Step-by-step explanation:
sin(x)×csc(x) - cos²(x) = sin²(x)
csc(x) = 1/sin(x) (basic definition)
therefore,
sin(x)×csc(x) = sin(x) × 1/sin(x) = 1
1 - cos²(x) = sin²(x)
1 = sin²(x) + cos²(x)
and that is again a basic definition based on the standard circle with radius = 1. there we have the Pythagoras principle, as sin and cos are the legs of a right-angled triangle, with radius 1 being the Hypotenuse.
Kayli made 3 times as many Peanut Butter
Cookies as Sugar Cookies. This can be modeled
using the equation below.
Answer:
p/3
Step-by-step explanation:
You can divide both sides by three.
P=3S
----/3
P/3=S
Thus, p/3 is the answer
0.021 +0.21 + 0.00021 +0.0021 = 0
O A. 0.0084
B. 0.084
OC. 0.2351
D. 0.23142
E. 0.23331
Answer:
E. 0.23331
Step-by-step explanation:
0.021 + 0.21 + 0.00021 + 0.0021⇒ As 21 is a common factor, take the remaining as powers of 10.
21 (10⁻³ + 10⁻² + 10⁻⁵ + 10⁻⁴)21 (0.001 + 0.01 + 0.00001 + 0.0001)21 (0.01111)21 x 0.011110.23331Annabelle missed 30 questions on her multiple choice science final that had a total of 200 problems. What percentage of questions did Annabelle answer correctly?
Answer:
Annabelle answered 85% of the answers correctly.
Step-by-step explanation:
You would do 200-30 questiosn to get 170 questions that she answered right. You would then do 170/200 to get 0.85. 0.85 in decimal form is equal to 85%. I hope this helps! :)
What two factors add to -9 and multiply to 18
Answer:
3 × 6 = 18 3 + 6 = 9
Step-by-step explanation:
3 × 6 = 18 3 + 6 = 9
The graph shown below expresses a radical function that can be written in the form f(x)=a(x+k)^1/n +c.what does the graph tell you about the value of a in this function?
Answer:
a is less than 0
Step-by-step explanation:
The value of a in this function is a is less than 0 .
What is radical function?A radical function contains a radical expression with the independent variable (usually x) in the radicand. Usually radical equations where the radical is a square root is called square root functions. An example of a radical function would be. y=√x.
According to the question
Radical function that can be written in the form
[tex]f(x)=a(x+k)^{1/n} +c.[/tex] ------------------------(1)
By solving this equation we will get value of a and c
differentiating the equation
[tex]f'(x)=\frac{1}{n}* (a(x+k)^{1/n-1})[/tex]
therefore
[tex]((x+k)^{1/n-1}) > 0[/tex]
As graph is decreasing monotonically
[tex]\frac{a}{n} < 0[/tex]
as n will be always n>0 ,
so a < 0
Now taking value of f(x)= 0 in equation (1)
[tex]f(x)=a(x+k)^{1/n} +c[/tex]
[tex]0 =-a(x_{0} + k)^{1/n} +c[/tex] as (a < 0)
[tex]0=-a(k)^{1/n} +c[/tex]
[tex]-c =-a(k)^{1/n}[/tex] multiplying (-1) both side
[tex]c =a(k)^{1/n}[/tex]
i.e
c > 0
Hence, the value of a in this function is a is less than 0 .
To know more about Radical function here:
https://brainly.com/question/27847549
#SPJ2
Use substitution to solve the system.
-4x+5y = -26
y = 3x-14
Answer:
x= 4, y= -2
Step-by-step explanation:
To solve the system by substitution, start by labelling the two equations:
-4x +5y= -26 -----(1)
y= 3x -14 -----(2)
Since the second equation already has y as the subject of formula, we can substitute equation (2) into (1). This means that we can replace all the 'y's in equation (1) with 3x -4, such that equation (1) will only be in terms of x.
Substitute (2) into (1):
-4x +5(3x -14)= -26
Expand:
-4x +15x -70= -26
11x= 70 -26
11x= 44
Divide both sides by 11:
x= 44 ÷11
x= 4
Substitute x= 4 into (2):
y= 3(4) -14
y= 12 -14
y= -2
I need help finding the mean
Answer:
there is 5 jokers
Step-by-step explanation:
the dot plot shows that
What is Three-fourths divided by one-sixth?
Answer:
[tex] \frac{9}{2} [/tex]
Step-by-step explanation:
[tex] \frac{3}{4} \div \frac{1}{6} [/tex]
[tex] \frac{3}{4} \times \frac{6}{1} [/tex]
[tex] \frac{18}{4} [/tex]
[tex] \frac{9}{2} [/tex]
Divide fractions:-
[tex]\displaystyle\frac{3}{4} :\frac{1}{6}[/tex]
Multiply the 1st fraction times the reciprocal of the 2nd fraction (flop the second fraction over) :-
[tex]\displaystyle\frac{3}{4} *\frac{6}{1} =\frac{3*6}{4*1}=\frac{18}{4}[/tex]
[If necessary, divide the top & bottom by 2, and you'll have 9/2]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
What is the Pythagorean Theorem used for?
Answer:
Pythagorean Theorem used for finding the missing side length for a triangle the formula is a^2 + b^2 = c^2
a= base
b= height
c= the diagonal side a.k.a. hypotenuse
Answer:
u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye
Step-by-step explanation:
Factorise the following quadratic:
m^2 - 5m + 6
Answer:
(m-3)(m-2)
Step-by-step explanation:
Here,
m^2- 5m + 6
=m^2-(3+2)m +6
=m^2 - 3m - 2m +6
=m(m - 3) - 2 (m - 3)
=(m-3)(m-2)
Find the volume of the triangular prism.
4 ft
8 ft
37 ht
Answer:
4 ft
Step-by-step explanation:
So to calculate the volume of a triangular prism, the formula is 4ft
Step-by-step explanation:
volume of prism = area of triangle * length
= 1/2*4*8*37
= 592ft^3
Joseph researched the ages of some of his favorite professional
football players. He recorded his results in the dot plot below.
Which of the following statements about the distribution are true?
I. There are two peaks at 27 and 28.
II. The distribution is skewed.
III. The distribution does not have an outlier.
IV. The distribution shows a spread of 5.
I only
I, II, and III only
I, III, and IV only
I, II, III, and IV
The statements that are true about the dot plot are: I, III, and IV only.
What is the Spread of a Data in a Dot Plot?The range, which is the difference between the maximum and minimum value, is a measure of the spread of a data distribution.
In the dot plot given, the spread of the data is: 30 - 25 = 5.
The peak points are at 27 and 28, and the data looks symmetrical in shape with no clear outlier.
Therefore, the statements that are true about the dot plot are: I, III, and IV only.
Learn more about dot plot on:
https://brainly.com/question/25957672
find the length of the missing side.
1) 52 cm
2) 42cm
3) 25 cm
4) 48 cm
Answer:
52 cm
Step-by-step explanation:
Use the pythagorean theorem to solve for missing sides in a right triangle.
20²+48²= missing side
20²+48²=2704
Take the square root of 2704 to get the missing side.
[tex] \sqrt{2704 } = 52[/tex]
Answer :
52 cm⠀
Explanation :
This is Right Angled Triangle.⠀
Solution :
We'll solve this using the Pythagorean Theorem.
where,
AB (20 cm) is the perpendicularBC (48 cm) is the Base.AC is the Hypotenuse.⠀
We know that,
[tex]{\longrightarrow \bf \qquad (AC) {}^{2} = (AB) {}^{2} +( BC) {}^{2} } \\ \\ [/tex]
Now, we will substitute the given values in the formula :
[tex]{\longrightarrow \sf \qquad (AC) {}^{2} = (20) {}^{2} +( 48) {}^{2} } \\ \\ [/tex]
We know that, (20)² = 400 and (48)² = 2304. So,
[tex]{\longrightarrow \sf \qquad (AC) {}^{2} = 400 + 2304 } \\ \\ [/tex]
Now, adding 400 and 2304 we get :
[tex]{\longrightarrow \sf \qquad (AC) {}^{2} = 2704 } \\ \\ [/tex]
Now, we'll take the square root of both sides to remove the square from AC :
[tex]{\longrightarrow \sf \qquad \sqrt{ (AC) {}^{2}} = \sqrt{2704} } \\ \\ [/tex]
When we take the square root of (AC)² , it becomes AC,
[tex]{\longrightarrow \sf \qquad AC = \sqrt{2704} } \\ \\ [/tex]
We know that, square root of 2704 is 52 .
