Answer:
Proof below
Step-by-step explanation:
Trigonometric Identities
Before we prove the given identity, we need to recall:
[tex](a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc[/tex]
We have to prove that:
[tex](1+\sin\theta+\cos\theta)^2=2(1+\sin\theta)(1+\cos\theta)[/tex]
Let's expand the square on the left side as indicated in the formula above:
[tex](1+\sin\theta+\cos\theta)^2=1^2+\sin^2\theta+\cos^2\theta+2\sin\theta+2\cos\theta+2\sin\theta\cos\theta[/tex]
Recall the fundamental trigonometric identity:
[tex]\sin^2\theta+\cos^2\theta=1[/tex]
Substituting and operating:
[tex](1+\sin\theta+\cos\theta)^2=2+2\sin\theta+2\cos\theta+2\sin\theta\cos\theta[/tex]
Factoring by 2:
[tex](1+\sin\theta+\cos\theta)^2=2(1+\sin\theta+\cos\theta+\sin\theta\cos\theta)[/tex]
Factoring cos θ in the last two terms:
[tex](1+\sin\theta+\cos\theta)^2=2[1+\sin\theta+\cos\theta(1+\sin\theta)][/tex]
Factoring [tex]1+\sin\theta[/tex]
[tex](1+\sin\theta+\cos\theta)^2=2(1+\sin\theta)(1+\cos\theta)[/tex]
Proven
Thunder is the sound caused by lightning. You hear thunder 5 seconds after a lightning strike. The speed of sound is about 1225 kilometers per hour. About how many miles away was the lightning?
Answer:
it is 1.05
Step-by-step explanation:
The lightning was 1.7 kilometer away.
What is speed?In unit time, the distance covered by any object is called speed.
In mathematical term, Speed is express as S=D/T,
where S=speed, D=distance, T= time.
Given that,
The speed of sound = 1225 kilometers per hour
The speed of sound = 340.277 meter/second
Also, the time after thunder heard = 5 seconds
To find distance, use formula distance = speed × time,
Distance = 340.277 × 5
= 1701.3 meter
= 1.7 kilometer
The lightning was 1.7 kilometer away.
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Someone help pls
by which rule are these triangles congruent?
In which pair do both decimals represent rational numbers?
O A. 2.71828182845904523536... and 0.1222
O B. 3.141592653589793238... and 0.684
O C. 3.141592653589793238... and 0.1222...
O D. 0.684 and 0.1222...
Answer: D
Step-by-step explanation:
0.684 and 0.1222
I kitten is gaining 0.6 pounds per week. The kitten is currently 7 pounds after how many weeks will the kids be at least 10 pounds? Write an inequality to represent each situation. Do not solve the inequality. Defined the variable.
Answer:
about 6 weeks
Step-by-step explanation:
Solve for W.
A = 5W
Please help
Answer:
1/5a
Step-by-step explanation:
I hope this helps ...
Find three consecutive even integers if their sum, decreased by the third, equals -22.
As per linear equation, the required three consecutive even integers those have a sum of - 22 are - 8, -10, - 12.
What is a linear equation?"An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line."
Let, three consecutive even integers are x, x+2, and x+4.
Therefore, sum of these three consecutive even integers is
= [x + (x + 2) + (x + 4)]
Given, the sum of the three consecutive even integers decreased by the third is - 22.
Now, [x + (x + 2) + (x + 4)] - (x + 4) = - 22
⇒ x + (x + 2) = - 22
⇒ 2x + 2 = - 22
⇒ 2x = -24
⇒ x = - 12
Now, x + 2 = - 12 + 2 = - 10
Similarly, x + 4 = - 12 + 4 = - 8
Therefore, required three consecutive even integers with a sum of - 22 are - 8, - 10, - 12.
