One angle in a triangle is 10 degrees larger than the smallest angle, while the third angle is 10 degrees less than twice the smallest angle. As a result, the three angles are 55°, 45°, and 80°.
Three vertices and three sides make up a triangle. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The sum of the triangle's three angles is 180 degrees.
Let's consider the three angles of the triangle as ∠P, ∠Q, and ∠R. Let's consider Q as the smallest angle. The sum of angles P, Q, and R is given as ∠P+∠Q+∠R=180°
Then, ∠P = ∠Q + 10° and ∠R = 2∠Q - 10°. Substituting these two angle values in the above equation,
[tex]\begin{aligned}\angle Q + 10^{\circ}+\angle Q+2\angle Q - 10^{\circ}&=180^{\circ}\\4\angle Q&=180^{\circ}\\\angle Q&=45^{\circ}\end{aligned}[/tex]
Then,
∠P = ∠Q + 10° = 45°+ 10° = 55°
∠R = 2∠Q - 10° = 2(45°) - 10° = 90° - 10° = 80°
The answers are 55°, 45°, and 80°.
The complete question is -
One angle of a triangle measure 10 degrees greater than the smallest angle and the third angle measure 10 degrees less than twice the smallest angle find the measure of the three angles.
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in a meeting at the office, 40 employees and their 4 managers sit in a row. what is the probability no two adjacent members are managers?
By combination, Three men and three women must be chosen among the six men and seven women that are available. necessary number of methods = [tex]^6C_3 * ^7C_3 = 20 * 35 = 700.[/tex]
What is combination?
The sequence of the selection is irrelevant since a combination in mathematics is a selection of items from a set having various members. Regardless of the sequence in which the items were chosen, a mathematical approach known as a combination may be used to calculate the number of alternative arrangements within a collection of objects. Any order can be chosen by a combination. Combinations and permutations are two alternative strategies to divide up a collection of items into subsets in mathematics. The subset's elements can be listed in any order in a combination. In a permutation, the components of a subset are listed in a certain order.
Three men and three women must be chosen among the six men and seven women that are available. necessary number of methods = [tex]^6C_3 * ^7C_3 = 20 * 35 = 700.[/tex]
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a flow field for a fluid is described by u=(2+y)m/s and v=(2y)m/s, where y is in meters.
The equation in the form at point (3m, 2m) is [tex]$\ln y^2+y=2 x-2.62$[/tex], the magnitude of the velocity is 7.81 m/s, the direction of the velocity is 50.19°.
Consider the flow field:
u=2+y & v=2 y
Determine the streamline equation by using the following equation:
[tex]& \frac{d x}{u}=\frac{d y}{v} \\ \frac{d x}{2+y}=\frac{d y}{2 y} \\\\& \int d x=\int\left(\frac{2+y}{2 y}\right) d y \\\\& x=\ln y+\frac{y}{2}+C[/tex]
(A)
Since the stream line passes through (3,2).
[tex]$$\begin{aligned}& x=\ln y+\frac{y}{2}+C \\& 3=\ln 2+\frac{2}{2}+C \\& C=2-\ln 2 \\& C=1.31\end{aligned}$$[/tex]
Substitute the value of C in equation (1).
[tex]& x=\ln y+\frac{y}{2}+C \\\\& x=\ln y+\frac{y}{2}+1.31 \\\\& 2 x-1.31 \times 2=2 \ln y+y \\\\& \ln y^2+y=2 x-2.62[/tex]
Therefore, the equation of streamline equation at point (3m, 2m) is [tex]$\ln y^2+y=2 x-2.62$[/tex].
(B).
Calculate the magnitude of the velocity of a particle located at point (5m , 3m).
[tex]V & =\sqrt{u^2+v^2} \\\\& =\sqrt{(2+y)^2+(2 y)^2} \\\\& =\sqrt{(2+3)^2+(2 \times 3)^2} \\\\& =\sqrt{5^2+6^2} \\\\& =7.81 \mathrm{~m} / \mathrm{s}[/tex]
Therefore, the magnitude of the velocity of a particle located at point (5m , 3m) is 7.81m/s.
(C).
