The answer is option C: B = 34.5°, C = 99.5°, c ≈ 27.1.
To solve the triangle, we can first use the law of sines to find angle B and angle C:
sin(B)/b = sin(A)/a
sin(B)/26 = sin(46)/33
sin(B) = (26/33)sin(46)
B ≈ 34.5°
Similarly,
sin(C)/c = sin(A)/a
sin(C)/c = sin(46)/33
sin(C) = (c/33)sin(46)
We can then use the fact that the angles in a triangle add up to 180° to solve for angle C:
C = 180 - A - B
C ≈ 99.5°
To find side c, we can use the law of cosines:
c^2 = a^2 + b^2 - 2abcos(C)
c^2 = 33^2 + 26^2 - 2(33)(26)cos(99.5)
c ≈ 27.1
Therefore, the answer is option C: B = 34.5°, C = 99.5°, c ≈ 27.1.
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Q base and height of a parallelogram 12 cm and 8 cm respectively find its area....
please give me fast answer.
Answer:
The area of a parallelogram is: 96 cm²
Step-by-step explanation:
Given
The base of a parallelogram b = 12 cmThe height of a parallelogram h = 8 cmTo determine
The area of a parallelogram A = ?
Using the formula to calculate the area of a parallelogram
A = bh
here
b is the base of a parallelogram h is the height of a parallelogramso substituting b = 12 and h = 8 in the equation
A = bh
A = 12×8
A = 96 cm²
Therefore, the area of a parallelogram is: 96 cm²
A rectangular pool at Andy's gym measures 25 meters by 50 meters. How many meters would Andy swim in order to swim diagonally across the pool?
Answer:
625 meters
Step-by-step explanation:
25 multiplied by 50 equals 1250 divided by 2 is 625 meters.
The equations f(x)=-2x+3
If (-5,n) is an ordered pair of the function rule, what is the value of n?
Answer:13
Step-by-step explanation:
one angle of a triangle measures 35°. A second angle measures (3x)°, and the third angle measures 2x - 20)°. what is the value of x?
Answer:
x = 33
Step-by-step explanation:
Sum of the angles in a triangle is 180 so,
35 + 3x + 2x - 20 = 180
35 + 5x - 20 = 180
15 + 5x = 180
5x = 180 - 15
x = 165/5
x = 33
Solve for p 7(p - 9) = -34.3
p=__?
Answer: p = 4.1
Step-by-step explanation:
Solve 4(5)^x= 500.
help please
Answer:
x=3
Step-by-step explanation:
Isolate x.
\(4(5)^x=500\) Divide both sides by four
\(5^x=125\) Take \(log_{5}\) of both sides. In other words, what power must you raise 5 to in order to get 125? (\(5^3=125\))
x=3
Graph the system of linear equations.
-1/2y=1/2x+ 5 and y = 2x + 2.
The solution to the system i
Answer:
Hi, the answer should be (-4,-6)
Step-by-step explanation:
A recipe for a cookie batch calls for 5/8 cup of flour. There are three and three-fourths cups of flour in a bag in the cupboard. How many batches of cookies can you make?
Answer:
So a batch is 5/8
There are THREE 3/4th cups of flour in the cupboard.
So 3 three fourths so basically
3/4 * 3 = 9/4 or
3/4 + 3/4 + 3/4 = 9/4
9/4 and each batch is 5/8.
9/4 ÷ 5/8 = 72/20 or 3 1/10
3 batches of cookies.
Find the Difference quotient f(x+h)-f(x)/h, where h does not equal zero for the function below f(x)=x^2-5 Simplify the answer as much as possible Thank you
Main Answer:The difference quotient for the function f(x) = x^2 - 5 is 2x + h.
Supporting Question and Answer:
How do we calculate the difference quotient for a given function?
To calculate the difference quotient for a function, we need to evaluate the expression (f(x + h) - f(x)) / h, where f(x) represents the given function and h is a non-zero value.
Body of the Solution:To find the difference quotient for the function f(x) = x^2 - 5, we need to evaluate the expression (f(x + h) - f(x)) / h.
First, let's find f(x + h):
f(x + h) = (x + h)^2 - 5
= x^2 + 2hx + h^2 - 5.
Now, let's subtract f(x) from f(x + h):
f(x + h) - f(x) = (x^2 + 2hx + h^2 - 5) - (x^2 - 5)
= x^2 + 2hx + h^2 - 5 - x^2 + 5
= 2hx + h^2.
