Select the correct answer.
Simplify the expression.
1³/32r5y3
214/2ry³ 3
2x4 √4xy³
2rty 4ry³
413/21²y3
The simplification of the indices can be seen in the explanation below.
[tex]\mathbf{= \dfrac{1^3}{32r^5y^3}}[/tex]
What is the simplification of indices?The simplification of indices entails simplifying the indices to the simplest form possible by using the laws of indices.
From the information given, we have:
1.
[tex]\mathbf{= \dfrac{1^3}{32r^5y^3}}[/tex]
2.
[tex]\mathbf{= \dfrac{214}{2ry^3}}\\[/tex]
[tex]\mathbf{=\dfrac{ 107}{ry^3}}[/tex]
3.
= 2×4 √4xy³
= 8 √4xy³
= 8 × 2√xy³
= 16√xy³
4.
= 2rty 4ry³
= 2tr²y⁴
5
= 413/21²y³
= 413/441 y³
Learn more about methods used in simplifying indices here:
https://brainly.com/question/170984
#SPJ1
Answer:
1.
2.
3.
= 2×4 √4xy³
= 8 √4xy³
= 8 × 2√xy³
= 16√xy³
4.
= 2rty 4ry³
= 2tr²y⁴
5
= 413/21²y³
= 413/441 y³
Step-by-step explanation:
Graph the inequality y ≤-3x - 3.
Answer: [tex]y\leq -3x-3[/tex] [tex]< --Graph[/tex]
In order to graph the equation "y ≤-3x - 3", we need to graph the inequality by finding the boundary line, then shading the appropriate area.
Help me please
calculate the value of x in the polygon
Answer:
122.5 degrees
Step-by-step explanation:
A six sided polygon's interior angles sum to
(n-2)(180) = (6-2) (180) = 720 degrees
then x + x + x + x+10 + 130 + 90 = 720
4x = 490 so x = 122.5 degrees
X-7/20=5/16 solve for x
x = 53/80 = 0.6625
if isn't right I have another equation
Answer:
13.25
Step-by-step explanation:
[tex]x - 7 \div 20 = 5 \div 16[/tex]
by cross multiplying
16(x-7)=5(20)
16x-112=100
16x=100+112
16x=212
x=212 /16
×=13.25
if the question is this
A job applicant estimates that his chance of passing a qualifying examination is , and his chance of being appointed if he does pass is . what is the probability that he will receive the job?
The probability that he will receive the job will be 1 / 6
The complete question is given below:-
A job applicant estimates that his chance of passing a qualifying examination is 2/3, and his chance of being appointed if he does pass is 1/4. What is the probability that he will receive the job?
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
It is given that:
The chance of passing a qualifying examination is 2/3=P
and chance of being appointed, if he does pass, is 1/4=P'
Now, we are asked to find the probability that he will receive the job.
We are asked to find the probability that he will receive the job.
The probability is calculated as The probability that he qualify the exam×Probability that he is being appointed.
=P×P'
=(2/3)×(1/4)
=1/6
Therefore the probability that he will receive the job will be 1 / 6
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
Using the graph, determine the coordinates of the y-intercept of the parabola.
Answer:
(0, -5)
Step-by-step explanation:
the y-intercept of the parabola is when x = 0 (crossing the y axis)
the lines y= 2x+4 and y=x-3 intersect. find the coordinates of the point of intersection
Answer:
(-7, -10)
Step-by-step explanation:
Solve for x and y in double variable equation
y = 2x + 4
y = x - 3
y = x - 3, plug in to first equation
x - 3 = 2x + 4
x = -7
y = -7 - 3
y = -10
(-7, -10)
A metronome is a device that ticks at adjustable intervals to help keep time when playing music. the metronome on ryan’s piano has the basic shape below. a square pyramid. the base is 9 centimeters by 9 centimeters. the triangular sides have a base of 9 centimeters and height of 20.5 centimeters. the pyramid has a height of 20 centimeters. if the metronome was created out of a piece of solid wood, what is the minimum amount of solid wood that was used? 369 centimeters cubed 450 centimeters cubed 540 centimeters cubed 810 centimeters cubed
When the metronome was created out of a piece of solid wood, the minimum amount of solid wood that was used from the pyramid will be C. 540 centimeters cubed.
How to calculate the pyramid?From the information given, the metronome ticks at adjustable intervals to help keep time when playing music.
In rhis case, when the metronome was created out of a piece of solid wood, the minimum amount of solid wood that was used from the pyramid will be:
= 20 × 9 × ✓9
= 20 × 9 × 3
= 540
Learn more about pyramid on:
https://brainly.com/question/218706
#SPJ4
Answer:
540
Step-by-step explanation:
C
A rectangular piece of paper with length 32 cm and width 14 cm has two semicircles cut out of it, as shown below.
