Using the law of sines, determine whether the given information results in one triangle, two triangle or no triangle at all. Solve any triangle that results. a=8angle B = 57 degreeAngle A =49 degree
Answers
step 1
Find out the measure of angle C
Remember that
In any triangle, the sum of the interior angles must be equal to 180 degrees
so
A+B+C=180 degrees
substitute given values
49+57+C=180
C=180-106
C=74 degrees
step 2
Find out the length side b
Applying the law of sines
[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]substitute
[tex]\frac{8}{s\imaginaryI n49^o}=\frac{b}{s\imaginaryI n57^o}[/tex]Solve for b
[tex]\begin{gathered} b=\frac{8*s\mathrm{i}n57^o}{s\imaginaryI n49^o} \\ \\ b=8.89\text{ ---> rounded to two decimal places} \end{gathered}[/tex]step 3
Find out the length side c
Applying the law of sines
[tex]\frac{a}{s\imaginaryI nA}=\frac{c}{s\imaginaryI nC}[/tex]substitute
[tex]\frac{8}{s\imaginaryI n49^o}=\frac{c}{s\imaginaryI n74^o}[/tex]solve for c
[tex]\begin{gathered} c=\frac{8*s\mathrm{i}n74^o}{s\imaginaryI n49^o} \\ \\ c=10.19\text{ ----> rounded to two decimal places} \end{gathered}[/tex]therefore
N of triangles is only oneb=8.89c=10.19C=74 degreesRelated Questions
Let f(x) = x² - 4x.
Use the limit definition of the derivative to compute the value of f'(3).
Answers
Using limit definition of the derivative, The value of f'(3) is 2.
What is limit definition of derivative?By determining the limit of a slope expression, one can get the instantaneous rate of change (derivative).
The derivative of a function f at x is the instantaneous rate of change of the function at x since the derivative is defined as the limit that determines the slope of the tangent line to a function.
Given function
f(x) = x² - 4x.
derivate with respect to x
f'(x) = 2x - 4
put x = 6
f'(x) = 2(3) - 4
= 6-4
=2
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Write an expression equivalent to \frac{9^5}{9^3} in the form of b^n.
Answers
The expression that is equivalent to \frac{9^5}{9^3} is 9^2.
What is an expression?It should be noted that an expression is simply used to shoe the relationship between the variables that are illustrated.
In this case the given expression is 9^5 / 9^3. It should be noted that when dividing powers, we have to subtract them. Therefore, 5 - 3 = 2.
The value will be:
= 9^5 / 9^3
9^2
The expression is 9^2.
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use the commutative law of multiplication to rewrite 146 x 48
Answers
Step-by-step explanation:
146 × 48 = 48 × 146
due to the commutative law of multiplication the sequence of the operands of a multiplication does not matter.
a × b = b × a
this bases on the fact that a multiplication is nothing else than a special kind of addition
a × b = add a b times; or add b a times.
and as already the addition follows the commutative law
a + b = b + a
so, does then the multiplication.
What is the fractional equivalent of the repeating decimal n = 0.1515... ? Answer the questions to find out.
1. How many repeating digits does the number represented by n have? (2 points)
ill give 100 points and maybe brainlist
Answers
The fractional equivalent of the repeating decimal n = 0.1515... is 5/33, with two repeating digits.
What is a fractional equivalent?A fractional equivalent is a fraction that shares the same equivalent value with a decimal.
For instance, the equivalent fraction of 0.1515 is 303/2000. But for a repeating decimal like 0.1515..., the equivalent fraction is 5/33.
When numbers or values are said to be equivalent, it means that they are equal.
By their nature, repeating decimals continue endlessly.
Let x = 0.1515... equation 1
100x = 15.1515... equation 2
Subtract equation 1 from equation 2:
100x = 15.1515...
x = 0.1515...
99x = 15
x = 15/99
x = 5/33
Thus, n = 0.1515... as a repeating decimal or 5/33 as a fraction.
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a wire of length 38 m is divided into two pieces and each piece is bent into a square. how should this be done in order to minimize the sum of the areas of the two squares? (give your answer in the form of a comma separated list of the lengths of the two pieces.)
Answers
The lengths of the two pieces of a wire will be 19,19.
Define square.A square is a closed, two-dimensional object with four equal sides and four vertices. On either side, it has parallel sides.
The square of a square's side determines its area.