Calculate the direction of the velocity of a particle located at point (5m , 3m) measured counterclockwise from the positive x-axis is
[tex]\tan \theta & =\frac{v}{u} \\\\& =\frac{2 y}{2+y} \\\\& =\frac{6}{5} \\\\& =50.19^{\circ}[/tex]
Therefore, the direction of the velocity of a particle located at point (5m , 3m) is 50.19°.
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A flow field for a fluid is described by u=(2+y) m/s and v=(2y) m/s, where y is in meters.
A.) Determine the equation of the streamline that passes through point (3m, 2m). Write the equation in the form
x={x(y)}, where y is in meters.
B.) Find the magnitude of the velocity of a particle located at point (5m , 3m).
C.) Find the direction ? of the velocity of a particle located at point (5m , 3m) measured counterclockwise from the positive x axis.
What’s the answer for this question?
Answer:
D
Step-by-step explanation:
The last one- monetary support that is used to help pay educational costs
:)
 use the discriminant to determine how many and what kind of solution to quadric equation X ^2- X = -1/4 
To determine the number and type of solutions to the quadratic equation x^2 - x = -1/4, we can use the discriminant, which is the part of the quadratic formula that determines the number of solutions. The quadratic formula is:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation. In this case, the coefficients of the equation are a = 1, b = -1, and c = -1/4. Plugging these values into the formula gives us:
x = (1 +/- sqrt(1^2 - 4(1)(-1/4))) / (2(1))
x = (1 +/- sqrt(1 + 1)) / 2
x = (1 +/- sqrt(2)) / 2
Therefore, the quadratic equation has two solutions: x = (1 + sqrt(2)) / 2 and x = (1 - sqrt(2)) / 2. These solutions are both real numbers.
n is and integer
Write the values of n such that -15<3n<6
Answer:
- 4, - 3, - 2, - 1, 0, 1
Step-by-step explanation:
- 15 < 3n < 6 ( divide each interval by 3 )
- 5 < n < 2
then integer value of n are - 4, - 3, - 2, - 1, 0, 1
A painter had 25 L of paint. He used 2.5 L of paint every hour . He finished the job in 5.5 hours . How much paint did he have left ?
Answer:
11.25
Step-by-step explanation:
If the painter used 2.5 liters of paint every hour, then in 5.5 hours he would have used 2.5 * 5.5 = <<2.5*5.5=13.75>>13.75 liters of paint.
If he had 25 liters of paint to begin with and used 13.75 liters of paint, he would have 25 - 13.75 = <<25-13.75=11.25>>11.25 liters of paint left. Answer: {11.25}.
The painter had 11.25 L paint left.
what is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given here in 1 hour he uses 2.5 L of paint
then in 5.5 hours he uses 2.5 × 5.5 = 13.5 L
Therefore quantity of paint left is = 25 - 13.5 = 11.5 L
Hence, The painter had left 11.25 L .
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Phillip made a milkshake with 2 cups of ice cream and 3/4 cups of milk. Matthew made his milkshake with 1 cup of ice cream and 1/3 cups of milk. Whose milkshake was thicker?
Answer: Matthew’s milkshake
Step-by-step explanation: The ratio of ice cream to milk in Philips milkshake is 1:3/8. The ratio of ice cream to milk in Matthew’s milkshake is 1:1/3. 3/8>1/3. Since you want a thicker milkshake, you want less milk in the ratio, Matthew’s milkshake would be thicker.
What is the domain of a radical?
If this answer helps you, brainliest is appreciated
The domain of a radical is the set of all values of the independent variable for which the radical is defined.
For example, consider the radical expression √x. This expression is defined for all nonnegative values of x, since the square root of a nonnegative number is always real. Therefore, the domain of the radical √x is the set of all nonnegative values of x:
{x | x ≥ 0}
This includes all real numbers that are greater than or equal to zero, such as 0, 1, 2, 3, and so on.
On the other hand, if we consider the radical expression √(x-2), this expression is defined for all values of x such that x-2 is nonnegative. This means that the domain of the radical √(x-2) is the set of all values of x such that x ≥ 2:
{x | x ≥ 2}
This includes all real numbers that are greater than or equal to 2, such as 2, 3, 4, 5, and so on.
In general, the domain of a radical is determined by the values of the independent variable that make the expression under the radical nonnegative. If the expression under the radical is always nonnegative, then the domain of the radical is the set of all real numbers. If the expression under the radical is not always nonnegative, then the domain of the radical is the set of all values of the independent variable that make the expression nonnegative.
