Answer:
See steps below
Step-by-step explanation:
We need to work with each side of the equation at a time:
Left hand side:
Write all factors using the basic trig functions "sin" and "cos" exclusively:
[tex]tan^2(x)\,cos^2(x)=\frac{sin^2(x)}{cos^2(x)} cos^2(x)=sin^2(x)[/tex]
now, let's work on the right side, having in mind the following identities:
a) [tex]sec^2(x)-1=tan^2(x)=\frac{sin^2(x)}{cos^2(x)}[/tex]
b) [tex]1-sin^4(x) =(1-sin^2(x))\,(1+sin^2(x))[/tex]
c) [tex]1-sin^2(x)=cos^2(x)[/tex]
Then replacing we get:
[tex]\frac{(sec^2(x)-1)\,(1-sin^4(x))}{1+sin^2(x)} =\frac{sin^2(x)(1+sin^2(x))(1-sin^2(x))}{cos^2(x)(1+sin^2(x)))} =\frac{sin^2(x)(1+sin^2(x))\,cos^2(x)}{cos^2(x)(1+sin^2(x)))}=sin^2(x)[/tex]
Therefore, we have proved that the two expressions are equal.
when sunayana purcased a video-game she paid Rs 162.50 as VAT at the rate of 13%. find its cost without levying VAT. Rs 1250 is answer please how to take out this answer PLEASE HELP ME
Answer: 1250
Step-by-step explanation:
Let price be x
13/100x = 162.50
x = (162.50/100) / 13 = 1250
Evaluate 2(x+1)-3 when x=6
Answer:
[tex]11[/tex]
Step-by-step explanation:
[tex]2(6+1)-3[/tex]
[tex]2(7)-3[/tex]
[tex]14-3[/tex]
[tex]11[/tex]
Answer:
11
Step-by-step explanation:
1. insert 6 in the x spot
2. add inside of the parenthesis (6+1)=7
3. multiply 2 and 7 to get 14
4. take 3 from 14 to get 11
Here are two rectangles.
6 cm
9 cm
8 cm
12 cm
Complete this sentence.
The two rectangles are similar and the scale factor is
Answer:
3/4
Step-by-step explanation:
Scale factor = 6/8 or 9/12 = 3/4
Solve for x. 2(4x - 1) + 3(3 - 2x) = 0
Answer:
x=-3.5
Step-by-step explanation:
[tex]2(4x - 1) + 3(3 - 2x) = 0 \\ open \: the \: bracets \: \\ 8x - 2 + 9 - 6x = 0 \\ [/tex]
[tex]collect \: like \: terms. \\ 8x - 6x = 0 + 2 - 9 \\ 2x = - 7[/tex]
[tex]divide \: both \: sides \: of \: the \: equation \: by \: 2 \\ \frac{2x}{2} = \frac{ - 7}{2} \\ x = - \frac{7}{2} or \: x = - 3.5[/tex]
Brainliest question please please help me please
Answer: C outside of the circle
Step-by-step explanation:
The answer is c because
point 4, -1 falls outside of the
circle.
Hope this helps :)
Answer:
Its on the circle
Step-by-step explanation:
How do you solve an standard form/ intercept in y=4x-10 ¿? Help me plzzzz :/
Answer:
Slope = 8.000/2.000 = 4.000
x-intercept = 10/4 = 5/2 = 2.50000
y-intercept = -10/1 = -10.00000
Step-by-step explanation:
y= mx + b is the slope intercept form of a line where m is the slope and b is the y intercept.
Step 1 : Equation of a Straight Line
Step 2: Graph of a Straight Line
Step 3: Calculate the Y-Intercept
Step 4: Calculate the X-Intercept
Step 5: Calculate the Slope
Hope this helps.
Answer correctly !!!!!! Will mark brainliest !!!!!!!!
Answer:
(x+9)(x+2)
Step-by-step explanation:
x(x+9)+2(x+9)
(x+2)(x+9)
the order of the (---) doesn't matter
A grocery store clerk can scan one product every 1/2 of a second at what rate Can she scan Products
Answer:
per second or minute or hour?
per second: 2 per second
per minute: 120 per minute
per hour: 7200 per hour
Step-by-step explanation:
two 1/2 seconds per second so 2 products per second. multiply by 60 for per minute is 120. multiply the minute amount by 60 for hour amount aka 7200.
hope this helps! pls mark brainliest! have a good day!
Answer: She scan products at
2 per second.120 per minute. 7200 per hour.Given that: A grocery store clerk can scan one product every 1/2 of a second.
That means:
Rate = 2 per second.
Rate = (2*60) = 120 per minute.
Rate = (120*60) = 7200 per hour
Learn more: https://brainly.com/question/12049968
Drag a symbol to the first box and a number to the second box to complete the solution to this inequality. Each number or symbol can be used once or not at all. –2(z + 5) + 20 > 6
Answer:
[tex]z<2[/tex]
Step-by-step explanation:
Given the inequality: [tex]-2(z + 5) + 20 > 6[/tex]
Step 1: Distribute the bracket
[tex]-2(z + 5) + 20 > 6\\-2z-10+20>6\\-2z+10>6[/tex]
Step 2: Subtract 10 from both sides
[tex]-2z+10-10>6-10\\-2z>-4[/tex]
Step 3: Divide both sides by -2
Note that when you divide an inequality by a negative sign, the inequality sign is reversed.
[tex]-2z>-4\\\dfrac{-2z}{-2}< \dfrac{-4}{-2}\\\\$Therefore, $z<2[/tex]
Answer:
z<2
That is the answer.
Step-by-step explanation:
define the word triangle
A plane 2-dimensional figure with three straight sides and three angles.
Answer:
The definition of triangle is a plane figure with three straight sides and three angles. Hope that's work.x^2+6x+8=0
someone help me with the equation. i’m super confused and don’t know if i’m doing it right
Answer:
I think the answer is (x + 4) • (x + 2)
Step-by-step explanation:
First multiply the coefficient of the first term by the constant
Step 2: Find two factors of 8 whose sum equals the coefficient of the middle term 6
Step 3: write the polynomial splitting the middle term using the two factors found in step 2
Step 4: Add up the first 2 terms, pulling out like factors :
x • (x+2)
Add up the last 2 terms, pulling out common factors :
4 • (x+2)
Step 5: Add up the four terms in step 4
(x+4) • (x+2)
Your final answer is (x + 4) • (x + 2)
given two consecutive numbers, we are told that twice the first number is twelve more than the second number. What are the two numbers?
Answer: The numbers are 13 and 14
Step-by-step explanation:
Since they are two consecutive numbers, let the numbers be x and x+1.
We are told that twice the first number is twelve more than the second number. This can be expressed as:
2 × x = x+1+12
2x = x+13
2x-x = 13
x = 13
Since x = 13, x+1 = 13+1 = 14
The numbers are 13 and 14
Which polynomial is in standard form? 2xy^3 +3x^3 y^4 -4x^4 y^5 +9x^5 y^6 Which polynomial is in standard form?
Answer:
(D) [tex]5x^7y^2+7x^6y^5-14x^3y^7+51x^2y^9[/tex]
Step-by-step explanation:
A polynomial is said to be in standard form when it is arranged in descending powers of x.
When there are more than one variable, the alphabetical order is followed. For example, if there are variables x and y in the polynomial, x must be in descending order and y will be in ascending order.
From the given options, the polynomial which is in standard form is:
[tex]5x^7y^2+7x^6y^5-14x^3y^7+51x^2y^9[/tex]
The correct option is D.
Answer:
d
Step-by-step explanation:
Multiply the binomials using the box method.
(y+3)(y−6) =
Answer:
y^2 -3y - 18
Step-by-step explanation:
y x y= y^2
3 x y = 3y
y x -6 = -6y
-6y +3y = -3y
3 x -6 = -18
y^2 -3y - 18
Calculate the length of the opposite side of a right triangle with a hypotenuse of 16 inches and angle of 25 formed at the intersection between the adjacent side and the hypotenuse
Answer:
6.76 in
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Sin α = opposite side / hypotenuse
Where α is the angle formed at the intersection between the adjacent side and the hypotenuse , and the opposite side is x :
Replacing with the values given:
Sin 25 = x/ 16
Solving for x
sin25 (16) =x
x= 6.76 in
Feel free to ask for more if needed or if you did not understand something.
Leigh is going diving and needs to descend to a depth of 360 feet below sea level. She wants to do it in 12 equal descents. How far should she travel in each descent?
Answer:
30 feet
Step-by-step explanation:
If they are equal, just divide 360 by 12.
360 ÷ 12 = 30
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was to . If there were 12,779 total votes, how many yes votes were there?
Answer: The question is incomplete
Step-by-step explanation: The answer to this question cannot be determined correctly since an important detail is missing.
However, let me explain how you would normally go about it by using an example of mine. If for example the ratio of yes votes to no votes was 8 to 5, and the question requires you to calculate how many yes votes were there as indicated in your question, then the first step would be to find the total number of both sides of the ratio. That is add 8 to 5 which gives you 13. This means if there was a total of 13 votes cast, every yes vote stands for 8 out of 13 votes and every no vote stands for 5 out of 13 votes.
To express it mathematically, every yes vote would be 8/13 of the total (12779) and every no vote would be 5/13 of the total (12779).
Therefore to determine how many yes votes there was, is calculated as follows;
Let yes votes be y and no votes be x'
y = (8/13) * 12779
y = 102232/13
y = 7864
Based on my example that the ratio of yes votes to no votes is 8 to 5,
Then the number of yes votes was 7,864.
Which of the binomials below is a factor of this
trinomial?
x2 + 13x + 40
O A. x+ 5
O B. X-5
O C. X+4
O D. X-4
Here is a list of numbers:
8.4, 6.2, 8.8, 1.5, 0.5, 1, 5.4, 3.3, 2.2
State the median.
