Prove the following
Answer:
Step-by-step explanation:
Sin² x - Cos² x = (1 - Cos² x ) - Cos² x {Sin² x + Cos² x = 1}
= 1 - 2Cos² x
= - (2Cos x -1)
[tex]= -(\dfrac{2}{Sec^{2} x} - 1)\\\\=-(\dfrac{ 2}{Sec^{2} \ x}-\dfrac{Sec^{2} \ x}{Sec^{2} \ x})\\\\=-(\dfrac{2-Sec^{2} \ x}{Sec^{2} \ x})\\\\=\dfrac{2-Sec^{2} \ x }{-Sec^{2} \ x}[/tex]
Hence proved
Interval notation of x<2
interval notation of x<2
x=1
4. Determine both the HCF and LCM of 25 and 200
Answer:
The LCM of 25 and 200 is 200.
Explanation:
Find the prime factorisation of 25
25 = 5 × 5
Find the prime factorisation of 200
200 = 2 × 2 × 2 × 5 × 5
Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM:
LCM = 2 × 2 × 2 × 5 × 5
LCM = 200
Answer:
the HCF of 25 and 200 is 25 because it divides both of them and is maximum factor of them.
LCM of 25 and 200 is 200 because it can be divided by both 200 and 25
How do you factorise with letters and numbers please explain clearly example
7ab+14b how do I put that in brackets and what are the rules when factoring
Answer:
7b(a+2)
Step-by-step explanation:
First. look at the coefficient. See if they are common multiple of some number. If so find the GCF between them.
Then find the variable both terms share.
Put the GCF coeffiecnt and the variable both terms share outside the parentheses.
Inside the parenthesis will be a term that multiplied by the term outside of the parenthesis will equal the original equation.
For example, 7ab+14b.
Set up equation.
[tex]7ab + 14b[/tex]
Both terms share a b variable and 7 and 14 GCF is 7 so
let factor out 7b.
[tex]7b(a + 2)[/tex]
Why is inside the parenthesis is the term (a+2). If we divide 7ab+14b by 7b separately we get
[tex]a + 2[/tex]
Name the algebraic property demonstrated in the example below:
3 ⋅ (x ⋅ y) = (3 ⋅ x) ⋅ y
Answer:
It's Associative Property of Multiplication.
Thank You
(x+1)(x+2)=0 solve it please by factorise
Answer:
2x+2
Step-by-step explanation:
(x+1)(x+2)=0
Because it has the same i think you can just put the x's to together and make it 2x and multiply the 1x2 and that equals 2 so i think its 2x+2 maybe it could be 2x+3 or 2x*3 or 2x*2 but im pretty sure its 2x+2it makes sense because both of the x's are in the front of the + and the 1 and 2 are in the back
(a+b+c)^2 - a^2+b^2..................
Answer:
[tex]2b^2 + c^2 + 2ab + 2ac + 2bc[/tex]
Step-by-step explanation:
Whenever you have a parentheses to a power of a number you have to make it the parentheses times itself, so (a+b+c)^2 becomes (a+b+c)(a+b+c), where you then multiply a by a, a by b, a by c, b by a, b by b, b by c, and so on and then add all those numbers up. If you do that you would get a^2 + ab + ac + ab + b^2 + bc + ac + bc + c^2, where you then add them up to get a^2 + b^2 + c^2 + 2ab + 2ac + 2bc. Since you have - a^2 after this, you cancel out the a^2, and finally, you have + b^2 so you add b^2 to it and you get a final answer of 2b^2 + c^2 + 2ab + 2ac + 2bc.
If g(x) = x^2 + 3, find g(4).
11 19 16 8
Answer:
19
Step-by-step explanation:
g(x) = x^2 +3
substituing x for 4,
g(4) = 4^2 + 3
g(4) = 16 + 3
g(4) = 19
BRAINLIEST:
The area of a rectangle is (16x^2– 9y^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work
Answer:
4x^2 -12x +9
now
4 x 9 = 36
first take out the LCM of 36
it will be
2 x 2 x 3 x 3
4x^2 -6x -6x +9
2x(2x-3) -3(2x-3)
(2x-3)(2x-3)
it is showing that
2x-3 is the length for part A
18. Mabel gave Margo a bag containing red, white, and
blue marbles. The bag contained half as many red
marbles as blue ones, and 1/4 of the marbles in the
bag were white. If 8 of the marbles were red, how
many marbles were in the bag?
Answer:
32.
Step-by-step explanation:
Let the number of red marbles be x then the number of blue = 2x
So we have 8 red and 16 blue marbles.
If the total number of marbles are y marbles the number of white one = y/4.
So y = y/4 + 8 + 16
3/4y = 24
y = 24 * 4/3
= 96/3
= 32 marbles.
=
Evaluate each expression if a=12, b=9, and c=4
b^2+2^a-c^2=?
Answer:
you have to substitute the value of the variables then solve
what is the relationship between the location of plate boundaries and the formation of mountainsa
Answer:
Movements of tectonic plates create volcanoes along the plate boundaries, which erupt and form mountains. A volcanic arc system is a series of volcanoes that form near a subduction zone where the crust of a sinking oceanic plate melts and drags water down with the subducting crust.
Question
What is the measure of JKL?
A. 186°
B. 174
C. 87
D. 267
Answer: 174
Step-by-step explanation:
A trader sold 250 articles for $525,000.00 at a profit of 25%.
a.Calculate the cost of each article.
b.If the trader had wanted 45% profit on the cost price then how much would he sell the articles?
Answer:
a. $2100 b. $945000
Step-by-step explanation:
You have to divide 525000 and 250 to solve for "a". To solve for "b" you need to find %100 of the profit and do %100 of the profit times 0.45 to see how much is %45 of profit.
You are offered two jobs. One with a yearly salary of $53,749, and the other an hourly
job with a rate of $26 per hour. Both require you to work for 45 hours a week. How
much more will you make by taking the hourly job?
Answer:
$1170
Step-by-step explanation:
you will have to multiply the the rate you earn hourly by 45hours then it will state the more you'll be making hourly $26×45=$1170
what is 5/12 + 1/4. Im in 7th grade btw
Answer:
2/3
I hope this helps!! :)
Please help will mark branliest
Answer:
RS = 17
Step-by-step explanation:
QS = 62
RS = ?
QR = 45
QS - QR = RS
62 - 45 = 17
Thus RS = 17
a fifth of the sum of number a and 34
Write as an algebraic expression
The answer you are looking for is 1/5(a+34).
Solution/Explanation:
"Of"="multiplication (x)."
So, therefore, write it like this, to get the better picture and visualization,
1/5 times the sum of a number "a" and "34."
"Sum" obviously is related to "addition."
So, therefore, we can simplify the algebraic expression a little bit more,
1/5 times (a+34).
Now, we can finally write it like this.
1/5x(a+34).
The more proper way to write it, however is like this:
1/5(a+34).
So, therefore, the final answer is 1/5(a+34).
I hope that this has helped you. Enjoy your day, and take care!
The given statement is required in the form of an algebraic expression.
The statement is a fifth of the sum of number a and 34.
The sum means addition
So, the sum is [tex]a+34[/tex]
The statement states a fifth of which, means multiplied by [tex]\dfrac{1}{5}[/tex]
The algebraic expression will be the product of [tex]\dfrac{1}{5}[/tex] and [tex](a+34)[/tex]
The algebraic expression is [tex]\dfrac{1}{5}(a+34)[/tex]
Learn more:
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help plss
----------------------------
Answer:
it ebtween 10 and negetive 4.5
Step-by-step explanation:
Fill in the missing work and justification for step 3 when solving 2(x + 1) = 10
Answer:
subtraction property of equality
2x +2 - 2 = 10 - 2
Find the value of the expression when x = 4 and y = 6.
8x + 2y + 3
Answer:
47
Step-by-step explanation:
8(4) + 2(6) + 3 = 47
32 + 12 + 3 = 47
On a winter day, the temperature changes by -3 1/2 degrees Fahrenheit in 1 3/4 hour. What is the average change in the temperature in 1 hour? Please answer fast and explain how you got that answer. Don't put a link i will report you. Please explain!
Answer:
-2 degrees per hour
Step-by-step explanation:
Rate of change = -3 1/2 / 1 3/4
= -7/2 / 7/4
= -7/2 * 4/7
= -28/14
= - 2
is this a function? help lol
Answer:
what is this lol can u tell u
Answer: no
Step-by-step explanation: Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
I own the collector’s edition of my favorite Pokemon card. It used to be worth $120 USD. Now it is worth $150 USD.
What is the percent change?
Answer:
25% increase
Step-by-step explanation:
= [tex]\frac{150-120}{120}[/tex] x 100
= [tex]\frac{30}{120}[/tex] x 100
= 0.25 x 100
= 25% increase
Given f(x)=(2x+1)^3. Find f^−1(x). (inverse)
Answer:
Step-by-step explanation:
[tex]f(x)=y=(2x+1)^3\\Exchanging\ x\ and\ y\\\\x=(2y+1)^3\\\\\\Finding\ y\\\sqrt[3]{x} =2y+1\\\\2y=\sqrt[3]{x}-1\\\\\boxed{y=\dfrac{\sqrt[3]{x}-1}{2} =f^{-1}(x)}[/tex]
If HJ=7x-27, find the value of x
Answer:
x= HJ+27/7
Step-by-step explanation:
HJ + 27 = 7x
HJ+27/7 = x
Last year, the girl's basketball team had 20 ninth-grade students and 10 sixth-grade students. what was the ratio of sixth-grade students to total students on the team
If DE = 4x+10 and EF= 2x-1 and DF = 9x-15 find DF
Answer:
89
Step-by-step explanation:
show your work
fraction into the statement 1:50000
Answer:
am I supposed to change this to a statement like a sentence then one is to fifty thousand
lines of latitude also called parallels do what
Answer:
Hi, there!
Lines of latitude are also called parallels because they never touch one another.
Step-by-step explanation
Circles of latitude are often called parallels because they are parallel to each other; that is, planes that contain any of these circles never intersect each other: