Describe and justify the methods you used to solve the quadratic equations in parts A and B. A and b are the problems in the picture.
Answers
We are asked to justify the method and solve the given quadratic equations.
Part A:
\(2x(x+1.5)=-1\)Let us solve the above quadratic equation using the quadratic formula
First, expand the equation to convert it into the standard form.
\(\begin{gathered} 2x(x+1.5)=-1 \\ 2x^2+3x=-1 \\ 2x^2+3x+1=0 \end{gathered}\)So, the coefficients of the quadratic equation are
a = 2
b = 3
c = 1
The quadratic formula is given by
\(\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-3\pm\sqrt[]{3^2-4(2)(1)}}{2(2)} \\ x=\frac{-3\pm\sqrt[]{9^{}-8}}{4} \\ x=\frac{-3\pm\sqrt[]{1}}{4} \\ x=\frac{-3\pm1}{4} \\ x=\frac{-3+1}{4},\; \frac{-3-1}{4}\; \\ x=\frac{-2}{4},\; \frac{-4}{4}\; \\ x=-0.5,\; -1\; \end{gathered}\)Therefore, the solution is x = -0.5 and x = -1
Related Questions
Rivas bought a can of paint. He used 3/8 of it to paint a bookshelf. He used 1/4 of it to paint a wagon. He used some of it to paint a birdhouse and has 1/8 of paint left. How much did he use for the birdhouse?
Answers
Answer:
he used 1/8 of paint .....
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 9 characters long, and that each character is either a lowercase letter, (a, b, c, etc.), an uppercase letter (A, B, C, etc.) or a numerical digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). Assume that the hacker makes random guesses. What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction, not a percentage.
Answers
The probability that the hacker guesses the password on their first try is extremely low.
What is the probability that the hacker guesses the password on his first try?
There are 26 lowercase letters, 26 uppercase letters, and 10 numerical digits, for a total of 62 possible characters for each position in the password. Since the password is 9 characters long, there are \(62^{9}\) possible passwords.
The probability that the hacker guesses the password on their first try is 1 out of the total number of possible passwords:
Probability = 1 / (\(62^{9}\))
Using a calculator, this can be simplified to approximately 1.2 x \(10^{-16}\)
Therefore, the probability that the hacker guesses the password on their first try is extremely low.
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17)A rocket is launched (from the ground) with an initial upward velocity of 256 feet per second. How long will it take for the rocket to return to the ground?
Answers
Solution:
Given that;
A rocket is launched (from the ground) with an initial upward velocity of 256 feet per second.
To find how long it will take, the formula for the height in feet per second is
\(h(t)=-16t^2+v_0t+h_0\)Where
\(\begin{gathered} h_0\text{ is the initial height} \\ v_0\text{ is the initial velocity} \\ t\text{ is the time taken} \\ h\text{ represent the height} \end{gathered}\)Since, the rocket was launch from the ground and the rocket will return to the ground,
\(\begin{gathered} h(t)=0 \\ h_0=0 \\ v_0=256 \end{gathered}\)Substitute the values of the variables into the formula above
\(\begin{gathered} h(t)=-16t^{2}+v_{0}t+h_{0} \\ 0=-16t^2+256t+0 \\ -16t^2+256t=0 \end{gathered}\)The equation is
\(-16t^2+256t=0\)Solving the quadratic equation
\(\begin{gathered} 16t^2-256t=0 \\ 16t(t-16)=0 \\ 16t=0 \\ t=0 \\ t-16=0 \\ t=16 \\ t=0\text{ or 16} \end{gathered}\)The time taken for the rocket to take off will be t = 0,
Hence, it will take 16 seconds for the rocket to return to the ground.
the length of a rectangular room is 15 feet more than 3 times the height of a room. the floor has an area that is represented by the function below, where h is the height of the room in feet. which statement describes the width of the room
Answers
The true statement about the width is that it is 30.75 feet long
How to describe the width of the room?From the question, we have the following parameters that can be used in our computation:
Length = 15 feet more than 3 times the height of a room
Floor area, A(h) = 4h² + 42h + 90
Where l is the length and h is the height
Mathematically, the length can be represented as
l = 15 + 3h
Make h the subject
h = l/3 - 5
Recall that:
A(h) = 4h² - 42h + 90
Differentiate
A'(h) = 8h - 42
Set to 0
8h - 42 = 0
So, we have
8h = 42
Divide both sides
h = 5.25
Substitute h = 5.25 in l = 15 + 3h
l = 15 + 3 * 5.25
Evaluate
l = 30.75
Hence, the true statement is that the width is 30.75 feet
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please help i will give u brainlyist
Answers
Answer:
B, E, and D
Step-by-step explanation:
I'm not 100% sure
Katie baked a cake. Her brother ate 1/8 of the cake, her father ate 1/4 of the cake, and her mother ate 1/8 of the cake. How much is left?
Answers
Answer:
1/2
Step-by-step explanation:
hope this helps and have a nice day!
Graph the function.
f (x) = sin (
Use the Sine tool. First plot a point on the midline of the function. Then plot either the maximum or
minimum point closest to the first point plotted.
Answers
Step-by-step explanation:
shown in the photo I have provided
The graph of the given function f (x) = sin (πx/2) is attached below.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
If we plugged in x = 0, then we get
f (x) = sin (πx/2)
Therefore, this sine curve goes through the origin. The point is on the midline y = 0, the x axis.
We need either a minimum or maximum point. the expression f (x) is the same as . We will divide 2π over the coefficient of π/2 to get
The plot of the the maximum or minimum point closest to the first point is plotted in the graph.
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Which situation best describes a positive correlation
Answers
let's see who can solve this. pleseeee
Answers
The correlation coefficient between X and Y is Corr(X, Y) = 0.
To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.
a. Marginal distribution of X:
To find the marginal distribution of X, we integrate the joint PDF over the range of Y:
∫[0, 1] J(x, y) dy
Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:
∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1
So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.
b. Expectation of X:
The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:
\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)
Therefore, the expectation of X is E(X) = 1/3.
c. Variance of X:
The variance of X can be calculated using the formula:
\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)
Therefore, the variance of X is Var(X) = 5/36.
d. Covariance of X and Y:
The covariance of X and Y can be calculated as:
Cov(X, Y) = E(XY) - E(X)E(Y)
Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:
\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)
\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)
Cov(X, Y) = 1/6 - (1/3)(1/6) = 0
Therefore, the covariance of X and Y is Cov(X, Y) = 0.
e. Correlation coefficient between X and Y:
The correlation coefficient can be calculated using the formula:
Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))
Since the covariance of X and Y is 0, the correlation coefficient will also be 0.
Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.
f. Conclusion based on the correlation coefficient:
The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the
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2x² + 10 factorización
Answers
Answer:
2(x² + 5)
Step-by-step explanation:
To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:
2x² + 10 = 2(x² + 5)
We can't factor anymore, so the answer is:
2(x² + 5)
Answer:
2(x² + 5)
Step-by-step explanation:
To factorise this, do the distributive property backwards. In other words:
2x² + 10
2x² ÷ 2 + 10 ÷ 2
x² + 5
2(x² + 5)
∴ 2(x² + 5) is the answer
The graph of f(x) = 2x + 4 shifts six units to the right when it is replaced with the graph of f(x) = 2x-k What is the value of k?
02
04
06
O 10
Answers
The value of k in the function f(x) = 2x-k is 6.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
f(x) = 2x + 4
f(x) = 2x-k
Now,
To shift a linear function to the right, we subtract a constant from the input variable x. For example, f (x) = 2x + 4 shifts to the right by 2 units when it is replaced with f (x) = 2 (x - 2) + 4.
In this case, f (x) = 2x + 4 shifts six units to the right when it is replaced with f (x) = 2 (x - k) + 4. To find the value of k, we can equate the expressions inside the parentheses and solve for k:
x - k = x - 6 k = 6
Therefore, by the given functions the answer will be 6.
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A candy shop sells a box of chocolates for $30. It has $29 worth of chocolates plus $1 for the box. The box includes two kinds of candy: caramels and truffles. Juanita knows how much the different types of candies cost per pound and how many pounds are in a box. She said,If x is the number of pounds of caramels included in the box and y is the number of pounds of truffles in the box, then I can write the following equations based on what I know about one of these boxes:• x + y = 3• 8x + 12y + 1 = 30Assuming Juanita used the information given and her other knowledge of the candies, use her equations to answer the following:a) How many pounds of candy are in the box?b) What is the price per pound of the caramels?c) What does the term 12y in the second equation represent?d) What does 8x+12y+1 in the second equation represent?
Answers
a)From the information given, x is the number of pounds of caramels included in the box and y is the number of pounds of truffles in the box. The given equations are
x + y = 3
8x + 12y + 1 = 30
The pounds of candy in the box is x + y = 3. Thus, there are 3 pounds of candy in the box.
b) Since x represents the number of pounds of caramels and equation 2 represents total cost, then, the price per pound of caramels is $8
c) 12y represents the the cost of y pounds of truffles.
d) 8x + 12y + 1 in the second equation represents
Cost of x pounds of caramels + cost of y pounds of truffles + cost of box = $30
What is C/a + 4 when a=2, and c= 10
Answers
Answer:
4 and 10/2 so actually 9
Step-by-step explanation:
Answer:
The answer is 9.
Step-by-step explanation:
You just need to substitute the variables, so:
10/2+4
= 9
I hope this helps!
6. a) Calculate the areas of the three squares. b) Is the triangle a right triangle? Explain. 3 cm 4 cm 2 cm
Answers
Answer
The total area of the squares = 29 square cm
The triangle is not a right-angled triangle
Step-by-step explanation:
We are given three squares
The first square has a length of 4cm
The second square has a length of 3cm
The third square has a length of 2cm
Part A
Total area = Area of square 1 + Area of square 2 + Area of square 3
Area of a square = l^2
Where l is the length of the square
Area of a square 1 = 4^2
Area of a square = 16 square cm
Area of square 2 = 3^2
Area of square 2 = 9 square cm
Area of square 3 = 2^2
Area of square 3 = 4 square cm
Total area of the square = 16 + 9 + 4
The total area of the square = 29 square cm
Hence, the total square of the figure is 29 square cm
Part B
\(\begin{gathered} \text{ To proof if the triangle is a right angled triangle} \\ \text{ We n}eed\text{ to appy Pythagora's theor}em \\ \text{Hypotenus}^2=perpendicular^2+base^2 \\ \text{Hypotenus = 4}cm \\ \text{Perpendicular =3cm} \\ \text{Base = 2cm} \\ 4^2=3^2+2^2 \\ 16\text{ = 9 + 4} \\ 16\text{ }\ne\text{ 13} \\ \text{ Since the hypotenus is not equal to the summation of the perpendicular and base} \\ \text{Hence, the triangle is a not right angled triangle} \end{gathered}\)Hector collected the data shown in the table for a basketball league. What are the attributes, measurements used, and observations of the data? Team Players Average score (per game) Average age of players Attributes: Measurements used: Observations: A 12 74 13.5 B 15 50 12.8 C 14 63 12.2 D 17 38 13.1 E 11 51 12.7 F 16 60 11
Answers
The attributes, measurements used, and observations of the data are given below as per the average age of the score.
Attributes:
The table is given in the attached image below.
Measurements used:
Number of players (count)
Average score per game (mean)
The average age of players (mean)
Observations:
There are six basketball teams denoted by A, B, C, D, E, and F.
Team A has 12 players, with an average score per game of 74 and an average age of 13.5.
Team B has 15 players, with an average score per game of 50 and an average age of 12.8.
Team C has 14 players, with an average score per game of 63 and an average age of 12.2.
Team D has 17 players, with an average score per game of 38 and an average age of 13.1.
Team E has 11 players, with an average score per game of 51 and an average age of 12.7.
Team F has 16 players, with an average score per game of 60 and an average age of 11.
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Johnny drove 300 miles to meet his mother on Tuesday. On Thursday, he drove 120 miles to meet friends at an amusement park. On Saturday, he drove 420 miles back home. The entire trip took 14 hours. What was his average driving speed?
Answers
Answer:
Since the other dude is being inappropriate-
Here's your answer!
Answer: 60 mph
Step by Step Explanation
300+120+420=840
840/14=60
Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms
Answers
Hint :-
Break the given sequence into two parts .Notice the terms at gap of one term beginning from the first term .They are like \(\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}\) . Next term is obtained by multiplying half to the previous term . Notice the terms beginning from 2nd term , \(4,7,10,13\) . Next term is obtained by adding 3 to the previous term .Solution :-
We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,
\(\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}\) .
We can see that this is in Geometric Progression where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,
\(\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right] \)
Notice the term \(\dfrac{1}{2^{25}}\) will be too small , so we can neglect it and take its approximation as 0 .
\(\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right] \)
\(\\\implies \boxed{ S_1 \approx 1 }\)
\(\rule{200}2\)
Now the second sequence is in Arithmetic Progression , with common difference = 3 .
\(\implies S_2=\dfrac{n}{2}[2a + (n-1)d] \)
Substitute ,
\(\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908} \)
Hence sum = 908 + 1 = 909
Find the Surface Area. I need the answer fast.
Answers
Answer:
1615
Step-by-step explanation:
Area of triangle is: A= B•H•1/2
Area of square is A= L•W
39•17•1/2= 331.5
331.5•4= 1326
17•17= 289
Add the square area to the area of the triangles
289+ 1326= 1615
hope this helps chu <3
Answer:
663
Step-by-step explanation:
Since we are finding the area we multiply Length times Width which is a way of finding formal. L x W so the Length is 17 and Width is 39 so
17 x 39 = 663. So the area is 663
What is the simplified expression for 5 a b + 9 a b minus a b?
Answers
Answer:
\(=13ab\)
Step-by-step explanation:
\(5ab+9ab-ab\\\mathrm{Add\:similar\:elements:}\:5ab+9ab-ab=13ab\\=13ab\)
I need help with this practice problem solving *Just so you know, I think this subject is complex numbers and vectors. I may be wrong on this though, just trying to help. I will send you an additional picture, it goes along with this practice, it is a graph, use the graph to solve
Answers
The first step to solve this question is to draw the vectors.
Let's start by a=(-3,-5):
Continue with b=(1,4):
The resulting vector of the substraction a-b is drawn by linking the head of both vectors:
The resulting vector is the one that is green.
Help me please urgent
Answers
Answer:
option B, option D
Step-by-step explanation:
the bar graph better shows the number of students that like each sport.the circle graph better shows proportion of each responses to total responses in percentage form.THIS IS DUE IN 5 MINUTES I WILL GIVE BRAINLIST ASAP! The table below shows the cost of downloading songs from a website.
Number of songs 6 the total cost of it is 3.78 If c represents the total cost in dollars and cents for any number of songs downloaded, s, write a proportional equation for c in terms of s that matches the context.
Answers
Answer:
c = 0.63(s)
Step-by-step explanation:
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The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range of the transformed function is the same as the parent function, but the domains of the functions are different. The domain of the transformed function is the same as the parent function, but the ranges of the functions are differe
Answers
Both the domain and range of the transformed function are the same as those of the parent function.
What are Range and Domain?
The collection of all potential output values that a function can generate given its domain is known as its range.
The set of all potential input values for which a function is specified is referred to as its domain.
The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.
Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.
A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.
Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.
A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well
So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.
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Evaluate sin 60° without using a calculator by using ratios in a reference triangle.
Answers
5.28 + 2.4 + what equals to 7.32
Answers
Answer:
5.28+2.4=7.68
is right answer
Find the Mean, Median, Mode and Range of the following data. 17, 11, 12, 8, 16,6
Answers
Answer:
Mean: 11.822.
Mode: 17,11,12,8,16,6.
Median: 12.
Step-by-step explanation:
Hope this helps! The mode is the number that occurs most in the set and since they all show up once the mode is all of them.
A direct variation includes the points (2,18) and (n,9). Find n?
Answers
The value of the n is 1
In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.
To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.
(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:
18 = k(2)
k = 18/2
k = 9
Now that we have found the value of k, we can use it to find n when y = 9:
9 = 9n
n = 1
Therefore, the value of n is 1.
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Valentino is buying a movie at an online store. He can choose to use one of the three deals that are shown below or to just buy the movie without a deal. The online store charges a flat rate of $2.99 for shipping. Valentino is buying a movie for $12.99. He could buy the same movie with a digital download for $2.50 more.
Answers
The cheapest alternative that Valentino can select is to make the computation and discover which is less expensive when compared to others.
What is Algebra?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.
Given that the info is incomplete, Valentino needs to analyze the three options and make additions for extra charges or deductions for discount and make a purchase of the cheapest alternative.
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|2x| if x<0
Help please
Answers
The expression simplifies to |2x| = -2x, when x<0 by definition of absolute value
If x<0, then the expression |2x| simplifies to -2x.
The absolute value of a number is the distance of the number from zero on the number line.
Since x is negative in this case, 2x will be negative as well.
Taking the absolute value of -2x will give us the opposite of -2x, which is 2x.
However, since we know that x<0, this means that -2x will always be a positive number.
Hence, the expression simplifies to |2x| = -2x, when x<0.
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Complete question
Simplify the expression |2x| when x is less than 0, x<0
Which of the following sets of numbers could not represent the three sides of a triangle?
\{4,16,17\}{4,16,17}
\{8,20,25\}{8,20,25}
\{13,16,30\}{13,16,30}
\{8,20,25\}{8,20,25}
Answers
Answer:
(c) {13,16,30}
Step-by-step explanation:
In order for the sides lengths to form a triangle, the sum of the shortest two must exceed the longest.
That will not be the case for ...
{13, 16, 30}
because 13 +16 = 29 < 30.
(13, 16, 30} could not form a triangle
__
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