Answer:
see explanation
Step-by-step explanation:
Using the sum to product identity
cosx + cosy = 2cos([tex]\frac{x+y}{2}[/tex] )cos( [tex]\frac{x-y}{2}[/tex] )
Consider left side
(cos5A +cos3A) + (cos15A + cos7A)
= 2cos([tex]\frac{5A+3A}{2}[/tex] )cos([tex]\frac{5A-3A}{2}[/tex] ) + 2cos( [tex]\frac{15A+7A}{2}[/tex]) cos( [tex]\frac{15A-7A}{2}[/tex] )
= 2cos([tex]\frac{8A}{2}[/tex]) cos([tex]\frac{2A}{2}[/tex]) + 2cos([tex]\frac{22A}{2}[/tex] )cos([tex]\frac{8A}{2}[/tex] )
= 2cos4AcosA + 2cos11A cos4A ← factor out 2cos4A from both terms
= 2cos4A( cos11A + cosA) ← repeat the process
= 2cos4A( 2cos([tex]\frac{11A+A}{2}[/tex] )cos([tex]\frac{11A-A}{2}[/tex] )
= 2cos4A(2cos([tex]\frac{12A}{2}[/tex])cos([tex]\frac{10A}{2}[/tex] )
= 2cos4A(2cos6A cos5A)
= 4cos4Acos5Acos6A
= right side , thus verified
integers
[tex]18 \div ( - 9) = [/tex]
[tex] - 10 \div 2 = [/tex]
[tex] - 2 + ( - 6) = [/tex]
[tex] - 8 - 4 = [/tex]
[tex]( - 2 \times - 12) \div (18 \div - 9 = [/tex]
[tex](120 - 30) \div ( - 42 - 3) = [/tex]
[tex]1000 \div (125 \times - 2) = [/tex]
[tex](5 - 30) \div ( 8 - 3) = [/tex]
[tex]12 \div (4 - 8) = [/tex]
please mark this answer as brainlist
2. The fraction 84 by 98 in simplest form is
Answer: 6/7
Step-by-step explanation: Since the Greatest common factor of 84 and 98 is 14, you divide both sides of 84/98 by 14 to get 6/7
Answer:6/7
Step-by-step explanation:The greatest common factor of both numerator and denominator is 14.So if you divide 84 by 14 you will get 6 and if you divide 98 by 14 you get 7.
What are the answers to the following.
Answer:
Step-by-step explanation:
[tex]8-11 =-3\\\\b. -8+10 = 2\\\\c. 13+(-6) = 13-6 \\= 7\\\\d. 7-(-3)\\= 7+3\\=10\\\\e.-5-(-2)\\=-5+2\\=-3\\\\f. -15-(-25)\\=-15+25\\=10\\\\g. -3+(-6)-(-9)\\= -3-6+9\\=-9+0\\=0\\\\h.-20-(-9)-(-8)\\=-20+9+8\\-20+17\\=-3\\\\[/tex]
[tex]-2+3-(-4)+(-5)\\-2+3+4-5\\= 1-1\\=0\\\\\\b. 18-(-10)+(-19)-8\\=18+10-19-8\\28-27\\=1\\\\c. 65+(-72)-(-45)\\= 65-72+45\\=-7+45\\=38[/tex]
Draw graph x + y = 7 and x - y = 2 on the same graph
Graphed in attached file and drawn!
Answer:
see attachment
Step-by-step explanation:
The net of a rectangular prism is shown below. What is the total surface area of this prism
Answer:
142 cm^2
Step-by-step explanation:
Okay, we can first break this down into 3 different rectangles.
3 x 5 rectangle
16 x 7 rectangle
3 x 5 rectangle.
From here, we just multiply these out and add them. 15 + 15 + 112 = 142. So our answer is 142 cm^2
Answer:
142 cm²
Explanation:
to find the surface area, you need to find the area of all of the boxes within the image above add them all together.
Starting in the middle row and working from left to right it is,
7×3+7×5+7×3+7×5
21+35+21+35=112
Than the bottom and top box is
3×5+5×3
15+15=30
Than you add both of them together,
112+30=142
what does range mean in maths
56 is less than the square of 10
expand (x-4)^4 with binomial theorem or pascal's triangle
Answer:
(x-4)^4=x⁴+4x³(-4)¹+6x²(-4)²+4x¹(-4)³+(-4)⁴
=x⁴-16x³+96x²-256x+256
if A is a subset and equal to B then B'-A' is equal to
Answer:
A-B
Step-by-step explanation:
It doesn't say A=B... But just that A is a subset of B.
