prove that:
cos20°cos40°cos80°=1/8
Answer:
see explanation
Step-by-step explanation:
Using the double angle identity for sine
sin2x = 2sinxcosx
Consider left side
cos20°cos40°cos80°
= [tex]\frac{1}{2sin20}[/tex] (2sin20°cos20°)cos40°cos80°
= [tex]\frac{1}{4sin20}[/tex] (2sin40°cos40°)cos80°
= [tex]\frac{1}{4sin20}[/tex] (sin80°cos80° )
= [tex]\frac{1}{8sin20}[/tex] (2sin80°cos80° )
= [tex]\frac{1}{8sin20}[/tex] . sin160°
= [tex]\frac{1}{8sin20}[/tex] . sin(180 - 20)°
= [tex]\frac{1}{8sin20}[/tex] . sin20°
= [tex]\frac{1}{8}[/tex] = right side , thus proven
Step-by-step explanation:
hope its helps you have a great day keep smiling be happy stay safe ☺
Make a graph that matches the rule y=2x – 3.
(Need help ASAP)
Answer:
Answer in image below :)
Step-by-step explanation:
Mr. Gorelick has gone crazy. He has climbed up to the rafters of the gym 35 feet up and has taken with him a large number of basketballs. Mr. Gorelick can throw a basketball so hard at an angle of declination of 40 degrees that it will knock you out for 17 hours. How far does one of his basketballs travel before hitting someone in the head?
Answer:
Let the amount of feet be x
Let declination be y
so 35x at a declionation of 40 degrees 35x+40y=feet traveled before hitting the head
35x
40y
35x +40y= 40-y =35x+40-y
and 35x=35-x
35+40=x-y
The ball travels 43ft
Jk its free points lol
Step-by-step explanation:
does 3/7 , 12/21 make a proportion
Answer:
No, it does not.
Step-by-step explanation:
The question, does 3/7 and 12/21 make a proportion, does not. It does not make a proportion, because for 3 to equal 12, you must multiply by four. when you multiply 7 by 4, you get 28. that is not right. if this explanation is too confusing, i added a picture
If x and y are positive real numbers, which expression is equivalent to the expression below?
[tex](125x {4}y^{ \frac{3}{2} })^{ \frac{1}{3} } \div (xy)^{ \frac{1}{2} } [/tex]
5x^5/6
Step-by-step explanation:
fivestar farm purchased 2400 apple trees. If 80 trees can be planted on each acre of land, how many acres will be needed to plant all the trees?
Answer:
30
Step-by-step explanation:
To find the answer you would need to do 2400 divided by 80 which = 30
Hope this helped :)
Please help I cannot figure out this math problem
10.3
divided by 200.3865
Answer: 0.0514006682 and yes i looked it up bc nobody has time for that
Step-by-step explanation:
Answer:
0.051
Step-by-step explanation:
Hope this helps!
Match the system of equations to their solutions
Answer:
2x + y = 12 & x = 9 - 2y --- (x = 5, y = 2)
x + 3y = 16 & 2x - y = 11 --- (x = 7, y = 3)
y = 11 - 2x & 4x - 3y = -13 --- (x = 2, y = 7)
2x + y = 11 & x - 2y = -7 --- (x = 3, y = 5)
Step-by-step explanation:
Consider this expression. Select the correct statements.
-6m + 12n + 24
A)
24 is a constant term.
B)
The expression has 3 terms.
The expression he terms.
D
-6 and 12 are coefficients.
E)
-6m and 12n are constant terms.
Answer:
A, B, D
Step-by-step explanation:
A: 24 is a constant term, TRUE
B: The expression has 3 terms, TRUE
Don't know where 'C' is?
D: -6 and 12 are coefficients, TRUE
Please help me again
Answer:
The choice is B
vertex is (-3, 25/2)
Two whole numbers have a least common multiple of 60. each number is less than or equal to12 the greatest common factor of the two numbers is 2 what are the two numbers
Answer:
The answer is 2 and 4. Their multiples can arrive at 60, they are less than 12, and the GCF for both numbers is 2.
Step-by-step explanation:
What is the decay factor of the exponential function
represented by the table?
