The question is which of these statements are true about radicals exponents and rational exponents
Answers
We have the following:
I)
[tex]\sqrt[n]{a}=a^{\frac{1}{n}}[/tex]It´s true
II)
[tex]a^{\frac{1}{2}}=\sqrt[]{a}[/tex]It´s true
III)
[tex]\begin{gathered} a^{\frac{p}{q}}=\sqrt[p]{a^q}=(\sqrt[p]{a})^q \\ (\sqrt[p]{a})^q=(a^{\frac{1}{p}})^q=a^{\frac{q}{p}} \end{gathered}[/tex]It´s false
IV)
[tex]\sqrt[]{a}[/tex]It´s true
V)
[tex]\begin{gathered} a^{\frac{1}{n}}=\sqrt[]{a^n} \\ \sqrt[]{a^n}=a^{\frac{n}{2}} \end{gathered}[/tex]It´s false
Related Questions
In triangle HIJ,△HIJ, overline{HI}cong overline{JH} HI ≅ JH and text{m}angle H = 118^{\circ}.m∠H=118 ∘ . Find \text{m}\angle J.m∠J.
Answers
The measure of angle J in the isosceles triangle is given as follows:
m<J = 31º.
What is an isosceles triangle?An isosceles triangle is a triangle in which:
Two of the angles have equal measures.Two of the sides have equal measures.In the context of this problem, the angles are given as follows:
118º. (angle H).x: angle J.x: angle I.Angles J and I are equal as the triangle is isosceles and the congruent angles are acute, that is, they cannot have measures above 90º.
The sum of the measures of the internal angles of a triangle is of 180º, hence we can solve for x as follows:
x + x + 118º = 180º
2x = 62º
x = 62º/2
x = 31º.
Hence the measure of angle J is of 31 degrees.
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Please help me with this question I have a test next week and I really have to study this is 11th grade algebra 2
Answers
ANSWER:
(a)
(b) P(x < 4) = 0.29
(c) P(x= 6) = 0.17
(d) P(x ≥ 5) = 0.34
STEP-BY-STEP EXPLANATION:
The probability in each case would be the specific amount divided by the total amount, therefore, we calculate the total amount and the probability in each case, like this:
[tex]\begin{gathered} 5+10+2+9+33+12+15+3+1\:=\:90 \\ \\ P(0)=\frac{5}{90}=0.06 \\ \\ P(1)=\frac{10}{90}=0.11 \\ \\ P(2)=\frac{2}{90}=0.02 \\ \\ P(3)=\frac{9}{90}=0.1 \\ \\ P(4)=\frac{33}{90}=0.37 \\ \\ P(5)=\frac{12}{90}=0.13 \\ \\ P(6)=\frac{15}{90}=0.17 \\ \\ P(7)=\frac{3}{90}=0.03 \\ \\ P(8)=\frac{1}{90}=0.01 \end{gathered}[/tex]Therefore, the table would look like this:
With this we calculate the probability in each case:
[tex]\begin{gathered} P\left(x<4\right)=P\left(x=0\right)+P\left(x=1\right)+P\left(x=2\right)+P\left(x=3\right)=0.06+0.11+0.02+0.10=0.29 \\ \\ P(x=6)=0.17 \\ \\ P(x\ge5)=P\left(x=5\right)+P\left(x=6\right)+P\left(x=7\right)+P\left(x=8\right)=0.13+0.17+0.03+0.01=0.34 \end{gathered}[/tex]Writing and evaluating a function modeling continuous exponential growth or decay given two outputs
Answers
Explanation
The model has the form
[tex]y=ae^{-kt}[/tex]Where a=initial amount
y= final amount
K= growth rate constant
t= time
When 140 kg of substance is left after 7 hours, the formula can be remodeled to be.
[tex]\begin{gathered} 140=400e^{-7k} \\ e^{-7k}=\frac{140}{400} \\ e^{-7k}=\frac{7}{20} \\ \ln (e^{-7k})=\ln (\frac{7}{20}) \\ -7k=\ln (\frac{7}{20}) \\ k=\frac{\ln(\frac{7}{20})}{-7} \\ \therefore k=\frac{\ln (\frac{20}{7})}{7} \end{gathered}[/tex]Therefore, the first solution is
[tex]y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}[/tex]For part b we have 16 hours.
[tex]\begin{gathered} y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}=400e^{-\ln (\frac{20}{7})\frac{16}{7}} \\ y=36.302\approx36\operatorname{kg}\text{ (To the nearest whole number)} \end{gathered}[/tex]Thus, the answer is 36kg
The diameter of a planet at its equator is 5790 kilometers.Estimate using scientific notation:
Answers
Explanation
Step 1
divide the number by 1000
remember:
[tex]1000=10^3[/tex][tex]\frac{5790}{1000}=5.79[/tex]Step 2
input the value of cubic ten instead of 100
[tex]\begin{gathered} 5790=5.79\cdot1000 \\ 5.79\cdot1000=5.79\cdot10^3 \end{gathered}[/tex]then, the answer is
[tex]5.79x10^3\text{ kilometers}[/tex]
Find the Z-score for which 5% of the distributions area lies between-z and z
Answers
The equation that will represent this situation will be:
[tex]\begin{gathered} P(-z\le x\le z)=P(x\le z)-(1-P(x\le z))=0.05 \\ \end{gathered}[/tex]Thus:
[tex]\begin{gathered} P(x\le z)-1+P(x\le z)=0.05 \\ 2\cdot P(x\le z)-1=0.05 \\ 2\cdot P(x\le z)=0.05+1 \\ 2\cdot P(x\le z)=1.05 \\ P(x\le z)=\frac{1.05}{2} \\ P(x\le z)=0.525 \end{gathered}[/tex]If we check in a standard normal table. the z-score that corresponds to a probability of 0.525 is 0.063.
Answer: z-score is 0.063.
In a right triangle, the side opposite angle β has a length of 16.4 cm. The hypotenuse of the triangle has a length of 25.1 cm. What is the approximate value of sin(β)?
Answers
Given
Length of hypotenuse= 25.1 cm
length of BC = 16.4 cm
Find
Value of
[tex]sin\beta[/tex]Explanation
As , we know
[tex]sin\beta=\frac{opposite}{hypotenuse}[/tex]now, put values
[tex]sin\beta=\frac{16.4}{25.1}=0.653[/tex]Final Answer
Value of
[tex]sin\beta=0.653\text{ approx}[/tex]If a square has a perimeter of 28 inches, what is its area in square inches?
Answers
Remember that
The formula to calculate the perimeter of a square is
[tex]P=4*b[/tex]where
b is the length side of the square
we have
P=28 in
substitute in the formula
[tex]\begin{gathered} 28=4*b \\ sol\text{ve for b} \\ b=\frac{28}{4}=7\text{ in} \end{gathered}[/tex]The area of a square is
[tex]A=b^2[/tex]substitute the value of b
[tex]\begin{gathered} A=7^2 \\ A=49\text{ in}^2 \end{gathered}[/tex]The area is 49 square inchesoption Cmake a conjecture about each value or geometric relationship.
The relationship between the angles of a triangle with all sides congruent.
Answers
Congruence of all sides implies congruence of all angles. All of the angles line up.
What is geometric conjecture?
According to Thurston's geometrization conjecture in mathematics, each of a select group of three-dimensional topological spaces has a distinctive geometric structure that can be connected to it.
How do the angles of a triangle with congruent sides relate to one another?
We refer to a triangle as being equilateral when its three sides are congruent. We add a slash mark to the sides that are congruent. An equilateral triangle always has 60° angles.Learn more about congruent
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ABC with coordinates (1.3), B.4.5), and C15,2), what are the coordinates of ABC after the glide reflection described by t (-1,1) R y-axis?
Answers
Answer:
A'(0,4)
B'(-3,6)
C(-4,3)
Step-by-step explanation:
A glide reflection is the combination of a translation with a rotation.
