Answers
Answer:
D
Step-by-step explanation:
The Percentages are as follows
History: 80%
English: 82%
Reading: 84%
Math: 85%
Science: 86%
Related Questions
What is the length of BD
Answers
Answer:
BD = 3 units
Step-by-step explanation:
since AB is a tangent to the circle, then the angle between the tangent and the radius at the point of contact A is 90°
Then Δ ABC is right
using Pythagoras' identity in the right triangle
BC² = AC² + AB² = 4.5² + 6² = 20.25 + 36 = 56.25 ( take square root of both sides )
BC = [tex]\sqrt{56.25}[/tex] = 7.5
now CD is a radius of the circle = 4.5
Then
BD = BC - CD = 7.5 - 4.5 = 3 units
quadratic equations. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 48.
Answers
Substituting y = x + 4 into the second equation, we get:
8(x + 4) + x^2 = 48
Expanding and rearranging, we get:
x^2 + 8x - 16 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 8, and c = -16. Plugging in these values, we get:
x = (-8 ± sqrt(8^2 - 4(1)(-16))) / 2(1)
Simplifying, we get:
x = (-8 ± sqrt(96)) / 2
x = (-8 ± 4sqrt(6)) / 2
x = -4 ± 2sqrt(6)
Since x is a positive real number, we take the positive root:
x = -4 + 2sqrt(6)
Now that we have found x, we can use y = x + 4 to find y:
y = -4 + 2sqrt(6) + 4
y = 2 + 2sqrt(6)
Therefore, the two real numbers are approximately -4 + 2sqrt(6) and 2 + 2sqrt(6).
a parallelogram has a base of 6 centimeters and a height of 10 centimeters. this parallelogram has the same area as a triangle with a height of 5 centimeters. what is the measure, in centi,of the base of the triangle?
Answers
The area of the parallelogram can be found using the formula A = base × height:
A = 6 cm × 10 cm
A = 60 cm²
The area of a triangle is given by the formula A = 1/2 × base × height. We know the height is 5 cm and the area is also 60 cm² (since it is equal to the parallelogram). So, we can solve for the base:
60 cm² = 1/2 × base × 5 cm
Dividing both sides by 1/2 × 5 cm gives:
base = 24 cm
Therefore, the base of the triangle is 24 centimeters.
Answer:
24cm
Step-by-step explanation:
A circular patio has diameter of 4 yards . What is the area of the patio?
Answers
The area of the circular pateo is 50.24 square yards.
What is the area of the patio?Remember that for a circle of radius R, the area is given by the formula:
A = pi*R²
Where pi = 3.14
Here we know that the patio is circular, and it has a diameter of 4 yards, then the radius is:
R = 4yd/2
R = 2 yd
Replacing that in the area formula we will get:
A = 3.14*(2yd)²
A = 50.24 yd²
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HELP ASAP I NEED THIS Use the image to determine the direction and angle of rotation.
90° clockwise rotation
180° clockwise rotation
180° counterclockwise rotation
90° counterclockwise rotation
Answers
Answer:
90 degrees counterclockwise
Please help i will mark brainliest
Use the graph to answer the question.
graph of triangle ABC with vertices at negative 2 comma negative 7, 3 comma negative 2, 2 comma negative 10 and a second triangle A prime, B prime C prime with vertices at 2 comma 7, negative 3 comma 2, negative 2 comma 10
Determine the direction and degree of rotation used to create the image.
90° counterclockwise rotation
270° counterclockwise rotation
90° clockwise rotation
180° clockwise rotation
Answers
Answer:
(d) 180° clockwise rotation
Step-by-step explanation:
Given points A(-2, -7), B(3, -2), C(2, -10) and A'(2, 7), B'(-3, 2), C'(-2, 10), you want to know the angle and direction that rotates ∆ABC to ∆A'B'C'.
