The expression 4∛16/2∛2 has a value of 4when simplified
How to evaluate the expression?From the question, the expression is given as
4∛16/2∛2
From the above parameter, we can see that the factors of the expression uses the cube root symbol
This means that the expression is a radical expression
Next, we have
4∛16/2∛2 = 4∛16/2∛2
Divide 4 by 2 in the equation
So, we have
4∛16/2∛2 = 2∛16/∛2
Solving further, we combine the cube roots (or radicals)
This is represented as
4∛16/2∛2 = 2∛(16/2)
Evaluate the quotient of 16 and 2
So, we have the following equation
4∛16/2∛2 = 2∛8
Take the cube root of 8
4∛16/2∛2 = 2 x 2
Evaluate the product
4∛16/2∛2 = 4
The expression cannot be further simplified
Hence, the solution to the expression 4∛16/2∛2 is 4
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Fill in the empty spaces to complete the puzzle. In any row, the two left spaces should multiply to equal the right-hand space. In any column, the two top spaces should multiple to equal the bottom space.
Explanation:
We will find the expression for each space in the following order
To find the first expression, we need to find a number that multiplied by 6 is equal to 18. This number is 3 because
6 · 3 = 18
Then, for the second space, we need to factorize the expression 36x² + 144x + 108 as follows
36x² + 144x + 108 = 8(2x² + 8x + 6)
So, the expression that multiplied to 8 is (36x² + 144x + 108) is (2x² + 8x + 6).
The third space can be calculated by factorizing 2x² + 8x + 6 as
2x² + 8x + 6 = (x + 3)(2x + 2)
Therefore, the expression in the third space is (2x + 2)
Finally, for the fourth and fifth space, we need to multiply the expression to the left, so
6(2x + 2) = 6(2x) + 6(2) = 12x + 12
3(x + 3) = 3(x) + 3(3) = 3x + 9
Answer
Therefore, the answer is
Evaluate the expression whenb= 48 c= 7simplify as much as possible
Given:-
[tex]\frac{b}{3}+2c^2[/tex]To find the simplified value when b=48 and c=7.
So now we simplify the solution by substituting the values of b and c in the given equation and get the required solution.
So now we simplify. so we get,
[tex]\frac{b}{3}+2c^2=\frac{48}{3}+2\times7\times7=16+98=114[/tex]So the simplified solution is 114.
You are redecorating your room and the only thing left to paint is your door. You're onlygoing to paint the side that faces the inside of your room. The door is 6 feet 10 inchestall and 30 inches wide. You need to know the surface area of the side of the door todetermine how much paint to buy. The hardware store sells paint by how much coversa square foot. What is the surface area of the garage door? Round your answer to thenearest square foot. (Hint: 1 square foot = 144 square inches) (gridded response)
The roblem tells us that a door needs to be painted on only one side that measures 6 ft and 10 in height by 30 in wide.
We need to find the area to be painted in order to buy the appropriate quantity of paint. The answer has to be given in square feet at the end.
We start by recalling that the door is represented by a rectangle, and the area of such is given by the height times the wid
MOSS 79 grom Volume 10 m
Mass=79gram
Volume=10ml
density=Mass/Volume
[tex]\text{Density}=\frac{79\text{gram}}{10ml}=7.9\text{ gram/ml}[/tex]solve the equation 3x^2 - 5x + 1 = 0 expressing your answer correct to two decimal places
You have th following equation;
[tex]3x^2-5x+1=0[/tex]In order to find the solution to the previous equation, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, a = 3, b = -5 and c = 1. By replacing these values into the quadratic formula, you obtain:
[tex]\begin{gathered} x=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(3)(1)}}{2(1)} \\ x=\frac{5\pm\sqrt[]{25-12}}{2}=\frac{5\pm\sqrt[]{13}}{2} \\ x=\frac{5\pm3.60}{2}=2.5\pm1.80 \end{gathered}[/tex]Hence, the solutions are:
x = 2.5 + 1.80 = 4.30
x = 2.5 - 1.80 = 0.70
$3.44 at the Farmers market at a grocery store the same oranges cost $8.40 for a bag of 20 find the better deal by calculating the unit rate for both locations how much would be saved per orange by purchasing oranges at the locations with the better deal solve the word problemFarmers market unit rate --------------grocery store unit rate ------------------better deal -------------how much is saved ------------A $0.01/ orangeslB $0.41 / orangeC grocery storeD Farmers marketE $0.43 / orangeF $0.40 / OrangeG $0.10 / Orange
Given :
At the farmer market : a bag of 8 oranges cost $3.44
At the grocery store : a bag of 20 oranges cost $8.4
So, the unit rate at the farmer market = 3.44/8 = $0.43/ orange
And the unit rate at the grocery store = 8.4/20 = $0.42/ orange
So, the better deal is the grocery store
how much is saved ?
the saving = 0.43 - 0.42 = $0.01/ orange
The sum of a number and -4 is greater than 15. Find the number
x > 19
Explanation:
Let the number = x
The sum of a number and -4 = x + (-4)
The sum of a number and -4 is greater than 15:
x + (-4) > 15
Multiplication of opposite signs gives negative number:
x - 4 > 15
Collect like terms:
x > 15 + 4
x > 19
Algebra 2 The answer choices are: A. -3 less then or equal to x less then or equal to 6B. -4 less than x less then or greater to 1C. X greater than or equal to 1D. X greater to or equal to 6
Given:
A graph is given.
Required:
Find the interval of the domain that the graph of exponential function represents.
Explanation:
The graph of the exponential function is given as:
Calculate the value of each expression.
1) (-5)
/
4
2) (-5)-(-/-)
3)-20
4)-20
(-20)
(4)
5)
Answer:
1) -15/4 or -3.75
2) 15/4 or 3.75
3) 5
4) -5
5) -5
Step-by-step explanation:
a positive integer is nice if there is a positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to . how many numbers in the set are nice?
Answer:
A positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.
What is an integer?
Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of the equivalent positive numbers, which are additive, are the negative numbers. The boldface Z or blackboard bold "Z" is frequently used in mathematical notation to represent a collection of numbers.
Step-by-step explanation:
We know That total No. of factors
=product of (prime no′s power+1)
If N is the number of different divisors:
N=(p1+1)⋅(p2+1)⋅⋅⋅(pn+1)
100= 2^2 × 5^2
=2×2×5×5= (1+1)(1+1)(4+1)(4+1)
Then the integer n= a1^p1⋅a2^p2⋅⋅⋅⋅an^pn
For the smallest value: p1=4,p2=4,p3=1,p4=1
Then,
n=a1^4×a2^4×a3^1×a4^1
=24⋅34⋅51⋅71
=16⋅81⋅5⋅7
=45360
Hence, the positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.
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There is $1.90 in a jar filled with quarters, dimes, and nickels. There are 2 more quarters than dimes and there are 2 more nickels than quarters. How many of each coin are there? quarters dimes [ ) nickels Enter the number that belongs in the green box.
5 quarters, 3 dimes, 7 nickels
Explanations:Let the number of quarters in the jar = q
Let the number of dimes in the jar = d
Let the number of nickels in the jar = n
1 quarter = $0.25
1 dime = $0.1
1 nickel = $0.05
The jar is filled with quarters, dimes, and nickels, totaling $1.90
This can be represented mathematically as:
0.25q + 0.1d + 0.05n = 1.90.........(1)
There are two more quarters than dime:
q = d + 2..............(2)
There are two more nickels than quarters
n = q + 2..............(3)
make d the subject of the formula in equation (2)
d = q - 2............(4)
Substitute equations (3) and (4) into equation (1)
0.25q + 0.1(q - 2) + 0.05(q + 2) = 1.90
0.25q + 0.1q + 0.05q - 0.2 + 0.1 = 1.90
0.4q - 0.1 = 1.90
0.4q = 1.90 + 0.1
0.4q = 2.0
q = 2.0/0.4
q = 5
n = q + 2
n = 5 + 2
n = 7
d = q - 2
d = 5 - 2
d = 3
There are 5 quarters, 3 dimes, 7 nickels
2) Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.
Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.
we know that
Applying the Pythagorean Theorem
DE^2=DEx^2+DEy^2
DEx -----> is the distance in the x-coordinate
DEy -----> is the distance in the y-coordinate
DEx=(-5-4)=-9 ------> subtract the x-coordinates
DEy=(-7+3)=-4 -----> subtract the y-coordinates
substitute in the formula
DE^2=(-9)^2+(-4)^2
DE^2=97
[tex]DE=\sqrt[]{97}\text{ units}[/tex]c^2=a^2+b^2
c -----> is the distance DE
a ----> horizontal leg
b ----> vertical leg
we have
a=(-5-4)=-9 ------> subtract the x-coordinates
b=(-7+3)=-4 -----> subtract the y-coordinates
substitute
c^2=(-9)^2+(-4)^2
c^2=97
[tex]c=\sqrt[]{97}\text{ units}[/tex]Question 7, pre calc, include the answer in bold please. I have bad WiFi so please finish question if I get disconnected so I can see it, thanks
Given the following function
[tex]f(x)=x^4-x^3+7x^2-9x-18[/tex]We want to find its roots. Since we already know that (x + 1) and (x - 2) are factors of this polynomial, we can divide our polynomial by those factors and factorize the result to get the other roots.
Let's start by dividing by the first factor
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}[/tex]To divide a polynomial by other, we start by dividing the leading term of the dividend by the leading term of the divisor(this will be the first term of our result)
[tex]\frac{x^4}{x}=x^3[/tex]Then, we ultiply it by the divisor
[tex]x^3(x+1)=x^4+x^3[/tex]Subtracting this result from the dividend, we have
[tex](x^4-x^3+7x^2-9x-18)-(x^4+x^3)=-2x^3+7x^2-9x-18[/tex]This means that our division is
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3+\frac{-2x^3+7x^2-9x-18}{x+1}[/tex]Repeating the whole process of division with the second term, we have
[tex]\begin{gathered} x^3+\frac{-2x^3+7x^2-9x-18}{x+1}=x^3-2x^2+\frac{9x^2-9x-18}{x+1} \\ \Rightarrow\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3-2x^2+9x-18 \end{gathered}[/tex]From this result, we can rewrite our function as
[tex]x^4-x^3+7x^2-9x-18=(x+1)(x^3-2x^2+9x-18)[/tex]Repeating this same process with the other know factor, the other division we have to solve is
[tex]\frac{(x^3-2x^2+9x-18)}{x-2}=x^2+9[/tex]Then, our function is
[tex]f(x)=(x^4-x^3+7x^2-9x-18)=(x+1)(x-2)(x^2+9)[/tex]Then, to find the roots we need to solve the following equation
[tex](x+1)(x-2)(x^2+9)=0[/tex]Since we have a product of 3 terms, the result will be zero if and only if one of the terms is zero. This means that the roots can be found by assuming each one is zero. The solutions for this equation are the same solutions for the following system
[tex]\begin{cases}x+1=0 \\ x-2=0 \\ x^2+9=0\end{cases}\Rightarrow\begin{cases}x=-1 \\ x=2 \\ x=\pm\sqrt[]{-9}=\pm3i\end{cases}[/tex]And those are the roots for our function. x = -1, 2, +-3i.
FIND THE MEASURE OF EACH EXTERIOR ANGLE OF 40
Solution
The sum of exterior angles is 360º for any polygon
So then we can find the measure of the exterior angles like this:
360/40 = 9º
Find the slope using the points (2,1) and (7,5). Justify your answer
the product of a number and 3, increased by 5, is 7 less than twice the number. write an equation
Answer:
[tex]3x + 5 = 2x - 7[/tex]
Estimate the difference between 7,472 and 3,827 by rounding each number to the nearest hundred.
Answer:
The difference is aproximately 3700.
Step-by-step explanation:
First, we'll round each number to the nearest hundred:
[tex]\begin{gathered} 7472\rightarrow7500 \\ 3827\rightarrow3800 \end{gathered}[/tex]Now, we can estimate the difference:
[tex]7500-3800=3700[/tex]This way, we can conlcude that the difference is aproximately 3700.
whic fracción is equivalente to 8/10
Given data
*The given fraction is 8/10
[tex]\frac{80}{100}=\frac{8}{10}[/tex]80/100 is the fraction equivalent to 8/10
What transformation would cause the change from ABC to A'B'C'?
Answer:
D. 1/4
Explanation:
When the coordinates of A, B, and C are multiplying by 1/4 we get A', B', and C'.
For example,
[tex]\frac{1}{4}\times A(-8,4)=A^{}(-\frac{8}{4},\frac{4}{4})[/tex][tex]\therefore A(-8,4)\rightarrow A^{\prime}(-2,1)[/tex]The same goes for B and C.
Hence, the transformation that gives us A'B'C' from ABC is Choice D DIlation using k = 1/4.
-6 subtracted from a number equals -12.What is the number?
Answer:
The number is -18
Explanation:
-6 subtracted from a number equals -12.
We want to find the value of the number
Let the number be x
We can write the statement mathematically as:
[tex]x-(-6)=-12[/tex]Solving this equation, the value of x is the number we are required to find.
[tex]\begin{gathered} x+6=-12 \\ \text{Subtract 6 from both sides} \\ x+6-6=-12-6 \\ x=-18 \end{gathered}[/tex]The said number is -18
A ball is dropped from a state of rest at time T = 0.The distance traveled after t seconds is s(t) = 16t^2 ft.
ANSWERS
(a) 68 ft
(b) 136 ft/s
(c) 128 ft/s
EXPLANATION
(a) The time interval is from 4s to 4.5s, so the distance the ball travels from 4s to 4.5s is,
[tex]\Delta s=16\cdot(4.5)^2-16(4)^2=68ft[/tex](b) As stated, the average velocity is the quotient between the distance traveled and the time,
[tex]\frac{\Delta s}{\Delta t}=\frac{68ft}{0.5s}=136ft/s[/tex](c) Here we have to find the distance as we did in part b and then divide by the time interval,
[tex]\begin{cases}\lbrack4,4.01\rbrack\to\Delta s=1.28016\to V=1.28016/0.01=128.16ft/s \\ \lbrack4,4.001\rbrack\to\Delta s=0.128016\to V=0.128016/0.001=128.016ft/s \\ \lbrack4,4.0001\rbrack\to\Delta s=0.01280016\to V=0.01280016/0.0001=128.0016ft/s \\ \lbrack3.9999,4\rbrack\to\Delta s=0.01279984\to V=0.01279984/0.0001=127.9984ft/s \\ \lbrack3.999,4\rbrack\to\Delta s=0.127984\to V=0.127984/0.001=127.984ft/s \\ \lbrack3.99,4\rbrack\to\Delta s=1.2784\to V=1.2784/0.01=127.84ft/s\end{cases}[/tex]As we can see in the middle values, as the time interval is shorter - the difference approaches 0, the value of the velocity is closer to 128ft/s.
Hence, the estimated instantaneous velocity at t = 4 is 128 ft/s
Which relation below is not a function
Answer:
0,0
Step-by-step explanation:
Two numbers can not equal another number
Suppose you roll a pair of six-sided dice and add their totals.(a) What is the probability that the sum of the numbers on your dice is 9 or 12?
We know we're dealing with two dice. Since each die has 6 different possibilities, the outcomes of rolling two dice are given by:
6 × 6, which is 36. This will be our denominator.
How many ways can we get 9 or 12 with two dices?
For a sum of 9:
3 + 6 = 9
4 + 5 = 9
There are two possibilities.
For a sum of 12:
6 + 6 = 12
There is only one possibility.
Summing it up, there are 3 possibilities to get a sum of 9 or 12 with the two dice.
The events are independent events since neither of them can ever occur at the same time.
Thus, the probability will be:
[tex]\text{ Probability = \lparen Probability of getting 9\rparen + \lparen Probability of getting 12\rparen}[/tex]We get,
[tex]\text{ Probability = }\frac{2}{36}\text{ + }\frac{1}{36}\text{ = }\frac{3}{36}\text{ = }\frac{1}{12}\text{ \lparen simplified\rparen}[/tex]Therefore, the probability is 1/12.
what is the volume of a pipe that has a diameter of 8 meters and a height of 3 meters of water, round to the nearest tenth
The pipe is in the form of cylinder.
[tex]\begin{gathered} d\text{ = 8 m} \\ r\text{ = 4 m} \\ h\text{ = 3 m} \end{gathered}[/tex]The volume of the pipe is calculated as,
[tex]\begin{gathered} \text{Volume = }\pi\times r^2\times h \\ \text{Volume = 3.14 }\times\text{ 4}\times4\times3 \\ \text{Volume = 150.72 }\approx150.70m^3 \end{gathered}[/tex]Thus the volume of water is 150.70 cubic m .
How do you find the range in a graph like this?
Answer
y can take on any real number value except around 1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Explanation
The range of a function refers to the region of values where the fumction can exist. It refers to the values that the dependent variable [y or f(x)] can take on.
From the graph attached to this question, we can see that the function has different forms at different values of x.
But it is also evident that y can take on any real number value except around
1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Hope this Helps!!!
Melissa works as a tutor for S12 an hour and as a waitress for S11 an hour. This month, she worked a combined total of 105 hoursat her two jobs.Lett be the number of hours Melissa worked as a tutor this month. Write an expression for the combined total dollar amount sheearned this month.
From the question
Melissa earns $12 an hour as a tutor
And $11 an hour as a waitress
Also,
This month, she worked a combined total of 105 hours
at her two jobs.
Let t be the number of hours Melissa worked as a tutor this month
Let w be the number of hours Melissa worked as a waitress this month
This implies
[tex]t+w=105[/tex]Since Melissa worked t hours as a tutor this month then
Total money earned as a tutor = $12t
Also,
Since Melissa worked w hours as a waitress this month then
Total money earned as a waitress this month = $11w
Therefore, the total combined earnings for the month is
[tex]\text{ \$12t }+\text{ \$11w}[/tex]What is the gcf of 16 and 28
Answer:
4
Step-by-step explanation:
in ️RST, RS ~=TR and m
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
ΔRST
RS ≅ TR
∠ T = 15
∠ S = ?
Step 02:
We must apply the properties of isosceles triangles.
∠ T = ∠ S = 15
The answer is:
∠ S = 15 °
Use the formula V=lwh and A=bg to complete the table below by evaluating the expression
we have that
the formula to calculate the area of a rectangle is equal to
A=L*W
we have
L=8.3 cm
W=4 cm
substitute
A=(8.3)*(4)
A=33.2 cm2
therefore
Formula A=L*W
Expression A=(8.3)*(4)
Solve A=33.2 cm2
Consider these functions:/(=) =-{=2 + 51g(I) = =2 + 2What is the value of fg(-2))?
Answer: Provided the two functions, f(x) and g(x), we have to find the composite of these two functions at x = - 2:
[tex]\begin{gathered} f(x)=-\frac{1}{2}x^2+5x \\ \\ g(x)=x^2+2 \end{gathered}[/tex]
The composite function is as follows:
[tex]\begin{gathered} f(g(x))=-\frac{1}{2}(x^2+2)^2+5(x^2+2) \\ \\ \\ f(g(x))=-\frac{1}{2}[x^4+4x^2+4]+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}+3x^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8=-8+12+8=12 \\ \\ \\ f(g(-2))=12 \end{gathered}[/tex]The answer is 12.