The factors of the given quadratic equations are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]
What is factorization?
When we try to write the given equation in terms of linear values from which we calculate the roots of the given equation then we say that we have factorized them. Root of a equation means a value which satisfies a equation.
We are given a quadratic equation
[tex]4x^2+13x-15[/tex]
We use quadratic formula to compute the factor of the equation
[tex]x=\frac{-b}{2a}[/tex]±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{169+240} }{8}[/tex]
[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{409} }{8}[/tex]
Therefore the factors are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]
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Consider the calculation x - y + (- z) where x and z are positive real numbers and y is a negative real number. i) What are the directions of motion for this calculation ? ii) Is the final answer positive , negative , or undetermined ? i) Right, left , left ii) Undetermined i) Right , right , left ii) Undetermined i) Right , left , left ii) Negative i) Right right , left ii) Positive
Given
x - y + (- z) where x and z are positive real numbers and y is a negative real number.
Find
i) What are the directions of motion for this calculation ?
ii) Is the final answer positive , negative , or undetermined ?
Explanation
i) as we have given
x - y + (- z)
x - y - z
(x - y) - z
right -left - left
ii) for this we take examples
let x = 2 , y = -1 and z = 2
2- (- 1) + (- 2) = 1 , positive
now
let x = 2 , y = -1 and z = 5
2 - (- 1) + (- 5) = 3 - 5 = -2 , negative
so , it is both negative or positive
hence it is undetermined
Final Answer
Hence , the correct option is
i) Right, left , left
ii) Undetermined
The coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4). What are the coordinates of the image if the quadrilateral is translated 4 units down and 3 units right
If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3,-2), B'(-2,-1), C'(10,-1) and D'(3,0)
The coordinates of the quadrilateral ABCD is
A (-6,2) , B(-5,3), C(7,3) and D(0,4)
The quadrilateral is translated 4 units down and 3 units right
After translation
A(x, y)⇒ A(x + a, y +b)
The value of a and b will be positive if the shift is right and up.
The value of a and b will be negative if the shift is left and down.
Therefore
a = 3, b = -4
The coordinates of A' =(-6+3,2-4)=(-3,-2)
The coordinates of B' =(-5+3,3-4)=(-2,-1)
The coordinates of C' =(7+3,3-4)=(10,-1)
The coordinates of D' =(0+3,4-4)=(3,0)
Hence, If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3, -2), B'(-2, -1), C'(10, -1) and D'(3, 0)
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Given a Figure whose points are A(4, 5), B(2, -1), C(0, 0), D(-4, -1).
What would be the image of that figure if it goes under a reflection across the x-axis, what is the coordinate
of A¹?
A. A'(-4,-5)
B. A'(-4, 5)
C. A'(4, 5)
D. A'(4,-5)
Answer:
(4,-5)
Step-by-step explanation:
A is 5 units above the x axis so a' will be 5 units below the x axis.
if the value of the response variable is uniquely determined by the values of the predictor variables, we say that the relationship between the variables is: (choose the correct response)
Deterministic.
The relationship between the variables is deterministic. A deterministic relationship refers to a relationship in which the dependent variable does not depend on other elements (variables) other than the independent element classified in the relationship. The independent variable (element) in the relationship possesses an exact value. Hence deterministic relationship is also named as the exact relationship between variables.
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20) g(a) = a² - 2
h(a) = -3a
Find g(a) + h(a)
The value of g(a) + h(a) is a²-3a-2 or (a-2)(a-1) using addition of functions.
What is the Function?Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where x belongs to X and y belongs to Y, with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y
Adding two functions-
g(a) = a²- 2
h(a) = -3a
Let h(a) be g(a) + h(a)
So h(a) = a² - 2 - 3a.
We can factorize the function into (a-2)(a-1).
So we get h(a) = (a-2)(a-1).
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Which of the following represents the polar equation r = (tan 2θ)(csc θ) as a rectangular equation?
