By the fundamental theorem of algebra, we can write the given quadratic in terms of its roots a and b as
3x ² - 5x + k = 3 (x - a) (x - b)
and upon expanding, we have
3x ² - 5x + k = 3x ² - (a + b) x + ab
Two polynomials are equivalent if their coefficients are equal, so
a + b = 5
ab = k
We're given that |a - b| = 2. If we assume a > b (that is, a is the larger root) then |a - b| = a - b = 2, or b = a - 2. Substitute this for b in the first equation above and solve for a :
a + (a - 2) = 5
2a - 2 = 5
2a = 7
a = 7/2
Solve for b :
b = 7/2 - 2
b = 3/2
Solve for k :
k = 7/2 × 3/2 = 21/4
The inverse of x→y is:
Answer:
This is invertible
Step-by-step explanation:
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have a great day!
Solve for the value of r.
Answer:
r = 20
Step-by-step explanation:
4r - 5 + 105 = 180
4r + 100 = 180
4r = 80
r = 20
you get a haircut that costs $23. You want to tip the barber 10%. How much tip will you leave him?
Answer:
$2.30
Step-by-step explanation:
Multiply 23 by .10 to get 2.3
2.3 is 2 dollars and 30 cents
Answer:
$2.30
Step-by-step explanation:
multiply 23 by the decimal form of 10% (0.10)
23*0.10=2.3
I need some help with this question. Can someone help me pls???
Answer:
24yd I think thats the answer
Answer:
B
Step-by-step explanation:
6 * 4 = 24
[ (9 - 6) * 4 ] / 2 = 6
24 + 6 = 30
Mischa wrote the quadratic equation 0=-x^2+4x-7 in standard form. If a = -1, what is the value of c in her equation?
Ac=-7 (correct answer on edg)
B.c=-1
C.c=4
D.c=7
The area of a rectangle is 192 cm. The length of the rectangle is 16 cm. What is the width?
192 = 16w -(solve for w)
Area =L×W
192=16W
192/16 =W
W=12cm
Use the image to determine the type of transformation shown.
A. Reflection across the x-axis
B. Horizontal translation
C. Vertical translation
D. 180° clockwise rotation
The orientation change and the symmetry across the center of rotation confirm that it is a 180° clockwise rotation. Therefore, the correct answer is D. 180° clockwise rotation.
Based on the image provided, the type of transformation shown is a 180° clockwise rotation.
A 180° clockwise rotation occurs when each point in the original shape is rotated by 180° in a clockwise direction around a fixed point. In the given image, we can observe that the original shape has been rotated by half a complete revolution, resulting in the new shape being a mirror image of the original shape but in the opposite orientation.
This transformation is evident by comparing the positions of the vertices and sides of the original shape to those of the transformed shape. The orientation change and the symmetry across the center of rotation confirm that it is a 180° clockwise rotation.
Therefore, the correct answer is D. 180° clockwise rotation.
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Which figures can have all of the properties shown below?
2 pairs of parallel sides
Sides that are perpendicular
Opposite sides that are equal
square, pentagon, rectangle
trapezoid, triangle, square
quadrilateral, square, rectangle
rectangle, hexagon, square
Answer:
Quadrilateral, square, rectangle
Step-by-step explanation:
An object have parallel sides if the sides have the same distance apart and they never meet.
Quadrilaterals usually have parallel sides
Polygons including triangles and pentagons do not have parallel sides
the sides of a quadrilateral are also perpendicular. the sides form a 90 degree angle with each other
Opposite sides of a quadrilateral are usually equal. For example, the opposite lengths of a rectangle are equal. the four sides of a square are equal
Tasha is mixing red and white paint to make pink paint. She uses 1/3 pint of red paint to make 1/2 pint of pink paint. How much red paint would she use to make 3 1/2 pints of pink paint?
Answer:
2 1/3
Step-by-step explanation:
Rewrite 0.81 x
104 in scientific notation.
x 10
HELP ME
Answer:
Ok ill help i guess
Step-by-step explanation:
0.81 X 10000
In a certain clothing store 6 shirts and 3 ties cost $79.50 and 3 shirts and 2 ties cost $41 determine the cost of each shirt
Answer:
Step-by-step explanation:
lets have the shirts represent s and the ties t.
1. 6s+3t=79.50
2. 3s+2t=41
These would be the equations.
you multiply the second equation by -2 to cancel s and add both equations.
6s+3t=79.50
-6s+-4t=-82
-1t=-2.5 (after adding you divide by -1)
t=2.5
You can then subsitute that in either equation.
I am going to ue teh second one.
3s+2t=41
3s+2(2.5)=41
3s+5=41 (subract 5 to isolate variable)
3s=36 (divide by 3 to isolate variable)
s=12
Hence, one shirt is 12$.
pls help me :( Find the value of x. Round to the
nearest tenth.
Answer:
11.3
Step-by-step explanation:
Set up your equation:
a² + b² = c²
Plug in your values:
a² + 4² = 12²
Get a² by itself:
a² = 12² - 4²
Square your numbers and subtract:
a² = 144 - 16
a² = 128
Find the square root of both sides:
√a² = √128
a = 11.3
Ebru is an entrepreneur. She plans to start 2 different very small businesses in the next year. Both businesses are independent of each other, and each business has a 50%, percent chance of being successful and a 50%, percent chance of failing.
Each business will make Ebru $200 if it succeeds or lose her $200 if it fails.
if X is a random variable that represents Ebru's profit from starting these 2 businesses, draw a graph to show the probability distribution for all possible values of X.
Answer:
Step-by-step explanation:
write 11/12 demoniator 84 to a equivalent fraction
Answer:
77/84
Step-by-step explanation:
84 ÷ 12 = 7
Multiply the numerator and denominator by 7
[tex]\frac{11}{12}=\frac{11*7}{12*7}=\frac{77}{84}[/tex]
The perimeter of the figure below is 54.9 in. Find the length of the missing side.
5.9 in
5.9 in
?
7-3 in
7.3 in
7.3 in
7.3 in
7.3 in
(Note: diagram is NOT to scale)
square root 3 minus X Minus x squared is equals to x - 2
Step-by-step explanation:
I hope it helps I was just trying. if I'm wrong you can tell me I I will ask the people who are around me. wish you all the best.
What is 6 7/13 divided by 5
Answer:
17/13
Step-by-step explanation:
Answer:
[tex]\frac{17}{13}[/tex] or 1 [tex]\frac{4}{13}[/tex]
Step-by-step explanation:
what is the cube root of -0.216?
Answer:
-0.6
Step-by-step explanation:
Help please !! need it asap
Answer:
AB = 6
m∠F = 70°
Step-by-step explanation:
1.) This is isosceles, from the angles you can tell
2.) Angles F and D are equal, this is also a form of isosceles
180-40 = 140
140/2 = 70
Is 8/10 greater than 63/100
Answer:
8/10 is greater than 63/100, it is grater because when u change them into a percentage 8/10 is higher
Step-by-step explanation:
Answer:
true :D
8/10 = 80/100 which is greater than 63/100
Suppose that the ingredients for a large bucket of popcorn cost a movie theater 80 cents
to buy. If the theater charges $9 for the bucket, what is the percent markup? Give your
answer as a percent rounded to the nearest whole percent.
Answer:
The percent markup is 91%.
Step-by-step explanation:
1. find the amount of profit per large bucket of popcorn
9 - 0.8 = $8.2
2. divide the amount of profit per large bucket of popcorn by the cost of a large bucket of popcorn
8.2 / 9 = 91%
Answer:
The percent markup is 91%.
1. find the amount of profit per large bucket of popcorn
9 - 0.8 = $8.2
2 divide the amount of profit per large bucket of popcorn by the cost of a large bucket of popcorn
8.2 / 9 = 91%
What is the radius of a circle that has an approximate circumference of 81.64 meters? (Use 3.14 for ).
r =
m
Answer:
r=13
Step-by-step explanation:
81.64/3.14=26(diameter)
26/2=13(radius)
Which of the following grids does the
shaded portion represent 10% of the grid?
Answer:
C
Step-by-step explanation:
Since the area all of the grids are 100 (10X10), in order for the shaded portion to be 10% of that it would have to be 10 of the squares. (10% = 10/100) Therefore because the one with 10 squares shaded is C, the answer is C!
Answer:
meow meow ............
.......
In a survey of 292 students, about 9.9% have attended more than one play. Which
is closest to the number of students in the survey who have attended more than one
play?
3 students
10 students
20 students
30 students
Answer: it's 30 I rook the quiz and got 100
Step-by-step explanat
10. For the system of linear equation: (2x₁ + 3x₂ + x3 = -1 3x₁ + 3x₂ + x3 = 1 (2x₁ + 4x₂ + x3 = -2 a. find the coefficient matrix A and the augmented matrix [AL b. use Gauss Jordan method to find the inverse of the coefficie c. find the solution set of 'he system using Matrix inverse Me-
a. Coefficient matrix A:
A = [[2, 3, 1],
[3, 3, 1],
[2, 4, 1]]
Augmented matrix [AL]:
[A|b] = [[2, 3, 1, -1],
[3, 3, 1, 1],
[2, 4, 1, -2]]
b. The resulting matrix will be [I|A^(-1)], where A^(-1) is the inverse of the coefficient matrix A.
c. The resulting vector [x1, x2, x3] represents the solution set of the system of linear equations.
a. The coefficient matrix A and the augmented matrix [A|b] for the given system of linear equations are as follows:
Coefficient matrix A:
A = [[2, 3, 1],
[3, 3, 1],
[2, 4, 1]]
Augmented matrix [AL]:
[A|b] = [[2, 3, 1, -1],
[3, 3, 1, 1],
[2, 4, 1, -2]]
b. To find the inverse of the coefficient matrix A using the Gauss-Jordan method, we perform elementary row operations until A is transformed into an identity matrix [tex][I|A^{(-1)][/tex].
Gauss-Jordan elimination steps:
Step 1: Perform row operations to convert the first column of A to [1, 0, 0]:
R1' = R1/2
R2' = R2 - (3/2)R1
R3' = R3 - R1
Step 2: Perform row operations to convert the second column of A to [0, 1, 0]:
R2'' = R2''/3
R1'' = R1'' - (3/2)R2''
R3'' = R3'' - (3/2)R2''
Step 3: Perform row operations to convert the third column of A to [0, 0, 1]:
R3''' = R3'''/2
R1''' = R1''' - R3'''
R2''' = R2''' - R3'''
The resulting matrix will be[tex][I|A^{(-1)][/tex], where [tex]A^{(-1)[/tex] is the inverse of the coefficient matrix A.
c. Once we have the inverse matrix A^(-1), we can find the solution set of the system of linear equations by multiplying A^(-1) with the augmented matrix [A|b]:
[A|b] [tex]\times[/tex] [tex]A^{(-1)[/tex] = [x1, x2, x3]
The resulting vector [x1, x2, x3] represents the solution set of the system of linear equations.
Note: To provide the numerical values for the inverse matrix [tex]A^{(-1)[/tex] and the solution set, the calculations need to be performed manually using the given coefficients of the equations.
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A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? a prime number a. 0.45 c. 0.71 b. 0.55 d. 0.73 Please select the best answer from the choices provided A B C D
Answer: B
Step-by-step explanation:
The prime numbers here are outcomes 2, 3, and 5.
Therefore, we must add the frequency numbers for these prime numbers:
36 + 44 + 30 = 110
Out of 200 dice rolls, 110 were prime numbers. This can be represented as:
110/200 = 11/20 (fraction form)
= 0.55 (decimal form)
Therefore, the answer is b. 0.55
the force keeping the moon in its orbit round the earth is inversely proportional to the square of the distance from the earth.if F =6×10^5KN and R =8×10^8.find the equation connecting Fand R.
9514 1404 393
Answer:
F = 3.84×10^23/R²
Step-by-step explanation:
No units are given for distance, so we cannot give a constant of proportionality that has suitable units.
The general form for inverse square variation is ...
F = k/R²
Then the value of k can be found from ...
k = F·R² = (6×10^5)(8×10^8)^2 = 3.84×10^23
The formula relating the given F and R is ...
F = 3.84×10^23/R²
what are some common work activities performed by Human Resources Managers? Check all that apply.
resolving conflicts and negotiating with others
operating vehicles, mechanized devices, or equipment
handling and moving objects
establishing and maintaining interpersonal relationships
inspecting equipment, structures, or material
communicating with supervisors, peers, or subordinates a
Answer:
A, resolving conflicts and negotiating with others
D,establishing and maintaining interpersonal relationships and F,communicating with supervisors, peers, or subordinates.
Step-by-step explanation:
Answer:
its A,B,D,F
developing objectives and strategies
assisting and caring for others
establishing and maintaining interpersonal relationships
interpreting the meaning of information for others
(1\6-1)(3-2/5)-(1/3-1/2)
Answer:
2 1/3 (simplified)
Step-by-step explanation:
(1/6 - 1) = -5/6
(1 = 6/6)
(3 - 2/5) = 2 3/5
[3= 18 (3 * 6)]
(1/3 - 1/2) = -1/6
(you can change both of the denominators to 6 by multiplying them both by 3 / 2
So the equation now is
(-5/6)(2 3/5) - (-1/6)
-5/6 * 2 3/5 = 2 1/6 (simplified)
2 1/6 - -1/6 = 2 1/3 (simplified)
PA = 0.5 PB = 0.3 and p A and b equals 0.15 what is p A or b
Answer:
P(A) = 0.2, P(B) = 0.5, P(A\B) = 0.3:
P(A\B) = P(A and B) P(B)
0.3 = P(A and B) 0.5
0.15 P(A and B)
P(A and B) = 0.15
B. P(A or B) = P(A) + P(B) - P(A and B)
0.2 + 0.5 - 0.15
0.70 - 0.15 = 0.55