Answers
Answer:
28. x=6 29. x=15 30. -56/5 31. -3 32. -10 33. 9.6
Step-by-step explanation:
The statement "y varies inversely as x" means that there is a constant (a number that doesn't change) k so that
[tex]y=\frac{k}{x}[/tex]
28. y = 12 when x = 3, so [tex]12=\frac{k}{3} \Rightarrow k=(12)(3)=36[/tex]. Now that you know the value of k (in THIS problem!), plug in 6 for y to find x.
[tex]6=\frac{36}{x}\\6x=36\\x=6[/tex]
All these problems work the same way.
29. [tex]5=\frac{k}{6} \Rightarrow 5(6)=k \Rightarrow k=30[/tex] Then, [tex]2=\frac{30}{x} \Rightarrow 2x = 30 \Rightarrow x=15.[/tex]
30.
[tex]4=\frac{k}{14} \Rightarrow (4)(14)=k \Rightarrow k=56\\-5=\frac{56}{x} \Rightarrow -5x=56 \Rightarrow x = -\frac{56}{5}[/tex]
31.
[tex]9=\frac{k}{9} \Rightarrow 81=k\\\\y=\frac{81}{-27}=-3[/tex]
Related Questions
Verify that:
1. (CosX)(CotX) = CscX - SinX
2. (Csc X - CotX)^2 = 1-CosX/1+CosX
These were the last two questions on my Homework that I couldn’t figure out after many tries! Thank you to anyone who helps!
Answers
Answer:
See Below.
Step-by-step explanation:
Problem 1)
We want to verify that:
[tex]\displaystyle \left(\cos(x)\right)\left(\cot(x)\right)=\csc(x)-\sin(x)[/tex]
Note that cot(x) = cos(x) / sin(x). Hence:
[tex]\displaystyle \left(\cos(x)\right)\left(\frac{\cos(x)}{\sin(x)}\right)=\csc(x)-\sin(x)[/tex]
Multiply:
[tex]\displaystyle \frac{\cos^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]
Recall that Pythagorean Identity: sin²(x) + cos²(x) = 1 or cos²(x) = 1 - sin²(x). Substitute:
[tex]\displaystyle \frac{1-\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]
Split:
[tex]\displaystyle \frac{1}{\sin(x)}-\frac{\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]
Simplify:
[tex]\csc(x)-\sin(x)=\csc(x)-\sin(x)[/tex]
Problem 2)
We want to verify that:
[tex]\displaystyle (\csc(x)-\cot(x))^2=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Square:
[tex]\displaystyle \csc^2(x)-2\csc(x)\cot(x)+\cot^2(x)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Convert csc(x) to 1 / sin(x) and cot(x) to cos(x) / sin(x). Thus:
[tex]\displaystyle \frac{1}{\sin^2(x)}-\frac{2\cos(x)}{\sin^2(x)}+\frac{\cos^2(x)}{\sin^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor out the sin²(x) from the denominator:
[tex]\displaystyle \frac{1}{\sin^2(x)}\left(1-2\cos(x)+\cos^2(x)\right)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor (perfect square trinomial):
[tex]\displaystyle \frac{1}{\sin^2(x)}\left((\cos(x)-1)^2\right)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Using the Pythagorean Identity, we know that sin²(x) = 1 - cos²(x). Hence:
[tex]\displaystyle \frac{(\cos(x)-1)^2}{1-\cos^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor (difference of two squares):
[tex]\displaystyle \frac{(\cos(x)-1)^2}{(1-\cos(x))(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor out a negative from the first factor in the denominator:
[tex]\displaystyle \frac{(\cos(x)-1)^2}{-(\cos(x)-1)(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Cancel:
[tex]\displaystyle \frac{\cos(x)-1}{-(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Distribute the negative into the numerator. Therefore:
[tex]\displaystyle \frac{1-\cos(x)}{1+\cos(x)}=\displaystyle \frac{1-\cos(x)}{1+\cos(x)}[/tex]
140.23 < 140.203 what is the answer true or false.
Answers
Answer:
true
Step-by-step explanation:
Answer:
false because 140.23 is not less then 140.203
Find the number exactly halfway between 1/5 and9/10
Answers
I am not pretty sure of the answer but maybe it's 5/10
Answer:
the number half way between 1-5 is 3. and the number half way between 9/10 is 9.5
Step-by-step explanation:
to find the number half way between 1/5 just write out all the numbers (1 2 3 4 5) and 3 is the halfway point because there are two numbers on the right and to numbers on the left
the number halfway between 9 and 10 is 9.5. all you do is add 9 +10 then divide by 2
9+10=19
19÷2= 9.5
You drive your car for 3 hours at an average speed of 130 km per hour. How far did you go? *
Answers
what if a man has 19 cows and he wants to give Half of them to his brother 1/4th to Son and 1/5th to daughter?
Answers
9.5 for the brother 19/4 for the son and 19/5 for the daughter I think
Step-by-step explanation:
So 9.5 would be 10. 19/4 would be 5 and 19/5 would be 4
SO the brother would get 10 the son would get 5 and the daughter would get 4
Answer:
Brother-9.5
Son-19/4
Daughter-19/5
Step-by-step explanation:
Also, pls help me on my phsyics Q3 work on graduation alliance. PLEASE PLEASE.
A library labels each book with a six-character code to identify the book in its computer system. The first character is either a letter or digit, and this is followed by three digits, then two letters. How many different codes are possible
Answers
Answer: There are 24336000 different codes that are possible.
Step-by-step explanation:
We know that,
Total alphabets = 26
Total digits = 10
Choices for First place = 26+10=36
Choices for next 3 places = 10 x 10 x 10 = 1000
Choices for last 2 places = 26 x 26 = 676
Total different codes are possible = 36 x 1000 x 676
=24336000
Hence, there are 24336000 different codes that are possible.
1,2,3,5 and 7 are all common factors of two numbers. Write down the digit that the two numbers must end in?
Answers
You invested $680 at 2.7% compounded monthly. How much money do you have after
8 years? Estimate your answer to two places after the decimal, if necessary.
Answers
Answer:
$843.74
Step-by-step explanation:
A = P (1 + r/n)^nt
A = 680(1 + 0.027/12)^12·8
A = 680( 1.00225)^96
A = 843.74
Which radio costs 150% as much as Radio D?
Answers
Isaac earns $15 per hour when he babysits. Let A be the amount he earns in dollars after babysitting for H hours.
Answers
Answer:
A= 15(H)
Step-by-step explanation:
A is the total amount he is going to get, And H is the hours. If he gets 15 an hour. it means however many hours he works multiplied by 15 is the total amount he gets.
Andrea bought 1 2/5 pounds of avocados at $4.20 per pound and 2 1/
4 pounds of asparagus at $3.80 per pound.
What was her total cost?
Answers
Answer:
$14.43¢
Step-by-step explanation:
We are given; [tex]1\frac{2}{5}[/tex] pounds, 1 pound = $4.20 and [tex]2\frac{1}{4}[/tex] pounds,1 pound = $3.80 that Andrea bought.
Now we need to find her total cost. To do that, we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert [tex]1\frac{2}{5}[/tex] to a decimal. It is 1.4. Now we can set up a graph.
Avocados
[tex]\frac{4.2}{1}=\frac{x}{1.4}[/tex]
Switch sides
[tex]\frac{x}{1.4}=\frac{4.2}{1}[/tex]
Apply rule: [tex]\frac{a}{1}=a[/tex]
[tex]\frac{x}{1.4}=4.2[/tex]
Multiply both sides by 1.4
[tex]\frac{1.4x}{1.4}=4.2\cdot \:1.4[/tex]
Simplify
[tex]x=5.88[/tex]
So, her cost for avocados is $5.88¢
Now we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert [tex]2\frac{1}{4}[/tex] to a decimal. It is 2.25. Now we can set up a graph.
Asparagus
[tex]\frac{3.8}{1}=\frac{x}{2.25}[/tex]
Switch sides
[tex]\frac{x}{2.25}=\frac{3.8}{1}[/tex]
Apply rule : [tex]\frac{a}{1}=a[/tex]
[tex]\frac{x}{2.25}=3.8[/tex]
Multiply both sides by 2.25
[tex]\frac{2.25x}{2.25}=3.8\cdot \:2.25[/tex]
Simplify
[tex]x=8.55[/tex]
So, her cost for asparagus is $8.55¢
Total cost
Now that we have found out how much both of the fruits Andrea bought costs, we need to sum it up (meaning add it) to find the total cost:
$5.88¢ + 8.55¢ =
5.88 + 8.55 = 14.43
Therefore, Andrea's total cost of the fruits is $14.43¢
Write a system of linear inequalities represented by the graph.
Answers
Answer:
Alright so youd havee to right the terms in order which should be easy then your done! Hope this helped!
Step-by-step explanation:
Good morning, can someone help me solve this problem? I already did some of it but I need help, thank you
Answers
Answer: (-4, -1)
This means x = -4 and y = -1 pair up together.
======================================================
You're on the right track. You'll replace the 'x' with 3y-1, but you made a typo. I think you meant to write the subtraction symbol instead of the equal sign.
Here's what your steps could look like
-2x + 5y = 3
-2(3y-1) + 5y = 3
-6y + 2 + 5y = 3
-y + 2 = 3
-y = 3-2
-y = 1
y = -1
x = 3y-1
x = 3(-1) - 1
x = -3-1
x = -4
Therefore, (x, y) = (-4, -1) is the solution
-------------------
As the steps above show, I replaced each copy of x in the second equation with (3y-1). This is due to x = 3y-1. From there, we isolate y. Once you determine that y = -1, it's plugged into the first equation to find x.
If you were to graph x = 3y-1 and -2x+5y = 3 on the same xy coordinate grid, then the two lines would intersect at (-4, -1)
Also, note how plugging x = -4 and y = -1 into the second equation leads to...
-2x+5y = 3
-2(-4)+5(-1) = 3
8 - 5 = 3
3 = 3
We get the same value on both sides, so that verifies the second equation. I'll let you verify the first equation.
The 2nd term of an arithmetic progression is (1/2) and the sum of the first 14th terms is -70. Find
(a) the common difference
(b) the last term.
Answers
Answer:
The common difference is -1.
The last term (the 14th term) is -11.5.
Step-by-step explanation:
In an arithmetic sequence, the second term is 0.5 and the sum of the first 14 terms is -70.
We want to determine the: (a) common difference and (b) the last term.
We can write an explicit formula to represent the sequence. An arithmetic sequence can be modeled by the formula:
[tex]\displaystyle x_n=a+d(n-1)[/tex]
Where a is the initial term, d is the common difference, and n represents the nth term.
Since the second term is 0.5:
[tex]x_2=0.5=a+d(2-1)[/tex]
Simplify:
[tex]x_2=0.5=a+d[/tex]
The sum of an arithmetic sequence is given by the formula:
[tex]\displaystyle S=\frac{k}{2}\left(a+x_k\right)[/tex]
Where k is the number of terms and x_k is the last term.
Since the sum of the first 14 terms is -70, S = -70 and k = 14:
Using our explicit formula, the last term is:
[tex]x_{14}=a+d(14-1)=a+13d[/tex]
Substitute:
[tex]\displaystyle -70=\frac{14}{2}(a+(a+13d))[/tex]
Simplifiy:
[tex]-10=2a+13d[/tex]
Rewrite the equation for the second term:
[tex]a=0.5-d[/tex]
Substitute:
[tex]-10=2(0.5-d)+13d[/tex]
Simplify:
[tex]-10=1-2d+13d[/tex]
Solve for d:
[tex]d=-1[/tex]
Hence, our common difference is -1.
Solve for a, the initial term:
[tex]a=0.5-(-1)=1.5[/tex]
So, our explicit formula is now:
[tex]x_n=1.5-1(n-1)=1.5-n+1=2.5-n[/tex]
So, the last term (which is 14) is:
[tex]x_{14}=2.5-(14)=-11.5[/tex]
Mr. Cobb is carpeting a 17.7 m long hallway. He has a piece of carpet 22 m long. How much does Mr. Cobb need to cut off the length of the piece of carpet?
Answers
Answer:5.7
Step-by-step explanation:
Help! How do I find AC in this equation?
Answers
Answer:
33
Step-by-step explanation:
add 25 & 8 together
Answer:
SEE IMAGE FOR SOLUTION
Hope it helps
Have a great day
6 ( 7y - 5) simplified
Answers
Answer:
42y-30
Step-by-step explanation:
here you go
Given that there is a 21% chance it will rain on any day, what is
the probability that it will rain on the first day and be clear (not
rain) on the next two days?
Answers
What are the adjacent and vertical pairs in this picture
Answers
Answer:
Step-by-step explanation:
Two line segments AD and CE intersects at a point B.
Two angles which represent the pair of adjacent angles are,
∠ABC and ∠DBC
Pair of vertical angles (Opposite angles between two intersecting lines) is,
∠ABE and ∠CBD
1) Base of an isosceles triangle is five more than three times the equal sides and perimeter of the triangle is 75 cm. Find the lengths of the sides of the triangle.
Answers
Answer:
14 +14 +47 = 75
Step-by-step explanation:
x= side length
2x+(3x+5) = 75
5x+5 = 75
3x =70
x=14
14(3) +5 = 47
Simon lost his library card and has an overdue library book. When the book was 5 days late, he owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was 21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book. Suppose the total amount Simon owes when the book is n days late can be determined by an arithmetic sequence. Determine a formula for an, the nth term of this sequence. Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book is 60 days late.
Answers
Answer:
[tex](a)\ y = 0.25n +1[/tex]
[tex](b)\ \$16[/tex]
Step-by-step explanation:
Given
[tex]n \to days[/tex]
[tex]y \to amount[/tex]
[tex](n_1,y_1) = (5,2.25)[/tex]
[tex](n_2,y_2) = (21,6.25)[/tex]
Solving (a): Formula that represents the scenario.
Calculate slope (m)
[tex]m = \frac{y_2 - y_1}{n_2 -n_1}[/tex]
[tex]m = \frac{6.25-2.25}{21-5}[/tex]
[tex]m = \frac{4}{16}[/tex]
[tex]m = 0.25[/tex]
The equation is calculated using:
[tex]y = m(n - n_1) + y_1[/tex]
This gives:
[tex]y = 0.25(n - 5) + 2.25[/tex]
[tex]y = 0.25n - 1.25 + 2.25[/tex]
[tex]y = 0.25n +1[/tex]
Solving (b): Amount after 60 days late.
This means that:
[tex]n = 60[/tex]
So:
[tex]y = 0.25 * 60 + 1[/tex]
[tex]y = 15 + 1[/tex]
[tex]y = 16[/tex]
PLS HELP WILL MARK BRAINLEST IF UR CORRECT
Answers
Answer:
52. (0,-3)
53. Slope= 4
54. Y=4x-3
Find the value of 3a+ 3b when: a = 6 and b = 4 a = 4 and b = 6 Your two answers should be the same. Look at the expression and the a and b values and explain why the answers are the same.
Answers
Answer:
The answer is 30.
Step-by-step explanation:
The given expression is :
3a+3b
Put a = 6 and b = 4 in the above expression.
3a+3b = 3(6) + 3(4)
= 18+12
= 30
Now put a = 4 and b = 6 in the above expression.
3a+3b = 3(4) + 3(6)
= 12+18
= 30
Hence, the answer in both case is same i.e. 30.
AABC has vertices at (1,5), (4,8), and (16, 12). A second triangle, ADEF, has vertices at (4, 20), (16, 32), and (64, 48). If the two triangles are related by a dilation factor, which of the following could be a rule for the dilation?
Select one:
O (I,y) → (4x, 4y)
0 (x,y) → (6x, 6y)
O (x,y) → (2, y)
0 (r,y) → (16x, 16y)
Answers
Answer: the first one
Step-by-step explanation:
(x,y)->(4x, 4y)
Plz help down below is the question
Answers
Answer:
The answer would be exactly 250 messages.
0.50 × x = $125
125÷ 0.50=250
Hope this helps!
PLEASE HELP! ( no random links )
“How many servings of fruit did you eat yesterday?” Is this a statistical question or non-statistical question?
Answers
Answer:
This is not a statistical question
Step-by-step explanation:
A statistical question is a question the gathers varying data
Pls answer quick 45 points :))
Answers
Answer:
5
Step-by-step explanation:
pls help me with these and can you do them all and mitch you show me how to and I don't care if you use photo math thank you and use give me the best will be thank and brainlist.
Answers
Point s is locaded 5 units to the right of point t plot the point that represents the location of point s select the place on the coordinate plane to plot the point
Answers
Answer:
See attachment for plot
Step-by-step explanation:
Given
[tex]t = (-1,2.5)[/tex] ---- coordinates of t
s = 5 units to the right of t
Required
Plot s
First, we determine the coordinate of s
The rule to translate a point to the right is:
[tex](x,y) \to (x + h,y)[/tex]
Where h is the number of units
i.e.
[tex]h= 5[/tex]
So, we have:
[tex]s = (-1 + 5, 2.5)[/tex]
[tex]s = (4, 2.5)[/tex]
See attachment for plot
Sasha order 3/5 of a pound of cheese .Each slice of cheese weighs 0.15 pounds. Enter the number of slices of cheese that Sasha will receive
Answers
Answer:
4. slices
Step-by-step explanation:
because If you turn 3/5 in to a decimal you get 0.6 and each slice of cheese weighs 0.15 so you do 0.6 divided by 0.15