An equivalent expression is given by (2 / x ^ 3) * sqrt (2)
We have the following expression
8 / x ^ 6
Rewriting we have
sqrt (8 / x ^ 6)
What is the expression?
The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.
sqrt (2 * 4 / ((x ^ 2) * (x ^ 2) * (x ^ 2)))
(2 / (x * x * x)) sqrt (2)
(2 / x ^ 3) * sqrt (2)
An equivalent expression is given by
(2 / x ^ 3) * sqrt (2)
Therefore an equivalent expression is given by (2 / x ^ 3) * sqrt (2).
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God loves you Have an amazing day or night
Answer:
tha nks
Step-by-step explanation:
write the next whole number after 123four in the base four system
Answer:
130
Step-by-step explanation:
can't have a 4 in units so carry over
The next whole number after 123 in base four is 130.
What is the base of a number system?The entire amount of digits employed in a specific number system is referred to as the base of that system. The [0, b -1] range is occupied by the digits of the base "b" number system. The radix of a number system is another name for this base of the number system.
Given, A number in base four, 123.
Now, In base four there are 4 numbers they are 0, 1, 2, 3.
the next whole number in the number (123)₄ will be (130),
As after adding 1 to the unit digit it will become 'zero' and 1 will carry over.
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Type the correct answer in each box. Use numerals instead of words.
What is the solution to this matrix equation?
By using a system of equations, we will see that the solution is:
x = 25, y = -50, z = -15
How to solve the matrix equation?We can write this as a system of equations:
4x + 2y - z = 15
x + y - z = -10
-3x - y + z = 60
Notice that if we add the second and third equations, we get:
(x + y - z) + (-3x - y + z ) = -10 + 60
-2x = 50
x = 50/-2 = -25
So we already got the value of x. Replacing that in the second equation we et:
25 + y - z = -10
Isolating y we get:
y = -10 - 25 + z = z - 35
Now we can replace that in the first equation:
4x + 2y - z = 15
4*25 + 2*(z - 35) - z = 15
100 + z - 70 = 15
z = 15 - 100 + 70 = -15
And using:
y = z - 35 = -15 - 35 = -50
Then the soution to the matrix equation is:
x = 25, y = -50, z = -15
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Select the action you would use to solve x-3= 12. Then select the property
that justifies that action.
Select all that apply.
A. Action: Add 3 to both sides.
B. Action: Multiply both sides by 3.
C. Action: Subtract 3 from both sides.
D. Property: Addition property of equality
E. Property: Multiplication property of equality
OF. Property: Subtraction property of equality
← PREVIOUS
Answer:
Add 3 to both sides
Property: Addition property of equality
Step-by-step explanation:
Action: Add 3 to both sides.
⇒ x - 3 = 12
(cancel out)+ 3 + 3
------------------------ -----
x = 15
The property used:
Addition property of equality.→ equation is true and the same #is added to each side the resulting equation is true. for any #s a,b,c,if a=b then a+c=b+c.
At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering.
The probability that a student is a female or major in civil engineering is 62%
How to determine the probability?Let A represent Female and B represents civil engineering.
So, we have:
P(A) = 49%
P(B) = 21%
P(A and B) = 8%
The required probability is calculated as:
P(A or B) = P(A) + P(B) - P(A and B)
This gives
P(A or B) = 49% + 21% - 8%
Evaluate
P(A or B) = 62%
Hence, the probability that a student is a female or major in civil engineering is 62%
Complete questionAt a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?
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Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown/ What is the greatest possible whole-number length of the unknown side?
8 inches
9 inches
12 inches
13 inches
The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is C.
What is the triangle inequality theorem?The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]
Given the length of the two sides of the triangle, therefore, we can write the inequalities,
8 + 5 > x ⇒ 13 > x
8 + x > 5 ⇒ x > - 3
5 + x > 8 ⇒ x > 3
Now, as per the inequality the value of x can lie between 3 to 13, but as the side needs to be greatest, therefore, the value of x will be 12.
Hence, the correct option is C.
