The answer is:
The rewritten expression is:
[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]
Why?To solve this problem we need to use the trigonometric identity of the double angle for the cosine which states that:
[tex]cos(2\alpha)=cos^{2}(\alpha)-sin^{2}(\alpha)[/tex]
Also, if we want to rewrite only with terms of cos(x) and sin(x), we can apply the following property:
[tex](a^{2} -b^{2})=(a+b)(a-b)[/tex]
So, rewriting the trigonometric equation, we have:
[tex]cos^{2}(\alpha)-sin^{2}(\alpha)=(cos(x)+sin(x))*(cos(x)-sin(x))[/tex]
Then, we are given the expression:
[tex]cos(2x)+sin(x)[/tex]
Now, rewriting the given expression with only sin(x) and cos(x), we have:
[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]
Hence, the answer is:
[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]
Have a nice day!
In the diagram below, AB and bc are tangent to o. What is the measure of ac?
Answer:
Option D. [tex]150\°[/tex]
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
[tex]m\angle ABC=\frac{1}{2}[arc\ ADC-arc\ AC][/tex]
substitute the given values
[tex]30\°=\frac{1}{2}[210\°-arc\ AC][/tex]
[tex]60\°=[210\°-arc\ AC][/tex]
[tex]arc\ AC=210\°-60\°=150\°[/tex]
Answer:
Option (D) is correct.
Step-by-step explanation:
OA is perpendicular to AB
OC is perpendicular to BC
Radius from the center is perpendicular to the tangent.
In quadrilateral ABCO,
∠ABC+∠BCO+∠AOC+∠OAB=360°
30°+90°+∠AOC+90°=360°
∠AOC+210°=360°
∠AOC=360°-210°
∠AOC=150°
Hence, arc AC=150°
Thus, the correct answer is option (D)
which shows how to use similar right triangles to find the equation of the line...
First Option
Step-by-step explanation:Triangles are are similar if we can turn one into the other by moving, rotating, flipping, or scaling. To solve this problem, we just need to match the ratios of the triangles. For both triangles we need to take the Change in y over the change in x, so:
[tex]\frac{change \ in \ y}{Change \ in \x}=\frac{y-b}{x-0}=\frac{m+b-b}{1-0} \\ \\ y-b=mx \\ \\ \boxed{y=mx+b}[/tex]
As you can see, this is the Slope-Intercept form of the equation of a line, where:
[tex]m: \ slope \\ \\ b: \ y-intercept[/tex]
Answer:
The first option would be the answer i believe
Step-by-step explanation:
The pizza shop offers a 15 percent discount for veterans and senior citizens. An employee uses the calculations shown to figure out how to charge a senior citizen for a $12 pizza. What is the employee’s error?
(100% − Discount %)(Original Amount) = Discounted Amount
(100% − 85%)($12) = Discounted Amount
(15%)($12) = Discounted Amount
(0.15)($12) = $1.80
The discounted price of pizza is $1.80.
A) The employee used the wrong formula.
B) The employee subtracted the wrong percents.
C) The employee used the wrong equivalent decimal for 15 percent.
D) The employee multiplied incorrectly.
PLEASE HELP ASAP!!!
Answer:
(B) The employee subtracted the wrong percent's.
Answer:
b she substracted wrong
Step-by-step explanation:
the company sells the ice cream cups in packages of 12, 18 and 24 units. and the ice cream cones in packages of 14 and 21 units which of the following statements is not true
Answer:
The statement which not true is (A)
Step-by-step explanation:
* At first lets revise the volume of the cone and the cylinder
- The cone has circular base and one vertex
- Its height is the line joining the vertex and the center of the base
- Its volume is 1/3(BH), where B is the area of its base and H is its height
- The cylinder has two circular bases
- Its height the line joining between the centers of the two bases
- Its volume = BH, where B is the area of its base and H is its height
* Now lets solve the problem
- The ice cream cup is shaped cylinder with diameter 3 inches
and height 3 inches
- The ice ream cone is shaped a cone with diameter 4 inches
and height 6 inches
* Lets find the volume of the ice cream cup
- The volume of the ice cream cup = BH
∵ B = πr² ⇒ area the circle
∵ Its diameter is 3 inches
∵ The radius = 1/2 the diameter
∴ r = 3 × 1/2 = 1.5 inches
∴ B = π(1.5)² = 2.25π inches²
∵ H = 3 inches
∴ V = 2.25 × 3 = 6.75π inches³
* Lets find the volume of the ice cream cone
- The volume of the ice cream cone =1/3 BH
∵ B = πr² ⇒ area the circle
∵ Its diameter is 4 inches
∵ The radius = 1/2 the diameter
∴ r = 4 × 1/2 = 2 inches
∴ B = π(2)² = 4π inches²
∵ H = 6 inches
∴ V = 1/3 × 4π × 6 = 8π inches³
* Lets find the right answer
# (A)
∵ The volume of 24-pack of ice ream cups = 24 × 6.75π = 162π inches³
∵ The volume of 21-pack of ice ream cones = 21 × 8π = 168π inches³
∵ 162π < 168π
∴ (A) Not true
# (B)
∵ The volume of 12-pack of ice ream cups = 12 × 6.75π = 254.5 inches³
∵ 254.5 inches³ > 250 inches³
∴ (B) is true
# (C)
∵ The volume of 14-pack of ice ream cons = 14 × 8π = 351.9 inches³
∵ 351.9 inches³ > 350 inches³
∴ (C) is true
# (D)
∵ The volume of 12-pack of ice ream cups = 12 × 6.75π = 81π inches³
∵ The cylinder container has height = 8 inches
∵ The cylinder container had diameter = 6 inches
∴ its raduis = 1/2 × 6 = 3
∵ The volume of the cylinder container = BH
∵ B = πr² = π(3)² = 9π
∴ Its volume = 9π × 8 = 72π
∵ 81π > 72π
∴ (D) is true
* The statement which not true is (A)
The stores below each have the same snowboard for an original price of $189.59. At which store can you get the snowboard for the lowest price? Store A: Sale of 30% off and a successive discount of 10% off. Store B: Sale of 20% off and a successive discount of 20% off. Store C: Sale of 40% off.
Answer:
Snowboard can be purchased for the lowest price from Store C offering 40% discount.
Step-by-step explanation:
We need to compare discounts of 3 stores and find the store selling snowboard lowest of them.
Store A: Sale of 30% off and a successive discount of 10% off.
The formula used for successive discount is = (x+y - xy /100)%
here x= 30 and y =10 so total discount is:
Total discount = ( 30 +10 - (30*10)/100)%
= (40 - 300/100) %
= (40 -3) % = 37%
Original price = $189.59
Discount offered = 37% of $189.59
= 37/100 * 189.59 = $70.15
Selling Price = Original price - Discount offered
= $189.59 - $70.15
= $ 119.44
Store B: Sale of 20% off and a successive discount of 20% off.
The formula used for successive discount is = (x+y - xy /100)%
here x= 20 and y =20 so total discount is:
Total discount = ( 20 +20 - (20*20)/100)%
= (40 - 400/100) %
= (40 -4) % = 36%
Original price = $189.59
Discount offered = 36% of $189.59
= 36/100 * 189.59 = $68.25
Selling Price = Original price - Discount offered
= $189.59 - $68.25
= $ 121.34
Store C: Sale of 40% off.
Original price = $189.59
Discount offered = 40% of $189.59
= 40/100 * 189.59 = $75.84
Selling Price = Original price - Discount offered
= $189.59 - $75.84
= $ 113.75
So, Store A Sale price is: $ 119.44
Store B Sale price is: $ 121.34
and Store C Sale price is: $ 113.75
So, Comparing them we found that snowboard can be purchased for the lowest price from Store C offering 40% discount.
Answer:
store c
Step-by-step explanation:
Rewrite the expression with rational exponents as a radical expression.
7 times x to the two thirds power
Answer:
9x^(3/2)=9 √(x^3 )
Step-by-step explanation:
We are given
9x^(3/2)
We have to write the expression in radical form, for that the power has to be a multiple of ½
=9x^(3*1/2)
As we can see now the power is a multiple of 1/2. ½ will convert to square root while 3 will become the power of radicand.
So, 9 will remain outside of the square root while x will be inside the square root while having power 3.
=9 √(x^3 )
Hence,
9x^(3/2)=9 √(x^3 )
Answer:
b. you're welcome
Step-by-step explanation:
which of the following could be folded to produce the object above
Answer:
the answer is the letter Y
Step-by-step explanation:
Answer:
letter y is the answer
Step-by-step explanation:
A circle has a radius of 16cm. Find the area of a shaded sector formed by a central
i believe its 803.84
The areas of the squares adjacent to two sides of a right triangle are shown below 40 POINTS!!!
Answer:
Given a=33 and c=44,
b = 29.10326 = 11√7
Step-by-step explanation:
The following is one way to perform the calculation. It may not be the best way.
b =√c2 - a2
=√442 - 332
=√847
=29.10326 = 11√7
∠α =arcsin(a/c)
=arcsin(33/44)
=arcsin(0.75)
=0.84806 rad = 48.59° = 48°35'25"
∠β =arcsin(b/c )
c
=arcsin(29.10326442171/44)
arcsin(0.66143782776615)
=0.72273 rad = 41.41° = 41°24'35"
h =a×b/c
=33 × 29.10326442171/44
=21.82745
area =a×b/2
=33 × 29.10326442171/2
=480.20386=363√7/2
perimeter =a+b+c
=33 + 29.10326442171 + 44
=106.10326
inradius =a×b/a+b+c
=960.40772591645/106.10326442171
=9.05163
circumradius =c/2
=44/2
=22
The area of the square on the third side of the triangle is 11 [tex]units^{2}[/tex]
How to find the area of the square?
Area of square A = [tex]a^{2}[/tex] = 33 [tex]units^{2}[/tex]
Side of square A = a = [tex]\sqrt{33}[/tex] units
Area of square B = [tex]b^{2}[/tex] = 44 [tex]units^{2}[/tex]
Side of square B = b = [tex]2\sqrt{11}[/tex] units
Side of square C = c = [tex]\sqrt{b^{2} - a^{2} } }[/tex]
=[tex]\sqrt{44 - 33}[/tex]
=[tex]\sqrt{11}[/tex] units
Area of square C = [tex]c^{2}[/tex]
= [tex](\sqrt{11}) ^{2}[/tex]
= 11 [tex]units^{2}[/tex]
To learn more about triangles, refer:
https://brainly.com/question/12111621
#SPJ2
can someone help me
Step-by-step explanation:
For a parabola y = ax² + bx + c, the vertex occurs at x = -b / (2a).
For f(x), a = -2, b = 0, and c = 9. So the vertex is at:
x = -0 / (2×-2)
x = 0
At x=0:
f(0) = -2(0)² + 9
f(0) = 9
The maximum of g(x) is at 11.
So g(x) has a greater maximum value than f(x).
what is the area of the regular octagon below? 9m
a). 114.5m
b). 229.1m
c). 391.1m
d). 458.m
Answer:
No diagram and no explanation what 9 is.
However, if it is an octagon with each side equal to 9 then
area = (# of sides * side^2) / (4 * tan (180 # of sides))
area = 8 * 9 * 9 / (4* tan (180 / 8)
area = 648 / 4 * 0.41421
area = 391.1059607446
answer is C
Step-by-step explanation:
The area of the considered octagon which has distance from its center to the vertex of 9 m is given by: Option b). 229.1 m²
How to find the area of a regular octagon?If the regular octagon has sides of 'a' units, then its area is:
[tex]A = 2(1+\sqrt{2})a^2 \: \rm unit^2[/tex]
Consider the attached figure below (second figure too).
If we find the value of 'a', then we can use the above formula.
Since there are 8 equal sides in a regular octagon, the angle from center to each of the side is full angle / 8 = 360/8 = 45 degrees.
Since the angle OA is perpendicular on BC, due to symmetry, we have the angle BOC divided into 2 parts.
Thus, we get:
m∠AOB = 45/2 degrees = 22.5°
Using the sine ratio from the perspective of angle AOB, we get:
[tex]\sin(m\angle AOB) = \dfrac{|AB|}{|OB|}\\\\\sin(22.5^\circ) = \dfrac{a/2}{9}\\\\a \approx 2 \times 9 \times 0.38268 \approx 6.888[/tex] meters
(since length of AB is half of length of BC, which is 'a' units).
Thus, we get:
[tex]A = 2(1+\sqrt{2})a^2 \approx 2(1+\sqrt{2})(6.888)^2 \approx 229.1\: \rm m^2[/tex]
Thus, the area of the considered octagon which has distance from its center to the vertex of 9 m is given by: Option b). 229.1 m²
Learn more about area of a regular octagon here:
https://brainly.com/question/858868
shape of distribution
choices
bimodal
random
skewed left
skewed right
uniform
unimodal
Answer:
1. unimodal
2. bimodal
3. skewed right
4. skewed left
5. uniform
6. random
Step-by-step explanation:
Answer:
1) Uni-modal 2) Bi-modal 3) Skewed right 4) Skewed left 5) Uniform 6) Random
Step-by-step explanation:
We are given the following information in the question:
1) Since we can see in the graph, there is one observation with highest frequency. Thus, this graph represents a uni-modal data
2) It s clearly seen that there are two values with highest frequencies. These two observations can be treated as the mode of the data. Thus, there are two modes. Thus, the graph represents a bi-modal data.
3) We can see that most of the data lies on the left side of data and very less data is there on the left tail. Hence, the graph is positively skewed or skewed on the right.
4) We can see that most of the data lies on the right side of data and very less data is there on the right tail. Hence, the graph is negatively skewed or skewed on the left.
5. Since all the observations are very close to each other almost equal we could say that the data have a uniform distribution.
6. The above data set have a random distribution since no pattern are observed.
Write the equation of the line with slope 4 through the point (-2, 5)
Answer:
y=4x+13 or y-5=4(x+2)
Step-by-step explanation:
we know that
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
In this problem we have
m=4
(x1,y1)=(-2,5)
substitute
y-5=4(x+2) ----> equation of the line into point slope form
Convert to slope intercept form
y-5=4x+8
y=4x+8+5
y=4x+13 ----> equation of the line into slope intercept form
Please explain your answer. Thank you!!
Answer:
(A) 180
Step-by-step explanation:
We have to treat those player selections as independent events, since one doesn't influence the other (the fact you chose Joe as a guard, shouldn't have an influence on who'll pick as center, unless there's bad blood between some players... but that's a whole other story).
So, how many ways to pick 2 guards from a selection of 4? The order doesn't seem to matter here, since they don't specify for example that Joe can only play on the left side). So, it's a pure combination calculation:
[tex]C(4,2) = \frac{4!}{2! * (4 - 2)!} = \frac{24}{2 * 2} = 6[/tex]
C(4,2) = 6.
How many ways to pick the 2 forwards from a group of 5? Using the same calculation, we get:
C(5,2) = 10.
And of course, the coach has 3 ways to pick a center player from 3.
Then we multiply the possible ways to pick guards, forwards and center...
6 * 10 * 3 = 180 ways.
