Step-by-step explanation:
We will use the LHS to find the RHS.
Step 1: Expand the LHS by multiplying through the brackets and simplify
(sinx + cosx)(1 − sinx cosx) ≡ sinx + cosx - (sinx + cosx (sinx cosx))
≡ sinx + cosx - sin²x cosx - sinx cos²x
Step 2: Use the identity sin²x + cos²x = 1, to rewrite the equation
≡ sinx + cosx - cosx (1 - cos²x) - sinx (1 - sin²x)
Step 3: Simplify the equation by adding like terms
≡ sinx + cosx - cosx + cos³x - sinx + sin³x
≡ sin³x + cos³x [QED]
Reminder:
1 - cos²x = sin²x 1 - sin²x = cos²x (cosx)(cosx) = cos²xa. 17 + 6 10=17,6 b. 45 + 6 100 5 c. 3 + + 10 2 100 7 8 d. 6 + + 9 + 10 100 1 000 6 e. 11 + + 10 8 1 000 f. 84 + 1 3 + 100 10
Need help me
Step-by-step explanation:
a. 17 + 6/10 = (17 x 10) / (1 x 10) + 6/10 = 170/10 + 6/10 = 176/10 = 17,6
b. 45 + 6/100 = (45 x 100) / (1 x 100) + 6/100 = 4 500/100 + 6/100 = 4 506/100 = 45,06
c. 3 + 5/10 + 2/100
= (3 x 100) / (1 x 100) + (5 x 10) / (10 x 10) + 2/100
= 300/100 + 50/100 + 2/100
= 352/100 = 3,52
d. 6 + 7/10 + 8/100 + 9/1 000
= (6 x 1 000) / (1 x 1 000) + (7 x 100) / (10 x 100) + (8 x 10) / (100 x 10) + 9/1 000
= 6 000/1 000 + 700/1 000 + 80/1 000 + 9/1 000
= 6 789/1 000 = 6,789
e. 11 + 6/10 + 8/1 000
= (11 x 1 000) / (1 x 1 000) + (6 x 100) / (10 x 100) + 8/1 000
= 11 000/1 000 + 600/1 000 + 8/1 000
= 11 608/1 000 = 11,608
f. 84 + 1/100 + 3/10
= (84 x 100) / (1 x 100) + 1/100 + (3 x 10) / (10 x 10)
= 8 400/100 + 1/100 + 30/100
= 8 431/100 = 84,31.
Hope this helps!!
Help ASAP please i will mark brainliest who finishes first
pls be nice and neat
dont send links you CAN send photos of your answers
but i prefer typing your answers down thank you so much
Answer:
1-a) 78+x+16+x+24=180°
118+2x=180
2x=62
so x=31
Step-by-step explanation:
thats a
Answer:
1a) x = 31
1b) x = 12
2) angle A = 60 degrees
3) x = 40 degrees
Step-by-step explanation:
need help
on this problem
Answer:
4.6
Step-by-step explanation:
23/5=4.6
Clara Clatter was born on December 27th, yet her birthday is always in the summer. How is this possible
Answer:
She lives in the Southern Hemisphere.
Step-by-step explanation:
Mr. Tanaka is loading his boat with many identical 45-pound boxes. Mr. Tanaka weighs 190 pounds. The boat can carry at most 1,000 pounds. If each box is fully-filled, how many boxes can he load on the boat?
Write an inequality that represents this situation.
Answer:
there should be 14, 45 pound boxes
Step-by-step explanation:
1000-190= 810
810/45=14 boxes
i have 7 bags with 2 marbles in each bags. then my friend have 10 bags with 2 marbles in each bag. how many more marbles does my friend have?
Answer:
your friend has 6 more marbles
Step-by-step explanation:
7×2=14
10×2=20
20-14=6
Answer:
6
Step-by-step explanation:
First you multiply 7 by 2 because there is 2 marbles in each bag and there is 7 bags so that is 14 marbles
Then you multiple 2 by 10 because there is 10 bags with 2 marbles each which is 20.