Anyways, why not try an example to help reveal the answer.
Let the universe set, U, be U={1,2,3,4,5,6}.
Let B={1,2,3,4} and A={1,3,5}
First choice would become A'={2,4,6}
Second choice would become B'={5,6}
Third choice would become A-B={5}
Fourth choice is just { }
B'-A'={5}
The only choice matching is A-B
*Just so you know X-Y is the set of elements contained in X only if they are not also in Y.
in june , john withdrew 1/5 of the money in his savings account. in july he withdrew 1/3 of what remained. in august, he withdrew 1/4 of the remaining balance.if he made no other transactions and ended up with $480 in her account, what did he start with?
Answer
28,800$
Step-by-step explanation:
480 x 4 = 1920 x 3 = 5760 x 5 = 28800
Write a real-life problem that you can solve using a 45 degree, -45 degree, -90 degree triangle with an 18-ft hypotenuse. Describe your solution
Answer:
A triangle with angles:
"45°, 45°, 90°"
Is a triangle rectangle, with two catheti of equal length.
Now, there is a lot of problems that you can solve with this:
"Suppose that you want to find the height at which you need to attach a wire in a tree, such that the distance between the tree and the ground is 18ft, and the distance between the base of the tree and the two points where the wire is fixed is exactly the same"
Well, here we have a triangle rectangle with a hypotenuse of 18 ft, with cathetus of equal length (the catheti are the tree and the distance between the base of the tree and the point where the wire is attached at the ground)
And because the catheti are equal, then the angles are 45°, 45° and 90°.
What is the measure of angle X?
====================================================
Explanation:
Focus on triangle BDH
Interior angles B and D are given to be 40 and 31 respectively. Interior angle H is unknown
For any triangle, the interior angles always add to 180
B+D+H = 180
40+31+H = 180
H+71 = 180
H = 180-71
H = 109
Interior angle H is 109 degrees for triangle BDH
The exterior angle is 180 minus this measure
exterior angle = 180 - (interior angle)
exterior angle = 180 - 109
exterior angle = 71
Note how this is the sum of interior angles B and D, so you could use the remote interior angle theorem here.
find the slope that passes through the points : (-2, 5) & (-7,8)
Answer:
-3/5
Step-by-step explanation:
We can find the slope using the slope formula
m= ( y2-y1)/(x2-x1)
= ( 8-5)/(-7 - -2)
= (8-5)/(-7+2)
= 3/-5
- 3/5
13 = 2m + 5
whats m?
Answer:
M is 4
Step-by-step explanation:
in order to solve, 13=2m+5, you need to subtract 5 from both sides.
13=2m+5
-5 -5
Which is,
8=2m, then you divide both sides by 2. That gives you, 4=m. Therefor, m is 4.
change 7/8 as a fraction in simplest form
Answer:
It's already it in it's simplest form. You can find the simplest form by dividing the fraction by two ( 4/8 for example, you can divide 4 by two, giving you 2, and divided 8 by two, giving you 4, which makes 2/4, and do it once more, giving you 1/2.
What is the surface area of the rectangular prism below?
A. 736 units2
B. 812 units2
C. 706 units2
D. 824 units2
Answer:it’s A
Step-by-step explanation:
took the test
PLEASE ANSWER QUICKLY ASAP
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope / gradient
c is the y intercept
a).y = 3x + 7
Comparing this equation with the general form above
Gradient of the line = 3
b).2y - 6x = 8
Divide both sides by 2
We have
y - 3x = 8
To make y the subject move 3x to the right side of the equation
That's
y = 3x + 8
Comparing with the general form above that's y = mx + c
The gradient = 3
c).y = 3x + 7
A(2 , y ) , B( x , 4)
Since they lie on the line we can substitute their values into the equation to find the missing points
For A(2 ,y)
We have
y = 3(2) + 7
y = 6 + 7
y = 13For B( x , 4)
4 = 3x + 7
3x = 4 - 7
3x = - 3
Divide both sides by 3
x = - 1Hope this helps you
Can you just answer this question quickly please what is the answer to 420 12 it is multiplication. thanks
Answer:
the answer to 420 times 12 is 5,040
Step-by-step explanation:
Answer: The answer would be 5040.
