[tex] \large \bf \implies{32 {m}^{15} {n}^{10} }[/tex]
Step-by-step explanation:[tex]\bf \longrightarrow{(2m^{3}n^{2})^{5} } \\ \\ \bf \longrightarrow {2}^{5} \times ( {m}^{3})^{5} \times ( {n}^{2})^{5} \\ \\ \bf \longrightarrow32( {m}^{3})^{5}( {n}^{2})^{5} \\ \\ \bf \longrightarrow32 {m}^{15} {n}^{10} [/tex]
Note : We have used the two exponent rules:
[tex](1) \: \: \large \bf \boxed{ \bf \green{(ab)^{n} = {a}^{n} \times {b}^{n} }}[/tex]
[tex](2) \: \: \large \bf \boxed{ \bf \green{(a^{n})^{m} = {a}^{nm} }}[/tex]
Which is the best definition of substitution?
The process of combining the coefficients of terms that have the same variable.
The process of simplifying an expression using the order of operations.
The process of replacing variables with numeric values.
The process of multiplying a base by itself three times.
The best definition of substitution is C. The process of replacing variables with numeric values.
What is substitution?It should be noted that substitution is the way that can be used to solve linear system algebraically.
Therefore, the definition of substitution is the process of replacing variables with numeric values.
In conclusion, the correct option is C.
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Which symbol will make the statement true?
Answer:
∉
Step-by-step explanation:
10 is not a member of the set {6, 8, 13, 14} and ∉ is used to represent "not a member of"
Answer:
B ( if you talking about Mathematics enhancement )
Step-by-step explanation:
First one make the statement true but ( 6, 8, 13 ,14 ) didn't related to 10 According to a pattern
A rectangular area is being fenced in along a river that serves as one side of the rectangle.
(a) Write an expression for the total amount of
fencing needed in terms of the width, w, and the
length, 1.
(b) If w=12 feet and 1= 20 feet, how much fencing
is needed? Use proper units
W
river
W
(c) If the amount of fencing we have available is 120 feet and we want to devote 30 feet of it to the length, 1,
then set up an equation to solve for w and find the width.
a. Total amount of fencing needed = perimeter of the rectangular area excluding one length of the side close to the river = F = l + 2w
b. F = 44 ft
c. The width (w) = 45 ft.
What is the Perimeter of a Rectangle?Perimeter of rectangle = 2(length + width)
a. Total amount of fencing needed = perimeter of the rectangular area excluding one length of the side close to the river = l + 2w
F = l + 2w
b. w = 12 ft
l = 20 ft
Amount of fencing needed, F = l + 2w = 20 + 2(12)
F = 44 ft
c. F = 120 ft
l = 30 ft
Substitute F = 120 and l = 30 into F = l + 2w to solve for w
120 = 30 + 2w
120 - 30 = 2w
90 = 2w
90/2 = w
w = 45
The width (w) = 45 ft.
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Write a quadratic function to model the graph to the right.
f(x)
The quadratic equation to model the graph is y = x² - 6 · x + 14.
How to derive the expression of a quadratic equation from a graph
The picture presents us the graph of a parabola, whose algebraic expression is a quadratic equation. In accordance with fundamental theorem of algebra, a quadratic equation can be derived by knowing three distinct points on Cartesian plane.
If we know that (x, y) = (0, 14), (x, y) = (3, 5) and (x, y) = (6, 14), then the coefficients of the quadratic equation in standard form:
14 = c (1)
5 = 9 · a + 3 · b + c (2)
14 = 36 · a + 6 · b + c (3)
The solution of the system of linear equations is (a, b, c) = (1, - 6, 14). Hence, the quadratic equation to model the graph is y = x² - 6 · x + 14.
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290951.867863 rounded to the nearest hundred
Which of the following expressions have the same value as the mixed number
Answer:
-29/4-7 - 1/4- (7 + 1/4)Step-by-step explanation:
your welcome <3
-1/4 divided by (-7/9)
Answer:
9/28
Step-by-step explanation:
when you divide a fraction by fraction you need to multiply the left fraction by the opposite of right fraction so -7/9 becomes -9/7 and then you multiply -1/4 by -9/7. When you multiply negative with negative you get a positive value.
it's better to display fractions vertically like this to understand better
1
_
4
Answer:9/28
Step-by-step explanation:
math wizard! help me out
Answer: 27 days 60 miles
Step-by-step explanation: 162/6=27
6x17=102 162-102=60
Step-by-step explanation:
no wizardry is needed, as the function is already there. we only need to use it.
(a)
find d, so that 162 - 6d = 0 (0 miles are left)
162 - 6d = 0
162 = 6d
d = 162/6 = 27
it will take them 27 days.
(b)
L(17) = 162 - 6×17 = 162 - 102 = 60 miles
after 17 days they still have to lay 60 miles.
A​ 150-pound person uses 5.9 calories per minute when walking at a speed of 4 mph. how long must a person walk at this speed to use at least 250 ​calories?
The time taken when the person wants to burn 250 calories will be 42.37 minutes.
How to illustrate the information?From the information, the 150-pound person uses 5.9 calories per minute when walking at a speed of 4 mph.
Therefore, the time taken when the person wants to burn 250 calories will be:
= Number of calories / 5.9
= 250 / 5.9
= 42.37 minutes.
Therefore, the time taken when the person wants to burn 250 calories will be 42.37 minutes.
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with show work please. a and b.
Step-by-step explanation:
(a)
the sum of all internal angles in a polygon with n sides is
(n - 2)×180.
since in a regular polygon all angles are equally large, we get for one internal angle :
(n - 2)×180/n
for our hexagon this means the internal angle is
(6 - 2)×180/6 = 4×30 = 120°
(b)
the area of the hexagon is (as the graphic so nicely suggests) the sum of the areas of all 6 inner triangles.
the area of a triangle is
baseline × height / 2
baseline = 10 cm
the height (from the tip of the triangle down to the baseline in a right angle) is half of 17.3 cm, because these 17.3 cm are the sum of the 2 heights of 2 triangles placed tip to tip.
so, height = 17.3/2 = 8.65 cm
the area of one of the triangles is therefore
10 × 8.65 / 2 = 5 × 8.65 = 43.25 cm²
the total area of the hexagon is then
6 × 43.25 = 259.5 cm²
3/1(x+9)-2
steps to figure out problem and answer
Answer: 3x+25
Step-by-step explanation: Fraction 3/1 is the same as 3. Using PEMDAS we multiply the numbers in the parenthesis 3x+3x9-2, 3x+27-2, Answer=3x+25
What does it mean to invest in a stock
Step-by-step explanation:
When you buy a company's stock, you're purchasing a small piece of that company, called a share. Investors purchase stocks in companies they think will go up in value. If that happens, the company's stock increases in value as well. The stock can then be sold for a profit.
Stocks are an investment that means you own a share in the company that issued the stock. Simply put, stocks are a way to build wealth. This is how ordinary people invest in some of the most successful companies in the world. For companies, stocks are a way to raise money to fund growth, products and other initiatives.
The volume of a triangular prism is 1380 cubic centimeters. Its base is a right triangle with legs measuring 8 centimeters and 15 centimeters. What is the height of the prism?
A. 34.5 \mathrm{~cm}
B. 23 \mathrm{~cm}
C. 17cm
D. 11.5 \mathrm{~cm}
Answer:
Step-by-step explanation:
V=Bh
Subsitute area of base by putting area of right triangle 1/2*8*15.
1380=1/2*8*15*h
Solve for value of h
h=23 cm
Option B is correct.
A lighthouse casts a revolving beam of light as far as the pier. what is the area that the light covers?
the area covered by the light of the lighthouse is given by: A = πx²
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Area of a circle having r as radius = πr²
Given: The revolving light beam that extends to the pier.
Let the distance to the pier x.
Typically, the rotating beam rotates 360 degrees.
Therefore, Its motion is circular.
The mathematical formula for the area that the light covers is: A = πx²
Hence, the area covered by the light of the lighthouse is given by: A = πx²
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Solve following proportion. 5/ 8 = y/3
Step-by-step explanation:
5/8 = y/3
(5/8) times 3 = 15/8
y=15/8
or
y = 1 and 7 over 8
or y = 1.875
Write the rational numbers as a decimal:
7/8
1/1
-7/9
-17/40
1 and 5/6
-2 and 17/18
-5 and 7/12
8 and 15/22
Answer:
7.8
-7.9
-17.40
1. 5.6
-2. 17.18
-5. 7.12
.8 15.22
Step-by-step explanation:
The sum of two numbers is 125 and their difference is 47. Find each of the numbers
86 and 39
Step-by-step explanation:
let A is the first letter and B is the second number
A+B=125
A-B=47
2A=172
A=86
A+B=125
86+B=125
B=125-86
B=39
In the segment below, QV = 23. QT = 8. TR = RS = SV.
Answer:
RS = 5
QS = 18
TS = 10
TV = 15
Step-by-step explanation:
Given QV = 23 and QT = 8 and TR = RS = SV
now, we subtract the length of QT from the whole line, QV
23 - 8 = 15 then we divide this by 3 because TR = RS = SV so there must be 3 equal pieces
15 ÷ 3 = 5
RS = 5
QS = QT + TR + RS so
QS = 8 + 5 + 5
QS = 18
TS = TR + RS so
TS = 5 + 5 and
TV = TR + RS + SV
TV = 15
Someone help please
a
Answer:
see explanation
Step-by-step explanation:
f(x) × g(x)
= 3x(4x - 1) ← distribute parenthesis by 3x
= 12x² - 3x
when x = 1 , then
= 12(1)² - 3(1) = 12(1) - 3 = 12 - 3 = 9
Based on the lesson, identify the first operation needed to solve the following equation.
x/3 - 3 = 11
multiplication
division
subtraction
addition
The length of a bacterial cell is about 4 x 10 to the negative power of 6 m, and the length of an amoeba cell is about 2.5 x 10 to the power of 4 m. How many times smaller is the bacterial cell than the amoeba
cell? Write the final answer in scientific notation with the correct number of significant digits.
A. 06.25 x 10²
B. 2x10²
C. 6x 10¹
D. 16 x 10¹
The number of times the bacterial cell is smaller than the amoeba cell is 1.6 * 10^-10
How many times smaller is the bacterial cell than the amoeba cell?The given parameters are:
Bacteria cell = 4 x 10^-6 m
Amoeba cell = 2.5 x 10^4 m
The number of times (n) is calculated as
n = Amoeba cell/Bacteria cell
This gives
n = (4 x 10^-6 m)/(2.5 x 10^4 m)
This gives
n = 1.6 * 10^-10
Hence, the number of times the bacterial cell is smaller than the amoeba cell is 1.6 * 10^-10
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Temperature Suppose there is a 1.6°F drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 46.2°F, what
will be the temperature when the plane reaches an altitude of 10,000 ft?
The temperature will be
PF. (Type an integer or a decimal.)
The temperature at 10,000 feet altitude will be 30.2 ° F.
We are given that:
As the airplane moves 1000 feet above the ground, the temperature drops by 1.6 ° F.
Now, the temperature on the ground is given as
Temperature on ground = 46.2 ° F
Now, the plane is at the altitude of 10,00 feet.
We need to tell the temperature at that altitude.
At 1000 feet, temperature drops by = 1.6 ° F.
At 10000 feet, the temperature will drop by = 1.6 ° F. × 10,000 / 1000
= 16 ° F.
So, the temperature will be = 46.2 ° F - 16 ° F
Temperature = 30.2 ° F
Therefore, the temperature at 10,000 feet altitude will be 30.2 ° F.
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9 A and B are integers. A = 300,000 to the nearest 100,000 B = 300,000 to the nearest 10,000 a) What is the greatest possible value of A + B? b) What is the smallest possible value of A + B? c) What is the greatest possible value of A - B?
The greatest possible value of A + B is 600000.
The smallest possible value of A + B is 600000.
The greatest possible value of A - B is 0.
How to illustrate the information?It should be noted that from the information, A and B are integers.
A = 300,000 to the nearest 100,000
B = 300,000 to the nearest 10,000
Therefore, the greatest possible value of A + B will be:
= 300,000 + 300,000
= 600000.
The smallest possible value of A + B is also, 600000.
The greatest possible value of A - B will be:
= 300,000 - 300,000
= 0.
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rita traveled 1,250 miles in the first 3 days of her trip. at this rate, how long will it take her to travel 1,875 miles? how much would it cost
the time taken by Rita to travel 1875 miles is 4.5 days, by unitary method.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
Travelled 1250 miles in 3 days.To find: Time taken to travel 1875 miles.
Finding:
By unitary method,
Time taken to travel 1250 miles = 3 days
Time taken to travel 1 mile = [tex]\frac{3}{1250}[/tex] days
Time taken to travel 1875 miles = [tex]\frac{3}{1250}(1875) = 4.5[/tex] days
Hence, the time taken by Rita to travel 1875 miles is 4.5 days, by unitary method.
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Find the coordinates of P that represents the weighted average of A and B, where point A has a weight of 4 and point B has a weight of 1
Using the weighted mean, the coordinates of P are given as follows:
x: (4xA + xB)/5.y: (4yA + yB)/5.What is the weighted mean?The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
In this problem, we have these following points:
Point A with a weight of 4.Point B with a weight of 1.Applying the weighted mean, the coordinates of P are given as follows:
x: (4xA + xB)/5.y: (4yA + yB)/5.In which xA and yA are the coordinates x and y of point A, and xB and yB are the coordinates x and y of point B.
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4 + −1 2/3= i have no clue, send help asap.......
Answer:
2 1/3 :)
Step-by-step explanation:
helllllp asap pls!!!!!
6. The measure of each angle is m∠ E = 46°, m∠ D = 46°.
Angle of elevation from point A to B (∠ E ) is the angle between the horizontal line from A to B.
And, Angle of depression from B to A ( ∠D ) is the angle from the horizontally downward line from B to A.
As we can see that all the horizontal lines are in parallel to each other,
Alternative Interior Angle : When two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent.
With the help of above theorem,
Angle of elevation from point A to B = Angle of depression from point B to A,
∠E and ∠D are interior opposite angles.
Then, m ∠ E = m ∠ D
3x + 1 = 2(x + 8) ( Given )
3x + 1 = 2x + 16
x = 15,
So, m∠ E = 3x + 1 = 45 + 1 = 46°
Hence, m∠D = 46°
7. The measure of each angle is m∠ E = 20°, m∠ D = 20°.
By following same method as given above we will solve this question.
So, As we know that
Angle of elevation from point A to B = Angle of depression from point B to A,
∠E and ∠D are interior opposite angles.
Then, m ∠ E = m ∠ D
5(x - 2) = (x + 14)
5x - 10 = x + 14
5x -x = 14 + 10
4x = 24
x = 24/4 = 6
So, m∠ D = (x + 14) = 6 + 14 = 20°
Hence, m ∠ E = 20°
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tickets to the zoo cost $4 for children, $5 for teenagers and $6 for adults. in the high season, 1200 people come to the zoo every day. on a certian day, the total revenue at the zoo was $5300. for every 3 teenagers, 8 children went to the zoo. how many teenagers went to the zoo? a. 100 teenagers c. 300 teenagers b. 200 teenagers d. 400 teenagers please select the best answer from the choices provided a b c d
According to the given statement the teenagers went to the zoo = 300
What is linear equation explain?First order equations include linear equations. In the coordinate system, the linear equations have been defined for lines. A linear equation throughout one variable is one in which there is a homogeneous variable having degree 1 (i.e., only one variable). many variables have present in a linear equation.
According tot the given information:6a+4c+5t = 5300......................(equation)
a+c+t = 1200
3c-8t = 0
So,
Putting the value a= 1/6
6a+4c+5t = 5300
0.333c+0.167t = 316.667
3c-8t = 0
solving for the value of t:
6a+4c+5t = 5300
3c-8t = 0
1.056t = 316.667
So,
t = 316.66666667/1.05555556
= 300
According to the given statement the teenagers went to the zoo = 300.
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Use the distribution property to rewrite the expression. Then evaluate.
-3(2x-6)
Answer: -6x+18
Step-by-step explanation:
-3(2x-6)=
-3*2x-(-3*6)= ==> During distribution
-6x-(-18)=-6x+18 ==> After distribution property
Mom is getting food ready for my birthday party! Including me, there will be 28 people at the party. Mom is baking cookies for us! She can bake 24 cookies per batch. How many batches should I tell Mom to make so we can each have 5 cookies?
Answer:
The answer would be six batches of cookies.
Answer:
6 batches
Step-by-step explanation:
so 28 people including you
24 cookies per batch
5 cookies each
24 cookies in each batch, if you round that up it would be 30 and 30 x 5 = 150, so instead of rounding the amount of cookies, add 1 more to the amount you multiply 24 by
then it would be 24 x 6 = 144
now divide that by 28
144/28= 5 1/6
it would take 6 (7 if everyone gets whole numbers of cookies because It would be a fraction if not 7) batches to make sure everyone gets cookies
double check:
24 times 6 = cookies
144/28= 5 1/6