SignsWe notice the signs of each of the coordinates of ABC have been reversed for the coordinates A'B'C'. For example, A(-2, -7) became A'(2, 7).
A line joining these points is a straight line through the origin. The measure of its angle at the origin is 180°. This is the angle of rotation of A'B'C' with respect to ABC.
The image is created by 180° clockwise rotation, choice D.
__
Additional comment
When rotation is 180°, the direction is immaterial. A clockwise rotation gets you to the same place as a counterclockwise rotation.
<95141404393>
5. Which graph represents 4x - 2y = 8?
Answers
Answer:
A
Step-by-step explanation:
4x - 2y = 8
x - int y = 0
4x = 8
x = 2
(2, 0)
y-int, x = 0
-2y = 8
y = -4
You save $8,500.00. You place 40% in a savings account earning a 4.2% APR compounded annually and the rest in a stock plan. The stock plan decreases 3% in the first year and increases 7.5% in the second year.
A. What is the total gain at the end of the second year for both accounts combined?
B. If you had invested 60% in the savings account and the rest in the stock plan, what is the difference in the total gain compared to the original plan?
Answers
The total gain at the end of the second year for both accounts combined is $509.09.
We have,
Amount saved = $8500
40% of 8500 is saved in saving account = 0.4 x 8500 = $3400
Remainder amount in stock plan = 8500 - 3400 = 5100
Working for savings plan
A = P(1 + r/n[tex])^{nt[/tex]
A = 3400(1 + 0.042/1)²
A = $3691.60
So, we gain = 3691.6 - 3400 = $291.6
Working for stock plan:
The stock plan decreases 3% in the first year
= 5100 x 0.97
= $4947
and increases 7.5% in the second year.
= 4947 x 1.75
= $5318.03
So, we gain = 5318.03 - 5100 = $218.03
Thus, the total gain is
= 291.06 + 218.03
= $509.09
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Accounting question.help
Answers
The computations of the net profit or loss using the following cost valuation methods are as follows:
FIFO, net profit = $20,000
Weighted Average, net profit = $17,555.54.
What are the inventory cost valuation methods?The inventory cost valuation methods include FIFO (First In, First Out), LIFO (Last In, First Out), WAC (Weighted Average Cost), and Specific Identification.
Under the FIFO basis, the cost of inventory is evaluated based on the assumption that inventory that are first brought in are the first to be sold.
Under the Weighted Average Cost method, the average cost is computed by dividing the total cost of goods available for sale by the number of units.
Other inventory cost valuation methods include LIFO and Specific Identification.
FIFO Basis:Cost of Goods Sold = $80,000 ($10,000 x 3 + $12,000 x 2 + $13,000 x 2)
Sales Revenue = $106,000 ($15,000 x 7)
Overhead = $6,000
Net Profit = $20,000 ($106,000 - $80,000 - $6,000)
Weighted Average Cost Basis:Weighted Average Cost per tractor = $11,777.78 ($106,000 ÷ 9)
Cost of Goods Sold = $82,444.46 ($11,777.78 x 7)
Sales Revenue = $106,000 ($15,000 x 7)
Overhead = $6,000
Net Profit = $17,555.54 ($106,000 - $82,444.46 - $6,000)
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Rachel works at a lemonade stand at the park on Monday. She used 1 2/5 bags of lemons on Tuesday. She used 1 1/4 times as many lemons as on Monday. How many bags of lemons did Rachel use on Tuesday?
Answers
Let's start by finding how many bags of lemons Rachel used on Monday. We know she used a whole number of bags plus a fraction, so we'll need to convert the mixed number to an improper fraction:
1 2/5 = 7/5
So Rachel used 7/5 bags of lemons on Monday.
On Tuesday, Rachel used 1 1/4 times as many lemons as on Monday. To find out how many bags of lemons that is, we can multiply the amount Rachel used on Monday by 1 1/4:
1 1/4 = 5/4
5/4 times 7/5 = 35/20 = 7/4
So Rachel used 7/4 bags of lemons on Tuesday, which is the same as 1 3/4 bags of lemons.
