the sum of two angles of a triangle is 6/5 of a right angle, and one of these two angles is 30 larger than the ohter
Answers
The measure of two angles are 39 degree and 69 degree. By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree, so the final angle is 72 degree. Therefore, the largest angle in the triangle is 72 degree.
Describe the Triangle Angle Sum property?According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
Given:
\(The\;sum\;of\;two\;angles\;in\;a\;triangle\;is\;\frac{6}{5}\;of\;a\;right\;angle\;is,\;\frac{6}{5} \times 90^{\circ} = 108^{\circ}\)
\(let\;x\;is\;the\;measure\;of\;the\;first\;angle\)
\(one\;of\;these\;two\;angles\;is\;30\;larger\;than\;the\;other,\;is\;x+30=108\)
We know that sum of two angles is 108
\(x+x+30=108^{\circ}\)
\(2x+30=108\)
\(2x=108-30\)
\(2x=78\)
\(x=39^{\circ}\)
Second angle y is,
\(y=x+30\)
\(y=39+30\)
\(y=69^{\circ}\)
By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree,
Third angle z is,
\(x+y+z=180\)
\(39+69+z=180\)
\(108+z=180\)
\(z=180-108\)
\(z=72^{\circ}\)
\(By\;comparing\;the\;angles\;39^{\circ},\;69^{\circ}\;and\;72^{\circ}, 72^{\circ}\; is\;greater\)
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Related Questions
Express the following numbers in standard form
i) 5,00,00,000 ii) 39087.8 (iii) The distance between Earth and Moon is 384,000,000 m.
Answers
Answer:
i) 5,00,00,000 (5 billion) in standard form would be 5 x 10^9
ii) 39087.8 in standard form would be 3.90878 x 10^4
iii) The distance between Earth and Moon is 384,000,000 m (384 million meters) in standard form would be 3.84 x 10^8 m.
Step-by-step explanation:
6) There are 11 marbles in a bag. Two are yellow, five are pink and four are green. Suppose you pull out one
marble, record its color, put it back in the bag and then pull out another marble. Find the probability that
when selecting 3 marbles, you have selected a yellow first, green second and pink last.
Answers
The probability is 0.1.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.acc to our question-
total marbles= 11yellow marbles=2pink marbles=5green marbles=30.01 + 0.04 + 0.05Hence,The probability is 0.1.
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what is the average of -5 -6 -2 0 3
Answers
Answer:
-2
Step-by-step explanation:
i'm in desperate need of help <\3
i'll give brainliest and points for anyone who answers these questions, thank you so much in advance!
Q8- what's the S.S of the inequality: x² + 4 > 2
a) R
b) ∅
c) R-
d) R+
Q9- if x + yi = (1 + i)⁴ , then x + y = ......
a) 4
b) - 4
c) 2
d) - 2
an explanation for future reference would be GREATLY appreciated, thank you again T^T
Answers
Answer:
8 Answer is a) R
And
9 Answer is b) -4
Answer of your Question bro and good evening and I hope this will help you and please mark me as brainliest and thank u have a amazing day
help me and ill give brainlist!!!!!
Answers
Hope this helps!
Mark me brainliest ^^
The graph of the function y= \(\frac{k}{x^2}\) goes through A(10,-2.4). For each given point, determine if the graph of the function also goes through the point.
C(-1/5, -6000)
Answers
Answer: Yes
Step-by-step explanation:
If \(y=k/x^2\) passes through point (10,-2.4), this means that k/100=-2.4, so k=-240
For y=k/x^2 where x=-1/5, y=-6000, so C is correct
Use the given graphs of f and g to evaluate the expression (assume that each point lies on the grid lines).
(f * g)(1) = ____
Answers
The expression, use the f and g graphs that are provided (assume that each point lies on the grid lines) (f * g)(1) = f(g(1)). A graph is a diagram or visual representation that organizes the presentation of facts or values.
In mathematics, a graph is a visual representation or diagram that arranges facts or values. The relationships between two or more objects are often shown by the points on a graph. No two vertices in a simple network are connected by more than one edge, and no edge starts or ends at the same vertex. To put it another way, a simple graph is one that has few loops and edges. Since they make information easily accessible and understandable, graphs and charts are valuable visual tools. So, it is not unexpected that print and electronic media frequently use graphs.
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What the answer question
Answers
Answer:
Step-by-step explanation:
UV & UT are the sides
Automatic Transmissions, Inc., has the following estimates for its new gear assembly project: price = $940 per unit; variable cost = $340 per unit; fixed costs = $3.4 million; quantity = 53,000 units. Suppose the company believes all of its estimates are accurate only to within ±15 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario?
Answers
In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.
In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.
On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.
Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units
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A rectangular schoolyard is to be fenced in using the wall of the school for one side and Problem:500 meters of fencing for the other three sides. The area in square meters of the schoolyard is a function of the length in meters of each of the sides perpendicular to the school wall.
Question: write an expression for a(x)
Answers
Answer:
x(150 - 2x) is the answer
Step-by-step explanation:
Diego measured the length of a pen to be 22 cm.
The actual length of the pen is 23 cm.
What is the percent error for Diego’s measurement?
Explain or show your reasoning.
Answers
Based on this question, we know that Diego measured the length of a pen which were to be 22cm so that we would get the actual length of the pen that is 23cm.
So what we need to do is do the percentage//which is decreasing
(22-22)/22x100
=1/22x100
=4.5%, therefore the percent error for Diego’s measurement is 4.5% because what we did was find the percentage decrease by multiplying 100 by 22 minus 22 over 22.
Answer:
let's talk here as to get rid of him
find the exact value of sin(cos^-1(2 5))
Answers
The exact value of sin(cos^-1(2/5)) is √21 / 5.
We know that cos(cos^-1(x)) = x for all x in [-1, 1]. Hence,
cos(cos^-1(2/5)) = 2/5
Now we need to find sin(cos^-1(2/5)).
We can use the identity sin^2(x) + cos^2(x) = 1 and substitute cos(x) = 2/5 to get:
sin^2(cos^-1(2/5)) + cos^2(cos^-1(2/5)) = 1
sin^2(cos^-1(2/5)) + (2/5)^2 = 1
sin^2(cos^-1(2/5)) = 21/25
Taking the positive square root (since sine is positive in the first and second quadrants), we get:
sin(cos^-1(2/5)) = √(21/25)
= √21 / 5
Therefore, the exact value of sin(cos^-1(2/5)) is √21 / 5.
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What is the value of the expression -218 - 72 - (-5)?
Answers
Answer:
The answer is -285
Step-by-step explanation:
PLEASEEE HELPPPP !!!!!!!!!!!!!!!!!!!!
Answers
Answer:
17.35
Step-by-step explanation:
All all divide by how many there were
Answer:
17.35
Step-by-step explanation:
Find the mean by adding all the numbers up and dividing by the amount of numbers in the data set
Let X
=
A
.
¯¯¯¯¯¯
B
C
. Evaluate X for
(a) A
=
1
,
B
=
0
,
C
=
1
, (b) A = B = C = 1 and ( c) A = B = C = 0.
Answers
The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.
To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.
(a) For A = 1, B = 0, and C = 1:
X = 1.¯¯¯¯¯¯01
To find the complement of BC, we replace B = 0 and C = 1 with their complements:
X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001
(b) For A = B = C = 1:
X = 1.¯¯¯¯¯¯11
Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:
X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111
(c) For A = B = C = 0:
X = 0.¯¯¯¯¯¯00
Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:
X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000
In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.
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What is the value of this expression when f = 4? 9 (3f + 2)- 7f
Answers
Answer:
The answer is 98
Step-by-step explanation:
9(3f + 2) - 7f, if f = 4
Now, Substitute the value of f
9(3f + 2) - 7f
9[3(4) + 2] - 7(4)
9(12 + 2) - 28
9(14) - 28
126 - 28 = 98
Thus, The answer is 98
-TheUnknownScientist 72
Answer: The answer is 98
Step-by-step explanation:
1. Which of the following is found in plant cells but not animal cells? In
(1 Point)
mitochondria
Chloroplast
Nucleus
Cytoplasm
Answers
Answer:
chloroplast is found in plant cells but not animal cells.
What quadratic function has 13 and 2 as its zeros? (write a quadratic function f whose zeros are 13 and 2.)
Answers
The quadratic function with the zeros 13 and 2 is f(x) = x^2 - 15x + 26
To find a quadratic function with the zeros 13 and 2, we can use the fact that the zeros of a quadratic function can be written in the form (x - a)(x - b), where 'a' and 'b' are the zeros.
The zeros are given as 13 and 2, which means that when x = 13 or x = 2, the function equals zero.
In this case, the zeros are 13 and 2, so we have:
(x - 13)(x - 2)
Expanding this expression, we get:
x^2 - 15x + 26
Therefore, the quadratic function with the zeros 13 and 2 is:
f(x) = x^2 - 15x + 26
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List the domain and range of each function (1,-4),(2,-3),(3,-2),(4,-1)
Answers
Answer:
Domain are all x values
Range are all y values
Domain:(1,2,3,4)
Range:(-4,-3,-2,-1)
Range(-1,-2,-3,-4)
x - 6
———- = 5
3
A.) x = 9
B.) x = 14
C.) x = 21
D.) x = 24
Answers
Graph the solutions of the linear inequality −4x + 2y > −8.
Answers
Answer:
y > −4 + 2 x
Step-by-step explanation:
write the product form of 3 a² b ³
Answers
Answer:
a³-b³= (a-b)(a²+ab+ b²)
Step-by-step explanation:
if you choose from the vending machine 12 times and choose gelatin 5 times, what is the experimental probability that gelatin is the one you choose?
Answers
Answer:
a
Step-by-step explanation:
Sung is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges $89 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.70 for every mile driven.
For what mileages will Company A charge less than Company B?
Use M for the number of miles driven, and solve your inequality for M .
Answers
Answer:
Step-by-step explanation:
Use the equation
89 < 75 + 0.7*M Subtract 75 from both sides
89 - 75 < 0.7M Combine
14 < 0.7 M Divide both sides by 0.7
14/0.7 < M
20 < M
If M goes over 20 then the flat rate is cheaper.
. write down a basis for the space of a) 3 × 3 symmetric matrices; b) n × n symmetric matrices; c) n × n antisymmetric (at = −a) matrices;
Answers
a) The basis for the space of 3 × 3 symmetric matrices consists of three matrices: the matrix with a single 1 in the (1,1) entry, the matrix with a single 1 in the (2,2) entry, and the matrix with a single 1 in the (3,3) entry.
b) The basis for the space of n × n symmetric matrices consists of n matrices, where each matrix has a single 1 in the (i,i) entry for i = 1 to n.
c) The basis for the space of n × n antisymmetric matrices consists of (n choose 2) matrices, where each matrix has a 1 in the (i,j) entry and a -1 in the (j,i) entry for all distinct pairs (i,j).
a) A symmetric matrix is a square matrix that is equal to its transpose. In a 3 × 3 symmetric matrix, the only independent entries are the diagonal entries and the entries above the diagonal. Therefore, the basis for the space of 3 × 3 symmetric matrices consists of three matrices: one with a single 1 in the (1,1) entry, another with a single 1 in the (2,2) entry, and the last one with a single 1 in the (3,3) entry. These matrices form a linearly independent set that spans the space of 3 × 3 symmetric matrices.
b) For an n × n symmetric matrix, the basis consists of n matrices, each having a single 1 in the (i,i) entry and zeros elsewhere. These matrices are linearly independent and span the space of n × n symmetric matrices. Each matrix in the basis corresponds to a particular diagonal entry, and by combining these basis matrices, any symmetric matrix of size n can be represented.
c) An antisymmetric matrix is a square matrix where the entries below the main diagonal are the negations of the corresponding entries above the main diagonal. In an n × n antisymmetric matrix, the main diagonal entries are always zeros. The basis for the space of n × n antisymmetric matrices consists of (n choose 2) matrices, where each matrix has a 1 in the (i,j) entry and a -1 in the (j,i) entry for all distinct pairs (i,j). These matrices are linearly independent and span the space of n × n antisymmetric matrices. The number of basis matrices is (n choose 2) because there are (n choose 2) distinct pairs of indices (i,j) with i < j.
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Find the midpoint of the segment with the following endpoints (6,3) and (10, – 7)
Answers
Answer:
-5/2
Step-by-step explanation:
-7-3/10-6 = -10/4 which equals -5/2
I need help please and thank you!
Answers
Answer:
v is 198 m/s
Step-by-step explanation:
\(v = \sqrt{gh} \\ v = \sqrt{9.8 \times 4000} \\ v = 198 \: m {s}^{ - 1} \)
Solve the problem. Round dollar amounts to the nearest cent. Use ordinary interest (360 days in a year) unless otherwise indicated. Chris Owens bought a new computer system. To pay for the system, he borrowed $3,290 from the credit union at 10(1/3)% interest for 110 days. Find the interest.
Answers
To find the interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days, we use the simple interest formula as follows:
Simple Interest = (P × R × T)/100Where:P = Principal or amount borrowedR = Rate of interest per annumT = Time in years or fraction of a year110 days ÷ 360 days = 0.3056 (time as a fraction of a year)The rate of interest, 10(1/3)% is equal to 10 + (1/3) percent = 10.33% per annum in decimal form = 0.1033Substituting the values we have into the formula,Simple Interest = (P × R × T)/100= (3,290 × 0.1033 × 0.3056)/100= $100.68 (rounded to the nearest cent)
Therefore, the interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days is $100.68.
A credit union loan is a type of personal loan that can be used for a variety of purposes. One of the most common reasons people take out credit union loans is to purchase big-ticket items like a new computer system. When you take out a loan, you must pay back the amount borrowed plus the interest charged by the lender. The interest rate is usually expressed as a percentage of the amount borrowed and is charged for a specific period of time known as the loan term. Simple interest is a method of calculating interest that is charged only on the principal amount borrowed.
It does not take into account the interest that has already been paid. Simple interest is calculated by multiplying the principal amount borrowed by the interest rate and the length of the loan term. The answer is more than 100 words.The interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days is $100.68. Therefore, he would pay $3,290 + $100.68 = $3,390.68 in total to the credit union over the loan term. It is important to note that when rounding dollar amounts to the nearest cent, amounts that end in .50 or higher are rounded up to the next highest cent, while amounts that end in .49 or lower are rounded down to the next lowest cent. In this case, $100.6847 would be rounded up to $100.68. In conclusion, the interest charged on a loan can significantly increase the total amount that must be repaid, making it important for borrowers to understand how interest is calculated and the terms of their loan.
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solve this math problem first you get a free crown!
-9/12 - (-1/3)
A. 8/9
B. -8/9
C. 5/12
D. -5/12
Answers
The answer is D.
-9/12 - (-1/3) = -5/12
in base $10$, the number $2013$ ends in the digit $3$. in base $9$, on the other hand, the same number is written as $(2676) {9}$ and ends in the digit $6$. for how many values of $b$ does the base-$b$-representation of $2013$ end in the digit $3$?
Answers
There are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$. For a number to end in the digit $3$ in base-$b$ representation, it must be congruent to $3$ modulo $b$.
We can rewrite $2013$ as $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$. Now, if $2013$ is congruent to $3$ modulo $b$, it means that $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$ is also congruent to $3$ modulo $b$.
Simplifying the expression, we have $2000 + 0 + 10 + 3$. Since the base-$b$-representation is formed by multiplying each digit by the corresponding power of $b$, we can rewrite the expression as $2 \cdot b^3 + 1 \cdot b^1 + 3 \cdot b^0$. We can now observe that the constant term $3 \cdot b^0$ will always be congruent to $3$ modulo $b$. However, the other terms $2 \cdot b^3$ and $1 \cdot b^1$ will not be congruent to $3$ modulo $b$ for any positive value of $b$. Therefore, the base-$b$-representation of $2013$ cannot end in the digit $3$ for any value of $b$.
Hence, there are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$.
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