The measure of angle A is 20 degrees, the measure of angle B is 65 degrees, and the measure of angle C is 95 degrees.
To find the measure of the angles in triangle ABC, we first need to determine the total ratio of measures.
The total ratio is 4 + 13 + 19 = 36.
Next, we can use the ratios to find the measure of each angle.
Let x be the measure of the smallest angle in triangle ABC.
Then the measures of the angles are:
Angle A = 4x
Angle B = 13x
Angle C = 19x
We know that the sum of the angles in a triangle is 180 degrees, so we can set up the equation:
4x + 13x + 19x = 180
Simplifying, we get:
36x = 180
Dividing both sides by 36, we get:
x = 5
Therefore, the measures of the angles in triangle ABC are:
Angle A = 4x = 4(5) = 20 degrees
Angle B = 13x = 13(5) = 65 degrees
Angle C = 19x = 19(5) = 95 degrees
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If A is a 9x6 matrix, what is the largest possible dimension of the row space of A? If A is a 6x9 matrix, what is the largest possible dimension of the row space of A? Explain.
If A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6. If the rank of A is less than 6, then the dimension of the row space will be less than 6.
The row space of a matrix is the span of its row vectors. Therefore, the dimension of the row space is equal to the number of linearly independent rows of the matrix.
For a 9x6 matrix A, the largest possible dimension of the row space is 6. This is because there can be at most 6 linearly independent rows in a 9x6 matrix. If there were more than 6 linearly independent rows, then the matrix would have rank greater than 6, which is impossible since the maximum rank of a 9x6 matrix is 6.
For a 6x9 matrix A, the largest possible dimension of the row space is also 6. This is because the number of linearly independent rows cannot exceed the number of columns in the matrix.
Therefore, if A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6.
However, if the rank of A is less than 6, then the dimension of the row space will be less than 6.
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can someone help me with this i'm really confused heh... i'll give you a 5 star rating and brainliest answer!
A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y. Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season. Which system represents this scenario? x + y = 500. 215 x + 615 y = 187,500 x minus y = 500. 215 x minus 615 y = 187,500 500 x + 500 y = 187,500. 215 x = 615 y 500 x = 500 y. 215 x + 615 y = 187,500
Answer:
x + y = 500
215x + 615y = 187,500
Step-by-step explanation:
The first equation can show the amount of land. The farmer has 500 acres to plant corn, x, and cotton, y.
x + y = 500
The second equation can show the cost. The farmer has $187,500 to invest when corn costs $215 per acre and cotton costs $615 per acre.
215x + 615y = 187,500
The system of equations is
x + y = 500
215x + 615y = 187,500
The correct system of represents this scenario will be,
⇒ x + y = 500
⇒ 215x + 615y = 187,500
Where,' x' is plant acres of corn and 'y' is acres of cotton.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.
And, Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season.
Now,
Let us take 'x' is plant acres of corn and 'y' is acres of cotton.
Since, A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.
So, we can formulate;
⇒ x + y = 500
And, He has $187,500 to invest this season for corn costs $215 per acre to produce, and cotton costs $615 per acre to produce.
So, We can formulate;
⇒ 215x + 615y = 187,500
Thus, The correct system of represents this scenario will be,
⇒ x + y = 500
⇒ 215x + 615y = 187,500
Where,' x' is plant acres of corn and 'y' is acres of cotton.
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Please see the image below(math)
Answer:
21
Step-by-step explanation:
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
AD AH
----- = ---------
AB AH +y
3 9
---- = ------
10 9+y
Using cross products:
3(9+y) = 9*10
27+3y = 90
3y = 90-27
3y =63
y = 63/3
y = 21
Answer:
y = 21
Step-by-step explanation:
According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.
