Answer:
1
Step-by-step explanation:
If a cubic polynomial ax³ + bx² + cx + d has three zeros α, β, and γ, then the product of the zeros is -d/a.
αβγ = -d/a
a = 2, d = -6, and αβ = 3.
3γ = 3
γ = 1
Three tickets to attend an Off-Broadway show cost $81, 4 tickets cost $108, and 5 tickets cost $135. Show that the relationship between number and the cost is a proportional relationship by making a table of tickets for 1 to 5 tickets. Show your work. Number of Tickets 1 2 3 4 5 Total Cost ($) What is the constant of proportionality, k? Write and Equation for the relationship. (Remember to state what the variables represent)
Answer:
k=27y=27xStep-by-step explanation:
3 tickets to attend an Off-Broadway show cost $81,
4 tickets cost $108; and
5 tickets cost $135.
Let the price of a ticket=k
Therefore:
3k=814k=1085k=135Solving any of the equation above gives: x=27
We therefore have:
[tex]\left|\begin{array}{c|c|c|c|c|c}$Tickets&1&2&3&4&5\\$Total Cost(\$)&27&54&81&108&135\end{array}\right|[/tex]
Let y be the total cost of x tickets
From the above, the constant of proportionality, k=27An equation for the relationship is therefore:
y=27x (where x is the number of tickets and y is the total costs (in $)).
Please help ASAP! Correct answer only! I need to finish this assignment today.
There are 9 college students running for student government class president. The candidates include 5 biology majors.
If 5 of the candidates are randomly chosen to give the first 5 speeches, what is the probability that exactly 3 of the chosen candidates are biology majors?
Write your answer as a decimal rounded to four decimal places.
Answer:
0.4762
Step-by-step explanation:
There are 9C5 = 126 ways to choose 5 candidates to give speeches. There are (5C3)(4C2) = 60 ways that 3 of those candidates can be biology majors (and the other two can be non-biology majors). The probability of interest is ...
60/126 ≈ 0.4762
__
nCk = n!/(k!(n-k)!)
Please answer the following:
CLASS 8 SPOT TEST
1. WHAT IS THE PROBABILITY THAT AN INTEGER CHOSEN AT RANDOM BETWEEN 1 TO 10 INCLUSIVE IS EVEN?
2. A BAG CONTAINS 5 WHITE, 4 BLACK AND 1 BLUE BALLS. ONE BALL IS CHOSEN AT RANDOM. WHAT IS THE PROBABILITY THAT IT IS BLACK?
3. FIND THE PROBABILITY OF GETTING AN ODD NUMBER IN A SINGLE TOSS OF A FAIR DIE?
4. A FAIR DIE IS THROWN 900 TIMES. FIND THE NUMBER OF TIMES YOU WOULD EXPECT TO GET A 6.
5. THE PROBABILITY THAT IT WILL BE CLOUDY TOMORROW IS 0.45. WHAT IS THE PROBABILITY THAT IT WILL NOT BE CLOUDY TOMORROW?
Step-by-step explanation:
1. Of the following 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Only these 5 are even: 2, 4, 6, 8, 10.
The probability on an even number is 5 / 10 = 0.5 = 50%
2. The total number of balls is 10.
5 WHITE, 4 BLACK AND 1 BLUE
The probability on a black ball is 4 / 10 = 0.4 = 40%
3. A fair die can show the following 6 numbers 1, 2, 3, 4, 5, 6.
Only these 3 are odd: 1, 3, 5.
The probability on an odd number is 3 / 6 = 0.5 = 50%
4. The probability of a six is 1 / 6. If the die is cast for 900 times you can expect it to be 900 * 1 / 6= 900/6 = 150. The number of times you would expect a 6 would be 150.
5. If the probability on a cloudy tomorrow is 0.45, then in mathematics, that defines the propability for an non cloudy tomorrow as 1 - 0.45 = 0.55, which is 55%.
(The total should always add up to 100%).
In RST, the measure of
Answer:
27.5 degrees
Step-by-step explanation:
First, choose which method would work in this problem, SOH, CAH, or TOA.
We have opposite, O and adjacent, A. So we have an O and an A.
Thus, we should use TOA.
Tangent x = 44/84
Tangent x= 0.52
x= Tangent^-1 (0.52)
x=27.5 degrees
Answer:27.6
Step-by-step explanation:
Please help me! Anyone know this answer :(
Answer:
A
Step-by-step explanation:
2x-3=5(x+6)
2x-3=5x+30
2x-33=5x
3x=-33
x=-11
Hope this helps!
Divide 21a^3-14a by -7
Answer:
A
Step-by-step explanation:
[tex]\dfrac{21a^3-14a}{-7}= \\\\\\\dfrac{-7(-3a^3+2a)}{-7}= \\\\\\-3a^3+2a[/tex]
Hope this helps!
Subtract the equations 5x+4y= 25 -(5x+2y=3)
ASAP ! I WILL GIVE BRAINLIEST! Pls simplify this fraction on the attached picture thank you!!! I
Answer:
[tex]\frac{x+3}{x}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x^2-9}{x^2-3x}[/tex] factorise numerator and denominator
x² - 9 = (x - 3)(x + 3) ← difference of squares
x² - 3x = x(x - 3) , thus
= [tex]\frac{(x-3)(x+3)}{x(x-3)}[/tex] ← cancel (x - 3) on numerator/ denominator, leaving
= [tex]\frac{x+3}{x}[/tex]
?ABC is an isosceles triangle with legs AB and AC. ?AYX is also an isosceles triangle with legs AY and AX. The proof that ?ABC ~ ?AYX is shown. Statements Reasons 1. ?ABC is isosceles with legs AB and AC; ?AYX is also isosceles with legs AY and AX. 1. Given 2. AB ? AC and AY ? AX 2. Definition of isosceles triangle 3. AB = AC and AY = AX 3. Definition of congruency 4. AY • AC = AX • AC 4. Multiplication property of equality 5. AY • AC = AX • AB 5. Substitution property of equality 6. 6. Division property of equality 7. 7. Division property of equality 8. ? 8. ? 9. ?ABC ~ ?AYX 9. SAS similarity theorem Which statement and reason are missing in the proof? ?A ? ?A; reflexive property ?X ? ?X; reflexive property ?ABC ? ?AYX; corresponding angles of similar triangles ?ABC ? ?AXY; corresponding angles of similar triangles
Answer:
The correct option is;
∠A ≅ ∠A ; reflective property
Step-by-step explanation:
1. ΔABC is isosceles with legs AB and AC
ΔAYX is also isosceles with legs AY and AX
2. AB ≅ AC and AY ≅ AX (Definition of isosceles triangle)
3. AB = AC and AY = AX (Definition of congruency)
4. AY · AC = AX · AC (Multiplication property of equality)
5. AY · AC = AX · AB (Substitution property of equality)
6. [tex]\dfrac{AC}{AX} = \dfrac{AB}{AY}[/tex] (Division property of equality)
7. [tex]\dfrac{AC}{AX} = \dfrac{AB}{AX}[/tex] (Division property of equality)
8. ∠A ≅ ∠A ; reflective property
9. ΔABC ~ ΔAXY SAS similarity theorem (The two triangles have the same vertex angle A hence they are similar based on the Side Angle Side theorem for uniqueness of triangles.
Answer:
∠A ≅ ∠A; reflexive property
Step-by-step explanation:
i got it right on the unit test..
B. Nina buys a variety of cereal bars. The box contains 5 blueberry bars, 3 strawberry bars, and
2 apple bars. Write the ratio that represents each relationship in words, in colon form, and in
fractional form.
1. strawberry bars to blueberry bars
2. apple bars to blueberry bars
3. strawberry bars to total bars
4. apple bars to total bars
5. blueberry bars to total bars
6. apple bars to strawberry bars
Answer:
The requested ratios in words, colon form, and fraction form are:
1. strawberry bars to blueberry bars = 3 : 5 = 3/5
2. apple bars to blueberry bars = 2 : 5 = 2/5
3. strawberry bars to total bars = 3 : 10 = 3/10
4. apple bars to total bars = 2 : 10 = 2/10= 1/5
5. blueberry bars to total bars = 5 : 10 = 5/10 = 1/2
6. apple bars to strawberry bars =2 : 3 = 2/3
Step-by-step explanation:
Let's start by doing an inventory of what Nina has:
Apple bars = 2
Blueberry bars = 5
Strawberry bars = 3
Total bars = 10
The requested ratios then are:
1. strawberry bars to blueberry bars = 3 : 5 = 3/5
2. apple bars to blueberry bars = 2 : 5 = 2/5
3. strawberry bars to total bars = 3 : 10 = 3/10
4. apple bars to total bars = 2 : 10 = 2/10= 1/5
5. blueberry bars to total bars = 5 : 10 = 5/10 = 1/2
6. apple bars to strawberry bars =2 : 3 = 2/3
What is the answer to 2(5x+4)=8
Answer:
So first we have 10x = 0. We divide by 10 on both sides, so then we get x = 0. We still have 0 because 0/10 = 0.
So that means that the answer is
Write 10 in the first box 10 in the secondx=0Answer:
? = 10
Step-by-step explanation:
2(5x+4)=8 - DISTRIBUTE
= 10x + 8 = 8
10x + 8 = 8
- 8
10x = 0
10x/10 = 0/10
x = 0
For each hour he babysit,Anderson earns 1$ more than half of carey's hourly rate.Anderson earns 6$ per hour. wich equation can be used to solve for carey's hourly rate,c?
Answer:
The expression to find Carey's hourly rate is: [tex]c = 2*a - 2[/tex]. Carey's hourly rate is $10.
Step-by-step explanation:
Anderson receives 1 more than half of carey's hourly rate. If we call Anderson's rate by "a" and Carey's by "c", we can express this phrase in the following equation:
[tex]a = \frac{c}{2} + 1[/tex]
We want to find the Carey's rate, therefore we need to isolate the "c" variable.
[tex]\frac{c}{2} + 1 = a\\\frac{c}{2} = a - 1\\c = 2*a - 2[/tex]
Since Anderson earns $6, then we can find Carey's rate:
[tex]c = 2*6 - 2 = 12 - 2 = 10[/tex]
Answer:
A)
6 = c/2 + 1
80 people were asked which was their favourite animal.
The pictogram shows the results.
The key is missing.
Cat
a)
Which animal was the least popular?
b)
How many people does
represent?
Dog
Giraffe DDI
Monkey D.
Dolphin
c)
How many more people preferred
giraffes than dogs?
Answer:
(a)Cat
(b)8 animals
(c)6 people
Step-by-step explanation:
From the attached diagram:
Let the [tex]\square[/tex] be x.
Half of [tex]\square[/tex] =x/2
From the pictogram, we then have:
[tex]Cat = x+\frac{x}{4} \\Dog=x+\frac{3x}{4}\\Giraffe=2x+\frac{x}{2}\\Monkey =x+\frac{x}{2}\\Dolphin=3x[/tex]
Therefore:
[tex]x+\frac{x}{4} +x+\frac{3x}{4}+2x+\frac{x}{2}+x+\frac{x}{2}+3x=80\\8x+\frac{x}{4}+\frac{3x}{4}+\frac{x}{2}+\frac{x}{2}=80\\10x=80\\x=8[/tex]
So we have the following numbers
[tex]Cat = x+\frac{x}{4} =8+\frac{8}{4}=10\\Dog=x+\frac{3x}{4}=8+\frac{3*8}{4}=14\\Giraffe=2x+\frac{x}{2}=2*8+\frac{8}{2}=20\\Monkey =x+\frac{x}{2}=8+\frac{8}{2}=12\\Dolphin=3x=3*8=24[/tex]
(a)Cat was the least popular
(b) [tex]\square[/tex] represents 8 animals
(c)
Number of People who preferred giraffe=20
Number of People who preferred dogs=14
Difference=20-14=6
Therefore, 6 more people preferred giraffes than dogs.
A pictogram is a simple drawing that represents something
(a). Cat is least popular animal
(b)Total 8 complete square in given pictogram represented 64 people.
(c) 6 more people preferred giraffes than dogs.
Let us consider that a large complete square represented by variable y .
Since, peoples whose favourite animal is cat is represented by a complete square and one fourth of square.
It means, Peoples who like cat = [tex]y+\frac{y}{4}[/tex]
Similarly,
People who like dog = [tex]y+\frac{3}{4}y[/tex]
Peoples who like Giraffe = [tex]2y+\frac{y}{2}[/tex]
Peoples who like monkey = [tex]y+\frac{y}{2}[/tex]
Peoples who like Dolphin = [tex]3y[/tex]
Since, total people = 80
Therefore,
[tex]y+\frac{y}{4}+y+\frac{3}{4}y+2y+\frac{y}{2}+y+\frac{y}{2} +3y=80\\\\10y=80\\\\y=\frac{80}{10}=8[/tex]
So, a complete large square is equivalent to 8 peoples.
Peoples who like giraffes = [tex]2y+\frac{y}{2}=2(8)+\frac{8}{2}=20[/tex]
Peoples who like dog = [tex]y+\frac{3}{4}y=8+(\frac{3}{4} ) 8=14[/tex]
So, 20 - 14 =6 more people preferred giraffes than dogs.
Thus,
(a) Cat is least popular animal
(b)Total 8 complete square in given pictogram represented 64 people.
(c) 6 more people preferred giraffes than dogs.
Learn more:
https://brainly.com/question/23021563
Ken built a 20 foot square fence in his back yard and planted a tree every 5 feet along the fence. How many trees did Ken plant?
Answer: 41
Step-by-step explanation:
Answer:
c:16
Step-by-step explanation:
Help pls! I ended up getting the wrong answer, so an explanation would help! (:
Answer:
4p squared - 28pqStep-by-step explanation:
4p(p−7q)
=(4p)(p+−7q)
=(4p)(p)+(4p)(−7q)
=4p squared −28pq
If f(x) = 3x2 + 1 and g(x) = 1 - x, what is the value of (f - g)(2)
Answer:
14
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= 3x² + 1 - (1 - x)
= 3x² + 1 - 1 + x
= 3x² + x , thus
(f - g)(2)
= 3(2)² + 2 = 3(4) + 2 = 12 + 2 = 14
Ursula tosses two six-sided number cubes and ADDS the numbers rolled. Which of these is a list of the outcomes of the two row? A) 3, 4, 5, 6, 7, 8 B) 2,4,6,8, 10, 12 C) 5, 8, 11, 14, 17, 20 D) 0/25, 1/25, 3/25, 5/25, 6/25, 25/2
Answer:
A) 3, 4, 5, 6, 7, 8
Step-by-step explanation:
2+1, 2+2, 2+3, 2+4, 2+5, 2+6= 3, 4, 5, 6, 7, 8
Lou's Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers. Determine which equation represents how much Kayla will spend on sandals after the discount. $13.50 = 0.75(x + 10) $13.50 – 10 = 0.75x $13.50 + 10 = 0.75x $13.50 = 0.25(x + 10)
Answer:
13.50=0.75(x+10)
Step-by-step explanation:
From the options given, it seems the price of either of Sandals or sneakers is given as 10 and the other is x
If Price of Sandals or sneakers=x
And the price of the other one is 10
Total price=(x+10)
25% discount is given
So she will pay 75% of the total cost
75%=0.75
Total cost =$13.50
She would pay 75% of (x+10)
Which is
0.75(x+10)=13.50
13.50=0.75(x+10)
Answer:
The answer is $13.50 = 0.75(x + 10)
Step-by-step explanation:
I am doing the assignment right now
Your Welcome :)
If g(x)=2x-1 and h(x)= swuare root x, find (g o h) (9)
Answer:
5
Step-by-step explanation:
To evaluate (g ￮ h)(9), evaluate h(9) , then use this value to evaluate g(x)
h(9) = [tex]\sqrt{9}[/tex] = 3, then
g(3) = 2(3) - 1 = 6 - 1 = 5
Help me please this is due today help me
Answer:
Below
Step-by-step explanation:
1. -4, -|2|, -1, |-3|, 4
2. -7.5, -7.2, 9.5, 10.5
3. 7
5. 13
6. -9
7. [tex]\frac{5}{12}[/tex]
8. -1.36
9. [tex]\frac{13}{5}*[/tex][tex]\frac{-4}{3}[/tex][tex]=\frac{-52}{15}[/tex]
10. -27.2
11. 22 * 2 + 7 * 0 - 5 * 1 = 39
If h(x) = x – 7 and g(x) = x2, which expression is equivalent to (g circle h) (5)?
Answer:
4
Step-by-step explanation:
[tex]h(x)=x-7 \\\\g(x)=x^2 \\\\(g\circ h)(5)= (5-7)^2=(-2)^2=4[/tex]
Hope this helps!
Using composite functions, it is found that the equivalent expression at x = 5 is given by:
[tex](g \circ h)(5) = 4[/tex]
What is a composite function?A composite function is when a function is used as an input to another function, hence, that is:
[tex](g \circ h)(x) = g(h(x))[/tex].
In this problem, we have that the functions are given as follows:
h(x) = x - 7.g(x) = x².Then, the composite function is given by:
[tex](g \circ h)(x) = g(h(x)) = g(x - 7) = (x - 7)^2[/tex].
We want to find the value of the composite function at x = 5, hence we have that:
(5 - 7)² = 4.
More can be learned about composite functions at https://brainly.com/question/17684028
#SPJ2
pls help me I need to finish it!!
Answer:
2/7
Step-by-step explanation:
7/8 ÷ 3 1/16
Change to an improper fraction
3 /16 = (16*3+1)/ 16 =49/16
7/8 ÷49/16
Copy dot flip
7/8 * 16/49
Rewrite
7/49 * 16/8
Simplify
1/7 * 2/1
2/7
How many inches are in a square foot?
Answer:
144 inches.
Step-by-step explanation:
One foot = 12 inches
One square foot = 144 inches.
Answer:
144
Step-by-step explanation:
Foot=12 inch
Square foot= foot times foot
Square foot= 12 inch times 12 inch
Square foot= 144 square inch.
Kate gets a paycheck twice a month. Every month, a total of $345.67 is deducted from her paychecks for taxes. If she has received 7 paychecks so far this year, which best represents the total effect the taxes have had on the amount she has earned??
Answer:
The correct answer is -$1,209.85-verified by Edg. Thank you.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Which property allows you to write the expression
(3 + 7i) + (8 − 6i) as (8 − 6i) + (3 + 7i)?
Answer:
3+7i
Step-by-step explanation:
Answer:
Associative
Step-by-step explanation:
I got it on edge hope ur not as far behind as me boys
James has a bicycle. Each wheel has diameter 45cm. James cycles his bicycle in a straight line in the playground. The front wheel makes 15 complete revolutions. How far does the bicycle travel? Give your answer in metres.
Answer: 21.21 meters
Step-by-step explanation:
Hi, to answer this, first we have to calculate the circumference (C) of the wheel:
C = π x diameter
Replacing with the values given:
C = π x 45 = 141.37 cm
Then we multiply it by the number of revolutions:
141.37 x 15 = 2,120.6 cm
Since
1 cm = 0.01 m
2,120.6 x 0.01 = 21.21 meters
Feel free to ask for more if needed or if you did not understand something.
which expression is equivalent to: -9x^-1y^-9/-15x^5y^-3
Answer:
3 / 5x^6y^6
Step-by-step explanation:
= -9x^-1y^-9/-15x^5y^-3
= -9y-9 / -15x^6y^-3
= -9 / -15x^6y^6
= 3 / 5x^6y^6
Answer:
b on edge
Step-by-step explanation:
Can someone help out pls
Answer:
-2
Step-by-step explanation:
x= -2 is the required equation
Please help asap. I dont have much time left
Answer:
k well sorry im 7 minutes late but anyways here: 52 and one half.
Step-by-step explanation:
How fast did the truck consume its fuel?
Pro
Choose 1 answer:
Tea
60 liters per kilometer
0.6 liters per kilometer
40 liters per kilometer
0.4 liters per kilometer
Answer: 0.6 liters per kilometer
Step-by-step explanation:
(A) 475L - 50km
(B) 375L - 200km
Subtract liters.
475-375=100L
Subtract km
200-50=150km
Divide liters per km
100/150=0.6L/km