The measure of three angles of triangle are 45°, 55° and 80°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Let the smallest angle of triangle be x.
One angle the triangle measures 10° greater the smallest angle, that is x+10°
The third angle measures 10° less than twice the smallest angle.
The third angle is 2x-10°
Now, x+2x-10°x+10°=180°
⇒ 4x=180°
⇒ x=45°
So, 2x-10°=80° and x+10°=55°
Therefore, the measure of three angles of triangle are 45°, 55° and 80°.
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This exercise demonstrates a connection between the curl vector and rotations. Let B be a rigid body rotating about the z-axis. The rotation can be described by the vector w = ωk, where ω is the angular speed of B, that is, the tangential speed of any point P in B divided by the distance d from the axis of rotation. Let r = ⟨x, y, z⟩ be the position vector of P.(a) By considering the angle θ in the figure, show that the velocity field of B is given by v = w × r.(b) Show that v = −ω y i + ω x j.(c) Show that curl v = 2w.
The relation between curl vector and rotations is v = wdj
What is curl vector?A vector field is a vector field's curl. The tendency of particles at point P to spin about the axis that faces the direction of the curl at P is measured by the curl of a vector field at P. If and only if its curl is zero, a vector field with a simply linked domain is considered conservative.
Let v represent the particle's velocity as a vector.
vector v=ui+vj+wk
curl v =
curl v = [tex]\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\u&v&w\end{array}\right][/tex]
= (dw/dy - dv/dz )i - (dw/dx - du/dz)j + (dv/dx - du/dy )k
Now by comparing with rotational matrix ,
We know that w = rotational matrix
[tex]w_{x}[/tex] = 1/2 (dw/dy - dv/dz )
[tex]w_{y}[/tex] = 1/2 (dw/dx - du/dz)
[tex]w_{z}[/tex] = 1/2 (dv/dx - du/dy )
w = [tex]w_{x} i +w_{y} j + w_{z} k[/tex]
w = 1/2[ (dw/dy - dv/dz )i + (dw/dx - du/dz)j + (dv/dx - du/dy )k]
w = 1/2 curl v , rotation = 1/2 curl v
let B be a rigid rotating about z axis
w = w.k
tangential speed =wk *di
v = wdj
curl of v= [tex]\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\0&w_{x} &0\end{array}\right][/tex]
v = wdj ,
The relation between curl vector and rotations is v = wdj
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If cos(x)=11/20 and x is in quadrant I, what is sin(2x)
Answer:
[tex]\frac{33\sqrt{31}}{200}[/tex]
Step-by-step explanation:
[tex]\cos x=\frac{11}{20} \implies \sin x=\sqrt{1-(11/20)^2}=\frac{3\sqrt{31}}{20} \\ \\ \sin 2x=2\sin x \cos x =2 \cdot \frac{3\sqrt{31}}{20} \cdot \frac{11}{20} =\frac{33\sqrt{31}}{200}[/tex]
Substitute 6 for x and evaluate the expression below.
|x + 10 - X
Answer: 16-x
Step-by-step explanation:
Collect like terms.
-x + (6 + 10)
Simplify.
16 - x
From my calculations using the Cymath calculator, 16 - x would be the answer, Hope I could help.
The area of the rectangle shown below is 24 square centimeters.
What is the area, in square centimeters, of the shaded triangle?
Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week.
Part A: Set up a system of equations to show how many rocks each has in their collection. You must write two equations for this. (2 points)
Part B: After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Write out the equation used and show all work. (1 point)
Part C: How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? Show work on how this is found. (1 point)
pls help
Part A:
We can set up a system of equations to represent the number of rocks in each person's collection. Let "S" be the number of rocks in Samuel's collection and "L" be the number of rocks in Lewis's collection. We can represent the situation as follows:
Equation 1: S = 18 + 4t
Equation 2: L = 30 + 3t
Here, "t" represents the number of weeks that have passed.
Part B:
To find out how many weeks it will take for Samuel and Lewis to have the same number of rocks in their collections, we need to set Equation 1 equal to Equation 2 and solve for "t". This gives us the following:
S = L
18 + 4t = 30 + 3t
1t = 12
t = 12 weeks
It will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
Part C:
To find out how many rocks Samuel and Lewis will have when the amount of rocks in their collection is equal, we can substitute the value of "t" that we found in Part B into either Equation 1 or Equation 2. For example, substituting "t = 12" into Equation 1 gives us the following:
S = 18 + 4(12)
S = 18 + 48
S = 66 rocks
Therefore, when the amount of rocks in their collection is equal, Samuel and Lewis will have 66 rocks each.
The number of bacteria in a sample is increasing according to an exponential model. After 2 hours, the sample contained 200 bacteria; and after 6 hours, the sample contained 800 bacteria. Write an exponential growth model for the number of bacteria in the sample after x hours.
[tex]P(x)=100_{e}({4}/{ln4} )x[/tex]
what is bacteria?
Microbes known as bacteria have simpler cell structures than many other types of creatures. One DNA loop serves as their command centre and houses all of their genetic data. Instead of a nucleus, some bacteria contain an additional ring of genetic material called a plasmid. Genes that offer the bacterium a competitive edge over other bacteria are frequently found on the plasmid.
There are a few options for doing this. A set of equations may be used.
Use the equation P = a*bx, where x is the number of hours and P represents the population of bacteria.
A and B are two unknowns.
We will enter form points to solve (x, P)
A point equals (2, 200). (after 2 hours, the population is 200)
Consequently, a formula is 200 = [tex]a*b^{2}[/tex]
Second, there is (6, 800).
A second equation is thus 800 = [tex]a*b^{6}[/tex]
We'll repeat the equations in writing:
800 = [tex]a*b^{6}[/tex]
200 = [tex]a*b^{2}[/tex]
These two equations can be divided.
When we divide the equations, we obtain 800/200 = 4 on the left.
When we split on the right side,the equations, we get [tex]a*b6 / (a*b2) = b4[/tex]
Therefore, [tex]4 = b^{4}[/tex]
Solve for b:
b = [tex]\sqrt[4]{4}[/tex]
Next, solve for a, by plugging in b into the second equation
[tex]200 = a * (\sqrt[4]{4})^{2} = a * \sqrt{4} = a * 2[/tex]
Therefore, dividing both sides by 2, gives us that a = 100
Lastly, write out the equation with the known values of a and b.
[tex]P(x)=100_{e}({4}/{ln4} )x[/tex]
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convert the ratio 4:15 into percentage
Answer:
26.7%
Step-by-step explanation:
PercentagePercentages are values in terms of values divided by 100.
Eg.
[tex] \frac{34}{100} = 34percent [/tex]
SolutionTo solve this question, we have to make sure the denominator is 100.
4 : 15
[tex] = \frac{4}{15} \\ = \frac{4 \\ \times 10}{15 \times 10} \\ = \frac{40 \div 1.5}{150 \div 1.5} \\ = \frac{26.667}{100} [/tex]
Therefore the percentage is 26.7%. (3 Significant Figures)
HELP PLS ASAPPPPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: C; 5.32
Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!
Michael had 20 minutes to do a three-problem quiz. He spent 11 9/10
minutes on questions A and 4 3/4 minutes on question B. How much time did he have left for question C?
Gavin has 6 9/20 minutes to solve the 3rd problem.
Find the solution ?An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters. A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.Add the time for the first two problems:
9 3/4 + 3 4/5
To add fractions rewrite them so they have a common denominator:
3/4 = 15/20
4/5 = 16/20
Now you have:
9 15/20 + 3 16/20 = 12 31/20 = 13 11/20 minutes.
Now subtract that from the time allowed:
20 - 13 11/20 = 6 9/20 minutes.
