[tex](-8)^\frac{1}{2} \neq -(8^\frac{1}{2})[/tex] because 8 is an odd power of 2 and [tex](-27)^\frac{1}{3} = -(27)^\frac{1}{3}[/tex] because 27 can be written with the power which a multiple of 3.
Consider [tex](-8)^\frac{1}{2}[/tex].
We know that 8 = 2³
So [tex](-8)^\frac{1}{2}[/tex] = [tex](-2^3)^\frac{1}{2}[/tex]
Also there is no real value for this expression. If 8 had an even power, then we would have got a real value. Because here 3 does not cancel with 2 completely.
Now for [tex]-(8^\frac{1}{2})[/tex] , this expression means the negative sign of the square root of 8. Even though 8 is not an perfect square, 8 has a real square root value. So this expression gives a real value. But the previous one does not.
Hence, [tex](-8)^\frac{1}{2} \neq -(8^\frac{1}{2})[/tex]
Consider [tex](-27)^\frac{1}{3}[/tex] = [tex](-3^3)^\frac{1}{3}[/tex] = -3, canceling out the 3 on the denominator with the power of (-3).
Also, [tex]-(27)^\frac{1}{3}[/tex] = [tex]-(3^3)^\frac{1}{3}[/tex] = -3 again.
Hence [tex](-27)^\frac{1}{3} = -(27)^\frac{1}{3}[/tex] .
This is because the power was a multiple of 3.
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Find the value of x to the nearest tenth.
Answer:
4.5
Step-by-step explanation:
a^2+b^2=c^2
64+16=80=c^2
c=80^0.5
x^2+80=100
x^2=20
x=4.5
Mrs Chua has a bag of sweets for some children. If each child gets 8 sweets, there will be 3 sweets extra. If she gives each child 9 sweets, there will be 2 sweets short. Find the extra number if sweets Mrs Chua needs to buy in order for each child to get either 8 or 9 sweets
Answer:
38
Step-by-step explanation:
It is clear that the number of sweets that should be bought so that each child can get either 8 or 9 sweets should be divisible by both 8 and 9
This is called the LCM or least common multiple of 8 and 9
Since 8 and 9 have no divisors in common LCM of 8 and 9 is 72 so 72 is the minimum number of sweets to buy so that there are no leftovers if each child gets 8 or 9 sweets
Let's compute the number of sweets that were bought the first time. Let the number of children be X
Since each child got 8 sweets and 2 were left over, the total of sweets must be 8X + 2
If each child were to get 9 sweets each then there would be 2 sweets short
This can be written as 9X -2 for the total number of sweets
Since these have to be equal,
9X - 2 = 8X + 2
Add 2 to both sides:
9X - 2 + 2 = 8X +2 + 2
9X = 8X + 4
Subtract 8X from both sides
9X - 8X = 8X - 8X + 4
1X = 4
==> X = 4
So number of children is 4
Total number of sweets bought
= 8 x 4 + 2 = 34
or
= 9 x 4 - 2 = 34
Therefore number of extra sweets to be bought = 72 - 34 = 38
Hope that helps and if you don't understand and need more explanation, please post a comment
Below is the graph of a function over the interval [-4,4]. Find the following for each function: the domain, the zeros of the function (the values of x where the value of the function is 0), and Intervals where the function is positive and negative.
From the graph of a function over the interval [-4,4]. the following are found for each function
The domain is x ≥ -4, -4 ≤ x ≤ 4, x ≤4the zeros of the function is ( 0, 0 ), ( 0, 0 )The function is positive at 0 ≤ x ≤ 4, x ≥ 4. The function is negative at x ≥ -4, -4 ≤ x ≤ 0What is domain of a function?The domain of a function refers to the input variables, often times the domain comprises of the x axis. for the given graph the domain is -4 ≤ x ≤ 4.
How to get the domain of a function.This would be through the points in the function. We are given [-4,4]
-4 is the negative side while 4 is the positive. We have to write this out as
-4 ≤ x ≤ 4.
The positive part part of the function is at 4. This is because we can assume a +4 sign.
The negative part is the point -4.
Hence we can say that the domain is -4 ≤ x ≤ 4 with the positive and negative at 4 and -4 respectively
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If (x+1) is a factor p(x)= x²+x+2 then find the value of X.
If (x+1) is a factor p(x)= x² + x + 2 then the value of x is -1.
What is a polynomial?An expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power
We have,
(x + 1) is a factor of p(x) = x² + x + 2
We need to find x.
Since (x + 1) is a factor of p(x) it should satisfy p(x).
x + 1 = 0
x = -1
Thus if (x+1) is a factor p(x)= x² + x + 2 then the value of x is -1.
