The solution of the equation 2x^2 + 5x + 3 = 0 is x = -3 and x = -1/2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions are x = (-b +/- sqrt(b^2 - 4ac))/2a.
The solution of the equation 2x^2 + 5x + 3 = 0 can be found by using the Quadratic Formula. The Quadratic Formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions are x = (-b +/- sqrt(b^2 - 4ac))/2a. By substituting the given coefficients a = 2, b = 5, and c = 3 into this equation, we can solve for x. First, we calculate the discriminant b^2 - 4ac, which in this case is 25 - 24 = 1. Because the discriminant is positive, the equation has two real solutions. Next, we use the Quadratic Formula to calculate the solutions. To calculate the first solution, we substitute the given coefficients into the formula and solve for x: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -3 and -1/2.
Therefore, the solution of the equation 2x^2 + 5x + 3 = 0 is x = -3 and x = -1/2.
Discriminant: b^2 - 4ac = 25 - 24 = 1
Solution 1: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -3
Solution 2: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -1/2
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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)
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.
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 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]
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
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 do you find the value of k in a function?
To find the value of k in a function, you need to know the equation of the function and the input values for which you want to find the output, and then substitute these values into the equation and solve for k.
What is a function?A function is a relationship between each element of a non-empty set A and at least one element of another non-empty set B. Functions are the central idea of calculus in mathematics. The functions are special types of relations. A function is a rule that generates a unique outcome for each input x in mathematics.
What is domain of a function?The collection of all input values that you can use in a function without running into problems or producing undefined results is generally referred to as the domain of the function. When dealing with functions, it is crucial to keep in mind the function's domain because utilizing input values outside of the domain might provide erroneous or undefinable outputs.
To find the value of k in a function, you need to know the equation of the function and the input values for which you want to find the output.
For example, if the function is defined as f(x) = kx + b, and you want to find the value of k for a particular value of x, you can substitute the value of x into the equation and solve for k.
For example, if the function is f(x) = kx + b and you want to find the value of k when x = 2, you can substitute 2 for x in the equation to get:
f(2) = k(2) + b
Solving this equation for k gives:
k = (f(2) - b)/2
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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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Find The Curvature At The Point (2, 8, -1). X = 2t, Y = 8t^3/2, Z = -T² K=
The curvature at the point (2,8,-1) X = 2t, Y = 8[tex]t^{3/2}[/tex], Z = -t² is √2/152 when the formula is k = | r'(t)×r''(t) |/||r''(t)||³.
Given that,
We have to find the curvature at the point (2,8,-1) X = 2t, Y = 8[tex]t^{3/2}[/tex], Z = -t².
We know that,
The curve is x = 2t, y = 8[tex]t^{3/2}[/tex], z = -t².
Putting 2t=2
t=1
So,
t=1 at the point (2,8,-1)
Also r(t) = <2t, 8[tex]t^{3/2}[/tex], -t²>
r'(t) = <2, 8(3/2)√t, -2t>
r''(t) = <0,6/√t,-2>
||r''(t)|| = √(2²+(12√t)²+(-2t)
||r''(t)|| = √(4+144t+4t²)
Cross product = r'(t) × r''(t) = [tex]\left[\begin{array}{ccc}i&j&k\\2&12\sqrt{t} &-2t\\0&6/\sqrt{t} &-2\end{array}\right][/tex]
=i(-24√t+12√t)-j(-4-0)+k(12/√t-0)
=-12√ti+4j+12/√tk
| r'(t)×r''(t) |= √(-12√t)²+4²+(12/√t)² = √(144t+16+144/t)
The curvature at the point t=1 is k = | r'(t)×r''(t) |/||r''(t)||³
k = √(144t+16+144/t) /√(4+144t+4t²)³
k = √(144(1)+16+144/(1)) /√(4+144(1)+4(1)²)³
k = √304/ (152)³
k = √2/152
Therefore, the curvature at the point (2,8,-1) X = 2t, Y = 8[tex]t^{3/2}[/tex], Z = -t² is √2/152 when the formula is k = | r'(t)×r''(t) |/||r''(t)||³.
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Calculate the perimeter:
7cm
17cm
Rectangle
Answer:
48
Step-by-step explanation:
2*(L+W)
=2*(7+17)
********
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!
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.
Find the slope of the line graphed below.
Answer:
Step-by-step explanation:
slope equals rise over run
count over from one dot to the other , starting on the left
down 3 , over 6
down means negative, so
- 3/6
or -1/2
Is 6th grade math hard?
Answer:
not really
Step-by-step explanation:
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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How do you solve direct and inverse proportion questions?
Direct Ratios and/or Variations
If the ratio of two values, x and y, is constant, then they are directly proportional to one another (which always remains same). This would imply that x and y would either change in tandem or separately by a fixed amount that doesn't affect the ratio.Indirect proportions, inverse proportions, or variations
When the product of two values, x and y, is a constant, they are inversely proportional to one another (always remains the same).Accordingly, as x rises, y falls, as well as opposite, by a certain quantity such that x and y remain constant.Forming an equation to predict the value of an unidentified variable is also made possible by understanding that the product doesn't quite change.Thus, Inverse proportion is defined as y = k/x, k is the proportionality constant .
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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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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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Which equation has an X intercept of 3 and a y intercept of 5?
y = -[tex]\frac{5}{3}[/tex]x+5 equation has an X intercept of 3 and a y intercept of 5 .
The point on a line where it crosses an axis is referred to as the "intercept." The slope of the line passes through a point called an intercept on the y-axis.
The equation for a line, which is written as y = mx+c, which stands for slope and y-intercept, respectively, reflects this.
The two main intercepts are X-intercept and Y-intercept. Where the line crosses the x and y axes, respectively, is where the line's x-intercept and y-intercept are situated.
In this case, you are given both intercepts.
Plot a line from the third x-axis point.
On the y-axis, place the coordinates y = 5.
The necessary line is a straight line that passes through these two places is
y = -[tex]\frac{5}{3}[/tex]x+5
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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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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
A 95-kilogram student climbs 4. 0 meters up a rope in 3. 0 seconds. What is the power output of the student?.
The power output of student is P = 1241.34W
Let the mass of the student be m, length of the rope be l and the time taken by the student to climb the rope be t seconds.
Therefore, it is given that
m = 95kg
l = 4m
t = 3 seconds
Now we know that the formula of work done against the gravity (W) is given by
W = m x g x h
where m is the mass of the object,
g is the gravitational constant with g = 9.8 [tex]m/s^{2}[/tex]
and h is the height of the object from refernce, which in this case is l = 4m
Now, putting these values in work done formula we get,
W = 95 x 9.8 x 4
W = 3724 J
Now to find the power output, we know that
Power = (Work done)/(time taken)
Power = 3724/3
Therefore, power output of the student is equal to 1241.34W
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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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[tex]−20x+40=−20x+20[/tex]
The solution to the equation for x is that the equation −20x + 40 = −20x + 20 has no solution
How to determine the solution to the equation?From the question, we have the following parameters that can be used in our computation:
[tex]−20x+40=−20x+20[/tex]
Rewrite the above equation properly
So, we have the following representation
−20x + 40 = −20x + 20
Collect the like terms in the above equation
This gives
20x - 20x = 20 - 40
Evaluate the like terms in the above equation
So, we have the following representation
0 = -20
The above equation is false
Hence, the equation has no solution
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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 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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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 )
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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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
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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