So, by resolving the given, we obtain the result: The final simplified expressions phrase is as follows: -4x + 38/3
what is expression ?Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
Let's start by condensing the first expression:
(2/3) (3x - 1) = 2x - 2/3
Now, we may reformat the phrase as follows:
(2x - 2/3) + 4x + 9 - 10x + 5
Mixing related concepts gives us:
-4x + 38/3
The final simplified phrase is as follows:
-4x + 38/3
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true or false law of sines can be used when you are given 3
sides of a triangle and you are solving for an angle
Answer:
False
Step-by-step explanation:
False, you need at least one angle and three sides to use the law of sines or two angles and two different sides.
sin A sin B sin C
------ = ------- = -------
a b c
True, the law of sines can be used when you are given 3 sides of a triangle, and you are solving for an angle.
The law of sines 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 sides and angles in a given triangle. Therefore, if you know the lengths of all three sides of a triangle, you can use the law of sines to solve for one of the angles.
What are angles?An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.
The unit of measurement associated with angles is degrees.
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The customer service company for an online retailer wants to rate the effectiveness of their support. At the end of the service phone call, customers are asked to answer questions about the friendliness and helpfulness of the customer service agent. What type of sampling method is this?
A. Cluster Sampling
B. Convenience Sampling
C. Stratified Random Sampling
D. Systematic Sampling
Consider the following vectors v1 = 1 , v2 = 2 , and v3 = -1 . For what values (s) -1 1 3
2 1 h
of h is the set. {v1, v2, v3] linearly dependent? Work must be shown for this question. h = -4
h = 4
all real number h ≠ 4 all real number h ≠ -4
The set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.
The set of vectors {v1, v2, v3} is linearly dependent if there exists a set of real numbers a, b, and c such that a*v1 + b*v2 + c*v3 = 0 and at least one of a, b, or c is not equal to zero. In this case, we can write the equation as:
a*1 + b*2 + c*(-1) = 0
We can rearrange this equation to solve for h:
h = -a - 2*b + c
Now we can plug in the values for v1, v2, and v3:
h = -1 - 2*2 + (-1)*(-1)
h = -4
Therefore, the set of vectors {v1, v2, v3} is linearly dependent when h = -4.
Alternatively, we can also use the determinant of the matrix formed by the vectors to determine when the set is linearly dependent. The determinant of the matrix is given by:
| 1 2 -1 |
| -1 1 3 | = (1)(1)(h) + (2)(3)(-1) + (-1)(-1)(2) - (-1)(1)(-1) - (2)(-1)(1) - (1)(3)(2)
| 2 1 h |
Simplifying this equation gives:
h - 6 - 2 + 1 + 2 - 6 = 0
h - 11 = 0
h = 11
Therefore, the set of vectors {v1, v2, v3} is also linearly dependent when h = 11.
So the set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.
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At the same time a 612 -ft teacher casts a 9-ft shadow, a nearby flagpole casts a 3112 -ft shadow. How tall is the flagpole?
The height of the flagpole is approximately 23,047.11 feet.
To resolve this issue, we can make use of the similar triangles property. The teacher, the flagpole, and each of their corresponding triangles are similar because they have the same angles.
Let h be the height of the flagpole. Then, we can set up the following proportion:
h / 3112 = 612 / 9
When we simplify this ratio, we obtain:
h = (3112 x 612) / 9
h = 207424 / 9
h ≈ 23,047.11 feet
Hence, the flagpole is roughly 23,047.11 feet tall.
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At Blue Coral Bay's annual beach clean-up, volunteers work together to pick up trash that gets washed ashore. This year, the volunteers averaged 1.5 more pounds of collected trash per person than last year. There were 80 volunteers this year, and together they removed a total of 360 pounds of trash from the beach.
The average amount of trash collected is found to be 3 pounds.
Explain about the equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 = 12.Let the average amount of trash collected be 'x'.
As per the given conditions, equation form:
80*(1.5 + x ) = 360
Applying the Distributive Property:
120 + 80x = 360
Simplifying:
80x = 240
x = 240/80
x = 3
Thus, the average amount of trash collected is found to be 3 pounds.
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The complete question is attached.
A) change the rectangular coordinates (-5V3, 5) to-polar coordinats with Give exact values ( No decíals) pls .. Show work B) Given a= (-5,2) b=<4-7> bind the following: Give exact values1/4 show work a. 3a-4b
A) To change the rectangular coordinates (-5√3, 5) to polar coordinates, we need to find the radius r and the angle θ.