Therefore, according to the Side Splitter Theorem:
\(\boxed{\sf AD : DB = AH : HC}\)
From inspection of the given triangle, the lengths of the line segments are:
AD = 3DB = 7AH = 9HC = yTo find the value of y, substitute the given line segment lengths into the proportion and solve for y:
\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)
Therefore, the value of y is 21.
what is the sum of 7, -6, and 7
the answer is 8 bro cuz yk
Answer:
8
Step-by-step explanation:
7 + (-6) + 7 = 8
because + - = -
Simplify the expression to a polynomial in standard form: (x + 1) (2x^2 - 3x - 7)
Answer:
2x^3-x^2-10x-7
Step-by-step explanation:
Distribute x to 2x^2, 3x, and -7
Then, distribute 1 to 2x^2, 3x, and -7
Hope this helps.
:)
You have an annual salary of $85,063. Your monthly expenses include a $1,555 mortgage payment, a $274 car lease payment, $139 in minimum credit card payments, and a $179 payment on your student loan. Calculate your DTI (debt-to-income) ratio as a PERCENTAGE
Answer:
DTI ratio in percentage = 30.29%
Step-by-step explanation:
Annual salary = $85,063
This means that gross monthly pay = 85063/12 = $7088.58
Now,
Total monthly debt payments = 1555 + 274 + 139 + 179 = $2147
Debt to income ratio = (2147/7088.58) × 100% = 30.29%
PLease Help me for a brainlist its a math problem please see image attached thanks
Answer:
b
Step-by-step explanation:
the answer is b if values are plugged in to function
Answer:
y = -(x - 2)² - 4
Step-by-step explanation:
The vertex of this function is (2, -4), which is given in the tableThe vertex form an equation is given as :
y = a(x - h)² + kSubstitute the vertexy = a(x - 2)² - 4Substitute any point in the table to find a :
-8 = a(0 - 2)² - 44a = -4a = -1Hence, the final equation :
y = -(x - 2)² - 4Option 2select all expressions equivalent
A and D are points on a polygon. A' and D' are the points under a
translation. Find D'.
A(-2,11)
A’(8,22)
D(-10,9)
Answer:
D' is (16,20)
Step-by-step explanation:
A translation is the movement of the graphed line, either vertically or horizontally. The two given points are A and D:
A (2,11)
D (10,9)
When the line is translated, point A becomes A' (8,22).
Pint A is moved to the right by 6, and up by 11. Lets do the same for point D to make it D'
D' = (10+6, 9+11)
D' = (16,20)
See the attached graph.
Numbered disks are placed in a box and one disk is selected at random. If there are 4 red disks numbered 1 through 4, and 6 yellow disks numbered 5 through 10, find the probability of selecting a red disk, given that an odd-numbered disk is selected.
The probability of selecting a red disk, given that an odd-numbered disk is selected, is 1/5.
If an odd-numbered disk is selected, it can only be one of the following: 1, 3, 5, 7, 9. Out of these, only one is a red disk, which is numbered 1.
Therefore, if we know that an odd-numbered disk is selected, the probability of selecting a red disk is simply the probability of selecting the red disk numbered 1, which is:
P(Red disk | Odd-numbered disk) = P(Red disk and Odd-numbered disk) / P(Odd-numbered disk)
We can calculate the denominator of this expression by noting that there are 5 odd-numbered disks in total, out of a total of 10 disks:
P(Odd-numbered disk) = 5/10 = 1/2
To calculate the numerator, we note that there is only one odd-numbered red disk, which is disk number 1:
P(Red disk and Odd-numbered disk) = 1/10
Therefore, we can substitute these values into the expression for conditional probability:
P(Red disk | Odd-numbered disk) = (1/10) / (1/2) = 1/5
Therefore, the probability of selecting a red disk, given that an odd-numbered disk is selected, is 1/5.
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Find the quotient.
514÷67
Answer: 7.6716
explanation:
which expressions represents 15 more than the product 6 and 8
Please i need help
Answer:
x-15 = 48
or
x= 15 + (6*8)
Step-by-step explanation:
Pls vote as brainliest
Hi,
The correct answer is x=15 + (6x8)
A laundry basket has 24 T-shirts In it 4 are navy 12 are red and the remaining or white.What is the probability of selecting green shirt?
Answer:
0%
Step-by-step explanation:
There are 4 navy shirts.
There are 12 red shirts.
The rest are white.
That means there isn't any green shirts.
