Answer:
We conclude that:
[tex]\sqrt{\left(-81\right)x^2}=9ix[/tex]
Step-by-step explanation:
Given the radical expression
[tex]\sqrt{\left(-81\right)x^2}[/tex]
simplifying the expression
[tex]\sqrt{\left(-81\right)x^2}[/tex]
Remove parentheses: (-a) = -a
[tex]\sqrt{\left(-81\right)x^2}=\sqrt{-81x^2}[/tex]
Apply radical rule: [tex]\sqrt{-a}=\sqrt{-1}\sqrt{a},\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]=\sqrt{-1}\sqrt{81x^2}[/tex]
Apply imaginary number rule: [tex]\sqrt{-1}=i[/tex]
[tex]=i\sqrt{81x^2}[/tex]
Apply radical rule: [tex]\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0[/tex]
[tex]=\sqrt{81}i\sqrt{x^2}[/tex]
[tex]=9i\sqrt{x^2}[/tex]
Apply radical rule: [tex]\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]=9ix[/tex]
Therefore, we conclude that:
[tex]\sqrt{\left(-81\right)x^2}=9ix[/tex]
Which is the correct equation for a line that has a slope of 2 and passes through the point (-1, -5). Use the graph below or graph paper if needed.
PLEASE HELP ASAP
A.y = 2x - 5
B.y = 2x + 5
C.y = 2x - 3
D.y = 2x + 3
9514 1404 393
Answer:
C. y = 2x - 3
Step-by-step explanation:
The y-intercept (b) can be found from ...
y = mx + b
y - mx = b . . . . . subtract mx
Here, you are given (x, y) = (-1, -5) and slope m = 2.
b = -5 -2(-1) = -5+2 = -3
The correct equation is ...
y = 2x -3 . . . . . matches choice C
_____
On the graph, you can plot point (-1, -5) left of the y-axis 1 unit and down from the x-axis 5 units. The slope of 2 tells you the line will rise 2 units from there to a y-value of -3 when it runs 1 unit to the right to an x-value of 0. That point (0, -3) is the y-intercept, showing you that choice C is correct.
A cylinder has a height of 14 centimeters and a radius of 17 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Volume = [tex] \sf{\pi r^2 h} [/tex]
[tex] = \sf{3.14 \times {17}^{2} \times 14 } = \sf{12704.45~cm^3} [/tex]
Enry can make 8 cupcakes (the y value) with one cup of flour (the x value). How many cupcakes can he make with 7 cups of flour?
Answer: 8x7=56 so 56
Step-by-step explanation:
Helpeoepeoeoeo show work
IMPORTANT THIGNS TO REMEMBER:
Has 20 lb. dog food!Gives dog 1 3/5 everyday!Find how much eaten after 2 days!Find how much is left!ANSWER:
Dog has eaten 3 1/5 after 2 days!
There is 16 4/5 left in bag!
EXPLANATION:
Since she gives 1 3/5 to her dog everyday and their asking for 2 days you would multiply 1 3/5 × 2 OR add 1 3/5 + 1 3/5
Which would give you 3 1/5
So, the dog has eaten 3 1/5 lb. of dog food in 2 days.
However then, you would subtract 20 lb. - 3 1/5 lb. because there is 20 lb. dog food in all and the dog has eaten 3 1/5 of it. This would give you 16 4/5 lb.
Meaning there is 16 4/5 lb. left in the bag of dog food!
Determine which function(s) are exponential. Select all that apply.
Answer:
option B and option C represent an exponential function.
Step-by-step explanation:
We know that following are some of the properties of different functions.
Linear Function:
The constant change in x and y
Quadratic Function:
The constant change in x
The constant 2nd differences in y
Exponential Function:
The constant change in x
The constant ratio in y
Determining the nature of the exponential function
Option A)
x 0 1 2 3 4
y 0 1 4 9 16
Here:
There is a constant change in x:
1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1
BUT, there is NO CONSTANT ratio, as
1/0 = ∞, 4/1 = 4, 9/4 ; 16/9
Thus,
Table A DOES NOT represents an exponential function.
Option B)
x 0 1 2 3 4
y 1/3 1 3 9 27
Here:
There is a constant change in x:
1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1
There is also a constant ratio, as
1/[1/3] = 3, 3/1 = 3, 9/3 = 3; 27/9 = 3
As there is constant change in x as well a constant ratio.