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PLEASE I NEED NOW TO FINISH
a) 16 or 2/5 ratio of blue marbles not chosen
b) 86 total no. of marbles was there before the game
c) 24 blue marbles were picked
Explanation:
a) total no of blue marbles = 40
ratio of chosen blue marbles = 3/5
blue marbles picked = 40 × 3/5 = 24
blue marbles not picked = 40-24 = 16
b) total no of blue marbles + total no of red marbles = 40+ 46
total no. of marbles was there before the game = 86
c) explained in a)
What is a Ratio?
A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division.
A survey of 20 respondents revealed that 13 of them preferred cake to ice cream and 7 preferred ice cream to cake. This data set can be represented as the ratio 13:7, where 13 is the antecedent and 7 is the consequent.
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Find the perimeter of a triangle with sides of 4, 6, and 8 feet.
16 feet
9 feet
18 feet
192 feet
The perimeter of the triangle is 18 feet.
What is a Triangle?Polygon which has three sides and three vertices is called as triangle.
Sum of all the angles of the triangle is 180°.
Given the sides of the triangle are 4 feet , 6 feet and 8 feet.
And the perimeter of the triangle
= sum of all three side of the triangle.
The perimeter of the triangle = 4 + 6 + 8
perimeter of the triangle = 18 feet
Therefore, the perimeter of the triangle is 18 feet.
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Can you please help me solve this #2
is that algebra?
If not it is [tex]2 < 2x < 6[/tex]
so 2 is smaller Then then 2x with is most likely a decimal I could be a decimal are you working on decimals?
I can't give a great answer as i might mix thing up Also what grade are you in?
free brainiest
Solve for x.
3.4>x+2/3
Answer:
x < 2 11/15
Step-by-step explanation:
Hope this helps!
11.) What is the algebraic representation for a translation of 5 units right and 4 units up?
Algebraic representation:
[tex]\frac{4}{5}[/tex]
7m + 29 = 2m + 9 ( please show work toooooo )
Answer:
m = -4
Step-by-step explanation:
7m + 29 = 2m + 9
-2m -2m
--------------------------
5m + 29 = 9
-29 -29
-----------------------
5m = -20
÷5 ÷5
--------------------
m = -4
I hope this helps!
To set a depth record, a submersible vehicle must reach a water depth less than -715 feet. A vehicle breaks the record by
more than 10 feet. Write and graph an inequality that represents the possible depths d reached by the vehicle.
The inequality that represents the possible depths d reached by the vehicle is d < -725.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Depth record = less than -715 feet.
This means,
The depth must be -716 or less.
The vehicle breaks the depth record by more than 10 feet.
This means,
-715 - 10 = -725
The depth record must be less than -725
Thus,
The possible depths d reached by the vehicle is d < -725.
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50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!
Identify the transformation that moves quadrilateral ABCD to A'B'C'D'.
Answer:
C - Reflect over the x-axis
Step-by-step explanation:
This is a reflection over the x-axis.
To remember the difference between reflectinon over the x-axis and reflectino over the y-axis, memorize this.
If you reflect over the x-axis, the x value of the reflected point stays the same. (only the y is multiplied by -1)
If you reflect over the y-axis, the y value of the reflected point stays the same. (only the x is multiplied by -1)
Roation about the origin involves multiplying both x and y by -1. (x and y change)
Use the given information to write and solve a system of linear equations to find the values of x and y. ΔLMN ≅ ΔPQR, m∠L = 40°, m∠M = 90°, m∠P = (17x - y)°, m∠R = (2x + 4y)°
Answer:
Step-by-step explanation:
Given that,
m∠L = 40°, m∠M = 90°
Since ΔLMN ≅ ΔPQR
(17x - y)° = 40°
(2x + 4y)° = 50°
Since, the sum of three angles of a triangle is 180 degrees.