Define T in L(C2) by T(w,z)=(−z,w).
Find the generalized eigenspaces corresponding to the distinct eigenvalues of T.
I believe that once I have the eigenvalues, I know how to find the eigenspaces, but I'm not sure I'm looking for the eigenvalues correctly.
I know that if the eigenvalues are a,b corresponding to (w,0) and (0,z) respectively, then (ab)=1, since a(w)=−z implies ab(−z)=−z. But I think my whole approach to this is wrong and that I'm missing some very elementary idea.
T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).
To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.
For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).
As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).
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The diameter of a circle is 12.8 meters. What is the circle's circumference?
Answer:
40.21 m is the circle's cirumference.
What is the solution (ordered pair) for the graph?
Answer:
(-1,3)
Step-by-step explanation:
We have to find where the two line intercept
the glass pictured to the left can hold a maximum volume of 473473473 cubic centimeters, which is approximately 161616 fluid ounces. question 9 of 38 report what is the value of kkk, in centimeters?
As per the volume of cylinder, the value of k is 3.06 centimeters.
Volume of cylinder:
According to geometry, the volume of a cylinder is defined as the capacity of the cylinder, which helps to find the amount of material that the cylinder can hold.
Given,
Here the glass pictured to the left can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces.
Here we need to find the value of k, in centimeters.
While we looking into the given question we have identified that the value of the following,
Volume of the glass = 473 cubic centimeter
Height of the glass = 16 fluid ounces.
Radius of the glass = k
Then the value of k is calculated by using the volume of cylinder formula,
=> V = πr²h
Here we have to apply the values on the formula, then we get,
=> 473 = π x k² x 16
Apply the value of π = 3.14,
=> 473 = 3.14 x k² x 16
=> k² = 9.41
=> k = 3.06
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In a month, Caleb can produce a maximum of either 30 bushels of pears or 15 bushels of apples, or any linear combination in between. Similarly, Donna can produce a maximum of either 24 bushels of pears or 6 bushels of apples, or any linear combination in between. 1st attempt Part 1 (2 points) What is the opportunity cost for Caleb to produce one more bushel of apples in terms of pears
The opportunity cost for Caleb to produce one more bushel of apples in terms of pears is 2 bushels of pears.
To determine the opportunity cost for Caleb, we need to compare the trade-off between producing apples and pears. The given information states that Caleb can produce a maximum of 30 bushels of pears or 15 bushels of apples in a month.
We can calculate the opportunity cost by dividing the change in the quantity of pears by the change in the quantity of apples. In this case, if Caleb produces one more bushel of apples, he would have to give up producing pears. Therefore, the opportunity cost can be calculated as follows:
Opportunity Cost = Change in Pears / Change in Apples
Opportunity Cost = 30 bushels - 0 bushels / 15 bushels - 0 bushels
Opportunity Cost = 30 bushels / 15 bushels
Opportunity Cost = 2 bushels of pears per bushel of apples
The opportunity cost for Caleb to produce one more bushel of apples in terms of pears is 2 bushels of pears. This means that if Caleb decides to produce one additional bushel of apples, he would have to give up producing 2 bushels of pears.
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what is the solution of the system if equations 7x + 12y = 13
Answer:
7x+12y-13=0
Step-by-step explanation:
A circle is circumscribed around a regular octagon with side lemgths of 10 feet. Another circle is inscribed inside the octagon. Find the area. Of the ring created by the two circles. Round the respective radii of the circles to two decimals before calculating the area
The area of the ring is 1,462.81 square feet, under the condition that a circle is circumscribed around a regular octagon with side lengths of 10 feet.
The area of the ring formed by the two circles can be evaluated using the formula for the area of a ring which is
Area of ring = π(R² - r²)
Here
R = radius of the larger circle
r = smaller circle radius
The radius of the larger circle is equal to half the diagonal of the octagon which is 10 feet. Applying Pythagoras theorem, we can evaluate that the length of one side of the octagon is 10/√2 feet.
