sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)
How to rewrite the expression?The sine expression is given as
sin^4x
The above means
sin x raised to the power of 4
This in other words, the expression is represented as
(sin(x))^4
Express 4 as 2 + 2
(sin(x))^(2 + 2)
Apply the law of indices
(sin(x))^2 * (sin(x))^2
This gives
sin^2(x) * sin^2(x)
Hence, sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)
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(4x + 5) - (2x - 3)
Answer:
2x + 8
Step-by-step explanation:
(4x + 5) - (2x - 3)
4x + 5 - 2x + 3
2x + 8
Answer: 2x+8
Step-by-step explanation:
4x+5-2x+3
=2x+8
do the quantities combine?
Answer:
D
Step-by-step explanation:
Widrawal is - 30
Deposit is +30
-30+30 = 0
Which expression can be used to find the sum of the polynomials?
(9 - 3x2) + (-8x2 + 4x + 5)
The expression which can be used to determine the algebraic sum of the given polynomials as in the task content is; -11x² +4x +14.
Which expression can be used to find the sum of the given polynomials?It follows from the task content that the polynomials whose sum are to be determined are; (9 - 3x2) + (-8x2 + 4x + 5).
Hence, the sum can be evaluated as follows;
= 9 - 3x² + -8x² + 4x + 5
= -11x² +4x +14.
Consequently, the required expression is; -11x² +4x +14.
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Answer:
Step-by-step explanation:
is 100 for the points
Barbara runs once around the track in 3 minutes 45 seconds. Liad runs around the track in 2
minutes 30 seconds. At these rates, after 10 minutes of running, the distance Barbara has run is
what fractional part of Liad's?
Answer:
2/3rds of liad's run
Step-by-step explanation:
3 min 45s = 3 3/4 min = 15/4 min; 10/(15/4) = 8/3 laps
2min 30s = 2 1/2 min = 5/2 min; 10/(5/2) = 4 laps
(8/3)/4 = 2/3
How many values are in the range?
0 to 50
Given the property:
a = am-n, for a 0
am
an
Explain the three cases for:
a. 0
b. 0
c.m=n
Could you try reposting the question clearly
PLEASE HELP ASAP PLEASE PLEASE
Answer:
transitive property
Step-by-step explanation:
This is the answer by definition.
The substitution property is demonstrated in the case of m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so, m∠AZF=m∠SZW+m∠LZF.
In order to find the value of the unknown, the substitution property is a concept in algebra that is used to substitute the value of a given variable or quantity into an expression.
According to the substitution property of equality, "If two variables x and y are equal, then x can be substituted for y in any equation or expression, and y can be substituted for x in any equation or expression."
According to the question, m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so by the substitution property, on substituting the value of m∠AZL+m∠LZF in the first expression, we get, m∠AZF=m∠SZW+m∠LZF.
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The percentage of each transaction contributed to the total transactions in the same Account. Use BASE_EQUIV_AMT as the unit.
The percentage that each transaction contributed to the total transactions in the same account (Cash Account and Service Revenue) is computed as follows:
Cash Account:1. Service Revenue $900 = 8%
2. Owner's Equity, Barbara Hanson $2,200 = 19.8%
3. Accounts Receivable $750 = 6.8%
5. Note Payable $6,000 = 54.1%
6. Unearned Revenue $1,250 = 11.3%
Total cash receipts = $11,100
Service Revenue:1. Cash $900 = 70.6%
4. Accounts Receivable $375 = 29.4%
Total $1,275
How is the percentage computed?The percentage that each transaction contributed to the total transactions in the same account can be computed by taking the dollar value of the transaction over the total value of transactions in the same account and then multiplying by 100.
Percentage values show the degrees of relationship among variables.
The formula for computing percentage in this scenario is transaction value/total transactions value × 100%.
Transaction Analysis:1. Cash $900 Service Revenue $900
2. Cash $2,200 Owner's Equity, Barbara Hanson $2,200
3. Cash $750 Accounts Receivable $750
4. Accounts Receivable $375 Service Revenue $375
5. Cash $6,000 Note Payable $6,000
6. Cash $1,250 Unearned Revenue $1,250
Question Completion:The following transactions occurred during July:
1. Received $900 cash for services provided to a customer during July.
2. Received $2,200 cash investment from Barbara Hanson, the owner of the business.
3. Received $750 from a customer in partial payment of his account receivable, which arose from sales in June.
4. Provided services to a customer on credit, $375.
5. Borrowed $6,000 from the bank by signing a promissory note.
6. Received $1,250 cash from a customer for services to be rendered next year.
Use the transactions to compute the percentage of each transaction relative to the total transactions in the same account.
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Suppose the length and width of the box double. Does the surface area S double? Complete the explanation.
Help!
Solve for x
(please write work)
Answer:
x = -9
Step-by-step explanation:
12 + 2x + 24 = 27 + x
(12 + 24) + 2x = 27 + x
36 + 2x = 27 + x
subtract 27 from both sides
36-27 + 2x = 27-27 + x
9 + 2x = x
subtract x from both sides
9 + x = 0
subtract 9 from both sides
x = -9
(the steps could've been faster but that shows the most work)
check:
12 + 2(-9) + 24 = 27 + (-9)
36 - 18 = 18
18 = 18
True!
so -9 is correct
Answer:
Step-by-step explanation:
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
A freighter has to go around an oil spill in the Pacific Ocean. The captain sails due east for 30 miles. Then he turns the ship and heads due north for 14 miles. What is the distance and direction of the ship from its original point of course correction? Round each number to the nearest whole number.
The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.
Let x represent the distance travelled, hence:
x² = 14² + 30²
x = 33 miles
tanФ = 14/33
Ф = 23°
The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.
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3. What is the measure of angle B from the right triangle below?
Answer:
angle B = 78.46°
Step-by-step explanation:
Use the cosine ratio
[tex]cosB=\frac{2}{10} =0.2[/tex]
[tex]B=cos^{-1} (0.2)=78.46^{0}[/tex]
Hope this helps
Determine the relationship between the angle θ of a circular sector of a circumference of radius 10 cm and the area Aθ of the sector; and calculate the area for an angle of π/4
The area is:
A = (θ/2)*R^2
The circumference is:
C = θ*R
And the area of the circle when the angle is π/4 is: 39.25 cm^2
How to find the area in terms of the angle?
For a circle of radius R, the area is:
A = pi*R^2
where pi = 3.14
And the circumference is:
C = 2*pi*R
Now, remember that a circle has an angle of 2pi radians, then if we only define an arc in the circle, defined by an angle θ, the area of said arc will be:
A = (θ/2pi)*pi*R^2 = (θ/2)*R^2
And the circumference is:
C = (θ/2pi)*2pi*R = θ*R
Now, we want to find the area when the circle has a radius R = 10cm and θ = pi/4
Replacing that in the area equation, we get:
A = (pi/4/2)*(10cm)^2 = (3.14/8)*(10cm)^2 = 39.25 cm^2
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jelissa determined she needs to have 800000 for retirement in 30 years. her account earns 6% interest
a. how much would she need to deposit in the account each month
b. how much total money will she put into the account.
c. how much total interest will she earn
The monthly payment is $796.40.
The total amount she would deposit is $286,705.51
The total interest earned is $513,294.49
What is the monthly payment, total amount deposited and interest?The payments made by Jessica are known as deferred annuities. Deferred annuities are when a series of payments are made in exchange for an amount of money in the future.
The formula that can be used to determine the amount of monthly deposit is: future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 6%/12 = 0.5%
n = number of years = 30 x 12 = 360
Annuity factor = ](1.005^360) - 1] / 0.005 = 1004.515
Monthly payments = 800,000 / 1004.515 = $796.40
Total amount she would deposit = monthly payment x number of years x number of months in a year
$796.40 x 30 x 12 = 286,705.51
Total interest earned = value of the retirement account - total amount deposited
800,000 - 286,705.51 = 513,294.49
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need heeeelp please
Answer:
7.61577310586
Step-by-step explanation:
Pythagoras Theorem 7 squared + 3 squared= 49+9=58
[tex]\sqrt{58}[/tex]
What is 500$ invested at 8% for 6 and a half years?
Answer:
$824.56
Step-by-step explanation:
Use the compound interest formula which is A = P(1+r/n)^nt
1st using the given information we are going to find out values:
P is our initial amount of $500
r is the annual rate of interest (expressed as a decimal) 8% becomes 0.08.
n is how many times interest is compounded per year, in this case since its not stated we are going to assume its annually, so n is 1
t is how long the money is deposited (in years) so t is 6.5
A is our final amount
2nd plug in our values into the equation
Plugging all these values we get A = 500 (1 +0.08/1)^(0.08)(6.5)
A = $824.56
can someone give the exact answer for all the blanks
Considering the given function, we have that:
f(a) = 4 - 2a + 6a²f(a + h) = 6a² + 12ah + 6h² - 2a - 2h + 4.[f(a + h) - f(a)]/h = 12a + 6h - 2.What is the function for this problem?The function is:
f(x) = 4 - 2x + 6x².
When x = a, we have that:
f(a) = 4 - 2a + 6a².
When x = a + h, we have that:
f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.
For the fraction, we have that:
[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h
Hence:
[f(a + h) - f(a)]/h = 12a + 6h - 2.
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Madison finished 4/5 of her homework before dinner. What percent of Maddison’s homework is left to finish?
Answer:
1/5 of it
Step-by-step explanation:
5/5 represents all of her homework
5/5-4/5= 1/5
4/5 represents the homework she did before dinner
1/5 represents the homework left to do
Karin has 13 coins (2 quarters, 6 dimes, 4 nickels, and 1 penny) in a piggy bank. She turns the bank
upside down and shakes the bank until a coin falls out, puts it aside, and the shakes until another coin
falls out.
What is the probability that the first coin is a nickel and the second coin is a quarter?
Select one:
OOO O
2 63 23
39
01/3
118
Using it's concept, the probability that the first coin is a nickel and the second coin is a quarter is: 2/39.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Hence:
For the first coin, out of 13 coins, 4 are nickels, hence the probability is 4/13.For the second coin, considering that a nickel was taken first, 2 out of 12 coins will be quarters, hence the probability is 2/12 = 1/6.Then the probability for both coins is:
p = 4/13 x 1/6 = 4/78 = 2/39
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need answers right now
tysm
If the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1) then the area of the rhombus is 16 square units.
Given the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1).
We are required to find the area of the rhombus when the fourth point Z is plotted.
We have to plot the points of the rhombus in the graph. We know that all the sides of the rhombus should be equal to each other. So by adjusting the blocks in the graph we will be able to plot Z as (-2,3).
In this way the diagonals are ZX and WY.
ZX=[tex]\sqrt{(3-3)^{2} +(6+2)^{2} }[/tex]
=[tex]\sqrt{64}[/tex]
=8 units
WY=[tex]\sqrt{(1-5)^{2} +(2-2)^{2} }[/tex]
=[tex]\sqrt{16}[/tex]
=4 units
Area of rhombus=1/2 *([tex]d_{1} *d_{2}[/tex])
=1/2* (8*4)
=8*2
=16 Square units.
Hence if the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1) then the area of the rhombus is 16 square units.
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A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 3 hours there will be 780 bacteria.
(a) Express the population after t hours as a function of t.
population: ? (function of t)
(b) What will be the population after 3 hours?
(c) How long will it take for the population to reach 1870 ?
