Determine whether each equation is True or False. In case you find a "False" equation, explain why is False.
Answers
Answer:
(1) TRUE.
(2) FALSE.
(3) FALSE.
(4) TRUE.
(5) FALSE.
Step-by-step explanation:
(1) [tex]\sqrt{32} = 2^{\frac{5}{2} }[/tex]
[tex]2^{\frac{5}{2} } = (\sqrt{2} )^5 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 4\sqrt{2}\\\\\sqrt{32} = \sqrt{16 \ \times \ 2}\ = \ \sqrt{16} \ \times \ \sqrt{2} \ = \ 4\sqrt{2}[/tex]
Thus, the equation is TRUE.
(2) [tex]16^{\frac{3}{8} } = 8^2[/tex]
[tex]16^{\frac{3}{8} } =(2^4)^{\frac{3}{8} } = 2^\frac{3}{2} }= (\sqrt{2} )^3 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 2\sqrt{2} \\\\8^2 = 64[/tex]
Thus, the equation is FALSE.
(3) [tex]4^{\frac{1}{2} } = \sqrt[4]{64}[/tex]
[tex]4^{\frac{1}{2} }= \sqrt{4} = 2\\\\\sqrt[4]{64} = (64)^{\frac{1}{4} } = (2^6)^{\frac{1}{4} }= 2^{\frac{6}{4} } = 2^{\frac{3}{2} }=(\sqrt{2} )^3 = (\sqrt{2} \times \sqrt{2} \times \sqrt{2} ) = 2\sqrt{2}[/tex]
Thus, the equation is FALSE.
(4) [tex]2^8 = (\sqrt[3]{16} )^6[/tex]
[tex]2^8 = 256\\\\ (\sqrt[3]{16} )^6 = (16)^{\frac{6}{3} } = (2^4)^{\frac{6}{3} } = (2)^{\frac{24}{3} } = 2^8 = 256[/tex]
Thus, the equation is TRUE.
(5) [tex](\sqrt{64} )^{\frac{1}{3} } = 8^{\frac{1}{6} }\\\\[/tex]
[tex]8^{\frac{1}{6} } = (2^3)^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} } = \sqrt{2} \\\\(\sqrt{64} )^{\frac{1}{3} } = (2^6)^{\frac{1}{3} } = 2^{\frac{6}{3} } = 2^2 = 4[/tex]
Thus, the equation is FALSE.
Related Questions
need a quick answer please
Answers
Answer:
5
Step-by-step explanation:
Bababoey
resolve into factors (4a+b)(4a-b)
Answers
Answer : [tex]16^a - b^2[/tex]
[tex](4a + b) (4a - b )[/tex]
[tex]= (4a + b) (4a - b )[/tex]
[tex]= (4a) (4a) + ( 4a) (-b) + (b)(4a) + (b) (-b)[/tex]
[tex]= 16^a - 4ab + 4ab - b^2[/tex]
[tex]= 16^a - b^2[/tex]
I need some help with MORE math if you could answer that would be great.
Answers
Answer:
bbbbbb
Step-by-step explanation:
:)
Answer:
D. [tex]\frac{81}{m^{7}}[/tex]
Step-by-step explanation:
[tex](3m^{-4})^{3}(3m^{5})[/tex]
[tex]\frac{81m^{5}}{m^{12}}[/tex]
[tex]\frac{81}{m^{7}}[/tex]
What is a good reasoner this help plz.
SO I copied an answer for my school and I accidentally copied "hope this helped" and she is wondering why I put that... PLZ HELP :/
Answers
Answer: I pushed the wrong button on my computer I apologize.
Step-by-step explanation: That's the best I got.
Answer:
say that you meant to say "hope this is correct" but accidentally put that
Step-by-step explanation:
Please help! 2nd time asking!
Answers
Answer:
4
Step-by-step explanation:
Function 1 is moving at a constant rate meaning it has the rate of change of 0/1 or 0.
Function 2 says y is 4x meaning that the rate of change is 4/1 or 4.
0 - 4= I-4I or 4
A color printer prints 29 pages in 12 minutes.
How many minutes does it take per page?