The radius r can be found using the Pythagorean theorem:
r = √(x^2 + y^2)
r = √((-5√3)^2 + (5)^2)
r = √(75 + 25)
r = √100
r = 10
The angle θ can be found using the inverse tangent function:
θ = tan^(-1)(y/x)
θ = tan^(-1)(5/(-5√3))
θ = tan^(-1)(-√3/3)
θ = -π/6
So, the polar coordinates are (10, -π/6).
B) Given a = (-5, 2) and b = <4, -7>, we need to find 3a - 4b.
3a = 3(-5, 2) = (-15, 6)
4b = 4(4, -7) = (16, -28)
3a - 4b = (-15, 6) - (16, -28) = (-15 - 16, 6 - (-28)) = (-31, 34)
So, the answer is (-31, 34).
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You put $113 into a savings account that has an interest rate of 6% compounded every week.
a. How much money is in your account after 4 years?
How much interest did you earn in those 4 years?
b.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus 52} \end{array}\dotfill &52\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A = 113\left(1+\frac{0.06}{52}\right)^{52\cdot 4} \implies \boxed{A \approx 143.63}\hspace{5em}\underset{ earned~interest }{\stackrel{ 143.63~~ - ~~113 }{\boxed{\approx 30.63}}}[/tex]
A varies directly as B and inversely as C . A is 12 when B is 6 and C is 2 . What is the value of A when B is 12 and C is 3 .
O 4 O 8 O 12
O 16
If A varies directly as B and inversely as C then The value of A when B is 12 and C is 3 is 16.
To find the value of A, we can use the formula for direct and inverse variation of the given :
A = k*B/C
We are given that A is 12 when B is 6 and C is 2. We can plug these values into the formula to find the value of k:
12 = k*6/2
12 = 3k
k = 4
Now that we know the value of k, we can plug in the new values for B and C to find the value of A:
A = 4*12/3
A = 48/3
A = 16
Therefore, the value of A when B is 12 and C is 3 is 16. The correct answer is O 16.
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Hint: Summaries do NOT tell how things look, feel, smell, or taste. A. My sister's wedding was a success. B. I ate yummy salmon at my sister's wedding. C. My dress at my sister's wedding was blue.
A summary is a brief overview of the main points or important details of a text or event. In the case of the statements provided, option A, "My sister's wedding was a success," is the best example of a summary.
A summary provides a general overview of the event without going into specific details about how things looked, felt, smelled, or tasted, as does option A.
Options B and C, "I ate yummy salmon at my sister's wedding" and "My dress at my sister's wedding was blue," are not summaries because they focus on specific details rather than providing an overview of the event.
In conclusion, alternative A. My sister's wedding was a success is correct.
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Compute the area of triangle, if x equals 3 less than 6
The correct option is C, the area of the triangle is 9 square units.
How to get the area of the triangle?For a triangle of base B and height H the area is:
A = B*H/2
Here we can see that:
B = x
H = 2x
And we know that x = 6 - 3 = 3
Then we can use the value of x to find the values of H and B.
B = 3
H = 2*3 = 6
Now we can replace these two values in the formula for the area, then we will get the area of the triangle:
A = 3*6/2 = 3*3 = 9 square units.
When x = 3, the area is 9 square units.
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Use the given feasible region to determine the maximum and minimum values of the objective function
P = 50x + 75y,
if they exist. (If an answer does not exist, enter DNE.)
The xy-coordinate plane is given. A 4 sided figure labeled S is located in the first quadrant. The five corner points of the figure are as follows:
(0, 2), (1, 9), (8, 4), and (3, 0)
Determine the minimum value.
Determine where the minimum value occurs.
The minimum value of P occurs at the corner point (8, 4).The minimum value of P occurs at all points on the line segment connecting (0, 2), (3, 0).The minimum value of P occurs at all points on the line segment connecting (0, 2), (1, 9).The minimum value of P occurs at the corner point (3, 0).The minimum value does not exist.
Determine the maximum value.
Determine where the maximum value occurs.
The maximum value of P occurs at all points on the line segment connecting (3, 0), (8, 4).The maximum value of P occurs at the corner point (8, 4).The maximum value of P occurs at all points on the line segment connecting (1, 9), (8, 4).The maximum value of P occurs at the corner point (1, 9).The maximum value does not exist.
The corner point (8, 4) and is equal to 550
The minimum value of P = 50x + 75y exists at the corner point (3, 0) and is equal to 150. The maximum value of P = 50x + 75y exists at the corner point (8, 4) and is equal to 550.
