Answer:
From the RHS:
Cot^4θ-tan^4θ
=(cos^2θ/sin^2θ)*(cos^2θ/sin^2θ)-(sec^2-1)*(sec^2-1)
=(1-sin^2θ)/(sin^2(θ))*(1-sin^2θ)/(sin^2(θ))-(sec^4θ+2sec^2θ+1)
=(cosec^2θ-1)*(cosec^2θ-1)-sec^4θ+2sec^2θ-1
=cosec^4θ-2cosec^2θ+1-sec^4θ+2sec^2θ-1
=cosec^4θ-2cosec^2θ-sec^4θ+2sec^2θ
=LHS
Step-by-step explanation:
Answer: see proof below
Step-by-step explanation:
Use the following Pythagorean Identities:
sec²A = tan²A + 1
csc²A = 1 + cot²A
Use group factoring: a(x + y) + b(x + y) = (a + b)(x + y)
Proof LHS → RHS
Given: 2sec²Ф - sec⁴Ф - 2csc²Ф + csc⁴Ф
Pythagorean: 2(tan²Ф + 1) - (tan²Ф + 1)² + -2(1 + cot²Ф) + (1 + cot²Ф)²
Group Factoring: (tan²Ф + 1)(2 - tan²Ф - 1) + (1 + cot²Ф)(-2 + 1 + cot²Ф)
Simplified: (tan²Ф + 1)(1 - tan²Ф) + (1 + cot²Ф)(cot²Ф - 1)
Multiplied: tan²Ф - tan⁴Ф + 1 - tan²Ф + cot²Ф - 1 + cot⁴Ф - cot²Ф
Simplified: 1 - tan⁴Ф + cot⁴Ф - 1
= - tan⁴Ф + cot⁴Ф
= cot⁴Ф - tan⁴Ф
cot⁴Ф - tan⁴Ф = cot⁴Ф - tan⁴Ф [tex]\checkmark[/tex]
can someone help me
Step-by-step explanation:
k(-5)= 6.(-5)+100
=30 + 100
=70
Answer:
70
Step-by-step explanation:
We can substitue -5 in for x:
k(-5) = 6(-5) + 100 = 70.
How many different two digit numbers can be formed from the digits, 7,8, and 9 if the numbers must be even and no digit can be repeated?
Answer:
2
Step-by-step explanation:
If the number must be even, the units digit must be 8. That leaves 2 choices for the tens digit. The possible numbers are ...
78
98
There are 2 of them.
Answer: Only two: 78 and 98
Step-by-step explanation: 8 is the only even number available to put in the units place where even or odd is determined. With no repetition allowed, the only possibilities left are to switch positions of the 7 and 9 in the tens place.
Barun said says, "The number sqrt49 is an irrational number." Do you agree or disagree? Explain using the definition of rational and irrational numbers.
Here's why:
sqrt(49) = sqrt(7^2) = 7
We can write 7 as a ratio or fraction of two integers 7 = 7/1
This shows that 7 is rational, so that makes sqrt(49) rational as well.
An irrational number is one where we cannot write it as a fraction of two integers. An example of an irrational number would be pi. Another irrational number is sqrt(2).
Note: the denominator can never be zero.
Please solve this question. cant understand
Answer:
x=150°
Step-by-step explanation:
A=180-60=120
B=180-60=120
C=45
D=360-120=240
E=45
The sum of the interiors of a polygon is (n-2)*180. Since this is a hexagon, (6-2)*180=4*180=720. SO..
B=720-120-120-45-240-45=150
Assuming the questions is asking to solve for x, the angle is 150°
Variable y varies directly with variable x. If x = 12, then y = 3. What is the value of y
when x = 8?
Answer:
y = 2Step-by-step explanation:
To find the value of y when x = 8 we must first find the relationship between the two variables.
The statement
y varies directly with variable x is written as
y = kx
where k is the constant of proportionality
when
x = 12
y = 3
Substitute the values into the above formula and solve for k
That's
3 = 12k
Divide both sides by 12
[tex]k = \frac{1}{4} [/tex]
So the formula for the variation is
[tex]y = \frac{1}{4} x[/tex]
when
x = 8
[tex]y = \frac{1}{4} \times 8[/tex]
we have the final answer as
y = 2Hope this helps you
what is the slope for y=3x+6
The formula for slope is y=mx+b.
In this problem m=3; meaning the slope is 3.
Answer:
m = 3
Step-by-step explanation:
y = 3x + 6
Slope formula
y = mx + b
m = 3
what is mean by vertically opposite angle
Answer:
Vertically Opposite Angles are the angles opposite each other when two lines cross "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.
