Step-by-step explanation:
[tex](\sec A - \csc A)(1 + \cot A + \tan A)[/tex]
[tex]=(\sec A - \csc A)\left(1 + \dfrac{\cos A}{\sin A} + \dfrac{\sin A}{\cos A} \right)[/tex]
[tex]=(\sec A - \csc A)\left(1 + \dfrac{\cos^2 A + \sin^2 A}{\sin A\cos A} \right)[/tex]
[tex]=(\sec A - \csc A)\left(\dfrac{1 + \sin A \cos A}{\sin A \cos A} \right)[/tex]
[tex]=\left(\dfrac{\frac{1}{\cos A} - \frac{1}{\sin A}+\sin A - \cos A}{\sin A\cos A}\right)[/tex]
[tex]=\dfrac{\sin A - \sin A \cos^2A - \cos A + \cos A\sin^2A}{(\sin A\cos A)^2}[/tex]
[tex]=\dfrac{\sin A(1 - \cos^2A) - \cos A (1 - \sin^2 A)}{(\sin A\cos A)^2}[/tex]
[tex]=\dfrac{\sin^3A - \cos^3A}{\sin^2A\cos^2A}[/tex]
[tex]=\dfrac{\sin A}{\cos^2A} - \dfrac{\cos A}{\sin^2A}[/tex]
[tex]=\left(\dfrac{1}{\cos A}\right)\left(\dfrac{\sin A}{1}\right) - \left(\dfrac{1}{\sin^2A}\right) \left(\dfrac{\cos A}{1}\right)[/tex]
[tex]=\sec^2A\csc A - \csc^2A\sec A[/tex]
Four complex numbers lie at the vertices of a square in the complex plane.
Three of the numbers are 1 + 2i, -2 + i and -1 – 2i. What is the fourth
number?
9514 1404 393
Answer:
2 -i
Step-by-step explanation:
The two diagonals have the same center point. Here, it is ...
(1 +2) +(-1 -2i) = 0 +0i
The fourth point is found by reflecting the 2nd point across the origin:
p4 = -p2 = -(-2 +i) = 2 -i . . . . . fourth corner of the square
if 18 : 6 = x : 3 then what is 5 + 3x
Answer:
32
Step-by-step explanation:
18 : 6 = 3
therefore, x : 3 has to equal 3.
X : 3 = 3
X = 3 × 3
X = 9
To verify:
18 : 6 = 9 : 3
3 = 3
It's true that X = 9, so now just replace the X with 9 in the next equation
5 + 3(9) = 32
Answer:
32
Step-by-step explanation:
18 : 6 = x : 3
Product of means = Product of extremes
6 * x = 3*18
x = [tex]\frac{3*18}{6}[/tex]
x = 3*3
x = 9
Now plugin x = 9 in the expression
5 + 3x = 5 + 3*9
= 5 + 27
= 32
The diagram below shows rectangle ABC is a midtsin of
BC, such that D,E and F are on the same line API AD
i = 53, 13" BE-sm
and DE 2 EF
84
2176
F
with reasons
3.1 Prove
AB - BF
3.2. Calculate AD
3.3 Complece. In are rigter angled A BEF, son 53, 13" - BE
Answer:
4x2+3=
Step-by-step explanation:
3. Determine the Area and Perimeter of the
shape below.
13
5
12
Answer:
Perimeter: 30 Area: 30
Step-by-step explanation:
Perimeter of a triangle= Add all sides = 5+12+13 = 30
Area of a triangle= (B*H)/2 = (5*12)/2 = 60/2 = 30
Hope this helps! :)
Solve a triangle with a =5, b =6, and c = 7. Round to the nearest tenth.
Answer:
<A ≈ 45 degrees
<B ≈ 57 degrees
<C ≈ 78 degrees
Step-by-step explanation:
Hi there!
1) Find <C with the law of cosines
Typically, we want to solve for the angle opposite the largest side first.
Law of cosines: [tex]cosC=\frac{a^2+b^2-c^2}{2(a)(b)}[/tex]
Plug in given values
[tex]cosC=\frac{5^2+6^2-7^2}{2(5)(6)}\\cosC=\frac{1}{5}\\C=cos^-^1(\frac{1}{5} )\\C=78[/tex]
Therefore, <C is approximately 78 degrees.
2) Find <B with the law of cosines
[tex]cosB=\frac{a^2+c^2-b^2}{2(a)(c)}[/tex]
Plug in given values
[tex]cosB=\frac{5^2+7^2-6^2}{2(5)(7)}\\cosB=\frac{19}{35}\\B=cos^-^1(\frac{19}{35})\\B=57[/tex]
Therefore, <B is approximately 57 degrees.
3) Find <A
The sum of the interior angles of a triangle is 180 degrees. To solve for <A, subtract <B and <C from 180:
180-57-78
= 45
Therefore, <A is 45 degrees.
I hope this helps!
help please i don't know how to do this
What is the value of h in the figure below? In this diagram, ABAD ~ ACBD.
Д.
С
0
20
А. 80
В. 16
ОО ооо
С. 60
D. 5
Е. 8
о
Е.
Answer:
[tex]h=\sqrt{16(4)}[/tex]
[tex]h=8[/tex]
[tex]ANSWER:E) 8[/tex]
-------------------------------
~HOPE IT HELPS
~HAVE A GREAT DAY!!
Find the image of the given point
under the given translation.
P(4, -7)
T(x, y) = (x+1, y + 3)
P' = ([?], []).
Answer:
P' (5, -4)
Step-by-step explanation:
P (4, -7)
x = 4 & Y =-7
T(4,. -7) = (4 + 1, -7 +3)
P' = (5, -4)
can someone help with this
Answer:
[tex]\frac{8}{45}[/tex]
Step-by-step explanation:
'of' means 'multiply'
4/5 × 2/9 = 8/45
What is the solution to the system of equations graphed below?
Answer:
D
Step-by-step explanation:
The 2 lines intersect at (1, 5)
Answer:
D
Step-by-step explanation:
the line intersects at 1（x-axis）and 5（y-axis）
Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the trunk at a height of 20 ft. Find the length of a wire.
14 ft
15 ft
20 ft
29 ft
Based on the height that the wires attach, and the base length of the stakes, the length of the wire is 29 ft.
How long are the wires?This can be solved with the Pythagorean theorem because the height can be treated as the height of a right-angled triangle. The base as the base of the triangle.
The length of the wire is the hypothenuse.
Length:
c² = a² + b²
c² = 21² + 20²
c² = 841
c = √841
= 29 ft
Find out more on the Pythagorean theorem at https://brainly.com/question/343682.
#SPJ1
In the coordinate plane, two vertices of square ABCD are A (0,0) and B (0, m). What are the coordinates of points C and D? Do not introduce any new variables.
Answer:
Step-by-step explanation:
As shown in the graph,
A, B, C and D are the vertices of a square, all sides of the square will be equal in measure.
Coordinates of A → (0, 0)
Coordinates of B → (0, m)
Distance between point D and point A = m
Therefore, coordinates of point D → (m, 0)
Now point C will be equally distant from the points B and D.
Coordinates of C → (m, m)
You work for a parts manufacturing company and are tasked with exploring the wear lifetime of a certain bearing. You gather data on oil viscosity used and load. You see the regression output given below.
Predictor Coef Stdev t-ratio P
Constant -147.973 41.972 -3.53 0.004181
viscosity 6.262 0.474 13.21 <0.0001
load 0.298 0.04 7.43 <0.0001
s = 13.507 R² = 95.73% R² (adj = 95.02%
Analysis of Variance
Source DF SS MS F
Regression 2 49131.93 24565.96 134.65
Error 12 2189.38 182.45
Total 14 51321.3
Required:
What is the correct conclusion about the regression slopes based solely on the F-test
Answer:
We reject the Null and conclude that There is significant evidence that the slope values are greater than 0.
Step-by-step explanation:
Based on the ANOVA output given :
The F critical value can be obtained thus ;
F(df regression, df error)
Using an α-value of 0.01
F(2, 12) at α = 0.01 is 6.927
The F statistic as obtained from the ANOVA table = 134.65
Since, F statistic > F critical we reject the Null and conclude that slope values are significantly > 0
Similarly,
Using the Pvalue :
The Pvalue of the slope are extremely small :
Viscosity <0.0001
Load <0.0001
At α = 0.01, 0.025
The Pvalue < α ; The null will be rejected.
PLEASE HELPP ITS AN EMERGENCY
Find the measure of angle A.
Will marl brainliest! Please help :,)
Answer:
x= -4
Step-by-step explanation:
A line is 180 degrees. This means that we can use the equation
60+x+124=180
Simplify:
184+x=180
x= -4
We can check this answer by plugging it back in:
60 + (-4) +124 =180
180=180
I hope this helps!
Step-by-step explanation:
[tex]60 + 124 + x = 180 \\ 180 - 184 = x \\ x = - 4[/tex]
a pie chart is divided into four sectors in fig. 12.42. Each sector represents a percentage of the whole. The two larger sectors are equal and each represents x%. What is the angle subtended by one of those larger sectors ?
Answer:
Angle formed by the sector measuring x% will be 126°.
Step-by-step explanation:
Since, sum of all sectors formed in a circle is 100%.
By adding the measures of all the sectors,
x + x + 21 + 9 = 100
2x + 30 = 100
2x = 70
x = 35%
Now we know sum of all the central angles formed at the center of a circle = 360°
Therefore, angle formed by x% = 360° × 35%
= [tex]\frac{360\times 35}{100}[/tex]
= 126°
how do you find the angle?
Fill in the blank.
The
numbers are {0, 1, 2, 3, 4, ...}.
Answer:
the answer is 5 and u know the rest
I need some help please!
Answer:
See below
Step-by-step explanation:
Given :-
y || zTo Prove :-
m∠5 + m∠2 + m∠6 = 180°Proof :-
Here we are required to prove that ,
[tex]\rm\implies m\angle 5 + m\angle 6 + m\angle 2 = 180^o [/tex]
And here it's given that , y || z . Therefore ,
∠3 = ∠6 ( alternate interior angles )∠1 = ∠5 ( alternate interior angles )Now we know that the measure of a straight line is 180°. Therefore ,
[tex]\rm\implies m\angle 1 + m\angle 2 + m\angle 3 = 180^o \\\\\implies\boxed{\rm m\angle 5 + m\angle 6 + m\angle 2 = 180^o} [/tex]
From 1 and 2 .Hence Proved !
What value of x will make the equation true?
Answer:
5
Step-by-step explanation:
When a square root of an expression is multiplied by itself, the result is that expression
5=x
What is the domain of f(x)=(1/2)^x
Answer:
all real numbers
Algebra Examples
The domain of the expression is all real numbers except where the expression is undefined
Hello!
The domain of an exponential function is the crowd of all real numbers, so: x ∈ ℝ.
Good luck! :)
Solve the system by substitution.
y + 4 = x
10x + 2y = 16
Answer:
(2, -2)Step-by-step explanation:
Given system:
y + 4 = x 10x + 2y = 16Substitute x into the second equation:
10(y + 4) + 2y = 1610y + 40 + 2y = 1612y = -24y = -2Find x:
x = -2 + 4x = 2Answer:
x = 2 and y = -2
Step-by-step explanation:
Given system :-
y + 4 = x
10x + 2y = 16
Solve the system by substitution:-
Let,
y + 4 = x ...(1)
10x + 2y = 16 ...(2)
Solve for y;
Substitute y + 4 as x in the eq.(2)
10( y + 4 ) + 2y = 16
Distribute 10.10y + 40 + 2y = 16
Combine like terms.12y + 40 = 16
Move constant to the right-hand side and change their sign.12y = 16 - 40
Subtract 16 from -40.12y = -24
Divide both side by 12.12y / 12 = -24/12
Hence, y = -2
Solve for x.
Substitute the value of y in eq.(1)-2 + 4 = x
Add -2 and 4.Hence, 2 = x
I need help on this. Please someone help. I would appreciate it!
Use the circular formula and divide the volume by 2
Step-by-step explanation:
Answer:
12.56
Step-by-step explanation:
3.14(8)/2
=12.56
PLEASE HELP ASAP! So the answer I got for this problem is 50.26. Can someone make sure that is the correct answer? Please let me know how to solve this problem if it is wrong.
Answer:
Step-by-step explanation:
every thing looks good, except the question says "round" and soooooo, if you are rounding to the 2nd decimal place, then the next two decimal places are 54, or 50.2654 so, to round that, round up , so your final answer would look like 50.27 :) see?
9514 1404 393
Answer:
50.24 inches (or 50.2 inches)
Step-by-step explanation:
The formula for circumference in terms of radius is ...
C = 2πr
Using the given values for radius and for pi, the circumference is ...
C = 2(3.14)(8 in) = 50.24 in
__
Additional comment
If you use a more accurate value of pi, the rounded value is 50.27 in. That is not the value requested by this problem. It helps to follow directions.
If you like, you can round to 50.2, since only one decimal place is required in the result.
hey Plz help me fast it's important.
Answer:
Step-by-step explanation:
a) 52 is divisible by 4 and 5 - 2 = 3
b) 63 is divisible by 9 and 3*2 = 6 -> ten digit
c) 50 is divisible by 10 and 5 + 0 = 5
d) 72 is divisible by 6 and 7*2 = 14
This set of ordered pairs defines a function.
{(-49,7), (-56,8), (-63,9), (-70,10)}
Which table represents the inverse of the function defined by the ordered pairs?
Answer:
option c
Step-by-step explanation:
becoz for inverse the number that is negative changes into positive like wise for the positive number it changes into negative , just opposites
Why does it help to rearrange
addends in Example B to show that
2.5n +9.9+(-3n) is equal to
2.5n + (-3n) + 9.9?
Answer:
You don't really need to do it, but it helps you keep things more organized and easier to follow. Imagine if you're doing some multi-variable equation,
2a + 5b + 4d + 3c + b + a + 2d
that looks like a mess, it'll be easier to look at if you put all the similar variables next to each others like this:
a + 2a + b + 5b + 3c + 2d + 4d
(a + 2a) + (b + 5b) + 3c + (2d + 4d)
now you can add them up much easier.
A Sociology instructor gives students points for each discussion-board post and points for each reply to a post. Ana wrote 6 posts and 8 replies and received 114 points. Jae wrote 5 posts and 4 replies and received 79 points. Determine how many points a discussion post is worth and how many points a reply is worth?
Answer:
5 points per post and 2 points per replies
A.109
B.87
C.98
D.69
Answer:
hey what's
Step-by-step explanation:
a question wow okay the answer is
(f⋅g) (x) = f(x) ⋅ g(x)
true
false**
Answer:
true
Step-by-step explanation:
(f×g)×x = f(x)×g(x)