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
Chase lives 1 and one half blocks west of Ellie. They draw a number line to model this situation. Because Ellie lives 1 and three fifths blocks east of school, they give her house the coordinate 1 and three fifths . Chase incorrectly claims that the coordinate of his house is 3 and one tenth . What is the correct coordinate of Chase's house? What is Chase's likely error?
Answers
Answer:
1/10
Step-by-step explanation:
A number line is a line which contains numbers marked at intervals (usually regular intervals). Points to the right of the origin are positive numbers while those to the left are negative numbers.
The school is used as the origin. Ellie house is 1 and three fifths blocks east (to the right) of the school. This means that it is + 1 and three fifths (+8/5).
Chase house is 1 and one half blocks (3/2) west of Ellie. Since it is west then it is to the left. Hence the coordinate of chase house = 8/5 - 3/2 = 1/10
Hence the coordinate of chase house is 1/10(one tenths).
The error may be as a result of thinking chase house is to the east of Ellie, hence adding to get 3 and one tenth.
In a party Tom paid $540 including the cake and drink for his friend the cost of a person attending the party is $15 the cost of cake and drinks are $75 and $90 respectively find the number of friends that attended the party
Answers
15+75+90=180
540/180=3
Saman drives a truck for $15 an hour. If she worked 40 hours, what would be her gross earnings for one week?
Answers
Answer:
$600
Step-by-step explanation:
because 40 hours at a rate of $15/hours adds up to $600.
(40*15= 600)
HELPPPP i don’t understand this
Answers
Answer:
60 degrees
Step-by-step explanation:
1. Find angle t. A and T are supplementary angles so both added together should equal 180. 180 - 120 = 60. Angle t is 60 degrees
2. All three angles inside the triangle should add up to 180 degrees. 60 +60 = 120 and 180 - 120 = 60. Angle s is also 60 degrees
Hope this helps and pls mark brainliest.
Tinky Winky is 2 years younger than Laa Laa. If the product of Tinky's and Laa Laa's ages is equal to 1 less than 5 times the sum of their ages, how old is Tinky?
Answers
Answer:
Solution:-Let
Tinky's age=x
Laa's age=x+2
According to the question
[tex]\qquad\quad {:}\longmapsto\sf 5 (x+x+2)-1=x (x+2)[/tex]
[tex]\qquad\quad {:}\longmapsto\sf 5(2x+2)-1=x^2+2x [/tex]
[tex]\qquad\quad {:}\longmapsto\sf 10x+5-1=x^2+2x [/tex]
[tex]\qquad\quad {:}\longmapsto\sf 10x+4=x^2+2x [/tex]
[tex]\qquad\quad {:}\longmapsto\sf 10x-2x+4=x^2 [/tex]
[tex]\qquad\quad {:}\longmapsto\sf x^2=8x+4 [/tex]
[tex]\qquad\quad {:}\longmapsto\sf x^2-8x-4=0 [/tex]
What is the b value of the equation
y= -4x - 10?
Answers
Answer: -10
Step-by-step explanation: In slope-intercept form, the formula is y = mx + b with m = slope and b = y-intercept. In the expression, the "b" is -10. Therefore, the b value of this equation is -10.
solve the proportion 4/(x+1) = 3/(x+2)
Answers
Answer:
x = -5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
4/(x + 1) = 3/(x + 2)
Step 2: Solve for x
Cross multiply: 4(x + 2) = 3(x + 1)Distribute: 4x + 8 = 3x + 3Subtract 3x on both sides: x + 8 = 3Subtract 8 on both sides: x = -5Answer:
to solve a proportion, you cross multiply. so you take the numerator of the first one, and multiply it by the denominator of the second one. and then the denominator of the first one is multiplied by the numerator of the second one:
4(x+2)=3(x+1) (set them = and then use the distributive property)
4x+8 = 3x+3 (subtract 3x from both sides)
x +8 = 3 (subtract 8 from both sides)
x= -5 (the answer)
Can y'all help me with dis
Factorise
a- 49a2 – 36b2
b- 3x3 – 48x
c- x2-20x+100
d- 4xy2 – 8x4y +16x2y2-2x3y
Answers
Answer:
i cant understand are they at the power of 2
Step-by-step explanation:
Blake must choose between two job offer. Evergreen Landscape will pay him $9.75 hours to mow lawns, but its is a long way from his house. He would probably spend $25 per week on gas. Just Jean will pay Blake $6.50 per hour to work as a retail clerk. Since the store is very close to his house, he would probably only spend $5 per week on gas. let x be the number of hours that Blake will work in a week and y be the amount of money he will have end of the week if he does not spend any money expect on gas.
a. Explain how the following two rules reflect the two jobs offer that Blake has.
B. Solve the system of equations in part A. (9.75x - 25 = 6.50x -5) indicates what its tell you about blake job offers and the amount of money he will have at the end of the week.
