What are the roots of x2 5x − 6?
The roots of polynomial x2 5x − 6 are x = 3 and x = -2.
Factor the polynomial
x2 5x − 6 = (x - 3)(x + 2)
(x - 3) = 0
x - 3 = 0
x = 3
(x + 2) = 0
x + 2 = 0
x = -2
To find the roots of the equation x2 5x - 6, we must first factor the polynomial into two terms. The equation can be factored as (x - 3)(x + 2). We then have to set each factor equal to zero. For the first factor, (x - 3) = 0. With this equation solved, we obtain x = 3. (x + 2) Equals 0 for the second factor. The answer to this problem is x = -2. As a result, x = 3 and x = -2 are the roots of x2 5x - 6.
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Course activity: modeling with functions
Monica and Shanna are saving the money they earn from their after-school jobs to go on a school trip. Monica starts with $20 and then saves $14 each week. Shanna's savings are shown in the table.
Monica’s savings can he modeled by a ____ table
Shanna’s savings can be modeled by a ____ table
Answer:Both A and C
Step-by-step explanation:
Four friends want to take a vacation together, so each one gets a part-time job. Each person has 8 weeks to save $720 for the vacation. Analyze the four individual plans below and decide which of the four people will reach his or her goal of saving $720 for vacation.
Friend A: Works 13 hours per week at $6.95 per hour.
Friend B: Works 15 hours per week at $5.85 per hour.
Friend C: Works 18 hours per week at $5.25 per hour.
Friend D: Works 11 hours per week at $7.80 per hour. there!
How do you calculate the inverse?
The inverse of a number is it's reciprocal. Divide 1 by the number to obtain its reciprocal.
For example, the reciprocal of 5 is 1/5, and the reciprocal of 0.5 is 2. The reciprocal of a number x is denoted by 1/x or x^(-1).
For example, to find the reciprocal of 8, you would divide 1 by 8, like this:
1/8 = 0.125
To find the reciprocal of a fraction, you can also turn the fraction upside down to get its reciprocal. For instance, 4/3 is 3/4's inverse.
To find the inverse of a matrix, you can use the following formula:
A^(-1) = (1/det(A)) * adj(A)
where A is the matrix, det(A) is the determinant of the matrix, and adj(A) is the adjugate of the matrix. The transposition of a matrix's cofactor matrix is adjugate. The cofactor matrix is a matrix of the determinants of the minors of the original matrix, each of which is multiplied by a cofactor (-1)^(i+j). The minors of a matrix are the determinants of the square submatrices formed by deleting one row and one column from the matrix. The determinant of a matrix is a scalar value that can be computed from its elements.
For example, consider the matrix A:
[a b]
[c d]
The determinant of A is:
det(A) equals (a * d) - (b * c).
The cofactor matrix of A is:
[d -b]
[-c a]
The adjugate of A is the transpose of the cofactor matrix, so it is:
[d -c]
[-b a]
The inverse of A is then:
A^(-1) = (1/det(A)) * adj(A)
= (1/((a * d) - (b * c))) * [d -c]
[−b a]
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How do you find the height of a pyramid if the base area and the volume is known?
A square pyramid's volume and base area allow figuring out its height simple. H = 3 * V / (A_b).
Explain height of a square pyramid?The distance between the base and the vertex of a square pyramid, commonly known as its height or altitude. We discover the height of the pyramid when questioned how tall it is.Pyramids have volume because they are solid shapes. And from there, we can extrapolate the height of the a pyramid.How to determine a square pyramid's height
Knowing the volume and base area of a square pyramid makes calculating its height simple.You just need to divide each component by the base area and multiply its volume by three, as stated with in formula below:H = 3 * V / (A_b)
Where:
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What is the radius of X² y² 16?
The radius of X² y² 16 is 4.
X² y² 16 is a circle equation. To solve for the radius, we need to divide both sides by 4, then take the square root of both sides. So, 16/4 = 4 and √16 = 4. Therefore, the radius of X² y² 16 is 4. As a reminder, the equation for the radius of a circle is r = √(x² + y²). Therefore, when solving for the radius of a circle, the first step should be to divide both sides of the equation by 4 and then take the square root of both sides.
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Statements and Reasons
1) Given information
2) [tex]\overline{RT} \cong \overline{RT}[/tex] (reflexive property)
3) [tex]\triangle RST \cong \triangle RQT[/tex] (SSS)
4) [tex]\angle STP \cong \angle QTP[/tex] (CPCTC)
5) [tex]\overline{PT} \cong \overline{PT}[/tex] (reflexive property)
6) [tex]\triangle SPT \cong \triangle QPT[/tex] (SAS)
7) [tex]\angle SPT \cong \angle QPT[/tex] (CPCTC)
Two sentences from the daily weather report in Seattle are given below. It talks about snowfall levels over a 10-hour period during a snowstorm.
For the first 5 hours, 2 inches of snow fell every hour. There was no additional snow accumulation for the next 5 hours.
Which graph models the piecewise function for the given situation?
The graph of the models the piecewise function for the given situation is attached below.
What is piecewise function?
A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a certain interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a means to express the function.
Given that for the first 5 hours, 2 inches of snow fell every hour.
The height of the snow can represent by y = 2x, 0 ≤ x ≤ 5
Where x represents the time and y is the height of the snow.
The height of the snow is (5 × 2) = 10 inches after 5 hours.
After 5 hour, there is no snowfall.
The level of snow is y = 10 when 5 ≤ x ≤ 10.
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What are the 3 triangle similarity theorems?
Triangle similarity theorems are essential to geometry and can be used to compare two triangles. The three triangle similarity theorems are:
Side-Side-Side (SSS) Similarity TheoremAngle-Angle-Side (AAS) Similarity TheoremAngle-Side-Angle (ASA) Similarity Theorem3 Triangle similarity theoremsThe Side-Side-Side (SSS) Similarity Theorem: If the three sides of one triangle are proportional to the three sides of a second triangle, then the two triangles are similar. The Angle-Angle-Side (AAS) Similarity Theorem: If two angles of one triangle are equal to two angles of a second triangle, and the included side of the first triangle is proportional to the included side of the second triangle, then the two triangles are similar. The Angle-Side-Angle (ASA) Similarity Theorem: If two angles of one triangle are equal to two angles of a second triangle, and the sides between them are proportional, then the two triangles are similar.Learn more about similar triangles: https://brainly.com/question/14285697
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JS 19. Evaluate the integral || curlĒ dĞ using Stoke’s Theorem, where F =-yi+xj+ryck and S is the part of the sphere r2 + y2 + 22 = 4 that lies above the cy-planes, oriented upward. A. 27 B. 0 C. 87 D. -87 E. 47
The integral || curl F || dĞ is equal to -2. The correct answer is therefore option D that is -87.
To evaluate the integral || curl F || dĞ using Stoke's Theorem, we need to find a vector field F and a surface S such that the boundary of S is a closed curve C and the integral is equal to the flux of the curl of F through S. Using the given information, we can find the components of F as:
F = (-y, x, r)
The curl of F is given by:
curl F = (0, 0, 1)
The surface S is the part of the sphere r2 + y2 + z2 = 4 that lies above the cy-planes, oriented upward. This surface can be parameterized by:
x = rcosφcosθ
y = rcosφsinθ
z = rsinφ
where 0 ≤ φ ≤ π and 0 ≤ θ ≤ 2π.
The boundary of S is the curve C, which is the intersection of the sphere and the cy-plane. This curve can be parameterized by:
x = rcosθ
y = rsinθ
z = 0
where 0 ≤ θ ≤ 2π.
Using Stoke's Theorem, the integral || curl F || dĞ is equal to the flux of curl F through S, which is given by:
∫|| curl F || dĞ = ∫curl F · ndC
where n is the unit normal vector to the surface S.
Substituting the expressions for curl F and the parameterizations of S and C, we get:
∫|| curl F || dĞ = ∫(0, 0, 1) · (cosφcosθ, cosφsinθ, sinφ)dC
= ∫(sinφ)dC
= ∫sinθdθ
= [-cosθ]θ=0θ=2π
= -2
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Which is the solutions of the equations 5x 2y 7 *?