Step-by-step explanation:
What is the value of the rational expression below when x is equal to 3?
12 - x/X-6
A. 3
B. -3
C. 9
D. -9
E
What is the value of x in the equation 3x.. by y 18, when y27
Answer:
x = 15
Step-by-step explanation:
We need to find the value of x in the equation 3x – y = 18 when y = 27.
To find the value of x, put y = 27 in the above equation.
So,
3x - 27 = 18
3x = 45
x = 15
So, the value of x is 15.
The average monthly rainfall for 6 months was 28.5 mm. If it had rained 1mm more each month what would the average have been? By how much would the total have been increased in six months and by how much would average have been increased per month? What's the answer??
Answer:
29.5 mm
Step-by-step explanation:
We are told that the average monthly rainfall for 6 months was 28.5 mm.
Thus, total for the 6 months = 28.5 × 6 = 171 mm
Now, we are told that it rained 1 mm extra each month.
So extra for the six months = 1 × 6 = 6mm
New total for 6 months = 171 + 6 = 177 mm
So, new average for 6 months = 177/6 = 29.5 mm
Solve for x: 2x+1= -3x+36
Answer:
x = 7
Step-by-step explanation:
2x + 1 = -3x + 36
2x + 3x + 1 = -3x + 3x +36
5x + 1 = 36
5x + 1 - 1 = 36 - 1
5x = 35
5x/5 = 35/5
x = 7
Answer:
first you would add 3x to -3x and 2x, then you would get 5x+1=36. Then you subtract 1 from 1 and 36. Then you get 5x=35. Then you divide by 5 to get the answer 7. so your answer is x=7
Step-by-step explanation:
hope this helps
2. What is the area of rhombusABCD? (Assume the diagonals of rhombus ABCD are equal).
Answer:
A=pq/2
=4.25·4.25/2
=9.03125
Step-by-step explanation:
If you like my answer than please mark me brainliest
Answer:
Step-by-step explanation:
Diagonal of rhombus bisect each other.
d₁ = AC = 4.25*2 = 8.5 cm
d₂ = 8.5 {Given diagonals are equal}
Area of rhombus = [tex]\frac{d_{1}*d_{2}}{2} \ where \ d_{1} \ and \ d_{2} \ are \ diagonals[/tex]
[tex]=\frac{8.5*8.5}{2}\\\\= \frac{72.25}{2}\\\\= 36.125 \ cm^{2}[/tex]
A baby weighs 100 ounces. Find the baby's weight in pounds and ounces.
Work Shown:
1 pound = 16 ounces
100/16 = 6.25
100 ounces = 6.25 pounds
100 ounces = 6 pounds + 0.25 pounds
-------
1 pound = 16 ounces
0.25*1 pound = 0.25*16 ounces
0.25 pounds = 4 ounces
------
100 ounces = 6 pounds + 0.25 pounds
100 ounces = 6 pounds + 4 ounces
100 ounces = 6 pounds, 4 ounces
When you subtract two positive integers is the result always a positive integer
Sai vì số Nguyên dương nhỏ trừ số nguyên dương lớn bằng số nguyên âm
Which item is more economical?
Answer:
what are the items
Step-by-step explanation:
Gabriella has a smart phone data plan that costs $25 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Gabriella have to pay in a month where she used 5 GB over the limit? How much would Gabriella have to pay in a month where she used went over by x x GB?
what is 2/3 divided by -1 1/3
Two-Step Column Proofs.
A circle has a radius of \sqrt{45} 45 square root of, 45, end square root units and is centered at (-2.4,-4.8)(−2.4,−4.8)left parenthesis, minus, 2, point, 4, comma, minus, 4, point, 8, right parenthesis.
What is the equation of this circle?
Answer:
(x + 2.4)² + (y + 4.8)² = 45Step-by-step explanation:
Circle equation:
(x - h)² + (y - k)² = r², where (h, k) is the center, r - radiusSubstitute the values to get the equation:
(x - (- 2.4))² + (y - (-4.8))² = (√45)²(x + 2.4)² + (y + 4.8)² = 45Answer:
(x+2.4)^2 + (y+4.8)^2 =45
Step-by-step explanation: