Work Shown:
tan(angle) = opposite/adjacent
tan(x) = 13/101
x = arctan(13/101)
x = 7.334379 approximately
x = 7.33
The sum of 7/8 of a number and 20 is 34 at minimum
Answer:
7/8x ≥ 14
Step-by-step explanation:
(sum means addition in case you forgot)
You would start by writing 7/8x + 20 ≥ 34
You would then subtract 20 from both sides to isolate the variable x.
You would then have 7/8x ≥ 14
Mark breaks up a 9-hour drive into 3 parts. He drives 2 1/2 hours before stopping for lunch. After driving some more, he stops for gas. If the second part of his drive was 1 2/3 longer than the first part, how long did he drive after stopping for gas?
Answer:
4 1/6 hours
Step-by-step explanation:
2 1/2 + 1 2/3 = 25/6 = 4 1/6
Using substitution, evaluate the expression b-a, if a = -14 and b = -7.
O 21
O -21
-7
7.
Please help
HELP ME ASAP!!!
Question 3(Multiple Choice Worth 5 points)
(04.04 MC)
If a sprinkler waters 1 over 15 of a lawn in 1 over 3 hour, how much time will it take to water the entire lawn?
5 hours
15 hours
18 hours
45 hours
It would take 5 hours.
1/15 of the lawn in 1/3 hours means it takes 1 hour to water 3/15 of the lawn aka 1/5
1/5 of the lawn in 1 hour would mean it takes 5 hours to finish watering the entire lawn.
Let f(x) = x^6( x − 8 )^7 / (x^2 +2)^2
Use logarithmic differentiation to determine the derivative.
f ' (x) =________
If
f(x) = x⁶ (x - 8)⁷ / (x² + 2)²
then taking the logarithm of both sides lets us expand the right side as
ln(f(x)) = ln(x⁶ (x - 8)⁷ / (x² + 2)²)
ln(f(x)) = ln(x⁶) + ln((x - 8)⁷) - ln((x² + 2)²)
using the property ln(ab) = ln(a) + ln(b).
We can also use the property ln(aⁿ) = n ln(a), so that
ln(f(x)) = 6 ln(x) + 7 ln(x - 8) - 2 ln(x² + 2)
Then differentiating both sides using the chain rule gives
f'(x)/f(x) = 6 x'/x + 7 (x - 8)'/(x - 8) - 2 (x² + 2)'/(x² + 2)
f'(x)/f(x) = 6 (1)/x + 7 (1)/(x - 8) - 2 (2x)/(x² + 2)
f'(x)/f(x) = 6/x + 7/(x - 8) - 4x/(x² + 2)
Solve for f'(x) :
f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) f(x)
and replace f(x) with the given function :
f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) • x⁶ (x - 8)⁷ / (x² + 2)²
We can expand the product :
f'(x) = 6 x⁵ (x - 8)⁷ / (x² + 2)²+ 7x⁶ (x - 8)⁶ / (x² + 2)² - 4x⁷ (x - 8)⁷ / (x² + 2)³
then simplify by factoring :
f'(x) = x⁵ (x - 8)⁶/(x² + 2)³ • (6 (x - 8) (x² + 2) + 7x (x² + 2) - 4x² (x - 8))
Simplify the rest :
f'(x) = x⁵ (x - 8)⁶ (9x³ - 16x² + 26x - 96)/(x² + 2)³
QD = 20000 -3P QS = 15000 +2P
The equilibrium price of the commodity at the given demand and supply is 1,000.
The given parameters:
Quantity demanded, QD = 20,000 - 3PQuantity supplied, QS = 15,000 + 2PThe equilibrium price of the commodity is calculated as follows;
At equilibrium price, the demand curve and supply curve cross each other.
[tex]QS= QD\\\\15,000 +2P = 20,000 - 3P\\\\2P+3P = 20,000 - 15,000\\\\5P = 5,000[/tex]
[tex]P = \frac{5,000}{5} \\\\P = 1,000[/tex]
Thus, the equilibrium price of the commodity is 1,000.
The complete question is below;
Determine the equilibrium price, if QD = 20000 -3P and QS = 15000 +2P.
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07
Question 4
What is the 11th term of the geometric sequence
-1.5, -3, -6, -12, ...? /(5 pts)
Your Answer:
Answer:
-1536
Step-by-step explanation:
By taking the general formula for the geometric sequence, we substitute the variables with the values of our sequence, finding -1536 as the 11th term
Differentiate y = sin^2x - cos^2x
Using the power and chain rules, the derivative of
y = sin²(x) - cos²(x)
is
dy/dx = 2 sin(x) cos(x) - 2 cos(x) (-sin(x))
dy/dx = 2 sin(x) cos(x) + 2 sin(x) cos(x)
dy/dx = 4 sin(x) cos(x)
and using the double angle identity for sine, this is equivalent to
dy/dx = 2 sin(2x)
Alternatively, we can first simplify y using the double angle identity for cosine:
cos(2x)= cos²(x) - sin²(x)
so that
y = -cos(2x)
and the derivative is
dy/dx = sin(2x) • 2
dy/dx = 2 sin(2x)
A traffic study determined that a larger city population indicates a
longer commute time for drivers. What can we say from this
information?
Answer:
There must he a circulation. May not be causation.
The sum of two numbers is 58.25. The second number is 14 less than 2 times the first number. What are the two numbers?
plz fast
Answer:
The first number is 24.08 and the second number is 34.17
If the cubic function P(x) includes the points (−4, 0), (0, 0), and (2, 0), which of the following represents this function?
Answer:
See below
Step-by-step explanation:
(-4,0) is the solution to x+4=0
(0,0) is the solution to x=0
(2,0) is the solution to x-2=0
Therefore, (x+4)(x-2)(x) = (x²-2x+4x-8)(x) = (x²+2x-8)(x) = x³+2x²-8x is the function that has the given zeroes
What are the prime numbers out of 4 5 6 7 8 9 ?
Pls help and show ur work ASAP I’ll add extra points
Answer:
Slope: 7/5 , Y-int: 1/5
Step-by-step explanation:
To find the slope, lets use the points (-3,-4) and (2,3)
The slope formula is (y2-y1)/(x2-x1) so we will plug in the numbers.
(3-(-4))/(2-(-3))=7/5. 7/5 is the slope (you can also do rise over run)
We find the y-int in many ways but i will show two.
We can make an equation in point-slope form. The formula is: y-y1=m(x-x1) and we use the point (-3,-4).
y-(-4)=7/5(x-(-3))
y+4=7/5x+21/5 (then move the 4 to the other side)
y=7/5x+1/5
The 1/5 is our y-int since we now have it in slope intercept form!
The other method we can use is putting it into slope intercept form first and using (-3,-4) to find the missing variable.
Slope intercept form is y=mx+b, let m be slope, b is y int, and (x,y) is our point
-4=(7/5)(-3)+b
-4=-21/5+b (move -15/7 to other side)
1/5=b !
we get the same answer I hope this helps sorry its long
-5(x + 6) = -(5x-9)
Please give me answer!
Answer:
There is no solution to this equation.
Hope this helps :)
Answer:
no solution.
Step-by-step explanation:
carry the -5 and - sign and multiply the numbers within the () signs. so - 5×x and -5×6. which is -5x + -30. the other side will be -5x + 9. so then if you take away the -5x your left with -30 = 9 which is impossible.
3+3=6! Easy for kids to learn!
Answer:
indeed
Step-by-step explanation:
3+3=6
I need help asap! Pls :)
Answer:
Step-by-step explanation:
6x + 10 + 2x + 26 = 180
8x + 36 = 180
8x = 144
x = 18
The chart below shows the number of tickets to the annual teachers VS.
students basketball game. What was the most number of tickets sold?
A. 12
B. 31
C. 40
D. 60
The most no. of tickets sold is 60.
What is bar graph?The pictorial representation of data in the form of vertical or horizontal rectangular bars, whose length is proportional to the data's measurement, is known as a bar graph. Data are typically grouped in this way. Bar charts are another name for them. In statistics, bar graphs are one way to handle data.
Given the graph between total student and number of ticket sold,
where students shown in Y axis and tickets sold in X axis,
as Shown in graph maximum number of tickets sold are 51 to 60
Hence the maximum number of ticket sold is 60.
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Joshua wanted to know the distance between two cities. The scale on the map was 1/2 in = 10 km. The distance between the cities on the map was 2 1/4 in. What was the actual distance between the cities?
Step-by-step explanation:
remark : it is very unusual for a map to mix two measurement norms. they are normally either fully in the American or fully in the metric system.
but let's do the exercise.
the scale says 1/2 in = 10 km
but our measurement on the map brought us quarter inches.
so,
1/2 in = 2/4 in = 10 km
therefore
1/4 in = 10/2 = 5 km
now,
2 1/4 = 9/4 in
this is 9 times 1/4.
therefore, the distance between the 2 cities is
9 × 5 = 45 km.
what rounds up to 5,620 to the nearest ten
5,610
Step by step explanation:When rounding to the nearest ten, like we did with 5620 above, we use the following rules:
We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.Answer: 5620
~~Step-by-step explanation~~
Rounding has a simple rule. 5 or above? Up you shove. 4 or below? Keep it low.
1. What are you using to round?
5620 : The tens place is the number we are either going to be rounding up or keeping. In this case, it is the 2 in 5620.5620 : When rounding to the nearest ten, you look at the ones section. In this case, it is the 0 in 5620.2. Execution
When rounding up to tens, look at the ones value. If the number is 5 or above, round the tens place up a number. (ex. 5625 --> 5630) If the number is a 4 or below, keep the tens value the same. (ex. 5624 --> 5620)Since the ones place in 5620 is below a four, we are going to keep the tens value the same, so the answer is going to be 5620.
Ax+2y=10 through the point (4,3)
Answer:
can you give more context to the question and I will answer it in the comments? thanks!
Answer:
Slope-intercept form y=10x-37
Point slope form y-3=10(x-4)
Step-by-step explanation:
2/8 and 1/2 write < or >
Answer:
0.5 > 0.25
Step-by-step explanation:
2/8 = 1/4 = 0.25
1/2 = 0.5
Answer:
<
Step-by-step explanation:
1/2 equals more than 2/8.
Because if u simplify 2/8 it would equal 1/4 which is less than 1/2.
Over a lengh of 101 inches the hight changes 5" what is the angle?
Answer:
2.83°
Step-by-step explanation:
The tangent of an angle is the ratio of rise to run.
θ = arctan(5/101) ≈ 2.83°
_____
We assume the length is referring to the horizontal distance.
If it is the distance along the path, then the angle is ...
θ = arcsin(5/101) ≈ 2.84°
How do I figure this out
Answer:
D
Step-by-step explanation:
yeah-ya....................... right?
Answer:
D
Step-by-step explanation:
hope it help correct me if wrong
you have to solve for X
Answer:
x = 5/8Step-by-step explanation:
(1/2) / 4 = x / 51 / 8 = x / 5x = 5 / 8Done
The ratio of girls to boys is 5:3 in a class. If there are 15 girls in the class, what is the class size? What is the unit ratio?
Answer:
Try setting up a proportion: [tex]\frac{5}{15}=\frac{3}{x}[/tex] then cross multiply to solve for x which will try you how many boys are in the class. Then add the number of boys and girls together.
Step-by-step explanation:
33. Jeremy works at a bank and earns $800 for a 40-hour week. His sister, Beth works at a school and only earns $700 for a 30-hour week. Who makes more per hour?
A. Jeremy makes $10 more per hour
B. Beth makes $10 less per hour
C. Beth makes at least $3 more per hour
D. Jeremy makes at least $5 more per hour
Answer:
Step-by-step explanation:
Jeremy
Pay = 800
Time = 40 hours
Per hour pay= 800/40 = 20 dollars per hour.
Beth
Pay = 700
Time = 30 hours
Per hour Pay= 700 / 30 = 23.33
The answer is C. She gets 23.33 which is 3.33 more than her brother makes.
Solve for x: 2x + 12= 18 (5 points)
Answer:
X = 3
Step-by-step explanation:
2x = 12 = 18
x +6 = 9
x = 9-6
x = 3
Hope its right <3 Like if it helped
What are the length and width of a rectangular traffic sign if the length exceeds the width by 4 inches and the perimeter is 152 inches?
Answer:
L = 40
w = 36
Step-by-step explanation:
P = 2*L + 2*w
L = w + 4
w = w
P = 152
P = 2*(w + 4) + 2*w Remove the brackets
P = 2w + 8 + 2w Combine and switch sides Use P = 152
4w + 8 = P
4w + 8 = 152 Subtract 8 from both sides.
4w = 152 - 8
4w = 144 Divide by 4
4w/w = 144/4
w = 36
L = w + 4
L = 36 + 4
L = 40
Problem Situation: Ben buys a table for $240. He also buys 6 chairs that all cost the same amount. His total cost is $720. What is the price of one chair? Use the drop-down menus to complete parts A and B below.
The price of one chair Ben bought is $80 and he bought 6 chairs in total.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Ben buys a table for $240. He also buys 6 chairs that all cost the same amount.
Assuming each chair costs $x and his total cost is $720.
∴ 240 + 6x = 720.
6x = 720 - 240.
6x = 480.
x = 80
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Find the difference (6d+5) - (2-3d)
Answer:
(9d+3)
Step-by-step explanation:
(6d+5)-(2-3d)
>(6d+5)+(-2+3d)
>{(6d+3d)+(5-2)}
=(9d+3)