Answer:
The domain of a radical is the set of all values that can be plugged into the radical without resulting in an undefined or imaginary value.For example, the domain of the square root function sqrt(x) is all non-negative real numbers, since the square root of a non-negative real number is always a real number. This means that the domain of sqrt(x) is the set of all real numbers x such that x >= 0.On the other hand, the domain of the square root function sqrt(x^2 - 4) is all real numbers except for the values x = 2 and x = -2, since the square root of a negative number is an imaginary number. This means that the domain of sqrt(x^2 - 4) is the set of all real numbers x such that x != 2 and x != -2.In general, the domain of a radical is the set of all values for which the expression inside the radical is greater than or equal to 0. This is because the radical of a negative number is an imaginary number, which is not included in the domain of the radical.
Step-by-step explanation:
describe the proof princple used in a proof that shows a property of some natural number abd goes on to show that the same property holds for all natural numbers
The proof principle that you are describing is known as induction. Induction is a method of proof that is used to establish that a property holds for all natural numbers (or, more generally, for all elements of a well-ordered set).
The basic idea behind induction is as follows:
First, you start with a base case, which is a specific natural number (usually 0 or 1) for which you can directly prove that the property holds.
Next, you assume that the property holds for some natural number n. This is known as the induction hypothesis.
Using the induction hypothesis, you then prove that the property also holds for the natural number n+1. This is known as the induction step.
Since you have already established that the property holds for the base case, and you have shown that if it holds for one natural number, it must also hold for the next natural number, it follows that the property holds for all natural numbers.
Induction is a very powerful proof technique and is used extensively in mathematics to prove theorems about the properties of natural numbers and other well-ordered sets.
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Use the SOLVE Process to determine the missing coefficient
of a given polynomial. P(x)=x^4 - 3x^3 +ax^2 - 6x + 14
Answer:
To determine the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, we can use the SOLVE process as follows:
S: Write down the given information and identify the problem.
We are given the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, and we need to find the value of the missing coefficient "a".
O: Organize the information and decide on a plan.
To find the value of "a", we can substitute specific values for x into the polynomial and solve for a.
L: Carry out the plan.
For example, let's say we substitute x = 2 into the polynomial. We get:
P(2) = 2^4 - 32^3 + a2^2 - 6*2 + 14
= 16 - 24 + 4a - 12 + 14
= -4 + 4a + 2
= 4a - 2
We are given that P(2) = 4a - 2 = 0, so 4a = 2.
Solving for a, we get:
a = 2 / 4
= 0.5
V: Check the solution.
We can check the solution by substituting 0.5 for a in the original polynomial and verifying that it gives us the correct result for P(x) when x = 2.
P(x) = x^4 - 3x^3 + 0.5x^2 - 6x + 14
Substituting x = 2 and a = 0.5, we get:
P(2) = 2^4 - 32^3 + 0.52^2 - 6*2 + 14
= 16 - 24 + 1 - 12 + 14
= 0
Since P(2) = 0, our solution appears to be correct.
Therefore, the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14 is 0.5.
PLease Help what is m% of n?
Answer:
mn/100
Step-by-step explanation:
m% = m/100
m% of n = m% × n = m/100 × n = mn/100
Solve the inequality. Graph the solution. -7<2c - 1<10
Answer:
-3<c<11/2
Step-by-step explanation:
-7<2c-1
-7+1<2c
-6<2c
-3<c
and
2c-1<10
2c<10+1
2c<11
c<11/2
Final answer (combine both):
-3<c<11/2
I need help with this. Please answer or explain how I have to do it.
Olivia is an athlete. During training this morning, she ran three
laps. It took her 5/6
minute to finish the first lap. The second lap
took her 1/12
more minutes than the first lap. The third lap took her
1/10
less minutes than the second lap. How much time did it take
her to finish the third lap?
Answer: 49/60 mins.
Step-by-step explanation:
First lap time = 5/6 minute
Second lap time = 11/12 minute
Third lap = ?
To find the 3rd lap mins, we need to find 5 x 6, which is 30. Then, we need to find 1 1/12 more than 30. Then, when we get that answer, we need to find 1 1/10 fewer mins to get the 3rd lap time. If you do it all right, you should end up with 49 mins or 49/60 mins as a fraction (The denominator was changed to 60 to make the problem more realistic and easier) I hoped this helped.
