∠1 and ∠2 are vertical angles. If m∠1 = (5x + 12)° and m∠2 = (6x - 11)°. What is m∠2?
Answers
Answer:
\(\boxed {\angle 2 = 127\textdegree}\)
Step-by-step explanation:
First, you need to write an expression by using the following measurements from both \(\angle 1\) and \(\angle 2\), and solve for \(x\):
\(\angle 1 = 5x + 12\)
\(\angle 2 = 6x - 11\)
\(5x + 12 = 6x - 11\)
Solve for \(x\):
\(5x + 12 = 6x - 11\)
\(5x + 12 - 6x = 6x - 6x - 11\)
\(-x + 12 = -11\)
\(-x + 12 - 12 = -11 - 12\)
\(-x = -23\)
\(\frac{-x}{-1} = \frac{-23}{-1}\)
\(x = 23\)
After you have the value of \(x\), use the value of \(x\) and the expression from \(\angle 2\) to get the actual measurement of \(\angle 2\):
-The value of \(x\):
\(x = 23\)
\(\angle 2 = 6x - 11\)
Solve for \(\angle 2\):
\(6x - 11\)
\(6(23) - 11\)
\(138 - 11\)
\(127\)
The measurement of \(\angle 2\):
\(\boxed {\angle 2 = 127\textdegree}\)
Related Questions
The first line in a system of linear equations has a slope of 2 and passes through the point (1, −1). The second line passes through the points (8, −5) and (10, −10). What is the solution to the system?
Answers
As a result οf answering the given questiοn, we may state that As a equatiοn result, the system's sοlutiοn is (4, 5).
What is equatiοn?In mathematics, an equatiοn is a statement stating the equality οr twο expressiοns. An equatiοn cοnsists οf twο sides split by an algebraic equatiοn (=). Fοr illustratiοn, the argument "2x + 3 = 9" argues that the statement "2x + 3" is equal tο the value "9". The gοal οf equatiοn sοlving is tο find the value οr values οf the variable(s) tο make the equatiοn true. Simple οr cοmplex equatiοns, regular οr nοnlinear, and including οne οr mοre factοrs are all pοssible. Fοr example, the equatiοn "x² + 2x - 3 = 0" has the variable x raised tο the secοnd pοwer. Lines are used in many fields οf mathematics, including algebra, calculus, οr geοmetry.
Tο begin, use the pοint-slοpe fοrm οf a line tο οbtain the equatiοn οf the first line:
where m is the slοpe and (x₁, y₁) is a line pοint. With m = 2 and (x₁, y₁) = (1, -1), we get:
y -y1 = m(x -x1)(x -x1)
Tο sοlve the system, we must lοcate the place where the twο lines intersect. When we put the twο equatiοns tοgether, we get:
y-(-1) = 2(x -1)(x -1)
y+1 = 2x-2 = 2x-3
When we substitute x = 4 intο either equatiοn, we get:
2x-3=(-5/2)x + 15(9/2)x = 18 = 4
As a result, the system's sοlutiοn is (4, 5).
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every polynomial function of odd degree with real coefficients will have at least
Answers
Every polynomial function of odd degree with real coefficients will have at least one real root or zero.
This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.
The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.
For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.
It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.
The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.
In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.
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Miki has 104 nickels and 88 dimes. She wants to divide her coins into groups where each group has the same number of nickels and the same number of dimes. What is the largest number of groups she can have?
13
11
8
4
Answers
Answer:
8
Step-by-step explanation:
To find the largest number of groups she can have, find the largest number that can divide 104 and 88 evenly.
This number is 8, since 8 divides 104 to 13 and it divides 88 to 11.
This means each group will have 13 nickels and 11 dimes.
So, the answer is 8 groups.
Answer:
eight
Step-by-step explanation:
The inequality < 4 represents the number of questions Lydia got wrong on her math test. Which sentence represents this inequality?
A Lydia got more than 4 questions wrong on her math test.