Given data -
Length of a wire = 38 m
As the wire is divided into two pieces,
Let the length of two pieces of wire be x and y m respectively.
As per given data, x + y = 38
Therefore, y = 38 - x
As each piece is bent into a square, area of squares will be
[tex](x/4)^{2}[/tex] and [tex](y/4)^{2}[/tex]
Therefore, the sum of areas of two squares will be A = [tex](x/4)^{2}[/tex] + [tex](y/4)^{2}[/tex]
A = [tex]x^{2}[/tex]/16 + [tex]y^{2}[/tex]/16
A = [tex]x^{2}[/tex]/16 + [tex](38-x)^{2}[/tex]/16
By differentiating, we will get
A' = [tex]\frac{2x}{16}[/tex] - [tex]\frac{2(38-x)}{16}[/tex]
In order to minimize the the sum of the areas of the two squares, we will take A' = 0
0 = x - (38 - x)
2x = 38
x = 19
Therefore y = 19
The length of two pieces of a wire should be 19 m each.
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Find the LCM of 6, 24 and 32
Answers
Answer:
96
Step-by-step explanation:
How do you figure out the area of a circle?
Answers
The area of the first and second circles is 36π m² and 9π m², respectively.
We are given two circles.The first circle has a radius of 6 m.The area of the circle is given by the formula πr².The area of the first circle is π(6)².The area of the first circle is 36π m².The second circle has a diameter of 6 m.The radius of the second circle is half of the diameter.The radius of the second circle is 3 m.The area of the second circle is π(3)².The area of the second circle is 9π m².To learn more about circles, visit :
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izzes
The radius of a circle is 4 centimeters. What is the area of a sector bounded by a 45° arc?
45⁰
Answers
The area of the sector is 6.28 cm².
What is a sector?A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the shape of a circle's sector.So, the area of the sector:
The formula for the area of the sector: θ/360 πr²Where θ is 45° and r is 4cm.Now, substitute the values in the formula as follows:
θ/360 πr²45/360 π4²1/8 π16π2(Let π be 3.14)
π2 = 6.28Therefore, the area of the sector is 6.28 cm².
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These marbles are placed in a bag and two
of them are randomly drawn.
What is the
probability of drawing two pink
marbles if the first one is NOT placed back
into the bag before the second draw?
Give your answer as a rational number, reduced to
simplest terms.
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to
get your answer.
Enter
Answers
If the first marble is not reinserted into the bag before the second draw, there is 1/15 probability of drawing two pink marbles.
What are dependent events?When the result of one event affects the result of another, two events are said to be dependent. The likelihood of two connected events is the sum of the probabilities of the occurrences X and Y that happen after X.
It is given that there are two yellow, three pink and 5 blue marbles.
So, in the first draw, the probability of drawing pink marble is the ratio of the number of pink marbles to the total number of marbles in the bag.
[tex]p_1=\frac{3}{10}[/tex]
Now, in the second draw, the probability of drawing pink marbles will be affected as it is not kept back. So, in the second draw, the probability of drawing pink marble is the ratio of the number of remaining pink marbles to the remaining number of marbles in the bag.
[tex]p_2=\frac{2}{9}[/tex]
Given that both occurrences occur concurrently, multiply the likelihood of the first event by the probability of the second event.
[tex]p=p_1\times p_2\\\\=\frac{3}{10}\times\frac{2}{9}\\\\ =\frac{1}{15}[/tex]
So, If the first marble is not reinserted into the bag before the second draw, there is 1/15 probability of drawing two pink marbles.
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Find the equation of the line that passes through (-1,2) and is perpendicular to 2y=x−3.
Leave your answer in the form y=mx+c
Answers
y = 1/2x - 1.5
If a line is perpendicular to another line, its gradient is the negative reciprocal of the first line.
y = -2x + c
2 = -2 x - 1 + 0
y = -2x
Answer:
y = -2x.
Step-by-step explanation:
2y = x - 3
y = 1/2x - 3/2
- so, the slope of this line is 1/2
and the slope of a line perpendicular to it is - 1/ 1/2
= -2.
Using the point slope form of a line the equation of the required line is
y - y1 = m(x - x1)
m = -2, x1 = -1 and y1 = 2.
So,
y - 2 = -2(x - (-1))
y - 2 = -2x - 2
y = -2x - 2 + 2
y = -2x.
A U.S. Geological Survey map has a scale of 1:24200. If two buildings are 3.38 miles apart, how many inchesapart are they on the map?They areinches apart on the map.Submit Question
Answers
Given:
A U.S. Geological Survey map has a scale of 1:24200
There are two buildings that are 3.38 miles apart.
We will find how they are inches apart on the map
First, convert from miles to inches
1 mile = 63 360 inches
So, 3.38 miles = 3.38 * 63 360 inches = 214156.8 inches
The map has a scale of 1:24200
So, using the ratio and the proportions, we will find the length on the map as follows:
[tex]\begin{gathered} 1:24200=x:214156.8 \\ \\ x=\frac{214156.8}{24200}=8.849 \end{gathered}[/tex]Rounding to the nearest hundredth
So, the answer will be: 8.85 inches
Victoria is studying the population of the town of Oak Hills for a class project. Based on census data, she found that the equation p = 660n + 14,400 can be used to estimate the population, p, of Oak Hills n years after the year 1900. What will be the estimated population of Oak Hills in the year 2100?
A. 3,012,000
B. 146,400
C. 15,300
D. 132,000
Answers
Answer:
Step-by-step explanation:
2100 - 1900 = 200
660(200) + 14,400
p = 146400
146,400 people
The answer is B
is it possible for a rectangle to have irrtaional sides and a rational area
Answers
Yes it is possible for a rectangle to have irrational sides and rational area.
What are rational numbers?
Ration numbers is an ordered pair of integers a, b written in the form a/b where b is not equal to zero.
We are given that sides of rectangle are irrational can the rectangle have rational area
Let us consider that sides of the rectangle be [tex]2\sqrt{2}[/tex] and [tex]\sqrt{2}[/tex]
Hence the area of the rectangle is the product of sides which is [tex]4[/tex] sq. units
Which is a rational number
Hence, Yes it is possible for a rectangle to have irrational sides and rational area
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in lixue's garden the green pepper plants grew 5 inches in 3/4 months. at this rate how many feet can they grow in one month
Answers
If in lixue's garden the green pepper plants grew 5 inches in 3/4 months then at this rate they can grow 0.555 feet in one month
The problem is solved as per the unitary method
In lixue's garden the green pepper plants grew 5 inches in 3/4 months.
In 3/4 months the green pepper grew by 5 inches.
3/4 months can be written as 0.75 months
in 1 month the green pepper plant will grow by (5/0.75) 1
The green pepper plant will grow by 6.66 inches
1 foot is equals to 12 inches
1 inch = 1/12 foot
6.666 inches = (1/12) 6.666
= 0.0833 x 6.666
= 0.555
the plant grew 0.555 feet in 1 month
Therefore, if in lixue's garden the green pepper plants grew 5 inches in 3/4 months then at this rate,they can grow 0.555 feet in one month
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Michael is going on a 3150 mile drive. He needs to stop for gas every 320 miles. How many times will he need to stop?
Answers
What does (1,12) mean in this situation
Answers
Which is the graph of g(x)?
Which graph
Answers
Answer:
Option D.
Step-by-step explanation:
We are given with three function.
Plug in x=-2 in first functionf(x)= 3 so f(-2) = 3Plug in x=-2 in second function.
Zane is making chew toys for his puppy. He uses 2/5 yd of rope to make one toy, Zane has 2 yd of rope to use. What model can show how many 2/5 s fit into 2yd?
Answers
Answer:
5
Explanation:
When we divide A by B, we are calculating how many Bs fit into A. So, if we want to know how many 2/5s fit into 2 yds, we need to divide 2 by 2/5. So:
[tex]\frac{2}{\frac{2}{5}}=\frac{\frac{2}{1}}{\frac{2}{5}}=\frac{2\times5}{1\times2}=\frac{10}{2}=5[/tex]So, 2 yds of rope can be divide into 5 ropes of 2/5 yd.