In this question:
T(-1,1): This means that the translation is given by:
(x,y) -> (x-1,y+1)
Rotation: Around the y-axis. This means that:
(x,y) -> (-x,y)
The triangle has the following coordinates:
A(1,3), B(4,5), C(5,2)
Applying the translation:
(x,y) -> (x-1,y+1)
A(1,3) -> (1-1,3+1) = (0,4)
B(4,5) -> (4-1,5+1) = (3,6)
C(5,2) -> (5-1, 2+1) = (4,3)
Rotation over the y-axis:
(x,y)->(-x,y)
A'(0,4)
B'(-3,6)
C(-4,3)
You are choosing between two health clubs. Club A offers membership for a fee
of $20 plus a monthly fee of $25. Club B offers membership for a fee of $25
plus a monthly fee of $24. After how many months will the total cost of each
health club be the same? What will be the total cost for each club?
Answers
Let:
x = Number of months
y1 = Total cost for Club A
y2 = Total cost for Club B
a = Fee of Club A per month
b = Fee of Club B per month
c = Initial fee of Club A
d = Initial fee of Club B
so:
[tex]\begin{gathered} y1=ax+c \\ y1=25x+20 \\ -------- \\ y2=bx+d \\ y2=24x+25 \end{gathered}[/tex]So, the total cost will be the same for:
[tex]\begin{gathered} y1=y2 \\ 25x+20=24x+25 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 25x-24x=25-20 \\ x=5 \end{gathered}[/tex]The cost will be the same for the month number 5. And the total cost will be:
[tex]\begin{gathered} y1(5)=25(5)+20=145 \\ y2(5)=24(5)+25=145 \end{gathered}[/tex]$145
Cilantro earns $17.43 per hour. If Cilantro works 27 hours in a week, what will Cilantro's earnings be for the week?
Answers
Let be "x" Cilantro's earnings (in dollars) for the week.
According to the explained in the exercise, Cilantro makes $17.43 per hour and works a total of 27 hours per week.
With that information, you can set up the following proportion:
[tex]\frac{$17.43\text{dollars}$}{1\text{hour}}=\frac{x}{27\text{hours}}[/tex]In order to find the value of "x", you need to solve for it. You can apply the Multiplication property of equality and multiply both sides of the equation by 27 hours.
Therefore, you get this result:
[tex]\begin{gathered} (27\text{hours)(}\frac{$17.43\text{dollars}$}{1\text{hour}})=(\frac{x}{27\text{hours}})(27\text{hours)} \\ x=470.61\text{dollars} \end{gathered}[/tex]Then, Cilantro's earnings for the week will be $470.61
State the domain using an appropriate notation and evaluate f(2)
Answers
The domain of a function or coordinates of a function are the input values of the function "x" for which the function exists.
For instance, given the coordinates of the function {(-7, 2), (0, -2), (2, 5), (8, 1)}, the corresponding value of the x-coordinates are the domain. Therefore the domain of the given coordinate points are given as;
[tex]\text{Domain}=\mleft\lbrace-7,0,2,8\mright\rbrace[/tex]Get the value of f(2).
To get the value of f(2), we will find the y-value of the coordinate with a domain of 2. From the given coordinates, we can see that the coordinate that has a domain of 2 is (2, 5) and the corresponding y-value of the coordinate is 5. Hence f(2) = 5
How to tell if a sequence is linear, exponential, quadratic or absolute value as simply as possible without graphing (8th grade algebra) examples will be greatly appreciated
Answers
We will have the following:
We will be able to tel apart sequences as follows:
Linear sequence: We have that linear sequences follow the form:
[tex]y=mx+b[/tex]Here "x" represents the iteration value for the sequence, "m" the ratio (slope) and "b" a value that modifies the "position" of the sequence. This sequences grows in a linear manner.
Example:
[tex]\begin{cases}y_{}=2x+2 \\ \\ y_1=4 \\ y_2=6 \\ y_3=8 \\ \ldots\end{cases}[/tex]Exponential sequence: We have that exponential sequences follow the form:
[tex]y=a_1(r)^{x-1}[/tex]Here "a1" is the first term of the sequence, "r" is the ratio and "x" the iteration of the sequence.
