1. Find the slope and the y-intercept of each equation.
a. y = 2x - 6
m=
b=
The equation y = 2x - 6 is a line in the form known as Slope-Intercept Form. This form organizes the equation so that you can easily discern the y-intercept and slope.
Slope-intercept form is y = mx + b. So here, m = 2, b = -6.
Please help me with this question
To derive the formula that goes through these two points, we use the general equation for an exponential equation.
Y = a(b)^x
There we will substitute the two points into this equation to get two equations
45 = a(b)^2
5/9= a(b)^-1
By dividing the first equation by the second, we obtain:
27 = b^3
Therefore b= 3
We plug b=3 into the first equation using the second point:
45 = a(3)^2
We get a = 5
Therefore the equation is y = 5(9)^x
We can verify this equation by plugging in the two points given to see if it works.
5/9 = 5(9)^-1
5/9 = 5/9
And:
45 =5(9)^2
45 = 45
It does, so the equation is correct.
The answer is y =5(9)^x
What is exponential equation?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.Exponential equations are equations in which variables occur as exponents.For example, exponential equations are in the form a x = b y .To solve exponential equations with same base, use the property of equality of exponential functions .To learn more about exponential equation refer to:
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Dan has a jar full of quarters and dimes. He has 21 more dimes than he has quarters. Overall, Dan has 67 coins. How many of each coin does Dan have?
The number of dimes and quarters that Dan has will be 44 and 23, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Dan has a container loaded with quarters and dimes. He has 21 additional dimes than he has quarters. Generally, Dan has 67 coins.
Let 'x' be the number of dimes and 'y' be the number of quarters. Then the equations are given as,
x = y + 21 ...1
x + y = 67 ...2
From equations 1 and 2, then we have
y + 21 + y = 67
2y = 46
y = 23
Then the value of the variable 'x' is calculated as,
x = 23 + 21
x = 44
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what is −2(x+6)=4x
x=
Answer:
x=-2
Step-by-step explanation:
Distribute, add 12 to both side, then simplify
Answer: -2
Let's solve your equation step-by-step.
−2(x+6)=4x:
Step 1: Simplify both sides of the equation.
−2(x + 6) = 4x
(−2)(x) + (−2)(6) = 4x (Distribute)
−2x + (−12) = 4x
−2x − 12 = 4x
Step 2: Subtract 4x from both sides.
−2x − 12 − 4x = 4x − 4x
−6x − 12 = 0
Step 3: Add 12 to both sides.
−6x − 12 + 12 = 0 + 12
−6x = 12
Step 4: Divide both sides by -6.
−6x/−6 = 12/−6
x = −2
PLEASE HELP If the tangent ratio of 0 is 4/3, which angle is 0?
The angle θ is ∠P
Trigonometric Ratios:A branch of mathematics called trigonometry in geometry deals with the angles and sides of a right triangle.
There are six trigonometric ratios in trigonometry namely sin, cos, tan, cot, cosec, and sec.
In a right-angled triangle,
Formulas of trigonometric ratios are given below
Sin θ = Opposite Side /Hypotenuse
Cos θ = Adjacent Side /Hypotenuse
Tan θ = Opposite Side/Adjacent
By the trigonometric ratios
tan = opposite side/Adjacent side
Given tan θ = 4/3 = QR/PQ
[Here QR is opposite to the angle P ]
This means 'θ' is taken from ∠P
Therefore,
The angle θ is ∠P
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Answer:
angle p
Step-by-step explanation:
just did the test
1,458, 486, 162, 54, … patterns
1,458, 486, 162, 54,
Every succeeding number is getting divided by 3.
What is patterns ?
A recurring arrangement of numbers, shapes, colors, and other elements is known as a pattern. The Pattern may be connected to any kind of occasion or thing. When a group of numbers are arranged in a certain way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Pattern of even numbers: 2, 4, 6, 8, 10, 1, 14, 16, 18...
Pattern of odd numbers: 3, 5, 7, 9, 11, 13, 15, 17, 19.
Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, and 21. so on.
The patterns among our 1,458, 486, 162, and 54 data must be found.
1458/3 = 486
486/3 = 162
162/3 = 54
54/3 = 18
18/3 = 6
6/3 = 2
so the patterns is Every succeeding number is getting divided by 3.
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at high temperatures, the partition function for rotational energy of a molecule of nitrogen is , where is the energy as in eq. 6.29.
True, at high temperatures, the partition function for rotational energy of a molecule of nitrogen is k T ϵ, where ϵ is the energy [tex]z_{rot}=\sum_{j=0}^{\infty}(2j+1)e^{-j(j+1)\epsilon/kT}[/tex].
As we know the rotational energy levels of a diatomic molecule are given by,
[tex]E_{rot}[/tex] (J) = BJ(J+1)
Where, B is the rotational constant.
From explicit summation, expression for rotational partition function ([tex]z_{rot}[/tex]), Equation 18.6.518.6.5, we can do an explicit summation
[tex]z_{rot}=\sum_{j=0}^{\infty}(2j+1)e^{-j(j+1)\epsilon/kT}[/tex]
When the rotational energy levels are lying very close to one another, we can integrate just as above, and we gets the equation you just provided.
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The right question is:
At high temperatures, the partition function for rotational energy of a molecule of nitrogen is k T ϵ, where ϵ is the energy in Eq. 6.29.
[tex]z_{rot}=\sum_{j=0}^{\infty}(2j+1)e^{-j(j+1)\epsilon/kT}[/tex]
A True
B False
2. Which of the following ordered pairs is a solution to the system of linear inequalities given below?
{2x³
(2y ≥-4x + 4
(x-2> 2y
I.(-2, 1)
II.(0, -2)
III.(4,-2)
IV. (1, 2)
The solutions to the given Inequalities are Option II. (0, -2) and Option IV. (1, 2).
What are inequalities:In mathematics, inequalities describe the connection between two non-equal numbers. Equal does not imply inequality.
Various types of inequalities are used to compare the values and determine whether they are smaller than or greater than.
It indicates that the phrase on the left should be either larger or smaller than that of the expression on the right, or vice versa.
Here we have
2y ≥ -4x + 4 --- (1)
x - 2 > 2y ---- (2)
Substitute each given point and find for which both equations will be satisfied
For Option I. (-2, 1)
(1) => 2(1) ≥ -4(-2) + 4
=> 2 ≥ - 4 [ Which is true ]
(2) => -2 - 2 > 2(1)
=> - 4 > 2 [ which is not true ]
For Option II. (0, -2)
(1) => 2(-2) ≥ -4(0) + 4
=> -4 ≥ 4 [ Which is true ]
(2) => 0 - 2 > 2(-2)
=> - 2 > - 4 [ which is true ]
For option III. (4,-2)
(1) => 2(-2) ≥ -4(4) + 4
=> - 4 ≥ - 12 [ Which is true ]
(2) => 4 - 2 > 2(1)
=> 2 > 2 [ which is not true ]
For option IV. (1, 2)
(1) => 2(2) ≥ -4(1) + 4
=> 4 ≥ 0 [ Which is true ]
(2) => 1 - 2 > 2(2)
=> - 1 > 4 [ which is true ]
From above calculations
The solutions to the given Inequalities are Option II. (0, -2) and Option IV. (1, 2).
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Find the value of the expression. x(x–y)–y(y^2–x) for x=4 and y=2
The angle formed between one side and another, always less than 180 degrees.
Answer:obtuse angle
Step-by-step explanation:
An obtuse angle is an angle of greater than 90° and less than 180°. It is bigger than an acute angle. It is smaller than a straight angle, which measures 180°. Angles are measured with a protractor obtuse angle is specifically present in hexagon and pentagon and others.
Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long. Each wreath requires 5 yards of uncut ribbon. How many wreaths can Ms. Brooks make?
