The solution to simplifying the given expression using laws of exponents is; B: 1 over quantity 27 times a raised to the sixth power times b raised to the twelfth power end quantity
How to use laws of exponents?
Some of the Laws of Exponents are;
When multiplying similar bases, retain the base as same and add the exponents. When raising a base with a power raised to another one, retain the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.We want to simplify a raised to the negative two power over quantity 3 times b raised to the fourth power end quantity all cubed. This is expressed as;
(a⁻²/3b⁴)³
Using the second law of exponent quoted above, we have;
(a⁻²*³)/(3³b⁴*³) = a⁻⁶/27b¹² = 1/a⁶27b¹²
Read more about Laws of Exponents at; https://brainly.com/question/11761858
#SPJ1
or
Colleen made a scale drawing of a house. She used the scale 3 millimeters = 1 meter. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
The scale factor that the drawing use is 3/1000.
How to calculate the scale?From the information, Colleen made a scale drawing of a house and she used the scale 3 millimeters = 1 meter.
It should be noted that 1000 millimeters = 1 meter
Therefore, the scale factor that the drawing use is:
= 3 millimeters / 1 meter
= 3/1000
Learn more about scale on:
brainly.com/question/25722260
#SPJ1
What is the value of x in the equation 5 x-2=182
O-50
O-40
O-8
O-6
Answer:
Answer is 36.8
Step-by-step explanation:
There's something wrong in your question... Because...
5x-2=182
5x=182+2
5x=184
5x/5=184/5
X=36.8
(a) Determine the net change between the indicated points on the graph.
b) determine the average rate of change between the indicated points on the graph.
The net change between the indicated points is -1 and the average net change is - 0 . 75 .
The difference between the two f(x) values is the net change.
The ratio between the net change and the change between the two input values is used to calculate average net change or average rate of change. The average rate of change can be calculated using the same two points and the formula: f(b)-f(a) / b-a .
The two given points on the graph are (1,4) and (5,1)
The net change is given by the change in the y -coordinates of the graph .
Δy = y₂ - y₁
Here y₂ = 1
and y₁ = 4
Therefore Δy = y₂ - y₁ or, Δy = 1 - 4 = - 3
Hence the net change is -3 units.
Now the average net change is calculate by the change in y divided by the change in x.
average net change = Δy ÷ Δ x
again , average net change = -3 ÷ ( 5 - 1 ) = - 0 . 75
The average net change for the function is - 0 . 75
To learn more about net change visit:
https://brainly.com/question/3003259
#SPJ1
PLS HELP
explain why it uses ≈ instead of = when giving the values for pi?
what would it mean if it said that pi+22/7? How would that change how you classify pi?
Answer:
Step-by-step explanation:
It's because the latter one is not a approximation, like about, while the first one is.
Austin and Cody went to a carnival. They got to the carnival at nine minutes to nine in the morning and didn't leave until half past four in the afternoon. How long did Austin and Cody stay at the carnival?
what is m decreased by 6
Answer:
m-6
Step-by-step explanation:
this is what I think it it
Find the area between the curve
Answer:
The first option (a) is the most approximate
Step-by-step explanation:
The area results:
a = 161.91315 = 162
[tex]e^{5} =148.4[/tex]
then
[tex]14+e^{5} =14+148.4=162.4[/tex]
Hope this helps
A salesperson earns a weekly base rate of
$210 plus $50 for each sale made. Write the
equation to model the salesperson's weekly
income, y, given he makes x sales.
You find that the number of messages you receive on your message board varies directly as the numbers of messages you post. When you post 5 messages, you receive 12 messages in return. Which variation equation can be used to predict how many messages you will post in order to receive 96 messages? A y = 12/5x - 96 B y = 5/12x + 96 C y = 12/5x
Answer: C) y=12/5x
Step-by-step explanation:
Divide 12 messages by 5 posts to find out how many messages you would receive for just posting 1 message (2.4)
Then determine how many times it goes into 96 (2.4 x 40 = 96)
Which of the following is a point -slope equation of a line that passes through the points (5, 2) and (- 1, - 6) ? A. y - 2 = 4/3 * (x - 5) B. y - 2 = 3/4 * (x - 5); y - 2 = - 4/3 * (x - 5) D D . . y - 2 = - 3/4 * (x - 5)
The point slope form are as follows:
y - 2 = 4 / 3(x - 5)y + 6 = 4 / 3(x + 1)How to represent equation in point slope form?The point slope equation can be represented as follows;
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinatesTherefore, (5, 2)(-1, -6)
m = slope = -6 - 2 / -1 - 5
m = slope = -8 / - 6
m = slope = 4 / 3
Therefore, using (5, 2) the point slope form is represented as follows;
y - 2 = 4 / 3(x - 5)
using (-1, -6) the point slope form is represented as follows;
y + 6 = 4 / 3(x + 1)
learn more on point slope equation here: https://brainly.com/question/24436844
#SPJ1
The ratio of the length of a soccer field to the width of the field is 3:2. A scale drawing of a soccer field has a scale of 1 in.: 20 yds. The length of the field in the drawing is 6 inches. What is the actual width of the field?