Thus,
Table B REPRESENTS an exponential function.
Option C)
x 0 1 2 3 4
y 5 5/2 5/4 5/8 5/16
Here:
There is a constant change in x:
1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1
There is also a constant ratio, as
[5/2]/5= 1/2,
[5/4]/[5/2] = 1/2
[5/8]/[5/4] = 1/2
[5/16]/[5/8] = 1/2
As there is constant change in x as well a constant ratio.
Thus,
Table C REPRESENTS an exponential function.
Option D)
x 0 1 2 3 4
y 4.5 4 3.5 3 2.5
Here:
There is a constant change in x:
1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1
BUT, there is NO CONSTANT ratio, as
4/4.5 = 4/[45/10] = 40/45 = 8/9
3.5/4 = [35/10]/4 = 35/40 = 7/8
3/3.5 = 3/[35/10] = 30/35 = 6/7
2.5/3 = [25/10]/3 = 25/30 = 5/6
Table D DOES NOT represent an exponential function.
Conclusion:
Therefore, option B and option C represent an exponential function.
The functions that are exponential would be:
B). [tex]x[/tex] 0 1 2 3 4
[tex]y[/tex] 1/3 1 3 9 27
C). [tex]x[/tex] 0 1 2 3 4
[tex]y[/tex] 5 5/2 5/4 5/8 5/16
What are Exponential Functions?
B). Given that,
[tex]x[/tex] 0 1 2 3 4
[tex]y[/tex] 1/3 1 3 9 27
As we see,
The value of [tex]x[/tex] undergoes a constant change of 1
[tex]1 - 0 = 1; \\2 - 1 = 1; \\3 - 2 = 1; \\4 - 3 = 1[/tex]
The ratio also remains constant
[tex]1/[1/3] = 3, \\3/1 = 3, \\9/3 = 3; \\27/9 = 3[/tex]
Thus, it exemplifies an exponential function.
Similarly,
C). [tex]x[/tex] 0 1 2 3 4
[tex]y[/tex] 5 5/2 5/4 5/8 5/16
As we see,
The value of [tex]x[/tex] undergoes a constant change of 1
[tex]1 - 0 = 1; \\2 - 1 = 1; \\3 - 2 = 1; \\4 - 3 = 1[/tex]
The ratio also remains constant
[tex][5/2]/5= 1/2\\\\[5/4]/[5/2] = 1/2\\\\[5/8]/[5/4] = 1/2\\\\[5/16]/[5/8] = 1/2[/tex]
Thus, it exemplifies an exponential function.
Thus, options B and C are the correct answers as the other two have a constant change but not a constant ratio.
Learn more about "exponential function" here:
brainly.com/question/15352175
What is the equation of the function that is graphed as line a?
Answer:
b
Step-by-step explanation:
help pleaseeee!!!!!! 30 points
Answer:
Pen = y
25.00 + y
Step-by-step explanation:
expressions do not have equal signs.
25 more than the pen is 25 + y
the expression would be
25 + y
Answer:
we will say that x stands for the pen
x + $25 = cost of the pencil
Step-by-step explanation:
Triangle EFG is dilated with a scale factor of 1/2 to create triangle E'F'G'.
The measure of angle G is 42 degrees. What is the measure of angle G'? *
a)21
b)42
c)84
d)148
4) Justin had 32 coins in nickels and quarters. He had 8 more quarters than nickels. How many of
each type of coin did he have?
how do I do this problem I'm doing test corrections and I have no idea how to do it
Answer:
i think its 3 but dont quote me
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
9 can help in completing square formula
10,295 - 3,429 = N
N = ?
Answer:
The Answer is 6,866
what is the slope of a line parallel to y = 4/3x-2
I'm not that sure but I want to help
Step-by-step explanation:
y=4/3×-2
y=2/3×
Divide 2/3×
Pls help I don’t get it
Answer:
Rotation 90 degrees counter clockwise, dilation of 6, translation down
Step-by-step explanation:
Greg and Carl work at neighborhood car wash facilities and are paid daily. Greg is paid $25 a day plus $7 for each car he washes. Carl earns the same amount per car washed, but his total earnings in a day are always $6 more than Greg's. Which equation expresses the total amount, t, that Carl earns, as a function of the cars he washes, c?