Find the domain and range: y=(x-5)/(2x+4)
Answers
The most appropriate choice for function and domain and range of a function will be given by -
Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}
Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}
What is a function and domain and range of a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
The set of values for which the function is defined is the domain of the function and the values obtained on substituting the values of domain in the function is the range of the function.
y = [tex]\frac{x -5}{2x + 4}\\[/tex]
For domain of y
y is not defined if 2x +4 = 0
y is not defined if [tex]x = -\frac{1}{2}[/tex]
Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}
For range of y
let [tex]\frac{x -5}{2x + 4}\\[/tex] = z
[tex]x - 5 = z(2x +4)\\x - 5 = 2zx + 4z\\x - 2zx = 4z + 5\\x(1 - 2z) = 4z + 5\\x = \frac{4z + 5}{1 - 2z}[/tex]
If y = [tex]\frac{1}{2}[/tex]
[tex]\frac{x-5}{2x + 4} = \frac{1}{2}\\2x - 10 = 2x + 8\\-10 = 8\\[/tex]
Not possible
[tex]\frac{1}{2}[/tex] is not in the range of y
Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}
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What is a x? Show your work
Answers
Answer:
a value that is not yet shown
Step-by-step explanation:
Mark me as branlist to help
show me the standard algorithm for 546 divided by 13
Answers
The value of the quotient expression 546 ÷ 13 is 42
How to evaluate the expressions?The expression is given as
546 divided by 13
Rewrite the expression as
546 ÷ 13
By the standard algorithm, we have
The expression can be solved using a calculator and with the use of standard algorithm i.e. partial decomposition
By the rule of partial decomposition, we have
a ÷ b = (c ÷ d) ÷ b
Where
a = c + d
Next, we expand the expression as follows:
546 ÷ 13 = (520 + 26) ÷ 13
Remove the brackets
So, we have
546 ÷ 13 = 520 ÷ 13 + 26 ÷ 13
Evaluate the quotients
So, we have
546 ÷ 13 = 40 + 2
Evaluate the sum
So, we have
546 ÷ 13 = 42
Hence, the solution of 546 ÷ 13 is 42
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Pls, Help Right Now For 10!!!!!!!
Answers
Answer:
9
01000101010101010101011101010110110101011010
10101010101010110101101010101011011001010101
10101010100101010101010101101101101010101010
Erin loves to play sports. In all, she has earned 3 tennis trophies, 4 basketball trophies, 7 soccer trophies, and 1 volleyball trophy.
What is the ratio of Erin's tennis trophies to all of her trophies?
A) 3:4
B) 3:7
C) 3:12
D) 3:15
Answers
Step-by-step explanation:
option D is correct..
can we become friends???
16047 divide by 60
4620 divide by 250
52080 divide by 15
brainleiest
Answers
Answer:
1) 267.45
2) 18.48
3) 3472
is 0.49 a rational or irrational number?
(please explain how you know this)
Answers
Answer:
Rational
Step-by-step explanation:
there are very few irrational numbers, such as
[tex] \sqrt{2} [/tex]
or π
most of irrational numbers have a lot of decimal digits. And also numbers with 2 decimal digits are all rational because you can write them as
[tex] \frac{49}{100} [/tex]
Stella went shopping for a new camera because of a sale. The store was offering a 20% discount. If the price on the tag was $23, what would be the price after the discount but before tax, to the nearest dollar and cent?
Answers
The price after the discount but before tax, to the nearest dollar and cent, is $18.4.
Given Information:
Price on the tag = $23
Amount of Discount =20%
A % or Percentage is a figure or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). A % lacks dimensions and has no associated unit of measurement.
Percentage Formula =[tex]\frac{value}{Total value} *100[/tex]
Calculating the discount,
There is a 20 % discount on the camera
So, the amount of discount by using the percentage formula = [tex]\frac{20*23}{100} = 4.6[/tex]
Hence, the amount of discount is $4.6
Subtracting the discount to calculate the price after the discount =
Initial Price - Discount amount = $23-$4.6 = $18.4
Thus, the price after the discount is $18.4
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what is the quotient of 3.7x10^3 and 1.4x10^6 in scientific notation
Answers
1.4x10^6 = 84
Nerissa has 5 pink bows, 1 blue bow, and 4 purple bows in a box. She will randomly choose 1 bow from the box.
What is the probability Nerissa will choose a purple bow?
1/2
2/5
1/10
3/5
Answers
Answer: 2/5 is
Step-by-step explanation: 2/5 is equal to 40% and there is 10 bows
Please help me solve
2/3|4v+6|-2<10
Answers
Answer:
-6<v<3
Step-by-step explanation:
hope this helps
Select the correct answer from the drop-down menu.
The solution set for 6a²-a-5=0 is
(2,-5/6)
{2,-12/5)
{-1,-5/6)
(1.-5/6)
Answers
Answer:
{1, -5/6}
Step-by-step explanation:
(6a+5)(a-1) = 0
6a+5 = 0 (or) a-1 = 0
a = -5/6 (or) a = 1