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Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)^2= 19
The solutions to the equation (3x - 5)²= 19 are: - [tex]\frac{\sqrt{19} + 5}{3}[/tex] and [tex]\frac{\sqrt{19} + 5}{3}[/tex] .
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
In this question we have been given an equation that is (3x - 5)²= 19
Now taking square root both sides
(3x - 5)² = 19
3x - 5 = ± [tex]\sqrt{19}[/tex]
Add 5 to both sides to make equation simpler
3x = ± [tex]\sqrt{19}[/tex]+ 5
Divide both sides by 3
x = ±[tex]\frac{\sqrt{19} + 5}{3}[/tex]
Now separating the solutions we get
x = [tex]\frac{\sqrt{19} + 5}{3}[/tex] .
x = - [tex]\frac{\sqrt{19} + 5}{3}[/tex] .
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What is the solution of log 6-log 3 x=-2 ?
Solution of log 6-log 3 x = -2 is , x =200
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function or equation
x is the expression
Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]According to given statement,
log 6-log 3 x= -2
using formula of log a - log b, we can write the eq. as
[tex]log \frac{6}{3x} = -2[/tex]
=> [tex]6 / 3x = 10^{ -2}[/tex]
=> [tex]3x = 600[/tex]
=> [tex]x =200[/tex]
Thus solution of log 6-log 3 x=-2 is , x =200
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One angle of an isosceles triangle measures 30°. What measures are possible for the other
two angles? Choose all that apply.
15°
75°
120°
30°
Answer:
the correct ones are 30 , 120, 75
What is the area of the triangle?
(-5, -2)«
(3, -7)
(3,-1)
24units² is the area of the given triangle.
What is a triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. A triangle is a two-dimensional shape with three sides, three vertices, and three angles. The sum of a triangle's interior angles is always 180, whether the triangle is isosceles, equilateral, or scalene.The formula of the area of a triangle using coordinates:
A = (x₁y₂ + x₂y₃ + x₃y₁ – x₁y₃ – x₂y₁ – x₃y₂)/2Now, substitute the values in the formula as follows:
A = (-5×-7 + 3×-1 + 3×-2 - -5×-1 - 3×-2 - 3×-7)/2A = (35 - 3 - 6 - 5 + 6 +21)/2A = (62 - 14)/2A = 48/2A = 24units²Therefore, the area of the given triangle is 24units².
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pls help w this pretty urgent
Answer:
Step-by-step explanation:
Given
How do we find the constant rate from two points?
Let the two points be given by:
[tex]P(x_{1},y_{1}) \\ Q(x_{2},y_{2})[/tex]
[tex]rate = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
At a grocery store, you want to buy 3 1/2
lb of turkey . What decimal should the digital scale show?
The decimal value the digital scale will show for 3¹/₂ lb of turkey is 3.5.
What is a decimal value?A decimal value is a fractional value. Sometimes, a decimal contains a whole number and some fractions.
In a decimal number, the first digit after the decimal is in the tenth place. The next digit after the first decimal value represents the hundredth place.
Decimal values are obtained during the mathematical operation of divisions to show that there are remainders or uneven dividends.
Thus, the decimal value that the digital scale will show for 3¹/₂ lb of turkey is 3.5.
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then find the value of x.
=
(5+8)°,
Answer:x=0
Step-by-step explanation:hope it helps, brainliest? i could really use it
i need helpp asapppp!!!!!!
Answer: anwser is negative 6
Step-by-step explanation:
i hope you get i had it too and got it right if its not they are giving diffrent anwser then
A line passes through the point (0, −1) and has a positive slope. Which of these points could that line pa
Check all that apply.
(12, 3)
O (-2,-5)
(–3, 1)
(1, 15)
O (5,-2)
The slope is positive for the points (12,3),(-2,-5),(1,15)
The slope of a line is that the quantitative relation of quantity|the quantity|the number} that y will increaseas x will increase some amount.
Slope tells you ways steep a line is, or what quantity y will increaseas x will increase. The slope is constant (the same) anyplace on the road.
One way to think about the slope of a line is by imagining a roof or a side. each roofs and ski slopes may be terribly steep or quite flat. In fact, each ski slopes and roofs, like lines, may be utterly flat (horizontal). you'd ne'er realize a side or a roof that was utterly vertical, however a line may be.
formula of slope for 2 point line =y2-y1/x2-x1
for point (12,3). m=3+1/12 =4/12 =1/3 which is correct.
for point (-2,-5)m=-4/-2=2 which is correct
for point (-3,1) m=2/-3 which is not correct
for point (1,15)m=16/1 which is correct
for point (5,-2)m=-1/5 which is not correct.
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a. How much potential energy would a 41kg diver have standing on a 10-m diving platform?
Potential energy required is 4,018 kg m² /s²
What is Potential Energy ?
Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy. Potential energy always measures if we know the height of the object and the mass of the object on which energy is applied as well.
Formula of potential energy :
U = mgh
where, U = gravitational energy
m = mass of object
g = gravitational acceleration
h = vertical height of object
In the question given,
g= -9.8m/s² , h = 10 m , m = 41kg
as, U = mgh
= (41 )(9.8)(10)
= 4,018 kg m² /s²
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The battery power available to run a satellite is given by the formula P=50e⁻t/₂₅₀, where P is power in watts and t is time in days. For how many days can the satellite run if it requires 15 watts of power?
By basic algebra, we can say that: the satellite to run for about 130 days if it requires 15W of power.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.Given:
P = 50 [tex]e^{\frac{-t}{250}}[/tex]P = Power in watts,t = time in daysTo find: t when P = 15.
Finding:
On substituting the given values in the given formula, by basic algebra, we get:
15 = 50 [tex]e^{\frac{-t}{250}}[/tex]
=> [tex]\frac{15}{50}=\frac{3}{10}[/tex] = [tex]e^{\frac{-t}{250}}[/tex]
=> log [tex]\frac{3}{10}[/tex] = [tex]\frac{-t}{250}[/tex]
=> - 0.522 = [tex]\frac{-t}{250}[/tex]
=> 130.5 = t
Hence, the satellite to run for about 130 days if it requires 15W of power, as solved by basic algebra.
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Rice is sold at a profit of $4 per kg. Find the overall profit if150 kg of rice is sold.
$600.
Given that
Profit per kg = $4.
we find out the overall profit for 150 kg of rice.
Profit is a term that often describes the financial gain a business receives when revenue surpasses costs and expenses.
Total Revenue - Total Expenses = Profit.
for 1 kg profit is $4
then for 150 kg profit is = (profit of 1 kg × total rice)
= 4×150$
= $600
Hence the overall profit on 150 kg of rice is $600 .
Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is. Every product has a cost price and a selling price. Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product.
Profit(P) - The amount gained by selling a product with more than its cost price.
Profit or Gain = Selling price – Cost Price
Profit percentage (P%) = (Profit /Cost Price) x 100
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Let P=(-2,2), Q=(3,4), R=(-2,5) , and S=(2,-8) . What are the component forms of the following vectors? -5RS
The components of -5RS are {-20; 65}.
The components of a vector in a two-dimensional coordinate system are usually thought of as the x and y components. This can be expressed as V = (vx, vy). where V is a vector. These are part of the vectors generated along the axis.
Suppose an angle θ is formed between the vector V and the x component of the vector. A vector V and its x component (vx) form a right triangle if you draw a line parallel to the y component (vy).
Due to the trigonometric relationship
cos θ = adjacent side/hypotenuse = vx/V
sin θ = opposite side/hypotenuse = vy/V
where V is the magnitude of vector V.
So, the Component of -5RS is Given by:
-5RS = -5* {Sx - Rx; Sy - Ry} = {2 - (-2); -8 - 5} = -5*{4; -13}
-5RS = {-20; 65}
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How much interest does 2560 earn in 17 months at a rate of 5 1/8%? Round to the nearest cent
The interest that 2560 earns in 17 months at a rate of 5 1/8% is $185.9.
How to calculate the interest?In the fields of finance and economics, interest is the payment of a sum over and above the principal amount to a lender or depositor by a borrower or deposit-taking financial institution at a set rate. It is not the same as a fee that the borrower might pay to the lender or another entity.
Principal = $2560
Time = 17 months = 1.417 years
Rate = 5.125%
Therefore, the Interest will be:
= (Principal × Rate × Time) / 100
= (2560 × 1.417 × 5.125) / 100
= $185.9
Therefore, the interest that 2560 earns in 17 months at a rate of 5 1/8% is $185.9.
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what is the formula for arithmetic mean
Answer:
A = arithmetic mean
n = number of values
a_i = data set values
Step-by-step explanation:
Hope it helps! =D
Write each expression in simplest form. (-32y¹⁵)¹/₅
The simplest form of the expression is determined by solving the fractional exponent.
If an exponent of the base (number) is expressed in a fraction, it is called a fractional exponent. In an expression say x^1/y, 1/y is the fractional exponent. Fractional exponent represents the power and root together.
In the given expression, the base term is -32y^15, while the exponent is 1/5.
Since, (ab)^m=a^mb^m
Hence, (-32y¹⁵)^¹/₅=(-32)^1/5*(y^15)^1/5
When a base number has a negative sign, and the power is an odd number, the negative sign is extracted.
(-32)^1/5*(y^15)^1/5=-(32)^1/5*(y^15)^1/5
Since, (a^m)^n=a^m*n
-(32)^1/5*(y^15)^1/5=-32^1/5y^15*1/5
As 32=2*2*2*2*2=2^5
The expression becomes.
-(2^5)^1/5*(y^15^)1/5
Multiplying the powers,
-(25)^1/5*(y^15)^1/5=-(2^5*1/5)(y^15*1/5)=-2y^3
The simplest form of expression is (-32y¹⁵)^¹/₅ is -2y^3.
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(10,0) (0,4) in distance formala
The distance is √116.
what is distance formula?The distance formula to calculate the distance between two points (x1,y1) ( x 1 , y 1 ) , and (x2,y2) ( x 2 , y 2 ) is given as,
D=√(x2−x1)²+(y2−y1)²
Given:
(10,0) (0,4)
Using Distance formula
=√(x2 - x1)² + (y2 - y1)²
=√(0-10)² + ( 4-0)²
=√100 + 16
=√116
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Complete the point-slope equation of the line through ( − 2 , 6 ) (−2,6)left parenthesis, minus, 2, comma, 6, right parenthesis and ( 1 , 1 ) (1,1)left parenthesis, 1, comma, 1, right parenthesis.
Hence, the complete the point-slope equation of the line through ( − 2 , 6 ) (−2,6) is y = 6 .
Point slope kind is employed to represent a line victimisation its slope and a degree on the road. That means, the equation of a line whose slope is 'm' and that passes through a degree is found victimisation the purpose slope kind. totally different forms are often wont to categorical the equation of a line. one amongst them is purpose slope kind. The equation of the purpose slope kind which is given by y - y₁ = m(x - x₁) .We have given two points ( − 2 , 6 )and (−2,6) .
Using slope formula , we get
m = 6 - 6 / -2 -(-2)
m = 0
Putting m = 0 , x₁ = -2 and y₁ = 6 in equation (1) , we get
y - 6 = 0
y = 6
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What is the equation of the graph below?
Please help me out please please please
Answer:
12-6 is the right answer
Step-by-step explanation:
Multiple 3 to 4 which is 12 and then then multiple it with two which is 6 so the answer is 12-6
Solve each equation.
log 5-log 2 x=1
log (5) - log (2x) = 1 => x = 0.2499, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
log(5) - (log (2x)) =1
=> log (5) - [log (2) + log (x)] = 1 (as log(ab) = log(a) + log (b))
=>log (5) - log (2) - log (x) = 1
=> log ([tex]\frac{5}{2}[/tex]) - log (x) = 1
=> 0.3979 - log (x) = 1
=> log (x) = 0.3979 - 1
Since, generally the base of log is 10, raising them to 10
=> [tex]10^{log_{10}x} = 10^{-0.6021}[/tex]
=> x = 0.2499
Hence, log (5) - log (2x) = 1 => x = 0.2499, by properties of logarithm.
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5 groups of 2 hundredths
It should be noted that 5 groups of 2 hundredths will be 3.2e-9.
How to illustrate the information?It should be noted that the information is simply about finding 5 groups of 2 hundredths.
In this case, this will be illustrated as:
= 5 × 2 hundredths
It should be noted that 2 hundredths simply means 0.02. Therefore, the information is to calculate 0.02 in 5 places. This will be illustrated thus:
= 0.02 × 0.02 × 0.02 × 0.02 × 0.02
= 3.2e-9.
Therefore, it should be noted that 5 groups of 2 hundredths will be 3.2e-9.
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find the range of possible values of x (x+20)=57
The range of possible values of x from the given equation is 37.
The given equation is (x+20)=57.
What are domain and range?The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and the range is the possible output given by the function. Domain→ Function →Range.
The domain and range are defined for a relationship and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.
Now,
Domain = the set of all x-coordinates
Range = the set of all y-coordinates
Here, x+20=57
⇒x=37
Verification:
Put x=37 in x+20=57 and verify.
37+20=57
⇒57=57
LHS=RHS
Therefore, the range of possible values of x from the given equation is 37.
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Please help I need to know this
Answer:
Step-by-step explanation:
Step 1: we write 23% in decimal form: 23%=0.23.Step 2: we find the multiplier. Since we're increasing by 23%, we add 0.23 to 1: 1+0.23=1.23.Step 3: we multiply 80 by the multiplier 1.23: 80×1.23=98.4
So that means your answer is 1.23
neeeed help pleaseeeeeee
Answer:
Step-by-step explanation:
A=(1/2) x b xh
h=6
A = (1/2) x b x 6
24=3b
b=24/3
b=8