Answer:
sqrt(3) + sqrt(7)
Step-by-step explanation:
3*sqrt(7) / sqrt(21) = 3/sqrt(3)
If you rationalize the denominator, you get 3*sqrt(3)/3. The threes cancel
You are left with sqrt(3)
7sqrt(3)/sqrt(21) = 7 / sqrt(7)
If you rationalize the denominator, you get
7 sqrt(7)/ 7 = sqrt(7)
The 7s have been canceled out
The answer is
sqrt(3) + sqrt(7)
In the American version of the Game Roulette, a wheel has 18 black slots, 18 red slots and 2 green slots. All slots are the same size. A person can wager on either red or black. Green is reserved for the house. If a player wagers $5 on either red or black and that color comes up, they win $10 otherwise they lose their wager. What is the expected value of playing the game once
Answer:
-$0.26
Step-by-step explanation:
Calculation to determine the expected value of playing the game once
Expected value= [18/(18+18+2) x $5)]- [20/(18+18+2) x $5]
Expected value= ($18/38 x $5) - (20/38 x $5)
Expected value= ($2.37-$2.63)
Expected value= -$0.26
Therefore the expected value of playing the game once is -$0.26
please me in math
[tex] \frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1} [/tex]
Step-by-step explanation:
hope this helps you thank you
[tex]\boxed{ \sf{Answer}} [/tex]
[tex] \large{\sf\frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1}} [/tex]
Use the algebraic identities ⟶
[tex]{\sf(a - b)(a + b) = {a}^{2} - b ^{2}} [/tex][tex]{\sf(a + b) {}^{2} = {a}^{2} + 2ab - {b}^{2}} [/tex][tex]{\sf(a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2}} [/tex]Squaring on both the sides
[tex] {\sf\frac{(a + 1 {)}^{2} + ( {a - 1)}^{2} }{(a - 1)(a + 1)}} [/tex]
[tex]=\frac{ {a}^{2} + 2a + 1 + {a}^{2} - 2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} +\bcancel 2a + 1 + {a}^{2} - \bcancel2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} + {a}^{2} + 1 + 1 }{ {a}^{2} - 1}[/tex]
[tex]\large\boxed{\sf{⟹\frac{ {2a}^{2} + 2}{ {a}^{2} - 1 }}} [/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
answer nowwwwwwwwwwwwwwwwwwwwwwwwwwww
Answer:
7/6
Step-by-step explanation:
(7x/12)/(x/2)
=7/6
If 40% of a number is equal to two-third of another number, what is the ratio of the first number to the second number.?
Answer:
5:3
Step-by-step explanation:
40% = 2/5
If the numbers are x and y, then
2/5 x = 2/3 y
Divide both sides by 2/5
x = (2/3 * 5/2)y
x = 10/6 y
x = 5/3 y
So the required ratio is 5 : 3.
Checking this result:
10% of 5 = 2
2/3 of 3 = 2 also.
How do I solve this?
Answer:
y = 0.8x – 2
Step-by-step explanation:
Slope (m) =
ΔY/ ΔX = 4 /5 = 0.8
y=.8x+b
plug in point
b=-2
Help!!!!!!!!!!!!!!!!
502.5 = -502.5
Now
x = -502.5
= -5025/10
= -1005/2 feet
Answered by Gauthmath must click thanks and mark brainliest
Translate sentence into equation
nine more than a product of a number and 4 is 8
Answer:
If x is the required number, equation will be 9+4x=8
Instructions: Fill in the last step of solving the quadratic equation by factoring. 3x2−2x−5=0 Step 1: Rewrite middle term. 3x2−5x+3x−5=0 Step 2: Group terms together and find GCF. (3x2−5x)+(3x−5)=0 x(3x−5)+1(3x−5)=0 (3x−5)(x+1)=0 Step 3: Apply the Zero Product Property. 3x−5=0 or x+1=0 Step 4: Solve. x= or x=
Answer:
x = (5/3)
x = -1
Step-by-step explanation:
[tex]3x^2 -2x - 5 =0\\\\(3x^2+3x) + (-5x - 5) = 0\\\\(3x-5)(x+1)=0\\\\\left \{ {{3x-5=0} \atop {x+1=0}} \right.\\\\===========\\\\3x - 5 = 0\\\\3x - 5 + 5 = 0 + 5\\\\3x = 5\\\\\frac{3x=5}{3}\\\\x = \frac{5}{3}\\\\===========\\\\x + 1 = 0\\\\x + 1 - 1 = 0 - 1\\\\x = -1 \\\\===========\\\\\boxed{\text{Therefore:}}\\\\\boxed{ x = \frac{5}{3} \text { or } x = -1}[/tex]
You would just need to solve the two equations from step three for 'x'.
Hope this helps you.
Which function has a domain of all real numbers?
Answer:
c part ....
please mark brainlest
A mixture of jellybeans is to contain twice as many red as yellow, three times as many green as yellow, and twice as many pink as red. Red jelly beans cost $1.50 per pound, yellow cost $3.00 per pound, green cost $4.00 per pound, and pink only costs $1.00 per pound. How many pounds of each color jellybean should be in a 10 pound canister that costs $2.20 per pound?
please help me with this question <3
9514 1404 393
Answer:
a) 30.7 million
b) 1.5% per year
c) 42.0 million
d) 2017
Step-by-step explanation:
a) The initial population is P(0) = 30.7 (million). The exponential term is 1 when t=0, so this number is the multiplier of the exponential term.
__
b) The growth factor is the base of the exponential term: 1.015. The growth rate is the difference between this and 1: 1.015 -1 = 0.015 = 1.5%.
The population is growing by 1.5% per year.
__
c) Fill in the value and do the arithmetic. t=2021 -2000 = 21.
P(21) = 30.7·1.015^21 ≈ 41.968 ≈ 42.0
The population in Canada in 2021 is predicted to be 42.0 million.
__
d) For this we need to solve for t when P(t) = 40.
40 = 30.7·1.015^t
40/30.7 = 1.015^t
Taking logarithms gives ...
log(40/30.7) = t·log(1.015)
t = log(40/30.7)/log(1.015) ≈ 17.773
In 2017, the population is predicted to be less than 40 million; in 2018, it is predicted to be more than 40 million. Canada should anticipate hitting 40 million people in 2017.
_____
Additional comment
The second attachment shows the prediction described here is a little high relative to the actuals in the last few years.
Guided Practice
Which model is most appropriate for the set of points?
(–3, 6), (–1, 0), (0, –1), (1, –1.5)
A.
exponential
B.
quadratic
C.
linear
Answer:
B. quadratic
Step-by-step explanation:
Answer: The model that is most appropriate for the set is: Quadratic
Answer:
exponential
Step-by-step explanation:
Just took the test
What is the range of 58, 59, 57, 59, 55
Answer:
4
Step-by-step explanation:
Hi there!
Range = largest number from data given - smallest number from data given
From the given data, 58, 59, 57, 59, 55,
59 is the largest number and 55 is the smallest number
So the range = 59 - 55 = 4
Find the measure of angle BAC.
Answer:
[tex]\angle 72=BC-86/2[/tex]
[tex]144+86=BC[/tex]
[tex]BC=230[/tex]
[tex]BC=230/2[/tex]
[tex]\angle BAC= 115[/tex]°
~OAmalOHopeO
Helppppp please
What is the slope of the line shown below?
Answer:
A.
[tex]{ \tt{slope = \frac{ - 4 - 2}{ - 1 - 2} }} \\ \\ = { \tt{ \frac{ - 6}{ - 3} }} \\ = 2[/tex]
DEFG is a cyclic quadrilateral. If ∠E = 27°, find ∠G.
For a cyclic quadilateral, the combination of opposite angles = 180°. So <G is opposite to <E so G must be 153°
(25 POINTS)Please help me, and show all of your work step by step.
Now say you invest $6,500 and the highest interest rate you can find is 2.5% compounded annually, but you would have to leave this investment in the account for a minimum of 5 years. If you decide to wait 5 years to buy the car, how much more money will you have to save to buy a car at the price of $8,000? Use the compound interest formula A = P(1 + i)^n.
A = accumulated amount
P = principle
i = interest rate
n = number of years
Answer:
$ 645.85
Step-by-step explanation:
First you would plug 6,500 into P. The plug 2.5% as 0.025 into i. And plug the years (5) into n.
A = 6500 (1 + 0.025)^5 = 7354.15
That is the amount that would be in the account at the end of the 5 years.
Then you take the cost of the car (8,000) and subtract the money left in the account (7,354.15).
8000 - 7354.15 = 645.85
Your final answer would be rounded to the nearest cent, or the hundredths place.
The power 9 squared is equivalent to 81. What is the value of 9 Superscript negative 2?
Answer:
1/81
Step-by-step explanation:
9^2 = 81
We know that a^ -b = 1/a^b
9^-2
1/9^2
1/81
Answer:
1/81
Step-by-step explanation:
Edge
A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in 10 hours? What is the rate of speed of the jet?
980 miles
Step-by-step explanation:
5 hours =490miles
1 hour =490/5=98miles
10hours = 98×10=980miles
giving crown
1) At the store, 2 pounds of beans cost $3.15, 5 pounds of rice cost $7.50, 4 pounds of cabbages cost $4.54, and 7 pounds of alfalfa cost $8.95. Which item has the lowest unit price?
(A) Beans(B) Rice(C) Cabbages(D) Alfalfa
2) Peanuts are sold at the general store in the following quantities: 2¢ for one peanut; 50 peanuts for 99¢, 100 peanuts for $1.99, and 50,000 peanuts for $1000. Which quantity has the lowest unit price?
(A) 1 peanut(B) 100 peanuts(C) 50 peanuts(D) 50,000 peanuts
3)The ratio of trees to shrubs in the garden was 7 to 13. If there were 273 shrubs in the garden, how many trees were there?
(A) 420(B) 147(C) 1911(D) 507
Answer:
3) = B
Explanation:There are 147 trees.
Bike speed of 21miles per hour. What is the speed per minute how many miles will the cyclist travel in 10 minutes
Answer:
First part: 0.35 miles per minute
Second part: 3.5 miles in 10 minutes
Step-by-step explanation:
Think about this as a fraction. Fractions can't be added nor subtracted unless they share the same denominator. So for this case, we have to turn hours into minutes. So 21 mph becomes 21 miles per 60 minutes. Then, we divide 60 from each side to find the speed per minute. 21/60 = 0.35, so the answer to the first part is 0.35 miles per minute.
Using what we got, we can answer the second part of the distance covered in 10 minutes. So, we just multiply 0.35 by 10 which is 3.5 miles covered in 10 minutes.
− 10x− 6y = 12
4x+ 7y =− 14
x=0, y=-2
tell me if u need the explanation
Evaluate:
3 - - 10-9 divided by (-1)
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{3 - -10 - \dfrac{9}{-1}}[/tex]
[tex]\mathsf{= 3 - (-10) - \dfrac{9}{-1}}[/tex]
[tex]\mathsf{= 3 + 10 - \dfrac{9}{-1}}[/tex]
[tex]\mathsf{3 + 10}\\\\\mathsf{= \bf 13}[/tex]
[tex]\mathsf{= \bold{13} - \dfrac{9}{-1}}[/tex]
[tex]\mathsf{\dfrac{9}{-1}}\\\\\mathsf{= 9\div-1}\\\\\mathsf{= \bf -9}[/tex]
[tex]\mathsf{= 13 - (\bf -9)}[/tex]
[tex]\mathsf{= 13 + 9}[/tex]
[tex]\mathsf{= \bf 22}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 22}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A bakery sold a total of 500 cupcakes in a day, and 83% of them were vanilla flavored. How many of the cupcakes sold that day were vanilla flavored?
Answer:
percent * base = amount
.83 * 500 = amount
amount = 415
Step-by-step explanation:
Write an equation of a polynomial with the given characteristics: a quadratic function has x -intercepts of -3 and 1, and a y-intercept of (0,9).
Answer:
f(x) = -3(x+3)(x-1)
Step-by-step explanation:
x = -3 & 1; f(x) = 9
f(x) = a(x-r1)(x-r2)
f(0) = a(x-r1)(x-r2) = 9; 9 = a(0-(-3))(0-1)
9 = a(3)(-1); 9 = a(-3)
a = -3
f(x) = -3(x+3)(x-1)
Answer:
f(x) = -3x^2 - 6x + 9.
Step-by-step explanation:
As the x intercepts are - 3 and 1 we can write it as:
f(x) = a(x - 1)(x + 3) where a is a constant to be found.
As the - intercept is at (0, 9), x =0 when f(x) = 9 so we can also write:
a( 0 - 1)(0 + 3) = 9
(-1)(3)a = 9
a = 9 / -3
= -3.
So the equation is f(x) = -3(x - 1)(x + 3)
In expanded form it is
-3(x^2 + 2x - 3)
= -3x^2 - 6x + 9.
Emily says that the lengths of the sides of her prism are 6 inches 5 inches
and 3 inches. Is Emily correct? Use words and numbers to explain why or
why not.
What is the value of f(x) = 2 • 2 x for f(–2)?
Answer:
-8
Step-by-step explanation:
you know, all you have to do in such a case is simply taking the given -2 and put it, where there is "x" in the function expression and then calculate this. if necessary with a calculator.
2×2×x with x=-2 is
2×2×-2 = -8
Answer:
- 8
Step-by-step explanation:
f ( x ) = 2 . 2 x
f ( - 2 )
= 2 . 2 ( - 2 )
= 2 x 2 x ( - 2 )
= - 8
Solve for x
Need help asap
Answer:
[tex]x=55[/tex]
Step-by-step explanation:
Corresponding angles of two parallel lines are always equal. The angle on "top" of [tex]2x+6[/tex] corresponds with the angle marked as [tex]x+9[/tex]. Therefore, its measure must also be [tex]x+9[/tex].
Since these two angles form one side of a line which has 180 degrees, we have the following equation:
[tex]2x+6+x+9=180[/tex]
Combine like terms:
[tex]3x+15=180[/tex]
Subtract 15 from both sides:
[tex]3x=165[/tex]
Divide both sides by 3:
[tex]x=\frac{165}{3}=\boxed{55}[/tex]
If b = -1, which one is the value of b^3?
Answer:
b=-1Put the value of b in b^3[tex] \\ \sf \longmapsto \: b {}^{3} \\ \\ \sf \longmapsto \: { - 1}^{3} \\ \\ \sf \longmapsto \: 1 \times - 1 \\ \\ \sf \longmapsto \: - 1[/tex]
Hence b^3=-1
The coach of a lacrosse team bought ice cream cones to celebrate a victory. A single-scoop cone was $3 and a double-scoop cone was $5 The coach bought 15 cones and paid $57. A system of equations describing this situation could be written in the form below where s represents the number of single cones andd represents the number of double cones. What is the sum of A, B, C and E?
Answer:
s=9
d=6
Step-by-step explanation:
s+d=15
3.s+5.d=57
⇒s=9 và d=6
The sum of A, B, C, and E is 23. Let's set up a system of equations based on the given information: s: number of single-scoop cones
d: number of double-scoop cones
1. The coach bought 15 cones in total:
s + d = 15
2. The cost of a single-scoop cone was $3 and the cost of a double-scoop cone was $5, and the total payment was $57:
3s + 5d = 57
Now, let's find the values of s and d by solving the system of equations.
First, we can use the first equation to solve for s in terms of d:
s = 15 - d
Now, substitute this value of s into the second equation:
3(15 - d) + 5d = 57
Now, solve for d:
45 - 3d + 5d = 57
2d = 57 - 45
2d = 12
d = 6
Now that we have the value of d, we can find the value of s using the first equation:
s = 15 - d
s = 15 - 6
s = 9
So, the number of single-scoop cones (s) is 9, and the number of double-scoop cones (d) is 6.
Now, let's find the sum of A, B, C, and E:
A: The number of single-scoop cones (s) is 9.
B: The number of double-scoop cones (d) is 6.
C: The cost of a single-scoop cone is $3.
E: The cost of a double-scoop cone is $5.
A + B + C + E = 9 + 6 + 3 + 5 = 23
So, the sum of A, B, C, and E is 23.
To know more about sum:
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