We will have the following:
[tex]r=\tan ^2(\theta)\csc (\theta)\Rightarrow r=(\frac{\sin(\theta)}{\cos(\theta)})^2(\frac{1}{\sin(\theta)})[/tex][tex]\Rightarrow r=\frac{\sin^2(\theta)}{\sin(\theta)\cos^2(\theta)}\Rightarrow r=\frac{\sin(\theta)}{\cos^2(\theta)}[/tex]Now, we corroborate with one of the expression, in our case we will analyze y = x^2:
[tex]r\sin (\theta)=(r\cos (\theta))^2\Rightarrow r\sin (\theta)=r^2\cos ^2(\theta)\Rightarrow r=\frac{\sin (\theta)}{\cos ^2(\theta)}[/tex]So, the expression taht represents the value given is:
[tex]y=x^2[/tex]The relationship between a distance in yards (y) and the same distance in miles (m) is described by the equation
y = 1,760m.
Find measurements in yards and miles for distances by filling in the table.
distance measured in miles 1 5 type your answer type your answer
distance measured in yards
type your answer type your answer 3,520 17,600
The equation for constant proportionality is y ∝ m .
1760 is a constant of proportionality.
What is meant by constant of proportionality?The ratio of two proportional values at a constant value is the proportionality constant. When either the ratio or the product of two variables results in a constant, the connection between the two is proportional. The ratio between the two stated quantities affects the proportionality constant's value.
The formula y = 1760m describes the relationship between a distance in yards (y) and a similar value in miles (m).
As a result, the graph of the aforementioned equation will be a straight line with a constant slope of 1760 that passes through the origin (0, 0).
As a result, a measurement in yards and a measurement in miles have the same proportionality relationship.
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The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?.
Percentage of the student body exists at least 21 years old exists 50%.
What is meant by normal distribution?A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.
When given a normal or Symmetric distribution, the mean of the distribution exists at the center with 0.5 or 50% of the distribution to either side (right and left) of the distribution.
Therefore, if the mean = 21 ; then the percentage of student body with at least 21 years is the percentage to the left of the distribution, which exists 50%.
P(x ≤ 21) = 0.5 = 50%
Therefore, 50 percentage of the student body exists at least 21 years old
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Select the correct answer.
Which of the following represents a function?
A. The first graph
B. The second graph
C. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
D.
x -5 -1 9 8 -1
y 1 7 23 17 1
The relation that represents a function is given as follows:
B. The second graph.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
For a point in the standard format (x,y), we have that:
x is the input.y is the output.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.In a graph, the equivalent to this is that there can be no vertically aligned points.
Then, for the options in this problem, we have that:
a does not represent a function, as the input -1 is mapped to two outputs, meaning that there are vertically aligned points.b represents a function, as each input value(-4, 9, 13 and -7) is mapped to only one output.c does not represent a function, as the input 3 is mapped to two outputs.d does not represent a function, as the input -1 is mapped to two outputs.More can be learned about relations and functions at https://brainly.com/question/12463448
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HELP ASAP PLSSSPLSPSLSPLSSSSSS
Graph g(x) = |x + 3|.
Answer:
Hope this helps!!
Which property is demonstrated below?
a(b+c)=(a.b)+(a.c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
( and 15 points for this and will make brainliest to best answer) Please be fast!
Which property is demonstrated below?
a(b + c) = (a*b) + (a*c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
Hi can someone help me with this?Writing the algebraic equation for the phrase below.. 1. The sum of X and 96 equals half of X .
Given:
1. The sum of X and 96 equals half of X.
To determine the algebraic equation, we note that the sum of x and 96 would be:
x+96
Next, half of x must be like this:
x/2
Then, the phrase equals means we set x+96 equals to x/2.
Therefore, the answer is:
[tex]x+96=\frac{x}{2}[/tex]ANSWER ASAPDonna received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.36 per pound after buying a coffee she had $26.85 left on your card how many pounds of coffee did she buy
The amount of coffee she bought is 5.16 pounds.
How to find the pounds of coffee she bought?She received a $70 gift card for a coffee store.
She used it in buying some coffee that cost $8.36 per pound after buying a coffee she had $26.85 left.