Explain your reasoning.
The actual width of the field 80 yard. when proportion is 3 : 2.
What in mathematics is a proportion?
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
We have the proportion
3/2 = 120/w
where in the numerator are the length and in the denominators the width of the field.
Now , 3 . w = 120 . 2
3w = 240
w = 80
Therefore , the actual width of the field 80 yard.
Learn more about proportion
brainly.com/question/2548537
#SPJ9
Marley worked 16 hours more than Herold last month. If Marley worked 7 hours for every 2 hours that Herold worked, how many hours did they each work?
Total number of hours both worked last month is; 28.8 hours
How to solve Algebra Word Problems?Let the number of hours that Herold worked last month be x. Thus, number of hours that Marley worked = 16 + x
Now, we are told that Marley worked 7 hours for every 2 hours that Herold worked. Thus;
(16 + x)/x = 7/2
Cross multiply to get;
2(16 + x) = 7x
32 + 2x = 7x
7x - 2x = 32
x = 32/5
x = 6.4 hours
Thus, total hours Marley worked = 16 + 6.4 = 22.4 hours
Total number of hours both worked last month = 22.4 + 6.4 = 28.8 hours
Read more about Algebra Word Problems at; https://brainly.com/question/13818690
#SPJ1
Find the area of the shaded region. (help needed asap. thank u)
The area of shaded region is calculated as: 112.5 cm².
How to Find the Area of the Shaded Region?The area of the shaded region in the diagram above is:
Area of shaded region = area of rectangle - area of triangle = (length)(width) - 1/2(base)(height).
Given the following:
Length of rectangle = 20 cm
Width of the rectangle = 9 cm
Base of triangle = 20 - 3 - 2 = 15 cm
Height of triangle = 9 cm
Plug in the values into the equation, area = (length)(width) - 1/2(base)(height):
Area of shaded region = (20)(9) - 1/2(15)(9)
Area of shaded region = 180 - 67.5
Area of shaded region = 112.5 cm²
Learn more about the area of shaded regions on:
https://brainly.com/question/14989383
#SPJ1
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The two representations are:
x > 5
A number line with an open circle at 5 and a line that points to the right.
Which are correct representations of the inequality?
We start with the inequality:
-3(2x - 5) < 5*(2 - x)
First, we need to solve this for x, expanding both sides we get:
-6x + 15 < 10 - 5x
Now we move the terms with x to the right side and the terms without to the left side.
15 - 10 < 6x - 5x
5 < x
This is a representation of the inequality.
The other will be a graph, to graph this on a number line we need to do an open circle at x = 5, and shade the region to the right (because x is larger than 5).
If you want to learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1
A pump is being used to fill a 1400-gallon tank. After the pump has run for 2 minutes the tank contains 110 gallons of oil. After 5 minutes the tank contains 200 gallons of oil. Assume the pump fills oil at a constant rate.
(a) Write a linear model that describes the gallons of oil (G) in the tank in terms of the time (t) since the pump was started.
(b) How much oil is in the tank after the pump has been running for 13 minutes?
(c) At what time, will there be 890 gallons of oil in the tank?
(d) What is the t-intercept for this equation? What does it represent in terms of the situation?
Answer:
See below
Step-by-step explanation:
From 2 minutes to 5 minutes the pump puts in (200-110) = 90 gallons ...in 3 minutes....so the rate of the pump is 30 gal / min
at two minutes the pump has put in 30 x 2 = 60 gallons......so there was 50 gallons in the tank to start ( 50 + 60 = 110)
the equation becomes :
G = 50 + 30 t
where t = minutes
and 50 is the initial volume in the tank
For 13 minutes G = 50 + 30 (13) = 440 gallons
For 890 gallons 890 = 50 + 30 t
840 = 30 t
t = 28 minutes
t intercept occurs when G = 0
0 = 50 + 30 t
t = - 5/3 minute <====this is the amount of time before measurements were taken.....or the time for the pump put in 50 gallons before the start
A student ran a distance of 3 miles each day for 5 days. Then the student ran a distance of 4 miles each day for the next 5 days. What was the total distance in miles the student ran during these 10 days?
A 23 mi
B 38 mi
C 42 mi
D 35 mi
Given ^MTW=^BGK, find the valued of x and y
Answer:
m×w plus x times x and the then 41 times Square 2 minus k
Step-by-step explanation:
x and y compkety le diff so w n m 41 than times b and g equivalent to 24 so asneer 24 negative
How can a number be a power of 10
Answer:
An exponent is often referred to as a power of 10, for instance, [tex]\sf 6\boxed{^7}[/tex], as the exponent is highlighted. A number can only become a power of 10 under certain circumstances in an expression, on the other hand, you have exponents alone in expressions like "45² + x", the exponent was assigned to a number and that means that we multiply that number by itself that number of times. Logically speaking, it's impossible for a number alone to be a power of 10 or to become one out of the blue, a power of 10 is assigned into an expression and before a whole number before you start working on it, which is the equation.
I hope that answered your question as much as possible, notify me of any concerns.
Answer:
Well:
Step-by-step explanation:
When it has a little 10 on the top of a number. like 7 with a little 10 in the corner. :]
Can u please help me make an essay with introduction, body, conclusion
How does mathematics play in your world?
Answer:
Mathematics is a fundamental part of human thought and logic, and integral to attempts at understanding the world and ourselves. Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art.
Step-by-step explanation:
if you need more I can help with that
The point J(5,3) is rotated 90° counterclockwise around the origin. What are the coordinates of the resulting point, J^?
If the point J (5,3) is rotated 90° counterclockwise around the origin, then the coordinates of the resulting point J' will be (-3, 5).
As per the question statement, a point J (5,3) is rotated 90° counterclockwise around the origin.
We are required to determine the coordinates of the resulting point J'.
To solve this question, we need to follow a rule of cartesian coordinate geometry which is, "If a point (x, y) is rotated 90° counterclockwise around the origin, then the coordinates of the new point lie on (y, -x).
Here, Coordinates of the original point (J) are (5, 3), i.e.,
(x = 5) and (y = 3).
Therefore, Coordinates of the resulting point (J') after J (5,3) is rotated 90° counterclockwise around the origin will be:
[x' = (y) = 5] and [y' = (-x) = (-3)], or, (-3, 5).
Coordinates: These are a pair of numbers that describe the exact position of a point on a coordinate plane, by using the horizontal and vertical distances from the two reference axes.To learn more about Cartesian Coordinates, click on the link below.
https://brainly.com/question/27749090
#SPJ1
What is the value of x?
X
II
m< BAE
11
m
m
E
4
B
2x 76°
U
D
Identify the type of conic given. x^2 - 6x + 7y - 33 = 0
What are the steps to turn it into standard form?
The standard form for the Parabola is given as
[tex]y=-\frac{1}{7} x^2+\frac{6}{7} x+\frac{33}{7}[/tex]
This is further explained below.
What are the steps to turn it into standard form?Generally, the equation for is mathematically given as
x^2-6 x+7 y-33=0
Solve for y.
Move all terms not containing y to the right side of the equation.
7 y=-x^2+6 x+33
Divide each term into 7 y=-x^2+6 x+33 by 7 and simplify.
[tex]y=-\frac{x^2}{7}+\frac{6 x}{7}+\frac{33}{7}[/tex]
To write a polynomial in standard form, simplify and then arrange the terms in descending order.
y=a x^2+b x+c
Reorder terms.