O1/3
O2/3
O 2
O 6
Fact: It is not 6!
And I swear I am not lying!
Answer:
A. 1/3
as x increases the values of the function all become one-third of each other !!
6 is 1/3 of 18
2 is 1/3 of 6
2/3 is 1/3 of 2
A restaurant's profits for the first three weeks of September are $15,000; $9,300; and $12,000. What are the average profits for the first three weeks of September?
Answer:
$12100
Step-by-step explanation:
Step one:
Given data
The given profits are
First week= $15,000
Second week= $9300
Third week = $12,000
Required
The average profit
Step two:
The number of weeks is 3
hence the average is
= 15000+9300+12000/3
=36300/3
=$12100
Will the solution (4, 6) satisfy the following equation: x + y = 18?
Determine the slope of the line perpendicular to that of the function graphed below.
I AM IN DYING NEED OF HELP
Answer:
y=4/5x -5
Step-by-step explanation:
the slope is x and x is on the point -5. and d
to find the y-intercept you do rise/run
what is thirty five percent
Answer:
i dont know what you need 35% as but..
Step-by-step explanation:
Decimal : 0.35
Fraction: 7/20
Can some one help me out!!
Answer:
The measure, in degrees, of ∠ABC = 25°
Hence, option A is true.
Step-by-step explanation:
Given
The exterior angle m∠CBD = 155°
To determine
The measure of ∠ABC
We know that the exterior angle and interior angle are supplementary angles.
In other words, adding the interior angle and an exterior angle would give us 180°.
Here:
m∠CBD = 155° is exterior angle
∠ABC is the interior angle.
When we add m∠CBD and m∠ABC we would get 180°.
m∠CBD + ∠ABC = 180°
substituting m∠CBD = 155°
155° + ∠ABC = 180°
∠ABC = 180° - 155°
∠ABC = 25°
Therefore, the measure, in degrees, of ∠ABC = 25°
Hence, option A is true.
Which expression can be used to find the retail price of an item that was bought at wholesale for $112 and sold at a 40% markup?
$112 + 4($112)
$112 – 4($112)
$112 – 0.40($112)
$112 + 0.40($112)
Answer:
$112 + 0.40($112)
Step-by-step explanation:
Stop playing and just put the answer :I
Answer:
Step-by-step explanation:
what is the solution of √5x+1-√x=5
Answer: x= 16
Step-by-step explanation:
Solve for x
√(5x + 1) − √x = 5
Add √x to both sides of the equation.
√(5x + 1)^2 = 5( + √x )^2
To remove the radical on the left side of the equation, square both sides of the equation.
√5x + 12 = (5 + √x)^2
Simplify each side of the equation.
5x + 1 = 25 + 10√x + x
Solve for 10√x.
10√x = 4x − 24
To remove the radical on the left side of the equation, square both sides of the equation.
(10√x)^2 = (4x − 24)^2
Simplify each side of the equation.
100x = 16x^2 − 192x + 576
Solve for x.
x = 9/4 , 16
Exclude the solutions that do not make √5x + 1 − √x = 5 true.x = 16
5. Read the problem carefully, then choose the inequality that best represents this real life situation. Explain your thinking. Lydia spent $2.50 per pound on apples and $1.80 per pound on oranges. She spent at most $22. Which inequality represents this situation?
(Let a = pounds of apples, and r = pounds of oranges)
a) 2.50 + 1.80 = 22
b) 2.50a + 1.80r = 22
c) 2.50a + 1.80r ≤ 22
d) 2.50a + 1.80r ≥ 22
Answer:
B
Step-by-step explanation:
The answer is B
GIVING BRAINLIEST!! Please answer.
if x ∆ y means x/y - x^2, then the value of 2/3 ∆ 4/5 is,
a)7/18 b)14/25 c)4/45 d)34/45 e)29/150
Answer:
a) 7/18
I hope this helps!
how would I show that on a number line?
Answer:
[tex]6h+26\ge \:80\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:h\ge \:9\:\\ \:\mathrm{Interval\:Notation:}&\:[9,\:\infty \:)\end{bmatrix}[/tex]
Please check the graph of a number line is also attached below.