Therefore, Rachel used 1 3/4 bags of lemons on Tuesday.
e desea estimar el gasto promedio mensual en dolares de una familia de cierta ciudad del pais gasta en embutidos.
a) Determine cuantas familias se debe tomar como muestra con una confianza del 95% y un error de 2 dolares . Un especialista a estimado una desviacion estandar de 9 dolares.
b) Haga el calculo para una nueva urbanizacion con 850 familias con un 99% de confianza y un error de 1.5 dolares considerando la desviacion estandar con un valor de 9 dolares.
Answers
Answer:
a) Utilizando la fórmula para el tamaño de muestra, tenemos:
n = (Z * σ / E)^2
donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 95% (Z = 1.96), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 2).
Sustituyendo los valores, obtenemos:
n = (1.96 * 9 / 2)^2 ≈ 77
Por lo tanto, se debe tomar una muestra de al menos 77 familias.
b) De manera similar, tenemos:
n = (Z * σ / E)^2
donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 99% (Z = 2.58), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 1.5).
Sustituyendo los valores, obtenemos:
n = (2.58 * 9 / 1.5)^2 ≈ 261
Por lo tanto, se debe tomar una muestra de al menos 261 familias.
Step-by-step explanation:
125-foot redwood tree is leaning 20° off vertical. How long will its shadow be when the angle the sunlight makes with the ground is 68°?
Answers
Answer:
To solve this problem, we can use trigonometry. Let's call the length of the shadow "s" and the height of the tree "h". Since the tree is leaning, we can't just use the height of the tree directly as one leg of a right triangle. Instead, let's draw a diagram of the situation and see if we can find a way to use trigonometry.
|\
| \
| \ h
|20\
| \
| \
________|____\
s
In this diagram, the angle between the ground and the sunlight is 68 degrees, and the angle between the tree and the ground is 70 degrees (since the tree is leaning 20 degrees off vertical). We can use the tangent function to relate these angles to the lengths of the sides of the triangle:
tan(68) = h / s
tan(70) = h / (s + 125)
We can solve for "h" in terms of "s" using the second equation:
h = (s + 125) * tan(70)
Then we can substitute this expression for "h" into the first equation and solve for "s":
tan(68) = [(s + 125) * tan(70)] / s
s * tan(68) = (s + 125) * tan(70)
s * tan(68) = s * tan(70) + 125 * tan(70)
s = 125 * tan(70) / [tan(68) - tan(70)]
s ≈ 318.8 ft
Therefore , the shadow will be approximately 318.8 feet long.
Step-by-step explanation:
$18,389
is invested, part at 10%
and the rest at 8%
. If the interest earned from the amount invested at 10%
exceeds the interest earned from the amount invested at 8%
by $621.02
, how much is invested at each rate? (Round to two decimal places if necessary.)
Answers
x + y = 18389 (equation 1)
0.10x - 0.08y = 621.02 (equation 2)
From equation 1, we can solve for y:
y = 18389 - x
Substituting this into equation 2, we get:
0.10x - 0.08(18389 - x) = 621.02
0.10x - 1471.12 + 0.08x = 621.02
0.18x = 2092.14
x = 11623
Substituting this back into equation 1, we get:
11623 + y = 18389
y = 6766
Therefore, $11623 is invested at 10% and $6766 is invested at 8%.