Then, m∠R = 1800 – 400 – 900 = 500
Remove degree from both side
17x – y = 40
2x + 4y = 50
Solving these two equations then,
x = 3, y = 11
The value of x and y would be x = 3 and y = 11.
What are congruent triangles?
Congruent triangles are triangles that have the same size and shape. In other words, congruent triangles are identical in all respects.
Given Data:
ΔLMN ≅ ΔPQR, m∠L = 40°, m∠M = 90°, m∠P = (17x - y)°, m∠R = (2x + 4y)°
as m∠L = m∠P
17x - y = 40 ----------(I)
we know that,
m∠L + m∠M + m∠N = 180
40 + 90 + m∠N = 180
m∠N = 50
As m∠N = m∠R
2x + 4y = 50 -------(II)
Solving (I) and (II), we get
x=3, y=11
Hence, the value of x and y would be x = 3 and y = 11.
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Subtract the rational expressions: a+1 / 2a + 3/a^2
Please Help within the hour !!
It wont let me copy the answers so please do the math?... Thank You
The simplification of the given expression is (a² + a + 1)/a².
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is a+1/2a + 3/a².
It can be evaluated as follows,
a+1/2a + 3/a²
Take the LCM of a and a² as a².
= (a(a + 1)+ 3)/a²
= (a² + a + 1)/a²
Hence, the given expression can be simplified to obtain (a² + a + 1)/a².
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50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! PLEASE HELP
A.
36°
B.
55°
C.
89°
D.
91°
Answer:
180 - (54 + 35) = 91
The answer is 'D'
solve the system of equations using elimination: -3x-4y=-54 and x+y=15.
Answer:
the solution of the system is x = 18/5 and y = 27/5.
Step-by-step explanation:
To solve a system of equations using elimination, we can add or subtract the equations to eliminate one of the variables. In this case, we can add the given equations to eliminate the x-variable:
(-3x - 4y) + (x + y) = -54 + 15
-2x - 3y = -39
Dividing both sides by -3, we get:
(2/3)x + (1/3)y = 13/3
This equation tells us that x is equal to 2/3 times the value of y. Substituting this expression for x in one of the original equations, we can solve for y:
-3(2/3)y - 4y = -54
This simplifies to:
(-6/3)y - 4y = -54
Combining like terms, we get:
(-10/3)y = -54
Dividing both sides by -10/3, we get:
y = 27/5
Substituting this value for y in the expression for x, we get:
x = (2/3)(27/5) = 18/5
Therefore, the solution of the system is x = 18/5 and y = 27/5.
Answer: x=6, y=9
(6,9)
Step-by-step explanation:
Multiply x+y=15 by 3 to eliminate x
3(x+y)=15(-3)
3x+3y=45
-3x-4y=-54
-1y=-9
y=9
sub in 9 to y to get x
x+9=15
x=6
help please and thank you
Answer:
1) 9x
2) 3b
3) 3m
4) 5a
5) 7x
6) 3a + 5b
7) 9x - 4
8) 2b + m
9) 13a + b + 6c
10) 9b + 1
11) 7p
12) 2a + b -10
Step-by-step explanation:
1. An animal shelter houses
only dogs
and cats. The ratio of cats to dogs at
the shelter is 11:9. What is the ratio
of the number of dogs to the total
number of animals at the shelter?
Answer:
Step-by-step explanation:
45 out of 100
NEED ASAP PLEASE!
A company is interested to know the variation in yearly sales amount for all 5 salespeople in the company.
The dataset shown below is the sales amount sold by the 5 salespeople in the company (expressed in thousands of dollars):
40,60,65,70,80
Find the variance for this dataset.
The variance in the sample data is 220
We are given the following data of 5 salespeople (expressed in thousands of dollars); 40, 60, 65, 70, 80
How is standard deviation calculated?Suppose that the considered data set is
Then, its standard deviation is the positive square root of the variance of this data set. Variance of data set is the sum of squared differences of the data values from its mean to the total count of data values.