[tex]y=-\left(\frac{1}{7} x^2\right)+\frac{6}{7} x+\frac{33}{7}[/tex]
[tex]y=-\frac{1}{7} x^2+\frac{6}{7} x+\frac{33}{7}[/tex]
Read more about the standard form
https://brainly.com/question/17264364
#SPJ1
and for d i put d, pls let me know xx
write a equation for the situation please
Step-by-step explanation:
let Irene's share be x and Charlie's share be y
x=2y-8
x+y=$47.50
x=$47.50-y
$47.50-y=2y-$8
$47.50+$8=2y+y
$55.50=3y
y=$55.50/3
y=$18.50
x=$47.50-$18.50
x=$29
Answer:
Irene's share = 29
Charlie's share = 18.5
Step-by-step explanation:
R bill = 47.5
Irene's share = (2 × Charlie's share )-8
Irene's share = y
Charlie's share = x
bill = x + y = 47.5
y = 2x -8
x + 2x - 8 = 47.5
3x = 47.5 + 8= 55.5
x = 18.5
y = 29
Rewrite using distributed property:
6a+21
Answer:
3(2a+7)
You find the common multiple and then distribute.
A developer is considering buying a triangular plot of land represented by the shaded figure below.
180 yd
550 yd
What is the total area of the land?
O 365 yd²
O 730 yd²
O 49,500 yd²
O99,000 yd²
The total area of the land that the developer is considering to buy is 49,500 yards².
We are given a triangular plot of land having the dimensions as:
Base = b = 550 yards
Height = h = 180 yards.
We need to find the area occupied by the triangular plot.
Area of a triangle refers to the space occupied by the shape or object.
Area = 1 / 2 × b × h
Substituting the values in the formula, we get that:
Area = 1 / 2 × 550 yards × 180 yards
Area = 550 yards × 90 yards
Area = 49,500 yards²
Therefore, we get that, the total area of the land that the developer is considering to buy is 49,500 yards².
Learn more about area here:
https://brainly.com/question/25292087
#SPJ9
Answer:
C. 49,500 yd2
Step-by-step explanation:
good luck
how is it possible that the formula for the area of a rectangle and the formula for tge area of a parallelogram are both base time?
Step-by-step explanation:
This is due to the fact that a parallelogram consists of both a triangle and rectangle .
The base of a parallelogram is rectangular
6( 3 + 5 ) 2 - 9a evaluate the expression when a = 3 and b = 5
The value of the expression 6( 3 + 5 ) 2 - 9a when a = 3 is 69
In this question,
we have been given an expression 6( 3 + 5 ) 2 - 9a
We need to evaluate given expression when a = 3 and b = 5
We substitute a = 3 in given expression and solve it.
6( 3 + 5 ) 2 - 9a ..........(given expression)
= 6( 3 + 5 ) 2 - 9(3) ..........(substitute a = 3)
= 6(8) 2 - 27
= 96 - 27
= 69
Therefore, the value of the expression 6( 3 + 5 ) 2 - 9a when a = 3 is 69
Learn more about an expression here:
https://brainly.com/question/14961928
#SPJ1
The table shows the linear relationship between the playing time in minutes of high-definition videos and the file size of these videos in megabytes (MB) What is the rate of change of this function?
180
60
120
30
the rate of change of the linear equation in the table is 120.
How to get the rate of change of the linear equation?
Remember that for any linear equation with an slope (also called rate of change) s and it passes through the points (a, b) and (c, d), then the slope can be written as:
s = (d - b)/(c - a)
Using that relation and the first two points on the table (0.5, 60) and (1.5, 180)
We get that the rate of change is:
s = (180 - 60)/(1.5 - 0.5) = 120
So the rate of change is 120.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
A zookeeper records the number of male and female penguins born in a particular year. 45% of the penguins are male, and 55% are female. 20% of the time, male penguins are born with red eyes, and 30% of the time, females are born with red eyes. The zookeeper created this diagram to represent the number of male and female penguins. How many blue squares should be shaded to represent the male penguins with red eyes?
9 squares should be shaded to represent the male penguins with red eyes.
What is percentage?Percentage is a fraction or a ratio in which the value of whole is always 100.
Given:
45% of the penguins are male, and 55% are female.
20% of the time, male penguins are born with red eyes,
and 30% of the time, females are born with red eyes.
To find the squares should be shaded to represent the male penguins with red eyes we have to perform the following step
20% of 45
=0.2* 45
=9
Hence, 9 squares should be shaded to represent the male penguins with red eyes.
Learn more about percentage here:
https://brainly.com/question/13244100
#SPJ1
Answer:
9 blue squares should be shaded
Step-by-step explanation:
20% of 45 = 9