The number wreaths that Ms. Brooks make will be 7 wreaths.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
It should be noted that an expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features. People make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects
Here, Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long.
Since each wreath requires 5 yards of uncut ribbon, the number of wreaths that Ms. Brooks make will be:
= (18 + 17) / 5
= 35 / 5
= 7 wreaths.
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What is the quotient of
102 and 5?
The leftover after dividing 102 by 5 is the quotient, which is:
Quotient 20
Remainder 2
102 5: Quotient and Remainder
The quotient and remainder method is one way to determine the quotient and remainder of a division. The dividend (102) and the divisor are already known to us (5). Now, we need to determine the residual and the quotient:
The Quotient and Remainder procedure is as follows:
20 quotient, 5 | 102 dividend, -10 2, and a reminder
As can be seen:
The remainder is 2, while the quotient is 20.
Sometimes, the remaining part is referred to as the "modulo," or simply "mod." This notation is used to say that:
102 mod 5 = 2
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Given two polynomials a and b, what polynomial operations may produce a result that is not a polynomial?
Two polynomials a and b, multiply a by three and divide by three times b. polynomial operations may produce a result that is not a polynomial.
Define polynomial.A polynomial is a mathematical expression made up of one or more terms. The phrases "poly" and "nomial," for example, are whence the name "polynomial" arose. The words "poly" and "nomial" both signify many. A polynomial is an algebraic expression with two or more algebraic terms, to put it simply. It has exponents, operators, coefficients, coefficients, variables, and constants. Algebraic expressions known as polynomials can have exponents that are multiplied, divided, or added. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively. A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a binomial.
Given
Two polynomials a and b, what polynomial operations may produce a result that is not a polynomial
c) Multiply a by three and divide by three times b.
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O MEASUREMENT AND DATA
Introduction to the probability of an event
A spinner with 12 equally sized slices has 5 red slices, 3 blue slices, and 4 yellow slices. The dial is spun and stops on a slice at random. What is the probabili
that the dial stops on a slice that is not red?
Write your answer as a fraction in simplest form.
Explanation
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The probability that the dial stops on a yellow or blue slice will be 0.6667.
What is probability?
Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A spinner with 12 similarly measured cuts has 5 yellow cuts, 3 blue cuts, and 4 red cuts. The dial is turned and stops on a cut indiscriminately.
The total number of the event is given as,
Total events = 5 + 3 + 4
Total events = 12
The probability that the dial stops on a yellow or blue slice will be given as,
P = 3 / 12 + 5 / 12
P = 0.25 + 0.4167
P = 0.6667
The probability that the dial stops on a yellow or blue slice will be 0.6667.
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a 9 foot ladder is leaning against a wall. if the top of the ladder is sliding down the wall at a rate of
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]
Given that,
Length of the ladder is, [tex]l=9ft[/tex]
Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.
Now, from triangle ABC,
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
[tex]h^{2} +b^{2} =l^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = 81 (Equation-1)
Differentiating the above equation with respect to time, 't'.
So,
We can write,
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0
[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0
[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0 (Equation-2)
In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.
Let us assume,
h = 3 ft and db/dt = 3 ft/s
We can substitute values in equation-1,
[tex]3^{2} +b^{2}[/tex] = 81
9 + [tex]b^{2}[/tex] = 81
[tex]b^{2}[/tex] = 81-9
[tex]b^{2}[/tex] = 72
b = [tex]\sqrt{72}[/tex]
b = 8.48 ft
Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]
3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0
3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0
3*[tex]\frac{dh}{dt}[/tex] = - 25.44
[tex]\frac{dh}{dt}[/tex] = -25.44/3
[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s
Therefore,
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
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explain the difference between arithmetic growth and exponential (geometric growth). would you recognize them if they were described in writing and/or by picture?
When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.
When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. An illustration of arithmetic growth is the ongoing elongation of roots. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.
The amounts added grow by a fixed rate of growth, expressed in percentages. Due to the fact that these remain constant while the amounts added rise, growth is then typically measured in doubling times.
Due to the fact that all populations of organisms have the potential to experience exponential growth, the concept of exponential growth is particularly intriguing in the field of population biology.
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what number is 16 2/3% more than 240
280 is the number which is 16 2/3% more than 240
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.
(1/6) th of 240 = 240/6 = 40
40 more than 240 = 280
So, 280 is the number which is 16 2/3% more than 240
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Is 8y-5xy=9 linear or nonlinear
Answer: The equation 8y-5xy=9 is nonlinear because it contains the product of the variables x and y. In general, an equation is linear if it can be written in the form ax + by = c, where a and b are constants and x and y are variables. Equations that cannot be written in this form are nonlinear.
please help meeeeeeee
Answer: B & A
Step-by-step explanation: I think?
-y + 7y -54 = 0 what is the linear equation for y
The linear equation for y is y=9.
What is 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) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
-y+7 y-54=0
Add similar elements: -y+7 y=6 y
6 y-54=0
Move 54 to the right side
6 y=54
Divide both sides by 6
[tex]\frac{6 y}{6}=\frac{54}{6}[/tex]
Simplify
y=9
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8.1.2 Exam: Semester 1 Exam Question 36 of 40 Solve 3-212. A. X≥-18 Correct! B. X. The answer is in the picture.
The solution to the given inequality is x ≤ -18 which is the correct answer that would be an option (D).
The inequality is given in the question as:
3 -x/2 ≥ 12
To solve this inequality, we need to isolate the variable x. To do this, we can start by subtracting 12 from both sides of the inequality:
3 - x/2 ≥ 12
3 - x/2 - 12 ≤ 0
Next, we can simplify the left side of the inequality by combining like terms:
-x/2 - 9 ≤ 0
Finally, we can solve for x by adding 9 to both sides and multiplying both sides by -2:
x ≤ -18
Thus, the solution to the inequality is x ≤ -18.
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stockholder's equity of $350,000 and net income of 59,400. Payout ratio of 20% and return on assets of 9%. How much was paid in cash dividends and what were its average total assets?
If stockholder's equity of $350,000 and net income of 59,400. Payout ratio of 20% and return on assets of 9%. The amount that paid in cash dividends is $11,880 and its average total assets is $660,000.
How to find the cash dividend and the average assets?a. Cash dividend:
Cash dividend = Net Income ×Dividend Payout Ratio
Cash dividend = $59,400 × 20%
Cash dividend = $11,880
b. Average Assets:
Average Assets = Net Income × Return on Assets
Average Assets = $59,400 / 9%
Average Assets = $660,000
Therefore the amount that paid in cash dividends is $11,880 and its average total assets is $660,000.
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Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered
.Mich statement is correct based on the data?
The ratio of smoothie size to mangos used for Kim is 1.7, and the ratio of smoothie size to mangos used for Bri is 3: 28.
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
The ratio of smoothie size to mangos used for Bri is 7:1, and the ratio of smoothie size to mangos used for Angela is 4: 28.
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
The solution is Option D.
The ratio of smoothie size to mangoes used for Kim is the same as the ratio of smoothie size to mangoes used for Angela
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the equation be represented as A
Now , the value of A is
The number of mangoes used by Bri = 1 mango
The amount of smoothie size of Bri = 7 oz
The number of mangoes used by Kim = 3 mangoes
The amount of smoothie size of Kim = 21 oz
The number of mangoes used by Angela = 4 mangoes
The amount of smoothie size of Angela = 28 oz
Now , the proportion is given by
The ratio of smoothie size to mangoes used by Kim = amount of smoothie size of Kim / number of mangoes used by Kim
Substituting the values in the equation , we get
The ratio of smoothie size to mangoes used by Kim = 21 / 3
The ratio of smoothie size to mangoes used by Kim = 7 : 1
Now , the proportion is
The ratio of smoothie size to mangoes used by Angela = amount of smoothie size of Angela / number of mangoes used by Angela
Substituting the values in the equation , we get
The ratio of smoothie size to mangoes used by Angela = 28 / 4
The ratio of smoothie size to mangoes used by Angela = 7 : 1
So , The ratio of smoothie size to mangoes used by Kim = The ratio of smoothie size to mangoes used by Angela = 7 : 1
Hence , ratio of smoothie size to mangoes used by Kim is equal to ratio of smoothie size to mangoes used by Angela
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Answer:
d
Step-by-step explanation:
i took the test and its right :)
How long is 10 percent of a 24 hour day
Answer:
Step-by-step explanation:
2.4 hours, aint no way this is college math
Answer:2.4 hours
Step-by-step explanation:
4. Solve the equation 10x = 10,563. Be sure
to provide the solution both exactly and
approximately.