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BMV Entertainment has more than 72 demos in the vault. In December, each of the 6 executives will receive an equal number of demos to review.
Which number sentence below represents the number of demos, D, that each executive will receive?
A. 72 + D > 6
B. 72 ÷ 6 < D
C. 72 - 6 < D
D. 72 × 6 > D
The number in the sentence that represents the number of demos, D, that each executive will receive is 72 ÷ 6 < D. Option B
How to find the sentence that represents the number of demosSince there are more than 72 demos
Each executive will receive at least 72/6 = 12 demos.
The number of demos that each executive will receive is 12 demos
Therefore, the number in the sentence that represents the number of demos, D, that each executive will receive is 72 ÷ 6 < D.
Hence, the correct inequality is 72 ÷ 6 < D.
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olve the polynomial equation in the comple 30x^(4)+83x^(3)-52x^(2)+4x+1=0 he solutions are
The polynomial equation in the complete 30x^(4)+83x^(3)-52x^(2)+4x+1=0. The solutions are: x = -1 and x = -1/7, 1/7, -5/7, 5/7.
The question asks you to solve the polynomial equation: 30x4 + 83x3 - 52x2 + 4x + 1 = 0.
To solve this equation, you will need to factor it into the form (ax + b)(cx + d) = 0. The solutions of this equation will be when either ax + b or cx + d are equal to 0.
First, factor out the Greatest Common Factor (GCF) of the polynomial, which is 4x. This will leave us with:
4x(7x3 + 20x2 - 13x + 1) = 0.
Now, factor this expression into two binomials. One of the binomials is already in the form ax + b, and the other will need to be factored further.
4x(7x2 + 5x - 1)(x + 1) = 0.
Therefore, the solutions of this equation are when
or
.
The solutions are: x = -1 and x = -1/7, 1/7, -5/7, 5/7.
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question is in the linked picture
WILL MARK BRAINLIEST
The equation that represents the proportional relationship between the initial height and the rebound height of the bouncy ball is D . r = 0.6 h
How to find the proportional relationship ?The proportional relationship can be found by the formula :
= Change in y / Change in x
= Change in rebound height / Change in initial height
= ( 0. 50 - 0. 30 ) / ( 0. 3 / 0 . 18 )
= 0.6 meters
The proportional relationship is :
= 0. 6 x initial height
= 0. 6 h
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Classify the polygon. Be as specific as possible.
Quadrilateral JKLM with JK = 10, KL = 7, ML = 10, and JM = 7
The response to the given question would be that JK || ML is a pair of parallel sides, and JM and KL are equal in length, making JKLM a trapezoid, more particularly an isosceles trapezoid.
what is quadrilateral?In terms of geometry, a quadrilateral is a four-sided polygon with four edges and four corners. Its origins are in the Latin terms quadri and latus (meaning "side"). A rectangle is a two-dimensional shape with four sides, four vertices, and four corners. Two main types of concave and convex exist. Convex quadrilaterals also have a number of subclasses, such as trapezoids, parallelograms, rectangles, rhombuses, and squares. A rectangle is a two dimensional shape with four straight sides. Quadrilaterals come in many various shapes, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
The quadrilateral JKLM's shape may be ascertained using the information provided as follows:
JK = ML signifies that the lengths of the opposing sides are equal.
JM = KL denotes that the length of neighbouring sides is the same.
Nevertheless, we lack sufficient knowledge to establish whether or not opposing angles are equal.
As a result, using the information provided, the quadrilateral JKLM would be classified in the following way:
JK || ML is a pair of parallel sides, and JM and KL are equal in length, making JKLM a trapezoid, more particularly an isosceles trapezoid.
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HELP PLSS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]\frac{y + x}{y\y - x}[/tex]
Step-by-step explanation:
Helping in Jesus' name.
2.077×10 −4 =?2, point, 077, times, 10, start superscript, minus, 4, end superscript, equals, question mark
This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.
What is algebraic expression?An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.
It may contain one or more variables, which are symbols that represent unknown quantities or values that can vary. Algebraic expressions can be written using letters, symbols, or a combination of both, and they can be used to model real-world situations, solve problems, and express mathematical relationships.
For example, "3x + 5" is an algebraic expression that represents a linear equation with one variable "x".
2.077×10⁻⁴ means "2.077 times 10 to the power of -4", which can be rewritten as 0.0002077. This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.