Find the area of the paper that remains. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer
Answer:
Step-by-step explanation:
Which is the graph of a logarithmic function?
5
4
3-
2
1
-2-1₁
1 2 3 4 5 6 7 8 x
-2
-3
-4
fin
5
For this exercise, the graph of a logarithmic function is shown in the image attached below.
What is a logarithmic function?A logarithmic function is a type of function that graphically represents the inverse of an exponential function. Mathematically, a standard logarithmic function is written as [tex]y = log_nx[/tex].
In Mathematics, the domain of any logarithmic function is from (x > 0) to infinity (+∞). Thus, its graph moves to the right on the vertical axis and it increases to infinity (+∞) as the value of x increases.
In this scenario, an image of all the graphs wasn't provided, so, I would proceed to add an attachment to illustrate the graph of a logarithmic function.
Note: The graph (u-shaped) shown in the image attached above is that of a parabolic function.
Read more on logarithmic function here: https://brainly.com/question/26788007
#SPJ1
The ratio of ann's age to bob's age is 3:4
in 7 years time this ratio will be 4:5
0) what are their ages now?
(1) after how many years (from now)
will the ratio be 5:6?
Ann and Bob's age is 21 years and 28 years respectively and after 14 years the ratio will be 5:6.
What is Ratio ?
The comparison of one quantity to other is called a ratio and when two ratios are equal they are said to be in proportion.
It is given in the question that
The ratio of Ann's age to bob's age is 3:4
in 7 years time this ratio will be 4:5
their ages now = ?
Let the age of Ann and Bob is x and y
x:y = 3:4
x =(3/4)y
After seven years
(x+7):(y+7) = 4 :5
(x+7)/(y+7) = 4/5
((3/4)y +7)/(y+7) = 4/5
(3y +28)/(y+7) = 16/5
5*(3y+28)= 16(y+7)
15y +140 = 16y+112
y = 140-112
y =28 years
x = 21 years.
After x years suppose the ratio is 5 :6
(21+x)/(28+x) = 5:6
126 +6x = 140 + 5x
x = 14 years.
Therefore after 14 years the ratio will be 5:6.
To know more about Ratio
https://brainly.com/question/13419413
#SPJ1
3. The table shows the production results for three factories. How many cars are manufactured at the fastest factory in one year?
A. 12,000
B. 13,500
C. 16,200
D. 22,000
Consider the given quadratic equations. Equations function it defines. Equation A y= 3x² - 6x + 21 Equation B y=3x² - 6x + 18 Equation C y= 3(x-1)2 +18 Equation Dy=3(x-1)² +21 Complete the following statement. equation. are equivalent , and of those, equation. is in the form most useful for identifying the extreme value of the function it define
Equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it defines.
Evaluation of the quadratic expressions
The quadratic expressions can be simplified as follows;
Equation A: y = 3x² - 6x + 21Equation C: y = 3(x - 1)² + 18Equation C is simplified as follows;
y = 3(x - 1)² + 18
y = 3(x² - 2x + 1) + 18
y = 3x² - 6x + 3 + 18
y = 3x² - 6x + 21
Thus, equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it defines.
Learn more about quadratic equations here: https://brainly.com/question/1214333
#SPJ1
use the information given to answer the question. write your answer as a decimal rounded to the nearest tenth
Answer: The value of x is 3.5
Explanation:
Equation:
y = 2x - 7
When the equation's Line intersects the x-axis, the value of y shall be always 0
Insert y = 0, to find x intercept
⇒ 0 = 2x - 7
⇒ 2x - 7 = 0
⇒ 2x = 7
⇒ x = 3.5
So coordinates: (x, y) → (3.5, 0)
What is the area of the triangle below?
On a coordinate plane, a triangle has a base of 6 units and a height of 9 units.
27 square units
45 square units
54 square units
90 square units
Answer:
27 units
Step-by-step explanation:
6 (base) × 9 (height) = 54
54 × 1/2 = 27
A neutron star has a density of about kg/m3. what would be the approximate mass of a 1-centimeter cube (a cube 1 cm on all sides)? kg (1.3 quadrillion pounds) kg (1.3 trillion pounds) kg (1300 trillion pounds) kg (1.3 billion pounds)
Answer:
Step-by-step explanation:
5.9 1014 kg (1300 trillion pounds)
5.9 108 kg (1.3 billion pounds)
5.9 1017 kg (1.3 quadrillion pounds)
5.9 1011 kg (1.3 trillion pounds)
those are the options
A function k whose domain is the set of positive integers is defined as k(1) = 4 and k(n) =
k(n - 1) - 2
Function k was evaluated for several numbers. Which of the following are true?
