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
Congruent Triangles and Proofs
Given: JK bisects
Answers
Answer:
Step-by-step explanation:
1S. JM bisects ∠ KJL and ∠JMK ≅ ∠JML
1R. Given
2S. ∠KJM ≅ ∠LJM
2R. Angle bisectors form ≅ ∠s
3S. JM≅JM
3R. Reflexive Propriety ( segment is ≅ with itself)
4S. ΔJMK ≅ΔJML
4R. ASA theorem of congruency
5S. JK≅JL
5R. Coresponding parts of congruent Δs are congruent (CPCTC)
A cylindrical water tank having radius rcm and height 2rcm has a hemispherical top. if the cylindrical portion can hold 600l water, then how much liters of water can the tank hold.
Answers
sorry for bad picture
Step-by-step explanation:
hope it helps you have a great day keep smiling be happy stay safe
please help i dont know how to do this
Answers
Answer:
B.
Step-by-step explanation:
jason is filling up a 3/4 gallon pitcher. the one he has to fill it up with is 1/3 of a gallon.
1/3 * x = 3/4
x/3 = 3/4
3 (x/3) = 3 (3/4)
3x/3 = 9/4
x = 9/4
9/4 is 2.25 so the answer is B
Bill is making accessories for the soccer team. He uses 777.35 inches of fabric on headbands for 32 players and 3 coaches. He also uses 301.76 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answers
Answer:
Fabric used on a headband for each player = 22.21 inches
Fabric used on a wristband for each player = 9.43 inches
Step-by-step explanation:
Let fabric used on each headband = [tex]h[/tex] inches
Let fabric used on each wristband = [tex]w[/tex] inches
Number of players for which headband is made = 32
Fabric used on 32 players = 32[tex]h[/tex] inches
Number of coaches for which headband is made = 3
Fabric used on 3 coaches = 3[tex]h[/tex] inches
As per question statement:
Total fabric used on headbands = 777.35 inches
[tex]32h + 3h = 777.35\\\Rightarrow 35h = 777.35 inches \\\Rightarrow h = 22.21\ inches[/tex]
Number of players for which wristband is made = 32
As per question statement:
Fabric used on wristbands = 301.76 inches
[tex]32w = 301.76\\\Rightarrow w = 9.43\ inches[/tex]
Therefore, the answer is:
Fabric used on a headband for each player = 22.21 inches
Fabric used on a wristband for each player = 9.43 inches
Given 3m+6n-6 when m=4 and n=3. I need help with this
Answers
Answer: 24
Step-by-step explanation:
Since we are given the value for m and n, we can plug them in and solve the expression.
3(4)+6(3)-6 [multiply]
12+18-6 [add]
30-6 [subtract]
24
Now, we know the value of the expression is 24.
18. The length of the minor arc AB of a circle,
centre 0, is 27 cm and the length of the major
arc is 221 cm. Find (a) the radius of the circle,
(b) the acute angle AOB.
Answers
{Stop scrolling} this is not a question but I just wanted you to know that you are doing absolutely amazing and I am extremely proud of you:) Ik school can be stressful but just know that you got this loves <3
I love u ♥️
Answers
Answer:
Ty :D
Step-by-step explanation:
School is hard
help me ill mark u brainliest xd
Answers
So the area would be 840 mm^2.
Choose the best graph that represents the linear equation:
6x = y + 8
Graph A
On a coordinate plane, a line goes through (negative 2, 4) and (0, negative 8).
Graph B
On a coordinate plane, a line goes through (0, negative 8) and (2, 4).
Graph C
On a coordinate plane, a line goes through (negative 2, negative 4) and (0, 8).
Graph D
On a coordinate plane, a line goes through (0, 8) and (2, negative 4).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D
Answers
Graph B the person above me got before I did
15PTS PLEASE HELP ASAP!
(dont write random answers pls)
look at the pic attached:
Answers
Answer:
a
Step-by-step explanation:
B
E
A
C
If the length of AC equals 50, what is the length of the midsegment DE?
Answers
If the length of AC equals 50, the length of the midsegment DE is 25.
Can you help me with this i have other questions to if u can't solve this one
Answers
Answer:
I think its -12 and increasing, but i may be wrong. Sry
Step-by-step explanation:
how wide is a poster that has a length of 9/2 feet and area of 45/4
Answers
Answer:
5/2 is your answer
Step-by-step explanation:
One litre of paint covers 1.5 square meters. How many litres must I buy so that I have enough to paint a wall 6 m long and 3 m high ?
Answers
Answer:
12 litres
Step-by-step explanation:
The area to be covered is
A = 6 × 3 = 18 m²
Divide the area by 1.5 for required amount of paint, that is
18 ÷ 1.5 = 12 litres
Solve for
x
x/
12
+
1
=
6
Answers
Answer:
x
=
−
2
1
2
Step-by-step explanation:
Answer:
x = 60
Step-by-step explanation:
x/12 is the same as 1/12x
so now the equation is 1/12x+1=6
then to simplify it even more we do -1 from both sides so
1/12x+1=6
-1 -1
again the equation is 1/12x=5
then we multiply both sides by 12 and get x = 60
how do we find the place value of 3a + b given that a=4, b=3, and c=-2
Answers
Answer:
3a+b
3(4)+3
12+3
15
Step-by-step explanation:
You substitute the variables with the given numbers. I think this is correct.
equation with variables on both sides: decimals & fractions 4x + 8 = 7.2 + 5x
Answers
Answer:
4x + 8 = 7.2 + 5x
1. 4x - 4x + 8 = 7.2 + 5x - 4x
2. 8 = 7.2 + x
3. 8 - 7.2 = 7.2 - 7.2 + x
4. 0.8 = x
Step-by-step explanation:
Final Answer: [tex]x = 0.8[/tex]
Steps/Reasons/Explanation:
Question: Equation with variables on both sides: decimals & fractions [tex]4x + 8 = 7.2 + 5x[/tex].
Step 1: Subtract [tex]4x[/tex] from both sides.
[tex]8 = 7.2 + 5x - 4x[/tex]
Step 2: Simplify [tex]7.2 + 5x - 4x[/tex] to [tex]7.2 + x[/tex].
[tex]8 = 7.2 + x[/tex]
Step 3: Subtract [tex]7.2[/tex] from both sides.
[tex]8 - 7.2 = x[/tex]
Step 4: Simplify [tex]8 - 7.2[/tex] to [tex]0.8[/tex].
[tex]0.8 = x[/tex]
Step 5: Switch sides.
[tex]x = 0.8[/tex]
~I hope I helped you :)~
A certain manufacturing plant produces electric fuses of which 20% are defective. Find the probability that in a sample of 8 fuses selected at random there will be atleast one defective and not more than one defective.
Answers
Answer:
0.419
Step-by-step explanation:
To calculate this, we shall make use of Bernoulli approximation of Binomial distribution
if 20% are defective, then 80% are not defective
Probability of selecting a defective fuse is 20/100 = 0.2
Probability of selecting a non defective one is 0.8
Probability of at least 1 being defective is = 1 - Probability of none being defective
Mathematically that will be;
0.8^8 = 0.168
The above is probability of none defective
So the probability of at least one will be
1 - 0.168 = 0.832
Probability of not more than 1 means;
Probability of none + probability of 1 being defective
We already have probability of none above
Probability of 1 being defective means 8 will be non defective
The probability in this case is;
8 C 1 0.2^1 0.8^7
= 8 * 0.2 * 0.8^7 = 0.336
Add this to the probability of none = 0.336 + 0.168 = 0.504
So the probability that we want to calculate from the question will be;
Probability of at least one defective * probability of not more than one defective
= 0.832 * 0.504 = 0.419
which of the following types of figures may not be a parallelogram?
(1) a rhombus. (3) a square
(2) a trapezoid. (4) a rectangle
Answers
Answer:
2) a trapezoid
Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides. A trapezoid can never be a parallelogram.
A towel set consisting of a towel and 6 napkins cost rupees 200 if the cost of each napkin is rupees 95 less than the cost of the towel what is the cost of the towel
Answers
Answer:
The towel costs 110 rupees
Step-by-step explanation:
Let n be napkins, and t be towels. Then:
6n+t=200
and
n=t-95
So:
6(t-95)+t=200
7t-570=200
7t=770
t=110....................
Among the set of towels and napkins, the cost of the towel will be equal to 110 rupees.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the data given in the question,
Assume that n is for napkins, and t is for towels then,
6n + t = 200 (i)
Also,
The cost of the napkin is rupees 95 less than the towel,
n = t - 95 (ii)
Use equations (i) and (ii)
6(t-95)+t=200
7t-570=200
7t=770
t=110
To know more about Expressions:
https://brainly.com/question/14083225
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PLSSSS SOMEONE HELP MEEE IM STUCK the question is below
Answers
Answer:
x=8, y=73/3
Step-by-step explanation:
they ask to solve by substitution so from second equation find y
4x-3y= -41 isolate y
4x+41 = 3y divide both sides by 3
(4x+41)/3= y substitute this y in the first equation
5x+2y = -34
5x+2(4x+41)/3 = -34 distribute and find the common denominator
3*5x+(8x+82)/3 = -34
15x+8x+82=-34*3 cross multiply
23x = -102-82
x=-184/23=8
y=(4*8+41)/3=73/3 is about 24.333..
calculate the quotient 9/4 divided by 3/8
Answers
Answer:
6
....................................