[tex]{\longrightarrow \sf{\pmb{ \qquad AC = 52 }}} \\ \\ [/tex]
So,
The measure of the missing side (AC) is 52 cm .The angle of elevation to a nearby tree from a point on the ground is measured to be 52
∘
∘
. How tall is the tree if the point on the ground is 82 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.
The elevation and the top of the tree form a right triangle
The height of the tree is 104.96 feet
How to determine the height of the tree?The given parameters are:
Angle of elevation = 52 degreesHorizontal distance (b) = 82 feetThe height (h) of the tree is calculated using the following trigonometry ratio
tan(α) = h/b
Make h the subject
h = b * tan(α)
Substitute known values
h = 82* tan(52)
Evaluate the product
h = 104.96
Hence, the height of the tree is 104.96 feet
Read more about right triangles at:
brainly.com/question/2437195
Answer:
Step-by-step explanation:
tan 52 = x/82
x= 82 x tan 52
x=104.96
Does anyone know if this is right?
In the diagram below, m//n. Select all of the angles that are congruent to 21
Not sure about Angle. 13
whats the slope of (0,1) and (3,-5)
2x+5y < 19 and x-2y <-9
Solve the system of equation and graph it.
Answer:
see attached
Step-by-step explanation:
The boundary lines and solution region are shown on the attached graph. It is convenient to let a graphing calculator plot them.
__
If you'd like to plot the boundary lines by hand, it is useful to note the equations for them are in standard form:
ax +by = c
This means the slope is m = -a/b, and the y-intercept is c/b. Here, the odd constant values mean that (most) intercepts will involve fractions.
2x+5y<19slope: -2/5
y-intercept: 19/5 = 3.8
points on the line: (7, 1), (2, 3)
The general form ...
x < ( ) . . . . means the line is dashed and shading is to the left.
__
x-2y<-9slope: 1/2
y-intercept: 9/2 = 4.5
points on the line: (1, 5), (-3, 3)
The general form ...
x < ( ) . . . . means the line is dashed and shading is to the left.
__
Solution RegionThe lines have slopes of opposite signs, so cross in a fashion that forms an "X" on the graph. Shading is left of both lines, so will be in the left quadrant of the X. The boundary lines are not part of the solution region.
_____
Additional comments
The boundary line will be solid when the inequalitiy includes the "or equal to" case. This is identified by the symbols ≤ or ≥. Here, we have the symbol <, which does not include the "or equal to" case, so the boundary line is dashed. (The same would be true for an inequality using >.)
To determine shading direction, it is convenient to pick a variable with a positive coefficient, and look at its relation to the inequality symbol. In the first inequality, we could choose either of ...
x < ( ) . . . . . shading left of the dashed liney < ( ) . . . . . shading below the dashed line__
In the second inequality, the only variable with a positive coefficient is x, and its relation to the inequality symbol is ...
x < ( ) . . . . . shading left of the dashed lineIf we were to rewrite the second inequality to give the y-variable a positive coefficient, we could get either of ...
y > ( ) . . . . . multiply by -1/2( ) < y . . . . . add the opposite of the y-termEither way, the shading is above the dashed line.
__
About points on the line:
The inequalities have odd constants (19, -9) and coefficients with different parity (one even, one odd). That makes it convenient to choose an odd value for the variable with the odd coefficient. The result will be an integer value for the variable with the even coefficient.
(3.6×10−5)÷(9×10−7) in Standard Form
Answer: 31/83 (decimal form 0.373494)
Step-by-step explanation:
60 ft
60 ft
30t)
60 ft
60ft
30 ft.
