Answer:
p = - 2 , q = - 1
Step-by-step explanation:
Rearrange the left side into standard form
- x² + 4x - 5
Factor out - 1 from - x² + 4x
= - (x² - 4x) - 5
Using the method of completing the square
add/subtract ( half the coefficient of the x- term)² tp x² - 4x
= - (x² + 2(- 2)x + 4 - 4) - 5
= - (x - 2)² - (- 4) - 5
= - (x - 2)² + 4 - 5
= - 1 - (x - 2)²
Comparing to q - (x + p)²
with p = - 2 and q = - 1
Determine the discriminant and then state how many solutions there are and the nature of the solutions. Do not solve. 6x^2-x-2=0
Given:
The quadratic equation is:
[tex]6x^2-x-2=0[/tex]
To find:
The nature of the solutions by using the discriminant.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then its discriminant is:
[tex]D=b^2-4ac[/tex]
If D<0, then both roots are complex.
If D=0, then both roots are real and equal.
If D>0, then both roots are real and distinct.
We have,
[tex]6x^2-x-2=0[/tex]
Here, [tex]a=6,b=-1,c=-2[/tex]. So, the value of the discriminant is:
[tex]D=(-1)^2-4(6)(-2)[/tex]
[tex]D=1+48[/tex]
[tex]D=49[/tex]
Since [tex]D>0[/tex], then both roots are real and distinct.
Hence, the discriminant of the given quadratic equation is 49 and both roots are real and distinct.
Find the slope of the line that passes through the points (2,4)and (6,12)
Answer:
2
Step-by-step explanation:
slope = rise/run
slope = (12-4)/(6-2) = 8/4 = 2
helppp helping my sister
(5x - 7y + 8) + (-y + 6 - 4x) + (9 - 3x + 8y)
Out of 100 employees at a company, 92 employees either work part time or work 5 days each week. There are 14 employees who work part time and 80 employees who work 5 days each week. What is the probability that a randomly selected employee works both part time and 5 days each week?
Answer: 0.02
Step-by-step explanation:
OpenStudy (judygreeneyes):
Hi - If you are working on this kind of problem, you probably know the formula for the probability of a union of two events. Let's call working part time Event A, and let's call working 5 days a week Event B. Let's look at the information we are given. We are told that 14 people work part time, so that is P(A) = 14/100 - 0.14 . We are told that 80 employees work 5 days a week, so P(B) = 80/100 = .80 . We are given the union (there are 92 employees who work either one or the other), which is the union, P(A U B) = 92/100 = .92 .. The question is asking for the probability of someone working both part time and fll time, which is the intersection of events A and B, or P(A and B). If you recall the formula for the probability of the union, it is
P(A U B) = P(A) +P(B) - P(A and B).
The problem has given us each of these pieces except the intersection, so we can solve for it,
If you plug in P(A U B) = 0.92 and P(A) = 0.14, and P(B) = 0.80, you can solve for P(A and B), which will give you the answer.
I hope this helps you.
Credit: https://questioncove.com/updates/5734d282e4b06d54e1496ac8
Answer:
The probability that a randomly selected employee works both part time and 5 days each week is 0.02
Step-by-step explanation:
What is probability?
Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event.
The total employees =100
Let A= Employees who work part time = 14
and B = Employees who work 5 days each week = 80
Then, A∪B= 92
We have to find, P(A∩B)
P(A∪B)=P(A)+P(B)-P(A∩B)
[tex]\frac{92}{100}=\frac{14}{100}+\frac{80}{100}-[/tex]P(A∩B)
0.92=0.14+0.8-P(A∩B)
0.92=0.94-P(A∩B)
P(A∩B)=0.02
Hence, the probability that a randomly selected employee works both part time and 5 days each week is 0.02.
To know more about probability here
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# SPJ2
14 more to go please help
Answer:
B) 31.25%
Step-by-step explanation:
The elevator at the state capital has a maximum weight capacity of 2000 pounds. If there are 3
people already on the elevator with a combined weight of 428 pounds, write an inequality to express
the possible weights that may be added to the elevator,
Part A: Define your variable
Part B: Write the inequality
Part C: Describe what your inequality looks like on a number line. Be sure to include whether the
circle is open or closed and the direction the line is shaded.
Answer:
Step-by-step explanation:
Maximum capacity of the elevator = 2000 pounds
Combined weight of the elevator = 428 pounds
A). Let the possible weights that can be added to the elevator = w pounds
B). Therefore, inequality representing this situation will be,
428 + w < 2000
C). By solving the given inequality,
(428 + w) - 428 < 2000 - 428
w < 1572 pounds
Now we draw this inequality on a number line.
what would be the answer
Answer:
B= 21.195
Step-by-step explanation:
Inner circle area = 3.14×1.5×1.5=7.065
Outer circle area = 3.14× 3×3 = 28.26
3 is the radius of the outer circle
Area of the shaded portion is = area of outer circle - area of inner circle
28.26-7.065=21.195
Answer B= 21.195
Rebecca is sharing a pizza with some friends. Below is an Image of how she cuts the pizza.
AE is a diameter of the 20 in pizza!
a) If rebecca wants the biggest piece which one would she choose ( name it by its arc)? Be careful the image may not be drawn to scale
b) Rebecca loves stuffed crust!! She decides to figure out the length of cheese in her piece of the crust ( hint find the arc length
Answer:
a) The piece of pizza she should choose is BE
b) The length of the cheese in her piece of the crust is approximately 20.07 inches
Step-by-step explanation:
The given diameter of the pizza, AE = 20 in.
The measure of the arc AB, [tex]m\widehat{AB}[/tex] = ∠ACB = 65°
The measure of the arc DE, [tex]m\widehat{DE}[/tex] = ∠DCE = 110°
Given that AE is the diameter of the circular pizza, we have;
[tex]m\widehat{BE}[/tex] = ∠BCE = 180° - ∠ACB = 180° - 65° = 115°
Similarly;
∠ACD = 180° - ∠DCE = 180° - 110° = 70°
a) The biggest piece of pizza is the piece with the largest angle which is the piece formed by arc BE, [tex]m\widehat{BE}[/tex] = 115°
The piece of pizza she should choose is the piece, BE
b) Arc length = (Arc angle)/360 × (Circumference of the circle)
The circumference of the circular pizza, C = π × Diameter = π × length [tex]\overline {AE}[/tex]
∴ C = π × 20 in.
The arc length of the arc BE = 115/360 × π × 20 = 115·π/18 ≈ 20.07
The length of the cheese in her piece of the crust, l = The arc length of the arc BE ≈ 20.07 inches.
Guys pls help
4) If f(-x)=-f(x) for all x, f is an
function.
Odd Function
Even Function
Neither
Answer:
Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f. A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f brainliest ?
It would take 150 minutes to fill a swimming pool using the water from 5 taps.
A) how many minutes will it take to fill the pool if only 3 of the taps are used? ______ minutes
B) an assumption being made in my working is that all the taps are flowing the same__ ___
Answer: points for points
Step-by-step explanation:
Hi t sure what to do?
$20 is what percent of $40?
Please help ples
Answer:
50%
Step-by-step explanation:
50%
$20=50%
$20 x 2= $40
The volume of the box is 60 cubic inches. What are
the length, width, and height of the box?
Answer: The volume is the product of the Length, Width, and Height: V = LWH.
Step-by-step explanation: We are given V = 240 in.3, and H = 6 in., and L = W + 3 in.
Thus 240 in.3 = (W+3 in.)*W*(6 in.) so W(W+3 in.) = 240 in.3 / 6 in. = 40 in.2
Using the distributive property and moving the constant to the left gives:
W2 + (3 in.)W - 40 in.2 = 0
This factors:
(W + 8 in.)(W - 5 in.) = 0
The first factor gives W = -8 in. which is nonsense because it is negative.
The second factor gives a valid answer of W = 5 in.
What is the length, in centimeters, of the hypotenuse of a right triangle with legs measuring V2 cm and 3 cm?
Answer:
[tex] \sqrt{13} [/tex]
Step-by-step explanation:
A is the hyp. And b/c are the sides
A²=b²+c²=3²+2²=9+4=13
Now take the square root of 13 as the answer
If who answers fast, correct and first, I WILL GIVE YOU THE BRAINLIEST!!!!!!!!!!!
Answer:
Is A.
Step-by-step explanation:
22 < 7x+57
7x+57>22
7x>-35
x>-5
helpppppppppppppp pleaseeeeeee
Answer:
C
Step-by-step explanation:
hope this helps
Answer:
Step-by-step explanation:
FYI
HeLp Me !!!!!!!!!!!!!!!!!!!
Answer:45.1%
Step-by-step explanation:
If you can help me I would be very thankful!
Answer:
4x + 2.5y = 184
x = y - 6
Step-by-step explanation:
Let the number of smoothies sold by stand = x
And number of cones sold = y
If the selling price of each cone = $2.5
Selling price of the 'y' cones = $2.5y
Selling price of each smoothies = $4
Then sales of smoothies = $4x
If the total sales of one day = $184
Equation for this situation will be,
4x + 2.5y = 184 -------(1)
If the stand sold 6 less smoothies than the cones,
x = y - 6 -----(2)
Therefore, system of equations contains two equations (1) and (2).
How do I find the missing side length to the nearest tenth of a millimeter.
Answer:
11.5
Step-by-step explanation:
Find the measurement of the angle indicated for each trapezoid
Answer:
45
Step-by-step explanation:
Without using a protractor, you can determine whether the angles are right angles by measuring the length of the diagonal and applying the converse of the Pythagorean Theorem.
Solve for x ax-bx/x+c = d, if a =/b+d
Answer:
dc/a-b-d
Step-by-step explanation:
ax – bx = d
x + c
Multiply both sides by x + c
ax – bx
(x + c) = d(x + c)
x + c
Simplify
ax – bx
(x+c): ax – bx
x + c
ax – bx = d(x+c)
Expand d(x+c): dx + cd
ax — bx = dx + cd
Subtract dx from both sides
ax – bx – dx = dx + cd – dx
Simplify
ax – bx – dx = cd
Factor ax – bx – dx: x(a – b – d)
x(a - b- d) = cd
Divide both sides by a – b – d; a + b + d
x(a – b - d) cd
a + b + d
a - b - d
a – b-d
Simplify
X =dc/a-b-d
The value of 'x' in the algebraic equation is [tex]\rm x= \frac{dc}{a-b-d} \\[/tex] where [tex]\rm a\neq b+d[/tex]
It is given that the algebraic equation [tex]\rm \frac{ax-bx}{x+c}= d[/tex]
It is required to solve the algebraic (polynomial) equation if [tex]\rm a\neq b+d[/tex]
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have an algebraic equation:
[tex]\rm \frac{ax-bx}{x+c}= d[/tex]
[tex]\rm \frac{ax-bx}{x+c}= d\\\\\rm ax-bx=d(x+c)\\\rm ax-bx=dx+dc\\\rm ax-bx-dx=dc\\\rm (a-b-d)x=dc\\\\\rm x= \frac{dc}{a-b-d} \\[/tex]
Thus, the value of 'x' in the algebraic equation is [tex]\rm x= \frac{dc}{a-b-d} \\[/tex] where [tex]\rm a\neq b+d[/tex]
Learn more about Polynomial here:
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A 68 kg deer has a momentum of 952 kg-m/s. What is its velocity?
Answer:
14 m/s
Step-by-step explanation:
(PLEASE HELP)
Which of the following would NOT work to make a triangle with the two slide lengths of 2 and 6
A.6
B.5
C.7
D.4
Given:
The two sides of a triangle are 2 and 6.
To find:
The side length that would NOT work to make a triangle with the two slide lengths of 2 and 6.
Solution:
For a triangle, the sum of two smaller sides must be greater than the largest side.
Let x be the third side.
Case 1: x is the largest side, then
[tex]2+6>x[/tex]
[tex]8>x[/tex] ...(i)
Case 2: x is not the largest side, then
[tex]2+x>6[/tex]
[tex]x>6-2[/tex]
[tex]x>4[/tex] ...(ii)
From (i) and (ii), we get
[tex]4<x<8[/tex]
Here, 4 and 8 are not included.
6, 5, 7 are included in the above interval, but 4 is not included in the above interval. It means 4 would NOT work to make a triangle with the two slide lengths of 2 and 6.
Therefore, the correct option is D.
Complementary, Supplementary or neither?
Answer:
whaats the question
Step-by-step explanation:
What is 57.9709 divided by 3.456072
Answer: 16.77363782
Step-by-step explanation:
PLZ HELP!! I RLY NEED IT!! Josie selected 6 books from thr library. However, he can only check out 4 books at a time. How many possible selections can he make?
Answer:
4 selections
Step-by-step explanation:
We are told in the question that:
Josie selected 6 books from the library. However, he can only check out 4 books at a time.
The number of possible selections can he make is 4 selections. This is because, He can only take 4 books out of the library at a time. This is the standard.
Find the volume for each.
Answer:
Volume of cuboid = 1,386 inch³
Step-by-step explanation:
Given:
Length of cuboid = 14 inch
Width of cuboid = 9 inch
Height of cuboid = 11 inch
Find:
Volume of cuboid
Computation:
Volume of cuboid = Length of cuboid x Width of cuboid x Height of cuboid
Volume of cuboid = 14 inch x 9 inch x 11 inch
Volume of cuboid = 126 inch² x 11 inch
Volume of cuboid = 1,386 inch³
What is the answer to question b and d
Answer:
Step-by-step explanation:
a) -3
b) 5
c) -2
d) -6
Answer:
a) (-3)
b) 5
c) (-2)
d) (-6)
Hope it helps!!
Tony answered all the questions on his math test but got 5 answers wrong. There is a 1 point pent
for every wrong answer. He received 4 points for every correct answer. His score was 72. How many questions did Tony answer correctly on his Math test?
Answer:
I believe he answered 18 questions correctly.