Answer:
Proof below
Step-by-step explanation:
Trigonometric Identities
We'll prove that:
[tex]\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=\sin A*\cos A[/tex]
Recall:
[tex]\displaystyle \sec A =\frac{1}{\cos A}[/tex]
[tex]\displaystyle \csc A =\frac{1}{\sin A}[/tex]
Applying those definitions:
[tex]\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=\frac{\sin A+\cos A}{\frac{1}{\cos A}+\frac{1}{\sin A}}[/tex]
Adding the fractions:
[tex]\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=\frac{\sin A+\cos A}{\frac{\sin A+\cos A}{\cos A*\sin A}}[/tex]
Dividing the fractions:
[tex]\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=(\sin A+\cos A)*\frac{\cos A*\sin A}{\sin A+\cos A}[/tex]
Simplifying:
[tex]\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=\cos A*\sin A[/tex]
Hence proved
Which ratio is proportional to 18/28 ?
Help me plzzzz i will give brainliest
Answer:
18/21 = 30/35
Step-by-step explanation:
so the problem says 18/21 so if that's the correct ratio to proportion to the answer would be. 30/35. the reason is that you can divide 18 and 21 by 3 to get 6/7 then if you multiply by 5 you get 30/35. Dividing and multiplying both the denominator and numerator keeps the ratio proportional.
Given the information in the diagram, which theorem
best justifies why lines e and f must be parallel?
оооо
alternate interior angles theorem
same side interior angles theorem
converse of the alternate interior angles theorem
O converse of the same side interior angles theorem
Answer:
the answer is D
Step-by-step explanation:
edu 2021
ayo
whats 2+2=?????
im so confused bro like frrrrrrr
also whats 9+10
thanks
8) The graphical representation of a linear polynomial is
Curve
Straight line
Parabola
Circle
Answer:
Straight line
Step-by-step explanation:
if for a linear polynomial ax + b, a ≠ 0, the graph of y = ax + b is a straight line which intersects the x-axis at exactly one point, namely, (- b/a, 0). Also, this linear polynomial has only one zero which is the x-coordinate of the point where the graph of y = ax + b intersects the x-axis.
sum1 please help me!!! its for math ughhh iv beeen stuck on this problem for a long time apromenctly an hour-
Answer:
i believe the answer would be 7
Step-by-step explanation:
3 + 20 ÷ 5 = 7
Answer:
5 x (3 + y) = 20
Step-by-step explanation:
The total amount collected is 20, so it goes on the right side of the = sign. There was a total of 5 students and each student had to pay an attendance fee of $3, so you need to multiply 5 by 3 because each student had to pay the fee. The students also need to pay a fee for supplies, but we do not know what that amount is, so we put a variable in its place. We need to put the total amount of money that each student pays together, so we put it in parentheses. We put the 5 outside of the parentheses, which are on the left side of the = sign. When you solve this equation, you would find that the supply cost would have to be $1 each.
Help me on this please
Answer:
i think your right
Step-by-step explanation:
Benson purchased a $1,800 certificate of deposit that earns simple annual interest. At the end of 1 year, the certificate was worth $1,857.60.
What is the annual interest rate on this certificate of deposit?
Answer:
3.2%
Step-by-step explanation:
Here, we want to calculate the annual interest rate
The interest is = Amount - principal = 1857.60 - 1800 = 57.60
‘Mathematically;
Interest = PRT/100
P is 1,800
r is rate
t is time = 1
57.60 = (1800 * r * 1)/100
100 * 57.60 = 1800r
r = 5760/1800
r = 3.2%
What can be concluded about a pair of triangles with some congruent corresponding parts? Select all that apply.
The two triangles are sometimes congruent.
A conclusion cannot be made based on the given information.
The two triangles are always congruent.
The two triangles are never congruent.
Answer:
The two triangles are sometimes congruent.
Step-by-step explanation:
I did it and got it correct
Pls get it right this a test I need the best grade
Answer:
9.6
Step-by-step explanation:
Answer:
the answer is 9.6
Step-by-step explanation:
your welcome
Write the equation of the line passing through points (2,-2) and (1,0) in slope intercept form.
Answer:
y=-2x+2
Step-by-step explanation:
hope it helps!
Answer:
y = -2x + 2
Step-by-step explanation:
find the slope then use the point slope formula to get to y = -2x + 2.
Find the value of x and y.
Answer:
x=13
y=132
Step-by-step explanation:
............
Chris labels every lattice point in the coordinate plane with the square of the distance from the point to the origin (a lattice point is a point such that both of its coordinates are integers). How many times does he label a point with the number $25$?
Answer:
4 times
Step-by-step explanation:
A lattice point may be defined as the point of intersection of two grid lines or more than two grid lines that is placed in a regularly spaced points arrays. This is called a lattice point.
In the context, Chris tries to label every lattice point in a coordinate plane with its square of distance from the point to its origin. The lattice points means that the numbers are both the integers. So for number 25, Chris has to label 4 times
i.e. (55),(-5,5),(5,-5),(-5,-5)
Which statements are correct interpretations of this graph?
Select each correct answer.
6/10 of a page is edited per minute
3 pages are edited every 5 min
1 2/3 of a page is edited per minute
5 pages are edited every 3 min
Answer:
✅6/10 of a page is edited per minute
✅3 pages are edited every 5 min
Step-by-step explanation:
On the graph, there are 3 points given, which are:
(5, 3), which means 3 pages are edited every 5 mins
(10, 6), which means 6 pages are edited every 10 mins.
(15, 9), which means 9 pages are edited every 9 mins.
Pages edited per minute, using the point (10, 6) would be:
y/x = 6/10. This means ⁶/10 of a page is edited per minute
The correct statements that interprets the graph are:
✅6/10 of a page is edited per minute
✅3 pages are edited every 5 min
Answer:
Step-by-step explanation: 6/10 paiges 3 purges
What is the answer to (m^2-7m-11)/(m-8)
Answer:
The final quotient is [tex]\bold{m+1-\frac{3}{m-8}}[/tex].
Step-by-step explanation:
This problem can be solved using two methods: long polynomial division and synthetic division.
Method 1: Long Polynomial Division
We can use long polynomial division to solve the equation. The steps are detailed below the work.
[tex]\displaystyle{\begin{array}{r}\bold{m+1-\frac{3}{m-8}\phantom{)}\\m-8{\overline{\smash{\big)}\,m^2-7m-11\phantom{)}}}\\\underline{-~\phantom{(}m^2-8m\phantom{-b)}}\\m-11\phantom{)}\\\underline{-~\phantom{()}m-8}\\-3\phantom{)}\end{array}}[/tex]
Steps
Set up your division. Place the divisor (the binomial) on the left hand side of the division symbol and the trinomial (or polynomial depending on the amount of terms) on the right hand side of the equation.Divide the divisor by the first term of the trinomial: [tex]\frac{m^2}{m}=m[/tex]Place the result above the first term of the trinomial (above the bar and directly above the first term of the polynomial.Multiply the m by the divisor: [tex]m(m-8) = m^2-8m[/tex]. Subtract this from the original trinomial: [tex](m^2-7m-11)-(m^2-8m)=m - 11[/tex]. Set this below the equation and then divide the leading term of the divisor by the leading term of the remainder: [tex]\frac{m}{m}=1[/tex].Place this to the right of the m located above - in this case, we add because our result is positive.Multiply that by the divisor: [tex]1(m-8)=m-8[/tex].Set this below the remainder from the previous division and subtract: [tex](m-11)-(m-8)=-3[/tex].Finally, divide the original divisor by the remainder: [tex]\frac{-3}{m-8}[/tex]. This divisor needs simplified: [tex]-\frac{3}{m-8}[/tex].Our final new polynomial (once evaluated), is [tex]\bold{m+1-\frac{3}{m-8}}[/tex].Method 2: Synthetic Division
We can also use synthetic division to solve the polynomial.
Table 1 (actual) Table 2 (model)
[tex]\begin{array}{c|ccc}8 & 1 & -7 & -11 \\ & \downarrow & 8 & 8 \\ \cline{2-4} \multicolumn{1}{c}{} & 1 & 1 & -3\end{array}[/tex] [tex]\begin{array}{c|ccc}a & b & c & d \\ & \downarrow & e & f \\ \cline{2-4} \multicolumn{1}{c}{} & g & h & i\end{array}[/tex]
Steps
Determine the coefficients of the polynomial: [tex]m^2-7m-11[/tex]. These are 1, -7, and -11. We need to determine the zero. We do this by setting the divisor equal to zero: [tex]m-8=0\rightarrow m=8[/tex]. Place this value in the upper left hand corner (in place of a).For the first term, we just drop the coefficient below the bar. Therefore, g becomes 1.Multiply a by g to get e : [tex]8 \times 1 = 8[/tex]. Therefore, e becomes 8.Add c to e : [tex]-7 + 8 = 1[/tex]. Therefore, h becomes 1. Multiply a by h to get f : [tex]8 \times 1 = 8[/tex]. Therefore, f becomes 8.Add d to f to get i : [tex]-11 + 8 = -3[/tex]. Therefore, i becomes -3.Our new coefficients are 1, 1, and -3. We lose one power (if the first term is squared, it now does not have an exponent).Use the new coefficients to get our new equation: [tex]m+1-3[/tex].Finally, the last term is the remainder. So, we divide this by the divisor: [tex]m+1-\frac{3}{m-8}[/tex].Our final expression is [tex]\bold{m+1-\frac{3}{m-8}}[/tex].What is the value of y in the solution to the system of equations below?
11x + 12y = 13
14x + 15y = 16
Answer:
(-1,2) is the answer
Which one is bigger -4 or -3
Answer:
the answer is -3 because -3 is closer to 0 than -4
1,900 + 76x. Use the Distributive Property to factor the expression.
PLEASE HELP WITH ANY OF THE QUESTIONS IN THE PICTURE I WILL GIVE 50 POINTS AND BRAINLEIST
Answer:
RU=4.44500 cementers
Step-by-step explanation:
I learned from my bigger sister
Find the solution to the following system of equations:
[2x-y=3
[x-y= -2
A.(-1,-5)
B.(1,3)
C.(4,5)
D.(5,7)
Answer:
the answer is D.(5,7)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
hope this help. :)
find the LCM and HCF of 110 and 220 by prime factorization, what do u observe
Answer:
GCF= 2 x 5 x 11 = 110
LCM= 2 x 2 x 5 x 11 = 220
Step-by-step explanation:
may someone please help me with this ill give brainlyest if i figure out how to
Answer: 5
Step-by-step explanation:
5x3+6=21
5x5=25
25-21=4
Let "the number" = [tex]n[/tex]
[tex]6 + 3n = 5n - 4[/tex]
[tex]6 + 3n - 5n = -4[/tex]
[tex]6 - 2n = -4[/tex]
[tex]-2n = -10[/tex]
[tex]n = 5[/tex]
Check my work:
Six added to 3 times (5) is equal to 4 less than 5 times (5)
Six added to 15 is equal to 4 less than 25
21 is equal to 21
solve the question.
Answer: 1
[tex](\frac{x^{a+b} }{x^{c} }) ^{a-b}.(\frac{x^{b+c} }{x^{a} }) ^{b-c} .(\frac{x^{c+a} }{x^{b} })^{c-a}\\\\= \frac{x^{(a+b)(a-b)} }{x^{c(a-b)} }.\frac{x^{(b+c)(b-c)} }{x^{a(b-c)} }.\frac{x^{(c+a)(c-a)} }{x^{b(c-a)} }\\\\=\frac{x^{a^{2}-b^{2} } }{x^{ac-bc} }.\frac{x^{b^{2}-c^{2} } }{x^{ab-ac} }.\frac{x^{c^{2}-a^{2} } }{x^{bc-ab} } \\\\=\frac{x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2} } }{x^{ac-bc+ab-ac+bc-ab} }\\\\=\frac{x^{0} }{x^{0} }=1[/tex]
Step-by-step explanation:
2. Which of the following states that if the product of two real numbers is zero, then either of the two is
equal to zero or both numbers are equal to zero?