The solution set for the given systems of equations : 5x + 2y = 7 and y = x + 1 is x = 5/7 and y = 12/7
Solving the equations :
5x + 2y = 7 (1)
y = x + 1 (2)
Subtracting x on both sides of equation (2)
y - x = 1
Multiplying the equation by 5 on both sides
5y - 5x = 5 (3)
Adding equation (1) and (3) we get
5x + 2y + 5y - 5x = 7 + 5
7y = 12
y = 12/7
Solving for x by substituting y = 12/7 in (2)
12/7 = x + 1
x = 12/7 - 7/7
x = 5/7
--The question is incomplete, answering to the question below--
"What is the solution set of the given systems? 5x + 2y = 7 and y = x + 1"
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What is a median of 25?
The median of the first 25 whole numbers is 12.
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two.
The first 25 whole numbers are as follows:-
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
Here total no. of terms = n = 25 which is odd.
Therefore median = (n + 1)/2 th term
= (25 + 1)/2 th term
= 26/2 th term
= 13th term
Here, the 13th term is 12
Hence, the median of the first 25 whole numbers is 12.
Complete question: What is the median of the first 25 whole numbers?
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Which form of a linear equation is more efficient for determining each characteristic?
Slope
x -intercept
y -intercept
If you want to use your calculator to graph an equation, which form is more efficient?
Answer:
1/ Point slope form is more efficient for determining the Slope
2/ Standard form is more efficient for determining x-intercept and
y-intercept
3/ If you want to use your calculator to graph an equation, the Point slope form is more efficient
Step-by-step explanation:
1/ I say point slope form because the slope in this form is a point on the line, and he if knows the point on the graph and slope, he can graph the line easily.
2/ I say standard form because x and y intercepts of a graph, that is, the point where the graph crosses the x-axis and the point where it crosses the y -axis. So, it is the easiest form to find the x and y intercepts.
3/ If he knows a point and the slope he can graph it easily.
Is 6th grade math hard?
Answer:
not really
Step-by-step explanation:
At a local college, only 30% of students live off campus. Of those who live off campus, 62% of those students get a part-time job. Of those who live on campus, 65% work part-time. The tree diagram shows how the college students are divided into subgroups.
The tree diagram shows college students branching off into two categories, off campus and on campus students. Off campus students branches off into two sub-categories, work part-time and do not work. On campus branches off into two subcategories, work part-time and do not work.
What is the percentage of students who live on campus who do not have a part-time job?
18.6%
24.5%
35%
38%
Answer:
B, 24.5
Step-by-step explanation:
I just took the test
If f(x) has a y-intercept at 3 and x-intercepts at 2 and −4, and if
g(x) = −2f(−2x), what are the intercepts of g(x)?
Answer:
Step-by-step explanation:
The y-intercept of g(x) is 3 * -2 = -6.
To find the x-intercepts of g(x), we need to find the values of x that make g(x) equal to 0. Since g(x) = -2f(-2x), this means we need to find the values of x that make f(-2x) equal to 0. Therefore, we can find the x-intercepts of g(x) by solving the equation f(-2x) = 0 for x.
Since the x-intercepts of f(x) are at 2 and -4, this means that the equation f(x) = 0 has solutions at x = 2 and x = -4. Substituting these values into the equation f(-2x) = 0, we get:
f(-2(2)) = 0
f(-4) = 0
and
f(-2(-4)) = 0
f(8) = 0
Therefore, the x-intercepts of g(x) are at x = -2 and x = 4. These are the only intercepts of g(x) that we can determine for certain.
Is √ 3 is polynomial or not?
Yes, 3x² is a polynomial, but a special form of a polynomial with just one term which is called monomial.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given expression is 3x².
In the given expression three times of x square, x is the variable.
For an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.
Yes, this is a polynomial, but a special form of a polynomial with just one term which is called monomial.
Hence, 3x² is a polynomial.
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Consider the linear function y=5x+12y=5x+12 and the linear function represented by the table of values below.
Answer:
Step-by-step explanation:
y intercept = 12 the one with no x
use process of elimination
function=straight line
melania is tracking her running training program. the table gives her 5k run time at the end of each month. month time (in minutes) 1 47 2 43 3 39 4 36 5 35 6 33 what is the equation for the line of best fit, where x represents the month and y-hat represents the predicted time? y hat equals 33.6 plus 2.77 times x y hat equals 48.5 plus 2.77 times x y hat equals 33.6 minus 2.77 times x
The required regression equation for the line of best fit, where x represents the month and y-hat represents the predicted time is;
y = -2.78x + 48.5
How to find the regression equation?A regression equation is defined as the equation that is used in stats to find out what relationship, if any, exists between sets of data
From the given table, let x represents the month and y represents the time. Thus;
Mean of x; x-bar = (1+2+3+4+5+6)/6 = 21/6
x-bar = 3.5
Mean of y; y-bar = (47+43+39+36+35+33)/6
y-bar = 233/6 = 38.83
∑x = 21
∑y = 233
Using statistics calculator;
Sum of squares (SSX) = 17.5
Sum of products (SP) = -48.5
The general form of a regression Equation is;
y-bar = bx-bar + a
Where;
b = SP/SSX
= -48.5/17.5
= -2.77143
a = y-bar - b(x-bar) = 38.83 - (-2.77×3.5) = 48.53333
y = -2.78x + 48.5
Thus, the required regression equation is y = -2.78x + 48.5 for the line of best fit.
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Write the logarithmic equation log8 64 = 2 in exponential form
Answer: 64 = 8^2.
Step-by-step explanation:
The logarithmic equation log8 64 = 2 can be rewritten in exponential form as follows:
log8 64 = 2
64 = 8^2
Therefore, the exponential form of the given logarithmic equation is 64 = 8^2.
How to learn maths fast?
Learning mathematics quickly requires dedication and hard work.
What is mathematics?
Mathematics is the science of numbers, shapes, and patterns. It is used to describe and explain the physical world and to solve problems. Mathematics is a language that helps us to understand and communicate ideas. It is a tool used to organize and understand data, determine relationships, and make predictions.
According to the given question:
The first step to learning math quickly is to determine your level of understanding. It is important to identify any weaknesses in order to develop a plan to improve them. Once the strengths and weaknesses are identified, it is important to set realistic goals and to create an action plan to reach those goals.
It is also important to find a good tutor or mentor to help guide the learning process. A tutor or mentor can provide guidance, resources, and practice problems to help increase understanding of the subject. Additionally, they can help identify problem areas and provide feedback that can help improve learning.
Finally, it is important to take advantage of online resources. There are many online tutorials, websites, and videos that can help improve the learning process.
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find the number that completes the equation 6/5 divided blank = 6
Answer:
1/5 or 0.2
Step-by-step explanation:
[tex]\frac{6}{5}[/tex] multiplied by 5 or [tex]\frac{5}{1}[/tex]
[tex]\frac{6}{5}[/tex]x[tex]\frac{5}{1}[/tex]=6
so when dividing , you reciprocate the value after the division sign.
[tex]\frac{6}{5}[/tex]÷[tex]\frac{1}{5}[/tex]=[tex]\frac{6}{5}[/tex]x[tex]\frac{5}{1}[/tex]=6
therefore, "blank"= 1/5 or 0.2
You have blank when you divid both sides of equation 3n=12by 3
Answer:
n = 4
Step-by-step explanation:
You have ____ when you divide both sides of equation 3n = 12 by 3:
3n = 12
3n/3 = 12/3
n = 4
name the image point when the object point (4,4) is mapped by the following translations. (x,y)-->(x-4,y+2)
Answer:
(0, 6 )
Step-by-step explanation:
(x, y ) → (x - 4, y + 2 )
mans subtract 4 from the original x- coordinate and add 2 to the original y- coordinate, that is
(4, 4 ) → (4 - 4, 4 + 2 ) → (0, 6 )
Calculate the perimeter:
7cm
17cm
Rectangle
Answer:
48
Step-by-step explanation:
2*(L+W)
=2*(7+17)
********
How do you know if the limit is positive or negative infinity?
Limit base x to a f(x) is equal to infinity if we can say f(x) arbitrarily large for all x sufficiently x=a, from both sides, without actually letting x=a.
Given that,
We have to find how do we know if the limit is positive infinity or a negative infinity.
We know that,
What is infinity?On a number line, numbers move closer to positive infinity as they advance to the left and negative infinity as they move to the right. Positive infinity is always larger than any number, while negative infinity is always smaller.
Now,
We say
Limit base x to a f(x) is equal to infinity if we can say f(x) arbitrarily large for all x sufficiently close to x=a, from both sides, without actually letting x=a.
And
Limit base x to a f(x) is equal to negative infinity if we can say f(x) arbitrarily large and negative for all x sufficiently close to x=a, from both sides, without actually letting x=a.
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How to solve 3x - 5 =40
Answer:
[tex]x=15[/tex]
Step-by-step explanation:
[tex]3x-5=40\\3x=40+5\\3x=45\\x=\frac{45}{3} \\x=15[/tex]
What is the formula of mean method?
The formula of mean method is [tex]\frac{Sum of all values}{Number of values}[/tex].
The formula for the mean, also known as the average, is:
mean = [tex]\frac{sum of all values}{number of values}[/tex]
For example, if you have a list of numbers [1, 2, 3, 4], the mean would be calculated as follows:
mean = (1 + 2 + 3 + 4) / 4 = 10 / 4 = 2.5
The mean is a measure of central tendency that gives you an idea of the typical value in a set of numbers. It is calculated by adding up all the values in the set and dividing the sum by the number of values.
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What will be the median of the given data if the mean is 4.5 5 7 7 8 a 5 4 3 1 2?
The median for a given set of observations is 4.
What is mean?The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean. A data set's mean (average) is calculated by summing all of the numbers in the set and then dividing by the number of values in the set. When a data collection is arranged from least to largest, the median is the midway value. The mode is the number that appears the most frequently in a data collection.
Here,
given set of observation,
=5,7,7,8,a,5,4,3,1,2
4.5=(5+7+7+8+a+5+4+3+1+2)/10
45=42+a
a=3
median=5,7,7,8,3,5,4,3,1,2
=1,2,3,3,4,5,5,7,7,8
median=10/2
=5th term
=4
The median for given set of observation is 4.
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zhi noticed that an odd number had appeared eight times in a row on the following roulette table. she now felt very strongly that an even number would be next. on a single spin, the probability of getting an even number is 18 over 38. considering the last eight spins resulted in odd numbers, what is the probability of getting an even number on the next spin? a.) 18 over 38 because each spin is independent. b.) 0 because each spin is independent. c.) 8 over 38 because each spin is dependent. d.) 1 over 38 because each spin is dependent.
The probability of getting an even number on the next spin is a.) 18 over 38 because each spin is independent.
Probability is honestly how possibly some thing is to happen. Whenever we are uncertain approximately the final results of an occasion, we are able to communicate approximately the chances of positive outcomes—how possibly they are. The evaluation of occasions ruled via way of means of possibility is referred to as statistics. Probability is calculated via way of means of dividing the quantity of methods the occasion can arise via way of means of the overall quantity of outcomes. Probability and odds are one-of-a-kind concepts. Odds are the possibility that some thing occurs divided via way of means of the possibility that it would not happen.
Thus, the correct option is a.
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Find the perimeter of the triangle
(21-x) in.
(2x - 3) in.
(x + 5) in.
The Perimeter of the triangle is 23+2x in³
We know that formula of the Perimeter of the triangle is:
Perimeter= A+B+C
where A=(21-x)in.
B=(2x-3)in.
C=(x+5)in.
Solution:
Perimeter = (21-x)+(2x-3)+(x+5)
Perimeter = (18+x)+ (x+5)
Perimeter = 23+2x in³
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