20-14=6
Can I get brainliest?
Does anyone get this?
Dilation is the transformation that changes the size of a shape.
4 is a positive number so the shape will increase in size.
So after dilating every side by 4:
0,1
-0.5,0
1,0
We get
0,4
-2,0
4,0
HELP IM LATE LOL In an aquarium, ⅖ of the fish are surgeonfish. Of these, ¾ are yellow tangs. What portion of all fish in the aquarium are yellow tangs?
Answer:
1 and 3/20 total, 15/20 of the fish are yellow tangs which would also be 75%.
Step-by-step explanation:
2/5 and 3/4 need to be converted into a fraction with a similar denominator. 5x4= 20, so 20 is our denominator.
To find the numerator, we need to multiply 2 by 4, which equals 8, and 3 by 5 which equals 15.
8/20 + 15/20 = 23/20 or 1 3/20
Decide if the following situation is a unit rate or not why or why not?
You score 12 points in one basketball game.
Answer:
Yes, because in 1 game you scored 12 points you didn't score multiple points in multiple games.
Help please :)) This is timed as well as mind boggling
Answer: Choice C
==========================================================
Explanation:
Recall that the form
[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]
can be abbreviated to
[tex]z = r*\text{cis}(\theta)[/tex]
The "cis" stands for the first letters of "cosine i sine" in that order.
The original fairly messy quotient can be shortened down to
[tex]\frac{90\text{cis}(\pi/4)}{2\text{cis}(\pi/12)}[/tex]
We have 90cis(pi/4) all over 2cis(pi/12) as one big fraction.
-------------------------------
Now we'll use this rule to divide two complex numbers
[tex]z_1 = r_1*\text{cis}(\theta_1)\\\\z_2 = r_2*\text{cis}(\theta_2)\\\\\frac{z_1}{z_2} = \frac{r_1}{r_2}*\text{cis}(\theta_1-\theta_2)\\\\[/tex]
As you can see, we divide the r1 and r2 values to form the final coefficient out front. The theta angles are subtracted to form the new argument.
-------------------------------
Let's apply that idea to what your teacher gave you
[tex]z_1 = 90*\text{cis}(\pi/4)\\\\z_2 = 2*\text{cis}(\pi/12)\\\\\frac{z_1}{z_2} = \frac{90}{2}*\text{cis}(\pi/4 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(3\pi/12 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(2\pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(\pi/6)\\\\[/tex]
That last step then converts directly to the expression shown in choice C.
A coat is priced $50. If the sales tax is 7% of the price, how much is the sales tax? What is the total cost including sales tax?
Answer:
The sales tax is $3.5
The total cost is $53.5
Step-by-step explanation:
To find the sales tax, you have to find the 7 percent of 50 dollars. In decimal form, 7% is 0.07. So you just have to multiply 0.07 to 50.
50 x 0.07 = 3.5
That's why $3.5 is the sales tax.
In order to get the total cost including sales tax. You just have to add $50 to the sales tax which is $3.5.
$50 + $3.5 = $53.5
Which point on the number line represents a loss of 5 yards in a football game? (number line is on picture)
A) Point A
B) Point B
C) Point C
D) Point D
please help me with this! it’s in need
3 (x-1)=3x-×-3-3+x+3
True or false
true
Step-by-step explanation:
Answer:
3x-3
Step-by-step explanation:
So false if you Multiply
The circumference of the planet Jupiter is approximately 2.7 x 109 miles, while the circumference of the Moon is 6.75 x 10° miles. How many times longer is the circumference of Jupiter than the circumference of the Moon?
Answer:
1738 kilometers
Step-by-step explanation:
x:y=2:3 and x+y=10.Find value of x and y
Answer:
We know that x is 2
Whilst y is 3
this can be changed due to it’s ratio
So in this code x+y=10
2+3=10
We can do it this way.
2+3=5 (add the ratios)
10/5=2 (Divide the sum by the number needed)
2*2=4 (multiply the quotient for each ratio)
3*2=6 (multiply the quotient for each ratio)
x is 4
y is 6
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day!!
We can solve this problem in two steps, Comprehension and Solving
I'll start off with comprehension.
Comprehension
We know that ratios are basically fractions as they both show comparison, so we can make x:y into [tex]\frac{x}{y}[/tex].
We also have another equation, making this problem a system of equations.
Now that we know what to do, we can begin solving!
Solving
We can solve this by first getting our two equations.
[tex]\frac{x}{y}=\frac{2}{3}[/tex]
We can simplify the 2nd equation so that we know what one variable is.
[tex]x+y=10\\x=10-y[/tex]
We can now input our second equation into the first equation.
[tex]\frac{10-y}{y}=\frac{2}{3}\\3(10-y)=2y\\30-3y=2y\\30=5y\\y=6[/tex]
If y is six, then we can use the second equation to solve for x.
[tex]x+6=10\\x=4[/tex]
We know that x is 4 and y is 6.
We can now check our answers.
1st Equation
[tex]\frac{4}{6}=\frac{2}{3}?\\[/tex]
[tex]\frac{2}{3}=\frac{2}{3}[/tex]
2nd Equation
[tex]4+6=10?\\10=10[/tex]
We've proven our answers to be right, therefore, x is 4 and y is 6.
Which proportion is not true?
A) BC/CD=FG/GH
B) AC/CD=EG/GH
C) BD/FH =AD/EH
D) AB/AE=EF/BF
Answer:
c I think that is the answer
Help me with this please
Answer:
5
Step-by-step explanation:
By process of elimination, we can say for sure that C and D are not the right answers because as x- the numbers on the top- increases, y- the numbers on the bottom- increases. This means that the slope is not negative, because the slope is the rate of change and it does not have a negative rate of change.
The equation for slope is y2-y1 / x2-x1. Meaning, y is on top and x is on bottom. This creates a fraction. So let's take 0 and 1 for X, the first and second values, and 3 and 8 for y, the first and second values. We swap them, because the second y value comes first, so we have 8 - 3 for the top, the numerator. Then we have 1 - 0 for the bottom, the denominator. Solving 8 - 3 and 1 - 0, we have 5/1. 5/1 simplifies to 5, and thus 5 is your slope.
Answer asap pleaseeeee
Answer:
I am not certified because I also struggle with these but-
it might be
A. t = -5h-4
Step-by-step explanation:
For the answer A in the paragraph it states that the temperature was 4 degrees BELOW 0 meaning we shall put as -4° and each HOUR it keep going down 5 degrees so I would suppose it would be answer A.
PLS ANSWER ASAPP!!
THX
Write the equation in point slope form
Answer:
5<6 so tbh I have no idea what this is I just need point
here!i need the answer!
[tex]\sf 13\times 13\times 1[/tex]
Answer:
[tex]169[/tex]
Step-by-step explanation:
[tex]13 \times 13 \times 1[/tex]
[tex] = 13 \times 13[/tex]
[tex] = 169[/tex]
Need help with this ASAP I’ll mark brainliest
Answer:
B' (3, 1 )
Step-by-step explanation:
Given
A (- 1, 3 ) → A' (- 3, 7 )
x- coordinate goes from - 1 → - 3 , that is - 2
y- coordinate goes from 3 → 7 , that is + 4
Translation rule is (x, y ) → (x - 2, y + 4 ) , then
B (5, - 3 ) → B' (5 - 2, - 3 + 4 ) → B' (3, - 1 )
HOW MUCH IT’S ( 4/2 - 1/2 ) + 3/4 I need the answer because I’m stay in test
Answer:
= 7.25
Conversion a mixed number 4 3/
4
to a improper fraction: 4 3/4 = 4 3/
4
= 4 · 4 + 3/
4
= 16 + 3/
4
= 19/
4
To find a new numerator:
a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/
4
= 16/
4
b) Add the answer from previous step 16 to the numerator 3. New numerator is 16 + 3 = 19
c) Write a previous answer (new numerator 19) over the denominator 4.
