Answer:
You use cotx = cosx/sinx.
Step-by-step explanation:
I guess you mean cotx sinx = cosx.
You substitute the identity cotx = cosx / sinx:
cotx sinx = (cosx / sin x) * sin x
The sin x ' s cancel to give cosx.
Final answer:
To verify that cot(x)sin(x) + cos(x) is a basic trigonometric identity, we can use the Pythagorean Identity which states that sin²(x) + cos²(x) = 1. The expression cot(x)sin(x) + cos(x) simplifies to 2cos(x), which confirms that it is a basic trigonometric identity.
Explanation:
To verify that cot(x)sin(x) + cos(x) is a basic trigonometric identity, we can use the Pythagorean Identity which states that sin²(x) + cos²(x) = 1. Let's start by expressing cot(x) in terms of sin(x) and cos(x). Since cot(x) = cos(x)/sin(x), we can substitute this into the equation:
cot(x)sin(x) + cos(x) = cos(x)/sin(x) * sin(x) + cos(x) = cos(x) + cos(x) = 2cos(x).
So, the given expression reduces to 2cos(x), which is indeed a basic trigonometric identity.
f(x)=x^3-9x
What is the average rate of change of f over the interval (1,6]?
Answer:
34
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 1, 6 ]
f(b) = f(6) = 6³ - 9(6) = 216 - 54 = 162
f(a) = f(1) = 1³ - 9(1) = 1 - 9 = - 8, thus
average rate of change = [tex]\frac{162-(-8)}{6-1}[/tex] = [tex]\frac{170}{5}[/tex] = 34
Final answer:
The average rate of change of the function f(x) = x^3 - 9x over the interval (1,6] is 34.
Explanation:
The average rate of change of a function f(x) over an interval is calculated by taking the difference in the function values at the end points of the interval divided by the length of the interval. For the function f(x)=x^3-9x over the interval (1,6], we calculate the function values at x=1 and x=6, then find the difference, and divide by the interval length, which is 6-1=5. So f(1)=1^3-9(1)=-8 and f(6)=6^3-9(6)=216-54=162. Therefore, the average rate of change is (162-(-8))/5 = 170/5 = 34.
two lines meet at a point that is also the endpoint of two rays. setup and solve the appropriate equations to solve for the values of angles x and y. show the steps you followed to find the unknown angles.
Answer:
x = 19°
y = 53°
Step-by-step explanation:
First we can find the value of x, then the value of y.
For x, we can observe from the figure that x is complementary to the angle of 71°, that is, they both summed have 90°.
So, we have that:
x + 71 = 90
x = 19°
Now we can solve for y.
From the figure we have that y is supplementary to the angle (37° + 71° + x°), that is, they summed form a angle of 180°.
So we have that:
y + 37 + 71 + 19 = 180
y = 180 - 37 - 71 - 19 = 53°
The angles x and y lie on a straight line at the intersection point of two lines and are therefore supplementary. Therefore, they add up to 180 degrees. Without further information, it's impossible to find the exact values of X or Y.
Explanation:Given that two lines intersect at a common point, and this point is also the end point of two rays, we create four angles around the intersecting point. Let's denote the angles formed by the intersecting lines as angle x and angle y. According to the properties of intersecting lines, adjacent angles are supplementary. Therefore, the measures of x and y add up to 180 degrees. We set up the equation as x + y = 180. Without any additional information, we cannot find the specific values of x and y. However, we can say that whatever the value of x is, y will be 180 - x, and vice versa.
Learn more about Angle Relationships here:https://brainly.com/question/31825145
#SPJ6
A test has a mean of 65 with standard deviation of 5. What percent of the students would you expect to receive a grade of 55 or more?
a. 2.5%
b. 95%
c. 13.5%
d. 97.5%
e. none of the above
How does the risk of needing insurance impact the cost of premiums?
A. In some cases, higher risk results in lower costs.
B. Higher risk always results in lower costs.
C. Higher risk always results in higher costs.
D. In some cases, higher risk results in higher costs.
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
because when you go to get health insurance, they never want to have to pay alot. for instance, when you smoke, do risky activities, etc. that ups the risks, making your health insurance cost much more to cover for the costs of the doctors appointments, screenings, and tests that come along with those risks. this is the answer on PLATO. please make me brainliest !