Question 3
Evaluate g(x)=-3x+1, when x=10
Give a numerical answer.
Does the given matrix, A, have an inverse? If it does, what is A^-1?
The inverse of the matrix A is (b) [tex]A^{-1} = \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
How to determine the inverse of the matrix?From the question, we have the following parameters that can be used in our computation:
[tex]A = \left[\begin{array}{cc}-7&-25\\2&7\end{array}\right][/tex]
To calculate the inverse of the matrix, we start by calculating the determinant of the matrix
This is calculated as follows
|A| = -7 * 7 + 25 * 2
Evaluate the products in the above equation
So, we have the following representation
|A| = -49 + 50
Evaluate the sum in the above equation
So, we have the following representation
|A| = 1
The inverse is then calculated as
[tex]A^{-1} = \frac{1}{|A|} * \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
Substitute the known values in the above equation, so, we have the following representation
[tex]A^{-1} = \frac{1}{1} * \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
Evaluate the quotient
[tex]A^{-1} = 1 * \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
This gives
[tex]A^{-1} = \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
Hence, the inverse is (b)
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Marco has $16.72. He spends $9.21 on a movie ticket. How much money does Marco have left?
Responses
A $7.68$7.68
B $7.51$7.51
C $7.48$7.48
D $7.61
Answer:
7.51
Step-by-step explanation:
16.72 - 9.21
Solve ABC using diagram and the given measurement A=64 a=7.4
The measurements in the given triangle ABC are A=64°, B=26°,
C=90°, a=7.4, b=3.61, c=8.23
What is meant by an angle?An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. These are referred to as dihedral angles. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can likewise be used to establish an angle between two intersecting curves.
Given,
In ΔABC, A=64°, a=7.4
From the figure we know that C=90°, as the given figure is a right triangle.
As we already know that,
Angles sum in a triangle=180°
A+B+C=180°
64°+B+90°=180°
B=180°-154°
B=26°
By using sine rule,
a/SinA =b/SinB=c/Sinc
7.4/Sin 64°=b/Sin 26°=c/ Sin 90°
b=7.4Sin26°/Sin 64°
b=3.61
c=7.4 Sin 90°/Sin 64°
c=8.23
Therefore, the measurements in the given ΔABC are A=64°, B=26°,
C=90°, a=7.4, b=3.61, c=8.23
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Kevin has an annual salary of $41,732, and he earned $33.52 interest from his savings account. He also paid $1050 in student loan interest and contributed $3900 to an IRA retirement account. Calculate Kevin’s adjusted gross income.
Kevin's adjusted gross income is $36, 815. 52
What is adjusted gross income?Adjusted gross income is simply described as gross income minus certain adjustments from the income.
These adjustments includes;
Educator expensesStudent loan interestAlimony paymentsContributions to an account, etcIt is calculated as;
Adjusted gross income = sum total of income - expenses
Now, let's substitute the values into the formula, we have;
Adjusted gross income = $(41,732 + 33.52) - $(1050 + 3900)
Add the values
Adjusted gross income = $(41, 765. 52 - 4950)
Subtract the values
Adjusted gross income = $36, 815. 52
Hence, the value is $36, 815. 52
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