B Lydia got fewer than 4 questions wrong on her math test.
C Lydia got 4 or fewer questions wrong on her math test.
D Lydia got at least 4 questions wrong on her math test.
Answers
Answer: B Lydia got fewer than 4 questions wrong on her math test.
The inequality < 4 means "less than 4," so the correct sentence that represents this inequality is C) Lydia got 4 or fewer questions wrong on her math test.
Can I get help pls ._.
Answers
Answer:
Hello!
_____________________
Your answer would be (A)
Step-by-step explanation: Simplify the expression.
Hope this helped you!
The cost of each ticket at the carnival was $0.25. Li bought $7.50 worth of tickets. How many tickets did she buy?
help me please
Answers
If a study determines the difference in average salary for sub populations of mechanical engineers and civil engineers is not significant then the sub populations of mechanical and civil engineers is not significant then the sub populations of mechanical and civil engineers are different salaries
Answers
If a study determines that the difference in average salary for subpopulations of mechanical engineers and civil engineers is not significant, it means that there is not enough evidence to conclude that there is a significant difference in salaries between the two subpopulations.
It does not imply that the subpopulations have different salaries.
When a study finds that a difference is not statistically significant, it means that the observed difference could have occurred due to random chance rather than a true difference in the populations being compared. In other words, the study does not provide strong evidence to support the claim that the subpopulations have different salaries.
To determine whether the subpopulations of mechanical and civil engineers have different salaries, further analysis or studies would be needed.
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a regression tree was developed to predict customer spending for a hotel during football season. one of the leaf nodes consists of six cases in the training set with the following values: 312.00, 350.00, 285.00, 295.00, 380.00, 220.00. what is the predicted spending amount on a hotel for the night for a customer that falls into this leaf node?
Answers
The predicted spending amount on a hotel for the night for a customer that falls into the leaf node with six cases (312.00, 350.00, 285.00, 295.00, 380.00, 220.00) in the training set is $307.17.
Regression tree is a type of decision tree which is used for regression analysis. Regression tree is a data mining technique that is used to find the relationship between a target variable and multiple predictor variables.
Regression trees are built by dividing the input space into smaller regions using the input variables, and then fitting a simple model (constant) in each region. In regression tree, the input space is divided into non-overlapping regions based on the independent variables.
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Re-write the quadratic function below in Standard Form
y=−2(x−8)(x−2)
Answers
y = -2(x - 8)(x - 2)
y = -2(x² -2x -8x +16)
y = -2(x² - 10x + 16)
y = -2x² + 20x - 32
Answer:
y= −2x^2+20x−32
Step-by-step explanation:
y = −2(x−8)(x−2)
= - 2(x^2 - 10x +16)
= - 2x^2 - (-10x)-2. 16
= - 2x^2 +20x - 32
Which value represents |-2½?
OA) 2%2₂
OB) -2½
OC) 2
OD) 3
Answers
The numeric value of the question is present in the in the option B. Thus, Option B is a correct option.
According to the statement
We have to find that the Numeric value.
So, For this purpose, we know that the
The Number value is the value refers to the worth of each digit depending on where it lies in the number.
From the given information:
The given value is a -2½.
And we have to find that the in which option the given value in the question is placed.
For example, if the value in the given question is a 1 then the in which option we have given value is 1.
Then
according to the statement,
In option B the value is similar to the those value which is given in the question.
So, The numeric value of the question is present in the in the option B. Thus, Option B is a correct option.
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Is the equation below true or false?
24 = 2 • 4
Answers
Answer:
false
Step-by-step explanation:
2 · 4 = 8
Answer:
False
Step-by-step explanation:
24 is not equal to 8 therefore it is not true
1. If g(x)= 4(3)* then g(-2)= ?
Help please
Answers
Answer:
-8
Step-by-step explanation:
Assuming that the in parentheses is what we are supposed to change (3)..We would replace the three with the negative two this means that we will solve for four times -2 which equals -8.Hope this helps!
