Answer:
Option 3 - five to the two thirds power
Step-by-step explanation:
Given : Expression 'the square root of 5 times the cube root of 5'.
To find : Simplify the expression ?
Solution :
Writing expression in numeric form,
The cube root of 5 means [tex]\sqrt[3]{5}[/tex]
The square root of 5 times the cube root of 5 means [tex]\sqrt{5\sqrt[3]{5}}[/tex]
Now, simplify the expression
[tex]\sqrt{5\sqrt[3]{5}}=\sqrt{5\times (5)^{\frac{1}{3}}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=\sqrt{(5)^{1+\frac{1}{3}}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=\sqrt{(5)^{\frac{4}{3}}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=((5)^{\frac{4}{3}})^{\frac{1}{2}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=(5)^{\frac{4}{3}\times \frac{1}{2}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=(5)^{\frac{2}{3}}[/tex]
The expression is five to the two thirds power.
Therefore, Option 3 is correct.
The correct option is d. To simplify [tex]\(\sqrt{5} \cdot \sqrt[3]{5}\)[/tex], we get [tex]\(5^{5/6}\)[/tex]. Therefore, the correct answer is five to the seven sixths power.
To simplify [tex]\( \sqrt{5} \times \sqrt[3]{5} \)[/tex], we combine the radicals:
[tex]\[ \sqrt{5} \times \sqrt[3]{5} = 5^{1/2} \times 5^{1/3} \][/tex]
Using the property of exponents [tex]\( a^m \times a^n = a^{m+n} \)[/tex]:
[tex]\[ 5^{1/2} \times 5^{1/3} = 5^{1/2 + 1/3} \][/tex]
Now, find a common denominator for the exponents:
[tex]\[ \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \][/tex]
Therefore,
[tex]\[ 5^{1/2} \times 5^{1/3} = 5^{5/6} \][/tex]
So, the simplified expression is [tex]\( {5^{5/6}} \).[/tex]
This corresponds to option (d) in your choices: five to the seven sixths power.
The complete question is- Simplify the square root of 5 times the cube root of 5.
a. five to the five sixths power
b. five to the one sixth power
c. five to the two thirds power
d. five to the seven sixths power
what is the value of s(6)
Answer:
6s
Step-by-step explanation:
sx6 = 6s
what is the answer to Simplify: √3/√15
Answer:
[tex]\frac{1}{\sqrt5}[/tex]
Step-by-step explanation:
[tex]\large{\frac{\sqrt{3}}{\sqrt{15}}=\frac{\sqrt{3}}{\sqrt{3.5}}=\frac{\sqrt{3}}{\sqrt{3}.\sqrt{5}}=\frac{1}{\sqrt{5}}}[/tex]
Solve for x: 5 - (x + 5) > -2(x + 4)
Please select the word from the list that best fits the definition
Understands how formulas are used
Interpersonal
Musical
Body-Kinesthetic
Spatial
Linguistic
Intrapersonal
Logical-Mathematical
Answer:
Logical-Mathematical
Step-by-step explanation:
According to the theory of multiple intelligences, human intelligence has 8 different modalities (musical-rhythmic, visual-spatial, verbal-linguistic, logical-mathematical, bodily-kinesthetic, interpersonal, intrapersonal, naturalistic). In order to understand how formulas are used, logical-mathematical intelligence is used.
The term that corresponds to understanding how formulas are used is Logical-Mathematical. This refers to an individual's proficiency in carrying out mathematical operations and understanding complex mathematical problems, including the use of formulas.
Explanation:The word from the list that best fits the definition 'Understands how formulas are used' is Logical-Mathematical. This term is one of Howard Gardner's Multiple Intelligences and it refers to the ability to calculate, quantify, consider propositions and hypotheses, and carry out complete mathematical operations. In an educational setting, people who are strong in logical-mathematical intelligence can understand complex problems, detect patterns, and excel in mathematics, with skills such as understanding formulas playing a key role.
Learn more about Logical-Mathematical Intelligence here:https://brainly.com/question/36415511
#SPJ6
Rectangle HIJK has vertices H(-3, 2), I(4, 2), J(4, -3), and K(-3, -3). What are the coordinates of the image of I after a dilation by a factor of 1.5 centered at the origin?
A. I’(3, 6)
B. I’(6, 3)
C. I’(6, 2)
D. I’(8, 4)
Answer:
B. I’(6, 3)
Step-by-step explanation:
Multiply I(4, 2) by 1½:
2 × 1½ = 3
4 × 1½ = 6
So, your new coordinate is I'(6, 3).
I am joyous to assist you anytime.
Answer: B. I’(6, 3)
Step-by-step explanation:
The coordinates (x,y) of a shape after dilation by a factor of k centered at the origin is given by :-
[tex](x,y)\rightarrow(kx,ky)[/tex]
Given : Rectangle HIJK has vertices H(-3, 2), I(4, 2), J(4, -3), and K(-3, -3).
The coordinates of the image of I after a dilation by a factor of 1.5 centered at the origin will be :_
[tex]I(4,2)\rightarrow I' (1.5\times4, 1.5\times2)=I'(6,3)[/tex]
Hence, the coordinates of the image of I after a dilation by a factor of 1.5 centered at the origin =I’(6, 3)
Teresa’s age is 5 years more than twice Ben’s age. If Ben is x years old, the expression _____ gives the sum of Ben’s and Teresa’s ages. If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is _____ years.
Using a system of equations, it is found that:
If Ben is x years old, the expression 3x + 5 gives the sum of Ben’s and Teresa’s ages. If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is 26 years.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given by:
Variable x: Ben's age.Variable y: Teresa's age.Teresa’s age is 5 years more than twice Ben’s age, hence:
y = 2x + 5
The sum of their ages is:
x + y = x + 2x + 5 = 3x + 5.
Ben is 7 years old, hence the sum is given by:
3(7) + 5 = 26.
Then:
If Ben is x years old, the expression 3x + 5 gives the sum of Ben’s and Teresa’s ages. If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is 26 years.
More can be learned about a system of equations at https://brainly.com/question/24342899
The sum of Ben's and Teresa's ages is represented by the expression 3x + 5, and when Ben is 7 years old, their total age is 26 years.
Explanation:The expression to represent the sum of Ben's age and Teresa's age, given that Ben is x years old and Teresa's age is 5 years more than twice Ben's age, is 2x + 5 + x. This can also be simplified to 3x + 5.
When Ben is 7 years old, we plug in the value 7 for x in the simplified expression to calculate the sum of their ages: 3(7) + 5, which equals 21 + 5.
Therefore, the sum of Ben's and Teresa's ages when Ben is 7 years old is 26 years.
PLZ HELP ME I NEED THIS ASAP
Mean = 110
Sample size = 45
Standard deviation = 6
Z score for 90% is 1.645 ( from Z-table).
Lower Limit = Mean - Z(SD/√Sample size))
Lower limit = 110 - 1.645(6/√45)
Lower limit = 108.5
Upper Limit = Mean + Z(SD/√Sample size))
Lower limit = 110 +1.645(6/√45)
Lower limit = 111.5
The interval is (108.5, 111.5)
Solve v= 1/3 bh for h
Answer:
Step-by-step explanation:
v= 1/3 bh
multiply by : 3
3v = bh
dividid by b : h = 3v/b
To solve for h in the equation v = (1/3)bh, you need to isolate h on one side. Multiply both sides by 3 to eliminate the fraction, then divide both sides by b to solve for h.
Explanation:To solve the equation v = (1/3)bh for h, we need to isolate h on one side of the equation.
First, we can multiply both sides of the equation by 3 to get rid of the fraction: 3v = bh.
Next, to solve for h, we divide both sides of the equation by b. This gives us the final answer: h = 3v / b.
Learn more about Solving equations here:https://brainly.com/question/18322830
#SPJ2
Given: Can you use ASA postulate or the AAS Theorem to prove the triangles congruent?
Answer:
by ASA only
explanation:
They are reflective towards each other making them congruent
What is the value of 128^3/7
Answer:
8
Step-by-step explanation:
Which number has the lowest value ?
a) 1/2 +0.30 b) 0.10 + 3/4 c) 1/3 + 0.50 d) 1/3 +0.40
Hey!
-------------------------------
Let's Solve A:
1/2 = 0.5
0.5 + 0.30 = 0.80
a = 0.80
-------------------------------
Let's Solve B:
3/4 = 0.75
0.10 + 0.75 = 0.85
b = 0.85
-------------------------------
Let's Solve C:
1/3 ≈ 0.33
0.33 + 0.50 = 0.83
c = 0.83
-------------------------------
Let's Solve D:
1/3 ≈ 0.33
0.33 + 0.40 = 0.73
d = 0.73
-------------------------------
Answer:
By solving each equation we can see that option A has the lowest value!
-------------------------------
Hope This Helped! Good Luck!
Among these options, option (d) with a value of 0.73 has the lowest value.
How did we determine the lowest value?
To determine which number has the lowest value among the given options, let's calculate the values of each option:
a) 1/2 + 0.30 = 0.5 + 0.30 = 0.80
b) 0.10 + 3/4 = 0.10 + 0.75 = 0.85
c) 1/3 + 0.50 = 0.33 + 0.50 = 0.83
d) 1/3 + 0.40 = 0.33 + 0.40 = 0.73
Among these options, option (d) with a value of 0.73 has the lowest value.
learn more about the lowest value: https://brainly.com/question/30236354
#SPJ3
The product of twice a number and six is the same as the difference of eleven times the number and 6/5 . Find the number
Answer:
-6/5
Step-by-step explanation:
solution;
let,the number be x,
product of twice of x and six = the difference
difference of eleven times x and 6/5
or, (2x×6)=(11×x)-(6/5)
or, 12x = 11x - 6/5
or, 12x - 11x = -6/5
therefore,x =-6/5
Therefore, the number required is (-6/5) whose product of twice a number and six is the same as the difference of eleven times the number and 6/5 .
f(x) = 8x – 2
g(x) = 9x + 2
What is h(x) = f(x) – g(x)?
Options:
h(x) = 17x + 14
h(x) = x + 4
h(x) = –x – 4
h(x) = –x + 14
Answer:
-x-4
Step-by-step explanation:
8x-2-(9x+2)
8x-2-9x-2
-x-4
Function h(x) = f(x) – g(x) = -x - 4
What is a function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given functions
f(x) = 8x – 2
g(x) = 9x + 2
h(x) = f(x) – g(x)
h(x) = (8x – 2) - (9x + 2)
h(x) = 8x - 2 -9x - 2
h(x) = (8x - 9x) + (-2 - 2)
h(x) = -x - 4
Hence, h(x) = -x - 4
Find out more information about function here
https://brainly.com/question/12544664
#SPJ3
AN ice cream factory makes 230 quarts of ie cream in 2 hours. how many quarts could be made in 12 hours?what was the rate per day
it makes 2760 per 12 hours
which of the following is the equation of a line parallel to the line y = -x + 1, passing through the point (4,1)?
Answer:
○ A. x + y = 5
Step-by-step explanation:
Parallel lines have SIMILAR RATE OF CHANGES [SLOPES], so -1 remains the same:
1 = -[4] + b
↑
-4
5 = b
You have the equation, but all answer choices are in Standard Form, so we need to convert from Slope-Intercept to Standard:
y = -x + 5 >> Parallel Equation
+x + x
_________
x + y = 5 >> Standard Equation
I am joyous to assist you anytime.
John and his three brothers share a cell phone plan. The cell phone company charges a flat rate of $90 per month, which the four brothers share equally. In addition, the cell phone company charges 25 cents per megabyte of data downloaded. Each brother pays for his own downloaded data.
John's share of the current cell phone bill is $147.50.
Which equation determines how many megabytes of data John downloaded?
Answer:
(147.50 - 22.5)/.25
Step-by-step explanation:
First subtract his portion of the $90. Which is $22.5, when subtracted from 147.5 you get $125. Now divide $125 by .25 cents and you get the amount of megabytes he downloaded.
Answer: 22.5+0.25x=147.50
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
Flat rate: $90, (share equally among the four brothers means 90/4 =$$22.5 each) Cost per megabyte: $0.25 John's share: $147.50So, the equation is
22.5+0.25x=147.50
Where "x" is the number of megabytes of data that john downloaded
Feel free to ask for more if needed or if you did not understand something.
0.003 is 1/10 of which decimal?
Ⓐ0.3
Ⓑ0.03
Ⓒ0.33
Ⓓ 0.333
How do I identify the rate of change on a linear function?
Answer:
Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run.
A baker has 5 1/4 pies in her shop. She cut the pies in prices that are each 1/8 of a whole pie. How many slices of pie does she have
5_1/4 = 21/4.
21/4 - 1/8
LCD = 8
(42 - 1)/8
41/8 remains.
What is the median of this list of numbers? 5, 10, 13, 7,5
Median: The middle number when all the numbers are listed in order.
To find the median of the data set shown here, we can first start by putting all the numbers in order from least to greatest.
Least to greatest - 5, 5, 7, 10, 13
Next, we locate the number that is exactly in the middle and if there is no number exactly in the middle, we find the two numbers and find halfway point between them.
The number that is exactly in the middle of the data set is 7 so our median is 7.
Catherine is 4 centimeters taller than ally, while Katrina is 5 centimeters shorter than ally. Let t represent ally's height in centimeters.
Answer:
4 is right yur
Step-by-step explanation:
what is 1/3 to the 2ed power
Answer:
1/9
1/3 x 1/3 = 1/9 (because 3x3 = 9)
Hey!
---------------------------------------------------------------
Solution:
Take the numerator and denominator and solve it to the 2nd power.
1² = 1
3² = 9
Put it back as a fraction.
1/9
---------------------------------------------------------------
Answer:
1/9
---------------------------------------------------------------
Hope This Helped! Good Luck!
Sam makes enough muffins to give 8 of her
friends 3 muffins each. Each tray holds 6
muffins. How many trays does she need?
Sam needs [tex]4[/tex] trays.
Given:
The number of friends is [tex]8[/tex].
Muffins required for each friend are [tex]3[/tex].
The capacity of each tray is [tex]6[/tex] muffins.
To find:
The required number of trays.
Explanation:
Let [tex]x[/tex] be the required number of trays.
Total quantity of muffins in [tex]x[/tex] trays is [tex]6x[/tex].
Total quantity of required muffins is:
[tex]8\times 3=24[/tex]
Now,
[tex]6x=24[/tex]
[tex]x=\dfrac{24}{6}[/tex]
[tex]x=4[/tex]
Therefore, Sam needs [tex]4[/tex] trays.
Learn more:
https://brainly.com/question/23168060
1.6w - 1.2w + 3.5 + 4.7w
Answer:
8.6
Step-by-step explanation:
basically just do the order of operations
lim (x^3-8)/(x)
x-2
Find three consecutive integers whose sum is 441
Answer:
146, 147 and 148
Step-by-step explanation:
Let the three integers be x, x+1, and x+2.
(they are consecutive)
Now, we are given that their sum is 441.
So,
(x) + (x+1) + (x+2) = 441
3x + 3 = 441
3x = 438
x = 438/3
x = 146
Thus, the integers are:
x = 146
x+1 = 147
x+2 = 148
Please mark Brainliest if this helps!
Kyle practices 2.5 times as many hours as Grant does. Write an expression to
show how many hours Kyle practices. Let t equal the number of hours Grant
practices.
The expression to show how many hours Kyle practices is 2.5t, where t equals the number of hours Grant practices.
Explanation:If Kyle practices 2.5 times as many hours as Grant does, and we let t represent the number of hours Grant practices, then the expression to show how many hours Kyle practices would simply be 2.5t. This is because we are given the ratio of Kyle's practice time to Grant's practice time, which we can use to express Kyle's practice time in terms of Grant's.
The total cost after tax to repair Deborah’s computer is represented by 0.07(4 0h) + 4 0h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of tax Deborah has to pay? Explain
Answer:
depending on the national/ regional legal provisions in favour of the tax contributor where either the work is provided/ the computer was aquired/ placed, repaired/ the repair company has declared fiscal residency the cost ( in hours) could be determined by 0.07 ( 40h)
Final answer:
The expression 0.07(40h) in the equation represents the amount of tax Deborah has to pay. 0.07 stands for the 7% tax rate applied to the cost of repair, which is denoted by 40h.
Explanation:
The student has asked to identify the part of the expression in 0.07(4 0h) + 4 0h, which represents the tax Deborah has to pay for her computer repairs, where h represents the number of hours it takes to repair the computer. In this expression, the tax component is given by 0.07(40h).
The 0.07 represents the 7% tax rate on the cost of repair. The cost of repair, before tax, is represented by the term 40h. When you multiply 40h by 0.07, you are calculating 7% of the repair cost which equates to the tax amount.
In Exercises 13 - 18 , find the value of x so that the function has the given value. (See Example 3.)
Answer:
-9
The problem:
If h(x)=-7x and h(x)=63, the what is the value of x?
Step-by-step explanation:
h(x)=-7x
You are asked to find x such that h(x)=63.
So you are solving:
h(x)=63 for x:
-7x=63
Divide both sides by -7:
x=63/-7
Simplify:
x=-9
Let's check:
h(x)=-7x
h(-9)=-7(-9)
h(-9)=63
So -9 is the answer.
The value of x in the equation y = 9 + 3x for a given y value can be found by rearranging the equation to x = (y - 9) / 3, and substituting the desired y value.
Explanation:The subject of this question is determining the value of x in the equation y = 9 + 3x. In this equation, the b term is 9 and the m term is 3, representing the y-intercept and the slope respectively. To find the value of 'x' that gives a specific 'y' value, one must rearrange the equation to solve for 'x': x = (y - 9) / 3. For example, if we wanted the y value to be 15, we would substitute into the equation and find that x = (15 - 9) / 3 = 2
Learn more about Solving equations here:https://brainly.com/question/19297665
#SPJ3
can you guys help me out?
Answer:
5 inches
Step-by-step explanation:
V = (b² h) ÷ 3
Given that V = 25 and h = 3:
25 = (b² × 3) ÷ 3
25 = b²
b = 5
Therefore, the length of the base's sides is 5 inches.