A)t=19+7c
B)t=25+7c
C)t=31+7c
D)t=25+13c
Answer:
Answer: It's easy, compare the same answers.
Step-by-step explanation:
A. 19+7= 16
B. 25+7= 32
C. 31+7= 38
D. 25+13= 38
what’s 35 divide by 4?
Answer:
Step-by-step explanation:
35/4 = 8.75 or 8 3/4
The first person to answer correctly I will give them a brainlies, 5 stars, and a thank you!
Which process in photosynthesis uses energy from the sun?(1 point)
1. splitting water into hydrogen and oxygen
2. combining carbon dioxide and hydrogen
3. absorbing carbon dioxide
4. releasing oxygen
Answer:
1. splitting water into hydrogen and oxygen
Step-by-step explanation:
Answer:
Photosynthesis takes place in two stages: the light-dependent reactions and the Calvin cycle. In the light-dependent reactions, which take place at the thylakoid membrane, chlorophyll absorbs energy from sunlight and then converts it into chemical energy with the use of water.
Step-by-step explanation:
can u pls go answer my question? Thank you and have a nice day :)
https://brainly.com/question/21589806
HELP ME ASAPPP
Write the standard equation of a circle with center (2, 1) and radius 8.
Answer:
C
=
(
a
,
b
)
the center coordinates of circle
a
=
2
,
b
=
−
1
,
r
=
8
Step-by-step explanation:
1) a mass of 300kg is increased by 8%.
workout the increase in mass
2) nelson scores 27 out of 40 in a test
work out his score as a percentage
Answer:
1. 324kg
2. 67.5%
Step-by-step explanation:
1. % increase = 100 + 8 = 108%
[tex]\frac{108}{100} x 300[/tex]
= 324kg
2. [tex]\frac{27}{40} x 100[/tex]
= 67.5%
What is the value of x that makes the number sentence true? x + (-5) = -5
What is the area of the trapezoid?
6 m
4 m
5 m
3 m
square meters
Part A:
Sheronda uses 1 3/4 cups of sugar in every batch of homemade muffins she makes. One day, while making muffins for her son's bake sale, she used 19 1/4 cups of sugar in all. How many batches of muffins did she make?
A)34
B)19
C)13
D)11
if in a parallelogram diagonals bisect each other at right angle and are equal then it is a ___________
14. Shawn usually sells umbrellas for $20. On rainy days, he sells them for
30% more. What is the cost on a rainy day of buying a new umbrella? *
$14
$26
O $6
O $30
Answer:
$26
Step-by-step explanation:
this will help me a lot if you anwser this
A+B=44
A : B is equvililent to 13 :8
Please solve
Step-by-step explanation:
13:8A=13x. B=8x13x + 8x = 44 21x=44 x=2.095I decided to add a room to my house and now need to know the total square feet of the house. The dimensions of the original house are (X + 8) by (x + 12) and the dimensions of the new addition are x by (x + 6). What is the total area of my new house. What's the area of the original house? What's the area of the new addition? What's the total area of the house?
Answer:
+) the area of the original house is:
(x + 8)(x + 12) = x² + 20x + 96.
+) the area of the new addition is:
(x + 6)x = x² + 6x
+) the total area of the house is:
x² + 20x + 96 + x² + 6x = 2x² + 26x + 96
the next algebra test is worth 100 points and contains 35 problems. multiple-choice questions are worth 2 points each and word problems are 7 points each. how many of each type of equation are there? Please leave steps.
Answer:
29 multiple choice questions, 6 word problems
Step-by-step explanation:
2x + 7y = 100
x + y = 35
y = 35 - x
2x + 7 (35 - x) = 100
2x - 7x + 245 = 100
-5x = -145
x = 29
29 + y = 35
y = 6
y=-2/3x+1
how do you find the slope and y intercept
Answer:
The slope is -2/3 and the y intercept is 1
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -2/3 x+1
The slope is -2/3 and the y intercept is 1
find the area cirlcle if the circle has a radius of 11 centimeters.
Answer:
380.133
Step-by-step explanation:
A = πr²
Hope this helps!
Pls 5 stars <3
The blue line is the graph of y = –4x + 5. Use the sliders to make the orange line represent y = –2x + 3. Examine the graph. What is the solution of the system of these two equations?
(0, 5)
(1, 1)
(2, 2)
(3, 0)
Answer:
1,1
Step-by-step explanation:
