Please help ASAP!!!!!!
9514 1404 393
Answer:
a) correct
b) needs parentheses: -1, (1±i√2)/3
Step-by-step explanation:
a) You can factor by grouping:
(x³ -2x²) -(5x -10) = x²(x -2) -5(x -2) = (x² -5)(x -2)
Roots are ±√5, 2.
__
b) The sum of odd-degree coefficients is equal to the sum of even-degree coefficients (3-1 = 1+1), so one root is x=-1. Factoring out that leaves the quadratic factor ...
3x³ +x² -x +1 = (x +1)(3x² -2x +1)
The quadratic formula can be used on the quadratic factor to find its roots:
x = (-(-2) ±√((-2)²-4(3)(1)))/(2(3)) = (2 ±√-8)/6 = (1 ±√-2)/3
Roots are -1, (1 ±i√2)/3.
The probability of college graduate getting employed within a year is 90 % 90%. The probability of a college graduate getting employed and buying a car within a year is 72 % 72%. What is probability that a college graduate bought a car within a year given that he got employed within a year?
Answer:
Step-by-step explanation:
Let the probability of getting employed after graduated within a year be P(A)
and the probability of buying a car within a year be P(B)
Given that:
The probability of getting employed after graduated within a year = 90% = 0.9
Then; Let that be P(A)
The probability of getting employed and buying a car within a year = 72% = 0.72.
Then; Let that be P(A∩ B).
The probability that a college student will get both events is P(B/A)
[tex]P(B/A) = \dfrac{P(A \cap B) }{P(A)}[/tex]
[tex]P(B/A) = \dfrac{0.72}{0.90}[/tex]
P(B/A) = 0.80
A 15 foot ladder is leaning against a building, with the base of the ladder 4 feet from the building. How high up on the building will the top of the ladder reach?
The ladder will reach
android:
nothing ft high up on the building.
(Round to the nearest tenth.)
Enter your answer in the answer box and then click Check Answer.
All parts showing
Answer: The height of the building = 14.5 feet.
Step-by-step explanation:
Given: Length of ladder = 15 feet
Distance of base of ladder from building = 4 feet
Since building is standing vertical on ground making right angle.
So with ladder a right triangle is formed , where base = 4 feet , Hypotenuse = 15 feet [Hypotenuse is side opposite to right angle]
According to the Pythagoras theorem ,
Hypotenuse² = Perpendicular² + Base²
⇒ (15)² = Perpendicular² + (4)²
⇒ 225 = Perpendicular² +16
⇒ Perpendicular² = 225 -16
⇒ Perpendicular² = 209
⇒ Perpendicular = √209 = 14.4568322948 ≈ 14.5 feet
Hence, the height of the building = 14.5 feet.
Inseri the missing number.
8 5 2
4 2 0
9 6 ?
Please help me out. Thanks
Answer:
61
Step-by-step explanation:
Rectangle area=
[tex]60 \times 40 = 2400yd ^{2} [/tex]
The area at the right
[tex](\pi \times 20^{2} ) \div 2 = 628yd^{2}[/tex]
Total area = 2400+628=3028yd^2
Now you have to find the quantity of grass seed needed (1pound for every 50yd square)
3028/50=60.56 (which is almost 61)
Is (1,8), (2,12), (3,16) (4,20) a function?
For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is approximated by the function below. Find the maximum blood pressure and the disage at which it occurs.
B(x)= 395x^2- 2370x^3, 0 <= x <= 0.16
a. The maximum is obtained for a dosage of __________________.
b. The maximum blood pressure obtained is ______________.
Answer:
A) Maximum for dosage is 0.11
B) maximum blood pressure = 1.625
Step-by-step explanation:
We are given the function;
B(x) = 395x² - 2370x³
To find maximum, we will find the derivative of the function and equate to zero.
B'(x) = 790x - 7110x²
Equating to zero gives;
790x - 7110x² = 0
790x = 7110x²
Dividing both sides by x gives;
790 = 7110x
x = 790/7110
x = 0.11
This falls in between the range of 0 <= x <= 0.16 given to us.