Can someone help with this?
Answer:
7
Step-by-step explanation:
4+3=7
7-4=3
7-3=4
is the potential that a chosen action may lead to an undesirable outcome. group of answer choices chance probability negativity risk
Risk is the potential that a chosen action may lead to an undesirable outcome.
About riskIn simple terms, the definition of risk is a condition that is uncertain, but contains an element of danger as a consequence or result of something. Once again, this something is a business, business, activity, or decision that you make.
Types of RiskThe risks themselves are divided into several types, complete with different characteristics.
1. Pure Risk
This pure risk is certain, meaning that when the risk occurs, you will experience a loss. And vice versa, if pure risk does not occur, then you will make a profit.
2. Speculative Risk
There are three possibilities that will happen, if you experience speculative risk, namely profits, losses, or maybe break even. What is meant by break even is the break even point.
Conditions where there are no profits or losses, so it's normal. The most obvious examples of speculative risk are the lottery, stock exchange, exchange risk, and others.
3. Particular Risk or Special Risk
Specific risks originate from individual activities, so the impact can still be estimated or anticipated at the outset because they are local in nature. For example, a turbine explosion, a shipwreck, or maybe a crash.
How to anticipate it (example for collision risk). You can take out insurance to provide guarantees or protection, both for the vehicle and for yourself.
4. Fundamental Risk
Fundamental risks come from the surrounding environment or nature which can have quite a big impact, because humans are not able to control them.
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Which equation represents the written description? Six times the difference between 51.2 and a number is equal to 68.3
Answer:
Below
Step-by-step explanation:
the difference between 51.2 and a number is : 51.2 - x
Now multiply this by 6 : 6 x (51.2-x)
and this equals 68.3 : 6 x (51.2-x) = 68.3
A circle of center (-3 , -2) passes through the points (0 , -6) and (a , 0). Find a.
Using the fact that all points on a circle are equidistant to its center, we will see that:
a = -3 ±√21
How to find the value of a?All the points on a circle are equidistant to its center. Here the center is at (-3, -2), and we know that (0, -6) is on the circle.
The distance between these two is:
d = √( (-3 - 0)^2 + (-2 + 6)^2) = 5
Then the distance between (a, 0) also should be 5 units, so:
5 = √( (-3 - a)^2 + (-2 - 0)^2)
5 = √( (-3 - a)^2 + 4)
5^2 = (-3 - a)^2 + 4
25 - 4 = (-3 - a)^2
21 = (-3 - a)^2
±√21 = -3 - a
a = -3 ±√21
these are the two possible values of a.
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Solve this please .p+5=-12 for p
Answer:
-17
Step-by-step explanation:
p+5=-12
p=-12-5
p=-17
Answer:
p+5=-12
p=-12-5
p=-17
so the solution set is -17
Annual salary at r rupees per month along with a Christmas bonus of Rs2000. Find the total annual salary with a festive bonus.
The total annual salary with a festive bonus is Rs (12r+2000)
What is multiplication?In maths, multiply means the repeated addition of groups of equal sizes.
Given that, there is an annual salary at r rupees per month along with a Christmas bonus of, Rs 2000.
Here, a person is getting monthly salary = Rs r
Therefore, his annual salary = Rs r × 12
= Rs 12r
He is also getting a bonus for Christmas = Rs 2000
So, in total, he will get = Rs (12r+2000)
Hence, The total annual salary with a festive bonus is Rs (12r+2000)
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f(x) =
2-x
x+1
g(x) = 18 - 3x
(fog)(x) =
The value of the composite function is 2x - 15
What is a function?A function can be defined as a rule, law ore equation that explicitly shows the relationship between two variables.
These variables are called;
The independent variablesThe dependent variablesFrom the information given, we have the functions;
f(x) = 2 - x + 1g(x) = 18 - 2xTo determine the composite function (fog)(x), we have to substitute the value of g(x) as the variable 'x' in the function, f(x), we have;
(fog)(x) = 2 - (18 -2x) + 1
Now, expand the bracket
(fog)(x) = 2 - 18 + 2x + 1
collect like terms
(fog)(x) = 2x - 15
Hence, the function is 2x - 15
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Subtract the expressions.
