Hi . Please I need help with these questions :
See image for question.
Answer no 5 and 6.
Answers
Answer:
(i) √23
(ii) 196√23
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Step-by-step explanation:
Step 1: Define
Standard Form: x² - 10x + 2 = 0
Step 2: Define variables
a = 1
b = -10
c = 2
Step 3: Find roots
Substitute: [tex]x=\frac{10\pm\sqrt{(-10)^2-4(1)(2)} }{2(1)}[/tex]Exponents: [tex]x=\frac{10\pm\sqrt{100-4(1)(2)} }{2(1)}[/tex]Multiply: [tex]x=\frac{10\pm\sqrt{100-8} }{2}[/tex]Subtract: [tex]x=\frac{10\pm\sqrt{92} }{2}[/tex]Simplify: [tex]x=\frac{10\pm 2\sqrt{23} }{2}[/tex]Factor: [tex]x=\frac{2(5\pm \sqrt{23}) }{2}[/tex]Divide: [tex]x=5\pm \sqrt{23}[/tex]Step 4: Define roots
α > β
α = 5 + √23
β = 5 - √23
Step 5: Evaluate
i
Substitute: [tex]\frac{1}{5-\sqrt{23} } -\frac{1}{5+\sqrt{23} }[/tex]Subtract: [tex]\sqrt{23}[/tex]ii
Substitute: [tex](5+\sqrt{23})^3-(5-\sqrt{23})^3[/tex]Evaluate: [tex](98\sqrt{23} +470)-(470 - 98\sqrt{23} )[/tex]Subtract: [tex]196\sqrt{23}[/tex]Answer:
(i) √23(i) 196√23Step-by-step explanation:
Given equation:
x² - 10x + 2 = 0Roots are:
α and βSum of the roots:
α + β = -b/a ⇒ α + β = -(-10)/1 ⇒ α + β = 10Product of the roots:
αβ = c/a ⇒ αβ = 2/1 ⇒ αβ = 2Finding the following:
(i)
1/β - 1/α =(α - β)/αβ =√(α - β)² / αβ =√((α + β)² - 4αβ) / αβ = √(10² - 4*2) / 2 =√92 / 2 =2√23 / 2 =√23(ii)
α³ - β³ =(α - β)(α² + αβ + β²) =√(α - β)²× ((α + β)² - αβ)√((α + β)² - 4αβ) × ((α + β)² - αβ) =√(10² - 4*2) × (10² -2) =√92 × 98 =2√23 × 98 =196√23Related Questions
What is the answer to
-100%+0.58= ?
Answers
Answer:
-0.42
Step-by-step explanation:
Answer: -0.42
Step-by-step explanation:
Help me complete this table please
Answers
Answer:
x -6 3 15 -12
y 11 5 -3 15
Step-by-step explanation:
Domain of a function represents the set of x-values (input values) and y-values (output values) of the function represent the Range of the function.
Given function is,
[tex]y = -\frac{2}{3}x +7[/tex]
If Domain (input values) of this function is,
{-12, -6, 3, 15}
Table for the input-output values of this function,
x -6 3 15 -12
y 11 5 -3 15
What is the length of the unknown side of the right triangle?
A right triangle with hypotenuse x and legs 21 and 20
21
29
400
441
Answers
According to Pythagoras theorem,
h² = b² + h²
=> x² = 21² + 20²
=> x² = 441 + 400
=> x = √841
=> x = 29
Thus, the length of the unknown side is 29 units.
Based on the line of best fit luther can expect the average speed of his pitches to be about _____ miles an hour in a game when he throws 80 pitches and to be 64 miles an hour in a game when he throws about ______ pitches.
Answers
Answer:
answer choices?
Step-by-step explanation:
Answer: 51 & 54
Step-by-step explanation:
Based on the line of best fit luther can expect the average speed of his pitches to be about __51___ miles an hour in a game when he throws 80 pitches and to be 64 miles an hour in a game when he throws about ____54__ pitches.
given the slope of the line and one point that it passes through, represent the equation of the line in point-slope form. then rewrite the equation in slope-intercept form.
(0,5) ; m =3
Answers
Answer:
Step-by-step explanation:
y - 5 = 3(x - 0)
y - 5 = 3x - 0
y = 3x + 5
Answer:
Step-by-step explanation:
answer on edmentum
How many sides does a decagon have?
sides
Answers
Answer:
It has 10 sides.
Step-by-step explanation:
Answer:
12 sides.
Step-by-step explanation:
A good way to remember this is "decagon" is called that because it has 12 sides, and the month December is the 12th month of the year.
PLEASE HELP
Solve for x 9^(x+2)=27^(8)
Answers
Answer:
I believe the answer is x=10
Hope this is correct! :)
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[tex] {9}^{(x + 2)} = {27}^{8} \\ [/tex]
[tex]( { {3}^{2} })^{x + 2} = ({ {3}^{3} })^{8} [/tex]
[tex] {3}^{2 \times (x + 2)} = {3}^{3 \times 8} [/tex]
[tex] {3}^{2(x + 2)} = {3}^{24} [/tex]
Thus :
[tex]2(x + 2) = 24[/tex]
Divide sides by 2
[tex] \frac{2(x + 2)}{2} = \frac{24}{2} \\ [/tex]
[tex]x + 2 = 12[/tex]
Subtract sides 2
[tex]x + 2 - 2 = 12 - 2[/tex]
[tex]x = 10[/tex]
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I need help plzzzzzzz!
Answers
4. The fire was very big
so many firefighters were there.
a. Independent Variable:
b. Dependent Variable:
Answers
Answer:
B. Dependent variable
Write each expression in standard form.
6(−5 − 4)− 2( − 7 − 3)
Answers
Answer:
heyyy wassuppp
Step-by-step explanation:
F a seed is planted, it has a 75% chance of growing into a healthy plant. If 9 seeds are planted, what is the probability that exactly 2 don't grow?
Answers
Answer:
0.3
Step-by-step explanation:
Given that:
Probability of growing into a healthy plant = probability of success (p) = 75% = 0.75
Number of seeds planted(n) = 9
Probability that exactly 2 don't grow is equivalent to having 7 that grows (9 - 2) = 7 = r
Using binomial distribution formula :
nCr * p^r * (1 - p)^(n-r)
9C7 * 0.75^7 * (1 - 0.75)^(9 - 7)
9C7 * 0.75^7 * 0.25^2
36 * 0.13348 * 0.0625
= 0.3003387
= 0.3
Hence, probability that exactly 2 don't grow is 0.3
Please help I have no idea what the answer is
Answers
Answer:
x = 59
Step-by-step explanation:
All the angles in a triangle add up to 180
Add all the known angles
83 + 38 = 121
To find the third angle, subtract the total of all the angles by the total of the known angles
180 - 121 = 59
PLEASE HELP MEEEEEEEEEE! NEED HELP FAST!! WILL GIVE BRAINLIEST!!! CORRECT ANSWERS ONLY PLEASEEEEEE!!!!!!
If 2+sqrt3 is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root.
Answers
Answer:
7
Step-by-step explanation:
At a sale, coats were sold for $118 each. If the coats originally cost $200 each, what percentage of its original price was a coat sold for?
Answers
rAnswer:
Step-by-step explanation:
20$
The price of nails, n, is $1.29 per pound, the price of washers, w, is $0.79 per
pound, and the price of bolts, b, is $2.39 per pound. Write an expression to
represent the total price of the supplies.
Answers
Answer:
Total price (P) = 1.29n + 0.79w + 2.39b
where n,w and b are pounds of respective items
Step-by-step explanation:
4. Find the slope of the line through the points (-6, 4) and (8,-4). m =
Answers
Answer: Hope it helps :)
-4
7
Step-by-step explanation:
You have to use the formula y2-y1
x2-x1
So -4-4
8--6
-4-4= -8
8--6= 14 (two negative signs become a positive sign)
You have -8 over 14
If you simplify it's -4/7 or -4
7
Answer:
-4/7
Step-by-step explanation:
Find the theoretical probability.
Simplify completely.
Answers
Answer:
3/8
Step-by-step explanation:
Favorable outcome is 3
Total outcome is 8
P(1, 2, or 3) = [tex]\frac{3}{8}[/tex]
The theoretical probability is 0.375
We have given that, a diagram of the circle.
We have to find the theoretical probability and simplify the probability.
What is the formula for probability?Theoretical Probability = Number of favorable outcomes / Number of possible outcomes.
The favorable outcome is 3.
The total outcome is 8
P(1, 2, or 3) = 3/8
The theoretical probability is 0.375
To learn more about theoretical probability visit:
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Solve for X. -15 = 22x + 7
Answers
Answer: x=-1
Step-by-step explanation: Here is one way of answering this question. First you need to subtract 7 from both sides and that will leave you with -22=22x. Then you just divide 22 on both sides. So that will give you an answer of -1=x or x=-1
Brad buys two packages of mushrooms. He paid $11.25 for 2/3 lb of Cremini mushrooms and $7.99 for 1/2 lb of Chanterelle mushrooms. Which mushroom cost less per pound?
Cremini mushrooms cost less by $0.10
Chanterelle mushrooms cost less by $0.10
Chanterelle mushrooms cost less by $0.90
Cremini mushrooms cost less by $0.90
Answers
Answer:
C. (Chanterelle mushrooms cost less by $0.90)
Step-by-step explanation:
Divide 11.25 by 2/3, for the total amount of pound for the Cremini.
Do the same thing for Chanterelle, but the numbers given for it.
We than find out that Cremini=16.87, and Chanterelle=15.98
Now that we know Cremini is more that Chanterelle, we need to find the difference, by subtracting The bigger number by the smaller number.
Our answer is 0.89, but we will round it to 0.90.
Now we know that the Cremini costs more by $0.90, and the Chanterelle costs less by $0.90
Answer:
Step-by-step explanation:
Cost of 1 lb of Cremini mushrooms= 11.25×3/2=33.75/2=16.875 $≈$16.88
Cost of 1 lb of Chanterelle mushrooms=7.99×2/1=$15.98
Chanterelle mushrooms cost 16.88-15.98=$0.90 less
Of the 345 7th graders in music programs, 35% are in choir, 25% are in orchestra and the remaining are in band. How many 7th graders in music programs are in band?
Answers
Answer: 138
Step-by-step explanation:
Number of 7th graders in music programs = 345
Percentage in choir = 35%
Percentage in orchestra = 25%
Percentage in band = 100% - (35% + 25%) = 100% - 60% = 40%
The number of 7th graders in music programs are in band will then be:
= Percentage in band × Total 7th graders
= 40% × 345
= 0.4 × 345
= 138 students
What number was added to 8 to get a sum of -4?
Answers
Answer:
-12
Step-by-step explanation:
8+(-12)=-4
there are 90 dogs and 60 casts at the east dallas animal shelter. of these animals, 9 dogs and 3 cats have parvovirus. what percentage of the animals in the shelter have parvovirus.
Answers
Answer:
8%
Step-by-step explanation:
12/250=0.08
0.08=8%
Answer:
8%
Step-by-step explanation:
WHICH GRAPH SHOWS A FUNCTION AND ITS INVERSE.
brainliest plz hurry timed test!!
Answers
A slope is also known as the gradient of a line. The correct option is B.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
Since for the two functions to be inverse of each other, the line of equations must bisect each other at 90° so that the product of the slope of the two equations is equal to -1.
For the second graph, the slope of the blue line is,
m₁ = (-1-0)/(0-4) = 0.25
The slope of the green line is,
m₂ = (-4-0)/[0-(-1)] = -4
Now, the product of the slope can be written as,
0.25×-4 = -1
Since the product is -1, the function is inverse of each other.
Hence, the correct option is B.
Learn more about Slope of Line:
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A team of runners is needed to run a 1/4 mile relay race . If each runner must run 1/16
mile. How many runners do they need to run the race?
Answers
Answer:
4 runners
Step-by-step explanation:
Help please I’m being timed
Answers
evaluate the function f (x)=-2x+3 for x=-1
Answers
Answer:
f ( - 1 ) = 5
Step-by-step explanation:
Step 1:
f ( x ) = - 2x + 3 Function
Step 2:
f ( - 1 ) = - 2 ( - 1 ) + 3 Input x value
Step 3:
f ( - 1 ) = 2 + 3 Multiply
Answer:
f ( - 1 ) = 5 Combine Like Terms
Hope This Helps :)
justin and his friends dan went to the movies if they each bought popcorn for $4.25 and soda for $2.25 what was their total bill after adding 5% of sales tax
Answers
Answer:
Step-by-step explanation:
4.25+2.25=6.50 per person
6.50*2 people= 13.00
13.00*5% tax=0.65 tax
13.00+.65= 13.65
Answer:
Step-by-step explanation:
4.25 x 2 + 2.25 x 2 = 13
Convert 5% into a decimal ( 0.05)
0.05 x 13 = 0.65
0.65 + 13 equals 13.65
HELP IS NEEDED
Allen’s score in a video game was changed by -125 points because he missed some targets. He got -25 points for each missed target. How many targets did he miss?
Group of answer choices
3,125
5
25
100
Answers
Answer:3,125
Step-by-step explanation:
A would be the answer
please help with math problem !! (explanation needed) -3 + (8 – 2x)4 = 29
Answers
Answer:
x = -4
Step-by-step explanation:
To solve this type of question, put the term with the exponent on one side and the numerical term on the other side
∵ -3 + [tex](8-2x)^{\frac{5}{4}}[/tex] = 29
→ Add 3 to both sides
∵ -3 + 3 + [tex](8-2x)^{\frac{5}{4}}[/tex] = 29 + 3
∴ [tex](8-2x)^{\frac{5}{4}}[/tex] = 32
→ Remember is [tex]x^{\frac{m}{n}}[/tex] = a, then x = [tex]a^{\frac{n}{m}}[/tex], that means to move the exponent
from one side to the other side reciprocal it
∴ 8 - 2x = [tex](32)^{\frac{4}{5}}[/tex]
→ Use your calculator to find the value of [tex](32)^{\frac{4}{5}}[/tex]
∵ [tex](32)^{\frac{4}{5}}[/tex] = 16
∴ 8 - 2x = 16
→ Subtract 8 from both sides
∴ 8 - 8 - 2x = 16 - 8
∴ -2x = 8
→ Divide both sides by -2
∴ x = -4
To check the solution substitute x by -4 in the left side and find its answer if it equals the right side, then the solution is right
∵ Left side ⇒ -3 + (8 - 2 × -4)[tex]^{\frac{5}{4}}[/tex] = -3 + (8 + 8)[tex]^{\frac{5}{4}}[/tex] =-3 + (16)[tex]^{\frac{5}{4}}[/tex] = -3 + 32 = 29
∵ Right side = 29
∴ The solution is right
The formula for the volume V of a cylinder is V=pier2h, where r is the radius of the base and h is the height of the cylinder. Solve the formula for h.
Answers
Answer:
h = V / πr²
Step-by-step explanation:
V = πr²h
Where,
V = volume of a cylinder
π = π
r = radius of the cylinder
h = height of the cylinder
V = πr²h
Solve for h
V = π × r² × h
Divide both sides by π × r²
h = V / π × r²
h = V / πr²
Height of the cylinder = volume of the cylinder / pie × r²