Answer:
a³(b-c) + b³(c-a) + c³(a-b) = (a-b)(b-c)(c-a) (a + b + c)(a² + b² + c² - ab - bc - ca)
This is a factorized form of the polynomial, as you can see it factorizes as a combination of difference of squares and difference of cubes.
here is one way to factorize the polynomial a³(b-c) + b³(c-a) + c³(a-b) step by step:
First, we can factor out a³ from the first term, b³ from the second term, and c³ from the third term:
a³(b-c) + b³(c-a) + c³(a-b) = a³(b-c) + b³(c-a) + c³(a-b)
Next, we can factor out (b-c) from the first and second terms, and (c-a) from the second and third terms:
a³(b-c) + b³(c-a) + c³(a-b) = (b-c)(a³ + b³) + (c-a)(b³ + c³)
We can factor out (a-b) from the first and third terms, and then we can use difference of cubes to factorise out:
(b-c)(a³ + b³) + (c-a)(b³ + c³) = (b-c)(a-b)(a² + ab + b²) + (c-a)(a-b)(b² + ab + c²)
Now we can combine like terms, and we get:
(b-c)(a-b)(a² + ab + b²) + (c-a)(a-b)(b² + ab + c²) = (a-b)(b-c)(c-a)(a + b + c)(a² + b² + c² - ab - bc - ca)
The factorized form of the polynomial is (a-b)(b-c)(c-a) (a + b + c)(a² + b² + c² - ab - bc - ca)
This is a general formula for the factorization of a polynomial of the form a³(b-c) + b³(c-a) + c³(a-b)
By using difference of cubes we can factorise the above polynomial, hope it helps.
Match a system of equations to each description.
System with one solution: (-1, 3)
System with no solutions
System with infinite number of solutions
2x + 2y = -8 and 3x + 3y = - 12
- 3x + 3y = 12 and 5x + 5y = 10
y +4 =-x and y = -x + 2
Answer:
Image result for System with one solution 1 3 System with no solutions System with infinite number of solutions 2x 2y 8 and 3x 3y 12 3x 3y 12 and 5x 5y 10 y 4 x and y x 2
You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.
Step-by-step explanation:
Answer:
1) 2x + 2y = -8 and 3x + 3y = - 12: Infinite: the lines are the same.
2) - 3x + 3y = 12 and 5x + 5y = 10: One solution (-3.10)
3) y +4 =-x and y = -x + 2: No solutions. Parallel
Step-by-step explanation:
See the attached worksheet. All three explanations are used to identify the three systems of equations. Some of the equations are equal to each other, apparent only when one rearranges the equations.
1/3x + 2y + 5/3x - 4y pls I have a 0 in math I need help with this
Answer:
2x-2y
Step-by-step explanation:
1/3x + 2y + 5/3x - 4y
= 1/3x + 5/3x - 4y + 2y
=6/3 x -2y
=2x-2y
lution set.
-y-8<-3 ory+5>19
The solution set of the expression is y > -5
How to determine the solution set of the expression?From the question, we have the following parameters that can be used in our computation:
-y-8<-3 ory+5>19
Express the inequality properly
So, we have the following expression
-y - 8 < -3 or y + 5 > 19
Collect the like terms
This gives
-y < 8 - 3 or y > 19 - 5
Evaluate the like terms
This gives
-y < 5 or y > 14
Rewrite as
y > -5 or y > 14
When combined, we have:
y > -5
Hence, the solution set is y > -5
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Complete question
For the following inequality expression, determine the solution set
-y-8<-3 ory+5>19
15/20, 20/21 determine if the ratio are proportional
According to definition of proportional ratios, 15 / 20 is not a multiple of 20 / 21.
How to determine whether that two ratios are proportional
In this problem we find two ratios in fraction form, both are proportional if the numerator and denominator of one of them are multiple of the corresponding elements of the other. First, write the fraction with the lowest numerator:
15 / 20
Second, multiply numerator and denominator by 4 / 3:
[15 · (4 / 3)] / [20 · (4 / 3)]
20 / 26.667
Ratio 15 / 20 is not proportional to ratio 20 / 21.
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How do you find the median of a cumulative frequency graph class 10?.
To find the median of a cumulative frequency graph the median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.
When a set of numbers is arranged in ascending order of magnitude, the middle number is known as the median. A collection of n numbers has a median value of (n+1)/2. N is the cumulative frequency in the case of a cumulative frequency curve.
The median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.
Create the cumulative frequency curve using the numbers provided first. Mark the point with the highest cumulative frequency, then draw a line perpendicular to the Y-axis that precisely passes through it. The lowest cumulative frequency is then marked, and a line is drawn parallel to the X axis. Mark the place where these two lines intersect.
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I really need help on this!
Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.
What is the product about?In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.
The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.
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How many perfect squares from 1 to 100?.
There are eight perfect squares from 1 to 100 (i.e., except 1 and 100). They are represented as 4, 9, 16, 25, 36, 49, 64 and 81.
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, we can say that a perfect square is a number that can be expressed as the product of an integer by itself or as the second power of an integer. Perfect Square Formula : Let us consider if N is a perfect square of a whole number x, then N can be represent as the product of x and x = x². So, the perfect square formula formula is , N = x². For example, If x = 3, and N = x². This means, N = 3× 3 = 3² = 9 . Here, 9 is a perfect square because it is equal to the square of a whole number, 3. We have to determine the number of perfect squares from 1 to 100.
1² = 1 ; 2² = 4 ; 3² = 9 ; 4² = 16 ; 5² = 25 ; 6² = 36 ; 7² = 49 ; 8² = 64 ; 9² = 81 ; 10² = 100
As we get, there are 10 perfect squares from 1 to 100. But, in actual manner they are only 8 perfect squares from 1 to 100 after excluding 1 and 100.
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make x the subject of the relation x/s-1+t/r+1=1
Answer:
s - 1 - t(s - 1)/(r + 1)
Step-by-step explanation:
x/(s - 1) + t/(r + 1) = 1
x/(s - 1) = 1 - t/(r + 1)
x = s - 1 - t(s - 1)/(r + 1)
The Hall family and the Cox family each used their sprinklers last summer.
The water output rate for the Hall family's sprinkler was 25 L per hour.
The water output rate for the Cox family's sprinkler was 20 L per hour.
The families used their sprinklers for a combined total of 40 hours, resulting in a total water output of 875 L.
How long was each sprinkler used?
The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.
How long was each sprinkler used?The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.
Let h and n represent the amount of hours each household uses its sprinkler, the Halls and the Nguyens, respectively.
They use for a total of 50 hours, thus either h + n = 50 or h = 50 - n.
Additionally, their total water output is 1050 L, thus we may use the equation below.
35h + 15n = 1050
Replace h with h = 50 - n to get
35(50 - n) + 15n = 1050
1750 - 35n + 15n = 1050
35n - 15n = 1750 - 1050
20n = 700
34 hours, n
15 hours equal 50 h, 50 n, and 35 n.
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do you have 8 cups of flour a recipe calls for 2/3 cup of flour of the recipe calls are 1/4 cup of flour how much flour do you have left after making the recipes
Answer: Total cup of flour=8 cups
One recipe calls for cup of flour=2/3
Cup of flour after making one recipe=8-2/3=(24-2)/3=22/3=7.33 cup of flour
Another recipe calls fro cup of flour=1/4
Cup of flour left after another recipe=22/3-1/4=(88-3)/12=85/12=7.08 cup of flour.
Amount of Floor left=7.08
Step-by-step explanation:
If the simple interest on $6,000 for 7 years is 2,100, then what is the interest rate?
Answer:
5%
Step-by-step explanation:
First, you do:
$2100/7 = $300
Then you do:
r x 6000 = $300
r = 300/6000 = 0.05
Finally, you do:
0.05 x 100 = 5%
So the interest rate is: 5%
Help me find x please!
Answer:
PSQ = x since PSQ + 3 x = 4 x
So the triangle PQS is an equilateral triangle
2 x + y = 180 (y = PQS the angle opposite 68)
y + 68 = 180 these must add to 180
x = 34 subtracting the previous two equations
How many times more intense is an earthquake that measures 8 on the Richter scale than an earthquake that measures 4 on the Richter scale?.
A measures magnitude 8 on the Richter scale of an earthquake is 10,000 times stronger than a magnitude 4 measure on the Richter scale.
Earthquake Intensity: An earthquake is the release of energy from the movement of tectonic plates. Earthquakes can be measured on the Richter scale, which ranges from 2 to 10 and measures the magnitude of an earthquake.
Earthquake intensity is a qualitative estimate of the effects caused by an earthquake, so it has no numerical value. The Richter scale is a logarithmic scale. This means that as you move up each digit, the power increases by a factor of 10. So let's set the damage from 4 earthquakes to X. Then, 5 = 10X
=> 6 = 100X
=> 7 = 1,000X
=> 8 = 10,000X
Hence, the required intensity is 10,000.
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Can sine law be used on a right triangle?.
No, the Sine law cannot be used directly on right triangles.
What is right triangle?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). The angle that measures 90 degrees is formed by two sides of the triangle, called the legs, and the third side, called the hypotenuse, is the side opposite the right angle. The legs of the right triangle are perpendicular to each other, meaning they form a 90 degree angle.
What is law of sines?
The sine law, also known as the "law of sines," is a mathematical relationship that relates the lengths of the sides of a triangle to the sines of its angles. the law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
What is Pythagorean theorem ?
The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, can be used to solve for unknown side lengths in a right triangle. This theorem is particularly useful in trigonometry, geometry and navigation.
A right triangle is a special type of triangle that has one angle that measures exactly 90 degrees (a right angle). Since the sine law relates the lengths of the sides of a triangle to the angles, it can be used to solve for unknown side lengths or angles in a right triangle, as long as the other side lengths and angles are known.
However, it is important to note that the sine law is typically used to solve for unknowns in non-right triangles, where the angle measures are not known. In a right triangle, the Pythagorean theorem can be used instead, which relates the length of the hypotenuse to the lengths of the legs.
So, Sine law cannot be used directly on right triangles, but it can be used in solving triangles which includes right triangles as well.
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A village parking lot is 120 feet wide by 180 feet long, and it has room for 75 cars. The village plans to increase the length by 30%.
Answer:
A) 234 feet
B) Area of new parking lot = 28080 square feet
C) The new parking lot will be able to fit 20 more cars than the original parking lot.
Step-by-step explanation:
We are given the following information:
Length of parking lot = 180 feet
Width of parking lot = 120 feet
Number of cars that can be parked = 75
A) Increase in length = 30%
New length =
B) New area =
C) Space required by 1 car = 288 square feet
Number of cars we want to fit = 75 + 20 = 95
Area required =
Hence, the new parking lot will be able to fit 20 more cars than the original parking lot.
Solve the equation 6z2-7z-5=0
Answer:
-1/2, 5/3
Step-by-Step Explanation:
6z^2 - 7z - 5 = 0
=> 6z^2 - 10z + 3z - 5 = 0
=> 2z(3z - 5) + 1(3z - 5) = 0
=> (2z + 1)(3z - 5) = 0
=> z = -1/2, 5/3
Hope it helps.
If you have any query, feel free to ask.
The city of Los Angeles wants to build a suspension bridge over Lake Casitas. The suspension
cables that are connected between the towers must have a parabolic curve. Let the y-axis
represent the axis of symmetry. The road/deck represents the directrix and sits 15 meters
above the water surface (which represents the x-axis). The vertex or minimum point of the
cable is 12 meters above the directrix. Write an equation to represent the parabolic shape of the
cables on the suspension bridge.
anchor
tower
cable
deck
foundations
hanger
approaches
A suspension bridge: a parabola represents the profile of the cable of a suspended-deck suspension bridge.
What is graph ?A graph is a topic which gives us the numerical facts into visual form.
That is, a graph gives the visual representation of the data collected.
The towers supporting the cable of suspension bridge are 15m apart and 12m above the bridge it supports.
Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.
lets have the bridged centered at the origin
Three points are needed on the parabola
x = 0, y = 20
x = -7.5, y = 12
x = +7.5, y = 12
using the form ax^2 + bx + c = y, we know that c=20
x=-7.5, y = 12 and x =+7.5, y = 12; write two equations
-7.5^2a - 7.5b + 20 = 12
+7.5^2a + 7.5 + 20 = 12
use elimination
56.25a - 7.5b + 20 = 12
56.25a + 7.5b + 20 = 12
addition eliminates b
112.5a + 40 = 24
112.5=16
a = 16/112.5
a = 0.1422
Now we can write the equation
y = 0.1422x^2 + 2
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1.
(04.02 LC)
Which of the following is a common characteristic of a binomial distribution? (4 points)
There are more than two possible outcomes.
The probability of success is the same in all trials.
There are infinitely many observations.
You should perform x trials until you observe a success.
Each trial is dependent on the previous trial.
Answer: The probability of success is the same in all trials.
The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.
What is the independent probability?Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.
You should perform x trials until you observe a success.
We have given that,
There are exactly two possible outcomes success and failure.
We have to determine the following is NOT a common characteristic of a binomial distribution.
By process of elimination:-
A binomial experiment is a statistical experiment that must meet certain requirements
All trials are independent.
There are a fixed number of n trials.
The probability of success, p, is the same for each trial.
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Is 6(4b + 3d) and 24b + 3d equivalent or not
Answer:
No
Step-by-step explanation:
You must distribute 6 to BOTH numbers in the bracket
[tex]6(4b + 3d) = 24b + 18d[/tex]
Answer:
No, they are not equivalent !
Step-by-step explanation:
Simplify 6(4b + 3d)....
6(4b + 3d)
→ 6*4b+6*3d
→ 24b+18d
and we have....
→ 24b + 3d
So, no 6(4b + 3d) and 24b + 3d are not equivalent.
What is the factor of 9x² 6x 1?.
The factored form of given equation 9x² - 12x + 4 is (3x - 2)(3x - 2).
The given expression is 9x² - 12x + 4
By splitting the middle term, let us factor this polynomial.
To identify the factors we have to consider factors of 36 as (9 × 4)
9x²- 6x - 6x + 4
=3x(3x - 2) - 2(3x - 2)
=(3x - 2)(3x - 2)
Another example of a quadratic polynomial can be taken to demonstrate similar factorization:
x² + 9x + 20
= x² + 5x + 4x + 20
= x × (x + 5) + 4 × (x + 5)
= (x + 5)(x + 4)
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For each transformation in the table below, indicate which properties are true and false by selecting true or false from the drop down menus in each box
Translation, rotation, and reflection are three of the fundamental transformations.
What properties do transformations have?Translation, rotation, and reflection are three of the fundamental transformations.The four main categories of transformations are as follows :Rotation.Translation.Dilation.ReflectionA metamorphosis is a significant alteration in appearance or form. The only change that might provide similarity is dilation.Non-rigid transformations are those that dilate when length and angle measurements are not preserved.Since they maintain length, translation, reflection, and rotation are isometries. Congruency transformations are hence translation, reflection, and rotation.An image that is congruent to the preimage is produced through stiff or isometric transformation.To learn more about transformation refer to:
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Compute Autin' total ocial ecurity and Medicare taxe for the fourth quarter, if he i elf-employed and earn $5,000. 00 on a emimonthly bai. (For elf-employed peron, ocial ecurity tax i 12. 4% of wage up to $128,400, and Medicare tax i 2. 9% of all wage. )
The total Social Security and Medicare taxes for the fourth quarter would be $728.00 ($600.00 for Social Security and $128.00 for Medicare). This is calculated by multiplying $5,000.00 by 12.4% for Social Security and 2.9% for Medicare.
The total Social Security and Medicare taxes for the fourth quarter would be $728.00. This is calculated by multiplying the total wages for the quarter ($5,000.00) by 12.4%, the Social Security tax rate for self-employed individuals, and then multiplying the same wages by 2.9%, the Medicare tax rate for self-employed individuals. This gives us $600.00 for Social Security taxes and $128.00 for Medicare taxes, for a total of $728.00. The Social Security tax rate is applied up to the wage base of $128,400 for the year.
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What is the argument of 4 3i?.
The Argument of 4 + 3i is arg(z) = 36.97◦.
Now, According to the question:
Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
The standard format of a complex number is:
[tex]a +bi[/tex]
In which:
a is the real part.b is the imaginary part.Given,
The complex number is:
z = 4 + 3i
We have to find the argument of the 4 + 3i.
The argument is given by:
θ = [tex]tan^-^1\frac{b}{a}[/tex]
tan θ = [tex]\frac{3}{4}[/tex]
θ = [tex]tan^-^1\frac{3}{4}[/tex]
θ = 36.97◦
The argument is θ = 36.97◦
We also have an abbreviation for argument: we write arg(z) = 36.97◦
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For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that used to find a solution for the equation. Be sure to include at least two terms from the word bank. 1/4 x < -3
The inequality equation is x ≤ ( -12 )
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
( 1/4 )x ≤ -3 be equation (1)
On simplifying the equation , we get
x/4 ≤ -3
Multiply by 4 on both sides of the equation , we get
x ≤ ( -3 ) ( 4 )
x ≤ -12
Therefore , the value of x is less than or equal to -12
Hence , the inequality equation is x ≤ -12
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Did Jas graph and find the solution correctly? If not, what was her mistake?