Four and three quarters is nineteen quarters
Conversion a mixed number 2 1/
2
to a improper fraction: 2 1/2 = 2 1/
2
= 2 · 2 + 1/
2
= 4 + 1/
2
= 5/
2
To find a new numerator:
a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/
2
= 4/
2
b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
c) Write a previous answer (new numerator 5) over the denominator 2.
Two and one half is five halfs
Add: 19/
4
+ 5/
2
= 19/
4
+ 5 · 2/
2 · 2
= 19/
4
+ 10/
4
= 19 + 10/
4
= 29/
4
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(4, 2) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 2 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - nineteen quarters plus five halfs = twenty-nine quarters.
Step-by-step explanation:
Answer:
you can write it in exact form which is 9/4 or decimal form which is 2.25 or mixed number form 2 1/4
Step-by-step explanation:
What is the value of the expression 3q - 6 when q = -2?
Answer:
-12
Step-by-step explanation:
3q-6=x q=-2
(3(-2))-6
-6-6=x
-12=x
2x+7y=5
2x-7y=19
elimanation or substution
Answer:
(6, -1)
Step-by-step explanation:
4x = 24
x = 6
2(6) + 7y = 5
12 + 7y = 5
7y = -7
y = -1
find the proabilty of rolling factors of 5 on both sides.
Solve for y.
6y - 2x = 20
Simplify fractions completely.
[?]
y =
= 4x + 1
+
Enter
Answer:
y= 10/3 + x/3
Step-by-step explanation:
not sure how to explain this
The value of y for the given equation is y = [tex]\frac{x}{3}[/tex] + [tex]\frac{10}{3}[/tex].
What is a linear equation?A linear equation is an equation where the maximum power of the variable is one. A linear equation may contain more than one variables. However, the highest power of any variable must be one.
Here, a linear equation is given that contains two variables x and y.
Therefore, 6y - 2x = 20
⇒ 6y = 2x + 20
⇒ y = (2x + 20)/6
⇒ y = [tex]\frac{2x}{6}[/tex] + [tex]\frac{20}{6}[/tex]
⇒ y = [tex]\frac{x}{3}[/tex] + [tex]\frac{10}{3}[/tex]
Hence, the value of y is [tex](\frac{x}{3}+\frac{10}{3})[/tex]
Learn more about a linear equation here: https://brainly.com/question/21835898
#Tag #SPJ2
solve for :
a_2=2(a_2+1)
Step-by-step explanation:
a_2=2a_4+2
a=_2+4_2
a=0
Antoin has 17.5 kilograms of clay. He divides it evenly into buckets that hold 2.5 kilograms. How many buckets of clay will he have?
Answer:
7 buckets.
Step-by-step explanation:
17.5 / 2.5 = 7
Answer:
7
Step-by-step explanation:
17.5/2.5=7
PLS HELP ASAP !!
A boy has climbed 210m up a 350m vertical cliff, and is trapped there.
A rescue helicopter is hovering 65m above the top of the cliff.
Calculate how far a rescue must be lowered to reach the boy.
You may draw a sketch to help you.
(i'll mark as brainliest if u answer:))
Answer:
205
Step-by-step explanation:
helicopter=65m
tap of the cliff=
the boy=350m
210=
that makes the answer 205
Answer:
205 meters
Step-by-step explanation:
The cliff is 350m, and the rescue helicopter is 65m above the top of the cliff.
This means that the helicopter is 415 meters above the bottom of the cliff.
The boy is 210m above the bottom of the cliff.
So, you have to subtract 210 from 415 to get 205.
Therefore, you have to lower the rescue 205m to reach the boy.