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Question 6(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
A helium tank shaped like a cylinder has 2,401π in3 of space inside the tank. If the diameter of the helium tank is 14 inches, what is its height?
49 inches
28 inches
12.25 inches
7 inches
The height of the helium tank is 49 inches.
What is Volume?Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.
The volume V of a cylinder is given by the formula:
V = πr²h
where r is the radius of the base and h is the height of the cylinder.
Since the diameter of the helium tank is given as 14 inches, the radius r is half of the diameter, which is 7 inches.
We also know that the volume inside the tank is 2,401π cubic inches. Therefore, we can write:
2,401π = π(7)²h
Simplifying the right-hand side, we get:
2,401π = 49πh
Dividing both sides by 49π, we get:
h = 2,401π / 49π
Simplifying, we get:
h = 49
Therefore, the height of the helium tank is 49 inches.
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Answer:
49
Step-by-step explanation:
I took the test and got it right :)
solve the following by using the elimination method a) 2a-b=-1 and a-2b=4 b) 3m-n=8 and m+n=4
The solution of the equations 2a-b=-1 and a-2b=4 is b = -3 and a = -2. The solution of the equations 3m-n=8 and m+n=4 is m = 3 and n = 1.
What is an elimination method?In the elimination method, the two equations are solved by eliminating one variable and by substituting the value of one variable in the equation to get the value of another variable.
The two equations can be solved as below,
2a-b=-1
a-2b=4
Multiply the second equation by two and subtract from the first equation,
2a-b=-1
2a - 4b = -8
________
3b = - 9
b = -3
2a + 3 = -1
2a = -4
a = -2
For the other two equations,
3m-n=8
m+n= 4
_______
4m = 12
m = 3
m + n = 4
n = 4 - 3
n = 1
Therefore, the solution of the equations 2a-b=-1 and a-2b=4 is b = -3 and a = -2. The solution of the equations 3m-n=8 and m+n=4 is m = 3 and n = 1.
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Marcus can choose between a monthly salary of $1,750 plus 6% of sales or $2,000 plus 3% of sales. He expects sales between $5,000 and $10,000 a month. Complete the explanation to show which salary option he should choose based on how much he could make. He should choose the option that pays (select) With option 1 he would make $ With option 2 he would make $ to $ to $
Answer:
Step-by-step explanation:
1500 + 5000x 0.055 - $1775
1500 + 10000 x 0.055 = $2050
with option 1 he would make 1775 to 2050
2400 + 5000 x0.04 =2600
2400 + 10000 x 0.04 = 2800
With option 2 hw would make $2600 to $2800
simple calculation :)
Lee is paid $8. 00 per hour plus a commission of 4% on all sales. Assuming Lee works 39 hours and has sales of $4,000, her gross pay is
Lee's gross pay is $472.
First, we need to calculate the commission Lee earned. To do this, we take her total sales and multiply it by her commission rate.
Commission = Total Sales x Commission Rate
Commission = $4,000 x 0.04
Commission = $160
So, Lee earned $160 in commission.
Next, we need to calculate her base pay. To do this, we multiply her hourly rate by the number of hours she worked.
Base Pay = Hourly Rate x Hours Worked
Base Pay = $8.00 x 39
Base Pay = $312
Now that we have calculated her commission and base pay, we can add them together to find her gross pay.
Gross Pay = Base Pay + Commission
Gross Pay = $312 + $160
Gross Pay = $472
This means that before any deductions (such as taxes), Lee would earn $472 for working 39 hours and making $4,000 in sales.
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HELP ME IM GIVING 16 BRAINLIEST IF HELP
Answer:
277 milliliters
Step-by-step explanation:
do 945-668
this gives you 277
Answer:
The answer to your problem is, 277 milliliters.
Step-by-step explanation:
The reason I say that is because our problem that you are is a subtraction problem, so.. :
945 - 668 = 277.
Then we just add milliliters.
Thus the answer to your problem is, 277 milliliters.
the following LP problem in a spreadshee MAX: 4x_(1)+4x_(2) Subject to: 2x_(1)+4x_(2)<=20 3x_(1)+5x_(2)<=15 x_(1),x_(2)>=0
x1 = 5 and x2 = 0
The following LP problem in a spreadsheet MAX: 4x1 + 4x2 Subject to: 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.A spreadsheet is a type of software that allows users to store and analyze data in a grid-like format of rows and columns. Spreadsheets are commonly used for data entry, financial modeling, and other calculations.In the given problem, we are supposed to find the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.The first two constraints are represented by inequalities. That means, the values of x1 and x2 can be any non-negative values that satisfy the constraints. Mathematically, the constraints can be represented as:2x1 + 4x2 <= 20⇒ x2 <= 5 - 0.5x1--------(1)3x1 + 5x2 <= 15⇒ x2 <= 3 - 0.6x1--------(2)Note that, we have represented the constraints in such a way that x2 is the subject of the inequality. This is done to make it easier to graph and find the feasible region.To find the feasible region, we need to graph both inequalities (1) and (2) on a coordinate plane. The feasible region is the shaded area that is common to both regions. It is given below:The feasible region is the triangular-shaped region. Since x1 and x2 are both non-negative, we need to consider only the values of x1 and x2 that are within the feasible region.Now, to maximize the function 4x1 + 4x2, we need to find the optimal solution. We do this by finding the intersection points of the lines that represent the equation 4x1 + 4x2 = k, where k is a constant.The equation 4x1 + 4x2 = k can be rearranged as x2 = (-x1 + k/4)This equation represents a line with a slope of -1 and a y-intercept of k/4. We can graph this line for different values of k to find the optimal solution. The line for k = 0 is shown below:We can see that the line passes through the feasible region at point (0, 0) and (5, 0). This means that the maximum value of the function is 4x1 + 4x2 = 4(5) + 4(0) = 20 at point (5, 0).Thus, the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0 is 20 at x1 = 5 and x2 = 0.
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3. Ratio fractions decimal percent
ex;17 percent
answer
ex; 0. 17
answer
3\4
3;4
The Ratio fractions decimal percent is as follows:
17% as a decimal = 0.17
17% as a fraction = 17/100
17% as a ratio = 17:100
3/4 as a decimal = 0.75
3/4 as a fraction = 3/4
3/4 as a ratio = 3:4
To convert 17% to a decimal, we move the decimal point two places to the left, which gives us 0.17.
To convert 3/4 to a decimal, we divide 3 by 4, which gives us 0.75.
To convert 0.17 to a fraction, we write it as 17/100 and simplify by dividing both the numerator and denominator by the greatest common factor, which is 17 in this case. Therefore, 0.17 as a simplified fraction is 17/100.
To convert 0.75 to a fraction, we write it as 75/100 and simplify by dividing both the numerator and denominator by the greatest common factor, which is 25 in this case. Therefore, 0.75 as a simplified fraction is 3/4.
To convert 17% to a ratio, we write it as 17:100.
Therefore:
17% as a decimal = 0.17
17% as a fraction = 17/100
17% as a ratio = 17:100
3/4 as a decimal = 0.75
3/4 as a fraction = 3/4
3/4 as a ratio = 3:4
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Gail has $5,500 that she wants to put in a new savings account. She is considering two banks that are very similar. One difference she notices are the interest rates: • Neighborhood Bank - 1.2% interest, compounded annually • Beautiful Day Bank - 1.2% interest, compounded daily Based on interest, which bank would you suggest Gail pick if she plans to have her money in the account for 15 years?
Gail should pick a Beautiful bank if she plans to have her money in the account for 15 years.
How to determine which will be best bank?To determine which bank would be better for Gail, we need to calculate the future value of her investment after 15 years for each bank and compare the results.
For Neighborhood Bank, we can use the formula:
FV = P(1 + r/n)^(n*t)
where FV is the future value,
P is the principal (the initial amount invested),
r is the annual interest rate (as a decimal),
n is the number of times the interest is compounded per year,
and t is the number of years.
Plugging in the values, we get:
FV = 5,500(1 + 0.012/1)^(1*15)
FV = 5,500(1.012)^15
FV = 7,130.34
For Beautiful Day Bank, we can use the formula:
FV = P(1 + r/n)^(n*t)
Plugging in the values, we get:
FV = 5,500(1 + 0.012/365)^(365*15)
FV = 5,500(1.000032876)^5475
FV = 7,145.25
Therefore, Beautiful Day Bank would be the better choice for Gail, as she would earn a higher amount of interest and end up with a higher future value for her investment after 15 years.
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A truck with 18 wheels has a tire radius of 21 in. and a profile, or tire width, of 12 in. If 20% of the tire is making contact with the ground, what is the total surface area of the tires that is making contact with the ground at any one time? Leave your answer in terms of ππ
Surface Area is
ππ square inches.
The total surface area of the tires making contact with the ground at any one time for the truck with 18 wheels, tire radius of 21 in, tire width of 12 in, and 20% contact area is approximately 5700.24 square inches.
The surface area of one tire making contact with the ground can be calculated as follows:
The diameter of the tire is 2 * radius = 2 * 21 in = 42 in
The length of the portion of the tire making contact with the ground is 20% of the circumference of the tire = 0.2 * π * 42 in ≈ 26.39 in
The width of the tire making contact with the ground is given as 12 in
Therefore, the surface area of one tire making contact with the ground is approximately 26.39 in * 12 in = 316.68 square inches
Since the truck has 18 wheels, the total surface area of all the tires making contact with the ground at any one time is 18 * 316.68 square inches = 5700.24 square inches.
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Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A-22, C - 51.4%, c-2.69 B=____ a=______ b=_______
Answer:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths of the triangle, and A, B, and C are the opposite angles, respectively.
We are given A, C, and c, so we can use the Law of Sines to find B, a, and b.
a/sin(A) = c/sin(C)
a/sin(22) = 2.69/sin(51.4)
a = sin(22) * (2.69/sin(51.4))
a = 1.00
b/sin(B) = c/sin(C)
b/sin(B) = 2.69/sin(51.4)
b = sin(B) * (2.69/sin(51.4))
We can use the fact that the sum of the angles in a triangle is 180 degrees to find B:
B = 180 - A - C
B = 180 - 22 - 51.4
B = 106.6
Now we can substitute the values we have found into the Law of Sines to find b:
a/sin(A) = b/sin(B)
1/sin(22) = b/sin(106.6)
b = sin(106.6) * (1/sin(22))
b = 2.69
Therefore, B is approximately 106.6 degrees, a is approximately 1.00, and b is approximately 2.69.
Does someone mind helping me with this question? Thank you!
Answer:
33361
Step-by-step explanation:
The equation appears to be
75 ( 1 + 0.84 )^x
Since it increases by 84% every 2 days, you'd devide 20 by 2, making 10
So to do the equation you'd shove that into a calculator since no one wants to hand do that sort of equation.
75 ( 1 + 0.84 )^10 = 33361.0332844 = 33361
Rationalize the denominator: (a)52+3510(b)33x+3y3xy
For (a): 52 + 35/10m, rationalizing the denominator gives the result (25√2 + 6√5)/10.
For (b): 33x + 3y/3xy, rationalizing the denominator gives the result √3(x+y)/xy.
To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of a binomial expression is the same expression with the sign between the terms changed. For example, the conjugate of (a+b) is (a-b) and the conjugate of (a-b) is (a+b). By multiplying by the conjugate, we eliminate any radicals in the denominator.
(a) 5/√2 + 3/√5
= (5/√2)(√2/√2) + (3/√5)(√5/√5)
= (5√2)/2 + (3√5)/5
= (25√2 + 6√5)/10
(b) (3√3x + 3√y)/(3√xy)
= (3√3x + 3√y)(3√xy)/(3√xy)(3√xy)
= (9x√3xy + 9y√3xy)/(9xy)
= (9√3xy(x+y))/(9xy)
= √3(x+y)/xy
Therefore, the rationalized denominators are (a) (25√2 + 6√5)/10 and (b) √3(x+y)/xy.
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Which functions are odd or even? (a) f(x) = -tan(x) is ____ (b) f(x) = tan(x+T/2) is ____
(c) f(x) = tan(x)+cot(x) is ___. (d) f(x) = 5cot(x) is ____
(e) f(x) = (tan(x))2 is ____
(f) f(x) = tan(4x) is______
The functions that are odd or even can be determined by replacing x with -x and seeing if the function remains the same or changes sign.
(a) f(x) = -tan(x) is an odd function because f(-x) = -tan(-x) = tan(x) = -f(x)
(b) f(x) = tan(x+T/2) is an odd function because f(-x) = tan(-x+T/2) = -tan(x+T/2) = -f(x)
(c) f(x) = tan(x)+cot(x) is neither an odd nor an even function because f(-x) = tan(-x)+cot(-x) = -tan(x)-cot(x) ≠ f(x) or -f(x)
(d) f(x) = 5cot(x) is an even function because f(-x) = 5cot(-x) = 5cot(x) = f(x)
(e) f(x) = (tan(x))2 is an even function because f(-x) = (tan(-x))2 = (tan(x))2 = f(x)
(f) f(x) = tan(4x) is an odd function because f(-x) = tan(4(-x)) = -tan(4x) = -f(x)
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