Approximate e^-0.11 to 4 decimal places
Answers
Answer: 0.8958
Step-by-step explanation:
rancher wants to enclose a rectangular plot of land, but have a divider in the middle. There is 240 feet of fencing available. What dimension will produce the largest area the rancher can make? What is the max area? Dimensions: __________________ Area:___________ --------------------------------------------------------------------------------------------------------- 2. (10 points) From a thin square piece of cardboard 20 in. per side, square corners (x) are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Dimensions: __________________ Volume:___________ ----------------------------------------------------------------------------------------------------------- 3. (10 points) During a recent oil spill in the gulf, the radius of the spill was increasing at a rate of 10 feet per second. How fast is the circular area of the spill increasing at the moment that the radius is 80 feet? dA = dt __________
Answers
The solution is the two dimensions will be 2121.32 by 1414.2.
Here, we have,
let X and Y be the two dimensions.
Area will be X times Y.
XY = 3000000
Y = 3000000 / X
Perimeter = 2x + 3y
substituting the values:
Perimeter = 2x + 3*3000000 / x
= 2x + 9000000 / x
so, we get,
2 = 9000000 / x^2
x^2 = 9000000 / 2 = 4500000
x = sqrt(4,500,000)
= 2121.32
= 1000 sqrt (4.5)
y = 3000000 / 2121.32
= 1414.2
= 1000 sqrt(2)
so the dimensions will be 2121.32 by 1414.2 .
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complete question:
A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
log3 55=x
Use the base of formula to solve for x in logaritm experssion
Answers
The change of base formula log 55 / log 3. The base we use to solve via change of base formula is Base 10. The value of x = 55.
The logarithmic expression given is
log₃ 55 = x
To solve for x using the change of base formula, we can use the formula
logₐ b = log c / log a
where a, b, and c are positive real numbers and a ≠ 1.
Using this formula, we can rewrite the given expression as
log x / log 3 = log 55 / log 3
We can simplify this expression by canceling out log 3 on both sides
log x = log 55
Now, we can use the definition of logarithms, which states that if log a b = c, then [tex]a^c[/tex] = b. Using this definition, we get
x = 55
Therefore, the solution is x = 55, rounded to the nearest hundredth of a decimal.
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Can you round off 20.900156 to 1 decimal place?
Answers
Answer:
Step-by-step explanation:
20.9 is solution
you have negioated a vehcile purchase rice of $37,000, will make a $7,000 down payment and finance the remainder. The terms of the loan are: monthly payments, 6.00 percent annual rate of interest, and you will finance the loan for six years.
a. calculate the amount of your monthly payments
b. at the end of the six-year loan term, what is the total amount of interest you will have paid the lenders?
Answers
a. To calculate the amount of your monthly payments, you can use the following formula:
P = (A / N) + (r * (A - ((A * (m - 1)) / N)))
Where:
P = monthly payment
A = total amount financed (purchase price - down payment)
N = total number of payments (6 years * 12 months = 72)
r = monthly interest rate (6% / 12 = 0.005)
m = the month of the payment (ranging from 1 to 72)
Plugging in the values, we get:
P = (30000 / 72) + (0.005 * (30000 - ((30000 * (1 - 1)) / 72)))
P = $483.23
So your monthly payment would be $483.23.
b. To calculate the total amount of interest paid over the six-year loan term, you can use the following formula:
Total Interest = (P * N) - A
Where:
P = monthly payment (from part a)
N = total number of payments (72)
A = total amount financed (30000)
Plugging in the values, we get:
Total Interest = (483.23 * 72) - 30000
Total Interest = $8,869.56
So the total amount of interest you will have paid the lenders over the six-year loan term is $8,869.56.
An insurance company offers an ordinary annuity that earns 6.5% interest compounded annually. A couple plans to make equal annual deposits into this account for 30 years and then make 20 equal annual withdrawals of €25,000, reducing the balance of the account to zero.
(i) Compute the value of the fund based on the withdrawals required. [5 marks]
(ii) Compute the amount of each deposit needed in order to maintain the fund. [5 marks]
(iii) Compute the total interest earned over the entire 50 years. [5 marks]
Answers
Answer:
(i) To compute the value of the fund based on the withdrawals required, we can use the formula for the future value of an annuity due:
FV = P * ((1 + r)^n - 1) / r) * (1 + r)
where FV is the future value of the annuity, P is the annual payment, r is the interest rate per period, n is the total number of periods, and the extra (1 + r) factor is because the payments are made at the beginning of each period.