What is the measure of < A B C ?
Answers
143.25 °
is the correct answer.
please mark my answer as brainest and follow me to get the answer faster.
Please help for section d) 100 points, must show all working and step by step
Answers
Answer:
Step-by-step explanation:
(a) and (b) see diagram
(c) you can see from the graph, the purple line hits the parabola twice which is y=6 or k=6
(d) Solving simultaneously can mean to set equal
6x - x² = k >subtract k from both sides
6x - x² - k = 0 >put in standard form
- x² + 6x - k = 0 >divide both sides by a -1
x² - 6x + k = 0
(e) The new equation is the same as the original equation just flipped (see image)
(f) The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal. I chose new)
discriminant formula = b² - 4ac
equation: x² - 6x + 6 = 0 a = 1 b=-6 c = 6
discriminant = b² - 4ac
discriminant= (-6)² - 4(1)(6)
discriminant = 36-24
discriminant = 12
Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.
how many solutions does 4x+1=3x+2
one solution
no solution
infinitely many solutions
Answers
Answer:
one solution
Step-by-step explanation:
If you simplify the equation, it becomes 1x+1=2. Then you subtract the 1 from 2 and get 1x=1. Therefore, x=1 which is ONE SOLUTION.
when summarizing heavily skewed data, the best measure of central tendency is:
Answers
When summarizing heavily skewed data, the best measure of central tendency is the median.
In situations where the data distribution is heavily skewed, the mean may not accurately represent the central tendency of the data. Skewness refers to the asymmetry of the data distribution, where the tail of the distribution extends more to one side. When data is heavily skewed, it can be influenced by extreme values, leading to an unbalanced representation of central tendency if the mean is used.
The median, on the other hand, is less affected by extreme values and provides a better measure of central tendency for skewed data. The median represents the middle value in a data set when the observations are arranged in ascending or descending order. Unlike the mean, it is not influenced by extreme values, making it a robust measure for summarizing skewed data.
By using the median, we can capture the central value that is more representative of the majority of the data points, even in the presence of outliers or skewed distributions. It provides a better understanding of the typical value or position within the data set, regardless of extreme values or asymmetric distributions.
Therefore, when summarizing heavily skewed data, the median is considered the best measure of central tendency as it provides a more accurate representation of the center of the distribution and is less influenced by extreme values.
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What is the area of the figure below?
Answers
Answer:
Your answer is 27
Step-by-step explanation:
4 x 3 = 12
5 x 3 = 15
12 + 15 = 27
Hi! I was shown the problem integral -3/sqrt(64-9x^2)dx but a classmate and was wondering if someone could explain it again. This is the work they showed me
Answers
From the problem, we have :
\(\int -\frac{3}{\sqrt[]{64-9x^2}}dx\)We need to think of a square number that if we multiply it by 9, the result is 64.
That would be 64/9
\(9\times\frac{64}{9}=64\)The square root of 64/9 is 8/3.
Let u = 3x/8
8u = 3x
x = 8u/3 (This value is the same as we've got above 8/3)
du = 3/8 dx
dx = 8/3 du
Subsitute x = 8u/3 and dx = 8/3 du
\(\begin{gathered} \int -\frac{3}{\sqrt[]{64-9(\frac{8u}{3})^2}}\times\frac{8}{3}du \\ \Rightarrow\int -\frac{8}{\sqrt[]{64-9(\frac{64}{9}u^2)}}du \\ \Rightarrow\int -\frac{8}{\sqrt[]{64-64u^2}}du \end{gathered}\)Extract the square root of 64 which is equal to 8.
\(\begin{gathered} \Rightarrow\int -\frac{8}{\sqrt[]{64-64u^2}}du \\ \Rightarrow\int -\frac{8}{8\sqrt[]{1-u^2}}du \\ \Rightarrow\int -\frac{1}{\sqrt[]{1-u^2}}du \end{gathered}\)Note that the identity :
\(\int \frac{1}{\sqrt[]{1-u^2}}du=\sin ^{-1}(u)+C\)It follows that :
\(\int -\frac{1}{\sqrt[]{1-u^2}}du=-\sin ^{-1}(u)+C\)Bring back u = 3x/8, the answer is :
\(-\sin ^{-1}(\frac{3x}{8})+C\)A right triangle is formed by the x-axis, the y-axis and the line y=-2x+3 Find the length of the hypotenuse. Round your answer to the nearest hundredth.
Answers
The length of the hypotenuse is about 3.3 units.
What is a right triangle?A triangle with one of its angles measuring 90° is known as a right triangle.
The given equation of the line is y = 2x +3.
The x-intercept of the line is:
0 = 2x +3
x = -3/2
The y-intercept of the line is:
y = 2(0) + 3
y = 3
Therefore, the line passes through the points (-3/2,0) and (0,3).
The distance between the points is the length of the hypotenuse, therefore the length of the hypotenuse is:
hypotenuse = √( (0+3/2)² + (3-0)² )
= √( 9/4 + 9)
= √(45/4)
= √11.25
= 3.35
Hence, the length of the hypotenuse is about 3.3 units.
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f(x)=x^3+8g(x)=4x^3−5x−8
find (f+g)(x)
A.
5x³-5x
B.
5x³-5x+16
C.
5x³-5x-16
Answers
The value of the sum of the functions f(x) and g(x), (f + g)(x) is 5x³ - 4x.
What is a function?The outputs for a certain set of inputs can be referred to as a function.
A function's inputs are referred to as its independent variables, while its outputs are referred to as its dependent variables.
Given, f(x) = x³ + 8 and g(x) = 4x³ - 5x - 8.
Let, f(x) = x³ + 0x + 8.
We know, (f + g)(x) = f(x) + g(x).
Therefore, (f + g)(x) = (x³ + 0x + 8) + (4x³ - 5x - 8).
(f + g)(x) = x³ + 4x³ + 0x - 4x + 8 - 8.
(f + g)(x) = 5x³ - 4x.
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At the Hardey Fitness Center, the management did a survey of their membership. The average age of the female members was $40$ years old. The average age of the male members was $25$ years old. The average age of the entire membership was $30$ years old. What is the ratio of the female to male members? Express your answer as a common fraction.
Hint: It isn't 5/8
Answers
The ratio of female to male members is 40:25, or 4:2. This can be expressed as a common fraction as 4/2 or 2/1.
What is fraction?A fraction is a way of representing a numerical value that is not a whole number. It is written in the form of a ratio and consists of a numerator and a denominator. The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts that make up the whole. Fractions are used to express part of a whole, such as when a pizza is divided into 8 equal slices, each slice would be represented as 1/8 of the pizza. Fractions are also used to represent a ratio between two numbers, such as when a recipe calls for 2/3 cup of sugar. In mathematics, fractions are used to represent division, to compare quantities, and to solve equations.
The ratio of female to male members can be found by taking the ratio of the average age of the female members to the average age of the male members.
Therefore, the ratio of female to male members is 40:25, or 4:2. This can be expressed as a common fraction as 4/2 or 2/1.
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given the cost function C(x)=0.76x+77,700 and the revenue function R(x)=1.81x find the break even point the intersection is________
Answers
To answer this problem we have to remember that the break even point occur where the revenue function and the cost function have the same value.
Then, this happens when
\(C(x)=R(x)\)Pluggin the expressions of our functions and solving for x we have:
\(\begin{gathered} 0.76x+77700=1.81x \\ 77700=1.81x-0.76x \\ 77700=1.05x \\ x=\frac{77700}{1.05} \\ x=74000 \end{gathered}\)Therefore the break even point occurs when x=74000. In this points both functions have value
\(\begin{gathered} C(74000)=133940 \\ R(74000)=133940 \end{gathered}\)
Discuss THREE ways on how bad behaviour in sport in a country can
dampen nation building.
(3 x 2) C
Fynlain
ba
ode
f
othie
in.
enorts can encourage positive
Answers
Answer:
Step-by-step explanation:
chicken
can someone help me please? and if its okay can you show the step by step explanation.
Answers
1. t=d/r
2. m=e/c^2
3. C= -P/R
And so on... You just divide/subtract the letters to the other side
Calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall.
Answer:
Logic - BMI formula
703*(lbs/inches^2)
703(118/64^2)=703(118/4096)
703*0.0288=20.2464
Answers
The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.
BMI stands for Body Mass Index.
It's a measure of body fat based on height and weight that applies to both adult men and women.
BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.
It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.
Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703
First, we need to convert the height into inches:5 feet 4 inches = 64 inches
Next, we plug the values into the formula and solve for the BMI:
BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464
Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.
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Consider a fractal line with fractal dimension D. The mean-square distance between monomers u and v along this line is ⟨(R(u)−R(v))2⟩=b2(v−u)2/D. Calculate the mean-square end-to-end distance R2 and radius of gyration Rg2 for this fractal line. Determine the ratio R2/Rg2 symbolically and then calculate this ratio for fractal dimensions D=1,1.7 and 2 .
Answers
The mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).
The mean-square end-to-end distance for the fractal line is as follows.⟨R2⟩ = ⟨(R(u)- R(v))^2⟩ for u = 0 and v = L where L is the length of the line.⟨R2⟩ = b²/L^2.D.L = b².L^(1-D).
Thus, the mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).
The radius of gyration Rg is defined as follows.
Rg² = (1/N)∑_(i=1)^N▒〖(R(i)-R(mean))〗²where N is the number of monomers in the fractal line and R(i) is the position vector of the ith monomer.
R(mean) is the mean position vector of all monomers.
Since the fractal dimension is D, the number of monomers varies with the length of the line as follows.N ~ L^(D).
Therefore, the radius of gyration for the fractal line is Rg² = (1/L^D)∫_0^L▒〖(b/v^(1-D))^2 v dv〗 = b²/L^2.D(1-D). Thus, Rg² = b².L^(2-D).
The ratio R²/Rg² is given by R²/Rg² = L^(D-2).
When D = 1, R²/Rg² = 1/L. When D = 1.7, R²/Rg² = 1/L^0.7. When D = 2, R²/Rg² = 1/L.
This provides information on mean-square end-to-end distance and radius of gyration for fractal line with a given fractal dimension.
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What is the Domain of the relation below:
{(0, 1), (-2,5), (3, 2), (-1, 5), (3,-2)}
Write your answer from smallest to largest with a comma.
D = {........
Answers
Answer:
(-2, -1, 0, 3,3)
Step-by-step explanation:
The domain simply refers to the possible x-values the function can take
so by listing out all the x-values of the individual points, we have all the domains
That will be ;
(-2, -1, 0, 3,3)
6) The exterior angle to the vertex angle of an isosceles triangle has measure 250. What is
the measure of each base angle of the triangle?
Answers
Answer:
12.5°
Step-by-step explanation:
In any triangle, an exterior angle is the sum of the remote interior angles.
The exterior angle at the vertex angle of an isosceles triangle will be the sum of the two congruent base angles. Hence, each base angle is half the value of the exterior angle.
25° = 2b
b = 25°/2 = 12.5° . . . . the measure of each base angle
PLEASE HELP IM CRYING Find the vertex of f(x)=(x+1)(x-6)
Answers
Answer:
(1/2,−25/4)
Step-by-step explanation:
just did this problem
Michael has 38 nickels and quarters in his backpack. If he has a total of $4.50. how many nickels, n, and how many quarters, q, does he have?
Answer Michael has
nickels and
quarters
Answers
Answer:
10 quarters and 2 nickels
Step-by-step explanation:
38 x .5 = 1.90
4.50 - 1.90 = 2.60
10 quarters and 2 nickels.