Therefore x = 0.11 is a maximum
Plugging this into B(x) = 395x² - 2370x³ gives;
B(0.11) = 395(0.11)² - 2370(0.11)³
B(0.11) = 1.625
Thus;
Maximum dosage is 0.11
maximum blood pressure = 1.625
At the city museum child admission is $5.40 and adult admission is $9.40. On Wednesday, 168 tickets were sold for a total sales of $1199.20. How many adult tickets were sold that day?
Given:
Selling price of child ticket = $5.40
Selling price of adult ticket = $9.40
Total tickets = 168
Total sales = $1199.20
To find:
The number of adult tickets sold.
Solution:
Let x be the number of child tickets and y be the number of adult tickets.
Total tickets : [tex]x+y=168[/tex] ...(i)
Total sales : [tex]5.40x+9.40y=1199.20[/tex] ...(ii)
From equation (i), we get
[tex]x=168-y[/tex]
Put this value in (ii).
[tex]5.40(168-y)+9.40y=1199.20[/tex]
[tex]907.2-5.40y+9.40y=1199.20[/tex]
[tex]4y=1199.20-907.2[/tex]
[tex]4y=292[/tex]
Divide both sides by 4.
[tex]y=\dfrac{292}{4}[/tex]
[tex]y=73[/tex]
Therefore, 73 adult tickets were sold that day.
12.32-8
Using mental math
Answer:4.32...i think
Step-by-step explanation:
Answer:
12.32-8= 4.32 OR 12 x 32 - 8 = 376
Step-by-step explanation:
12.32
- 8.00
= 4.32
OR
32
x 12
= 376
Just depends if the dot was a multiplication dot or decimal.
Hope it helps!!
What value of x is in the solution set of 2x-3 > 11 - 5x?
Answer:
x ≤ 3
Step-by-step explanation:
Answer:
The value of x is 2.
Step-by-step explanation:
The key to this solution is to combine like terms.
2x-3 > 11-5x
There are lots of ways to combine them but the way I think would be the most simple would be to avoid negative numbers (although I personally enjoy it) but anyways,
First, you can add 5x to both sides of the inequality.
This would cancel out 5x and leave you with: 7x-3 > 11
The next terms that you can combine can be the constants. You can combine -3 and 11 and to do that, you add 3 on both sides. That would cancel 3 out and leave you with: 7x > 14
Now, the last step is to get x by itself and to do that, you divide 7 on both sides to get:
x > 2
I hope my explanation wasn't too confusing for you
7. A new car depreciates as soon as you drive it out of the parking lot. A certain car depreciates to
half its original value in 4 years. If you bought a car 8 years ago and it is now worth $5,000, how
much did you pay for the car originally?
Given :
A new car depreciates as soon as you drive it out of the parking lot. A certain car depreciates to half its original value in 4 years. If you bought a car 8 years ago and it is now worth $5,000.
To Find :
How much did you pay for the car originally.
Solution :
Let, original price is x.
It is given that price gets half after 4 years.
So, price after 8 year is, P = x/4 .
x/4 = 5,000
x = $20,000
Therefore, price of new of car is $20,000.
Hence, this is the required solution.
The hypotenuse is always the __________ side of a right triangle.
Answer:
the answer is opposite
If a bug can flap its wings at a rate of 77 times in 9 seconds, how many times do they flap their wings in 1.119 minutes? Round to 1 decimal.
Answer:
574.4 flaps
Step-by-step explanation:
77/9 = 8.5555555 flaps per second
60 seconds x 1.119 minutes = 67.14 seconds
8.5555555 x 67.14 = 574.42 flaps
Christen has to run around the rectangular soccer field during practice. The soccer field measures 60 meters
long by 45 meters wide.
How far did Christen run?
Answer:
210m
Step-by-step explanation:
60+60+45+45
120+90
210m
Gina says that for all real numbers a and b, ab=ba. is this statement true or false? If false, give a counterexample
Answer:
True
Step-by-step explanation:
The communative property states that the order in addition and multiplication dosen't matter.
Can someone help me with this? am i supposed to graph
Answer:
Step-by-step explanation:
1). a(x) = -4x + 7 If x > 1
a(8) = -4(8) + 7
= -32 + 7
= -25
2). a(x) = 2x - x² If -6 < x ≤ 1
a(1) = 2(1) - 1²
= 2 - 1
= 1
3). a(x) = |x - 8| If x ≤ -6
a(-7) = |- 7 - 8|
= |-15|
= 15
4). a(x) = 2x - x² If -6 < x ≤ 1
a(-3) = 2(-3) - (-3)²
= -6 - 9
= -15
5). a(x) = 2x - x² If -6 < x ≤ 1
[tex]a(-\frac{1}{2})=2(-\frac{1}{2})-(-\frac{1}{2})^{2}[/tex]
= - 1 - [tex]\frac{1}{4}[/tex]
= [tex]-\frac{5}{4}[/tex]
6). a(x) = -4x + 7 If x > 1
[tex]a(\frac{9}{4})=-4(\frac{9}{4})+7[/tex]
= -9 + 7
= -2
The radius of the base of a cylinder is increasing at a rate of 11 meter per hour and the height of the cylinder is decreasing at a rate of 44 meters per hour. At a certain instant, the base radius is 55 meters and the height is 88 meters. What is the rate of change of the volume of the cylinder at that instant (in cubic meters per hour)?
Answer:
The volume of the cylinder is decreasing at a rate of 83629.2 m³/h.
Step-by-step explanation:
The volume of a is given by:
[tex] V = \pi r^{2}h [/tex]
Where:
r: is the radius = 55 m
h: is the height = 88 m
We can express the rate of change of the volume of the cylinder as follows:
[tex] \frac{dV}{dt} = \pi[h\frac{2rdr}{dt} + r^{2}\frac{dh}{dt}] [/tex]
If dr/dt = 11 m/h and dh/dt = -44m/h, we have:
[tex] \frac{dV}{dt} = \pi[88 m*2*55 m*11 m/h + (55 m)^{2}*(-44 m/h)] = -83629.2 m^{3}/h [/tex]
Therefore, the volume of the cylinder is decreasing at a rate of 83629.2 m³/h.
I hope it helps you!
NEED HELP NOW!!!!!!
Androcles
adapted from Aesop’s Fables
scene 1:
(Backdrop—forest. Enter Androcles looking over his shoulder)
ANDROCLES: (Speaking to himself) I’ve just escaped from my master. I need to find a place to hide. (As he searches for a place to hide, he sees a lion moaning in pain. He turns to run but changes his mind.) Oh! You poor thing. (He looks at the lion’s paw, which is swollen and bleeding. He finds a large thorn, which is the cause of the pain, pulls it out, and binds the paw. The lion rises and licks Androcles's hand. The lion leads him to a cave stage right.)
ANDROCLES: (Speaking to the audience) The lion brought me meat to live on for the next few days until we were captured.
(Curtain)
scene 2:
(Backdrop—arena. The Emperor enters stage right downstage and moves to stage left upstage. Androcles is surrounded by guards who enter from stage right upstage. Androcles moves to center stage. His head is bowed.)
EMPEROR: The slave shall be thrown to the lion as punishment. Ensure that the lion has a good appetite.
(The Emperor and the members of court are gathered stage left upstage. Androcles is center stage. The lion charges in from stage rightdownstage. Androcles steps back. The lion recognizes Androcles and begins to lick his hand.)
EMPORER: (Surprised) What is this? Guards! I wish to speak with him. (Speaking to Androcles) How did you do that? Are you a sorcerer?
ANDROCLES: (Bowing to the emperor) When I escaped and ran into the forest, I found him with a large thorn. It caused him much pain. I took it out, and he has been grateful since then.
EMPORER: (Impressed) Very well! You are pardoned and the lion shall be released into the wild.
(Curtain)
12
Select the correct answers.
Based on the passage, which two adjectives best describe Androcles?
courageous
vicious
kind
lazy
cowardly
Answer:
the answer is courageous and kind
Answer:
Courageous and Kind
Step-by-step explanation:
At least all the animals showed Courage and Kindness to the others.
Have a great day mate!
Solve.
-2(3x + 7) = -8x
Answer:
x=7
Step-by-step explanation:
-6x-14=-8x
-6x+8x=14
2x=14
x=7
yes it. is right man ansls gqbevih wo
one angle of a triangle is 60 degree and the other two are in the ratio 2:3.Find these angles
Answer:
48 and 72 degrees.
Step-by-step explanation:
The sum of the other 2 angles = 180-60 = 120 degrees.
So they are 2 / (2+3) * 120 = 2/5 * 120 = 48 and 3/5 * 120 = 72 degrees.
The hanger image below represents a balanced equation.
Answer:
[tex] \frac{1}{5} + z = \frac{3}{5} [/tex]
Answer:
1/5+z=3/5
Step-by-step explanation:
1)) Norachai school is selling tickets for the annual talent show. On the first day of ticket sales, the school sold 5 adult tickets and 4 student tickets for a total of $ 85. The school received $ 55 on the second day selling 5 adult tickets and 2 student tickets. What is the price of each adult and student ticket?
9514 1404 393
Answer:
adult: $5student: $15Step-by-step explanation:
If we let 'a' represent the price of an adult ticket, and 's' represent the price of a student ticket, the two sales can be described by ...
5a +4s = 85
5a +2s = 55
Subtracting the second equation from the first gives ...
(5a +4s) -(5a +2s) = (85) -(55)
2s = 30 . . . . simplify
s = 15 . . . . divide by 2
Substituting this into the second equation, we have ...
5a +2(15) = 55
5a = 25 . . . . subtract 30
a = 5 . . . . . divide by 5
Each adult ticket sold for $5; each student ticket sold for $15.
how would you round 1.2983 to the thousandth
Answer:
1.298
Step-by-step explanation:
After the decimal the numbers go
tenths Hundredths and then thousands
Then take the number that's after thousands and raise the thousands number up is the numbers after is above 5 keep it the same if its 4 or under.
Evaluate and Solve for the variable
-2 = y + 5
Answer:
y = -7
Step-by-step explanation:
Minus the five from both sides
Answer:
Y = -7
Step-by-step explanation:
subtract 5 from both sides
-7 = y
What is the sum of 347+645=
Answer:
347 + 645 = 992
Step-by-step explanation:
347
+645
922
It takes Amy 18 minutes to read 4 pages of a book. The Hunger Games has 374 pages, Catching Fire has 391 pages, Mockingjay has 517 pages and the newest book, The Ballad of Songbirds and Snakes, has 390 pages. If she has already read The Hunger Games, how long will it take her to read the rest of the book series?
The answer is 5841 minutes.
May u please help me ill give out the brainly
Answer:
the answer is a
Step-by-step explanation:
they are just flipped thats all
Show work for branliest
Which expression is equivalent to =
(4x^ 3 ) (2x)^-4
A. 1/(4x)
B. 4/x
C. 8/x
D. 128/x
Can anyone help me ????
Answer:
i know i had this question let me find it
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
the formula for a parallelogram is A=b*h
(01.01 MC)Why is 2 + (−3) equal to −1? Because it is 3 units to the left of 2 on a horizontal number line Because it is 3 units to the right of 0 on a horizontal number line Because it is 3 units to the left of 0 on a horizontal number line Because it is 3 units to the right of 2 on a horizontal number line
Answer:
Because it is 3 units to the left of 2 on a horizontal number line
Step-by-step explanation:
Given
[tex]2 + (-3) = -1[/tex]
Required
Why?
The interpretation of the question is that:
[tex]2 + (-3) = -1[/tex]
What is the result when 2 is shifted 3 units in the negative direction (i.e. towards the left)?
First, we have a horizontal to have the the following representation:
<.....-4 -3 -2 -1 0 1 2 3 4 5 ......>
Taking the positions of 2 and -1 into consideration,
<.....-4 -3 -2 -1 0 1 2 3 4 5 ......>
We can see that the distance between 2 and -1 is 3 units towards the left
In other words, -1 is 3 units from 2 in the left direction
Hence, option A answers the question
Answer:
Because it is 3 units to the left of 2 on a horizontal number line
Step-by-step explanation: