Answers
The simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is [tex]2\sqrt{2}[/tex]
The given expression = [tex]64^{\frac{1}{4} }[/tex]
The exponential function is the function in the form of f(x)= [tex]a^{x}[/tex], where x is the variable and a is the constant. The constant term is the base of the exponential function.
The given expression = [tex]64^{\frac{1}{4} }[/tex]
Here we have to use the power rule of the exponents
[tex](a^{m})^{n}=a^{mn}[/tex]
To increase a number with an exponent to the power, we have to multiply the exponent times the power
We know
64 = [tex]2^{6}[/tex]
Then
[tex]64^{\frac{1}{4} }[/tex] = [tex](2^{6})^{\frac{1}{4} }[/tex]
Apply the power rule of the exponent
[tex](2^{6})^{\frac{1}{4} }[/tex] = [tex]2^{(6)(\frac{1}{4} )}[/tex]
= [tex]2^{\frac{3}{2} }[/tex]
= [tex]2\sqrt{2}[/tex]
Hence, the simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is [tex]2\sqrt{2}[/tex]
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Related Questions
The sum of the digits of a certain two-digit number is 11. When you reverse its digits you increase the number by 45. What is the number?
Answers
Answer:
6 and 9.
Step-by-step explanation:
Let the number be xy [note: x is a digit in tens place and y is another digit in ones place]
Learn to translate the words into formulas:
"When you reverse the digits in a certain two-digit number you increase its value by 45." means
10y + x = (10x + y) + 45 [eq1]
"the sum of its digits is 11" means x + y = 11 [eq2}
Now, solve (let's use substitution):
y = 11-x [from eq2]
Put that into eq1:
10y + x = (10x + y) + 45 [eq1]
10(11-x) + x = 10x + (11-x) + 45
110 - 10x + x = 10x + 11 - x + 45
110 - 9x = 9x + 56
-18x = -54
x = 3
Now, put that into either equation to find the value of y:
3 + y = 11 [eq2]
3 + y = 11
y = 8
The number is 38.
Check:
Is 83 = 38 + 45 ?
83 = 83 ?yes
Is 3 + 8 = 11 ?
11 = 11 ?yes
I really need help you guys pleaseeee
Answers
help i don’t get it
answers pls
Answers
Answer: x=13°
Step-by-step explanation: We know total amount of degrees in a triangle is 180°. We also know two of the angles' degrees: 39° and 90°. Now, with this info, we set up an equation: (3x+12)+39+90=180. We add 39 and 90 to get 129; then we subtract 129 on both sides of the equation. Our equation should now look like this: 3x+12=51. Subtract 12 on both sides to get: 3x=39. Lastly, divide 3 on both sides to find the value of x.
David is starting a new job in sales. he can choose to earn only a 10% commission on sales each month, or earn a monthly base salary of $1,500 with a 3% commission on sales over $7,500. which pay method would earn him more money if he has an average sales of $16,000 each month?
Answers
Answer:
Method 2, a monthly base salary of $1,500 with a 3% commission on sales over $7,500, will earn more money.
Step-by-step explanation:
given -
method 1 - he can choose to earn only a 10% commission on sales each month,
method 2-earn a monthly base salary of $1,500 with a 3% commission on sales over $7,500.
also, he has an average sales of $16,000 each month.
according to the question;
method 1 earning =>
10% of $16,000 =>(10/100)*$16,000=$16,00.
method 2 earning =>
$1,500+(3/100)*($16000-$7500)=$1755.
in method 2, a monthly base salary of $1,500 with a 3% commission on sales over $7,500. he will earn more.
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out of 150 students appeared in an examination 60% of the students passed in math 50% in Science and 20% in both subjects how many students where failed in both subjects ?by using Venn diagram find the number of student Wawa passed in maths only .
Answers
Answer:
5000 students
Step-by-step explanation:
Let total number of students appeared in the exams is x.
20% of x have failed in both maths and science.
Here,in maths 60% of students passed.
%ag of students failed in maths= 40%
%ag of students failed in math — % of students failed in both maths and science = students passed in science but failed in maths i.e. 40–20 = 20%.
Likewise as 70% of students passed science
So 30% failed in science.
And Students failed in science only but passed in maths= %ag of students failed in science- % of students failed in both maths and science.
i.e. 30–20= 10%.
Given 2500 number of students passed in both maths and science = 100–(students failed in both maths and science+ students failed only in maths and passed in science+ students failed only in science but passed in maths)%
= 100–(20+20+10)= 50% of students passed both.
50% of x = 2500
50x/100= 2500
=> x= 5000.
So total number of students appeared in exam is 5000 in number
eighteen faculty members in a college math department range in age from 32 to 68. a stemplot follows: 3 2 4 8 9 9 4 0 3 5 6 9 5 3 4 7 8 9 9 6 3 8 the 1.5 × iqr rule would identify an age as a high outlier if it exceeded years. group of answer choices
Answers
The Stem plot is displayed below of eighteen faculty members in a college math department range in age from 32 to 68.
How do you make a stem plot?
On the left hand side of the page, write down the thousands, hundreds or tens (all digits but the last one). These will be your stems. Draw a line to the right of these stems. On the other side of the line, write down the ones (the last digit of a number).
A Stem Plot is a chart for demonstrating the distribution of numeric variables .
It is used to analyze the shape of the distribution.
The data provided is as follows:
S = {32,48,99,40,35,69,53,47,89,96,38}
The Stem plot is displayed as follows:
3 | 2 5 8
4 | 0 7 8
5 | 3
6 | 9
8 | 9
9 | 6 9
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vince is cutting a rectangular piece of pegboard to use in his garage for organization. the width of the pegboard is 8 inches less than half the length. the perimeterof the pegboard is 224 inches. what is the length of the pegboard?
Answers
The most appropriate choice for linear equation will be given by -
Length of the rectangle is 80 inches
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Let the length of the pegboard be l inches
Width of the pegboard = [tex]\frac{1}{2}l - 8[/tex]
Perimeter =
[tex]2(l + \frac{1}{2}l - 8 )\\2(\frac{3l}{2} - 8)\\[/tex]
[tex](3l - 16)[/tex] inches
But the problem,
[tex]3l - 16 = 224\\3l = 224 +16\\3l = 240\\l = \frac{240}{3}\\[/tex]
[tex]l = 80[/tex] inches
The length of the rectangle is 80 inches.
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a couple has narrowed down the choices of a name for their new baby to first names and middle names. how many different first- and middle-name arrangements are possible?
Answers
There are 28 ways in which a couple can choose the name of the baby for its name.
What is defined as the combination?A combination is an algebraic technique for determining the number of possible arrangements in a set of items in which the order of the selection is irrelevant. You can choose the items in just about any order in combinations. Permutations and combinations are often confused.If we need to choose objects from two groups of x and n objects so that one object from each group is chosen, we can do so by calculating the combinations possible by:
= ˣC₁ × ⁿC₁
Let 'x' be the set of first name = 7
Let 'n' be the set of second name = 4
Putting the values in formula;
= ⁷C₁ × ⁴C₁
= 7 × 4
= 28
Thus, there are 28 ways in which a couple can choose the name of the baby for its name.
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The complete question is-
A couple has narrowed down the choices of a name for their new baby to 7 first names and 4 second names.
How many different first- and second-name arrangements are possible?
tim and his sister drove 18 miles in 27 minutes. How long will it take them to drive 24 miles
Answers
It will take them 36 minutes to drive 24 miles.
What is unitary method?A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Because of this, the goal of this method is to determine values in reference to a single unit. For instance, we can use the unitary technique to determine how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.
Given Data
Tim and his sister drove 18 miles in 27 minutes.
They drove 1 mile in :
18 mile = 27 minutes
1 mile = [tex]\frac{27}{18}[/tex] minutes
1 mile = 1.5 minutes
For 24 miles,
1 mile = 1.5 minutes
24 miles = 1.5(24) minutes
24 miles = 36 minutes.
It will take them 36 minutes to drive 24 miles.
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(15, −41) (29, 37).
What is the sum of the two vectors?
Answers
Based on the vectors given, the sum of the vectors can be found to be (44, 4)
How to add vectors?When given two vectors such as (15, −41) (29, 37) and you are required to add them, the sum of the vectors can be found by the formula:
= (a1 + b1, a2 + b2)
Where the vectors are:
(a1, a2) (b1, b2)
The sum of the vectors (15, −41) (29, 37) is therefore:
= (a1 + b1, a2 + b2)
= (15 + 29, -41 + 37)
= (44, -41 + 37)
= (44, 4)
In conclusion, the sum of the vectors are (44,4).
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1.998 x 10^27
Ordinary number
Answers
The representation of the number is 1.998 multiplied by 10^27
How to evaluate the expression?The expression is given as
1.998 x 10^27
The above mathematical representation is a number in scientific form and is already in its most simplified form
This means that the scientific form cannot be further simplified
However, the scientific number can be rewritten as a mathematical statement
Recall that, we have
1.998 x 10^27
The pronunciation of the above expression is:
1.998 multiplied by 10^27
And it is evaluated by
Moving the decimal point 27 places to the right.
This gives
1998000000000000000000000000
See that the above result does not have a proper representation compared to 1.998 x 10^27
Hence, the representation of the scientific number given as 1.998 x 10^27 is the 1.998 multiplied by 10^27
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The probability of a telesales represented making a sale on a customer call is 0.15. find the probability that more than 3 sales are made in 20 calls.
Answers
Using Binomial probability distribution,
X = 20, 0.15
P (X ≤ 3) =[tex]20 C_{0} (0.15)^{0} (1-0.15)^{20} + 20C_{1} (0.15)^{1} (1-0.15)^{19} + 20C_{2} (0.15)^{2} (1-0.15)^{18} + 20C_{3} (0.15)^{3} (1-0.15)^{17}[/tex]
P(X ≤ 3) = 0.648
P (X ≥ 3) = 1 - P(X ≤ 3) = 1 - 0.648
P ( X ≥ 3) = 0.352
Therefore, thee required probability is 0.352.
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If K=tm^(p/q) create a formula for q
Answers
The formula for q will be q = p*logm/(logK - logt)
Logarithm
A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction.
Given equation:
[tex]K=tm^{(\frac{p}{q} )}[/tex]
We have to find a formula for q.
Raising the whole equation to the power of q, we get
[tex]K^q=t^qm^{p}[/tex]
We can rewrite it as,
[tex]\frac{K^q}{t^q}=m^p[/tex]
[tex](\frac{K}{t})^q=m^p[/tex]
Operating with logarithm on both sides, we get,
q*log(K/t) = p*logm
q = p*logm/log(K/t) = p*logm/(logK - logt)
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489.22 divided 10 to the fourth power
Answers
A particle moves in a circular orbit x^2+y^2=16. As it passes through the point (2,2sqrt3), its y-coordinate decreases at a rate of 3 units per second. at what rate is x-coordinate changing?
Answers
The rate at which the x-coordinate is changing is 3√3 units per second .
In the question ,
it is given that
the equation of the particle moving in the circular orbit is x²+y²=16
given the y coordinate decreases at 3units per second
So, dy/dt = -3.
to find the rate at which the x-coordinate is changing , we will differentiate the given equation.
Differentiating the equation x²+y²=16 with respect to t , we get
d/dt(x²+y²) = d/dt(16)
2x(dx/dt) + 2y(dy/dt) = 0
2x(dx/dt) = -2y(dy/dt)
Dividing both sides by 2 ,
we get ,
x(dx/dt) = -y(dy/dt)
[tex]\frac{dx}{dt} =\frac{-y(\frac{dy}{dt}) }{x}[/tex]
As the particle is passing through the point (2,2√3) , So, the point will satisfy the equation.
Substituting the value of x=2 , y=2√3 and dy/dt= -3 ,
we get ,
dx/dt = ((-2√3)*(-3))/2
= (6√3)/2
= 3√3
Therefore , the rate at which the x-coordinate is changing is 3√3 units per second .
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PLEASE HELP
find two functions define implicity by this equation. x + y^2 = 25
PHOTO ATTACHED
Answers
Answer:
y = √25 - x
y = -√25 - x
Step-by-step explanation:
x + y² = 25
-x -x
----------------------
y² = -x + 25
√y² = √-x + 25
y = √25 - x
y = -√25 - x
I hope this helps!
J. The Math Club found a company that will sell it t-shirts for $5.00 each, but there is a set-up fee of $50.
Answers
The t stands for how many t shirts you sell and the 50 is the set fee for the start up.
fully factorise
[tex]12x^3 + 38x^2 - 14x[/tex]
Answers
Answer:
2x(2x + 7)(3x - 1).
Step-by-step explanation:
12x^3 + 38x^2 - 14x
= x(12x^2 + 38x - 14)
= 2x(6x^2 + 19x - 7)
To factor the expression in the parentheses we need 2 numbers whose product is (6 * -7) = - 42 and whose sum = +19.
These are +21 and - 2.
So, we write:
6x^2 - 2x + 21x - 7
= 2x(3x - 1) + 7(3x - 1)
= (2x + 7)(3x - 1)
So, the answer is 2x(2x + 7)(3x - 1).
Answer:
[tex]2x(3x-1)(2x+7)[/tex]
Step-by-step explanation:
[tex]12x^3+3x^2-14x\\[/tex]
Factor out common factor: (2x)
[tex]=2x(6x^2+19x-7)[/tex]
Factor [tex]6x^2+19x-7[/tex]
[tex]= 2x(3x-1)(2x+7)[/tex]
Hope this helps! :) Sorry for the late reply
What is the solution to |x – 2| + 3 > 17?
x < –12 or x > 16
x < –14 or x > 7
–12 < x < 16
–14 < x < 7
Answers
Answer:
Option 1
Step-by-step explanation:
[tex]|x-2|<14 \\ \\ x-2<-14, x-2>14 \\ \\ x<-12, x>16[/tex]
Montel heated a 12-cup pot filled with soup. He served bowls of soup to his family.
How can Montel find out how much soup his family ate?
Answers
He can find out by using mathematical operation - subtraction.
What are Mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. A constant is an operation with arity zero, often known as a nullary operation. An example of an operation of arity 3, sometimes known as a ternary operation, is the mixed product.
The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.
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Sally wants to buy a used truck for her delivery business. Truck A is priced at $450 and
gets 25 miles per gallon. Truck B costs $650 and gets 35 miles per gallon. If gasoline costs
$4 per gallon, how many miles must Sally drive to make truck B the better buy?
Answers
Answer:
Step-by-step explanation:
How to solve this question
Answers
The value of the limit of piece wise function is 2k.
What is termed as the piece wise function?A piecewise function is one whose independent variable is described by a series of intervals. It displays a different function for each interval of real numbers. The domain of a function is defined as a set of valid values for such independent variable (in the this case, x) that can be embedded into the function. The range of the a function is the collection of possible values for y that can be obtained after running the function.For the given question;
The piece wise function is defined as a;
f(x) = (x² - k²)/(x - k) , x ≠ k
f(x) = 4 - k , x = k
For the value of lim (x → k⁻) f(x);
Use function for x ≠ k, as the left hand limit of the functions is to be evaluated.
= lim (x → k⁻) f(x)
Let x = k - h, put in the function.
= lim (h → 0) ((k-h)² - k²)/(k - h - k)
= lim (h → 0) h(h - 2k)/-h
= lim (h → 0) 2k - h
Pu h = 0
= 2k
Thus, the value of the limit of piece wise function is 2k.
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PLS HELP!! DUE TODAY! Will give branliest to the best answer, 40 points!!
What is the slope of a line that is perpendicular to the line y = 18x + 5?
A. -8
B. -1/8
C. 1/8
D. 8
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:B. \:\: - \dfrac{1}{18} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given equation of a line is in its slope intercept form, that is :
[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]
The original equation is :
[tex]\qquad \tt \rightarrow \:y = 18x + 5[/tex]
by comparing the two equations we get slope (m) of this line equal to 18
we need to find the slope (n) of line perpendicular to this.
By the property of perpendicular lines, we know :
[tex]\qquad \tt \rightarrow \:m \times n = - 1[/tex]
[tex]\qquad \tt \rightarrow \:18 \times n = - 1[/tex]
[tex]\qquad \tt \rightarrow \:n = - \cfrac{1}{18} [/tex]
So, slope of required line is -1/18
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer: -1/18
Step-by-step explanation:
Let y=k₁x+b1 be the line. Given the perpendicularity of lines, the equation of the line perpendicular to the given line has the form:
[tex]\displaystyle\\y=-\frac{1}{k}x+b_1[/tex]
[tex]\displaystyle\\So,\ y=18x+5\\\\\Rightarrow\ -\frac{1}{18}[/tex]
Find the midpoint of the line segment with endpoints P1(11/2,3/8) and P2 (-7/2,5/8)
Answers
To find:
The midpoint of the line segment with the endpoints P1(11/2,3/8) and P2 (-7/2,5/8).
Solution:
The midpoint formula is:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Put the values:
[tex]\begin{gathered} (\frac{\frac{11}{2}-\frac{7}{2}}{2},\frac{\frac{3}{8}+\frac{5}{8}}{2})=(\frac{\frac{4}{2}}{2},\frac{\frac{8}{8}}{2}) \\ =(\frac{2}{2},\frac{1}{2}) \\ =(1,\frac{1}{2}) \end{gathered}[/tex]Thus, the midpoint is (1, 1/2).
What value of c in the equation 7c-cy=10x will give a line
with slope +5?
Answers
The value of c in the equation 7c - cy = 10x will give a line with slope +5 is -2.
We can rewrite the equation as:-
-cy = 10x - 7c
y = (-10/c) x + 7
Now the equation is in slope-intercept form which is given by:-
y = mx + b
Where,
m represents the slope of the line
b represents the y-intercept of the line
(x,y) represents ordered pair of each point of the line
Comparing both the equations, we get
m = -10/c
b = 7
We have to get m = +5
Hence, equating both the values of m, we get
5 = -10/c
c = -10/5
c = -2
Hence, the value of c is -2.
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Adrian has $620 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $322.09.
He buys 3 bicycle reflectors for $9.54 each and a pair of bike gloves for $22.01.
He plans to spend some or all of the money he has left to buy new biking outfits for $61.82 each.
Use the drop-down menu below to write an inequality representing oo, the number of outfits he can buy while staying within his budget.
Answers
Answer:
4 outfits
Step-by-step explanation:
So to find out how much he has left after all his purchases to buy new biking outfits we can add:
9.54 x 3 = 28.62
22.01 + 28.62 + 322.09 = 372.72
Now we subtract his budget by how much he has already spent:
620 - 372.72 = 247.28
He has $247.28 left for outfits so we can divide 247.28 by $61.82 (the amount per outfit) to find how many he can buy:
247.28 / 61.82 = 4
Adrian can buy 4 outfits.
1. A.
a_____________
is a fraction where
a and/or b are fractions and b is not equal to 0.
pitel
Answers
Rational fraction is a fraction where a and/or b are fractions and b is not equal to 0.
What is rational fraction?Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K. Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere.
Given Data
a_____________ is a fraction where a and/or b are fractions and b is not equal to 0.
A rational fraction is a fraction where a and/or b are fractions and b is not equal to 0.
Example 1. f(x) =[tex]\frac{x}{x-3}[/tex]
The denominator has only one zero, x = 3.
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Write the equation of the line that passes through the points (3,−8) and(−4,−9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answers
Answer:
y + 9 = [tex]\frac{1}{7}[/tex](x+4)
Step-by-step explanation:
Point slope form: y − y1 = m(x − x1)
First, we find the slope (m):
m = [tex]\frac{y2-y1}{x2-x12} = \frac{-8-(-9)}{3-(-4)} = \frac{1}{7}[/tex]
Now insert your points and slope into the form:
y + 9 = [tex]\frac{1}{7}[/tex](x+4)
In the figure below, m<2=43°. Find m<1.
m<1 =
Answers
Answer:
137°
Step-by-step explanation:
Given: ∠2 = 43°
Find: ∠1 = ?
Solution:
∠1 + ∠2 = 180°
∠1 = 180° - ∠2
∠1 = 180° - 43°
∠1 = 137°
Reflection and Rotation
A. Preserve
B. Do not Preserve
ABC is
A. Equal to the
B. Twice the
C. Not related to the
D. Three times the
And AC is
A. 8,9, and 13
B. 7,9 and 10
C. 2, 14, and 10
D. 8,9 and 10
Answers
Reflection and rotation preserve length , so the perimeter of ΔABC is equal to the perimeter of ΔXYZ. A possible set of values for AB, BC and AC is 7,9 and 10 units.
A rotation is a transformation that occurs when a figure is turned a preset number of degrees around a fixed point (referred to as the center of rotation).
You will currently need geometry software in order to graph a rotation in general. This allows any figure to spin a certain amount of times around any point.A reflection is a kind of transformation that flips the preimage, or original shape, across the line of reflection to produce a new shape (called the image). If the form were to be reversed to graph a reflection, consider what would happen.The given figure is a triangle ABC such that it is transformed by a rotation of 90 °and reflection about y=-5.
The image thus formed will be congruent to the object and will have same sides and perimeter.
Hence the perimeter will be 26 units and the possible length of AB,BC and AC will be 7,9 and 10 units which is the only possible option as a triangle cannot have sides 2 , 14 and 10.(2+10<14)
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