Answer:
all of them are true
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. B = 137°, c = 6, b = 11
The measurements given can form a triangle, and to solve it, we would use the Law of Sines. After confirming the possibility of a triangle, we solve for the unknown angle C using the known values and compute the remaining angle and side.
Explanation:To determine if a triangle is formed by the given measurements and solve it using the Law of Sines, we need to check if the given angle and sides satisfy the triangle inequality. The measurements given are angle B = 137°, side c = 6, and side b = 11. A triangle is possible if the sum of the two smallest sides is greater than the length of the longest side. Here the angle is very large, suggesting that the opposite side (b) must be the longest; however, since side b is indeed longer than side c, this condition is satisfied, so a triangle can be formed.
To solve the triangle using the Law of Sines, we set up the following ratio:
b/sin(B) = c/sin(C)
After substituting the known values into the equation, we get:
11/sin(137°) = 6/sin(C)
Now, we solve for sin(C) to find the angle C, and subsequently use the sum of angles in a triangle (180°) to find the remaining angle A. Once angle A is known, we can use the Law of Sines again to find the remaining side a. If at any point we find that the calculation results in an invalid sine value (greater than 1 or less than -1), we must then state that no real solution exists.
It is important to note that if we find angle C to be obtuse (greater than 90°), the triangle will not have a unique solution because it would contradict our initial assumption that angle B, being the largest given angle, is opposite the longest side.
What is the range of the function f(x) = |x − 1| − 2?all real numbersall real numbers less than or equal to −2all real numbers less than or equal to 1all real numbers greater than or equal to −2?
The range of the function f(x) = |x - 1| - 2 is all real numbers greater than or equal to -2.
Explanation:The function f(x) = |x - 1| - 2 represents the absolute value of x minus 1, subtracted by 2.
The range of the function can be determined by finding the minimum and maximum values it can take.
Since the absolute value of a number is always greater than or equal to zero, the lowest value that f(x) can take is when |x - 1| = 0, which happens when x = 1.
Therefore, the minimum value of f(x) is -2.
As x increases or decreases from 1, the value of f(x) increases.
So, there is no upper bound for the range of f(x).
Therefore, the range of the function is all real numbers greater than or equal to -2.
8b^2-7b-1=(8b+1)() Find The Missing Factor
A small combination lock on a suitcase has 6 wheels, each labeled with the 10 digits 0 to 9.
How many digit combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different?,
There will be, 590490 possible combinations.
What is combination?The number of different groups which can be formed from the available things can be calculated using combinations.
Given that, A small combination lock on a suitcase has 6 wheels, each labelled with the 10 digits 0 to 9.
We have 10 for the first wheel, but second wheel only has 9 options because 2nd number can't be the same as first. The third and fourth wheels also has 9 options for the same reason.
10x9x9x9x9x9 = 590490 combinations
Hence, There will be, 590490 possible combinations.
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1)
What is the area of a sector with a central angle of 5π/7 radians and a diameter of 5.6 in.?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
2)
What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
The area of the given sectors of circles is required.
The area of the sector is [tex]8.79\ \text{in}^2[/tex]
The area of the sector is [tex]151.98\ \text{cm}^2[/tex]
Area of sector[tex]\theta[/tex] = Central angle = [tex]\dfrac{5\pi}{7}\ \text{rad}[/tex]
d = Diameter = 5.6 in
r = Radius = 2.8 in
Area of a sector is given by
[tex]A=\dfrac{\theta}{2}r^2\\\Rightarrow A=\dfrac{\dfrac{5\times 3.14}{7}}{2}\times 2.8^2\\\Rightarrow A=8.79\ \text{in}^2[/tex]
[tex]\theta=\dfrac{4\pi}{5}\ \text{rad}[/tex]
r = 11 cm
[tex]A=\dfrac{\dfrac{4\times 3.14}{5}}{2}\times 11^2\\\Rightarrow A=151.98\ \text{cm}^2[/tex]
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Find the exact value of sin(x+y) when sinx=-1/4 and cosy=-3/5 in q2
When calculating total savings, you must ____. (1 point)
A. calculate the total cost of the item when not on sale and subtract the sales cost.
B. calculate the total cost of the items at their sale price.
C. add all of the items together and divide by the total number of items.
D. calculate the total cost of the items at their sale price and subtract the original cost.
What fraction of 1 gallon is 5 cups
Find the equatio of the line tht contains the point (5,6) and is perpendicualr to the line 4x+2y=2
Final answer:
The equation of the line that passes through the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.