Step-by-step explanation:
please help me on this
Answer:
(-3,-2)
Step-by-step explanation:
well, you take the difference between the midpoint and given endpoint and add it on in the other direction
PLZ HELP DUE IN 1 HOUR Do you think the mean would be an appropriate measure of center to describe the data shown in the histogram? Explain your answer.
Answer:
Step-by-step explanation:
the mean would be appropriate measure of center to describe the data shown in the histogram because the data is symmetrical.A symmetric histogram is a distribution in which the 2 halves appear to be the same on both sides.
Solve the equation below for x. −12(3x−4)=11 A. −1323 B. −813 C. −6 D. 6
-1/2( 3x -4) = 11
Use distributive properties:
-3/2 + 2,= 11
Subtract 2 from both sides:
-3/2x = 9
Divide both sides by -3/2
X = 9/ -3/2
X = -6
The answer is c. -6
The winning car in a race beat the second car by 19 ··· 100 of a second. The third car was ·4· 10 of a second behind the second car. By how much did the first car beat the third car?
Add the times together:
19/100 + 4/10
Find the common denominator, which is 100 so rewrite 4/10 as 40/100
Now add:
19/100 + 40/100 = 59/100
The first car beat the third car by 59/100 seconds.
Use the distributive property to multiply the polynomials.
-5x²(6x - 1)
Enter the simplified polynomial expression in the box.
Answer:
-30x^3+5x^2
Step-by-step explanation:
Given: DC =6x, and DA =4x+18 EB =4y-12, and ED =y+17 Y Find y. Then find ED, DB and EB.
Given:
(1) DC = 6x, and DA = 4x + 18, find the value of x. Then find AD, DC, and AC
(2) EB = 4y - 12, and ED = y + 17. Find y. Then find ED, DB and EB.
Answer:
x = 9, AD = 54, DC = 54, AC = 108
y = 23, ED = 40, DB = 40, EB = 80
Step-by-step explanation:The diagram for this question has been attached to this response.
(1) From the diagram, it can be observed that;
(a) DC and DA have equal lengths. i.e
=> DC = DA ---------------------(i)
(b) AC = DA + DC --------------------(ii)
But;
DC = 6x
DA = 4x + 18
Substitute the values of DC and DA into equation (i) as follows;
6x = 4x + 18 [Solve for x]
6x - 4x = 18
2x = 18
x = 9
Since x = 9, then
DC = 6x = 6(9) = 54
DA = 4x + 18 = 4(9) + 18 = 54
Therefore
DC = 54
AD = DA = 54
AC = 54 + 54 = 108 [using equation (ii)]
(2) Also, from the diagram, it can be observed that;
(a) ED and DB have equal lengths. i.e
=> ED = DB ---------------------(iii)
(b) EB = ED + DB --------------------(iv)
=>EB = ED + ED [since ED = DB]
=>EB = 2ED ------------------(v)
But;
EB = 4y - 12
ED = y + 17
Substitute the values of EB and ED into equation (v) as follows;
4y - 12 = 2(y + 17) [Solve for y]
4y - 12 = 2y + 34
4y - 2y = 34 + 12
2y = 46
y = 46 / 2
y = 23
Since y = 23, then
EB = 4y - 12 = 4(23) - 12 = 80
ED = y + 17 = 23 + 17 = 40
Therefore
EB = 80
ED = DB = 40
Answer:
x = 9, AD = 54, DC = 54, AC = 108
y = 23, ED = 40, DB = 40, EB = 80
Step-by-step explanation:
A teacher is making a history test composed of the same number of multiple choice questions as short answer questions she estimates it will take students an average of two minutes to complete each multiple-choice questions and an average of 3.5 minutes to complete each short answer questions, n,quality to determine how many questions and the teacher can include if the test must take students less than 45 minutes to complete
Answer:
8 questions each for short answer questions and 8 questions of Multiple Choice Questions type.
A total of 16 questions.
Step-by-step explanation:
Given:
The number of multiple choice questions and number of short answer type questions are same.
Let it be equal to [tex]x[/tex].
Average Time taken to attempt multiple choice question = 2 minutes
Total time taken to attempt multiple choice question = 2[tex]\times x[/tex] minutes
Average Time taken to attempt short answer type question = 3.5 minutes
Total Time taken to attempt short answer type question = 3.5[tex]\times x[/tex]
Total time for test should be less than 45 minutes.
Therefore, the equation becomes:
[tex]2x+3.5x<45\\\Rightarrow 5.5x <45\\\Rightarrow x<8.18[/tex]
Hence, the value of [tex]\bold{x=8}[/tex]
Therefore, the answer is:
8 questions each for short answer questions and 8 questions of Multiple Choice Questions type.
A total of 16 questions.
Answer:
Step-by-step explanation:
2n+3.5n <45
Find the missing value to the nearest hundredth.
Answer:
Option (A)
Step-by-step explanation:
Let the Sine of the given angle θ is,
Sinθ = [tex]\frac{x}{y}[/tex]
Then θ = [tex]\text{Sin}^{-1}(\frac{x}{y} )[/tex]
From the given values in the question,
Sinθ = [tex]\frac{7}{29}[/tex]
θ = [tex]\text{Sin}^{-1}(\frac{7}{29} )[/tex]
θ = 13.97°
Therefore, measure of the angle 'θ' will be 13.97°.
Option (A) will be the answer.
Factor the following polynomial completely.
Hello, please consider the following.
[tex]\begin{aligned}1280x^{11}-405x^7&=5x^7(256x^4-81)\\\\&= 5x^7(16^2(x^2)^2-9^2)\\\\&=5x^7(16x^2-9)(16x^2+9)\\\\&=5x^7((4x)^2-3^2)(16x^2+9)\\\\&\large \boxed{=5x^7(4x-3)(4x+3)(16x^2+9)}\end{aligned}[/tex]
So, the last one is the correct answer.
Thank you.
Please
9a × 3 + 8a + 4 -11a
Please help
I'm confused
35a_11a+4
24a+4
hope it helps
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's simplify step-by-step.
[tex]9a * (3) + 8a + 4 -11a[/tex]
[tex]= 27a + 8a + 4 + -11a[/tex]
Combine Like Terms:
[tex]= 27a + 8a + 4 + -11a \\= ( 27a + 8a + -11a ) + (4) \\= 24a + 4[/tex]
Answer : [tex]\boxed {24a + 4}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
how do you rewrite the formula to solve for r?
Answer:
The answer is C.
The steps are :
[tex] {T}^{2} = ( \frac{4 {\pi}^{2} }{GM} ) \times {r}^{3} [/tex]
[tex] {T}^{2} \div ( \frac{4 {\pi}^{2} }{GM}) = {r}^{3} [/tex]
[tex] {T}^{2} \times \frac{GM}{4 {\pi}^{2} } = {r}^{3} [/tex]
[tex] \frac{GM {T}^{2} }{4 {\pi}^{2} } = {r}^{3} [/tex]
[tex] \sqrt[3]{ \frac{GM {T}^{2} }{4 {\pi}^{2} } } = r[/tex]
[tex]r = \sqrt[3]{ \frac{GM {T}^{2} }{4 {\pi}^{2} } } [/tex]
Answer :
C
[tex]r = \sqrt[3]{ \frac{ {T}^{2}GM} {4 {\pi}^{2} } } [/tex]
Step-by-step-explanation :
[tex] {t}^{2} = ( \frac{4 {\pi}^{2} }{gm} ) {r}^{3} \\ {t}^{2} = \frac{4 {\pi}^{2} {r}^{3} }{gm} [/tex]
[tex] {t}^{2} gm = 4 {\pi}^{2} {r}^{3} \\ \frac{ {t}^{2} gm}{4 {\pi}^{2} } = \frac{4 {\pi}^{2} {r}^{3} }{4 {\pi}^{2} } [/tex]
[tex] {r}^{3} = \frac{ {t}^{2} gm}{4 {\pi}^{2} } [/tex]
[tex] \sqrt[3]{ \frac{ {t}^{2} gm}{4 {\pi}^{2} } } = \sqrt[3]{r} [/tex]
[tex]r = \sqrt[3]{ \frac{ {t}^{2} gm}{4 {\pi}^{2} } } [/tex]
write 0.18 repeating as a fraction in simplest form.
Answer:
180/1000 or 18/100 0.18
Step-by-step explanation:
The repeating decimal 0.18 to a fraction is 2/11
Converting the repeating decimal to a fraction.From the question, we have the following parameters that can be used in our computation:
Number = 0.18
Express as fraction
So, we have
Number = 18/100
Subtract 1 from the denominator
Number = 18/99
Simplify
Number = 2/11
Hence, the fraction is 2/11
Read more about fraction at
brainly.com/question/31896427
#SPJ6
Three times the sum of half a number and 7 is 36
Answer:
your answer is 19.34
Step-by-step explanation:
let the number be x
half a number = ½ x
three times means multiplied by three
so,
3( ½ x) + 7 = 36
3( ½ x) = 36 - 7
3( ½ x) = 29
½ x = 29/3
½ x = 9.67...
x = 9.67 × 2 (when we moved ½ on the other side of the equal sign it › turns into 2/1 )
x = 19.34
Item 15 Question 1 Write and solve an equation to answer the question. The perimeter of the Norwegian flag is 190 inches. What are the dimensions of the flag? Equation: =190 y= Question 2 Label the dimensions of the flag in inches.
Answer:
40 inches by 55 inches.Step-by-step explanation:
The question lacks the required diagram. Find the diagram in the attachment.
The flag is rectangular in nature and the formula for calculating the perimeter of a rectangle is P = 2(L+W) where;
L is the length of the flag
W is the width of the flag
From the diagram, L = y and W = 11y/8
Since the perimeter = 190 inches, we will substitute the given parameters into the formula and firs calculate the value of y.
190 = 2(y+11y/8)
190 = 2y + 11y/4
multiply through by 4
760 = 8y+11y
760 = 19y
y = 760/19
y = 40
The length of the flag is 40 inches and the Width of the flag is 11(40)/8 = 55inches.
Hence, the dimensions of the flag in inches is 40 inches by 55 inches.
Can someone please help me ASAP .
Answer: Hi!
A number that is bigger than 5 2/3 but smaller than 6 could be 5.7.
A number that is bigger than 5.6 but smaller than 5 2/3 could be 5.62.
Hope this helps!
In fact 5 2/3 means 5+2/3 for this. So,5+2/3 = 17/3 = 5.6
For first question, if "numbers" are also include rational numbers, you can write any rational number according to this interval. For example, 5.7 , 5.75, 5.9
But the second one, the interval that is shown us has the same value 5.6 and 5.6. So you cannot find a number which should bigger 5.6 and smaller 5.6 . It seems impossible I mean.
S is in between T and U. ST = x + 4 and SU = 2x. TU = 16. Find the value of x.
Solve for x. A. 24 B. 32 C. 22 D. 35
Answer:
B. 32
Step-by-step explanation:
The product of the lengths of segments to the near and far circle intercepts are the same, where the length is measured from the point where the secant and tangent meet. The tangent point counts as both circle intercepts, so we have ...
30×30 = 18×(18 +x)
900 = 324 +18x . . . . eliminate parentheses
576 = 18x . . . . . . . . . subtract 324; next, divide by 18
32 = x
George had $6,000 in a savings account earning simple interest at a rate of 5% per year. At the end of the year, George paid 25% in taxes on his interest. How much money did George earn in interest that year after paying taxes?
Answer:
$225
Step-by-step explanation:
Given that:
Principal = $6,000
Interest rate = 5%
Time = 1 year
Taxes paid = 25% on the interest earned
To find:
Money earned after paying taxes ?
Solution:
First of all, let us calculate the total interest earned:
Formula for Simple Interest is given as:
[tex]SI =\dfrac{PRT}{100}[/tex]
Where P is the principal
R is the rate of interest
T is the time taken
Putting the given values:
[tex]SI =\dfrac{6000 \times 5\times 1}{100} =\$300[/tex]
Now, it is given that 25% of the interest earned is given as taxes.
Taxes paid = 25% of $300
[tex]\Rightarrow \dfrac{25}{100} \times 300 =\$75[/tex]
Therefore, the money earned = Interest earned - Taxes paid
The money earned = $300 - $75 = $225
Plzzz solve question 8 and 9. I will mark as BRAINLIEST FOR correct answers.
Answer:
a) >
b) =
c) =
d ) >
this number 8
9 .A B B C C C D E E F F F G H H I I I J KK L L L M NN OOO P QQ RRR S TT UUU V WW XXX Y ZZZ
THE 45TH LETTER IS W
Dr.Hong prescribed 0.019 liter more medicine then Dr.Tannenbaum. Dr.Evans prescribed 0.02 Less then Dr.Hong. Who prescribe the most medicine? Who Prescribed the lest?
Answer:
Dr. Hong prescribed the most medicine
Dr. Evans prescribed the less medicine
Step-by-step explanation:
Dr. Hong =0.019 liters more than Dr.Tannenbaum
Dr.Evans prescribed 0.02 Less than Dr.Hong.
Let
Dr.Tannenbaum=x liters
Dr. Hong =0.019 + x liters
Dr. Evans= 0.019 + x - 0.02 liters
= x - 0.001 liters
Therefore,
Dr. Hong prescribed the most medicine
Dr. Evans prescribed the less medicine
solve each system by elimination 7x-4y=-6
-5x+4y=-2
Answer:
(-4, -5.5).
Step-by-step explanation:
7x - 4y = -6
-5x + 4y = -2 Adding these 2 equations:
2x = -8
x = -4
Substituting for x:
7(-4) - 4y = -6
-4y = - 6 + 28 = 22
y = -5.5.
If B is the midpoint of AC, AB = x + 6, and AC = 5x - 6, then what is BC?
BC =
HELP PLEASE
Answer:
bc= 12 :)
Step-by-step explanation:
please help me on this geometry
Answer:
x = 30
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , thus
x + 4x + 30 = 180
5x + 30 = 180 ( subtract 30 from both sides )
5x = 150 ( divide both sides by 5 )
x = 30