A card is drawn from a standard deck of cards. Find the probability, given that the card is a non dash face card. P(nine)
Answer:
Step-by-step explanation:Knowing that
There are 26 black cards and 26 red ones. Face card consists of jack (J), queen (Q), king (K). There are (26-6)=20 non face red cards. “Either ... or ...” here means bundle of both kinds of cards.
So, there are (26+20)=46 expected cards.
If you also ask for the probability, so the probability of the question asking above is equal to
23/26
a bell rings every 2 hours, a second bell rings every 3 hours, and a third bell rings every 4 hours. if all 3 bells rind at 9:00am., at what time will all 3 bells next ring?
Answer:
9:00 P.M.
Step-by-step explanation:
All 3 bells ring at 9AM
1st bell: every 2 hours:
9AM, 11AM, 1PM, 3PM, 5PM, 7PM, 9PM
2nd bell: very 3 hours:
9AM, 12AM, 3PM, 6PM, 9PM
3rd bell: every 4 hours:
9AM, 1PM, 5PM, 9PM
So All 3 bells will ring at 9PM again
Answer:
the answer is that they will all ring at 9:00 pm
Step-by-step explanation:
9am=2, 3, 4
10am=0
11am= 2
12pm=3
1pm=2, 4
2pm= 0
3pm=3, 2
4pm= 0
5pm= 2, 4
6pm= 3
7pm=2
8pm= 0
9pm=2, 3, 4
Apply the distributive property to create an equivalent expression.
4
(
x
−
2
+
y
)
=
Answer:
4x-8+4y
Step-by-step explanation:
Explain how you can use a number line to find the sum of -8.3 + 10.5. Please help!
Final answer:
You can use a number line to find the sum of -8.3 + 10.5 by marking both numbers on the line, moving left to the negative value, and then moving right by the positive value to find the sum.
Explanation:
To find the sum of -8.3 and 10.5 using a number line, you start by drawing a horizontal line and marking the positions of -8.3 and +10.5 on it. You then move from 0 to -8.3 as this is a negative number. To add 10.5, you move 10.5 units to the right. Because 10.5 is greater than 8.3, your final position will be to the right of zero which makes the sum positive.
Let's break down the steps:
Draw a number line with enough space to mark both -8.3 and +10.5.
Mark the point -8.3 on the left side of zero since it's a negative number.
From -8.3, move 10.5 units to the right because you are adding a positive number.
The point you land on is the sum of -8.3 + 10.5.
If you need to subtract numbers, change the sign of the number being subtracted and then add according to the rules of addition. For instance, to subtract 3 from 5, you would change 3 to -3 and then add: 5 + (-3) = 2.
6u+4-3u+11 simplify PLZ
Answer:
3u+15
Step-by-step explanation:
6u-3u
4+11
3u+15
Answer:
3u+15
Step-by-step explanation:
6u-3u +4+11
3u + 15
write the solution as an ordered pair (x,y)
Answer:
(-2, -3)
Step-by-step explanation:
2x + 1 = 3x + 3
minus 3 from both sides
2x - 2 = 3x
minus 2x from both sides
-2 = x
then plug in -2 for x
y = 2(-2) + 1
y = -4 + 1
y = -3
(-2, -3).
Which is a negatively skewed distribution?
Answer:
Option D) This plot shows a negatively skewed data
Step-by-step explanation:
We are given the four distributions.
We have to find those which are negatively skewed.
Negatively Skewed Distribution:
A negatively skewed also known as left-skewed distribution is a type of distribution in which more values are concentrated on the right side of the distribution while the left tail of the distribution graph is longer.Mode > Median > MeanA) The given plot shows a normal distribution as the maximum values lie around the mean.
B) The given histogram shows a normal distribution as the maximum values lie around the mean.
C) The given box and whisker plot shows a positively skewed data due to tail on the right side.
D) This plot shows a negatively skewed data as most of the data lies on the right side and a tail could be seen on left side due to less data on left side.