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Answer:
12in
Step-by-step explanation:
Which of these tables represent a linear function
Answer:
y=mx+c
Step-by-step explanation:
if any one of them have this form it's the linear function
The table represents a bicycle rental cost in dollars as a
unction of time in hours.
Bicycle Rental
Time
Cost
(hours)
($)
0
0
2
10
4
20
6
30
8
40
Which explains whether or not the function represents a
direct variation?
O This function represents a direct variation because it
passes through the origin and has a constant rate of
change of $5 per hour.
O This function represents a direct variation because it
has a positive, constant rate of change of $10 per
hour.
O This function does not represent a direct variation
because it does not represent the cost for 1 hour.
This function does not represent a direct variation
because the function rule for the cost is to add $10,
not multiply by a constant.
Answer:
(a) This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
Step-by-step explanation:
The equation of direct variation is ...
y = kx
for some constant k. Here, we have x in hours and y in dollars. We can see if k is constant for the values given in the table.
__
constant of variationSolving the direct variation formula for k, we have ...
k = y/x
Using the table values, we can see if this is constant:
k = dollars/hour = 10/2 = 20/4 = 30/6 = 40/8 = 5
The "rate of change" is constant at $5 per hour.
The function represents direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
a body starts from rest and moves with uniform acceleration of 4m/s² until it travels a distance of 800m,find the velocity
Answer:
80 m/s
Explanation:
Given:
i) initial velocity (as starts from rest) = 0 m/s
ii) acceleration: 4 m/s²
iii) distance travelled: 800 m
Formula required:
(final velocity)² - (initial velocity)² = 2 × acceleration × distance
Now solve:
v² - 0² = 2 × 4 × 800
v² = 6400
v = √6400
v = 80 m/s
Kyle wants to buy a television on a hire purchase agreement. the cash price of the television is R5600. she is required to pay a deposit of 15% and pay the remaining loan amount off over 24 months at an interest rate of 14% p.a. what are kyles monthly repayment? keep your answer to the nearest rand.
Kyles's monthly repayment on the television based on hire purchase agreement is R229
What is the monthly repayment?The monthly repayment is the amount paid monthly with interest on a particular loan or to recover from debt.
From the given information:
The price of the television = R5600Initial deposit = 15% of cash price = 0.15 × 5600 = 840Thus
principal amount left to be repaid = 5600 - 840 = 4760
Using the formula:
[tex]\mathbf{M=\dfrac{P( \dfrac{r}{12}) (1+\dfrac{r}{12})^n }{(1+\dfrac{r}{12})^n - 1}}[/tex]
[tex]\mathbf{M=\dfrac{4760( \dfrac{0.14}{12}) (1+\dfrac{0.14}{12})^{24} }{(1+\dfrac{0.14}{12})^{24} - 1}}[/tex]
M = R228.54
M ≅ R229
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Of the following three statements, choose the best option and write a viable argument showing how it is reflected by the Cost Function for Wichita’s factory.
___ The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.
___ The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
___ Overtime wages were required to produce at levels above 25,000 units.
The cost per unit actually comes down to 0.8$per unit.
We have given that,
The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.
The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
Overtime wages were required to produce at levels above 25,000 units.
What is the cost?
A cost is an expenditure required to produce or sell a product or get an asset ready for normal use.
The cost of production per unit of the item produced is 1$ as long as the total units produced are less than 2500.
If more than 2500 units are produced then the cost per unit actually comes down to 0.8$per unit.
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please answer asap!!!
A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in
seconds after the timer was started) is given by the equation h (t) = -(t-14)² +74 Which of the following statements is true?
O The airplane reaches its minimum height of 14 feet in 74 seconds.
O The airplane reaches its minimum height of 74 feet in 14 seconds.
O The airplane reaches its maximum height of 14 feet in 74 seconds.
O The airplane reaches its maximum height of 74 feet in 14 seconds.
9
12 13 14 15 16 17
18
Next
10 11
Answer:
The airplane reaches its maximum height of 74 feet in 14 seconds.
Step-by-step explanation:
The easiest thing to do here is to plug in the two numbers given in the answer choices. Finding the height at 14 seconds and the height after 74 seconds is straightforward from here.
h (14) = -(14-14)²+ 74
h (14) = 0 + 74
h (14) = 74
h (74) = -(74-14)² + 74
h (74) = -(60)² + 74
h (74) = -3600 + 74
h (74) = -3,526
Now, we know that a height of an airplane won't be negative, as the height below the ground cannot be reached.
because our equation includes -(t-14)², any number greater than 14 will be a larger negative than 0--setting the height to an impossible number.
{However, we add +74 feet, so our t-14 could be any number that is less than 74 when squared (after first subtracting 14 from the number). Numbers like 15, (resulting in subtracting 1 from 74), 16 (resulting in -4 from 74), 17 (74-9), 18 (74-16), 19 (74-25), 20 (74-36), 21 (74-49), 22 (74-64) are still above the minimum input}
{So, our t could be up to 22, and any number above this maximum limit, such as 23, result in a height of 0}
for example: -(23-14)² + 74
-(9)² = -81
-81 + 74 = -7
All numbers below 14, which would end in an eventual negative outcome [ -(x)² = negative if x < 0 ]
are greater than a t of 14.
-(13-14)² = -1
; showing that t = 14 is our maximum height
(remember that if you have -(x)² you get the negative version of x² [pemdas. the negative outside of the parenthesis is equivalent to multiplying the parenthesis by -1. (E)xponents comes before (M)ultiplication].)
Giovanni was playing with blocks and started with one blue triangular block and kept adding more
blocks to create the following pattern sequence:
See picture
How many blocks would he need on the 12th step of the pattern?
O 34
O 36
O 33
O 37
Blocks would he need on the 12th step of the pattern is 34.
The correct option is A
What is series?A series is the cumulative sum of a given sequence of terms.
Given:
We can write the series as follows:
1,4,7,10,13,.......
First term =1
common difference= 4-1=3
Using Arithmetic series
[tex]a_{12}\\[/tex]= a+11d
= 1 +11*3
= 1+33
= 34.
Hence, 34 blocks need on 12th step.
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A number cube is rolled. What is the probability
of rolling a number that is
less than 5 or odd?
Step-by-step explanation:
a complicated way to say "the probability to roll a number that is less or equal to 5".
and that is
5 desired cases over 6 total cases, and that means
5/6 = 0.833333333...
1.___________a representation to show the total outcomes.
Study the situation and make a listing to solve for the answer.
Brilliant Spa offers a variety of uniform styles from which they can choose. Polo shirts come with yellow, red, and green. The pants come with black, blue, and white. Using the listing methods, how many possible uniforms are there?
Make a diagram to find the total number of possible outcomes.
As an opening promo, a café offers snack combos for P250.00. The meal includes a sandwich, a pasta, and a drink. The choices are below.
Sandwiches: chicken, tuna, bacon
Pasta: carbonara, fettuccine, seafoods
Drinks: iced tea, pineapple, calamansi
By using the listing method, the number of possible uniforms that Brilliant Spa can choose from is equal to 9 uniforms.
What is a listing method?In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.
From the information provided above, we have the following points:
Polo shirts come with color yellow, red, and green. The pants come with color black, blue, and white.By using the listing method, a list of all the elements in this data set is given by:
List = {(yellow, black), (yellow, blue), (yellow, white), (red, black), (red, blue), (red, white), (green, black), (green, blue), (green, white)}
Number of possible uniforms = 9 uniforms.
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What is the domain of the function shown in this graph?
Answer:
[tex] - \infty < x < \infty [/tex]
Step-by-step explanation:
On the right hand side of the y axis, the x values will continue to increase. They will go to positive Infinity. On the left hand side of the y axis, the x values will continue to decrease, this means that they will become more negative. They will go to negative Infinity.Explain why In 4 is greater than 1 but is less than 2.
PLEASE HURRY
Answer:
whats the solution you looking at?
Step-by-step explanation:
4 can be greater than 1 by number wise but also 4 could be -4 or 4 could not add up to the full amount of w for like if you have 4 2 by 2s and 2 16 by 16s 4 would be smaller
A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
Both plans cost the same when 22 texts are sent.
Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
Both plans cost the same when 50 texts are sen
Answer:
Both plans cost the same when 50 texts are sent
Step-by-step explanation:
Both the plans cost the same amount $22.5 when 50 texts are sent:
[tex]20+0.05*50 = 10+0.25*50[/tex]✔️
Have a nice day! :)
HELP (WORTH 20 POINTS)
Answer:
1 matter
2 atoms
3 molecules
4 matter and energy
5 solid liquid and gas
6 mass
i dont know the rest to be honest
Step-by-step explanation:
Solve the rational equation:
2x 2x-5 -3 x-1 x²-3x+2 X-2
A. x= -0.47, X = -3.27 O
B. There is no solution.
C. X = -2, x = -1
D. x = 1, x = 2
The solution to the equation [tex]\frac{2x}{x - 1} - \frac{2x -5}{x^2 - 3x + 2} = \frac{-3}{x -2}[/tex] is (b) there is no solution.
How to solve the rational equation?The equation is given as:
[tex]\frac{2x}{x - 1} - \frac{2x -5}{x^2 - 3x + 2} = \frac{-3}{x -2}[/tex]
Factorize the quadratic numerator
[tex]\frac{2x}{x - 1} - \frac{2x -5}{(x - 1)(x - 2)} = \frac{-3}{x -2}[/tex]
Multiply through by (x - 1)(x - 2)
2x(x - 2) - (2x -5) = -3(x - 1)
Expand
2x² - 4x - 2x + 5 = -3x + 3
Collect like terms
2x² - 4x - 2x + 3x + 5 - 3 = 0
Evaluate the like terms
2x² - 3x + 2 = 0
Using a graphical tool, the above equation has no real solution
Hence, the solution is (b) there is no solution.
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(q-1)²
please help!! urgent!!
Answer:
[tex]q^2-2q+1[/tex]
Step-by-step explanation:
[tex](q-1)^2=(q-1)(q-1)[/tex]
Distribute: [tex]q^2-q-q+1[/tex]
Solve: [tex]q^2-2q+1[/tex]
Hope this helped! Have a great day/night! :)
Type the expression that results from the following series of steps:
Start with
y
, subtract 7, multiply by 3, then add 6.
Answer:
3y-15
Step-by-step explanation:
(y-7)3=3y-21
3y-21+6=3y-15
Find the x-intercepts of the parabola with
vertex (-3,405) and y-intercept (0,360).
Write your answer in this form: (X₁,Y₁), (X2,₂).
If necessary, round to the nearest hundredth.
Enter the correct answer.
Answer: (-12, 0) and (6, 0)
Step-by-step explanation:
The equation of the parabola is of the form
[tex]y=a(x+3)^2 + 405[/tex]. To find a, we can substitute in the coordinates (0,360).
[tex]360=a(0+3)^2 + 405\\\\360=9a+405\\\\-45=9a\\\\a=-5[/tex]
So, the equation is [tex]y=-5(x+3)^2 + 405[/tex]. Setting this equal to 0,
[tex]-5(x+3)^2 + 405=0\\\\5(x+3)^2 = 405\\\\(x+3)^2 = 81\\x+3=\pm 9\\\\x=-12, 6[/tex]
So, the x-intercepts are (-12, 0) and (6, 0).
The graph represents a person’s heart rate in beats per minute during 30 minutes of exercise.
A graph titled Cardiac Exercise. The horizontal axis shows time (minutes), numbered 3 to 30, and the vertical axis shows Heart Rate (b p m) numbered 15 to 150. The line starts at 75 b p m in 0 minutes, to 135 b p m from 6 to 25 minutes, and ends at 105 b p m at 30 minutes.
Which statement best describes the relationship between heart rate and time during exercise?
The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes.
The heart rate decreases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes.
The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.
The heart rate remains constant for 6 minutes, increases for 19 minutes, and then gradually decreases for 5 minutes.
Answer:
the heart rate increases for 6 minutes, remains constant for 19 minutes ,and then gradually decreases for 5 minutes
A school charges £5 for tickets to a show.
The school raises £x in total from ticket sales.
Write an expression for the total number of tickets sold by the school.
Answer:
x/5
Step-by-step explanation:
The revenue from sales is the product of the selling price of the ticket and the number of tickets sold.
__
If n represents the number of tickets sold, then the revenue from selling tickets for £5 each will be ...
(n)(£5) = £x
Dividing by the coefficient of n will given the number of tickets sold:
n = £x/(£5) = x/5
The number of tickets sold is x/5.
En un concurso de damas chinas hay 12 participantes, se premiaran 2 primeros lugarrs con medallas de oro y plata respectivamente. Calcula de cuantas maneras diferentes se pueden otorgar las medallas
Usando el teorema fundamental de conteo, se encuentra que 132 maneras diferentes de otorgar las medallas.
¿Qué es el teorema fundamental de conteo?Es un teorema que establece que si hay n cosas, cada una con [tex]n_1, n_2, \cdots, n_n[/tex] formas de hacer, cada cosa independiente de la otra, el número de formas en que se pueden hacer es:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
En este problema:
12 participantes pueden ganar la medalla de oro, o sea, [tex]n_1 = 12[/tex].11 participantes pueden ganar la medalla de plata, todos con excesion de lo que gano la medalla de plata, o sea, [tex]n_2 = 11[/tex].Así, el número de maneras diferentes en que se pueden otorgar las medallas es dado por:
[tex]N = n_1 \times n_2 = 12 \times 11 = 132[/tex]
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find the x
please help me asap
Sum of two interiors=Exterior
[tex]\\ \rm\Rrightarrow 39+6x+11=11x-10[/tex]
[tex]\\ \rm\Rrightarrow 6x+50=11x-10[/tex]
[tex]\\ \rm\Rrightarrow 60=5x[/tex]
[tex]\\ \rm\Rrightarrow x=12[/tex]
What is the simplest radical form of the expression? (8x5y3)2/3
The simplest radical form of the expression is [tex]\mathbf{40 ^{2/3}x^{{10}/{3}}y^2}[/tex].
What is the simplification of power indices?When we have indices in the form [tex]\mathbf{ax^{2/3}}[/tex], we are going to find the cube root of the (ax)². This can be mathematically expressed as:
[tex]\mathbf{=(\sqrt[3]{ax})^2 }[/tex]
From the given information:
[tex]\mathbf{=(8x^55y^3)^{2/3}}[/tex]
[tex]\mathbf{=(\sqrt[3]{8x^55y^3} } )^2[/tex]
[tex]\mathbf{=(\sqrt[3]{40x^5y^3} } )^2[/tex]
[tex]= (\sqrt[3]{40x^5} \times \sqrt[3]{y}^3)^2[/tex]
[tex]\mathbf{= 40 ^{2/3}x^{{5*2}/{3}}y^2}[/tex]
[tex]\mathbf{= 40 ^{2/3}x^{{10}/{3}}y^2}[/tex]
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Marco's living room is 4 meters wide and 6 meters long. He wants to install white carpet that costs $8.91 per square meter. How much will it cost to buy enough carpet for the living room?
Answer:
$213.84
Step-by-step explanation:
Think of a rectangle. In the case the length is 6 meters and the width is for meters. To be able to find the area of this rectangle, you need to multiply the length by the width. 6 multiplied by 4 is 24. In the equation it tells you that 1 square meter is $8.91, so now you are trying to figure how much 24 square meters would cost. To figure this out, you will need to multiple 24 by $8.91 giving you $213.84.
Hope this helps.
A tree casts a shadow of 20 meters when the angle of elevation of the sun is 24°
Find the height of the tree to the nearest meter.
The height of the tree is 9 meters
What is angle of elevation?This is the angle the line of sight makes with the horizontal.
Analysis:
The line of sight , the shadow length and height of tree form right angled triangle.
Let the height of tree be h
so that, tan 24 = h/20
h = 20 tan 24
h = 20(0.445) = 8.9m = 9m
In conclusion, the height of the tree is 9m.
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