In this case, P = €25,000, r = 0.065, n = 20. We want to find the future value at the end of the 20-year period:
FV = 25000 * ((1 + 0.065)^20 - 1) / 0.065) * (1 + 0.065)
FV ≈ €743,704.96
Therefore, the value of the fund based on the withdrawals required is approximately €743,704.96.
(ii) To compute the amount of each deposit needed in order to maintain the fund, we can use the formula for the present value of an ordinary annuity:
PV = P * ((1 - (1 + r)^(-n)) / r)
where PV is the present value of the annuity, P is the annual payment, r is the interest rate per period, and n is the total number of periods.
In this case, PV = €743,704.96, r = 0.065, n = 20. We want to find the annual payment:
PV = P * ((1 - (1 + 0.065)^(-20)) / 0.065)
P ≈ €22,630.53
Therefore, the amount of each deposit needed in order to maintain the fund is approximately €22,630.53.
(iii) To compute the total interest earned over the entire 50 years, we can subtract the total deposits from the total withdrawals, and then subtract the initial balance. The total deposits are the annual deposit amount times the number of years (30), and the total withdrawals are the annual withdrawal amount times the number of years (20). The initial balance is the present value of the annuity that we calculated in part (ii).
Total deposits = €22,630.53 * 30 = €678,915.90
Total withdrawals = €25,000 * 20 = €500,000
Initial balance = €743,704.96
Total interest earned = Total withdrawals - Total deposits - Initial balance
Total interest earned = €500,000 - €678,915.90 - €743,704.96
Total interest earned ≈ -€922,620.86
Note that the negative sign indicates that the insurance company actually earned interest on this annuity, rather than the couple earning interest on their investment. This is because the withdrawals are greater than the deposits, and the interest rate earned by the insurance company is greater than the interest rate paid to the couple.
Step-by-step explanation:
What is 2 plus 2 please tell me
Answers
Answer:
Step-by-step explanation: The answer is 4 all u do is add 2 to 2
Answer: 2+2=4
Step-by-step explanation: The sum of two and two results in a value of four in a quantitative analysis.
2y+3y-18=-83?????????????
Answers
Answer:
-13
Step-by-step explanation:
(Please help in image)
Answers
Answer:
[tex] {x}^{2} + 11x + 18 = [/tex]
[tex](x + 2)(x + 9)[/tex]
The two numbers are 2 and 9.
2 + 9 = 11, and 2 × 9 = 18.
Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
<[tex]\sqrt{74}[/tex]
Answers
The inequality is -8 < √74 < 9. A mathematical expression that's values on the left and right are not equal is referred to as having an inequality.
A mathematical expression that's values on the left and right are not equal is referred to as having an inequality. In essence, an inequality analyses any two values that demonstrates whether one is bigger than, less than, or neither greater nor equal to the other quantity. Numbers are compared using inequalities to determine a range of quantities that are contained inside the parameters of a variable.
Let A = √74
A² = 74
8² < A² < 9²
Hence, the inequality is -
8 < √74 < 9
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How many lines are shown in the drawing
Answers
The given images shows us that we have a total of two lines
How to identify the lines?In mathematics, a point is referred to as the particular location on a plane. A point is identified by a dot. It has no length, shape or size.
A line is straight, without any type of thickness and it is the shortest distance that exists between 2 points. It has only length. It is without width.
A line segment has two end points. The difference that a line segment has with a line is that a line is extensive while the line segment has two end points.
Ray is defined as a line that has only one endpoint. The other end of the line just goes on. It has one start point and one end point.
From the attached image, it is vert clear that we have two lines which are the horizontal line and the line that divides it.