Explanation:
The question asks us to find the equation of a line that passes through a given point and is perpendicular to a given line. To solve this, we first need to determine the slope of the given line, then find the perpendicular slope, and finally, use the point-slope form of a line to write the equation for our new line.
Here are the steps:
Find the slope of the given line. For the equation 4x + 2y = 2, we rearrange it to slope-intercept form (y=mx+b), which gives us y = -2x + 1. The slope is -2.
Since we want a line that is perpendicular to the given line, we need the negative reciprocal of -2, which is 1/2.
Now we use the point-slope form of a line, y-y1 = m(x-x1), with point (5,6) and slope 1/2. This gives us y - 6 = 1/2(x - 5).
Solving for y to get the slope-intercept form, we multiply both sides by 2 to get rid of the fraction: 2y - 12 = x - 5, and then solve for y: y = 1/2x + 7/2.
The equation of the line that contains the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.
Brainliest for best answer!
A= 48 degrees what is C
What is the following quotient? 2- sqrt 8 / 4 + sqrt 12
we have
[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}[/tex]
Multiply the numerator and denominator by the conjugate of the denominator
so
[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}*\frac{4-\sqrt{12}}{4-\sqrt{12}}=\frac{(2-\sqrt{8})(4-\sqrt{12)}}{4^{2}-(\sqrt{12})^{2}}\\ \\= \frac{2*4-2*\sqrt{12}-4*\sqrt{8}+\sqrt{12}*\sqrt{8}}{16-12}\\ \\=\frac{8-4\sqrt{3}-8\sqrt{2}+4\sqrt{6}}{4} \\ \\=2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]
therefore
the answer is
[tex]2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]
Write log4 14 as a logarithm of base 3.
1) (log4)3/(log14)3
2) (log14)3/(log4)3
3) (log3)4/(log3)14
4) (log3)14/(log3)4,
To convert log4 14 to a logarithm of base 3, you can use the change of base formula. The required conversion would be log3 14 divided by log3 4.
Explanation:To write log4 14 as a logarithm of base 3, we would use the change of base formula. The change of base formula is logba = logca / logcb, where logba is the logarithm we want to convert, c is the new base, a is the number, and b is the original base. So, in this case, we want to write log4 14 as a logarithm of base 3, so using the formula, it would be (log3 14) / (log3 4).
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John wants to buy a new bike that cost 337 and he already has saved 103. Estimate to find about how much more John needs to save to buy the bike
Sally buys a hand bag. there was a discount of 23%. If sally paid $20.02, what was the original price?
A rectangular piece of sheet metal has a length that is 6 in. less than twice the width. a square piece 3 in. on a side is cut from each corner. the sides are then turned up to form an uncovered box of volume 1014 in. cubed find the length and width of the original piece of metal.
Determine the dimensions of the metal sheet by setting up and solving equations based on the given volume of the box and the relationship between its length and width.
Explanation:This problem can be tackled by using a bit of algebra and understanding volume calculations. We can use the equation for the volume of a box which is V=length*width*height. The problem gave us the volume of 1014 cu in. When a 3 in. square is cut from each corner of the rectangular piece of metal, the sides fold up to form the box, the height of the box becomes 3 in. This means we're missing the length and width of the box to solve for volume.
Since the length equals to twice the width minus 6 in., we can express the length as 2W - 6. Substituting these into the volume equation we get: 1014 = (2W - 6)(W)(3) which when simplified gives W, the width of the metal piece. Then substitute W into the length formula 2W - 6 to solve for the length.
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How to solve this question ? use appropriate metric prefix to write the following measurment without use exponents?
2.3x10^-10 L
4.7x10^-6 g
1.85x10^-12 m
16.7x10^6 s,
What is the slope of a line perpendicular to the line with equation y = 4x + 5?
The slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex].
What is a slope of a straight line?A straight line is a combination of endless points joined on both sides of the point.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope 'm' of any straight line is given by:
The given equation in the problem is;
y = 4x + 5
The slope of the given equation is found from the standard equation of the straight line as;
y=mx+c
On comparing, we get, m = 4.
The perpendicular line slopes are reciprocals with the negative sign of each other.
Hence, the slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex]
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The segment image is drawn from F(2, 9) to H(10, 1) with point G on the segment. What coordinates for point G will divide image so that is imageis 3:5?
The value of x must be greater than _____.
PLEASE HELP NOWWWWWWWW 20 POINTS PLEASE HELP
Using the transformation T: (x, y) (x + 2, y + 1). Find the distance named.
Find the distance CA (the answer must be in the square root form)
What is the value of h when the function is converted to vertex form?
Note: Vertex form is p(x)=a(x−h)^2+k .
p(x)=x^2−14x+29
H = ___
Does anyone know the answer?
easy math problem 5pts
If you are dealt 44 cards from a shuffled deck of 52 cards, find the probability of getting oneone queenqueen and threethree kingskings.
The sum of 555 consecutive integers is 505505505. What is the third number in this sequence?
Answer: The answer is 101!
Step-by-step explanation:
Call the first number in the sequence x
The next integer in the sequence is x + 1
The sum of the 5 consecutive integers is:
x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4) = 505
5x + 10= 505
5x = 495
x = 99
Since x is the first number, x + 2 is the third integer.
Thus, the third number in the sequence is 101
For which data representation is the median the better measure of center
Answer with explanation:
Mean is sum of all the observation divided by total number of observation, where as median is middlemost observation of the data set, while mode is most occurring variate or data value in the data set.
1. Variate or Data set which is represented in Histogram is
3,8,4,8,3
Arranging it in ascending order, we get
3,3,4,8,8
Data is skewed right.So, Mean >Median>Mode
Mean =5.2
Number of observation is 5. So,Median will be Middle term,that is third term equal to 4.
Mode =3 or ,8 which will be equal to 3,as data is skewed right.
→Mean gives better representation of data set,because, 5.2-3=2.2 and, 8-5.2=2.8
2. Variate or Data set which is represented through dots is
2, 2, 3,5,5
Arranging it in ascending order, we get
2,2,3,5,5
Data is skewed right.So, Mean >Median>Mode
Mean=3.4
Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.
Mode =2 or 5 which will be equal to 2,as data is skewed right.
→Mean gives better representation of data set,because, 3.4-2=1.4 and, 5-3.4=1.6
3. Variate or Data set which is represented in Histogram is
6,2,6,2,6
Arranging it in ascending order, we get
2,2,6,6,6
Data is skewed left.So, Mean <Median<Mode
Mean=4.4
Number of observation is 5. So,Median will be Middle term,that is third term equal to 6.
Mode =6
→Mode gives better representation of data set.
4.Variate or Data set which is represented through dots is
1,3,4,3,1
Arranging it in ascending order, we get
1,1,3,3,4
Data is skewed left.So, Mean <Median<Mode
Mean=2.4
Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.
Mode =1 or 3,data is skewed left,so mode =3
Here, in this data set, both mode and median are better measure of center than Mean,as there are two modes in the data set, so choosing median as measure of center,because data is skewed left,
For ,Option 4: Median is the better measure of center.
A waiter earned $69.81 on a shift, and then bought himself a discounted meal for $4.75. How much did he have left over, to the nearest dollar?
What is the graph of y = x - 3 (shown below) translated up 2 units?
Answer:
The graph is that one which corresponds to the equation y = x-1. The graph is shown in the image below.
Step-by-step explanation:
Translate a linear curve means to move the whole curve up or down, where the final line will be in parallel to the original curve.
For translate the graph up to 2 unit, it must to be summed 2 unit in the right member of the original equation:
[tex] y = (x-3) + 2 [/tex]
[tex] y = x-3 + 2 [/tex]
[tex] y = x-1 [/tex]
PLEASE HELP
Find the solution of this system of equations
-5x=-21+6y
-5x+y=-84