Step-by-step explanation:
Given the inequality
[tex]6h+26\:\ge \:\:80[/tex]
solving inequality
[tex]6h+26\ge \:80[/tex]
subtract 26 from both sides
[tex]6h+26-26\ge \:80-26[/tex]
Simplify
[tex]6h\ge \:54[/tex]
Divide both sides by 6
[tex]\frac{6h}{6}\ge \frac{54}{6}[/tex]
Simplify
[tex]h\ge \:9[/tex]
Therefore,
[tex]6h+26\ge \:80\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:h\ge \:9\:\\ \:\mathrm{Interval\:Notation:}&\:[9,\:\infty \:)\end{bmatrix}[/tex]
Please check the graph of a number line is also attached below.
A circular disc has an area that measures between 1,650 and 1,700 square inches. What could be the length of its radius? Use 3.14 for . 23 in. 24 in. 25 in. 26 in.
Answer:
23 in
Step-by-step explanation:
We know the area of the circular disc is A = πr² where r = radius and π = 3.14.
So, r = √(A/π)
Now, if A = 1650 square inches,
r = √(A/π)
= √(1650 in²/π)
= √525.48 in²
= 22.92 in
≅ 22.9 in
Also, if A = 1700 square inches,
r = √(A/π)
= √(1700 in²/π)
= √541.40 in²
= 23.27 in
≅ 23.3 in
If the area is between 1650 in² and 1700 in², that is 1650 in² < A < 1700 in²
then, the radius is between 22.9 in < r < 23.3 in.
Since the left and right side of the inequality are approximately 23 in, the radius of the circular disc is 23 in.
The length of the radius of the circular disc is approximately is 23 in.
Hence, option A)23 in is the correct answer.
What is a circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
Where r is radius and π is constant pi ( π = 3.14 )
Now, if the area of the circular disc is 1650in², the radius r will be;
A = πr²
1650in² = 3.14 × r²
r² = 1650in² / 3.14
r² = 525.4777in²
r = √( 525.4777in² )
r = 22.9in
Also, if the area of the circular disc is 1700in², the radius r will be;
A = πr²
1700in² = 3.14 × r²
r² = 1700in² / 3.14
r² = 541.40127in²
r = √( 541.40127in² )
r = 23.3in
Next we take the average of the two radii
Radius = ( 22.9in + 23.3in )/2 = 46.2/2 = 23.1 ≈ 23 in
The length of the radius of the circular disc is approximately is 23 in.
Hence, option A)23 in is the correct answer.
Learn more about circles here: https://brainly.com/question/11952845
#SPJ5
Can someone help me with this question Please.
Solve for the slope, x- and y-intercepts given the equation below.
7x + 2y = -10
x-intercept:
y-intercept:
Slope:
Harry is reading a book that is 597 pages long. He tells a friend that he is about 2/3 of the way done. About how many more pages must Harry read before he finishes the book?
Answer:
This reading habit has helped me finish 7 books in 10 weeks. ... reports he had brought with him and said, “Read 500 pages like this every day. ... You simply have to make time to read.
Five years ago you deposited a sum of money into a savings account which has earned $150 in interest. The interest rate for the account is 3% simple interest per year. How much money was originally deposited in the account?
Answer:
$1000
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 3%/100 = 0.03 per year,
then, solving our equation
I = 1000 × 0.03 × 5 = 150
I = $ 150.00
The simple interest accumulated
on a principal of $ 1,000.00
at a rate of 3% per year
for 5 years is $ 150.00.
The length of a rectangle is 15 more than 3 times the width. The perimeter is 110. What is the area
Answer:
450 units squared
Step-by-step explanation:
2(length)+2(width)=Perimeter
W=x Length=15+3w Perimeter=110
2(15+3w)+2w=110
30+6w+2w=110
8w=80
w=10
So: Length is 45 and Width is 10
Area is l*w
Area=45*10
Area is 450 units squared
7 times what equals 17?
Answer:
119
Step-by-step explanation:
Anybody know the answer for this? ;-;
Answer: the first answer choice
Step-by-step explanation:
Answer:
i think its the bottom one but i dont know
Step-by-step explanation: