Answer:
Step-by-step explanation:
{15,16,17,18,19,20,21}
For g(x)=x^2-2, determine g(x+2)
Answer:g(x)=-4^2+4x-5
Step-by-step explanation:
prove cos x / 1+sinx = tan ( π\4 - x/2)
Answer:
[tex]\displaystyle \frac{\cos x}{1 + \sin x} = \tan\left(\frac{\pi}{4} - \frac{x}{2}\right)[/tex].
Overview of the steps:
Apply the double-angle identity of sines and cosines to the left-hand side of the equation.Apply the Pythagorean identity to the left-hand side of the equation.Apply the angle sum and difference identity of sines and cosine to the right-hand side of the equation.Step-by-step explanation:
Double-angle identity of sines and cosines:
[tex]\cos (2\,\alpha) = \cos^2\alpha - \sin^2\alpha = (\cos\alpha + \sin\alpha)\, (\cos\alpha - \sin\alpha)[/tex].[tex]\sin(2\,\alpha) = 2\, \sin\alpha\, \cos\alpha[/tex].Pythagorean identity for the sine and cosine of the same angle:
[tex]1 = \cos^2\alpha + \sin^2\alpha[/tex].
Angle sum and difference identity of sines and cosines:
[tex]\sin(\alpha - \beta) = \sin\alpha\, \cos\beta - \cos\alpha \, \sin\beta[/tex].
[tex]\cos(\alpha - \beta) = \cos\alpha\, \cos\beta + \sin\alpha \, \sin\beta[/tex].
Consider [tex]x[/tex] as the sum of two angles of size [tex](x/2)[/tex]. Start by applying the double-angle identity to the left-hand side.
[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\end{aligned}[/tex].
Apply the Pythagorean identity to rewrite the "1" in the denominator as [tex]\left(\cos^2(x / 2) + \sin^2(x / 2)\right)[/tex].
[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{\sin^2(x/2) + 2\,\sin(x/2)\, \cos(x/2) + \cos^2 (x/2)}\end{aligned}[/tex].
Note that the denominator is now a perfect square. On the other hand, the numerator is in the form [tex](x^2 - y^2)[/tex], which is equal to [tex](x + y)\, (x - y)[/tex]. Rewrite and simplify this expression:
[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{\sin^2(x/2) + 2\,\sin(x/2)\, \cos(x/2) + \cos^2 (x/2)} \\[1em] &= \frac{(\cos(x/2) + \sin(x/2))\, (\cos(x/2) - \sin(x/2))}{\left(\sin(x/2) + \cos(x/2)\right)^2} \\ &= \frac{\cos(x/2) - \sin(x/2)}{\sin(x/2) + \cos(x/2)}\end{aligned}[/tex].
The tangent of an angle is equal to the ratio between its sine and its cosine. Apply the angle sum and difference identity of sine and cosine to the right-hand side.
Note, that the sine and cosine of [tex](\pi/4)[/tex] are both equal to [tex]\left(\sqrt{2}/2\right)[/tex].
[tex]\begin{aligned}\text{R.H.S.} &= \tan\left(\frac{\pi}{4} - \frac{x}{2}\right) \\ &= \frac{\sin((\pi/4) - (x/2))}{\cos((\pi/4) - (x/2))}\\ &= \frac{\left(\sqrt{2}/2\right)\, \cos(x/2) - \left(\sqrt{2}/2\right)\, \sin(x/2)}{\left(\sqrt{2}/2\right)\, \cos(x/2) + \left(\sqrt{2}/2\right)\, \sin(x/2)} \\ &= \frac{\cos(x/2) - \sin(x/2)}{\cos(x/2) + \sin(x/2)}\end{aligned}[/tex].
Therefore:
[tex]\displaystyle \text{L.H.S.} = \frac{\cos(x/2) - \sin(x/2)}{\sin(x/2) + \cos(x/2)} =\text{R.H.S.}[/tex].
[tex]\displaystyle \frac{\cos x}{1 + \sin x} = \tan\left(\frac{\pi}{4} - \frac{x}{2}\right)[/tex].
2.
Find the distance between A and B.
O A. 355 units
B. 7 units
O C. 3 units
OD. 153 units
Answer:
D
Step-by-step explanation:
Delta x is 7 and delta y is 2, according to Pythagoras a^2+b^2=c^2 so 49+4=53 and sqrt(53) is your answer.
Find the measure of angle A.
2x +13 5x
A tree is 66 inches tall. How tall is it in feet and inches?
Answer:
5 feet and 6 inches
Step-by-step explanation:
5 feet is 60 inches
Answer:
5 feet 6 inches
a foot is 12 inches. Go by 12s until you get to a number that's as close as you can make it without going overboard, then count what's left. 12 × 5 = 60, 66 - 60 = 6, hence 5 feet 6 inches
Solve for f: −5f=20
30 POINTS TO SOMEONE WHO HELPS
Answer:
[tex]\huge\boxed{\sf f = -4}[/tex]
Step-by-step explanation:
[tex]\sf -5f = 20\\\\Dividing\ both\ sides\ by\ -5\\\\\frac{-5f}{-5} = \frac{20}{-5} \\\\f = -4[/tex]
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807Simplify the given expression below: (−3 + 2i) ⋅ (2 + i) A. −8 + i B. −6 + 3i C. −3 + 4i D. −1 + 2i
Answer:
-8 + i
Step-by-step explanation:
(-3 + 2i) * (2 + i)
= -6 + -3i + 4i + 2i^2
= -6 + i - 2
= -8 + i
what is the answer please help 3[(8-4)^5 ÷ 8 please please help me!
Solution:
3[(8 - 4)^5] ÷ 8
3[4^5] ÷ 8
3[1024] ÷ 8
3072 ÷ 8
384
Best of Luck!
Answer:
384
Step-by-step explanation:
[tex]3[(8-4)^5][/tex]÷[tex]8[/tex]
Using the rules of PEMDAS I know that I have to do the math inside of the parenthesis first.
8 - 4 = 4
Our new equation is
[tex]3[(4)^5][/tex]÷[tex]8[/tex]
Next we have to solve for the exponent.
[tex]4^5[/tex] = [tex]4*4*4*4*4[/tex] = 1,204
Our new equation looks like:
[tex]3[1024][/tex]÷[tex]8[/tex]
Now we will multiply, because we follow the rules of operation.
[tex]3 *1024= 3072[/tex]
Finally we will divide 3,072 by 8.
[tex]3072/8= 384[/tex]
Our final answer is:
384
Please help me thanks!
Answer:
1278.8 ft^3
Step-by-step explanation:
radius of cylinder = r = 5.8 ft
height of cylinder = h = 8.9 ft
radius of cone = r = 5.8 ft
height of cone = H - h = 18.5 ft - 8.9 ft = 9.6 ft
volume = volume of cylinder + volume of cone
V = (pi)(r^2)h + (1/3)(pi)(r^2)(H - h)
V = (3.14159)(5.8^2 ft^2)(8.9 ft) + (1/3)(3.14159)(5.8^2 ft^2)(9.6 ft)
V = 1278.8 ft^3
Answer:
If you use 3.14 for pi
1278.1 ft^2
Using the pi button on the calculator
1278.8 ft^2
Step-by-step explanation:
First find the volume of the cylinder
V = pi r^2 h where r is the radius and h is the height of the cylinder
V = pi ( 5.8) ^2 ( 8.9)
V = pi *33.64 * 8.9
V = 299.396 pi
The find the volume of the cone
V= 1/3 pi r^2h
The height of the cone is 18.5- 8.9 =9.6
V= 1/3 ( pi ) ( 5.8)^2 ( 9.6)
V= 1/3 ( pi ) 33.64 ( 9.6)
V = 107.648 pi
Add the two volumes together
299.396 pi + 107.648 pi
407.044 pi
If you use 3.14 for pi
1278.11816 ft^2
Rounding to the nearest tenth
1278.1 ft^2
Using the pi button on the calculator
1278.76644
Rounding to the nearest tenth
1278.8 ft^2
14. Joe has 3 more than half the number of pets his
friend does. Joe has 4 pets. He represented this
situation with the following equation: 4 = 3 + x.
1
2
To figure out how many pets his friend has, Joe wants
to subtract a number from four. He will then multiply the
result by a number to determine how many pets his
friend has.
What number should Joe subtract?
What number should Joe multiply by?
Hey I
Answer:
3 and 1 respectively.
Step-by-step explanation:
Subtract 3 from 4.
4 = 3 + x
4 - 3 = x
1 = x
Multiply 1 by 1.
The no. of pets friend has = 1
Let X be a binomial random variable with p=0.3 and n=15. What is P(X=5)?
Answer:
0.20613038098
Step-by-step explanation:
The formula for Binomial Probability =
P(X) =[ n!/(n - x)! × x! ] × p^x × q^n - x
From the question
x = 5
n = 15
p = 0.3
q = 1 - p
= 1 - 0.3 = 0.7
P(x = 5) = [15!/(15 - 5)! × 5! ] × 0.3^5 × 0.7^15 - 5
P(x = 5) = 3,003 × 0.3^5 × 0.7^10
P(x = 5) = 0.20613038098
Therefore, P(x = 5) = 0.20613038098
27. Reason Adam invests $8,000 in an account that
earns 1.25% interest, compounded quarterly
for 20 years. On the same date, Jacinta invests
$8,000 in an account that earns continuous
compounded interest at a rate of 1.25% for
20 years. Who do you predict will have more
money in their account after 20 years? Explain
your reasoning.
Answer:
Jacinta will have more money
Step-by-step explanation:
For the same amount of investment and interest rate, compound interest is greater with greater number of compounds.Continuous compound is closer to daily compound which makes more compounds and returns than quarterly compound.The interest amount is provided below for quarterly and daily compound:
2,268.202,307.89Jacinta will have more money
helpp me please !!!!
Step-by-step explanation:
55. 162 +54=216
216-75=141
balance $141
Write the number 0.00044 in scientific notation.
At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. Which expression represents how much she will receive in commission from the sale?
569 (0.18)
569 (0.72)
569 (1.18)
569 minus left-bracket (569) (0.18) right-bracket
Answer:
its A
Step-by-step explanation:
Answer:c
Step-by-step explanation:
3g-9+11g-21 simplyfy
Answer:
g = 15/7
Step-by-step explanation:
3g - 9 + 11g - 21
group like terms
3g + 11g = 21 + 9
14g = 30
g = 30/14
g = 15/7
How do you do number 4 cuz omggg
LM + MN = LN
5x + 5 = 11x - 1
Add 1 to both sides and subtract 5x from both sides
6 = 6x
Divide each side by 6
1 = x
MN = 5
LM = 5(1) = 5
LN = MN + LM = 5 + 5 = 10
Integer expression
-20-55-2-5-1-27
-20-55=-75-5=-80
-80-2=-82-1=-83
-83-27=-110
hope it helps!
explain the rules for multiplicación and division to convert units. How do you know when to multiply and when to divide to convert units of measurement
Answer:
What do u mean? For example, meters (works with other units of measurement) its based on an Acronym. King Henry Died By Drinking Chocolate Milk. The first letters stand for: Kilo, Hecto, Deca, Base (your unit of measurement), Deci, Centi, Mili
Step-by-step explanation:
One cattle farmer plans to grow his cattle population 2% each year, modeled by the function f(t) = 100(1.02)t. Another farmer intends to add 20 cattle per year, modeled by the function g(t) = 100 + 20t. For this application, the domain is restricted to t ≥ 0. If the farmers become partners, which function represents the total cattle they will have after t years? h(t) = 200(21.02)t h(t) = 200(20.4)t h(t) = 100(1.02)t + 20t + 10 h(t) = 2,000t(1.02)t + 100
Answer:
h(t) = 100(1.02)t + 20t + 10
Step-by-step explanation:
I got it right on the test : )
Answer:
h (t) = 100(1.02)t + 20t + 100
Step-by-step explanation: edge 2021
took the unit test got it right.
100%
BE
A leaf fell into a river and traveled 140 meters in 4 minutes.
How many meters did the leaf travel per minute?
Answer:
35 meters / minute.
Step-by-step explanation:
Speed of the leaf = 140 / 4 = 35 meters / minute.
the midpoint of is M(4,-3) One endpoint is G(-2,2). find the coordinates of end point
There are 34 people in a restaurant. Four groups of 3 people leave, and then
5 groups of 2 people arrive. Evaluate the expression 34 4 3 5 2 −•+• to
determine how many people are in the restaurant.
Answer:
22 people
Step-by-step explanation:
If 4 groups of 3 people leave, multiply:
4 x 3 = 12
5 groups of 2 people leave, multiply:
5 x 2 = 10
Now add:
12 + 10 = 22 people that left the restaurant.
Good luck, hope this helped!
Change 66 inches to feet
Answer:
5.5
Step-by-step explanation:
divide the length value by 12
Answer:
5.5 ft
Step-by-step explanation:
30cm=1ft
12inch= 1ft
66/12 = 5.5ft
Can you help me find x/5+7=16 Because I don’t know what it is.
Answer: x=45
STEPS:
1
Add the same term to both sides of the equation
2
Simplify
3
Multiply all terms by the same value to eliminate fraction denominators
4
Simplify
Answer:
x = 45
Step-by-step explanation:
x/5 + 7 = 16
- 7 = - 7
x/5 = 9
x times 5 = 9 times 5 = 45
therefore x = 45
6x+14y=28 in slope incerpt form?
Answer:
y = -2/7x + 2
Step-by-step explanation:
If we rewrite 6x+14y=28 into slope intercept form, it becomes 14y = -6x +28. When we divide the whole thing by 14 to get a singular y, -6x becomes -2/7x since 6/14 = 2/7, and 28 becomes 2.
Error Analysis your friend evaluate (10-5)/5 and gets 9 for an answer. Explain your friend's error
Answer:
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEeeeeEEEEEEEEEEEEeeeeeee make sure you thank it.
Step-by-step explanation:
Find the average rate of change from 1 to 6
Let f(x)=8x-3
Answer:
8
Step-by-step explanation:
To find the average rate of change we use the function
[tex]f(x) = \frac{f(b) - f(a)}{b - a} \\ f(x) = \frac{f(6) - f(1)}{6 - 1} \\ \frac{(8(6) - 3) - (8(1) - 3)}{5} \\ \frac{48 - 3 - (8 - 3)}{5} \\ \frac{45 - 5}{5} \\ \frac{40}{5} \\ 8
[/tex]
It is known that 4 PLEASE HELP
Answer:
4 < 2a -4 < 10
Step-by-step explanation:
You have an expression for 'a'. To get an expression for 2a-4, multiply it by 2 and subtract 4.
4 < a < 7
8 < 2a < 14 . . . . . . multiply by 2
4 < 2a -4 < 10 . . . subtract 4
Peter bought 8 lemons for $6dollar sign, Each lemon was the same price.
Answer: Each lemon costs 75 cents
Step-by-step explanation:
If you divide 8 from 6 then the answer is .75 and that is your answer.