What set of fractions is ordered from least to greatest? A) 2/5,1/4,3/8 B) 3/8,2/5,1/4 C) 1/4,3/8,2/5 D) 3/8,1/4,2/5
Answer:
C) 1/4,3/8,2/5
Step-by-step explanation:
First of all, let's rewrite all the fractions listed as decimal numbers:
[tex]\frac{2}{5}=0.400[/tex]
[tex]\frac{1}{4}=0.250[/tex]
[tex]\frac{3}{8}=0.375[/tex]
So the correct order from least to greatest should be
0.250, 0.375, 0.400
Which corresponds in fractional form to
1/4, 3/8, 2/5
So the correct option is
C) 1/4,3/8,2/5
The correct set of fractions ordered from least to greatest is C) 1/4, 3/8, 2/5.
To determine the set of fractions ordered from least to greatest, we need to compare them by finding a common denominator or converting them to decimals.
Let's convert the fractions to decimals:
2/5 = 0.41/4 = 0.253/8 = 0.375Next, we order the decimals from smallest to largest:
1/4 (0.25)3/8 (0.375)2/5 (0.4)Therefore, the correct order from least to greatest is: C) 1/4, 3/8, 2/5.
Who can help me out with this please
Answer:
a.) 14:6
b.) 6:8
Hope this helped!
Step-by-step explanation:
Answer:
see rexplanation
Step-by-step explanation:
A
There are a total of 14 marbles of which 8 are red and 6 are blue
ratio of all : blue = 14 : 6 = 7 : 3 ← in simplest form
B
ratio of blue : red = 6 : 8 = 3 : 4 ← in simplest form
If a spinner is spun 5 times then each event is independent
True or false?
Answer:
True
Step-by-step explanation:
Each time a spinner is spun, there is an equal chance that each result will occur, thus each of these spins are independent.
The answer is true
Hope this helped
What is the LCM of 9 and 15?
A) 15
B) 30
C) 45
D) 54
Answer:
C
Step-by-step explanation:
The multiples of 9 are : 9, 18, 27, 36, 45, 54, 63,......
The multiples of 15 are : 15, 30, 45, 60, 75, ........
The LCM of 9 and 15 is 45
C is the most reasonable answer
Write the relation as a set of ordered pairs
WILL MARK BRANLIEST
Answer:
option B
{(-2,4) , (0,6), (2,8)}
Step-by-step explanation:
To answer this you will determine which element of the domain is paired with exactly which element of the range.
The first oval (leftmost) represent the domain (-2 , 0 , 2)
The second oval (rightmost) represent the range (4 , 6 , 8)
(x , y)
x represent the element of domain and y represent the element of y.
Pretty sure it’s B.
which graph fits the question?? HURRY PLEASE
Answer:
this is the Answer
What is the product?
Answer:
Step-by-step explanation:
To find this product, multiply each of the 6 numbers in the given matrix by 6. The third possible answer choice is the correct one.
Jong earnee $100, and saved $30. What decimal part did he save
Answer:
Hi, this question is a little unclear. If you want to know what percentage he saved, it would be 30%, and to convert that percentage into a decimal would be a decimal of 0.30
Answer:
$70.00
Step-by-step explanation:
Add .00 to the end of each amount.
Make sure that the decimal points are lined up like a straight line.
Subtract 100.00 - 30.00
You should receive 70.00 and don't forget the dollar sign at the end so the answer is $70.00.
I need help with the question
Answer:
B
Step-by-step explanation:
B is correct. That "-7" will shift the graph of F(x) down by 7 units.
Answer:
B
Step-by-step explanation:
Given
y = f(x), then f(x) + c represents a vertical translation parallel to the y- axis.
• If c > 0 then translation up of + c units
• If c < 0 then translation down of - c units
Hence
g(x) = f(x) - 7
then g(x) is the graph of f(x) shifted 7 units down → B