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PLEASE HELP ( WILL GIVE BRAINLIEST)
Answers
Answer: Option C.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Given that the diameter of the container is 24 ft, the radius (r) would be half of that, which is 12 ft.
The depth of the container (h) is given as 4 ft.
Plugging in these values into the formula, we get:
V = π(12^2)(4)
V = 3.14(144)(4)
V = 1808.6 cubic feet (rounded to the nearest tenth)
So, the storage container can hold approximately 1808.6 cubic feet of wood, rounded to the nearest tenth.
Step-by-step explanation:
Alice finds shirts on sale for $18.99.She buys twelve how much money does she spend?
Answers
Answer:
Well, if Alice buys 12 shirts which each cost $18.99 the equation would be 18.99 * 12 which = 227.88
Alice spent $227.88 on 12 shirts
Step-by-step explanation:
Answer:
Well, if Alice buys 12 shirts which each cost $18.99 the equation would be 18.99 * 12 which = 227.88
Step-by-step explanation:
(ILL GIVE YOU 100 POINTS!!)
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8
Step 2: 6x − 8 = 16 + 2x
Step 3: 6x − 2x = 16 + 8
Step 4: 4x = 24
Step 5: x = 6
In which step did the student first make an error and what is the correct step?
a Step 2; 8x − 4 = 2(6 + x + 6)
b Step 2; 8x − 16 = 16 + 2x
c Step 3; 6x − 2x = 16 − 8
d Step 3; 6x + 2x = 16 + 8
Answers
Answer:
step 2 is wrong
Step-by-step explanation:
4 multiply by 2x = 8x4 multiply by -4 = -16CORRECT STEP4(2x - 4) = 8 + 2x + 88x - 16 = 8 + 2x + 88x - 16 = 2x + 16 6x = 32x = 32/6 = 5 ( approximately )Here, The work of a student to solve the equation :
[tex]4(2x - 4) = 8 + 2x + 8[/tex]
The steps for calculating the value of x are :
Step 1: [tex]4(2x - 4) = 8 + 2x + 8[/tex]
Step 2: [tex]6x - 8 = 16 + 2x[/tex]
Step 3: [tex]6x - 2x = 16 + 8[/tex]
Step 4: [tex]4x = 24[/tex]
Step 5: [tex]x = 6[/tex]
Step 2 is incorrect, as the student instead of multiplying, adds the number as:
[tex]4(2x - 4) = 8 + 2x + 8[/tex]
Here, the correct step is:
[tex]\boxed{\bold{8x - 16 = 16 + 2x}}[/tex]
[tex]6 x = 32[/tex]
[tex]x = 5.33[/tex]
So, the error is in STEP 2 and the correct option is (B).
Write the quadratic equation in standard form:-4x – 19 = x
Answers
Answer: x^2 + 0x + 19/5 = 0
Step-by-step explanation: The initial step involves the equation -4x - 19 = x, which can be simplified by performing the operation of subtracting x from both sides.
The given equation can be represented as -5x - 19 = 0 in standard algebraic form, where 'x' denotes the unknown variable.
The process of combining similar or like terms leads to the consolidation of terms that share the same variable and corresponding exponents.
The given expression, 5x - 19 = 0, can be rewritten in an academic manner as a linear equation. Specifically, this expression represents a linear equation in one variable, where x is the unknown. The equation can be solved to find the value of x that satisfies it. This can be done through various methods, such as isolation of x, substitution, or using algebraic properties. The solution of this equation is x = 19/5, which can be verified by plugging it back into the original equation and observing its validity.
In order to render this equation in a standard format, it is imperative to eliminate the fixed element present on the left-hand side. The aforementioned task can be accomplished by simultaneously augmenting 19 to each side of the equation.
The equation 5x = 19 can be expressed in an academic manner as a linear equation with one variable. Specifically, it states that there is a value, x, that when multiplied by the constant factor of 5, results in a final product of 19. This equation could be used as a starting point for further mathematical analysis or application, such as solving for the specific value of x or incorporating it into a larger system of equations.
The left-hand side of the expression contains the linear term and the constant term, while the right-hand side is equal to 0. In order to express this equation in a standardized form, it is necessary to perform division by a factor of negative five to isolate the variable x.
The numerical value of the variable x is equivalent to negative nineteen divided by five, expressed as x = -19/5.
The standard form of the quadratic equation can be expressed as follows:
The mathematical expression, x + 19/5 = 0, may be restated in a formal academic style as follows: "The equation is of the form x + 19/5 = 0."
In order to determine the coefficients of the squared and constant terms, it can be observed that the coefficient of the squared term equates to 1 by virtue of the squared exponent of x, while the constant term evaluates to 19/5. This analytical approach yields the appropriate identification of the relevant coefficients in the given equation. Henceforth, the standard format for the quadratic equation is expressed as follows:
The equation in question is x^2 + 0x + 19/5 = 0.
Use a half-angle identity to find the exact value of tan5π/12
Answers
The required exact value of tan(5π/12) is (2 + √3) / 3.
We can use the half-angle identity for a tangent:
tan(x/2) = [1 - cos(x)] / sin(x)
to find the exact value of tan(5π/12), since 5π/12 is a half-angle of 5π/6.
First, we find the values of sin(5π/6) and cos(5π/6) using the unit circle:
sin(5π/6) = sin(π - π/6) = sin(π/6) = 1/2
cos(5π/6) = cos(π - π/6) = -cos(π/6) = -√3/2
Now we can use the half-angle identity for a tangent with x=5π/6:
tan(5π/12) = tan[(5π/6)/2] = [1 - cos(5π/6)] / sin(5π/6)
= [1 - (-√3/2)] / (1/2)
= (2 + √3) / 3
Therefore, the exact value of tan(5π/12) is (2 + √3) / 3.
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help please
(instructions: chose from the word bank below to describe the type of multiplication being used. you may use an answer more than once.)
[ identity commutative associative inverse distributive]
1. 14 x 6 = 6 x 14 ________
2. 4(5 + 7) = (4 x 5) + (4 x 7) ________
3. 8 x 1 = 8 ________
4. 7 x (6 x 2) = (7 x 6) x 2 ________
5. 12 x 3 = 3 x 12 ________
6. 1/8 x 8/1 = 1 ________
7. 1 x 9 = 9 ________
8. 3 x (7 x 2) = (3 x 7) x 2 ________
9. 2(8 + 5) = (2 x 8 ) + (2 x 5) ________
(page 2)
(instructions: choose the correct multiplication property for the problems below)
10. which property is demonstrated below?
12 x 1 = 12
A. identity
B. commutative
C. associative
D. inverse
E. distributive
11. which property is demonstrated below?
2/5 x 5/2 = 1
A. identity
B. commutative
C. associative
D. inverse
E. distributive
12. which property is demonstrated below
5 x 8 = 8 x 5
A. identity
B. commutative
C. associative
D. inverse
E. distributive
13. which property is demonstrated below?
8 x (7 x 9) = (8 x 7) x 9
A. identity
B. commutative
C. associative
D. inverse
E. distributive
14.which property is demonstrated below?
4(6 + 3) = (4 x 6) + (4 x 3)
A. identity
B. commutative
C. associative
D. inverse
E. distributive
Answers
The blanks are filled as follows
1. Commutative
2. Distributive
3. Identity
4. Associative
5. Commutative
6. Inverse
7. Identity
8. Associative
9. Distributive
10. A. Identity
11. A. Identity
12. B. Commutative
13. C. Associative
14. E. Distributive
What is distributive law of multiplication?The distributive law of multiplication is a distinct attribute in mathematics that distinguishes how multiplication interacts with the operations of addition or subtraction.
It is exemplified in the problem as
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