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A large pizza at Mama Jane's costs $10 plus $1.25 per topping added. A large pizza at Planes costs $12.50 plus $0.75 per topping. How many toppings need to be added for pizzas from Mama Jane's and Planes to cost the same amount?
a. 2
b. 3
c. 4
d. 5
Answer:
it will be a
Step-by-step explanation:
cuz if you add 1.25 to 10$ it would Be 11.25 then you add 1.25 to 11.25 it would Be 12.5
find two possible factors for the estimate product
Answer:
This is a rather simple question. Two possible factors for a product can be any 2 real numbers. This includes: 7,2 9,3 -9,1.
Step-by-step explanation:
Graph y - 2 = -3/4 (x - 6)
Select two points on the line
Answer:
i dont understand the question can you write the rest of the question.
Step-by-step explanation:
n
Please help 6x - 3y < 9
Answer:
y>2 x - 3
Step-by-step explanation:
2. Niko was solving the equation 4(x-5)+7=13 and wrote as his first step 4x – 20+7=13. Which of the
following justifies this manipulation?
(1) the commutative property of multiplication
(2) the distributive property
(3) the multiplicative property of equality
(4) the additive property of equality
Answer:
2) The distributive property
Solve the following system of equations algebraically:
y=
y=
\,\,x^2+6x+7
x
2
+6x+7
y=
y=
\,\,-2x+7
−2x+7
Answer:
Step-by-step explanation:
Walk through examples of solving systems of equations with elimination. ... 2) Use elimination to solve the following system of equations. − 7 y − 4 x = 1 quad -7y-4x = 1 ... Systems of equations with elimination: 2x-y=14 & -6x+3y=-42 · Systems of ... (2 of 2) · Systems of equations number of solutions: y=3x+1 & 2y+4=6x.
8
According to the Red Cross, about 42% of Americans have Type A blood. Suppose 80
people show up at a typical blood drive.
What's the expected proportion of people who are Type A (p-hat)?
Answer:
33
hope this helped :)
HELP ASAP BHYUKFCY FVCTUKF
Answer:
a
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
this is because both number are to the left of zero which makes both numbers negative which leaves you with one answer.
-4
- 2
What is the solution to the systems of equations shown above?
Helppp me :(
Answer:
6
Step-by-step explanation:
-4+-2 ?? did that hellp
A bakery sells 3 muffins for every 5 pizza pies. The bakery sold a total of 24 muffins and pizza pies together. How many of each kind did the bakery sell?
6 muffins and 18 pizza pies
√2y-5+4=8 solve for y. What is the root, if there is no root, choose none.
8 1/2
10 1/2
5 1/2
none
Write 24/200 as a decimal.
Answer:
0.12 is your answer.
Step-by-step explanation:
i need brainlyest PLZ!!!!!!!
Amarah uses 4 2/5 pounds of meat to make five hamburgers. How much meat is used to make one
hamburger? ___ pound per burger
Answer:
8/25 Ib per burger.
Step-by-step explanation:
2/5 * 4 = 1.6
1.6 / 5 = 8/25
PLEASEEEE HELPPPPP!!!!!!
Answer:
the answer is c. d=15t.
I WILL MARK BRAINLIEST Write the equation of each line in slope-intercept form. Then graph the line. Show work.
1) Horizontal line through (2,3)
2) x-intercept 4, y-intercept -3
Answer: 1.) y= 3
2.) y = 3/4 x -3
Step-by-step explanation:
1. A horizontal line passes through the y-axis.and includes all x values.
2. use slope intercept form y = mx + b
To find the slope, m, take difference in y-values divided by difference in x-values. b is the y-intercept , given in the question. -3
0 -(-3)/ 4-0 = 3/4 = m
insert the values into the equation:
y = 3/4 x - 3
Mr. Haynes orders carry out from Outback. The cost of his order is $82.37. If Mr.
Haynes would like to add a 10% tip, what will be the total cost of the carry out
order?
Answer:
I'm pretty sure its $90.61?
Step-by-step explanation:
10% of 82.37 is 8.237, and you add that to 82.37 and you'd get about 90.61.
GIVING BRAINLY!!!!! PLSSSSS HELPPPP
the sum of two whole numbers is 63 . The difference between these 2 whole numbers is less than 10. FInd all the possible pairs
Answer:
(32, 31) (33,30) (34, 29) (35, 28) (36,27) (37, 26)
Step-by-step explanation:
Can someone please help me with this question so i can i get my grades up: (2/9v)−(−1/3v+5/9)
Answer:
5v/9−5/9
Step-by-step explanation:
If its right can i plz have brainliest :)
(9^3 ● 9^5 ● 9^-8)^14
Answer:
1Step-by-step explanation:
(9^3 · 9^5 · 9^-8)^14 =9^((3 + 5 - 8)·14) =9^(0·14) =9^0 =1Which statement best describes the formation of metamorphic rocks?
A. Magma cools and crystallizes slowly beneath Earth’s surface.
B. Liquid lava erupts from a volcano and cools quickly at Earth’s surface.
C. Sand and gravel are deposited at the mouth of a river and, over time, form layers that solidify into rock.
D. Ancient sandstone beaches become buried deep beneath Earth’s surface, where they are exposed to extreme heat and pressure.
Answer:
D
Step-by-step explanation:
Metamorphic rock is formed when rocks or minerals are subjected to high heat and high pressure, or a combination of these two factors. Answer D is the only answer that explicitly describes a rock or mineral being subject to these two things, so therefore D is the best answer.
A carpenter is building a rectangular room with a fixed perimeter of 180 ft. What are the dimensions of the largest room that can be built? What is its area?
Answer:
Answer: 45ft x 45ft
Step-by-step explanation:
we know that
Perimeter = 2(Length) + 2(Width)
180 = 2L + 2W
90 = L + W
90 - L = W
Area = Length *Width
= L(90 - L) → = 180L - L²
There are 2 different methods for solving (depending on which math course you are taking).
Calculus: find the derivative, set it equal to zero, and solve for L.
= 90L - L² → 0 = 90 - 2L → 2L = 90 → L = 45
Algebra: find the vertex.
= - L² + 90L → L = -b/2a → L = -90/2(-1) → L = 45
insert L it into the Perimeter equation to solve for W:
90 - L = W → 90 - 45 = W → W = 45
Answer: 45ft x 45ft
Will, an art student, randomly sampled oil paintings in a museum. He wanted to find out how many oil paintings in the museum contained the color ultramarine blue. The proportion of paintings that were created using the color ultramarine blue was 0.17, with a margin of error of 0.02. Construct a confidence interval for the proportion of oil paintings that contained ultramarine blue.
Answer:
The confidence interval is [tex]0.15 < p < 0.19[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\^ p = 0.17[/tex]
The margin of error is [tex]E = 0.02[/tex]
Generally the confidence interval for the proportion of oil paintings that contained ultramarine blue is mathematically represented as
[tex]\^ p - E < p < \^ p + E[/tex]
=> [tex]0.17 - 0.02 < p < 0.17 + 0.02[/tex]
=> [tex]0.15 < p < 0.19[/tex]
A local BBQ restaurants offers 2 side dishes with a lunch plate. There are 7 side dishes. How many choices of side dishes does a customer have
Step-by-step explanation:
This is a question that bothers combination. Combination has to do with selection.
When selecting r objects out of a pool of n objects, the number of ways this can be done is:
nCr = n!/(n-r)!r!
If a local BBQ restaurants offers 2 side dishes with a lunch plate, and there are 7 side dishes, the number of choices that the customer have is expressed as:
7C2 = 7!/(7-2)!2!
7C2 = 7!/(5)!2!
7C2 = 7*6*5!/5! * 2
7C2 = 7*6/2
7C2 = 42/2
7C2 = 21 choices
Hence the customer has 21 choices of side dishes to make
Find all points of intersection between the graphs of the functions f(x) = (x + 5)(2-4) and
g(x) = x +5.