Thus, we get:
[tex]\sigma = \sqrt{\dfrac{1}{n} \sum_{i=1}^{n} (x_i-\overline{x})^2[/tex]
In the formula above, x represents the mean of the data points, x is the value of an individual data point, and N is the total number of data points.
x = (40+60+65+70+80)/5
x=63
So, the mean of the sample data is 63
Variance =
[tex]\sigma^2 = \dfrac{\sum_{\forall x_i} (x_i - \overline{x})^2}{n}[/tex]
Therefore, the variance is 220
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Use the image to answer the question. A vertical number line starting at negative 10 on the bottom of the line with tick marks every one unit up to positive 10 at the top. The point negative 4.5 is labeled. What does the absolute value of the point labeled in the image mean if the number line represents temperature change? There was no change in temperature. The temperature equals 4.5 degrees. The temperature decreased 4.5 degrees. The temperature increased 4.5 degrees. HURRY UP
Since the point negative 4.5 (-4.5) is labeled on this number line representing temperature change, the absolute value of the point labeled in the image means that: B. the temperature equals 4.5 degrees.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In conclusion, the absolute value of a number is always positive and it can be used for describing the distance of a number from zero (0) on the number line, without taking its direction into consideration.
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Consider the proportions m/n=1/2 and n/k =2/5. What is the ratio m/k?EXPLAIN YOUR REASONING WITH ALL STEPS
Answer:
To find the ratio m/k, we need to combine the proportions m/n and n/k. One way to do this is to multiply the fractions to get the product m/k. This can be done by multiplying the numerators to get m, then multiplying the denominators to get k.
For example, if we let m=1, n=2, and k=5, then we have the following:
m/n = 1/2
n/k = 2/5
If we multiply the numerators and denominators to get the product m/k, we get:
(1 * 2) / (2 * 5) = 2/10 = 1/5
Therefore, the ratio m/k is 1/5.
Another way to find the ratio m/k is to use the fact that proportions are equivalent to equations. We can set up an equation using the given proportions, then solve for m/k.
For example, using the same values as before, we have:
m/n = 1/2
n/k = 2/5
We can set up an equation by setting the two proportions equal to each other:
m/n = (1/2) = n/k = (2/5)
Then we can cross-multiply to solve for m/k:
m/n * n/k = (1/2) * (2/5)
(m * 2) / (n * 5) = 1/5
m/k = (2/5) = 1/5
Therefore, in this case, the ratio m/k is also 1/5.
In general, to find the ratio m/k given the proportions m/n and n/k, we can either multiply the fractions or set up and solve an equation using the given proportions.
Solve for X please and thanks
Answer:
8.857142857
Step-by-step explanation:
10÷what equals 67.50
Answer:
0.15
Step-by-step explanation:
10/x=67.50
10=x*67.5
10/67.5 = x
x=0.14814814814
Given the following table of values of the polynomial f(x), what is the minimum number of zeros of f(x) that are guaranteed to exist by the Intermediate Value Theorem?
The number of zeros of f(x) that are guaranteed to exist by the Intermediate Value Theorem is given as follows:
0.
What is the Intermediate Value Theorem?The intermediate value theorem defines that if a continuous function passes in two points, it will pass through all the points between these two values.
The zeros of a function are all the values of x for which the function assumes a value of zero.
Hence, if for a value of x = a the function is positive, and then for a value of x = b > a the function is negative, or vice versa, a zero is guaranteed to exist in the interval between a and b.
In this problem, the function does not assume any negative values, hence a zero is not guaranteed to exist in the function, and the number is of zero.
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Farmer Smith has 160 feet of fencing that she is using to make a rectangular enclosure for her chickens. She will use the side of an existing chicken coop as one side of the enclosure and use the fencing for the other three sides.
Which function gives the area A, in square feet, as a function of the length of one of the sides perpendicular to the existing coop
Answer:
C
Step-by-step explanation: