The value of n is 20 from the given indices
How to determine the variable in an exponential functionGiven the exponential function expressed as:
[tex]\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{0.001}}.\][/tex]
This can be further expressed as:
[tex]\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{10^{-3}}}.\\\[10^n = 10^{3}\sqrt{10^{34}\\10^n = 10^3\cdot 10^{17}[/tex]
Since the use are equal, add the exponents
[tex]10^n= 10^{3+17}\\10^n=10^{20}\\n=20[/tex]
Hence the value of n is 20 from the given indices
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Answer:
20
Step-by-step explanation:
convert the following to powers first then simplify and then write answer as a radical
Answer:
[tex]\sqrt[15]{m^2n^4}[/tex]
Step-by-step explanation:
[tex](\sqrt[5]{m^2n^4} )^{\frac{1}{3}}\\\\\implies( (m^2n^4)^{\frac{1}{5}})^{\frac{1}{3}}\\\\\implies (m^2n^4)^{\frac{1}{5}\times \frac{1}{3}}\\\\\implies (m^2n^4)^{\frac{1}{15}}\\\\\implies (m^2)^{\frac{1}{15}} (n^4)^{\frac{1}{15}}\\\\\implies m^{\frac{2}{15}} n^{\frac{4}{15}}[/tex]
[tex]\sqrt[15]{m^2n^4}[/tex]
A cell phone company charges $20 a month for the base plan. They charge 10 cents for
every text, minute, or kilobyte of data use. Write and equation to express your cell phone bill.
O y = .20x - 10
O y = 10x – 20
O y = .10x + 20
O y = 20x + .10
A hot-air balloon has a 14-foot diameter that is being deflated at a rate of 0.25 feet per minute.
How many minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet?
CLEAR CHECK
Write the equation that represents the situation.
−
x =
Solve for the time taken for the balloon to shrink to a diameter of 8 feet.
It will take
minutes.
Answer:
24 min
Step-by-step explanation:
14-8 is 6 so you need to shrink it 6 feet until it has a daimiter of 8.
6 divided by .25 is 24 so you have your answer
14-.25x=8
The equation is 14 - 0.25x = 8.
It will take 24 minutes for the balloon to shrink.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given:
A hot-air balloon has a 14-foot diameter.
Rate of 0.25 feet per minute.
Now, equation to represent the situation is
14 - 0.25x = 8
On further solving
6= 0.25x
x= 6/0.25
x= 24
Hence, it will take 24 minutes for the balloon to shrink.
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Reduce the following fraction 25/55
Pls help quickly
Answer:
5/11
Step-by-step explanation:
what percent of 610 is 457.5?
Answer:
75%
Step-by-step explanation:
457.7/610
divide it out
.75
make it a percentage
.75 × 100 = 75%
Hey guys! Person above me is correct, I made a mistke in my calculations!
Subtract.
The difference is?
Answer:
11m^3+16m+16
Step-by-step explanation:
First, you have to subtract the m^3, then the m, and the 11 and -5.
Answer:
11m^3-21m^2+20m+16
Step-by-step explanation:
ill mark brainlest if correct
Please help me with this question
Answer:
18
Step-by-step explanation:
House number:
1. has 3 people
2. has 2 people
3. has 3 people
4. has 2 people
5. has 3 people
6. has 2 people
7. has 3 people
looking at each rule, it all fits.
so now add it all up so its 18
Write the equation of a parabola with the focus at (3, 0) and the directrix at x = –3. X2 = –3y y2 = –3x x2 = 12y y2 = 12x.
The equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.
What is the Equation of a parabola?y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
As it is given that the focus of the parabola is at F(3,0) and its directrix is the line x=−3, therefore, we can write that
x=-3
x+3=0
Now, Let A(x,y) be any point in the plane of the directrix and focus, and MA be the perpendicular distance from A to the directrix, therefore, A lies on parabola if FA=MA,
[tex]FA=MA\\\\\sqrt{(x-3)^2 +(y-0)^2}=\dfrac{|x+3|}{1}\\\\{(x-3)^2 +(y-0)^2}={(x+3)^2}\\\\-6x^2+y=6x\\\\y=6x^2+6x[/tex]
Hence, the equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.
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Angela has 3 pennies. She tells her friend that she has 3/10 of a dollar. Is she correct? Why or why not?
Answer:
Yes
Step-by-step explanation:
She is correct because 3/10 of 100 (a full dollar) is 0.3 which is 3 in pennies/cents. You could also do 3% of 100 which is 3 (pennies/cents)
Surface Area of Cylinder=2πrh+2πr2
Where r is the radius of the cylinder and h is the height of the cylinder. Find the surface area when r is 3 inches and h is 5 inches.
A. 112π in²
B. 48π in²
C. 80π in²
D. 50π in²
Answer: B. 48 pi in^2
Step-by-step explanation:
Plug the given values into the equation.
So the SA = 2*pi*3*5 + 2*pi*3^2
SA = 30pi + 18pi
SA = 48 pi in^2
What is the factored form of the polynomial? x2 − 15x 36 (x − 4)(x − 9) (x − 3)(x − 12) (x 4)(x 9) (x 3)(x 12).
Polynomials consist of both indeterminates and coefficients. The factors of the polynomial x² - 15x + 36 is (x-3)(x-12).
What are polynomials?A polynomial consists of both indeterminates and coefficients and involves mathematical operations such as addition, subtraction, multiplication, and division.
Given to us
x² - 15x + 36
To find the factors of the polynomial,
[tex]x^2 - 15x + 36 \\\\[/tex]
We will replace -15 with two numbers such that their sum is -15 while, their product must be 36.
[tex]x^2 - 15x + 36 \\\\ = x^2 -12x-3x +36\\\\[/tex]
now, we will take x as the common term from the first two-term, while 3 as the common term from the next two terms.
[tex]= x^2 -12x-3x +36\\\\= x(x-12) - 3 (x - 12)\\\\= (x-3)(x-12)[/tex]
Hence, the factors of the polynomial x² - 15x + 36 is (x-3)(x-12).
Learn more about Polynomials:
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Answer:
its b.
Step-by-step explanation:
your welcome
It takes 6 hours to drive 342 mi. He will drive for 8 hours tomorrow. if he drives at the same rate, how far will Aron drive in 8 hours?
Answer:
456 miles
Step-by-step explanation:
We can use proportions to solve
342 miles x miles
------------ = --------------
6 hours 8 hours
Using cross products
342 * 8 = 6x
2736 = 6x
Divide by 6
2736/6 = x
456 miles
Answer:
Aron will drive 456 miles in 8 hours
Step-by-step explanation:
set up as proportion and cross multiply to solve:
6 hours/342 miles = 8 hours/x
x = 456
Write the equation in slope-intercept from the two points given: (4,2) and (0,-5)
Explain. (step by step)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{4}}}\implies \cfrac{-7}{-4}\implies \cfrac{7}{4}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{7}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-2=\cfrac{7}{4}x-7\implies y=\cfrac{7}{4}x-5[/tex]
help pls i really need it
Answer:
RHS
Step-by-step explanation: the hypotenuse and one side of the triangle is respectively equal to the hypotenuse and one side of the other triangle
so, its rhs
Sai reads 100 words each 1/2 minute. which statement is true
How can you rewrite ( ^12 sqrt 12 ) ^5 without a radical?
Answer:
b
Step-by-step explanation:
Sameen bought 2 1/5 pounds of carrots for $6.60. At that rate, how much would 1 pound of carrots cost?
Answer:
3$
Step-by-step explanation:
HELP ANOTHER QUESTION, I REALLY NEED HELP. !!!!!!!!!!!!!!!!!!!!!
Answer:
i dont know Ecactly but i think mybe its 10 or 15
The scale of a map is 2cm:15km. Find the actual distance for each map distance. 5cm
Step-by-step explanation:
2cm : 15cm so
5cm : 37.5cm
so 5cm is therefore=37.5cm
The senior class at South High school raised $80,000 from raffle tickets. Tickets cost $150 for a chance to win a Disney Vacation and $200 for a chance to win a car. If a total of 475 tickets were sold, how many were sold for the Vacation and how many were sold for the car?
Answer:
y = 175. x = 300. Disney vacation is 300 sold. Cars sold were 175.
Step-by-step explanation:
They want to raise $80,000. There are a total of 475 tickets.
150x + 200y (Disney Vacation + Win a car) = 80,000
x + y = 475.
__
y=475-x
150x+200(475-x)=80000
150x+95,000-200x=80,000.
-50x + 95,000 = 80,000.
-50x = -15,000
x = 300.
Disney vacation is 300 sold.
300 + y = 475.
y = 175.
Cars sold were 175.
Additional Info:
I am 14 years old and I'm learning solving the systems by elimination and substitution, etc. Hope this is the correct answer.
Give a solution to the equation in "c" that you can see from the graph.
3. Marcus had an average score of 90% on two biology tests about protists. If his first test score was 96%, which score did he receive on the second test? A.45% B.84% C.90% D.102%
Answer:
B: 84%
Step-by-step explanation:
Wyatt is going to a carnival that has games and rides. Each game costs $1. 25 and each ride costs $2. 75. Wyatt spent $20. 25 altogether at the carnival and the number of rides he went on is twice the number of games he played. Determine the number of games Wyatt played and the number of rides Wyatt went on.
In the carnival the number of games number of rides Wyatt went on is 3 and 6 respectively.
What is system of equation?
A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
The number of unknown objects can be find using the system of solution.
Given information-
The cost of each game is $1.25.
The cost of each ride is $2.75.
Total amount of money spent by the Wyatt is $20.25.
The number of rides he went on is twice the number of games he played.
Suppose the number of games Wyatt played is x and the number of rides he went in the carnival is y.
As, the number of rides he went on is twice the number of games he played. Thus,
[tex]y=2x[/tex]
Let the above equation as equation one.
As total amount of money spent by the Wyatt is $20.25 and The cost of each game is $1.25 and the cost of each ride is $2.75. Thus,
[tex]1.25x+2.75y=20.25\\[/tex]
Put the value of y in the above equation from the equation one as,
[tex]1.25x+2.75(2x)=20.25\\1.25x+5.5x=20.25\\6.75x=20.25\\x=3[/tex]
Thus the number of games he played is 3.
Put this value of x in the equation one as,
[tex]y=2\times3\\y=6[/tex]
Thus the number rides Wyatt went on is 6.
Hence, In the carnival the number of games number of rides, Wyatt went on is 3 and 6 respectively.
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A right triangle has legs measuring 16 in. And 28 in. What is the length of the hypotenuse? Round your answer to the nearest tenth. 23. 0 in. 32. 2 in. 44. 0 in. 1040. 0 in.
In a right-angled triangle, the Pythagoras theorem is used to find the hypotenuse. Then the hypotenuse is 32.2 inches.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Given
A right triangle has legs measuring 16 inches And 28 inches.
We know the Pythagoras theorem
[tex]\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2[/tex]
Then the hypotenuse will be.
[tex]\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2\\\\\rm Hypotenuse ^2 = 16^2 + 28^2\\\\ \rm Hypotenuse ^2 = 256 + 784\\\\\rm Hypotenuse ^2 = 1040\\\\\rm Hypotenuse \ = 32.2[/tex]
Thus, the hypotenuse is 32.2 inches.
More about the right-angle triangle link is given below.
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To buy a car, Rachel
borrowed $3,000 at
9% interest per
year for 3 years
How much money
did she have to pay
back?
You use the formula
3000*.09*3=810
She will have to pay back the amount of $3,810.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
We have been given data as:
Principal (P) = $3,000
Rate of Interest (R) = 9% = 9/100 = 0.09
Time (T) = three years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
⇒ Simple interest = 3,000× 9% × 3
⇒ Simple interest = 3,000× 9/100 × 3
⇒ Simple interest = 3,000× 0.09 × 3
Apply the multiplication operation, and we get
⇒ Simple interest = $810
The total payback amount = $3,000 + $810 = $3,810
Therefore, she will have to pay back the amount of $3,810.
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Triangle DEF has vertices D(2,1), E(3,6), and F(5,-2). Find the vertices of triangle D’E’F’ after a translation of 4 units to the left and 3 units down.
D=
E=
F=
The graph I have attached shows the translation. The dashed triangle shows the first step (traveling left 4 units). The red triangle is the finished product.
So the new coordinates...
D- (-2,-2)
E- (-1,3)
F- (1,-5)
Find the value of (3 + 4) 2.
25
49
14
Answer:
14
Step-by-step explanation:
[tex](3 + 4)2 \\ add \: 3 \: to \: 4 = 7 \\ (7)2 \\ 7 \times 2 \\ 14[/tex]
Scott wanted to buy a notebook. He saw a sale at Staples onnotebooks, $4.50 for 5 notebooks. What is the cost for one notebook at Staples?
Answer:
90 cents or $0.90
Step-by-step explanation:
To find the answer, we need to find UNIT RATE
In this equation, to find unit rate, divide $4.50 (4.5) by 5 to get your answer
When we do this, we get an answer of…
90 cents!
I hope this helps!
(Please award brainliest if possible)
Which set of numbers could represent the lengths of the sides of a right triangle?
2,3,4
12, 15, 20
8, 9, 10
9, 40, 41
Answer:
D. 9, 40, 41
Step-by-step explanation:
We can use Pythagorean theorem (a²+b²=c²) to answer this question by squaring the smallest 2 lengths then seeing if it equals the square of the 3rd length.
2²+3² = 4+9 = 13 ≠ 4²
12²+15² = 144+225 = 369 ≠ 20²
8²+9² = 64+81 = 145 ≠ 10²
9²+40² = 81+1600 = 1681 = 41²