(5.62n − 2.8) − (4 + 14.3n)
A.19.92n + (−1.2)
B. 8.42n − 18.3
C. −8.68n − 6.8
D. −86.80n − 0.8
The result of the subtraction of the algebraic expression (5.62n − 2.8) − (4 + 14.3n) is -8.68n - 6.8 Third option is correct.
What is algebraic expression?
An algebraic expression is a mathematical phrase that uses numbers, operations such as addition and multiplication, and variables (letters or symbols that represent unknown values). Algebraic expressions are used to represent real-world problems and situations. Algebraic expressions can be combined and simplified, and they can also be used to solve equations. Algebraic expressions can be used to describe anything from the area of a circle to the cost of a car. Algebraic expressions are an essential part of algebra, and they are used to help students understand mathematics concepts in a more concrete way.
The given algebraic expressions are 5.62n - 2.8 and 4 + 14.3n
Now,
(5.62n − 2.8) − (4 + 14.3n)
5.62n - 2.8 - 4 - 14.3n
-8.68n - 6.8
Third option is correct
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Answer:
the answer is b
Step-by-step explanation:
answer this question (people)
Answer:
1/11
Step-by-step explanation:
Add 1/5 + 2 then divide 1/5 by the result
If f(x) = x² and g(x) = x - 3, then g(f(x)) = ?
Answer:
x² - 3
Step-by-step explanation:
g(f(x))
=> g(x²)
=> x² - 3
thanks for all the help y’all
Answer:
Step-by-step explanation:
Lacey you can do this one :D
J = H ( b/c of red marks)
180= 128 + ∠j
52 = ∠j
t = ∠j
t = 52
180 = s + 2*t
180 = s + 2*52
180 = s + 104
180-104 =s
76 = s
Which ordered pair is in the solution set of y ≥ 3x - 5?
Answer:
Slope: 3
y-intercept: ( 0, −5)
Graph a solid line, then shade the area above the boundary line since
y is greater than 3x −5.
y ≥ 3x −5
PLS HELP identify the function in this graph
Answer:
y = 2x - 3
Step-by-step explanation:
A (0,-3)
B (2,1)
slope = (-3-1)/(0-2)
-4/-2
2
y intercept = -3
HELP MEEEEEEEE PLEASEEEEE
Simple random sampling is a good way because he will have a more representative sample if he chooses randomly. which is the correct answer would be an option (B).
What is simple random sampling?A sample is randomly chosen from the population in basic random sampling, guaranteeing that each person has an equal chance of being chosen.
Simple random sampling is a good way for a librarian to check a sample of books from the library to get an idea of how many need replacing because it will provide a more representative sample.
In simple random sampling, a sample is selected from the population at random, ensuring that each member of the population has an equal chance of being selected. This means that the sample will accurately represent the characteristics of the population as a whole.
Thus, He will have a more representative sample if he chooses randomly.
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in the 2011 current population survey conducted by the us census bureau, two average household incomes were reported: $49,445 and $67,530. one of these averages is the mean and one is the median. which is the mean?
The mean is $67,530 from the reported two average household incomes i.e, $49,445 and $67,530.
What is mean?Averages can only be computed for numeric variables, regardless of whether the variables are discrete or continuous. This is obtained by simply dividing the sum of all values in the dataset by the number of values.
Mathematically, X-bar = Sum of x values/ number of values
We have, the current population survey is conducted by the US Census bureau,
Averages of household income are $49,445 and $67,530. Mean of average incomes is expected to be a right skewed distribution because some individuals belongs to exceptionally high income group which are outliers and which will cause the mean to inflate. Hence, value which is greater will be the mean i.e. $67,530
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if a=b(1/n) is equivalent to an=b then 43 is equivalent to
43 is equivalent to 64(1/3)
What are equivalent numbers?Equivalent is different from equal. Equal means same in all aspects, whereas equivalent means similar but not identical.
For example, 2 is said to be equal to 2 but equivalent to 1 + 1.
Given that, if a=b(1/n) is equivalent to an=b then 43 is equivalent to
If we see the number 43, then converting it according to given pattern
4ⁿ(1/n)
Here, n = 3
So, 43 = 4³(1/3) = 64(1/3)
Hence, 43 is equivalent to 64(1/3)
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