We obtain the ratio as follows:
[tex]r=\frac{y_n}{y_{n-1}}[/tex]Example:
[tex]\begin{cases}y=1(5)^{x-1}_{} \\ \\ y_1=1 \\ y_2=5 \\ y_3=25 \\ \\ \ldots\end{cases}[/tex]The ratio for this case:
[tex]r=\frac{y_3}{y_2}\Rightarrow r=\frac{25}{5}\Rightarrow r=5[/tex]Quadratic sequence: A quadratic sequence follows the general form
If you are given odds of 5 to 6 in favor of winning a bet, what is the probability of winning the bet?
Answers
5 to 6 odds means that, out of 11 possible outcomes, odds are that there will be 5 of one kind of outcome and 6 of another kind of outcome.
In this case, you are given 5 to 6 odds, which means that out of 11 possible outcomes you will win a bet 5 times, and lose it 6.
In fraction, it will look like this:
[tex]\frac{11}{11}\text{ \lparen these are all the possible outcomes, which equals 1\rparen = }\frac{5}{11}(the\text{ outcomes in which you win, which equals .4545, so 45.45\%\rparen + }\frac{6}{11}\text{ \lparen the outcomes in which you lose, which equals 0.5454, so 54.54\% \rparen}[/tex]Because of that, the probability of winning the bet is 45.45%, and in a fraction, it is 5/11, which means you will win in 5 out of 11 scenarios.
Bryan's hockey team is purchasing jerseys. The company charges $250 for a onetime set-up fee and $23 for each printed jersey. Which expression represents the total cost of x number of jerseys for the team?Group of answer choices23x23 + 250x23x+250
Answers
To find the right answer, we have to remember that
[tex]\text{Total cost= Variable cost+ Fixed cost}[/tex]The variable cost is that which changes, in our case, the variable cost is the price of each jersey. since each cost $23 and it increases as the number of jerseys increases.
Thus, the variable cost will be
[tex]23x[/tex]The fixed cost is always constant. The fixed cost is the one-time set-up fee of 250.
Thus, we can combine the two costs to get the total cost.
The answer will be:
[tex]\text{Total cost=23x+250}[/tex]What is the factored form of the expression 18x +12y -30?
Answers
Let's begin by listing out the information given to us:
[tex]18x+12y-30[/tex]Factoring means we will use the common factor of the elements to break down the expression into a simpler form:
[tex]6(3x+2y-5)[/tex]What’s the total of all the present values of the payments? $320,640 $787,116 $878,611 $987,116
Answers
The total of all the present values of the payments is $2,973,483.
What is the present value?The present value is the future cash flows discounted to the present day's values.
The present value can be determined using an online finance calculator that inputs the future cash flows, the interest rate, and the period.
How is the total present value determined?The total present value is a function of the summation of the four present values.
Since the present values are given, computing the total involves the mathematical operation of addition.
Present Values:1st payment $320,640
2nd payment $787,116
3rd payment $878,611
4th payment $987,116
Total PV $2,973,483
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Answer:
The correct answer is $878,611 for plato users
Step-by-step explanation:
The sum of two numbers is 83. The difference of the 2 numbers is 13. What is the product of the two numbers?A.1632B.1650C.1666D.1680
Answers
Answer:
Let the first number be
[tex]=x[/tex]Let the second number be
[tex]=y[/tex]The sum of two numbers is 83 can be represented below as
[tex]x+y=83\ldots\ldots(1)[/tex]The difference of the 2 numbers is 13 can be represented below as
[tex]x-y=13\ldots\ldots\text{.}(2)[/tex]Step 1:
From equation (1) make x the subject of the formula to to give equation (3)
[tex]\begin{gathered} x+y=83\ldots\ldots(1) \\ x=83-y\ldots\text{.}(3) \end{gathered}[/tex]Step 2:
Substitute equation (3) in equation (2)
[tex]\begin{gathered} x-y=13\ldots\ldots\text{.}(2) \\ x=83-y\ldots\text{.}(3) \\ 83-y-y=13 \\ 83-2y=13 \\ \text{collect similar terms,} \\ -2y=13-83 \\ -2y=-70 \\ \text{divide both sides by -2} \\ \frac{-2y}{-2}=\frac{-70}{-2} \\ y=35 \end{gathered}[/tex]Step 3:
Substitute y= 35 in equation (3)
[tex]\begin{gathered} x=83-y\ldots\text{.}(3) \\ x=83-35 \\ x=48 \end{gathered}[/tex]Hence,
The product of the two numbers will be calculated as
[tex]\begin{gathered} =x\times y \\ =35\times48 \\ =1680 \end{gathered}[/tex]Hence,
The final answer is = 1680
OPTION D is the final answer
what is the rate change of the equation?Y=8x+20Remember Y=MX+B
Answers
The general equation of the line : y = m * x + b
where m is the slope , b is y -intercept
Given the function :
[tex]y=8x+20[/tex]The rate of change of the equation = the slope of the function
So, by comparing the given equation to the general from
The slope = m = 8
So, the rate of change = 8
Find the simple interest owed for the following loan. Principal = 2775 Rate = 7.5% Time = 5 1/2 years
Answers
We would apply the simple interest formula which is xpressed as
I = PRT/100
Where
I represents interest
P represents principal or amount borrowed
T represents time in years
R represents rate.
From the information given,
P = 2775
R = 7.5
T = 5 1/2 = 5.5
I = (2775 * 7.5 * 5.5)/100
I = 1144.6875
Rounding to the nearest cent,
I = 1144.69
Which expressions are equivalent to (1/3x−4x−5/3x)−(−1/3x−3) ? Select all correct expressions. Responses −3+5x negaive 3 minus 5 x −2x+3−3x negative 2 x plus 3 minus 3 x −5x+3 negative 5 x plus 3 2x−3+3x 2 x minus 3 plus 3 x
Answers
The equivalent expression for the given expression (1/3x - 4x - 5/3x) - (- 1/3x - 3) is 3 - 7x / 3
Given,
The expression;
(1/3x - 4x - 5/3x) - (- 1/3x - 3)
We have to solve this and find the equivalent expression;
Here,
(1/3x - 4x - 5/3x) - (- 1/3x - 3)
= 1/3x - 4x - 5/3x + 1/3x + 3
= 3 - 4x - 5/3x
= 3 - (12x - 5x) / 3
= 3 - 7x / 3
That is,
The equivalent expression for the given expression (1/3x - 4x - 5/3x) - (- 1/3x - 3) is 3 - 7x / 3
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f(x) = x^3- 9x^2 + 10.c ) list the x values of all the inflection points of F
Answers
To find the inflection points the first step we have to follow is to find the second and third derivatives of the function:
[tex]\begin{gathered} f\mleft(x\mright)=x^3-9x^2+10 \\ f^{\prime}\left(x\right)=3x^2-18x \\ f^{\prime}^{\prime}\left(x\right)=6x-18 \\ f^{\prime}^{\prime}^{\prime}\left(x\right)=6 \end{gathered}[/tex]Now, find the values of x for which the second derivative is 0:
[tex]\begin{gathered} 0=6x-18 \\ 18=6x \\ x=\frac{18}{6} \\ x=3 \end{gathered}[/tex]Evaluate the third derivative at this values of x, if the third derivative is different from 0, then that value is an inflection point:
[tex]f^{\prime}^{\prime}^{\prime}\left(3\right)=6[/tex]It means that there is an inflection point at x=3.
can you help me to find midpoint
Answers
First, locate the given points.
Then, draw the line that connects them
Next, add the two x-coordinates of the endpoints and divide by 2. In this case, (1 + 4)/2 = 5/2 = 2.5
Then, draw a line perpendicular to the x-axis that passes through x = 2.5, until it intersects the other line. The intersecting point is the midpoint.
In this case, the coordinates of the midpoint are (2.5, 0.5), as can be seen in the figure
Can someone please help me with this drag and drop? I would appreciate It a lot! Please explain :) I’ll give brainliest
Answers
Answer:
move B to true then everything is right ✅
A contractor bought 10.8 ft² of sheet metal. He has used 3.5 ft² so far and has $219 worth of sheetmetal remaining. The equation 10.8x - 3.5x = 219 represents how much sheet metal is remainingand the cost of the remaining amount. How much does sheet metal cost per square foot?
Answers
The first step to do is to combine 10.8x - 3.5x and that is equal to 7.3x.
[tex]7.3x=219[/tex]The next step is to divide both sides by 7.3 to solve for x.
[tex]\begin{gathered} \frac{7.3x}{7.3}=\frac{219}{7.3} \\ x=30 \end{gathered}[/tex]Therefore, the remaining sheet metal is 7.3 ft² and the cost per square foot of sheet metal is $30.
Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters asdimes. Write a system of equations that could be used to determine the number ofdimes and the number of quarters that Sophie has. Define the variables that you useto write the system.
Answers
d = 2q .........................................................................(1)
0.1d + 0.25q = 4.20 ................................................(2)
Explanation:Let d be the number of dimes, and q be the number of quarters Sophie has.
Since she has twice as many quarters as dimes, and they are worth $4.20, we have:
d = 2q .........................................................................(1)
Also, because:
1 dime = $0.1
1 quarter = $0.25
0.1d + 0.25q = 4.20 ..................................................(2)
Equation (1) and (2) can be solved to determine the number of dimes and quarters
product of the equationa^4•a^6
Answers
Okay, here we have this:
Considering the provided operation, we are going to perform it, so we obtain the following:
Let us remember that when two terms with the same base are multiplied, then the base is preserved and the exponents are added, in this case we have:
[tex]\begin{gathered} a^4\cdot a^6 \\ =a^{(4+6)} \\ =a^{10} \end{gathered}[/tex]Finally we obtain that the operation is equal to a^10.
The population of the county, which follows the exponential growth model,
increased from 491,675 in 2000 to 782,341 in 2010.Write the exponential growth function.
Answers
Step 1
Given; The population of the county, which follows the exponential growth model,
increased from 491,675 in 2000 to 782,341 in 2010.
Write the exponential growth function.
Step 2
The exponential function is given as;
[tex][/tex]which expression is equivalent to 5^-2 x 5^5
Answers
Given the expression:
[tex]5^{-2}\ast5^5[/tex]To find the equivalent expression, let's simplify the expression using power rule.
[tex]a^m\ast a^n=a^{m+n}[/tex]Since they have the same base, we are to add the exponents.
We have:
[tex]5^{-2}\text{ }\ast5^5=5^{-2+5}=5^3[/tex]Therefore, the eqivalent expression is 5³
ANSWER:
[tex]5^3[/tex]We a
what are the lenghths of the legs in the triangle?give your answer in simplest radical form or rounded to the nearest hundredth.
Answers
Here, we are given a 45°-45°-90° triangle.
Let's find the length of the legs.
A 45°-45°-90° triangle is an isosceles triangle, and the two legs of an isosceles triangle are of equal lengths.
To find the length of each leg apply the formula:
[tex]c=a\sqrt[]{2}[/tex]Where;
c = 12
Thus, we have:
[tex]12=a\sqrt[]{2}[/tex]Solve for a:
Divide both sides by √2
[tex]\begin{gathered} \frac{12}{\sqrt[]{2}}=\frac{a\sqrt[]{2}}{\sqrt[]{2}} \\ \\ \frac{12}{\sqrt[]{2}}=a \\ \\ a=\frac{12}{\sqrt[]{2}} \\ \\ \text{Simplify the denominator:} \\ a=\frac{12}{\sqrt[]{2}}\ast\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ \\ a=\frac{12\sqrt[]{2}}{2} \\ \\ a=6\sqrt[]{2} \end{gathered}[/tex]Therefore, the length of each leg in radical form is 6√2
ANSWER:
[tex]6\text{ }\sqrt[]{2}[/tex]