Answers
Answer:
b b
Step-by-step explanation:v gv g
divide 29 by 12
29/12= 2.4 pages a minute
but for a single page divide it by 60 (60 seconds in a minute)
2.4/60= .04 pages a second
now we divide 1 page by it
the answer is 25 seconds a page
Brainliest to correct answer
Answers
Answer:
No, zack will finish first.
Step-by-step explanation:
I would rather not write it out but zack should finish first
angle a= 6x-5 degrees angle b=4x+45 degrees
Answers
Answer:
180
Step-by-step explanation:
Answer: the correct answer is 125°
Step-by-step explanation: i just had to get it wrong so i could get it right
Mrs. Rodriquez has 24 students in her class. Ten of the students are boys. Jeff claims that the ratio of boys to girls in this class must be 5:12. What is Jeff’s error and how can he correct it?
Answers
Answer:
See Below
Step-by-step explanation:
Total no of students = 24
No of boys = 10
So, no of girls = 24 - 10 = 14
Ratio of boys to girls = 10/14 = 5/7 = 5 : 7
So the ratio of boys to girls should be 5 : 7 and not 5 : 12
Been stuck on this for hours, it's the Law of Sines. 25 POINTS!!
Answers
Answer:
Step-by-step explanation:
(Sin27) / 11 = (sin x) / 15
cross multiply
15 sin27 = 11 sin x
keep in calculator as you divide 15sin27 by 11.
sin x = .6190779542
do sin ^ -1 (.6190779542) (It’s a key on the calculator.)
x = 38.25*
9514 1404 393
Answer:
38.2°
Step-by-step explanation:
According to the equation you are give, ...
sin(x)/15 = sin(27°)/11
Multiplying by 15 gives you ...
sin(x) = 15·sin(27°)/11 ≈ 0.619078
The inverse sine function is used to find the angle x. It may show as sin⁻¹ on your calculator.
x = arcsin(0.619078)
x ≈ 38.2°
_____
Additional comment
x is shown in the figure as an acute angle, so that is the value we have chosen. The other angle that has sin(x) = 0.619078 is the supplement of this, or 141.8°. The two solutions are shown in the 2nd and 3rd attachments.
Which matrix represents the total expected?
O A.
[20
24
20
8
2201
264
220
88
B.
200
240
200
80
E.
[240]
288
240
96
C.
(210)
250
210
90
Answers
Answer: the answer is B
Step-by-step explanation:
You add the A,B,C numbers together for the soda for example,
Cola: 70(A) + 30(B) + 100(C) = 200
Now you just continue that for the other sodas hope this helps :)
Are these good notes on math?
Quarter 2 Lesson 4: Scientific Notation
All Vocabulary words learned in 2020
A base is the number being used as a factor in an exponential expression.
An exponent is the number that shows how many times a base is used as a factor.
An equation is a statement that tells you two expressions are equivalent.
A cube root is any number that is multiplied together three times to get the original number.
A perfect cube is the product of an integer multiplied together three times.
A repeating decimal is a decimal that never ends but instead repeats the same digit or group of digits over and over.
A terminating decimal is a decimal that ends, or terminates.
An irrational number is a number that cannot be expressed as the quotient of two integers. The decimal never terminates or repeats.
A rational number is a number that can be expressed as the quotient of two integers.
A power of ten is a number that can be written as a product of tens.
Scientific Notation is a way to express a number as the product of a number greater than or equal to 1 but less than 10 and a power of ten.
A function is a relationship between an independent variable,x, and a dependent variable,y, where each value of x (imput) has one and only one value of y (output)
Answers
Answer:
yes
Step-by-step explanation:
it sounds good to me
Find the perimeter of the triangle.
Answers
Answer:
39
Step-by-step explanation:
Alll the sides equal each other because of that curve u see at each angle, that curve means that the angles are the same, having the same angles means same sides, so just pick two equations to do this:
21 - x = 2x -3
add 3 to both sides
24 - x = 2x
add x to both sides
24 = 3x
divide by 3
8 = x
Now input 7 into the equations:
21 - x = 21 - 8 = 13
2(8) - 3 = 16 - 3 = 13
x + 5 = 8 + 5 = 13
Now add: 13 + 13 + 13 = 26 + 13 = 39
Another way for u to save time is remember how i said all the sides were the same? you could just solve one equation, so it'll be 13 and multiply that with 3 to get the perimeter since ur adding 13 three times anyway
So just a simple: 13(3) = 39
The drama club at NAMS sells hot chocolate and coffee at the high school football games. At the last game, they had sales of $200. They need to keep track of how many of each type drink was sold so that they can make predictions for future sales. Monica knows that they used 275 cups that night. If the hot chocolate sells for 75 cents and coffee sells for 50 cents, how much of each type of drink were sold?