I need help ASAP
what is the total amount of sap produced that day?
Answer:
8 gallons
Step-by-step explanation:
Already a question from another person.
Answer:
5 gallons
Step-by-step explanation:
QUESTION 2 of 10: Your house is for sale for $210,000. A realtor will charge you a 3% sales commission. If you choose a "sale by owner"
option by passing a realtor, you will pay no commission, but you will have to pay an attorney an average of $950 at your closing. What will you
save by choosing the sale by owner" option?
a) $1,865
b) $2,150
C) $5,350
d) $9.500
Answer:
c) $5,350
Step-by-step explanation:
sale price= $210000sales commission= 3% = 3*$210000/100= $6300The difference between the commission and an attorney
$6300- $950= $5350Option C is correct
Answer:
C
Step-by-step explanation:
Solve the equation
The equation is -3 = 8x -4y for y
Answer:
[tex]y=\frac{3}{4}+2x[/tex]
Step-by-step explanation:
Which equation represents a circle with a center at (2,8) and a radius of 11?
(x – 3)2 + (y + 2)2 = 11
(x-2)2 + (y + 8y2 = 121
(x + 2)2 + (y - 3)2 = 11
(x + 3)2 + (y – 2y = 121
Answer:
[tex](x-2)^2+(y-8)^2=121[/tex]
Step-by-step explanation:
This is because if you can see that the, x is being subtracted by 2, making the x-coordinate +2. and the y is being subtracted by 8, making the y coordinate +8.
(2, 8) = Coordinates
And the reason it has a radius of 11 is because the 121 on the other is the product of 11 times 11.
PLEASE ANSWER THIS QUESTION !! WILL GIVE BRAINLIEST !! 15 POINTS !!
Answer:
The answer is C
Step-by-step explanation:
Please mark me Brainliest
What is the base of the expression g 12?
Answer:
Step-by-step explanation:
number A 3
Tick the correct answer
Please answer Fast.......
Answer:
c
Step-by-step explanation:
2^1\6
4√(3√2^2)= 2^1\6
Tamir wants to build a square wooden stage. His original pin for a stage x
feet long and x feet wide had to be made smaller to fit the space. The stage
needs to be 5 feet narrower and 3 feet shorter than his original plan. Which
multiplication problem represents this situation? What is the area of the
smaller stage?
Answer:
b .
Area=(x-5) (x-3)
Area = x^2 -8x+15
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Area of a rectangle = width x length
The original length and width was x, so if the stage needs to be 5 feet narrower and 3 feet shorter.
x-5
x-5
The formula is:
A=(x-5) (x-3)
Solving:
A = (x.x) + (x.-3) + (-5.x)+ (-5.-3)
A = x^2 -3x -5x+15
A = x^2 -8x+15
PLEASE HELP 20 POINTS!
This pattern follows the rule add 2. What is another feature of this pattern?
An image of a pattern. Term one has one dot, term two has three dots, term three has five dots, term four has seven dots.
A. The terms appear even, odd, even, odd.
B. All the terms are even.
C. Two terms are even, then two terms are odd.
D. All the terms are odd.
Answer:
Option D
Step-by-step explanation:
According to the image description provided:
Term one starts with one dot. One is an odd number.
If you add two to an odd number, the sum would be another odd number. This is what's happening with the pattern.
For example:
[tex]3+2 =5[/tex]
Three is an odd number. If you add two to it, you would get five, which is another odd number.
Term two has 3 dots, term three has 5 dots, term four has 7 dots.
So, all terms should be odd.
Option D should be the correct answer.
Find the sum of the first 18 terms of the arithmetic sequence whose nth term is an = 3n - 1.
Answer:
495
Step-by-step explanation:
In order to find the sum of the first 18 terms you have to find the 18th term and the first term using the equation given.
a1=3(1)-1 a1=2
a18=3(18)-1 a18= 53
Then plug in 53 for an, 18 for n, and 2 in for a1 in the sum equation: Sn=n/2(a1+an)
Sn=18/2(2+53) Solve for sn= 495
1 of 10
Colin buys a tv for £810.
It depreciates at a rate of 3% per year.
How much will it be worth in 3 years?
Give your answer to the nearest penny where appropriate.
7
8
9
q
W
e
r
t
y
u
o
Answer:
I=72.9
Step-by-step explanation:
I=PRT When P= the principal=810, R=rate=3% and T=time(by year)=3 years
I=810*3/100*3
I=24.3*3
I=72.9
Answer:
Simple interest/Interest = £72.9
Step-by-step explanation:
We have to find the simple interest at this point.
So use the formula:
I = prt or I = p x r x t
I = amount of interest
P = principal amount (810)
R = interest rate (in years) (.03)
T = amount of time in (years) (3)
All we need to do is multiply.
I = (810)(.03)(3)
I = £72.9
