The equation for regression line is ŷ = -0.0192X + 39.288,
The correlation coefficient is -0.9817,
The population of Detroit in 2008 is 0.73 millions.
What is a regression line?A line that, using the bivariate data gathered, summarises the linear relationship (or linear trend) between the two variables in a linear regression study.
An estimate of the line that depicts the actual, but the unidentified, linear relationship between the two variables is called a regression line. When the value of the explanatory variable is known, the regression line's equation is used to predict (or estimate) the value of the response variable.
Given table showing the population of Detroit each decade.
year 1960 1970 1980 1990 2000
Population (millions) 1.67 1.51 1.20 1.03 0.95
A. equation for regression line,
X - Mx Y - My (X - Mx)² (X - Mx)² (X - Mx)(Y - My)
-20 -20 400 0.158 -7.96
-10 -10 100 0.057 -2.38
0 0 0 0.005 0
10 10 100 0.059 -2.42
20 20 400 0.104 -6.44
Sum: 1000.00 Sum: 0.382 Sum: -19.200
Sum of X = 9900
Sum of Y = 6.36 millions
Mean X = 1980
Mean Y = 1.272
Sum of squares (SSX) = 1000
Sum of products (SP) = -19.2
Regression Equation = ŷ = bX + a
b = SP/SSX = -19.2/1000 = -0.0192
a = MY - bMX = 1.27 - (-0.02*1980) = 39.288
ŷ = -0.0192X + 39.288
B. correlation coefficient,
X Values
∑ = 9900
Mean = 1980
∑(X - Mx)² = SSx = 1000
Y Values
∑ = 6.36
Mean = 1.272
∑(Y - My)² = SSy = 0.382
X and Y Combined
N = 5
∑(X - Mx)(Y - My) = -19.2
r Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -19.2 /√((1000)(0.382)) = -0.9817
Meta Numerics
r = -0.9817
The value of R is -0.9817.
High X variable scores correlate negatively with low Y variable scores because of this strong negative connection (and vice versa).
C. population in 2008
y = -0.0192X + 39.288
substitute x = 2008
y = -0.0192(2008) + 39.288
y = 0.7344
population in 2008 is 0.73 millons.
Hence the equation is ŷ = -0.0192X + 39.288,
the correlation coefficient is r = -0.9817
and population of Detroit in 2008 is 0.73 millions.
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Can anyone help me please
Answer:
2
Step-by-step explanation:
-4+6=2
Triangle ABC is transformed to triangle A′ B′ C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0. Which equation shows the correct relationship between the measures of the angles of the two triangles? (1 point) The measure of angle CAB = The measure of angle C prime B prime A prime The measure of angle BCA = The measure of angle A prime B prime C The measure of angle CAB = The measure of angle C prime A prime B prime The measure of angle BCA = The measure of angle C prime A prime B prime
The correct option when Triangle ABC is transformed to triangle A′ B′ C is A.The measure of angle BCA = The measure of angle C prime A prime B prime.
How to illustrate the triangle?Triangle ABC is changed into triangle A′B′C′ and on the x- and y-axes, a coordinate grid ranging from -4 to -4 to 4 is displayed. A is at ordered pair negative 1, 3, B is at ordered pair 0, 1, and C is at ordered pair negative 3, 0 in the triangle ABC.
A triangle Primes A, B, and C have A prime is at ordered pair minus 1, minus 3, B prime is at ordered pair minus 0, and C prime is at ordered pair minus 3, 0.
A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
Therefore,
<BAC = <B'A'C'
<ABC = <A'B'C'
<ACB = <A'C'B'
In this case, the correct option is A.
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Please help ASAP! Unit 5.4-5.5 Pre-Calculus question needed so I can retake a test!
Using half angle formula,
the exact value of sin(α/2) = √[5(√5 + 2)]/10the exact value of tan(α/2) = 1/(√5 - 2)What are half angle formula?Half angle formulas are equations that contain the half angles of the trigonometric ratios.
How to find the exact value of sin(α/2)?Given that tanα = -1/2 and π/2 < α < π
To find sin(α/2), we use the half angle formula
sin(α/2) = √[(1 - cosα)/2]
Also, tan²α + 1 = sec²α = 1/cos²α
⇒ cosα = ±1/√(1 + tan²α)
Since π/2 < α < π
cosα = -1/√(1 + tan²α)
Substituing this into the equation for sin(α/2), we have
sin(α/2) = √[(1 - cosα)/2]
sin(α/2) = √[(1 - (-1/√(1 + tan²α)))/2]
Substituting tanα = -1/2 into the equation, we have
sin(α/2) = √[(1 + 1/√(1 + tan²α))/2]
sin(α/2) = √[(1 + 1/√(1 + (-1/2)²))/2]
sin(α/2) = √[(1 + 1/√(1 + 1/4))/2]
sin(α/2) = √[(1 + 1/√(5/4))/2]
sin(α/2) = √[(1 + 1/√5/2)/2]
sin(α/2) = √[(1 + 2/√5)/2]
sin(α/2) = √[(√5 + 2)/√5)/2]
sin(α/2) = √[(√5 + 2)/2√5
sin(α/2) = √[(√5 + 2)/2√5 × √5/√5
sin(α/2) = √[5(√5 + 2)]/2 × 5
sin(α/2) = √[5(√5 + 2)]/10
So, sin(α/2) = √[5(√5 + 2)]/10
b. How to find the exact value of tan(α/2)?Using the half angle formula,
tan(α/2) = sinα/(1 + cosα)
Using the trigonometric identity cosα = ±1/√(1 + tan²α)
cosα = ±1/√(1 + (-1/2)²)
cosα = ±1/√(1 + 1/4)
cosα = ±1/√(5/4)
cosα = ±1/√5/2
cosα = ±2/√5
Since π/2 < α < π
cosα = -2/√5
Also, since the trigonometric identity sinα = ±√(1 - cos²α)
So, sinα = ±√(1 - (-2/√5)²)
sinα = ±√(1 - 4/5)
sinα = ±1/√5
Since π/2 < α < π
sinα = +1/√5
Substituting cosα = -2/√5 and sinα = +1/√5 into the equation for tan(α/2), we have
tan(α/2) = sinα/(1 + cosα)
tan(α/2) = +1/√5/(1 + (-2/√5))
tan(α/2) = +1/√5/(1 - 2/√5)
tan(α/2) = +1/√5/(√5 - 2)/√5)
tan(α/2) = 1/(√5 - 2)
So, tan(α/2) = 1/(√5 - 2)
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 7600(1.262)
This exponential function represents growth at a rate of 26.2% per unit increase in x.
This represents growth at a rate of 26.2% per unit increase in x.
This is an exponential function, so it will represent either growth or decay. To determine whether it is growth or decay and what rate it is, we need to look at the coefficient of the exponential term, which in this case is 1.262. Since this is larger than 1, the function is growing, and the rate of increase is equal to the coefficient minus 1, which is 26.2%.
This exponential function represents growth at a rate of 26.2% per unit increase in x.
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A hypothesis test was conducted to investigate whether the population proportion of students at a certain college who went to the movie theater last weekend is greater than 0.2. A random sample of 100 students at this college resulted in a test statistic of 2.25. Assuming all conditions for inference were met, which of the following is closest to the p-value of the test
The p-value is a probability and it should be between 0 and 1.
The p-value of a hypothesis test is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.
In this case, the null hypothesis is that the population proportion of students who went to the movie theatre last weekend is equal to 0.2 and the alternative hypothesis is that the population proportion is greater than 0.2.
Given that the test statistic is 2.25, the p-value would be the probability of getting a test statistic as extreme or more extreme than 2.25 assuming the null hypothesis is true. Without more information, we can't give you an exact p-value, but you can use a one-sided test and find the p-value using a z-table or using software that can calculate the p-value.
It is also important to note that the p-value is a probability and it should be between 0 and 1.
Therefore, The p-value is a probability and it should be between 0 and 1.
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Daniel LaRusso borrows $1,200 from a bank with 8% simple interest per year. How much will he have to pay back TOTAL (principal AND interest combined) in 2 years?
$150
$192
$1,350
$1,392
Answer:
Step-by-step explanation:
To calculate the total amount Daniel LaRusso will have to pay back in 2 years, we first need to calculate the interest he will owe on the loan.Simple Interest (I) = P * r * t
where P is the principal (the amount borrowed), r is the annual interest rate (expressed as a decimal), and t is the time (in years) for which the loan is borrowed.In this case, the principal is $1,200, the annual interest rate is 8%, and the time is 2 years.I = $1,200 * 0.08 * 2 = $192So, he will have to pay back a total of $1,200 (principal) + $192 (interest) = $1,392So, Daniel LaRusso will have to pay back a total of $1,392 in 2 years.
Answer:
D) $1392---------------------------------
The amount of interest at 8% simple for 2 years is 16% of the loan:
$1200* 16% =$1200*16/100 = $192The total amount including both the principal and interest is:
$1200 + 192 = $1392Correct choice is D.
If tanθ = 13 what is the value of 7sin2θ+3cos2θ
I think the question should be tan theta = 1/√3, but I have given the solutions of both.
Hope it helps.
If you have any query, feel free to ask.
If the floor of a cuboidal hall has a perimeter of 225m and height 25m then find (i). lateral surface area (ii). Total cost to paint its four walls if it costs Rs.9/- per sq.m
The lateral surface area is 1562.5 If the floor of a cuboidal hall has a perimeter of 225m and height 25m.
What is volume of Cuboid ?
volume of cuboid can be defined as the product of length , breadth and height.
Given,
If the floor of a cuboidal hall has a perimeter of 225m and height 25m
Lateral Surface area = 2h(l+b)
Given perimeter is 225m
so,
perimeter = 4 (l+b+h)
225 = 4 (l+b+25)
Given h = 25
225 = 4(l+b) + 100
4(l+b) = 225-100
4(l+b) = 125
l+b = 125/ 4
So,
Lateral surface area = 2h (l+b)
= 2 * 25 * ( l+b)
= 50*125/4
= 1562.5
Hence , The lateral surface area is 1562.5 If the floor of a cuboidal hall has a perimeter of 225m and height 25m.
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at present 1 us dollar can be exchanged with Nepali rupees 120.if Nepali currency is devaluated by 10%how much Nepali currency is needed to exchange 450 us dollar
48600 rupees is needed to exchange 450 us dollars
What is Percentage Decrease?Percentage Decrease is the percentage change in the value when it is decreased over a period of time.
How to determine this
When 1 us dollar is exchanged at 120 rupees
And devaluated by 10%
i.e 10% of 120 rupees
= 10/100 * 120
= 1200/100
= 12 rupees devaluated
So, 120 - 12 = 108 rupees can be exchanged
How much is 450 us dollars
Let x represent the number
If 1 us dollars = 108 rupees
450 us dollars = x
x = 450 * 108/1 rupees
x = 48600 rupees
Therefore, 48600 rupees can be exchanged for 450 us dollars
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Write down the equations corresponding to the augmented matrix in Exercise 12 and verify your answer to Exercise 12 is correct by substituting the solutions you obtained back into the original equations.
Both equations are satisfied, so the solutions to the equations are correct.
What is matrix?Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.
The augmented matrix in Exercise 12 is:
\begin{bmatrix}
1 & 4 & 5 & -10 \\
2 & 8 & 6 & -20
\end{bmatrix}
The corresponding equations are:
1x + 4y = -10
2x + 8y = -20
To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:
1(5) + 4(-2) = -10
2(5) + 8(-2) = -20
Both equations are satisfied, so the solutions to the equations are correct.
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Both equations are satisfied, so the solutions to the equations are correct. This can be solved using the concept of matrix.
What is matrix?Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.
The augmented matrix in Exercise 12 is:
[tex]\left[\begin{array}{cccc}1&4&5&-10\\2&8&6&-20\end{array}\right][/tex]
The corresponding equations are:
1x + 4y = -10
2x + 8y = -20
To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:
1(5) + 4(-2) = -10
2(5) + 8(-2) = -20
Both equations are satisfied, so the solutions to the equations are correct.
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Factorise 6-y^2
Please help
Answer:
6-y^2 can be factored by using the difference of squares formula which states that:
a^2 - b^2 = (a+b)(a-b)
We can factorize 6-y^2 by using the following:
6 - y^2 = (sqrt(6) + sqrt(-y^2))(sqrt(6) - sqrt(-y^2))
= (sqrt(6) + yi)(sqrt(6) - yi)
where i is the imaginary unit.
So, 6-y^2 = (sqrt(6) + yi)(sqrt(6) - yi) is the factored form of 6-y^2
Please note that the factorization is only true for real values of y, when y is not real the expression can't be factorized.
decision point: determining the first step as the marketing consultant for bolt, you need to determine the first step in understanding the underlying motivations of bolt's consumers. what method of research do you think would best help bolt understand its consumers' purchase motivations? select an option from the choices below and click submit. talk in depth to a few consumers for an extended period of time. ask many consumers many questions in a representative statistical sample. ask many consumers a few brief questions
I would recommend asking many consumers a few brief questions in a survey. This method would help Bolt quickly and easily obtain a broad view of its consumers’ purchase original cost motivations, which could then be analyzed to develop more targeted strategies.
Surveys are a great way to quickly obtain a broad view of a target audience’s motivations for purchase. By asking many consumers a few brief questions, Bolt can gain insight into what motivates them to purchase their products, or why they may choose not to purchase them. This data can then be analyzed to develop more targeted strategies to increase sales. Surveys also provide an efficient way to sample a large number of people, allowing Bolt to get a representative statistical sample of its consumers’ motivations. This data can also be used to inform future marketing campaigns, allowing Bolt to better target their customers and maximize sales.
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Solve for X, Leave in simplest radical
The value of x in the simplest radical form is 6.633
What is value ?
Value in mathematics can refer to a number of concepts that are closely related. Any specific mathematical object can be a mathematical value in general. In elementary mathematics, this is typically a number, such as a real number like or an integer like 42.
The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. For illustration, let's look at the number 45.
The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important." Examples include valor, integrity, freedom, and creativity, among others.
cos Ф = adjacent / hypotenuse
cos 45° = √22 / x
x = √22 / cos 45°
= (√22* √2 )
= √44
= 6.633
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Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.
A(−7, — 5), B(-2, 0); 1 to 4
The coordinates of P are
Therefore , the solution of the given problem of ratio comes out to be the coordinate P = (7, 0.4).
A ratio is defined.A ratio as well as fraction in mathematics shows how frequently one value is present in another. For instance, if there are eight grapefruit and six lemons in a fruit plate, the ratio from oranges to citrus is eight to six, or 8:6, which is comparable to the ratios 4:3 or the decimal 1.333.
Here,
Ratios are a useful tool for segmenting lines into smaller units.
P's coordinate is P = (7, -0.4)
The criteria are as follows:
A = (8,0)\sB = (3,-2) (3,-2)
m: n=1:4
Using P = mx2+nx1 my2+ny
m+n
m+n, line ratio is computed.
The result is:
P 1x3+4x8 /1x-2+4x0 = 1+4 / 7
=> P = 35, 2
=>P = (7, -0.4) (7, -0.4)
1+4
P therefore has the coordinate P = (7, 0.4).
Therefore , the solution of the given problem of ratio comes out to be the coordinate P = (7, 0.4).
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Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function.
R(x)=8x/x+19
Answer:
Below in bold.
Step-by-step explanation:
R(x) = 8x/(x + 19)
When x = -19 the denominator = zero so there is a vertical asymptote which is
x = -19.
If we divide 8x by x + 19 we get 8 remainder -152.
So horizontal asymptote is R(x) = 8.
As the degree of the numerator and denominator are the same ( both 1) there is no oblique asymptote.
Find the following functions. Simplify your answers.
Answer:
[tex]f(g(x)) = \boxed{\dfrac{x}{2}}[/tex]
[tex]g(f(x)) = \boxed{2x - 5}[/tex]
Step-by-step explanation:
We have the following two functions
[tex]f(x) = \dfrac{1}{x-5}\\\\g(x) = \dfrac{2}{x}+\:5[/tex]
To find [tex]f(g(x))[/tex] substitute the expression for [tex]g(x)[/tex] wherever you see an [tex]x[/tex] in [tex]f(x)[/tex]
[tex]\mathrm{For}\:f=\dfrac{1}{x-5}\:\mathrm{substitute}\:x\:\mathrm{with}\:\dfrac{2}{x}+5[/tex]
[tex]=\dfrac{1}{\dfrac{2}{x}+5-5}\\\\[/tex]
[tex]=\dfrac{1}{\dfrac{2}{x}}\\\\\\= \dfrac{x}{2}[/tex] ANSWER
To find [tex]g(f(x)[/tex], substitute the expression for [tex]f(x)[/tex] wherever you see an [tex]x[/tex] in [tex]g(x)[/tex]
[tex]\mathrm{For}\:g=\dfrac{2}{x}+5\:\mathrm{substitute}\:x\:\mathrm{with}\:\dfrac{1}{x-5}\\\\=\dfrac{2}{\dfrac{1}{x-5}}+5\\\\[/tex]
[tex]=2\left(x-5\right)+5\\\\= 2x - 10 + 5\\\\= 2x - 5\\\\[/tex]ANSWER
Note:
[tex]\dfrac{2}{\dfrac{1}{x-5}}=2\left(x-5\right)\\\\[/tex]
The long jump pit was recently rebuilt to make it level with the runway. volunteers provided pieces of wood to frame in the pit. each piece of wood provided measures 6 ft, which is approximately 1.8 to 8 7. determine the amount of wood, in meters, needed to rebuild the frame.
The amount of wood, in meters, needed to rebuild the frame is 1.8288 m.
What is amount and example?
amount to (something) : to produce (a total) when added together. The bill amounted to 10 dollars. They have debts amounting to thousands of dollars.
To calculate the amount of wood, in meters, needed to rebuild the frame, we can use the following formula:
wood (m) = (wood (ft) x 0.3048) / 6
Since each piece of wood provided measures 6 ft (approximately 1.8 to 8.7), we can calculate the amount of wood, in meters, needed to rebuild the frame as follows:
wood (m) = (6 ft x 0.3048) / 6
wood (m) = 1.8288 m
Therefore, the amount of wood, in meters, needed to rebuild the frame is 1.8288 m.
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suppose you play a game where you roll a set of 2 fair dice. if you roll a 4, 5, or 6, you will lose $6, but if you roll anything else, then you win $3. how much money will you gain or lose per each throwing?
Answer:
The outcome of rolling a set of 2 fair dice is a number between 2 and 12, and there is a probability of 1/9 for each outcome.
For the outcomes 4,5,6, you will lose $6, and for the other outcomes, you will win $3.
There are 3 outcomes 4,5,6, and 9-3 = 6 outcomes where you win $3.
So your expected gain/loss per roll is:
(3/9) * $3 + (3/9) * (-$6) = -$1
Therefore, on average, you will lose $1 per each throwing.
B. Reviewing Key Terms
Complete each sentence by writing the correct term in the blank.
15. When a bank borrows money from another bank, the interest rate it pays is called the
16. Ownership of more than one bank constitutes a
17. When a bank customer writes a check, the check will go through the process of
M
18. A bank's total assets minus its total liabilities make up its
19. Banks repay loans from the Federal Reserve at a rate of interest called the
The correct term for each term is -
Federal Fund Rate
Bank holding company
Check clearing
Net worth
Discount rate
What is an account?
A certain kind of financial asset or debt that is kept and owned in your name.
When a bank borrows money from another bank, the interest rate it pays is called the Federal Fund Rate.
Ownership of more than one bank constitutes a bank holding company.
When a bank customer writes a check, the check will go through the process of check clearing.
A bank's total assets minus its total liabilities make up its net worth.
Banks repay loans from the Federal Reserve at a rate of interest called the discount rate.
Therefore, these are the key terms used in banking.
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In 2009 a survey of Internet usage found that 79 percent of adults age 18 years and older in the United States use the Internet. A broadband company believes that the percent is greater now than it was in 2009 and will conduct a survey. The company plans to construct a 98 percent confidence interval to estimate the current percent and wants the margin of error to be no more than 2.5 percentage points. Assuming that at least 79 percent of adults use the Internet, which of the following should be used to find the sample size (n) needed
The sample size (n) needed can be calculated using
[tex]0.025 =2.33\sqrt{\frac{0.79*0.21}{n} }[/tex].
What is the Confidence Interval and Margin Of Error?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within.Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.Given:
We have the following confidence interval of proportions in a sample of n people who were polled, with a success probability of [tex]\pi[/tex] and a confidence level of [tex]1- \alpha[/tex].
π ± [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
Here z is the z score which has a pvalue of
[tex]1 -\alpha /2[/tex]
The margin of error is given as:
[tex]M = z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
79 percent of adults age 18 years and older in the United States use the Internet as found by a survey.
So, [tex]\pi =0.79[/tex]
98% confidence level
Now [tex]\pi =0.02[/tex], z is the value of Z that has a pvalue of [tex]1-\frac{0.02}{2} =0.99[/tex].
So, Z =2.33.
The sample size (n) needed can be estimated using:
We have to find n for which M = 0.025
The required equation is:
[tex]M =z\sqrt{ \frac{\pi (1-\pi )}{n} }[/tex]
[tex]0.025 = 2.33\sqrt{\frac{0.79*0.21}{n} }[/tex]
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(0) To wash a window that is 9 meters off the ground, Hazel leans a 10-meter ladder against
the side of the building. To reach the window, how far away from the building should Hazel
place the base of the ladder? If necessary, round to the nearest tenth.
The distance between base of ladder and the building should be
4.4 meter.
What is Pythagoras theorem?The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
AC² = AB² + BC²
Given,
Height of the window from the ground AB = 9 meter
Length of the ladder AC = 10 meter
Distance between base of ladder and building BC = ?
By Pythagorean theorem,
In the right ΔABC
AC² = AB² + BC²
10² = 9² + BC²
BC² = 10² - 9²
BC² = 100 - 81
BC² = 19
BC = √19
BC = 4.359 meter
BC = 4.4 meter
Hence, base of ladder should be 4.4 meter away from the building.
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How do I solve this?
Answer:
y=200/9. x= 329/9
Step-by-step explanation:
3x=-43-3y; x=-43/3-y. 5(43/3-y)-8y=5; y=200/9. x= 329/9
The sum of two numbers is 19, and their difference is 55. What are the two numbers?
Answer:
37 and -18
Step-by-step explanation:
Answer:
let x and y be two numbers
Which set of ordered pairs does not represent a function?
medians are drawn from point $a$ and point $b$ in this right triangle to divide segments $\overline{bc}$ and $\overline{ac}$ in half, respectively. the lengths of the medians are 6 and $2\sqrt{11}$ units, respectively. how many units are in the length of segment $\overline{ab}$?
The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.
What is right triangle ?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees, also known as a right angle. The side opposite the right angle is called the hypotenuse and it is the longest side of the triangle. The other two sides are called legs, and one of them is the base and the other one is the height.
We know that the medians are 6 and $2\sqrt{11}$ units, respectively.
Therefore, the length of $\overline{ab}$ is twice the median length from $a$ to segment $\overline{bc}$ + twice the median length from $b$ to segment $\overline{ac}$
so the length of $\overline{ab}$ = 2(6) + 2($2[tex]\sqrt{11}[/tex]$) = 12 + 4$\sqrt{11}$
so the length of $\overline{ab}$ = 12 + 4$[tex]\sqrt{11}[/tex]$ units.
Hence , The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.
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Suppose the slope of a line is positive. Describe what happens to the graph of the line as you move from left to right.
As you move the graph of the line from left to right, the output value of the function increases.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the linear function.b is the intercept, representing the initial value of the linear function.The slope determines if the function is increasing or decreasing over it's domain, as follows:
Positive slope: increasing function.Negative slope: decreasing function.A positive slope means that the function increases when it moves from left to right, that is, when x increases.
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Solve the equation.
free
if necessary:
combine terms
*x+3-2x = 4 x5
apply properties:
add
subtract
multiply
divide
to start over:
reset
The solution to given equation (3/4)x + 3 - 2x = -(1/4) + (1/2)x + 5
is x = -1
Consider given equation.
(3/4)x + 3 - 2x = -(1/4) + (1/2)x + 5
We need to solve this equation.
First we combine the like terms on each side of the equation.
(3/4 - 2)x + 3 = (-1/4 + 5) + (1/2)x
Simplify each side of the above equation.
(-5/4)x + 3 = 19/4 + (1/2)x
Now subtract (1/2)x from each side,
(-5/4)x + 3 - (1/2)x = 19/4 + (1/2)x - (1/2)x
Simplify each side
(-5/4 - 1/2)x + 3 = 19/4 + 0
(-7/4)x + 3 = 19/4
Add -3 to each side of the equation.
(-7/4)x + 3 - 3= 19/4 - 3
(-7/4)x = 7/4
Multiply each side of equation by (-4/7)
(-7/4)x × (-4/7) = 7/4 × (-4/7)
x = -1
Therefore, the solution is x = -1
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Look at picture for question.
Answer: $23,800
Step-by-step explanation:
It was worth $37,000 at first and now it's worth $1800.
So we have 37,000 - 1800 = $35,200 that left away.
And we know that 8 years passed away.
So we have 35,200/8 = $4400 each year.
We are looking for 3 years later.
So we have 440*8 = $13,200 that left after 3 years.
And lastly, it's worth 37,000 - 13200 = $23,800 3 years later.
How many unique triangles can be drawn with side lengths 5 inches 15 inches and 30 inches
Answer:
Step-by-step explanation:
The idea is, for each triangle, sort all of its sides and then store it in a map, if all those three sides are already present in the map then increase the frequency by 1, else its frequency will be 1. The count of elements of the map which have frequency 1 in the end will be the answer.
Select the correct description for the quadratic expression below
the product of x and a factor not depending on x
What is quadratic equation
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The equation given 3x(m-6n)²
This expression contains two factors:
1 factor: 3x
2 factor: (m-6n)²
Hence the product of x and a factor not depending on x.
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