Radius of the larger circle is
R = 5(10/√2)
= 25√2/2 feet
≈ 17.68 feet
Staging these values into the formula for the area of a ring,
Area of ring = π(17.68² - 10²) square feet
Area of ring ≈ 1,462.81 square feet
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Davis saved $1000 and then found a savings account that will give him 10% interest per year.
Represent the money in his account after n years.
1) Arithmetic or Geometric:
2) Common difference/ratio:
3) Recursive Formula:
4) Explicit Formula:
Answer:
1000x0.1=n
Step-by-step explanation:
first year he had 1000
second year they times the 1000 by .1 because thats ten percent
Answer both pls. True or false? explain
Answer:
False
Step-by-step explanation:
It is not because a linear function make a straight line, since it contains \(x^{2}\) is is not linear. It creates a parabola.
Can someone help me
Answer:
B
Step-by-step explanation:
As the text states, "Like terms are terms that have the same variable and are raised to the same exponent." We can eliminate choices A and C because they don't have the same variable, and we can also eliminate D because while the terms have the same variable, they aren't raised to the same exponent, hence, the answer is B. This makes sense because B follows all the criteria for like terms.
Answer:
sorry I cant help u I'm in class 6
If secβ =–2, find csc(
Maths assignment
a^4-16
Answer:
\(a^4-16\)
\(\left(a^2\right)^2-4^2\)
\(\left(a^2+4\right)\left(a^2-4\right)\)
\(=\left(a^2+4\right)\left(a+2\right)\left(a-2\right)\)
------------------------
Hope it helps...
Have a great day!!
Step-by-step explanation:
The difference of squares: a² - b² factors to (a - b) (a + b)
Let x⁴ = (x²)²
Let 16 = 4²
Now by difference of squares x⁴ - 16 factors as (x² - 4)(x² + 4)
The front factor, (x² - 4), can factor by difference of squares again as (x - 2)(x + 2)
t is given that point P (2, π/4, 2) and a vector A = cos Ø- O sin Ø + 2 cos 0 sing defined in Cylindrical coordinates. Express vector A in Cartesian coordinates and evaluate A at point P (10 marks, C2)
At point P (2, π/4, 2), vector A in Cartesian coordinates is A = <1, 2.5, 2>.
To express vector A in Cartesian coordinates, we can use the following conversions between cylindrical and Cartesian coordinates:
x = ρ * cos(θ)
y = ρ * sin(θ)
z = z
Given vector A = cos(θ) - ρ * sin(θ) + 2 * cos(θ) * sin(θ), we can substitute the corresponding expressions for ρ, θ, and z:
x = cos(θ) * cos(θ) - ρ * sin(θ) * sin(θ) + 2 * cos(θ) * sin(θ)
y = cos(θ) * sin(θ) + ρ * cos(θ) * sin(θ) + 2 * cos(θ) * sin(θ)
z = 2
Simplifying these expressions, we get:
x = cos^2(θ) + 2 * cos(θ) * sin(θ) - ρ * sin^2(θ)
y = cos(θ) * sin(θ) + ρ * cos(θ) * sin(θ) + 2 * cos(θ) * sin(θ)
z = 2
Now, we can evaluate vector A at point P (2, π/4, 2):
x = cos^2(π/4) + 2 * cos(π/4) * sin(π/4) - 2 * sin^2(π/4)
y = cos(π/4) * sin(π/4) + 2 * cos(π/4) * sin(π/4) + 2 * cos(π/4) * sin(π/4)
z = 2
Simplifying further, we have:
x = (1/2) + 1 - (1/2) = 1
y = (1/2) + 1 + 1 = 2.5
z = 2
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Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms.
7, 3, −1, −5, ...
an unnormalized relation is a table that has more than one row.
An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.
Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.
In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.
To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.
In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.
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1. How can you tell that a point on the graph is a maximum or minimum?
2. How would you explain average rate of change to a classmate who was absent today? What does it tell us and how do we find it?
Answer:
1) To see whether it is a maximum or a minimum, in this case we can simply look at the graph. f(x) is a parabola, and we can see that the turning point is a minimum. By finding the value of x where the derivative is 0, then, we have discovered that the vertex of the parabola is at (3, −4).
2