C. blake plan to work at least 15 hours per week. Which job should he take.
Answers
Answer:
A. The explanation of the rules are;
For the job offer for the Evergreen Landscape, Blake will have 9.75 times by the number of hours worked less the $25 for gas at the end of the week
For the job offer for the Just Jean, Blake will have 6.50 multiplied by the number of hours worked less the $5 for gas at the end of the week
B. The solution to the equations is that the number of hours Blake will work to have the same amount in both Jobs is 6.1538 hours
C. Blake should take the Job at Evergreen Landscape
Step-by-step explanation:
The amount Evergreen Landscape will pay Blake to mow lawn = $9.75
The amount Blake would spend to work per week on gas for work at Evergreen Landscape = $25
The amount Just Jean will pay Blake to work per week as a retail clerk = $6.50
The amount Blake would spend to work per week on gas for work at Just Jean = $5
Whereby, x = The number of hours that Blake will work in a week
y = The amount of money he will have end of the week, if he does not spend any money except gas
A. The given rules are;
y = 9.75·x - 25
y = 6.50·x - 5
For the job offer for the Evergreen Landscape, we have;
y = 9.75·x - 25
Blake has to put aside $25 out of his weekly earnings for gas
Blake will have 9.75 multiplied by the number of hours worked less the $25 for gas
For the job offer for the Just Jean, we have;
y = 6.50·x - 5
Blake will have 6.50 multiplied by the number of hours worked less the $5 for gas
B. The common solution of the both equations is given by equating both values of y as follows;
9.75·x - 25 = 6.50·x - 5
9.75·x - 6.50·x = 25 - 5
3.25·x = 20
x = 20/3.25 = 6.15385
x = 6.15385
The number of hours Blake will work to have the same amount in both Jobs = 6.1538 hours
C. Given that the number of hours Blake can work each week = 15 hours, we have;
For the job offer for the Evergreen Landscape, we have;
y = 9.75 × 15 - 25 = 121.25
The amount of money he will have end of the week = y = $121.5
y = 6.50 × 15 - 5 = 92.5
The amount of money he will have end of the week = y = $92.5
Therefore, given that by working 15 hours a week, Blake earns $121.5 on the Evergreen Landscape job and $92.5 on the Just Jean job, Blake should take the Job at Evergreen Landscape.
Evaluate
2x - Y when x= 5, y=3
Answers
Answer:
the answer is 7
Step-by-step explanation:
2x-y
2*5 - 3
10 - 3
7
What is the slope intercept form for the equation that has these two points (5,-6) and (15,-10)
Answers
Answer:
Y = -2/5x - 4
Step-by-step explanation:
Hope this helps. Pls give brainliest.
Solve for N!! Please
Answers
Answer:
18
Step-by-step explanation:
[tex]\frac{6}{5} =\frac{N}{15} \\N=\frac{6}{5} \times 15=18[/tex]
Urgent, please help.
The width of a rectangle is a whole number of centimetres.
The length of the rectangle is 7cm longer than the width.
The perimeter of the rectangle is less than 152cm.
Find the greatest possible width of the rectangle.
I will give whoever answers this 50 points please it’s desperate.
Answers
According to the perimeter of the rectangle, it is found that it's greatest possible width is of 34 cm.
What is the perimeter of a rectangle?The perimeter of a rectangle of length l and width w is given by:
[tex]P = 2(l + w)[/tex]
In this problem, the length of the rectangle is 7cm longer than the width, hence l = 7 + w. Considering that the perimeter is less than 152 cm:
[tex]2(l + w) < 152[/tex]
[tex]l + w < 76[/tex]
[tex]7 + w + w < 76[/tex]
[tex]2w < 69[/tex]
[tex]w < 34.5[/tex]
Rounding, it's it's greatest possible width is of 34 cm.
More can be learned about the perimeter of a rectangle at https://brainly.com/question/10489198
Examine whether x + 2 is a factor of x³ + 3x² + 5x + 6 and of 2x + 4.
Answers
Step-by-step explanation:
x+2=0 x=-2
x^3+3x^2+5x+6
(-2)^3+3(-2)2+5(-2)+6
-8+12-10+6
0
hence x+2 is a factor of x^3+3x^2+5x+6
x+2=0
x=-2
2x+4
2(-2)+4
-4+4
0
also x+2 is a factor of 2x+4
Did I do this right???!
Answers
Answer:
idrk
Step-by-step explanation:
What are the numbers that multiply to -12 but add to +1?
Answers
Answer:
4 and -3
Step-by-step explanation:
the survey report suggest that 2 out of three boy likes to play baseball what is the decimal expansion of two thirds
Answers
Need HELP
Evaluate the expression
14.3-2x5²÷5
Answers
Answer:
4.3
Step-by-step explanation:
14.3 - 2 × 5² ÷ 5
14.3 -2 ×25÷5
14.3 -2 × 5
14.3 - 10
4.3
Look at the picture below. Do the diagonals bisect each other?
A) Yes
B) No
Answers
Answer:
Yes
Step-by-step explanation:
Since the lines cross over each other, yes, they do bisect each other.
~theLocoCoco
A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each T-shirt printed with your design costs an additional $8.
A. write a linear model that represents the Total cost of purchasing your team's T-shirt with your design as a function of the number of T-shirts.
B. your team has 35 members. If a T-shirt is purshased for every member. what would be the cost?
Answers
Answer:
Part A)
[tex]C(t)=25+8t[/tex]
Part B)
[tex]C(35)=\$305[/tex]
Step-by-step explanation:
We will let t represent the total number of t-shirts printed.
We are charged an initial fee of $25. So, for our linear model, our constant is 25. And each t-shirt printed costs an additional $8. So, for t t-shirts, it will cost an additional 8t dollars.
Part A)
So, from the above information, we can write the following function:
[tex]C(t)=25+8t[/tex]
Where C(t) is the total cost for t shirts.
The 25 represents our initial fee and the 8t represents the cost for t t-shirts.
Part B)
So, if we have a team of 35 members, we will need 35 t-shirts.
Then the total cost will be given by:
[tex]\begin{aligned}C(35)&=25+8(35)\\&=25+280\\&=\$305\end{aligned}[/tex]
So, it will cost a total of $305.
Last year, Jackson made 24 one-cup servings of chili for a school party. This year, he will make ten times the amount of chili that he made last year. If there are 4 cups in 1 quart and 4 quarts in one gallon, how many gallons of chili will Jackson make this year?
Answers
Answer: 15
Step-by-step explanation:
You have to multiply what Jackson made last year (24 cups) times 10 which equals 240. after that you do 240 divided by 4, which equals 60, and 60 divided by 4 again, which gives us the answer (15) (hope you could understand that) Also sorry for not answering in time!
Solve the system of inequalities graphically. Which point is in the solution?
y2x-4
y S-2x - 8
Answers
Answer:
(d). ( - 4, 0 )
Step-by-step explanation:
(a). ( 5 , - 2 ) --- Coordinates do not satisfy both inequality.
(b). ( - 2 , - 8 ) --- Coordinates satisfy y ≤ - 2x - 8, but do not satisfy y ≥ x - 4 .
(c). ( 0 , 0 ) --- Coordinates satisfy y ≥ x - 4, but do not satisfy y ≤ - 2x - 8 .
(d). ( - 4, 0 ) --- The solution of the task.
Explain it too and what specific subject is it
Answers
Answer:
The correct answer would be A. I have attached a picture of how to solve it below. Please have a look at it and give the crown.
9. Find a and the length all sides.
Answers
Answer:
a = 8
Bottom and top length are 68
left and right are 28
Step-by-step explanation:
6a + 20 = a + 60 (same length do to the little tick marks)
5a = 40 (subtract 1a from both sides and 20 from both sides)
a = 8 (Divide)
Answer: A = 8
Step-by-step explanation:
Since Side BC and AD are equal
then we can plug both equations to each other to find A
6a + 20 = a + 60
solve it
6a + 20 = a + 60
- 20 -20
6a = a + 40
-a -a
5a = 40
a = 8
You can now find the length of all sides :)
Pleaseeeee answer correctly !!!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!
Answers
Answer:
24
Step-by-step explanation:
a2+b2=c2
gimme that brainly
solve for a
15=3(a+7)
Answers
Answer:
a = -2
Step-by-step explanation:
15 = 3(a+7)
15 = 3a + 21
-6 = 3a
a = -2
CALCULATE PR :)
Merry Xmas btw
Answers
Answer:
PR = 7.9
Step-by-step explanation:
By sine rule:
[tex] \frac{12.5}{ \sin \: 66 \degree} = \frac{PR}{ \sin \: 37 \degree} \\ \\ \frac{12.5}{ 0.9135454576} = \frac{PR}{ 0.6018150232} \\ \\ PR = \frac{12 \times 0.6018150232}{0.9135454576} \\ \\ PR = \frac{12 \times 0.6018150232}{0.9135454576} \\ \\PR = \frac{7.22178028}{0.9135454576} \\ \\ PR = 7.90522269 \\ \\ PR \approx \: 7.9[/tex]
Please help me........
Answers
Answer:
70
Step-by-step explanation:
180 minus 40 divided by 2
The distance between two towns is 75 km. The distance between the two towns on a map is 1.5 cm. What is the scale on the map?
Scale = 1cm :
km
Answers
Answer:
50
..................
Step-by-step explanation:
1.5cm => 75km
1cm => 75km * (1/1.5) = 50km
Hence the scale of the map is 1cm : 50km.
Johnny’s electric bill is a variable expense. What is the average amount he pays for electricity if he paid $235 in December, $119 in January, $109 in February, $122 in March and $135 in April?
$200
$132
$144
$125
Answers
Answer:
$200
Step-by-step explanation:
Hope this helped you!!