Therefore, base on the card, the number of pounds of coffee she bought can be calculated as follows;
Hence,
let
the amount of coffee she bought in pounds = x
Hence,
70 = 8.36x + 26.85
70 - 26.85 = 8.36x
43.15 = 8.36x
divide both sides by 8.36
43.15 / 8.36 = x
x = 5.16148325359
Therefore, the amount in pounds is 5.16 pounds.
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classify in as many ways possible
The figure above is a rectangle
The classifications of a rectangle are:
1. A rectangle has 4 sides and angles, therefore, it is a quadrilateral.
2. Each interior angle is a right-angle, that is 90⁰
3. The sum of the interior angles equals 360
4. The opposite sides are parallel
5. The opposite sides are equal
6. The diagonals bisect each other
7. The diagonals have the same length
Gwen says that the sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4 is Gwen correct explain why or why not
The sum of -1 and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.
First we will convert the mixed fractions into improper fractions.
-1 and 3/4 = -7/4
2 and 1/2 = 5/2
Sum of -1 and 3/4 and 2 and 1/2 = -7/4 + 5/2 = -7/4 + 10/4 = 3/4
Difference between 2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4
As both the values equal to 3/4 , we can say that the sum of -1 and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.
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If Judy completes a puzzle by herself, it takes her 3 hours. Working with Sal, it only takes them 2 hours.
A table showing Rate in part per hour, Time in hours, and Part of Project Completed. The first row shows Judy, and has, question mark, 2, and StartFraction 2 Over 3 EndFraction. The second row shows Sal, and has, r, r, and 2 r.
What is the missing value from the table that represents Judy's rate?
r
3 – r
StartFraction 1 Over 3 EndFraction.
3
The missing value is 1/3 from the table that represents Judy's rate which is the correct answer that would be an option (C).
What is the relation?In mathematics, relations are used to describe the link between the components of two sets. They aid in mapping items from one set (known as the domain) to elements from another set (known as the range), resulting in ordered pairs of the form (input, output).
We have been given the rates of time taken by Judy and Sal to complete a puzzle.
Sal's rate is r, as we can see from the table. Judy is said to take 3 hours to solve a puzzle by herself. It barely takes them two hours to work with Sal.
Because Judy completes the task in three hours, the portion of the puzzle finished in one hour is 1/3.
Therefore, the missing value is 1/3 from the table that represents Judy's rate
Hence, the correct answer would be an option (C).
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Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark (/) for the fraction bar.
Each midpoint's coordinate is given by the mean of the respective coordinates of the two endpoints of the segment. Then, if we say M is the midpoint of that segment, we have:
Mx = (-4 + 4)/2 = 0/2 = 0
My = [6 + (-2)]/2 = (6 - 2)/2 = 4/2 = 2
Therefore, writing those coordinates as an ordered pair, we have:
M = (0, 2)
You have to write an equation then solve.
Name the line(s) through
point A that appear
perpendicular to GH.
Answer:
AD
Step-by-step explanation:
Peter says,
"If you subtract 18 from my number and multiply the difference by -6, the result is -84."
What is Peter's number?
I already made the equation, I just am struggling solving it
-6(x-18)=-84
Answer:
x = 32
Step-by-step explanation:
-6(x-18) = -84
Divide both sides by -6
x - 18 = 14
Add 18 to both sides
x = 32
Slope And Rate Of Change
Based on the linear relationship between the ticket numbers and the total cost, the cost of one ticket can be found to be A. $10.50
How to find the cost of one ticket?First, find the rate of change in ticket pricing assuming the number of tickets is x and the total cost is y.
The rate of change is:
= Change in y / Change in x
= (67.50 - 46.50) / (5 - 3)
= $10.50
Then find the y-intercept:
y = Slope(x) + y-intercept
67.50 = 10.50(5) + y-intercept
y-intercept = 67.50 - 52.50
y-intercept = 15
Linear equation is:
Total cost = Rate of change (Tickets) + y-intercept
A single ticket would cost $10.50 which is the rate of change.
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The required rate of change and slope of the given relationship is $10.50.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope for the linear function is given as,
m = (y₂ - y₁) / (x₂ - x₁)
From the table substitute the value in the above equation,
m = [67.50-46.50]/[5-3]
m = 21 / 2
m = 10.50
Thus, the required rate of change and slope of the given relationship is $10.50.
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given that tank=8 and sinx is negative determine sin(2x) cos(2x) and tan(2x)
Answer:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
Explanation:
the tangent of an angle is equal to the opposite side over the adjacent side. So, if the tan(x) = 8, we can represent this as the following diagram:
Therefore, we can calculate the value of the hypotenuse as:
[tex]\text{Hypotenuse = }\sqrt[]{8^2+1^2}=\sqrt[]{64+1}=\sqrt[]{65}[/tex]With the hypotenuse, we can calculate sin(x) and cos(x) as follows:
[tex]\begin{gathered} \sin x=\frac{Opposite}{hypotenuse}=-\frac{8}{\sqrt[]{65}} \\ \cos x=\frac{\text{Adjacent}}{\text{hypotenuse}}=-\frac{1}{\sqrt[]{65}} \end{gathered}[/tex]We type the negative sign because the question says that sin(x) is negative.
Now, we will use the following trigonometric identities to find sin(2x), cos(2x) and tan(2x)
[tex]\begin{gathered} \sin 2x=2\sin x\cos x \\ \cos 2x=1-2\sin ^2x \\ \tan 2x=\frac{2\tan x}{1-\tan ^2x} \end{gathered}[/tex]Therefore, replacing the values, we get:
[tex]\sin 2x=2(\frac{-8}{\sqrt[]{65}})(\frac{-1}{\sqrt[]{65}})=\frac{16}{65}[/tex][tex]\cos 2x=1-2(\frac{-8}{\sqrt[]{65}})^2=1-2(\frac{64}{65})=-\frac{63}{65}[/tex][tex]\tan 2x=\frac{2(8)}{1-8^2}=-\frac{16}{63}[/tex]So, the answers are:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
7) 5x - 125 5x-:5 OTROW VOITA U Name Samantha Date 3/3 Kuta Software - Infinite Algebra 2 Graphing Linear Inequalities Sketch the graph of each linear inequality. 1) yz-2x-2 9) y 25 *2=5 2) ys-*+1 Yst
It is not possible to write a linear inequality such that the solution contains only positive values of x and y.
This happens because every line on the coordinate plane must have a y-intercept and/or an x-intercept. When the line crosses an axis, either the variable x or y changes its sign.
Add or subtract the following mixed numbers. First change each mixed number to an equivalent improper fraction. Then find a common denominator, and proceed as before. Leave your answer as an improper fraction. Be sure your answers are reduced to lowest terms. 3 1/4 + 6 1/2
In terms of the calculation, the answer is 39/4 in improper fraction.
What is an improper fraction?An improper fraction has a denominator that is greater than or equal to the numerator. Based on the numerator and denominator values, proper fractions and improper fractions are the two main types of fractions in mathematics.
What is a mixed fraction?A mixed fraction is a fraction formed by combining a natural number and a proper fraction. It is a shortened version of an improper fraction.
The given equation is [tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] .
Taking 4 as LCM from the above equation.
[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13/4) + (13/2)
[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13+26)/4
[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = 39/4
Now, since the solution must be proffered in an improper fraction.
Therefore, the obtained improper fraction is 39/4.
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Simplify by dividing
Answer: -27/40
Step-by-step explanation:
What’s the answer plsss
Answer:
option a is the right answer .
Step-by-step explanation:
Cos theta = B/h = 8/21
theta = 67.6 °
Step-by-step explanation:
imagine the triangle being flipped upwards around DE, so that F is on top instead of on the bottom.
then you see clearly that
DF (21) is the radius of the trigonometric circle,
DE is cos(angle D)×radius,
EF (8) is sin(angle D)×radius.
so,
8 = sin(angle D)×21
sin(angle D) = 8/21 = 0.380952381...
angle D = 22.39268781...° ≈ 22.4°
and so, something is wrong with your problem definition.
the answer options seem to aim for angle F, for which EF (8) is the cosine × radius.
but for angle D EF is clearly the sine × radius.
and for answer option b (20.9°) EF would have to be about 7.5 units long (with the radius DF still being 21). that is all too much off.
your teacher made a mistake. send him/ her my regards.
which of the following is not a step in a hypothesis test? a. state the null hypothesis about a population. b. set the alpha level. c. if the sample data is not located in the critical region, we accept the null hypothesis. d. if the sample data is located in the critical region, we reject the null hypothesis.
The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.
How to form the hypotheses?There are two hypotheses. The first one is called the null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test.
The hypothesis which substitutes the null hypothesis is an alternate hypothesis.
We know that the Null hypothesis is the one that researchers try to disprove.
The null hypothesis must be rejected if we choose the 99.7 percent of confidence level.
The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.
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Help This is due at the end of class
The coordinates of the vertices of the image of the square are S'(x, y) = (- 1, - 4), T'(x, y) = (- 1, 1), U'(x, y) = (4, 1) and V'(x, y) = (4, - 4).
How to translate a geometric locus set on a Cartesian plane
In this problem we need to make use of a translation on a geometric locus on a Cartesian plane, which is generated by four points representing the vertices of the square. The translation is a kind of rigid transformation, whose formula is shown below:
P'(x, y) = P(x, y) + t(x, y)
Where:
P(x, y) - Original pointt(x, y) - Translation vector.P'(x, y) - Resulting pointIf we know that S(x, y) = (- 6, - 5), T(x, y) = (- 6, 0), U(x, y) = (- 1, 0) and V(x, y) = (- 1, - 5) and t(x, y) = (5, 1), then the locations of the vertices of the triangle are:
S'(x, y) = (- 6, - 5) + (5, 1)
S'(x, y) = (- 1, - 4)
T'(x, y) = (- 6, 0) + (5, 1)
T'(x, y) = (- 1, 1)
U'(x, y) = (- 1, 0) + (5, 1)
U'(x, y) = (4, 1)
V'(x, y) = (- 1, - 5) + (5, 1)
V'(x, y) = (4, - 4)
The location of the image of the square is shown below.
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d = 12 cm42°Find the area of the green sector.
We will determine the area of the green section as follows:
[tex]A=r^2\cdot\frac{\alpha}{2}[/tex]Here alpha is the angle [In radians] and r is the radius-
*First: We determine the angle:
[tex]\alpha=360-42-180\Rightarrow\alpha=138[/tex]Now, we transform it to radians:
[tex]138\cdot\frac{\pi}{180}=\frac{23}{30}\pi[/tex]*Second: We replace on the equation:
[tex]A=(6)^2\cdot\frac{(\frac{23}{30}\pi)}{2}\Rightarrow A=\frac{69}{5}\pi[/tex]So, the area of the green sector is 69pi/5 square centimeters. [Approximately 43.4 square centimeters]
Answer:
A ≈ 43.4 cm²
Step-by-step explanation:
the area (A) of the green sector is calculated as
A = area of circle × fraction of circle
given d = 12 then r = 12 ÷ 2 = 6 cm
the central angle of the green sector = 180° - 42° = 138°
then
A = πr² × [tex]\frac{138}{360}[/tex] ( simplify fraction by dividing numerator/denominator by 6 )
= π × 6² × [tex]\frac{23}{60}[/tex]
= 36π × [tex]\frac{23}{60}[/tex]
= [tex]\frac{36\\pi (23) }{60}[/tex]
≈ 43.4 cm² ( to the nearest tenth )
I need help with my Pre-Calculus homework, the image of the problem is attached!
Answer:
Question 4
Answer: Alternative C - 0
Step-by-step explanation:
Since x→∞, we can substitute the values of x for values as 10, 100, 1000 and see the tendency of the function when the values are getting higher (closer to ∞):
For x = 10
f(10) = 0.5*10^(-3/4)
f(10) = 0.089
For x = 100
f(10) = 0.5*100^(-3/4)
f(10) = 0.016
For x = 1000
f(10) = 0.5*1000^(-3/4)
f(10) = 0.003
As we can see, when the x-values are getting closer to infinite, the y-values tends to zero. Thus, alternative C is correct.