She did not find the correct solution. She graphed the bottom equation of the System incorrectly.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
According to the Problem
y = 3x - 3.....(1)
2x + 2y = 8........(2)
Substitute the value of y from equation 1 to equation 2
2x + 2(3x -3 ) = 8
2x + 6x -6 = 8
8x = 14
x = 1.75
Tus,
y = 3 * 1.75 - 3
y = 2.25
Therefore, she did not find the correct solution to the system of equations.
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What is the solution to this system of linear equations x − 3y − 2 x 3y 16 7 3 3 7 − 2 − 3 − 3 − 2?.
Solving the system of equations by the method of elimination we get
x = 7 and y = 7/3
Here we are given the system of equations:-
x - 3y = -2 [1]
x + 3y = 16 [2]
Since nothing is mentioned we will use the method of elimination for the question
Subtracting equation [2] rom [1] we get
-6y = -14
or, y = 14/6
or, y = 7/3
Now adding equation [1] and [2] gives us
2x = 14
or, x = 14/2
or, x = 7
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Complete Question
What is the solution to this system of linear equations
x - 3y = -2,
x + 3y = 16
How do you multiply 3-digit numbers by 2 digit numbers with regrouping?.
Multiply the number in the one's place, Multiply the number in the ten's place and multiply the one's and ten's place with the hundred place number, then add them up.
Follow along with example 343 × 32:
Place one number above the other so that the ones' place digits and tens' place digits are lined up. Mark a line just below the bottom number.
3 4 3
×3 2
_______
Multiply the ones' place digits (2 × 3 = 6), one's place of the second number by the ten's place of the first number (2 × 4 = 8), and one's place of the second number by the hundred place of the first number (2 × 3 = 6). Place the 6 below the line in the ones' place column, 8 below the line in the tens' place column and 6 below the line in the hundred place column.
3 4 3
×3 2
_________
6 8 6
Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9; multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12, and multiply the digit in the tens' place column (3) by the digit in the hundred place of the first number (3). The outcome is 3 × 3 = 9. Now add the numbers and place the answer below the line.
3 4 3
×3 2
__________
6 8 6
10 2 9×
__________
10 976
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You have a list of 600 random, normally distributed numbers with a mean of 10 and a standard deviation of 2. Which of these statements is true?.
About 285 numbers lie between the values 10 and 14. (option C).
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or a Gaussian distribution. In statistics and the natural and social sciences, normal distributions are crucial concepts.
There are 600 numbers and their mean is 10 where the standard deviation is 2.
47.5% of the numbers should fall between 10 and 14, as expected. In a normal distribution, 47.5% of the sample size will fall between the mean and two standard deviations on either side of it.
By doing calculation on option C, we got that = [tex]\frac{285}{600}*100=47.5[/tex]
Hence, option C is correct, i.e., about 285 numbers would lie between the values 10 and 14.
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An 8-foot-long board is leaning against a building. The angle formed by the ground and the board is 70 ∘ . How far up the side of the building does the board reach?
The height of the board up the side of the building is 7.5 feet.
How to find the side of a right triangle?An 8-foot-long board is leaning against a building. The angle formed by the ground and the board is 70 degrees.
The height of the board to the side of the building can be calculated as follows:
Therefore, the situation forms a right-angle triangle.
Using trigonometric ratios,
sin 70° = opposite / hypotenuse
sin 70° = x / 8
cross multiply
x = 8 sin 70°
x = 8 × 0.93969262078
x = 7.51754096629
Therefore,
distance of the board up the building = 7.5 feet
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6. Find m/ADB.
D
A
E
(13x-16) C
B
(9x+4)
The value of Angle ADB, which is the angle created while moving from A to D to B. Angle ABM is the angle created while moving from point A to point B to point M is [tex]41^{0}[/tex]
Finding the value of m∠ADB:Due to the fact that angle ADB is an inscribed angle, its measure is halved compared to the angle of the arc that it intercepts. In other words, the angle is 40 degrees in length, which is equal to half of an 80 degree angle.
By adding up all of your balances at the end of each day for each eligible month, you may get your average daily balances (ADB) by dividing that amount by the number of days in that qualifying month.
3x - 16 = 9x + 4
4x = 20 x = 5 m
with BCE: 9 (5) + 4 = 49°
m with ADB = 41°
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