Solve the equation by completing the square: z^2 - 2z = 323
a. -17, 19
b. -17, -19
c. 17, -19
d. 17, 19
Answer: A. -17 , 19
Step-by-step explanation:
Move all terms to one side.
z^2-2z-323=0
z^2 −2z−323=0
Factor : z^2-2z-323
z^2−2z−323.
(z-19)(z+17)=0(z−19)(z+17)=0
Solve for z.
z=19,−17
the vertices of figure QRST and translation 3 units left and 11 units down to form Q'R'S'T'. Explain the similarities and differences between two figures
Answer:
Similarities: same size, and same orientation
Differences: different location, and different points
Step-by-step explanation:
When your doing a translation, the only thing that changes is the location. For example if you for your pencil, the location changes not size.
Thank you :D
I Hope This Helps You And Stay Safe!
Amber is on a family cell phone plan with the other 3 members of her family. The family gets 840 shared cell phone minutes a month, and each family member is limited to his or her equal share of the minutes. The only free calls are calls between family members.
How many minutes per day can Amber talk on her cell phone with her friends during a 30-day month, without going over her share of the minutes?
Minutes per day can Amber talk on her cell phone with her friends during a 30-day month, without going over her share of the minutes will be 7 minutes
ConceptFirst of all we will find the total minutes per family member will get by dividing the total minutes of cell phone plan to total family memberAfter finding total minutes each family member will get we will divide it by 30 to get how many minutes per day Amber will get to talk on her cell phone with her friend.How to solve this problem?The steps are as follow:
Given, there are total 4 family members including Amber.Also the family gets 840 minutes shared cell phone minutes for a monthTo find total minutes per family member we will using following formula:total minutes per family member = total minutes / number of family member
total minutes per family member = 840 / 4
total minutes per family member = 210 minutes
To find the minutes per day Amber will get we will use following formula:Minutes per day Amber will get = total minutes per family member / total days in month
Minutes per day Amber will get = 210 / 30 = 7 minutes per day
So Amber will get 7 minutes per day to talk on her cell phone with her friends during a 30-day month, without going over her share of the minutes
Learn more about Division here:
https://brainly.com/question/2475734
#SPJ2
A combination lock has 3 dials. The first 2 dials have a setting for digits 0 through 9, and the third has settings for all 26 letters of the alphabet. A combination consists of one setting from each of the dials. How many combinations are possible
Answer:
There is 2600 combinations possible.
Step-by-step explanation:
The combinations for the first lock has 10 combinations
The combinations for the second lock has 10 combinations
The combinations for the third lock has 26 combinations
The total combinations is the product of all the locks.
There is 2600 combinations possible.
How many pairs of vertical angles are formed by five distinct lines that have a common point of intersection?
The total number of pairs of vertical angles formed by five distinct lines that have a common point of intersection is: 10 pairs.
To find how many pairs of vertical angles are formed by five distinct lines that all intersect at a common point, we need to understand a few key concepts about vertical angles and intersecting lines.
Intersection Point: When multiple lines intersect at a single point, they form various angles at that point.Vertical Angles Definition: Vertical angles are the angles that are opposite each other when two lines intersect. They are congruent (having the same measure).Pairs of Intersections: Each pair of lines forms a set of vertical angles at the intersection point.Number of Intersecting Pairs: With five distinct lines, any two lines can form an intersection. The number of ways to choose 2 lines out of 5 to intersect can be calculated using the combination formula:
[tex]\binom{n}{2} = \frac{n(n-1)}{2}[/tex]
Where [tex]n[/tex] is 5 in this case.
Calculation: Plugging in the values, we get:
[tex]\binom{5}{2} = \frac{5 \cdot 4}{2} = 10[/tex]
So, there are 10 pairs of intersecting lines.
Vertical Angle Pairs per Intersection: For each of these 10 intersections, there is exactly one pair of vertical angles.
Each intersection of two lines forms one pair of vertical angles, and with 10 intersections, we have 10 pairs of vertical angles.
What is the momentum of a 1.5-kg ball rolling at 3.0m/s
Answer:
4.5 kg m/s
Step-by-step explanation:
[tex]Momentum = mass \times velocity \\ \hspace{60 pt} = 1.5 \times 3.0 \\\hspace{60 pt} = 4.5 \: kg \: m/s[/tex]
Final answer:
The momentum of a 1.5-kg ball rolling at 3.0 m/s is calculated by multiplying the mass by the velocity, resulting in 4.5 kg*m/s.