Finally, divide the result by h: (f(x + h) - f(x)) / h = (2hx + h^2) / h = 2x + h.
Final Answer: So, the simplified difference quotient for the function f(x) = x^2 - 5 is 2x + h.
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The difference quotient for the function f(x) = x^2 - 5 is 2x + h.
How do we calculate the difference quotient for a given function?To calculate the difference quotient for a function, we need to evaluate the expression (f(x + h) - f(x)) / h, where f(x) represents the given function and h is a non-zero value.
To find the difference quotient for the function f(x) = x^2 - 5, we need to evaluate the expression (f(x + h) - f(x)) / h.
First, let's find f(x + h):
f(x + h) = (x + h)^2 - 5
= x^2 + 2hx + h^2 - 5.
Now, let's subtract f(x) from f(x + h):
f(x + h) - f(x) = (x^2 + 2hx + h^2 - 5) - (x^2 - 5)
= x^2 + 2hx + h^2 - 5 - x^2 + 5
= 2hx + h^2.
Finally, divide the result by h: (f(x + h) - f(x)) / h = (2hx + h^2) / h = 2x + h.
So, the simplified difference quotient for the function f(x) = x^2 - 5 is 2x + h.
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11. Which of the following lines is perpendicular to the line 3x-9y = 17?
A) 12x + y = 4
B) 9x - 3y = 11
C) 6x + 2y = 8
D) 3x - y = 5
Step-by-step explanation:
When using the equation of a line, one calculates the value of
y
in terms of
x
, say
y
=
m
x
+
c
, then
m
is the slope of the line and
c
is its intercept on
y
-axis.
As
3
x
−
9
y
=
15
can be written as
3
x
−
15
=
9
y
or
y
=
3
9
x
−
15
9
or
y
=
1
3
x
−
5
3
Hence slope of
3
x
−
9
y
=
15
is
1
3
Product of slopes of two perpendicular lines is
−
1
Hence, the slope of the line that is perpendicular to the line
3
x
−
9
y
=
15
is
−
1
1
3
=
−
1
×
3
1
=
−
3
graph{(3x-9y-15)(3x+y+5)=0 [-10, 10, -7.04, 2.96]}
what is the answer for this, I have to solve the proportion,
n/18 = 12/7.5
Answer:
n = 28.8
Step-by-step explanation:
\(\frac{n}{18} =\frac{12}{7.5}\)
n × 7.5 = 18 × 12
7.5n = 216
7.5n ÷ 7.5 = 216 ÷ 7.5
n = 28.8
Convert -145 degrees to radians.
Answer:
\(\frac{-29}{36}\)π
Step-by-step explanation:
Please help me. The first one is 301. Thank you
Answer:
Decreasing by 10
Step-by-step explanation:
I'm pretty sure it's decreasing by 10s, so 301, 291, 281, 271, 261, 251, 241, 231, 221, 211, 201, 191, 181, 171, 161, 151, 141, 131, 121, 111, 101, 91
HELPPPPP
This table models a linear function.
x −12 −8 −4 4
y 4 2 0 −4
Enter the coordinates of the y-intercept in the boxes.
Answer:
(0,-2) is the correct answer.
Step-by-step explanation:
consider an undirected graph that has 100 vertices. for any pair of vertices, only 1 edge can connect them. in other words, you cannot have 2 edges connecting vertex a directly to vertex b. also assume that there are no self-loops, i.e. an edge that goes from vertex a to vertex a. what is the maximum number of edges that can be in this specific graph?
So the maximum number of edges in an undirected graph with 100 vertices is 4950.
In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.
In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:
n * (n-1) / 2
Substituting n = 100, we get:
100 * 99 / 2 = 4950
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The Great Pyramid in Giza, Egypt is a square-based pyramid. It was constructed in 2056 BC out of lime stone. The length of one side of the base was 755 feet, it had a height of 481 feet and a slant height of 610 feet. About how much interior space did the Egyptians have to place the tombs and worship their beloved leaders?
Answer:
i think its 274,182,025 cubic feet
Step-by-step explanation:
.
a 17 feet ladder is placed against a building. the bottom of the ladder is sliding away from the building at a rate of 5 feet per second. find the rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building.
The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second
The length of the ladder = 17
Consider the length of the base as x and the height is h
The rate at which the ladder is sliding = 5 feet per second
dx/dt = 5
Apply the Pythagorean theorem
x^2 + h^2 = 17^2
h^2 = 289 - x^2
h = \(\sqrt{289-x^2}\)
The rate of change of height with respect to x is
dh/dx = - x / (289 - x^2)^(1/2)
dh/dt = dh/dx × dx/dt
Substitute the values in the equation
= - 15 / (289 - 15^2)^(1/2) × 5
= -15/8 × 5
= -75/8 feet per second
Therefore, the rate of change of height when x = 15 is -75/8 feet per second
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Calculate L4 for f(x) = 68 cos (x/3) over [3phi/4, 3phi/2 ]. L4=
The value of L4 for f(x) = 68cos(x/3) over [3π/4, 3π/2] is 0.
To find the value of L4, we first need to calculate the Fourier coefficients of the function f(x). Using the formula for the Fourier coefficients, we get: an = (2/π) ∫[3π/4,3π/2] 68cos(x/3)cos(nx) dx = (2/π) [68/3 sin((3π/2)n) - 68/3 sin((3π/4)n)]
bn = (2/π) ∫[3π/4,3π/2] 68cos(x/3)sin(nx) dx = 0 Since the function f(x) is even, all the bn coefficients are 0. Therefore, we only need to consider the an coefficients. Using the formula for L4, we get: L4 = (a0/2) + Σ[n=1 to ∞] (an cos(nπ/2))
Since a0 is 0 and all the bn coefficients are 0, the sum simplifies to: L4 = Σ[n=1 to ∞] (an cos(nπ/2)) = (2/π) [68/3 cos(3π/8) - 68/3 cos(3π/4) + 68/3 cos(5π/8)] = 0
Therefore, the value of L4 for f(x) = 68cos(x/3) over [3π/4, 3π/2] is 0.
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ABCD is a trapezium with AB parallel to CD. Find the value of x and the value of y.
Answer:
x = 107 , y = 60
Step-by-step explanation:
Each lower base angle is supplementary to the upper base angle on the same side, then
x + 73 = 180 ( subtract 73 from both sides )
x = 107
and
y + 2y = 180
3y = 180 ( divide both sides by 3 )
y = 60
.
How many point-slope equations can you write to represent a single line?
an infinite number of equations
5 equations
2 equations
1 equation
Only (d) 1 equation can you write to represent a single line using a point-slope equations
How to determine the number of equations?From the question, we have the following parameters that can be used in our computation:
Equation = Linear equation
A linear equation can only be represented with one equation
When it is represented with multiple equations, the equations are equivalent equations
This means that the equations can be converted to one another
Hence, the solution is (d) 1 equation
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Malcolm is driving 1,323 miles from witchita to charleston for a family reunion. He drives 443 miles for the first day and 409 miles the second day. Round each distance to the nearest ten and estimate about how many miles Malcom has left to drive
Answer:
470
Step-by-step explanation:
1323 rounds to 1320
443 rounds to 440
409 rounds to 410
1320 - (440 + 410) =
1320 - 850 =
470 <=== malcolm has about 470 miles left to go
List the first five terms of the sequence. an = [(?1)^n ? 1] / 5n
WHAT IS SEQUENCE?
A sequence is a list of numbers arranged in a specific order according to a rule or pattern. Each number in the sequence is called a term. The terms of a sequence can be finite (limited to a certain number of terms) or infinite (continuing indefinitely).
Sequences can be described by explicit formulas or recursive formulas.
The first five terms of the sequence are:
a1 = 0
a2 = 0
a3 = -2/15
a4 = 0
a5 = -2/25
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Solve the absolute value inequality
|2x + 6 |< 14
Answer:
Yamato's Here!
Step-by-step explanation:
− 10 < x < 4
Hope this helps! (-o- )/
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
\(16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)
Each lap around the park is 0.58 mile. Jessica walked 3.25 laps around the park. How many miles did Jessica walk around the park?
Answer:
5 miles but she did walk part of another mile so that would be 5.35.
Step-by-step explanation:
you can take 3.25 and subtract that by 0.58 until you can't do it anymore. Also I didn't know if you wanted the exact amount which would be 5.35 but total miles is only 5. Hope this helps!
the probability of tails of a weighted coin is 0.65. the number of tails is noted each of the 15 times the coin is tossed. if this procedure is repeated 100 times, what type of distribution is simulated?
Sampling distribution type distribution is simulated with the sample proportion with n = 15 and p = 0.65.
It is defined as a probability distribution of a statistic that is from a larger number of samples from a specific population.
