Answers
The expression written as a single power(exponent) is 9⁶ .
Exponentiation, abbreviated as bⁿ, is a mathematical process that involves the base number (b) and the exponent (or power) number (n). The word is pronounced "b (elevated) to the (power of) n."
When n is a positive integer, exponentiation corresponds to repeated base multiplication because bn is the result of multiplying n bases. Normally, the exponent is shown as a subscript to the right of the base. The term "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most simply, "b to the nth," is used to describe bⁿ.the given expression is of the form:
9⁶÷9³
Which is equivalent to:
9⁶⁻³ (properties of exponents)
this is equal to 9⁶ .
The value of the expression is 9⁶ .
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Related Questions
A rectangular room has lengths 2i and (4 - 5i). What is the Area of the rectangular room? Express your answer in standard form? (A = lw)
Answers
The area of rectangular is 10 + 8i.
Given,
A rectangular room has lengths and width are 2i and (4 - 5i) respectively.
To find the area of rectangular.
Now, According to the question :
We know that,
Area of rectangular = L x B
where,
L = Length of rectangular
B = Breadth of rectangular
Here, Length and breadth are complex numbers.
and hence, we should remember [tex]i^2[/tex] = -1
Area of Rectangular is = (4 - 5i) x 2i
=8i - 10[tex]i^2[/tex]
= 8i - 10 (-1)
= 8i + 10
Hence, The area of rectangular is 10 + 8i.
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(x + 3) (x + 5) expanded
Answers
Expansion of (x + 3) (x + 5) [tex]=x^{2} +8x+15[/tex]
How is the expansion done?
Applying the Product of binomials rule,
(x+a) (x+b) = [tex]x^{2} +(a + b)x +ab[/tex]
Here, in the given expression:
a = 3 and b = 5
[tex](x + 3) (x + 5) =x^{2} +(3 + 5)x +15\\\\ =x^{2} +8x+15[/tex]
What is the product of binomials rule?
The FOIL (First Outer Inner Last)method is being applied to multiply binomials quickly. It is the arrangement of multiplying terms in a two-binomial product.The expression for the product of the sum and difference of two binomials is (x + y) (x- y) Assume that each binomial is a difference rather than a sum the the resultant expression is in (x- y) (x -y).To learn more about product of binomials, refer:
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Need help It’s on Plato classesWhich function represents this graph.
Answers
ANSWER :
D.
EXPLANATION :
From the problem, we have a graph that goes to positive infinity as x goes to the positive infinity.
Note that in an exponential function :
[tex]f(x)=a^x[/tex]The function goes to positive infinity if "a" is greater than 1
The function goes to negative infinity if "a" is less than 1
Since the given graph goes to positive infinity, we are looking for the function whose "a" is greater than 1.
We have Options A and D.
Next is to check the y-intercept.
The graph intersects the y-axis at (0, -3)
Substitute x = 0 and f(x) should be -3
For Option A :
[tex]\begin{gathered} f(x)=10^x \\ f(0)=10^0=1 \end{gathered}[/tex]For Option D :
[tex]\begin{gathered} f(x)=10^x-4 \\ f(0)=10^0-4 \\ f(0)=1-4=-3 \end{gathered}[/tex]Therefore, the answer is D.
when -1 < k < 1, describe the effect of k on f(kx) and kf(x).
Answers
The effects of the transformations on the functions are given as follows:
-1 < k < 0: f(kx) is reflected over the y-axis and horizontally stretched.-1 < k < 0: kf(x) is reflected over the x-axis and vertically compressed.0 < k < 1: f(kx) is horizontally stretched.0 < k < 1: kf(x) is vertically compressed.What are the effects of the transformations on the functions?When one function is multiplied by a negative number, the function is reflected, either over the x-axis or over the y-axis, depending on where the multiplication happened, hence:
-1 < k < 0: f(kx) is reflected over the y-axis.-1 < k < 0: kf(x) is reflected over the x-axis.In the context of this problem, in both cases, the function is being multiplied by a number that has absolute value between 0 and 1, which can either horizontally stretch the function, in the case of function f(kx), , or vertically compress, in the case of function kf(x).
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Brooklyn line‘s upright retanglar prisms like the one shown. She aligns each prism behind the previous prism to make a larger prism. The larger prism has a surface area of 1288 and squared. How many prisms does Brooklyn align? Show your work
Answers
In terms of geometry, a rectangular prism is a 3-dimensional solid shape with six faces and rectangles as its base.
Answer: The figure's surface area is 1672 [tex]cm2[/tex]. Detailed explanation: Surface area of the prism plus surface area equals the surface area of the figure.
How do you calculate a rectangular prism's surface area and volume?
Rectangular prisms have surfaces equal to the sum of their side areas, and their volumes are equal to their length times breadth times height.
Use the formula SA=2B+ph to determine a prism's surface area. SA stands for surface area, B for the prism's base area, p for the base's perimeter, and h for the height of the prism.
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find the values of a and b that the solution to 2(3x+5)+ax=5(4x-b) real numbers
Answers
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Let's try solving the equation to the best of our ability before the two variables 'a' and 'b' limit us
[tex]\text{Copy down the equation}\\2(3x + 5) + ax =5(4x - b)\\\\\text{Multiply the outside constants into the function in the parentheses}\\}6x + 10+ax = 20x - 5b\\\\\text{Let's put the coefficients of the variable on the left-side together in parentheses}\\6x + ax + 10 = 20x - 5b\\(6 + a)x+ 10 = 20x - 5b[/tex]
Now to make the equation works:
The coefficient of the variables, '6 + a' and '20' must be equal⇒ [tex]6 + a = 20[/tex] ⇒ a = 14
The constants, '10' and '-5b' must also be equal⇒ -5b = 10 ⇒ b = -2
Answer:
a = 14b = -2
Hope that helps!
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Answer:
a = 14b = -2Step-by-step explanation:
You want the values of 'a' and 'b' that make 2(3x+5)+ax=5(4x-b) a tautology.
SolutionOne way to do this is to rewrite the equation in general form. You can do that by subtracting the right-side expression.
2(3x +5) +ax -5(4x -b) = 0
6x +10 +ax -20x +5b = 0 . . . . . . eliminate parentheses
(6 +a -20)x +(10 +5b) = 0 . . . . . . collect terms
This can be made identically zero by making the coefficients be zero.
6+a-20 = 0 . . . coefficient of x
a = 14 . . . . . . . add 14 to both sides
and ...
10 +5b = 0 . . . constant term
2 +b = 0 . . . . divide by 5
b = -2 . . . . . . subtract 2 from both sides
To make the expression always true, you must have a = 14, b = -2.
At a festival, 380 people out of 500 people questioned say that they are camping. There are 55 300 people at the festival. Calculate an estimate of the total number of people camping at the festival.
Answers
Answer:
55800
Step-by-step explanation:
55300+500=55800
Points A and B are on a circle with centre O and radius n so that AOB = (360/n). Sector AOB is cut out of the circle. Determine all positive integers n for which the perimeter of sector AOB is greater than 20 and less than 30
Answers
The positive integers (n) for which the perimeter of sector AOB is greater than 20 are 7, 8, 9 and 10. Also, the positive integer (n) for which the perimeter of sector AOB is less than 30 is 11.
How to determine all the positive integers (n)?The length of an arc of a circle increases as the sector angle increases, provided that the radius of the circle remains the same. Additionally, the ratio of the length of an arc (arc length) of a circle to the circumference of the circle is equal to the ratio of the sector angle to angle measure of a circle (360°).
By applying this ratio to this circle, we would have the following mathematical expression:
Length of arc AB/Circumference = Sector angle/360°
Rearranging the above mathematical expression, we have:
Length of arc AB = (Sector angle/360°) × Circumference
Note: Circumference = πd = π × 2n = 2πn
Sector angle = 360°/n
Substituting the given parameters into the expression, we have;
Length of arc AB = (360°/n/360°) × 2πn
Length of arc AB = 2π
Next, we would calculate the perimeter of sector AOB:
Perimeter of sector AOB = Length of arc AB + AO + OB
Perimeter of sector AOB = 2π + n + n
Perimeter of sector AOB = 2π + 2n
If the perimeter of sector AOB is greater than (>) 20, the positive integers (n) is given by:
P > 20
2π + 2n > 20
2n > 20 - 2π
n > 10 - π
n > 10 - 3.142
n > 6.858 ≈ 6.9.
Therefore, n = 7, 8, 9, and 10.
If the perimeter of sector AOB is less than (<) 30, the positive integers (n) is given by:
P < 30
2π + 2n < 30
2n < 30 - 2π
n < 15 - π
n > 15 - 3.142
n > 11.858 ≈ 11.9.
Therefore, n = 11.
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order the numbers from least to greatest based on their absolute value. |-7|, |4|, |-2|, |3|
Answers
Answer: |-2|, |3| |4|, |-7|
Step-by-step explanation:
Very simple question: an absolute basically means you replace the sign with a positive one.
So |-7| = 7, |4| = 4, |-2| = 2, |3| = 3
PLS HELP MEE!!!! )
What does Point P on the number line represent? (Use the hyphen for negative numbers, such as –5)
Answers
Answer:
Step-by-step explanation:
Because P is located between -8 and -10, your answer would be P=-9. I hope this answered your question!
Two similar triangles. The first triangle has a side length of 21 meters, which corresponds to the second triangle's side of 3 meters. The missing side of the first triangle corresponds to a side of 8 meters on the second triangle.
© 2017 StrongMind. Created using GeoGebra.
How many meters long is the missing side?
Note: The triangles may not be drawn to scale.
Enter your answer as a number, like this: 42
Answers
Answer:
x/8 = 21/3
x = 21/3 * 8
x = 56 m
What is the value of the absolute value expression |−127| + |5| − |−43|?
−165
−79
89
175
Answers
Step-by-step explanation:
|127|+|5|-|-43|=127+5-43=89
Answer:89
Step-by-step explanation:
What are the terms in the expression 10p + 3q + 2?
Responses
10 and 3
10 and 3
p and q
p, and , q
10p, 3q, and 2
10, p, , 3, q, , and 2
10, 3, and 2
Answers
In the expression 10p + 3q + 2 we have total three terms -
10p, 3q and 2.
What is expression in mathematics?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given in the question is a expression as follows -
10p + 3q + 2
In order to identify the number of terms in this expression, it is important to keep in mind that the terms of an expression are separated from one another by the following → + (Addition), - (Subtraction). In some cases, (equal to) '=' , (less than) '<' , (greater than) '>' are also used
There are total 3 terms as -
10p, 3q and 2.
Therefore, in the expression 10p + 3q + 2 we have total three terms -
10p, 3q and 2.
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Helena can buy 2 shirts for $25 or 3 shirts for $36. do these quantities have a proportional relationship? explain. yes; the ratio of cost to shirts is equivalent. yes; the constant of proportionality is 12. yes; the constant of proportionality is 12.5. no; the ratio of cost to shirts is not equivalent.
Answers
The quantities do not have a proportional relationship because the ratio of the cost to shirts is not equivalent.
Are the quantities proportional?The two quantities would have a proportional relationship if the constant of proportionality are equal. The constant of proportionality would be equivalent to the cost of one shirt.
The equation that can be used to determine the constant of proportionality is:
k = y / x
Where:
y = total cost of the shirts x = number of shirts boughtk = 25 / 2
k = 12.60
k = $36 / 3
k = $12
The quantities are not proportional because the constant of proportionality are different.
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i need help with my math problem look at the picture
Answers
The domain and range of the of this function C(n) = 120 + 8n, in the context of the situation is 10 ≤ n ≤ 24 and 200 ≤ C ≤ 312 respectively.
What is domain?The set of inputs a function can accept is referred to as the domain of the function in mathematics. DOM (f) or DOM f, where f is the function, may be used to indicate it.
A function f: X to Y has X as its domain, to put it more precisely. The domain of a function is not a property of it, but rather a part of the definition in contemporary mathematical terminology.
The function f can be represented graphically using the Cartesian coordinate system in the unique situation where X and Y are both subsets of R. A projection of the function's graph onto the graph's x-axis in this instance serves as the domain's representation.
We have given the function C(n) = 120 + 8n where n is no. of children going to trip which must be at least 10 and function C is the total cost trip.
If at least 10 children must go to make the trip possible, then n must be greater than 10 and the total no. of children is 24 which gives us
10 ≤ n ≤ 24, n is restricted between 10 and 24
Also, if n is at least 10, the putting the value in the function C(n) = 120 + 8n gives us
C(n) = 120 + 8(10)
= 200
Which means C must be greater or equal to 200 but we also take the condition in consideration that all students are going to the trip meaning 24 children is n, which gives us
C(n) = 120 + 8(24)
= 312
This gives us, 200 ≤ C ≤ 312, that is C is restricted between 200 and 312.
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an angle of size 124 degrees has been rotated degrees around a center 0. what is the size of the rotated angle? how do you?
Answers
The size of the angle after the transformation is 124 degrees
How to determine the size of the rotated angle?The transformation is described by
Rotation by degrees around a center 0
The measure of the angle is given as
Angle = 124 degrees
There are four types of transformation, and they are:
DilationRotationReflectionTranslationThe representation of the types of transformation are:
Dilation: k(x, y)Rotation: rotation by anglesReflection: reflection across linesTranslation: (x + h, y + k)As a general rule of rotation:
When a shape, line or an angle is rotated, the size of the angle in the rotated figure remains unchanged
This means that the angle remains 124 degrees
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-3.7+1/4 Write your answer as a decimal to the nearest hundredth.
Answers
Find the area of this irregular figure above 8ft 9ft 26ft 15ft
Answers
Answer:
The area is 426 square feet.
The number of words latisha can text,y,varies directly with x, the number of minutes spent texting. if latisha texted 180 words in 5 minutes,find k,the constant of proportinality
Answers
The value of the constant of proportionality k = 36
The Direct Variation :
Direct Variation is said to be the relationship between two variables in which one of the variables is multiple of the other variable.
When x is directly proportional to y then the relation can be written as
= > x ∝ y
=> x = ky [ here k is constant value ]
Here we have,
The number of words Latisha can text 'y' is varies directly with 'x' the number of minutes spent texting
Here, y = 180 and x = 5
From the above data,
=> 180 = k (5)
=> k = 180/5 = 36
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(7x-6)
What is the value of x?
Answers
In this linear equation with one variable (7x-6), the value of x is 6/7.
How to find the value of x?The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution.
steps for finding x value:
Step 1: Add or subtract on both sides of the equation to keep the constants on one side and the variable term on the other.
Step 2: Make the constant terms simpler.
Step 3: By multiplying or dividing the variable on one side of the equation into both sides, isolate it.
Step 4: Write the solution down and simplify.
given that
7x-6 =0
7x = 6
x = 6/7
Hence the value of x is 6/7.
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Find the value of x in each case.
Answers
Check the picture below.
Rico found a hailstone after a recent thunderstorm and calculated its volume to be 9.2 × 10
Instead of gallons, which of the following units would be most appropriate for measuring the volume of Rico's hailstone?
Omilliliters
kiloliters
cubic feet
cubic meters
gallons.
Answers
Rico found a hailstone after a recent thunderstorm and calculated its volume to be 9.2 × 10 gallons, instead of gallons, among the following units the cubic meter would be the most appropriate unit for measuring the volume of Rico's hailstone.
As Rico found a hailstone after a recent thunderstorm and calculated its volume to be 9.2 × 10 gallons.
We know that,
The hailstone is in form of a sphere.
So, the volume of the sphere will be [tex]\left(\frac{4}{3}\right) \pi r^3[/tex]
So, [tex]\text { Volume of hailstone }=\left(\frac{4}{3}\right) \pi r^3[/tex]
From above, we can conclude that,
The unit of volume of hailstone depends on the value of the radius of the hailstone. (As here the other value is 4/3 and [tex]\Pi[/tex] is constant.
The most appropriate unit for measuring the value of the radius of the hailstone is the meter.
Hence, among the given, he should use the cubic meters for measuring the volume of the hailstone.
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The coleman family purchased a camper van for $38,000. the van is predicted to depreciate by about 15% each year. write an exponential equation in the form y=a(b)x that can model the value of the van, y, in x years.
Answers
The exponential equation that can model the value of the camper van , in x years is y = 38000*(0.85)ˣ .
In the question ,
it is given that
the present value of the camper van (P₀) = $38000
given the depreciation rate is 15% each year (r)= -0.15
The future value y ,of the camper van can be given by the formula
y = P₀*(1 + r)ˣ
On putting the values , we get
y = 38000*( 1 - 0.15)ˣ
y = 38000*(0.85)ˣ
Therefore , The exponential equation that can model the value of the camper van , in x years is y = 38000*(0.85)ˣ .
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Antarctica's Average Low temperature
Answers
about -71 degrees Fahrenheit
branliest?
unit 3 lesson 1 NEED HELP ASAP!!!
Answers
Answer:
Step-by-step explanation:
For number 8 the answer is y=2x+7 because our equation is y+1=2(x+4) distribute the 2 to get y+1=2x+8 and you then do inverse operation by subtracting the 1 on both sides to get y=2x+7 and the slope intercept form is y=mx+b so that’s why
for number 9 the answer is (0,7) as to find the y-intercept, substitute in 0 for x and solve for y as y+1=2((0)+4) distribute the 2 after doing 0+4 to get y+1=8 inverse operation so subtract 1 to get 7 so that’s why it’s (0,7)
and for 10 the answer is 2x−y=−7
Javier says all even numbers less than 20 are composite.
Which of the following is an even number less than 20 that is NOT composite?
How can Javier rewrite his statement so that it is true?
Answers
Answer: 2
Step-by-step explanation: 2 is less than 20 and is not composite. 2 is only divisible by one and itself.
All even numbers greater than 2 are composite.
Answer: 2
Step-by-step explanation:
2 is the only even prime number. It is less than 20 and not composite. It is divisible only by 1 and itself, as are all primes.
What is equivalent to 1 1/4 +2/5???
Answers
Answer:
1 13/20
Step-by-step explanation:
Which of the following are equal to the expression below? Check all that apply.
A.
B.
C.
D.
4
Answers
Answer:
B, C
Step-by-step explanation:
√16 = 4 and √64= 8
so if √16 / √64,
then 4/8
lastly, 4/8 equals to 1/2
you can find this because 4 goes into 4 and 8 so 4/4=1 and 8/4=2
so 1/2
hope this helps :)
Mathematical Connections: The composite solid is made up of a cube and a rectangular prism.
(Picture below)
a. Write a polynomial that represents the volume of the composite solid.
b. The volume of the composite solid is equal to 25x. What is the value of x? Explain your reasoning.
Answers
a) The volume of the composite figure is represented by the cubic equation V = x³ + 16 · x.
b) The measure of the missing side x in the composite figure is 3 inches.
How to determine missing length of a composite figure
a) In the first part of the question we need to derive the volume formula of the composite figure, which is the sum of the volumes of the cube and the rectangular prism:
V = V' + V''
V = x³ + 16 · x, where x is in inches.
The volume is represented by V = x³ + 16 · x.
b) If we know that V = 25 · x, then the measure of the missing side is:
First, set the volume formula found in section a):
V = x³ + 16 · x
Second, replace the volume:
25 · x = x³ + 16 · x
Third, simplify the expression and clear x within the resulting equation by algebra properties:
25 = x² + 16
x² - 9 = 0
x² = 9
x = 3
The measure of the missing side x is 3 inches.
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The ratio of the measure of the sides of a triangle is 4:7:5 if the perimeter is 128yd find the measure of each side
Answers
Answer:
The answer is 56 yards
Step-by-step explanation:
Im sorry I'm not smart enough to answer I just look around for it but I'm sorry I can't explain.