Answer:
7290ft^2
Step-by-step explanation:
60*30=1800
then multiply that by 4 because of the 4 rectangle
1800*4=7200
multiply 30*30 to get 90 then add that on
7290
There are 5 cups of oatmeal in a container.Stella has1/3 cup of the oatmeal every day for breakfast. In how many days will Stella finish all the oatmeal in the container
3. Two ocean beaches are being rected by crosionThe table shows the winteet of each beach measured at high tide where 1905 is represented by year
Year number
Western Beach width (info
Dunes Beach width (in feet)
100
20
25
5
90
70
10
80
13
75
12
76
30
15
70
95
A Describe the patterns shown by the crosion data measurements shown for each of the beaches in the table
B. Between which years will the beaches have approximately the same width?
C. Assuming these rates remain constant what can you do to get a becer approximation of when the two beaches will have the same wich?
Answer:
Answer given in the image below
I hope my answers helps you.
A bus makes a stop at 2:30, letting off 13 people and letting on 5. The bus makes another stop ten minutes later to let off 3 more people. How does the number of people on the bus after the second stop compare to the number of people on the bus before the 2:30 stop?
Answer:
net loss of 10
Step-by-step explanation:
stop 1 :
13 off
5 on
7 net loss
stop 2 :
3 off
3 net loss
total net loss = 3+10
=10
Find the area and the circumference of a circle with diameter 3ft.
Use the value 3.14 for pie, and do not round your answers. Be sure to include the correct units in your answers.
Answer:
Step-by-step explanation:
hello :
the circumference is :P=2pi×r=2×3.14×3= .... continu
Answer:
Area= 7.065ft^2
Circumference= 9.42ft
Step-by-step explanation:
The area of a circle is,
area=Pi*r^2
and the circumference,
circumference=2*Pi*r
with r being the diameter/2
so we get,
area=(3.14)(1.5)^2=7.065ft^2
circumference=2(3.14)(1.5)=9.42ft
• Write an expression that is equivalent to 3(7 + x).
3(7+ x) =
Step-by-step explanation:
3(7 + x) = 3×7 + 3x = 21 + 3x
remember, when you multiply two expressions, you need to multiply every term of the first expression with every term of the second expression, and then add all partial results (by considering the individual signs, of course).
What is the value of 1500 divided by (6 squared + 43) x 37
Rewrite : [tex]1500 : (6^{2} +43)[/tex] x 37
Simplify : [tex]1500 : 79[/tex] x 37 = 702.531646...
Round to :
- Nearest whole number : 703
- 1 d.p : 702.5
- 2 d.p : 702.53
- 3 d.p : 702.532
The value of the expression when 1500 divided by (6 squared + 43) x 37 using simplification is 702.531647.
A collection of constants, variables connected using one or more arithmetic operator is called an expression.
The way of writing the complex mathematical problems into simpler forms using certain way is called simplification.
Simplification is solved using BODMAS rule.
The expression 1500 divided by (6 squared + 43) x 37 can be written in mathematical form as:
[tex]\dfrac {1500}{((6)^2 + 43)} \times37[/tex]
This can be simplified as,
[tex]\dfrac {1500}{(36 + 43)} \times37[/tex]
[tex]\dfrac {1500}{79} \times37[/tex]
On further solving, it results to 702.531647.
The value of the given expression is 702.531647.
Learn more about expressions here :
https://brainly.com/question/28170201
#SPJ6
Helppppppp pls :))))))))
Answer:
g(x) = 1 * (x + 1)^2
Step-by-step explanation:
Answer:
g(x) = 1 * (x + 1)^2
Step-by-step explanation:
An oatmeal container is in the shape of a right circular cylinder. The radius of the base is 4 centimeters, and the height is 17 centimeters. What is V, the volume of the container in terms of π?
V =
π cm3
Answer:
V = 272 π cm^3
Step-by-step explanation:
r = 4 cm
h = 17 cm
V = πr^2h
V = π((4)^2)(17) cm^3 = 272 π cm^3
okay, triangular prism volume formula. b is base, B is area of base (i think) V is volume, h is height, but I forgot what H is.
Also, how has your day been? :)
Answer:
good and how do you forget wut H is?
Step-by-step explanation:
How many lines of symmetry does the letter have?
0
1
2
3
1. The equation of a circle is x² + y² - 4x +2y-11-0. What are the center and the radius of the circle?
www
Show your work.
Answer:
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Circles,
so we get as,
centre as ==> ( -g, -f) ==> (2,-1)