Explanation:
The momentum of an object is calculated using the formula momentum (p) = mass (m) * velocity (v). Applying this formula to the given problem, where a 1.5-kg ball is rolling at a speed of 3.0 m/s, the momentum can be found by multiplying the mass of the ball by its velocity.
So, the momentum p is given by:
p = 1.5 kg * 3.0 m/s = 4.5 kg*m/s.
Therefore, the momentum of the 1.5-kg ball rolling at 3.0 m/s is 4.5 kilogram meters per second (4.5 kg*m/s).
WORTH BRAINLIST!!!!!!!!!!!!!!!!!!!!!!!What is the solution to the equation x + 3 = 27? 24 30 81 90
Answer:
should be 24
Step-by-step explanation:
x+3=27
-3 -3 take away 3 on both sides to leave the variable by itself
x = 24
How much is 9 1/12 - 7 1/3?
Answer:
1.75 or 1 3/4
Step-by-step explanation:
Answer:
1 3/4
Step-by-step explanation:
Find a common denominator for both fractions
9 1/12 - 7 4/12 = 1 9/12 = 1 3/4
4x-6 <30
what is the answer?
Hope this will help u....:)
Can someone pls help me
Simplify:
[tex] \frac{21x {}^{6} {y}^{5} }{ {14x}^{2} {y}^{9} }[/tex]
Look at the attached picture ⤴
Hope it will help u...
Find the slope.
A 17
Answer:
C
Step-by-step explanation:
Slope = rise / run
in this case, rise is 17 yd and run is 295 yd.
so its 17/295
Which statements can be represented by this equation? Select three options.
2n-9.2 =n+4/5
Answer:
1, 3, 5
Step-by-step explanation:
Let the number be n
1.Twice a number minus nine and two tenths is the same as the number plus four fifths.
Twice a number is 2n. nine and two tenth = 9.2. Therefore twice a number minus nine and two tenths = 2n - 9.2. the number plus four fifths = n + 4/5
The resulting equation is 2n-9.2 =n+4/5
2.Nine point two decreased by double a number is the same as the number added to four fifths.
Nine point two = 9.2, double a number = 2n. Therefore, Nine point two decreased by double a number is 9.2 - 2n
The resulting equation gives 9.2 - 2n = n + 4/5
3.Nine point two less than twice a number is equal to the number added to four fifths.
Nine point two = 9.2, twice a number = 2n. Therefore Nine point two less than twice a number = 2n - 9.2
The resulting equation is 2n-9.2 =n+4/5
4.Two times the difference of a number and nine and two tenths is equal to the number plus four fifths.
The difference of a number and nine and two tenths is given by n - 9.2. Therefore, Two times the difference of a number and nine and two tenths is 2(n - 9.2).
The resulting equation is 2(n - 9.2) = n + 4/5
5.Double a number decreased by nine and two tenths is the same as the sum of four fifths and the number.
Double a number decreased by nine and two tenths is 2n - 9.2
The resulting equation is 2n-9.2 =n+4/5
Answer:
1 Twice a number minus nine and two-tenths is the same as the number plus four-fifths.
3 Nine point two less than twice a number is equal to the number added to four-fifths.
5 Double a number decreased by nine and two-tenths is the same as the sum of four-fifths and the number.
Step-by-step explanation:
The diagram below shows scalene triangle WXY. The measure of ZWXY is 710
Answer:
[tex]m\angle WYX=46^o[/tex]
[tex]m\angle YWX=63^o[/tex]
Step-by-step explanation:
The complete question in the attached figure
we know that
A scalene triangle has three different interior angles and three different length sides
In this problem
[tex]m\angle WYX=46^o[/tex] ----> by vertical angles
[tex]m\angle WXY=71^o[/tex] ----> is given
Find the measure of the third angle ∠YWX
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]46^o+71^o+m\angle YWX=180^o[/tex]
[tex]m\angle YWX=180^o-117^o=63^o[/tex]
Verify each statement
1) [tex]m\angle WYX=46^o[/tex] ---> is true (see explanation)
2) [tex]m\angle YWX=63^o[/tex] ---> is true (see explanation)
3) [tex]m\angle WXY=46^o[/tex] ---> is not true because ∠WXY is given and is 71 degrees
4) [tex]m\angle YWX=46^o[/tex] ---> is not true because [tex]m\angle YWX=63^o[/tex]
5) [tex]m\angle WYX=134^o[/tex] --> is not true because [tex]m\angle WYX=46^o[/tex]
The question seems to contain an error - a triangle's angles cannot sum to more than 180 degrees. Assuming the triangle issue is corrected, principles like the Triangle Sum Theorem, and laws of sines and cosines would be applied to solve it.