Answers
Answer:
Coffee = 25
Hot Chocolate = 250
Step-by-step explanation:
Coffee: c
Hot Chocolate: h
0.75h + 0.50c = 200
h + c = 275
h + c = 275
h = 275 - c
0.75h + 0.50c = 200
0.75(275 - c) + 0.5c = 200
206.25 - 0.75c + 0.5c = 200
-0.25c = -6.25
-0.25c/-0.25 = -6.25/-0.25
c = 25
0.75h + 0.5(25) = 200
0.75h + 12.5 = 200
0.75h = 200 - 12.5
0.75h = 187.5
0.75h/0.75 = 187.5
h = 250
Check: c = 25; h = 250
0.75h + 0.50c = 200
h + c = 275
0.75(250) + 0.5(25) = 200
187.5 + 12.5 = 200
200 = 200
h + c = 275
250 + 25 = 275
275 = 275
The drama club sold 250 hot chocolates and 25 coffee drinks.
EquationEquation is an expression used to show the relationship between two or more numbers and variables.
Let x represent the number of hot chocolate and y represent the number of coffee. From the question the equation are:
x + y = 275 (1)0.75x + 0.5y = 200 (2)From both equations:
x = 250, y = 25
The drama club sold 250 hot chocolates and 25 coffee drinks.
Find out more on Equation at: https://brainly.com/question/13763238
You are give 3 sticks .Make 4 out of them without breaking...how will do this?
Answers
Answer:
take the sticks and make the number 4 out of them
Step-by-step explanation:
Need help ASAP !!!!!!!!
Answers
Answer:
b 1 1/7
Step-by-step explanation:
pretty sure its B 1 1/7
1 1/7 hope it helps
What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?
Answers
Answer: C :>
Step-by-step explanation:
Answer:
the answer is number 3
Dr. Brown did 6 experiments at 7AM. Dr. Rachal did 8 experiments at 6PM. They both had 564 tools each. Dr. Brown used 386 and Dr. Rachal used 236. How many more experiments do they do with the tool? How many tools are left?
Answers
Answer:
Step-by-step explanation:
Total number of tools for both = 564.
Dr Brown used 386 tools for 6 experiments.
average number of tools per experiment used by Dr Brown = [tex]\frac{386}{6}[/tex]
= 64[tex]\frac{1}{3}[/tex]
Dr Rachal used 236 tools for 8 experiments.
average number of tools per experiment used by Dr Rachal = [tex]\frac{236}{8}[/tex]
= 29[tex]\frac{1}{2}[/tex]
i. The number of more experiment that can be done by Dr Brown = (564 - 386) ÷ (64[tex]\frac{1}{3}[/tex])
= 2.7668
Dr Brown can do two more experiments.
The number of more experiments that can be done by Dr Rachal = (564 - 236) ÷ (29[tex]\frac{1}{2}[/tex])
= 11.1186
Dr Rachal can do 11 more experiments.
ii. Number of tools left after Dr Brown's experiments = 564 - 386
= 178
Number of tools left after Dr Rachal's experiments = 564 - 236
= 328
Select all the correct systems of equations.
Which systems of equations have infinite solutions?
Answers
Answer:
y = 14 - 2x
6x + 3y = 42
2x + y = 17
-6x = 3y - 51
Step-by-step explanation:
The following system of linear equations have infinite solutions:
y = 14 - 2x
6x + 3y = 42
2x + y = 17
-6x = 3y - 51
please help timed
Match the reasons with the statements.