The solutions to the exponential growth problem are:
A. [tex]P(t) = 260e^0.3662t[/tex]
B.[tex]P(3) = 260e^0.3662(3) = 779[/tex]
C.3.367 hours
What is the formular for the exponential growth problem?The exponential growth problem obeys the equation:
P(t) = P0ekt
P0=population
time t
We can find the value of k At t=3 hours as,
780 = 260e^k(3)
k = (1/3) ln(780/260) hours-1 ≅ 0.3662 hours-1
A. [tex]P(t) = 260e^0.3662t[/tex]
B. [tex]P(3) = 260e^0.3662(3) = 779[/tex]
C. 1870 = 260e^0.3662t
To Solve for t, w2e make t the subject of the formula
t = ln(1870/260) / 0.3662 hours = 3.367 hours
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Maria had a seven square-foot piece of construction paper. She used four square feet of the paper to make a large greeting card for a friend. Which operation would help to find the amount of paper she could use for another card? O division O addition subtraction multiplication
Answer:
subtraction
Step-by-step explanation:
If she had 7 sqft and used up 4 sqft, she no longer has that 4 sqft. It's used up, gone, taken away. We remove it from her total. That is "take away" this means subtraction.
7 - 4
= 3 she has 3sqft of construction paper left.
2/120=X/80=Y/300
x=? & y=?
X=1.33
Y=4.9875;approx. 5.0
Answer:
(2/120=X/80)=Y/300
2×80=120×X
X=160/120
X=1.33
X/80=Y/300
But X=1.33
By substituting
X=1.33, We have that
1.33/80=Y/300
80×Y=1.33×300
80Y=399
Y=399/80
Y=399/80
Y=5.0 approx.
PLEASE HELP ASAP!!! ALSO PLEASE ADD A DESEND EXPLANATION!! Find the original price if the price was: $8a after 60% increase.
Answer: $3.2a
Step-by-step explanation: We need to decrease $8a by 60 percent because $8a is the price after a 60% increase. 8 x 6/10 is 48/10 which as a mixed number is 4 8/10 or 4.8. Now, we subtract 4.8 from 8 which yields our answer of 3.2.
Is -2.3456 an irrational number
Answer:
No.
Step-by-step explanation:
Negative decimal numbers are rational numbers since rational numbers include all the integers both positive and negative integers, decimal as well as a fraction because decimals can be written as fractions.
Find the value of x.
Answer:
x = 52
Step-by-step explanation:
Since the inscribed angle measures 64 degrees, the minor arc is 64*2 = 128 degrees. Therefore the major arc is 180-128 = 232 degrees. Angle X is the difference of major and minor arc divided by 2, so X = (232-128)/2 = 52 degrees.
PLEASE help with question ASAP ASAP
Answer:
No classification is guaranteed.
HELP ASAP WITH EXPLANATION: If f(x) + f(2 − x) = 4 for all x, find f(y − 2) + f(4 − y)
Answer:
f(y-2)+f(4-y)=4
Step-by-step explanation:
Assume (let) x=y-2
So: y=x+2
f(y-2)+f(4-y)=f(x)+f(-x+2)=f(x)+f(2-x)
The value of that expression is 4 from the given.
Use the method of equating coefficients to find the values of a, b, and c: (x+4)(ax2+bx+c)=−2x3−7x2+3x−4.
The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Given the polynomial:
-2x³ - 7x² + 3x - 4
Simplifying:
= -(2x² - x + 1)(x + 4)
Hence:
-2x³ - 7x² + 3x - 4 = (-2x² + x - 1)(x + 4)
(x + 4)(ax² + bx + c) = −2x³ − 7x² + 3x − 4
The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.
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ASAP help me with this PLEASE
Answer:
98 degrees
Step-by-step explanation:
In a quadrilateral, we have 4 angles whose sum is 360 degrees which can be derived using the Exterior Angle Sum Theorem which essentially states that any convex polynomial will have a sum of 360 degrees for it's exterior angles.
Since we know that two of the angles are equal, we can just represent angle A and D as "x", and since they're congruent, and there is two of them, the sum can be represented as "2x"
So using all the known values we can set up the following equation:
[tex]2x+64+100=360[/tex]
Simplify on the left side
[tex]2x+164=360[/tex]
Subtract 164 from both sides
[tex]2x=196[/tex]
Divide both sides by 2
[tex]x=98[/tex]
Since we know that "x" represents both angle A and B, then the angle A is 98 degrees.