A. Multiplication Property C. Identity Property
B. Zero Product Property
D. Transitive Property
Answer:
b
B zero product property
Answer:
The Zero property
Step-by-step explanation:
anything multiplied by zero will give you a product of zero
please helpppppp :((
Answer:
[tex]4^{21}[/tex]
Step-by-step explanation:
[tex]\frac{4^{12}}{4^{-9}}\\[/tex]
Given 4 = a
From the properties of exponents for the example...
[tex]\frac{a^4}{a^{-2}} = \frac{a*a*a*a}{\frac{1}{a^2} } = (a*a*a*a)*a^2 = a^4 * a^2 = a^{4+2} = a^6[/tex]
Therefore, the answer is....
[tex]4^{12}*4^{9} = 4^{12+9} = 4^{21}[/tex]
Alessia uses her bank card to buy lunch 3 times. Each time she buys lunch, it costs $12.50. She then deposits $30 in her bank account. What is the change in her bank balance in dollars as a result of these transactions?
Answer: She has a $-7.50 balance
Step-by-step explanation: A = 3*12.5
A= 37.5
37.5-30= -7.5
Answer:
Her balance will be $7.50 in the red.
Step-by-step explanation:
expenses: (12.50)*3 = 37.50
funds added: 30
$30 - $37.50 = -$7.50
Mara and alex are running laps around a track. Alex completes a lap every 45 secs and Mara every 36. If they starts at the same time, how long will it be until they cross the start line together? Plz its for homework that is due TOMORROW...
Answer:
180
Step-by-step explanation:
Keep multiplying 45 until you get a number divisible by 36. This is called the least common multiple.
Which of these statements about savings is incorrect? *
1 point
People often believe they are saving when they buy products at a listed
discount, even if they didn't need the product in the first place
It is extremely difficult to open a savings account, as you typically need at
least $10,000 for your initial deposit
Without a vehicle to save (like a savings account), it's much easier to spend
and harder to keep track of finances
Billions of dollars is spent on marketing to persuade consumers to spend
money instead of saving it
dinion in high school and Hust started his
1
Answer:
The answer is "Option b"
Step-by-step explanation:
The numbering of the choices was defined in the attached file please find it.
In the question except for option b, all choices were correct, that can be defined as follows:
Citizens also believe because they save by buying products at a price, even if the product wasn't required first. It's cheaper to take and tough to maintain track of funds without a way to invest (like a bank account). Billions of lives were expended on ads and convince consumers to invest money in the junior high rather than saving their union so Hust started his career.Select the function that defines the given sequence.
Answer:
D.
Step-by-step explanation:
a1 = -8
a2 = -8 * 2.5
a3 = -8 * 2.5 * 2.5
a4 = -8 * 2.5^3
an = -8 * 2.5^(n - 1)
The first term is -8. Each subsequent term is 5/2 times the previous term.
Answer: D.
Can you please explain how I got it wrong and how to get it right (thank you)
Answer:
x = 42°
Step-by-step explanation:
Since (3x+3) and 129 are corresponding angles, we can set them equal to one another and solve for x.
3x + 3 = 129
- 3 - 3
3x = 126
/3 / 3
x = 42°
James and Ahmik went to a bicycle show. Of the bicycles they saw at the show, 32% were blue, 25% were red, 25% were green, and 18% were black. In ratio form, what percent of the bicycles were red or black?
Answer: 43:100
Step-by-step explanation:
Percentage of bicycles that are blue = 32%
Percentage of bicycles that are red = 25%
Percentage of bicycles that are green = 25%
Percentage of bicycles that are black = 18%
Percentage of bicycles that are red or black = 25% + 18% = 43%
Therefore, 43% will be written in ratio form as 43:100