Select each correct answer.
k(2)=
k(1)-24-22Option C is true
k(3)
k(2)-22-20D is true
k(4)
k(3)-2=0-2=-2k(5)
-2-2-4k(6)
-4-2-6E is not true
k(1)
k(0)-2So
k(0)-2=4k(0)=6B is false
Similarly
k(-1)-2=k(0)=6k(-1)=8-1 is not in domain even though
A is false
Only C and D are trueAnswer:
[tex]k(2) = 2[/tex]
[tex]k(3) = 0[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}k(1)=4\\k(n)=k(n-1)-2\end{cases}[/tex]
The function [tex]k(n)[/tex] tells us that each term is 2 less than the preceding term.
Therefore:
[tex]\implies k(1)=4[/tex]
[tex]\implies k(2)=k(1)-2=4-2=2[/tex]
[tex]\implies k(3)=k(2)-2=2-2=0[/tex]
[tex]\implies k(4)=k(3)-2=0-2=-2[/tex]
[tex]\implies k(5)=k(4)-2=-2-2=-4[/tex]
[tex]\implies k(6)=k(5)-2=-4-2=-6[/tex]
Rearranging the formula to make the preceding term the subject:
[tex]\begin{aligned} k(n) & = k(n-1) - 2\\\implies k(n)+2 & = k(n-1)\\k(n-1) & =k(n)+2\end{aligned}[/tex]
Therefore:
[tex]\implies k(1)=4[/tex]
[tex]\implies k(0)=k(1)+2=4+2=6[/tex]
[tex]\implies k(-1)=k(0)+2=6+2=8[/tex]
Conclusion
Therefore, the correct answers from the answer options are:
[tex]k(2) = 2[/tex] and [tex]k(3) = 0[/tex]
Determine, which is the shorter path from A to B is: Around the two small semi circles or around the large semi-circle? Verify your answer by calculating the length of the path in each case.
Aurelio is purchasing carpet tiles to cover an area of
his living room floor that is 8 feet wide by 10 feet
long. each carpet tile is a square 20 inches wide by
20 inches long. what is the minimum number of carpet
tiles that aurelio must purchase to cover this area of
his living room floor?
a. 5
b. 11
c. 21
d. 30
e. 84
Answer:d.33
Step-by-step explanation: To begin we convert his living room floor length and width to inches. 8 1 slash 3 feet = 100 inches
10feet= 120 inches
hence the area in square inches of the living room floor is 100 inches times120 inches = 12000 inches squared.
Each carpet tile has an area of 20 by 20 which = 400inches squared. dividing the area of the living room by 400inches of each carpet tile, would yield 30 carpet tiles needed to cover this area.
As per linear equation, the minimum number of carpet tiles that Aurelio must purchase to cover the area of his living room floor is 29.
What is a linear equation?A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.
Given, the room has a length of 10 feet = 12 × 10 inches = 120 inches
The width of the room is = 8 feet = 12 × 8 inches = 96 inches
Therefore, the area of the room is
= 120 × 96 square inches
= 11520 square inches
Length of each carpet tile is 20 inches
Width of each carpet tile is 20 inches
Therefore, the area of each tile is
= (20)² square inches
= 400 square inches
The number of tiles require
= (11520/400)
= 28.8
≈ 29
Therefore, 29 tiles will be required.
Learn more about linear equation here: https://brainly.com/question/13841284
#SPJ3
A circle is divided into 9 equal parts what is the angle measure of one of those parts?
Answer: 40°
40 * 9 =360° Each part has 40° angle
how many pattern block trapezoids would create 4 hexagons?
Answer:
8
Step-by-step explanation:
2 pattern block trapezoids makes one hexagon
There are 4 hexagons so you have to multiply 2 by 4
you get 8
8 is your answer
John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the
function v= 20,000(0.84), where t is the number of years from the time of purchase. One of the factors John is using to make his decision is
the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this
context?
The reasonable domain of the function is [0,4)
How to determine the domain?The function of the car value is given as:
V(x) = 20000 * (0.84)^x
When the car reaches half its value, we have:
V(x) = 10000
Substitute V(x) = 10000 in V(x) = 20000 * (0.84)^x
10000 = 20000 * (0.84)^x
Divide both sides by 20000
0.84^x = 0.5
Take the logarithm of both sides
x log(0.84) = log(0.5)
Divide both sides by log(0.84)
x = 4
This means that the maximum value of x is 4
Hence, the reasonable domain of the function is [0,4)
Read more about domain at:
https://brainly.com/question/1770447
#SPJ1
Please how to answer.
