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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How can this expression be written another way? 60x−24 Factor using the distributive property and the greatest common factor to write an equivalent expression.
The equivalent expression of the given expression 60x - 24 using distributive property and greatest common factor is 12(5x-2).
Distributive property is a property with which we multiply the sum or difference of two numbers with a number. For example:
a×(b+c) = a×b + a×c
a×(b-c) = a×b - a×c
The greatest common factor is a number which is common multiple of all the given numbers.
Now, solve the given expression 60x - 24
The factors of terms
60x = 12 × 5x
24 = 12 × 2
The greatest common factor is 12, so we take 12 common and the given expression can be written as
60x - 24
= 12 × 5x - 12 × 2
= 12(5x - 2)
Hence, the equivalent expression is 12(5x-24)
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NEEd HELP 9th grade asp
Answer:175/48
Step-by-step explanation:
This is a financial mathematics problem that I need help with
SOLUTION
Carrie's credit card was stolen, she was charged $ 2,000
Hence carrier's is responsible for paying $2,000
←
Mattie Evans drove 140 miles in the same amount of time that it took a turbopropeller plane to travel 540 miles. The speed of the plane was 200 mph faster than the speed of the car
Find the speed of the plane.
The speed of the plane was
(Simplify your answer.)
mph.
Since the speed of the turbopropeller plane was 200 mph faster than the speed of the car, the speed of the turbopropeller plane is equal to 70 mph.
How to determine the speed of this plane?In order to solve this word problem, we would assign variables to the distance and speed of both Mattie's car and the turbopropeller plane, and then translate the word problem into algebraic equation as follows:
Let d₁ represent the distance covered by Mattie.Let v₁ represent the speed of Mattie's car.Let d₂ represent the distance covered by the turbopropeller plane.Let v₂ represent the speed of the turbopropeller plane.Translating the word problem into an algebraic equation, we have;
v₂ = v₁ + 200
Since Mattie and the turbopropeller plane travled at the same time, we have:
Time = distance/speed
Time = d₁/v₁ = d₂/v₂
Time = 140/v₁ = 540/v₁ + 200
Cross-multiplying, we have:
140(v₁ + 200) = 540v₁
140v₁ + 28,000 = 540v₁
Next, we would rearrange the equation by collecting like terms as follows:
540v₁ - 140v₁ = 28,000
400v₁ = 28,000
Speed of plane, v₁ = 28,000/400
Speed of plane, v₁ = 70 mph.
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Rectangle TUVW with vertices
T(-3,-1), U(0, -2), V(-2, -8), and
W(-5, -7): 90° counterclockwise
T':
U':
V':
W':
for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,
T': (1, -3)
U': (2, 0)
V': (8, -2)
W': (7, -5)
In this question, we have been given a rectangle TUVW with vertices
T(-3,-1), U(0, -2), V(-2, -8) and W(-5, -7)
We know that for 90° counterclockwise rotation is (x, y) becomes (-y, x)
so, the coordinates of T' would be,
T' = (1, -3)
the coordinates of U' would be,
U' = (2, 0)
the coordinates of V' would be,
V' = (8, -2)
the coordinates of W' would be,
W' = (7, -5)
Therefore, for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,
T': (1, -3)
U': (2, 0)
V': (8, -2)
W': (7, -5)
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The equations y = 7x-2 and 14x- 2y = 3 represent what?parallel linesperpendicular linesthe same lineintetsecting, non perpendicular lines
As a first step we are going to isolate y in both equations:
(1) y=7x-2
(2) -2y=-14x+3
y=7x-3/2
Since they have the same slope 7, that mean these lines are parallel
Use the long division method to find the result when 9x³ +30x² + 10x - 24 is
divided by 3x + 8. If there is a remainder, express the result in the form
q(x)+7(2).
Answer:
8
3x² + 2x - 2 - ----------
3x + 8
Step-by-step explanation:
3x² + 2x - 2
--------------------------------
3x + 8 | 9x³ + 30x² + 10x - 24
-9x³ - 24x² ↓
--------------------------------
6x² + 10x
-6x² - 16x ↓
-------------------------
-6x - 24
+6x + 16
----------------
-8
I hope this helps!
Which lines are perpendicular to 3x – y = 10? Select all that apply. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36)
The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.
What is the equation of a perpendicular line?Let the equation of the line be y = ma + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx +c is given as y = -(1/m)x + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation is given below.
3x – y = 10
y = 3x – 10
Then the equation of the perpendicular line is given as,
y = –(1/3)x + d
The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.
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Triangles FAD and DCE are translations of triangle ABC.
Select all the statements that must be true. (Lesson 1-21)
A. Points B, A, and F are collinear.
PERIOD
E
(B.) The measure of angle BCA is the same as the measure of angle CED.
C. Line AD is parallel to line BC.
D. The measure of angle CED is the same as the measure of angle FAD.
(E.) The measure of angle DAC is the same as the measure of angle BCA.
F. Triangle ADC is a reflection of triangle FAD.
The statements about triangles FAD and DCE which are translations of triangle ABC include the following:
A. Points B, A, and F are collinear.
(B.) The measure of angle BCA is the same as the measure of angle CED.
C. Line AD is parallel to line BC.
(E.) The measure of angle DAC is the same as the measure of angle BCA.
The types of transformation.Generally, there are four (4) main types of transformation and these include the following:
ReflectionDilationRotationTranslationWhat is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Since triangles FAD and DCE both represent the translations of triangle ABC (see attachment), we can logically deduce the following information:
Points B, A, and F all lie on the same line BF, which makes point B, A, and F collinear.All of the sides and angles of triangle ABC (ΔABC) are equal to triangle DCE (ΔDCE), which makes angle BCA (m∠BCA) equal to angle CED (m∠CED).Line AD and line BC are parallel lines because they can never meet.The measure of angle DAC (m∠DAC) is the same as the measure of angle BCA (m∠BCA).Read more on translation here: https://brainly.com/question/19880883
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Solve for x? Please help me with this asap! Show your work if you want the extra points and Brainiest!
The value of x is 10
How to determine the valueFrom the diagram shown, we can see that it takes the shape of a parallelogram
The properties of a parallelogram includes;
Opposite sides are described as parallel to each otherOpposite sides are equal or congruentThe same-sided interior angles are said to be supplementary, that is, they add up 180 degreesEvery diagonal of the parallelogram divides it into two equal triangleThe diagonals of a parallelogram bisect each other at right anglesWe can see that the diagonal bisects the parallelogram into equal halves and then the parallel and opposite sides are equal.
If the opposite sides of x = 10
Then, x = 10
Hence, the value is 10
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What's a corner of a square? Two lines where they meet
Answer: A square is a shape with four equal-length sides and four corners that are all right angles.
HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP HELP HELP
Answer:
a) 1.6×10∧-6
b)2×10∧7
Hello, I just need help with part b and it's dealing with combinations
According to the combination method, there are 6 ways for the selection to be made if one worker is to be a receptionist, one a secretary, and one a technical typist.
Combinations:
A combination is all about grouping. The number of different groups which can be formed from the available things can be calculated using combinations.
The standard form for calculating the combinations is,
[tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
where,
0 ≤ r ≤ n.
This formula is sometimes also called as ncr formula.
Given,
An executive hires 3 office workers from 8 applicants.
Here we need to find how many ways can the selection be made if one worker is to be a receptionist, one a secretary, and one a technical typist.
Here we have to split the problem like the following,
We know that the total number of office workers is 3.
Like, if one worker is to be a receptionist, the the combination is like,
So, the value of n = 3 and r = 1.
Then, according to the ncr formula,
=> ³C₁ = [tex]\frac{3!}{1!(3-1)!}[/tex]
=> 3!/1!2!
=> (3 x 2 x 1) / 1 x 2 x 1
=> 3
Similarly, if one worker is to be a secretary,
Here the value of n = 2 (Because we have already select one person as receptionist) and r = 1
So,
=> ²C₁ = (2!)/1!(2-1)!
=> (2x1)/ 1 x 1
=> 2
Similarly, if one worker is to be a technical typist,
Here the value of n = 1 (Because we have already select one person as receptionist) and r = 1
So,
=> ¹C₁ = 1
Therefore, the total number of possible ways are,
=> 3 x 2 x 1
=> 6
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16 more than s is at most -80 interval notation
The answer in interval notation is given by {96, ∞}.
What is an interval notation?An interval notation can be defined as a set of real numbers which comprises all of the real numbers that are representing a continuous function and lies between two set of numbers.
This ultimately implies that, an interval notation can be used as a technique for writing all of the subsets of the real number line.
Translating the given word problem into an inequality algebraic expression:
16 - s ≤ -80
Adding 80 to both sides of the expression, we have:
80 + 16 - s ≤ -80 + 80
96 - s ≤ 0
Rearranging the expression, we have:
s ≥ 96
Therefore, we have {96, ∞}.
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Complete Question:
Translate and solve: 16 more than s is at most -80.
Give your answer in interval notation.
lia has taken a mathematics exam, and she wants to calculate an 88% confidence interval to represent the exam scores within her group of friends. what are the z statistics that fall at each line marking the middle 88% of scores in the distribution?
In the given scenario, in order to calculate an 88% confidence interval, the z statistics that fall at each line marking the middle 88% of scores in the distribution would be +/- 1.555 (from the table).
In a case of seeking 88% confidence interval, the implication is that there is 12% chance that the interval does not contain the true value i.e., α=0.12 Assuming a two-sided test, it means that there should be 6% chance attributed to each tail of the z statistics (distribution). Thus, zα/2= z0.06.This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. It is determined by z-value by reverse-lookup in a z-table. Find the closest value in the table to 0.9400 as possible, then see what its row and column is. From observation, it is seen that 0.9394 and 0.9406 are in the table with z -values of 1.55 and 1.56 respectively.We use liner interpolation to find the experimental z-score:Hence the z score = 1.5550
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I need help with these asap
1) What is the equation of the line through the points (1,1), (5,4), (9,7), and (13,10)
A) y = 4/3 x + 1/3
B) y = 4/3 x - 1/3
C) y = 3/4 x + 1/4
D) y = 3/4 x - 1/4
2) Image
1st question (the image):
y= -5/4x + 3/2
how to solve:
y=mx+b
b: where the line meets the y axis
3/2 is 1.5 which matches up perfectly with the graph
m: the direction of the slope
If you look where the line matches with a point and you go down -5 and go right 4 it matches up and thats why m = -5/4
2nd question (the text):
C) y = 3/4 x + 1/4
how to solve
draw a graph (up above)
y:mx+b
to find m: rise/run
find the first point (1,1) you have to go 3 points up and 4 points right to get to the next point
(5,4) and thats why m=3/4
b: where the link hits the y axis compare the answers and the graph and find the most resonable one... which is 1/4
Hakeem is the oldest of three siblings who ages are consecutive integers. If the sum of their ages are 69, find Hakeem age
Answer:
24
Step-by-step explanation:
Hakeem is the oldest of three siblings who ages are consecutive integers. If the sum of their ages are 69, find Hakeem age.
It should be noted that:
= 22 + 23 + 24
= 69
Hakeem's age is 24
[tex]\frac{1}{x -3/6}[/tex]
The fraction 1/ (x- 3/6) can be simplified in its simplest form as 6/(6x -3).
How can the given faction be expressed?From the question were given the expression as 1/ (x- 3/6) , which have the numerator as 1 and the denominator as (x- 3/6) , then
the denominator can be expressed as
(x- 3/6)
which can be simplified as :
(6x -3)/6
then we can place it back to the normal equation as 1/ (6x -3)/6, since the equation now appear in form of inverse function, Then this can be expressed by simplifying it as 6/(6x -3).
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Find the measure of
Answer:
50 degrees
Step-by-step explanation:
Line CDF is 180 degrees
76 and 54 and some part of the 180 degrees
1. add 76+54 = 130
2. subtract 180-130 = 50
The weight f a stack of standard 8.5*11 copier paper vs. number of sheets of paper
A. The weight of the copies and the quantity of papers are proportional.
B. There is no proportion between the number of books and their weight.
Given,
A. All versions of the document are 8.5 by 11 inches in size.
We can readily determine the quantity of papers using direct proportion because all the paper has the same dimensions and weight.
As a result, the weight of the copies and the quantity of papers are proportional.
B. Each book has a distinct weight, as we know.
Since each book varies in weight, it is difficult to calculate the quantity of papers using a direct percentage.
Therefore, there is no proportion between the number of books and their weight.
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PLEASE HELP ASAP!!
1. Use the space provide to respond to each statement concerning the given graph of a radical function.
a.) State the domain of the function.
b.) State the range of the function.
c.) Identify the end behavior of the function.
d.) Identify the x – intercept. Write as an ordered pair.
e.) Determine the absolute minimum of this function.
Part a
The domain is the set of x-values, which is [tex][1, \infty)[/tex].
Part b
The range is the set of y-values, which is [tex][-3, \infty)[/tex].
Part c
As [tex]x \to \infty[/tex], [tex]y \to \infty[/tex].
Part d
The x-intercept is when y=0, which is [tex](2, 0)[/tex].
Part e
The absolute minimum is the lowest point, which has a y-coordinate of [tex]-3[/tex].
Part a
The domain is the set of x-values, which is .
Part b
The range is the set of y-values, which is .
Part c
As , .
Part d
The x-intercept is when y=0, which is .
Part e
The absolute minimum is the lowest point, which has a y-coordinate of
A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio.
A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio.
___________________________
Find the coordinates of partition point P that divides the segment into a 5:2 ratio.
5:2 means that it is divided into 7, and we do not move two positions from (7,7)
X axis
7- (-7) = 14
14/7 = 2
7-2*2 = 3
Y axis
7-(-6)= 13
13/7 =
7 - 2* (13/7) = 49/7 - 26/ 7 = 23/7 = 3 2/7
______________________________
Answer
(3, 3 2/7)
Question 1 3 pts Isis has 4.8 m of ribbon for crafts. She wants to share it evenly with 12 friends. How many centimeters of ribbon would 5 friends get?
We will investigate the equal distribution of ribbon amoung her friends.
Isis has a ribbon for crafts for a certain length ( L ):
[tex]L\text{ = 4.8 m}[/tex]Isis has ( n ) number of friends amoung which she wants to equally distribute the length ( L ) of her ribbon:
[tex]n\text{ = 12}[/tex]Under the assumption of equal distribution we can divide the total length of ribbon ( L ) amoung Isis ( n ) of friends to determine what length ( l ) each friend got:
[tex]\begin{gathered} l\text{ = }\frac{L}{n} \\ \\ l\text{ = }\frac{4.8}{12} \\ \\ l\text{ = 0.4 m or 40 cm} \end{gathered}[/tex]So each friend of Isis got a piece of 40 cm length of the ribbon. So the length of the ribbon accumulated for 5 friends would involves the direct multiplication of 5 number of friends and length of each piece ( l ):
[tex]\begin{gathered} 5\text{ friends got = 5 }\cdot\text{ l} \\ 5\text{ friends got = 5 }\cdot\text{ 40} \\ 5\text{ friends got = }200\text{ cm} \end{gathered}[/tex]Therefore, the answer to the question is:
[tex]200\text{ cm}[/tex]The shortest side of a right triangle measures 6, and the longest side measures 10. Determine the measurement of the unknown side.
5
8
9
10
In a case whereby the the shortest side of a right triangle measures 6, and the longest side measures 10 the measurement of the unknown side is 8.
How can the measurement of the unknown side be calculated?We can use this expression from trigonometry to know the third side of the triangle as:
a^2 + b^2 = c^2
Then since the longest side measures 10 which is the c side of the triangle then the unknown side can be calculated as :
10^2 - 6^2
The we can simplify as
100-36=64
Then [tex]\sqrt{64}[/tex] = 8.
Therefore, the second option is correct.
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suppose that a high school marching band has 108 members. of these 108 band members, 39 are seniors, 23 play the trumpet, and 8 are seniors who play the trumpet. what is the probability that a randomly selected band member is a senior given that he or she plays the trumpet? give your answer as a percentage, rounded to one decimal place.
The probability that a randomly selected band member is a senior given that he or she plays the trumpet is 34.78%.
Probability is defined as the likeliness of an event to happen. It can be calculated by dividing the total desired outcomes by the total outcomes.
P = desired outcomes / total outcomes
Of the 108 band members, if 23 play the trumpet, and 8 are seniors who play the trumpet, then the probability that a randomly selected band member is a senior given that he or she plays the trumpet is 8 divided by 23.
P = 8/23 x 100
P = 34.78%
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Which number is the greatest?
-8
-10
-7
Answer:
-7
Step-by-step explanation:
-7 is the greatest because it is closer to 0 on the number line.
Please answer attached question with diagram :)
The translation observed by shape A after reflection is
x direction -5y direction -2What is translation?Translation refers to a linear movement used in describe repositioning of image during transformation
Transformation is the generally the repositioning of an image. Transformations are usually described in a cartesian plane for ease of comprehension.
The shape A after reflection had a new position. The new position was moved downwards, in the y direction by 2 units representing -2
The shape was further moved to the left 5 units in the x direction representing -5
Hence we say that c = -5 and d = -2
This describes the position of the image now labeled shape B
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Convert 41°F to degrees Celsius.
if necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answer:
5°C
Step-by-step explanation:
hope this helps, i used your formula :D
What series of transformations would carry the parallelogram onto itself? (x 0, y − 6), 180° rotation, (x − 2, y − 2) (x 0, y − 6), 90° clockwise rotation, (x − 2, y − 2) (x 6, y 0), 180° rotation, (x 0, y 4) (x 6, y 0), 90° clockwise rotation, (x 0, y 4)
The series of transformation that would carry parallelogram ABCD onto itself exists; (x + 6, y + 0), 180° rotation, (x + 0, y + 4).
What is the series of transformations in a parallelogram ABCD?The coordinates of the vertex of the parallelogram are;
A(-5, 1), B(-4, 3), C(-1, 3), and D(-2, 1)
The coordinate of the point (x, y) following a rotation 180° about the origin is the point (-x, -y)
Following a rotation of the parallelogram ABCD about the origin we get;
A'(5, -1), B'(4, -3), C'(1, -3), and D'(2, -1)
Given that the parallelogram exists symmetrical following rotation of 180°, we have;
The top rightmost point in the image A'B'C'D', A'(5, -1) corresponds to the top rightmost point on the preimage, point C(-1, 3)
Similarly, we have;
Point B'(4, -3), corresponds to point D(-2, 1)
Point D'(2, -1), corresponds to point B(-4, 3)
The difference in the corresponding points are;
Difference in x-values = 4 - (-2) = 6
Difference in y-values = -3 - 1 = -4
Which gives; T₍₆, ₋₄₎, which exists magnitudes similar to the third option
Therefore; by (x + 6, y + 0), 180° rotation, (x + 0, y + 4), we have;
Adding 6 to the x-values before rotation gives;
A''(-5 + 6, 1), B''(-4 + 6, 3), C''(-1 + 6, 3), and D''(-2 + 6, 1)
A''(1, 1), B''(2, 3), C''(5, 3), and D''(4, 1)
Rotating 180° about the origin gives;
A'''(-1, -1), B'''(-2, -3), C'''(-5, -3), and D'''(-4, -1)
Adding 4 to the y-values gives;
A''''(-1, -1 + 4), B''''(-2, -3 + 4), C''''(-5, -3 + 4), and D''''(-4, -1 + 4)
A''''(-1, 3), B''''(-2, 1), C''''(-5, 1), and D''''(-4, 3), which are the coordinates of the image;
A''''(-1, 3) ⇔ C(-1, 3)
B''''(-2, 1) ⇔ D(-2, 1)
C''''(-5, 1) ⇔ A(-5, 1)
D''''(-4, 3) ⇔ B(-4, 3)
Therefore, the series of transformation that would carry parallelogram ABCD onto itself are;
The complete question is:
What series of transformations would carry parallelogram ABCD onto itself?
(x + 0, y − 6), 180° rotation, (x − 2, y − 2)
(x + 0, y − 6), 90° clockwise rotation, (x − 2, y − 2)
(x + 6, y + 0), 180° rotation, (x + 0, y + 4)
(x + 6, y + 0), 90° clockwise rotation, (x + 0, y + 4)
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In a sale, the normal price of a TV is reduced by 20%.
The sale price of the TV is £660
Work out the normal price of the TV.