We are given that
The probability of tails of a weighted coin, p=0.65 and n=15
We have to find the type of distribution that is simulated if this procedure is repeated 100 times.
The random variable is a proportion of a number of tails therefore, the type of distribution is the sampling distribution of the sample proportion.
Probability is something that is to happen.
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What is this answer?
Answer:
qljffIWN.LWJHABF,NCUKGKQW,DN
Step-by-step explanation:
;F.wrkfhuawlfmslfihbsfjvnsdcjhkugcv sd
Answer:
You don't have an answer up there, so I don't know what I'm supposed to answer for you
round 9.725 to 2 decimal places
Answer:
9.73
explanation:
9.725 = 9.73 rounded to nearest 2 decimal places.
two decimal places should be in two decimals example: 2.63, 8.14
Answer:
\(\huge\boxed{\sf{9.73}}\)
Step-by-step explanation:
Hello.
Remember the Rounding Rules:
If the number you are rounding is followed by a number less than 5, you round down.
If the number you are rounding is followed by a number greater than or equal to 5, you round up.
Let's check our number.
9.725
We have 3 decimal places, and we need to round to 2.
The 2nd decimal place is followed by 5, therefore, we round up:
9.725 => 9.73
And we're done!
I hope it helps & have an outstanding day!
\(\boxed{imperturbability}\)
parallelogram ABCD with vertices A(6,8) B(10,9) C(9,3) and D(5,2): 90 counterclockwise rotation about P(4,1)
A ( , )
B ( , )
C ( , )
D ( , )
Answer:
A(-3 , 3) B(-4 , 7) C(2 , 6) D(3 , 2)
Step-by-step explanation:
Rotation of the parallelogram about the point P(4, 1), is done by taking
point P as the origin, and using relative coordinates for the rotation.
\(\underline{A(-3, \, 3)}\)\(\underline{B(-4, \, 7)}\)\(\underline{C(2, \, 6)}\)\(\underline{D(3, \, 2)}\)Reasons:
The given parameters are;
Vertices of the parallelogram ABCD are;
A(6, 8), B(10, 9), C(9, 3) and D(5, 2)
Point about the parallelogram is rotated = P(4, 1)
Angle of rotation = 90°
Direction of rotation = Counterclockwise
90° rotation counterclockwise of (x, y) about the origin gives → (-y, x)
Therefore, we have;
The given points relative to the point P are;
A'(6-4, 8 - 1) = A'(2, 7)
B'(10 - 4, 9 - 1) = B'(6, 8)
C'(9 - 4, 3 - 1) = C'(5, 2)
D'(5 - 4, 2 - 1) = D'(1, 1)
Therefore, we get;
A'(2, 7) \(\underrightarrow {R_{180^{\circ}}}\) A''(-7, 2)
B'(6, 8) \(\underrightarrow {R_{180^{\circ}}}\) B''(-8, 6)
C'(5, 2) \(\underrightarrow {R_{180^{\circ}}}\) C''(-2, 5)
D'(1, 1) \(\underrightarrow {R_{180^{\circ}}}\) D''(-1, 1)
Which then gives;
The image location are;
A(-7 + 4, 2 + 1) = A(-3, 3)
B''(-8 + 4, 6 + 1) = B(-4, 7)
C''(-2 + 4, 5 + 1) = C(2, 6)
D''(-1 + 4, 1 + 1) = D(3, 2)
Therefore, we have;
A(-3, 3), B(-4, 7), C(2, 6), and D(3, 2)
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Abrianna sold 20, 23, 18, 4, 17, 21, 15, and 56 boxes of cookies after different football games. Which data value(s) are outliers? Select all that apply.
The data value that is an outlier in the data for boxes of cookies is: E. 56.
How to Determine Outliers in a Data?The simple rule is that values lower than Q1 - 1.5 × IQR and values greater than Q3 + 1.5 × IQR are outliers of a data distribution.
Given the data, 20, 23, 18, 4, 17, 21, 15, 56, find the Q1, Q3, and IQR of the data distribution:
First Quartile (Q1) = 15.5
Third Quartile (Q3) = 22.5
Interquartile Range (IQR) = 22.5 - 15.5 = 7
Q1 - 1.5 × IQR = 15.5 - 1.5 × 7 = 5
Q3 + 1.5 × IQR = 33
None of the values are lower than 5.
However, the only value that is greater than 33 is 56.
The outlier in the data is: E. 56.
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