Find the slope of the line through each pair of points (5, 18), (15, -17)
Answers
Answer:
-3.5
Step-by-step explanation:
Slope of the line
[tex] = \frac{ - 17 - 18}{15 - 5} = \frac{ - 35}{10} = - 3.5 \\ [/tex]
Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answers
[tex]\pink{\sf Third \: side \: of \: the \: triangle = 45}[/tex]
Solution :As, the given triangle is a right angled triangle,
Hence, We can use the Pythagoras' Theorem,
[tex]\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}[/tex]
Here,
H = Hypotenuse of triangleB = Base of triangle P = Perpendicular of triangleIn given triangle,
Base = 24Hypotenuse = 51Perpendicular = ?Now, by Pythagoras' theorem,
[tex]\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}[/tex]
[tex] \sf : \implies (51)^{2} = (24)^{2} + P^{2}[/tex]
[tex] \sf : \implies 51 \times 51 = 24 \times 24 + P^{2} [/tex]
[tex] \sf : \implies 2601 = 576 + P^{2}[/tex]
[tex] \sf : \implies P^{2} = 2601 - 576[/tex]
[tex] \sf : \implies P^{2} = 2025[/tex]
By squaring both sides :
[tex] \sf \sqrt{P^{2}} = \sqrt{2025}[/tex]
[tex] \sf : \implies P^{2} = \sqrt{2025}[/tex]
[tex] \sf : \implies P^{2} = \sqrt{(45)^{2}}[/tex]
[tex] \sf : \implies P^{2} = 45 [/tex]
[tex]\pink{\sf \therefore \: Third \: side \: of \: the \: triangle \: is \: 45}[/tex]
━━━━━━━━━━━━━━━━━━━━━
Factor completely.
25x2-121
Answers
Assuming you meant x to the 2nd power:
Factor: 25x2−121
25x2−121
=(5x+11)(5x−11)
Answer:
(5x+11)(5x−11)
Tritan played in a football game he caught the ball at the goal line and ran forward 30 yards before he was tackled how could tristansrun be represented as a fraction and decimal of the whole football field
Answers
Answer:
As a fraction = [tex]\dfrac{30}{100}[/tex]
As a decimal = 0.3
Step-by-step explanation:
Recall that: The total yard of a football field = 100 yards
Tritan played in a football game he caught the ball at the goal line and ran forward 30 yards before he was tackled,
As a fraction;
Tristan run can be represented as = number of run from goal-line/ total length of the field
= [tex]\dfrac{30}{100}[/tex]
As a decimal= 0.3
Circumference of the circle
Answers
Answer:
The formula of circumference in a circle is 3.14 times diameter.
Step-by-step explanation:
3.14×20=62.8
The circumference is 62.8
She needs a little less than 4 pounds to make 12 turkey burgers because 1/3 times 12 is about 3.99 pounds. But she only has 3 3/8 pounds which is about 3.375 pounds.
Answers
Answer:
10 burgers
Step-by-step explanation:
[tex]{3.375pounds}(\frac{12 burgers}{3.99pounds})=(\frac{xburgers}{3.375pounds}){3.375pounds}\\xburgers=10.15\\[/tex]
so you get 10 burgers
or you could approach it
[tex]\frac{3.375}{(1/3)} =[/tex]3.375×3=10.125
On Tuesday, Ashley walked the first dog for 27 minutes, the second dog for 35 minutes, and the third dog for 15 minutes. If she started walking the first dog at 8:00 am, what time did she finish walking all the dogs?
Answers
Answer:
9:17
Step-by-step explanation:
Answer: 9:17 am
Step-by-step explanation: I added all the minutes together and got 77 minutes. Then I simplified the 77 minutes into an hour and 17 minutes. Then I added the 1hour and 17minutes to 8:00 am.
The following cards are used in a game.If each of the cards is turned over and shuffled
Answers
Answer:
than that means the cards are not turned over
im sorry i didnt really get you question
Step-by-step explanation:
There is 1/2 of a greater chance in drawing a spade over drawing a 7
How to determine the probability?From the complete question added as an attachment, we have the following parameters:
n(Spade) = 4n(7) = 1Total = 6The probability of getting a spade is:
P(Spade) = 4/6
The probability of getting a 7 is:
P(7) = 1/6
The difference between both probabilities is:
Difference = 4/6 - 1/6
Evaluate
Difference = 3/6
Simplify
Difference = 1/2
Hence, there is 1/2 of a greater chance in drawing a spade over drawing a 7
Note that the question is incomplete, and the missing part of the question can be found online
Read more about probability at:
https://brainly.com/question/251701
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