Answer:
Blue Rectangle: 135 mm²
Blue Triangle: 45 mm²
Not sure if you need this but the Total Square: 225 mm²
Step-by-step explanation:
Area of a rectangle: length x width
Area of a triangle: [tex]\frac{1}{2}[/tex] x base x height
First find the area of the blue rectangle.
Length = 15 mm
Width = 9 mm
Area = 135 mm²
Now find the area of the blue triangle:
Base = 6 mm (because the bottom is 15 total and you subtract the 9)
Height = 15 mm
Area = 45 mm²
Hope it helps!
Peppers are sold in packs of 3 for $111,or in individual for $29 which is the best value
which of thse numbers 516090,221640,814550 are divisible byy 4
The degree of the polynomial 10x² + 2xy-4y is 3. What is the value of m?
A.1
B.2
C.3
D. 4
If the degree of the polynomial is 3. Then the value of m will be 2. Then the correct option is B.
The complete question is attached below.
What is the degree of the polynomial?Let the polynomial is given below.
axⁿ + bxⁿ⁻¹ + .... + kx¹ + lx⁰
Then the highest power of the polynomial is known as the degree of the polynomial.
The polynomial is given as
[tex]\rm 10x^2 + 2x^my-4y[/tex]
The degree of the polynomial is 3. Then the value of m will be
m + 1 = 3
m = 2
Then the correct option is B.
More about the degree of the polynomial link is given below.
https://brainly.com/question/2284746
#SPJ1
It is the middle of the heatwave, and you AC unit has broken. You have 2 companies that come highly qualified. Company A charges $200 to come out plus $50 per hour to look at your AC and determine what is wrong. Company B charges $125 plus $75 an hour for the same exact service.
After how many hours (x) will both companies charge you the same amount(y)?
By solving a linear equation, we will see that after 3 hours, both companies will charge the same amount.
After how many hours will both companies charge you the same amount?
We know that company A charges $200 plus $50 per hour. So if they work for x hours, they charge:
A(x) = $200 + $50*x
And company B charges $125 plus $75 per hour, so if they work for x hours, they charge:
B(x) = $125 + $75*x
We want to find the value of x such that A(x) = B(x), then we want to solve the linear equation:
$200 + $50*x = $125 + $75*x
$200 - $125 = $75*x - $50*x
$75 = $25*x
$75/$25 = x = 3
This means that after 3 hours, both companies will charge the same amount.
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. the table used to place bets contains 38 numbers, and each number is assigned to a color and a range. what is the probability of winning when betting on two lines that touch each other on the table as in 1-2-3-4-5-6?
The probability of winning when betting on two lines that touch each other on the table is 6/38
How to determine the probability?The sample size is given as:
n = 38
The numbers on the range 1-2-3-4-5-6 is:
Range = 6
So, the probability is calculated as:
P = Range/n
This gives
P = 6/38
Hence, the probability of winning is 6/38
Read more about probability at:
https://brainly.com/question/251701
#SPJ4
Can somebody help me solve this inequality it’s kinda hard for me to solve
Answer:
54 chickens
Step-by-step explanation:
This problem requires you find the area of Thomas's field, then use that area to find the number of chickens he can keep. The irregularly-shaped field can be considered as composed of shapes that you know how to find the area of.
__
field areaThere are many ways the area can be divided. One of them is shown in the attachment. That shows the area to be the sum of the areas of a triangle and a trapezoid.
The triangle has a base of 20 m and a height of 7 m, so an area of ...
A = 1/2bh
A = 1/2(20 m)(7 m) = 70 m²
The trapezoid has bases of 11 m and 18 m, and a height of 14 m. Its area is ...
A = 1/2(b1 +b2)h
A = 1/2(11 m +18 m)(14 m) = 1/2(29 m)(14 m) = 203 m²
The area of the field is the sum of these areas:
field area = triangle area + trapezoid area
field area = 70 m² +203 m² = 273 m²
__
chickensEach chicken requires an area of 5 m², so the total area for n chickens is ...
area for n chickens = 5n . . . . square meters
This area cannot exceed the area of the field, so an inequality can be written:
area for n chickens ≤ field area
5n ≤ 273
n ≤ 54.6 . . . . . . divide by 5
Thomas can keep a maximum of 54 chickens in the field.
please help please help please help please help please help please help please help please help please help please help please help please help please help please help