GIVEN: x2 + 6x + 2x + 12 = 0
TO PROVE: x = -6 or x = -2
1. x2 + 6x + 2x + 12 = 0 Combining like terms
2. x2 + 8x + 12 = 0 Distributive Postulate
3. (x + 6)(x + 2) = 0 Zero product postulate
4. x + 6 = 0 or x + 2 = 0 Subtraction property of equality
5. x = -6 or x = -2 Given
Answers
Answer:
Step-by-step explanation:
Start by combining like terms like 2x, 2x, and 6x to get 10x + 12= 0. thats a start
You are working alone and your shift is due to be over at 6 PM. The individual who is scheduled
to begin working at 6 PM does not show up. What do you do?
Answers
A weather balloon is dropping at a rate of 4/3 miles per hour from an
initial height of 2 miles. If the balloon's height were graphed as a functio
of time, what would be the x-intercept?
Answers
Helpppppppppppppphxhxhxhxhx
Answers
Answer:
C [tex]\frac{48}{70}[/tex]
Step-by-step explanation:
Option C - [tex]\frac{48}{70}[/tex] is incorrect because when multiplying the numerator and denominator of the fraction [tex]\frac{7}{10}[/tex] by 7, you’re suppose to get [tex]\frac{49}{70}[/tex].
Help!!! Which graph represents the system of inequalities
Answers
Answer:
A
Step-by-step explanation:
This can be seen becuase if y is greater it will be shaded above the line. If y is less than then it will be shaded under the liner.
Answer:
A
Step-by-step explanation:
Ay can anybody please help me with this question !
Answers
Answer: a = 45°
Step-by-step explanation:
The measure of∠PSR is given: 90°
Given PS = RS, this is an isosceles triangle. so measure of ∠SPR, labeled "a" is equal to the measure of ∠SPR.
The total of all angles in a triangle is 180. So subtract 90, then divide by 2.
180-90 = 90
90/2 = 45
a = 45°
If "b" is supposed to be the measure of ∠SRQ, that is 15° The larger triangle is equilateral; all the angles are 60°. 60 - 45 = 15
Can somebody plz answer this math problem correctly thanks!
WILL MARK BRAINLIEST :D
Answers
Answer:
Ellen and Blake answered 20 questions correctly since Ellen had 0.8 correct and that is 80% same with Blake
Stephen scored a .84 or an 84%
I hope this helps :)
Step-by-step explanation:
plz mark B R A I N L I E S T
Answer:
Stephen: 21
Ellen: 20
Blake: 20
Step-by-step explanation:
If youre looking for more in depth answers:
Stephen received a 21 / 25 (84%)
Ellen received a 20 / 25 (80%)
Black received a 20 / 25 (80%)
David earns a 4% commission for all the furniture he sells. If David sales were 187500 what was the dollar amount of his commission?
Answers
Answer:195000
Step-by-step explanation: We add 4% to 187500 Since He gets 4% for his sales
Simplify (3x – 5) + (5x + 1).
Answers
Answer:
(-2x - 6)
Step-by-step explanation:
The given expression is ( 3x - 5 ) - ( 5x + 1 )
We have to simplify the given expression
First we will open the bracket having negative notation outside.
( 3x - 5 ) - 5x - 1
3x - 5 - 5x - 1
Now we will collect the similar terms together.
3x - 5x - 5 -1
-2x - 6
So the simplified form of the expression is (-2x - 6)
Answer:
8x - 4
Step-by-step explanation:
queifnsldnalbdejsjsbsjas
i will mark you as brianilest The school band sold T-shirts to raise money for an upcoming trip. The band sold 400 T-shirts on Saturday and on Sunday, it will sell 30 percent of that amount. Which statements are true about the number of T-shirts that the band will sell on Sunday? check that all apply A. the answer will be less than 400 because 30 is less than 100 B. The answer will be greater than 400 because 300 percent is greater than 100 C. (100)(4)=400 so 30 (4) is the number of T-shirts the band will sell on Sunday. D. The band will sell 430 T-shirts on Sunday or E. The band will sell 120 T-shirts on Sunday.
Answers
Answer:
A and E
Step-by-step explanation:
A is correct because if you have less than 100 percent of something then the value will be less than the original value.
E is correct because 30 percent of 400 is 120 so the band will sell 120 t-shirts on Sunday.
Pls can any one help me with question two pls
Someone kind answered question one for me soo can u pls answer question two for me plssss
Answers
Answer:
b is the correct answer