour = 0.3 hours
Calculate the distance Car 1 travels during the 18-minute head start.
Distance = Speed × Time
Distance = 45 mph × 0.3 hours
Distance = 13.5 miles
Now that we know Car 1 has traveled 13.5 miles when Car 2 starts, we need to find out how long it takes for Car 2 to catch up, which is essentially the time needed to cover this distance at the speed difference between the two cars.
Calculate the relative speed of Car 2 compared to Car 1.
Relative Speed = Speed of Car 2 - Speed of Car 1
Relative Speed = 65 mph - 45 mph
Relative Speed = 20 mph
Calculate the time it takes for Car 2 to catch up.
Time = Distance ÷ Relative Speed
Time = 13.5 miles ÷ 20 mph
Time = 0.675 hours
Convert the time from hours to minutes for better understanding.
0.675 hours × 60 minutes/hour = 40.5 minutes
So, it will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.
Trevor had 4 small boxes of raisins to share equally among himself and 2 friends.
How many boxes of raisins would each person receive?
A.
B.
C.
D.
thirty-eight and ninety-seven hundredths kilograms in standard form
Answer:
The answer is 38.97 kilograms.
Step-by-step explanation:
Thirty-eight and ninety-seven hundredths kilograms in standard form is 38.97 kilograms.
Thirty eight is simply 38.
And ninety-seven hundredths means that 97 is written after decimal. This is because when there exists an 'and' in a mathematical number, this means there is a decimal.
So, the answer is 38.97 kilograms.
Gwen, Tristan, and Keith like to work out at the gym. They each have an app on their phone that estimates the calories they burn. By the time Tristan and Keith started exercising, Gwen had already burned 100 calories. Gwen burns 10 calories every minute, Tristan burns 125 every 10 minutes, and Keith burns 300 calories every 30 minutes. Let x represent the number of minutes since Tristan and Keith started exercising and y represent the number of app-estimated calories burned. Part A
Answer:
For part A)
Let's make a function for each person, and then combine them to find total calories
Gwen burns 10 cal/min, and had already burned 100 calories when Tristan and Keith started (Yg=100 when x=0)
Yg= 10x + 100
Step-by-step explanation:
I got a 100% on it.
Find the first partial derivatives of the function. f(x, y) = ax + by/ cx + dy
The partial derivatives of the given function f(x, y) = ax + by / cx + dy with respect to x and y have been calculated, showing how the function changes with each variable while holding the other constant.
Explanation:For the function f(x, y) = ax + by / cx + dy, the first partial derivatives with respect to x and y are:
∂f/∂x = a(cy - by') / (cx + dy)²∂f/∂y = (ax - ay) / (cx + dy)²These partial derivatives measure the rate of change of the function f(x, y) with respect to x and y while treating the other variable as constant.
Divide (8.6 x 108) by (3.2 x 103). Express your answer in scientific notation.