Explanation:The question refers to a diagram depicting scalene triangle WXY, which suggests a problem in geometry, a branch of mathematics. However, the information about the measure of angle ZWXY being 710 degrees seems incorrect since the sum of angles in any triangle cannot exceed 180 degrees. It appears there's a typographical error or a misunderstanding in the transcription of the problem. In a triangle, the measures of the three interior angles always add up to 180 degrees, and no single angle can measure more than 180 degrees because it would no longer be a triangle.
Without a correct diagram or clarification of the angle measures, providing a step-by-step solution to this geometric problem is not feasible. Nonetheless, if the problem was corrected and it involves solving for missing angles or sides of a scalene triangle, one could apply geometry principles and theorems such as the Triangle Sum Theorem, the Law of Sines, and the Law of Cosines depending on the given information.
The sum of the angle measures in a 50-gon is
Answer:
Interior: 8640°
Exterior: 360° (Every shapes' exterior angle sum is 360°)
Step-by-step explanation:
Formula: 180(Sides - 2)
180(50-2) = 180(48) = 8640
Which statement is true?
N is a point of tangency on circle P.
PT is a secant of circle P.
Line S R is a secant of circle P.
VU is a tangent of circle P.
Answer:
c: line sr is a secant of circle p
Step-by-step explanation:
The true statement is (c) line SR is a secant of circle P
From the diagram, we can see that line SR passes through the circle, without passing through the center (i.e. point P) of the circle
This indicates that line SR is a secant
Given that the center of the circle is point P
Hence, the true statement is (c) line SR is a secant of circle P
Read more about secants at:
https://brainly.com/question/25871159
Joseph opens a checking account with $400. each month he adds $150 to the account wright an equation representing the total amount A in the account at the end of any given month M
Answer:
[tex]A=400+150m[/tex]
Step-by-step explanation:
since 'A' is the final amount it acts as the 'y' value, and if it's 150 per month then you would multiply the number of months (m) by 150 plus the 400 that was already there.
Tim's piggy bank contains dimes and nickels worth $5.50. He has 70 coins in all. Use substitution to solve the system of equations to find out how many of each coin Tim has.
Tim has a total of 30 nickels and 40 dimes.
What is Linear Equation?Linear equations are the equations which consist of two or more variables having the exponent of the variable equals 1.
Total number of coins in the Tim's piggy bank = 70 coins
Let d be the number of dime coins and n be the number of nickel coins.
So d + n = 70
Total dollars = $5.50
10 dimes = 1 dollar
1 dime = 1/10 dollar = 0.1 dollar
20 nickels = 1 dollar
1 nickel = 1/20 dollar = 0.05 dollar
0.1 d + 0.05 n = 5.50
So we have two linear equations here : d + n = 70 and 0.1 d + 0.05 n = 5.50.
d + n = 70 ⇒ d = 70 - n
Substituting d = 70 - n in the equation 0.1 d + 0.05 n = 5.50,
0.1 (70 - n) + 0.05 n = 5.50
(0.1 × 70) - 0.1n + 0.05n = 5.50
7 - 0.05n = 5.50
-0.05n = -1.5
n = 30
So d = 70 - n = 70 - 30 = 40
Hence the number of nickel coins is 30 and number of dime coins is 40.
Learn more about Linear Equations here :
https://brainly.com/question/29739212
#SPJ3
Mr. Morrison and Ms. Johnson are teaching their classes how to write in cursive. Mr. Morrison has already taught his class 12 letters. The students in Ms. Johnson's class, who started the unit later, currently know how to write 7 letters. Mr. Morrison plans to teach his class 2 new letters per week, and Ms. Johnson intends to cover 3 new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take? How many letters will the students know?
In
weeks, the students in both classes will know how to write
letters in cursive.
Solve the equation
8 + 10 = 14
Answer:
4
Step-by-step explanation:
8+10
= 18
18-14
=4
Answer:
Step-by-step explanation:
8+10=14? 8-10= 2 2+8=10 8+10=18.....This is what I am think....
I am not sure..
A lawn had a length of 10 feet and a width
of 8 feet. What is the perimeter of the
lawn?
1.80 feet
2. 80 square feet
3. 36 square feet
4. 36 feet
geometric mean between 1/4 and 80 please answer
Answer:
Geometric mean: 6.8399037867068
Step-by-step explanation:
a²+6²=C²
72+10º=122
Does this work?
Explain
[tex] {10}^{2} + {7}^{2} = {c}^{2} \\ \sqrt{100 + 49} = c \\ c = \sqrt{149} [/tex]
but c=12. 12^2=144
Answer: It isnt a right triangle
A crane has a cable with a breaking strain of 6400 kg
measured to 2 significant figures.
It is used to lift crates which weigh 90 kg measured to the nearest 10 kg.
What is the greatest number of crates that can safely be lifted
at one time without breaking the cable?
Some working must be shown.
The greatest number of crates that a crane with a breaking strain of 6400 kg can safely lift at one time (with the crate weight marked to the nearest 90 kg) is 71 crates.
Explanation:In this problem, we need to determine the maximum number of crates a crane can lift without breaking its cable. The breaking strain of the cable can be interpreted as the maximum weight, or load, the cable can safely support. This is given as 6400 kg. Each crate the crane is lifting is said to weigh 90 kg.
To find the maximum number of crates that can be safely lifted, we divide the breaking strain (the total load the cable can bear) by the weight of each individual crate. Therefore:
6400 kg (total load) / 90 kg (load per crate) = 71 crates
However, since we can't lift fractions of a crate, we should round down to the nearest whole number, which gives us a maximum of 71 crates that can be lifted safely without the cable breaking.
Learn more about Lifting capacity of a crane here:https://brainly.com/question/36454874
#SPJ12
To find the maximum number of crates that can be lifted without exceeding the cable's breaking strain of 6400 kg, divide the breaking strain by the weight of one crate (90 kg) and round down to the nearest whole number, which results in 71 crates.
To determine the greatest number of crates that a crane cable with a breaking strain of 6400 kg can lift at one time, you perform a simple division. The weight of each crate is given as 90 kg (measured to the nearest 10 kg).
To ensure safety, you take the total breaking strain of the cable and divide it by the weight of one crate:
Breaking strain of cable = 6400 kg
Number of crates = Breaking strain of cable / Weight of one crate
Number of crates = 6400 kg / 90 kg/crate
Number of crates = 71.111...
Since you cannot lift a fraction of a crate, round down to the nearest whole number.
The greatest number of crates that can be lifted without breaking the cable is 71 crates.
A person walking starts 0 m/s and after 6 seconds is traveling at
5 m/s. What is the acceleration of the walker?
Final answer:
To find the acceleration, we subtract the initial velocity from the final velocity and then divide by the time. For the given values, this results in an acceleration of 0.833 m/s² for the walker.
Explanation:
The student has asked about the acceleration of a person who starts at 0 m/s and reaches 5 m/s in 6 seconds. To find acceleration, we use the formula:
acceleration = (final velocity - initial velocity) / time
Inserting the given values:
acceleration = (5 m/s - 0 m/s) / 6 s = 5/6 m/s²
Therefore, the acceleration of the walker is 0.833 m/s².
V= u + at
u = 2 a = -5 t = 1/2
Work out the value of v.
Answer:
-0.5
Step-by-step explanation:
2+-5x1/2
-5x1/2=-2.5
2+-2.5=-0.5
Answer:
-1/2
Step-by-step explanation:
u=2
a=-5
t=1/2
Using
v=u+at
v= 2+(-5×1/2)
v=2+(-5/2)
v=2-5/2
v= -1/2
Which two problems below does this model represent?
12 x 2
24 ÷ 6
6 x 4
24 x 6
Answer:
6 x 4
24 ÷ 6
Step-by-step explanation:
6 x 4 – There are 6 boxes with 4 stars in each box. When something looks like this, it mean multiplication.
24 ÷ 6 – There are 24 stars in total. Those 24 stars are being divided by 6 boxes. In the end there are 4 stars in each box. (So basically, 24 ÷ 6 = 4)