[tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] can be simplified into 8.48.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 6= 2 x 3
Prime factorization of 12= 3 x 2 x 2
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m} )^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]
According to the given condition,
Applying the laws of indices mentioned above,
∴[tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] = [tex](2 X 3)^{\frac{1}{2} } . (3 X 2^{2}) ^{\frac{1}{2} }[/tex]
= [tex](3^{2} X 2^{3})^{\frac{1}{2} }[/tex]
= [tex]\sqrt{72}[/tex] = 8.48.
Thus, [tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] can be simplified into 8.48.
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need this last inequality equation
Answer:
II and III
Step-by-step explanation:
I.
-9 - 5x > -1
-9 - 5(2) > -1
-9 - 10 > -1
-19 > -1
False
II.
-9 - 5x > -1
-9 - 5(-5) > -1
-9 + 25 > -1
16 > -1
True
III.
-9 - 5(-10) > -1
-9 + 50 > -1
41 > -1
true
I hope this helps!
show work please
2x + 3(4x – 1)
What is a rational number with a diameter of 7 that is between the square root of 7 and the square root of 8? Write your answer as an improper fraction.
The rational number between the square root of 7 and the square root of 8 is 27/10
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.
This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the rational number?The features of the rational number are given as
Value = between the square root of 7 and the square root of 8
Rewrite the value properly
So, we have
Value = between √7 and √8
Evaluate the values of √7 and √8
So, we have
√7 = 2.65
√8 = 2.83
This means that the rational number is between 2.65 and 2.83
A number between 2.65 and 2.83 is 2.7
Express as fraction
value = 27/10
Hence, the rational number between the square root of 7 and the square root of 8 is 27/10
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Somebody please solve the Absolute Value Inequality.: |-7b+1|-8<-70
Answer: the answer is no solution
Step-by-step explanation:
Answer:
No Solution
Step-by-step explanation:
An absolute value will always have a positive value. If you isolate the absolute value it shows the abs val LESS THAN a negative number. Its not possible to have a positive less than a negative.
If you just go on and do the problem in auto-pilot, the answers don't check. ALSO since it it a LESS THAN inequality statement BOTH of the inequalities have to be true at the same time which is not possible.
See image.
I need help with this today please!
Answer:
kevin ate 1/6 more than Kathy or un simplified, 2/12
Step-by-step explanation:
least common denominator
2(5-8) ³+3(7-10) ²+9-2
Answer:
Brainliest pls
Step-by-step explanation:
-20
Answer:
The answer is -20.
Step-by-step explanation:
REMEMBER THIS:
Please excuse my dear aunt sally…
PLEASE = PARENTHESIS
EXCUSE= EQUATION
MY = MULTIPLICATION
DEAR = DIVISION
AUNT = ADDITION
SALLY = SUBTRACTION
^In that order^
Remember to use this statement to remember how to simplify the expression. PEMDAS.
Find the distance.
1. (-2,2) (4, -1)
2. (-3,-5) (2, 5)
3. (-4,0). (2, 3)
Answer:
1)3√5
2)5√5
3)3√5
There are 1,120 calories in 5 servings of Anna’s favorite dessert. If Anna eats a single serving of the dessert, how many calories will she eat?
224 calories
112 calories
280 calories
225 calories
Answer: 224 calories ==> 1st option
Step-by-step explanation:
1 serving * 1,120 calories/ 5 servings=
1*1120/5=
1*224=224 calories ==> 1st option
Answer:
Step-by-step explanation:
224 calories I think
2/3x - 5/8 = 1
pls help asap
Given the linear function below identify the slope (m).
y=-3x - 5
m=
Answer:
m is always the number in front of x
y=mx+c
so m=-3
Step-by-step explanation:
24 By the age of 21, the best violinists and pianists will have practiced at
least 10,000 hours. If you practice an instrument 45 minutes (or 0.75
hours) a day for 365.25 days, the length of a year, how many hours
will you have practiced?
26 show your work
Answer:
True
it represents 2/3 because it has 1/1 in each question
Solve each equation. Check your answers. ln 3 x=6
After solving the equation ln 3x =6, the value of x is equal to [tex]\frac{e^6}{3}[/tex]
We have been asked to find x in ln 3 x=6
⇒ ln 3 x = 6
⇒ 3x = [tex]e^6[/tex]
⇒ x = [tex]\frac{e^6}{3}[/tex]
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Write a polynomial function with rational coefficients and the given roots.
-√7, 1+2 i
The polynomial function is [tex]x^{2}-x-2ix+\sqrt{7}x-\sqrt{7}-2\sqrt{7}i[/tex]
What are polynomial functions ?In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
roots are -√7 , 1+2i
Thus the factors are :
(x - (-√7)) (x-(1+2i))
=> (x+√7)(x-1-2i)
=>x²-x-2ix+√7x-√7-√7.2i
Thus polynomial function for given roots is x²-x-2ix+√7x-√7-√7.2i.
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Solve. Check for extraneous solutions. 3 √2x -3=9
No extraneous solution to the equation.
The equation is:
3[tex]\sqrt{2x}[/tex] - 3= 9
To know whether the equation has an extraneous solution, first we need to find the value of x.
[tex]3\sqrt{2x}[/tex] = 12
[tex]\sqrt{2x}[/tex] = 4
2x = 16
x = 8
Now put the value of x in the equation.
3[tex]\sqrt{2 * 8}[/tex] - 3 = 9
3× 4 - 3 = 9
12 - 3= 9
9 = 9
Therefore there is no extraneous solution to the equation, x = 8 is the solution of the equation.
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27 less than four times a number is equal to the number. What is the number
Answer:
Step-by-step explanation:
Also written as-
4x - 27 = x
+ 27 +27
(add 27 to both sides)
The new equation would be written as-
4x = x + 27
-x -x
(subtract x from both sides)
[tex]3x = 27 \\ \\ \frac{3x}{3} =\frac{27}{3} \\ \\ x=9[/tex]
The number is 9
15 A function is graphed on the set of axes below.
State the domain of this function. State the range
of this function.
The domain of the function is: [-1, 10]
And the range of the function is: [-1,0,1,2,3,4,5,6,7,8,,9,10]
According to the question, the intervals can be defined by a common difference of one value.
Therefore, the domain of the function is: [-1, 10]
And the range of the function is: [-1,0,1,2,3,4,5,6,7,8,,9,10]
What is domain and range in the function?
The domain of a function can be defined as the complete set of all the possible values for the dependent variables. Similarly, the range of the function can be expressed as the set of all the values which can be assumed by the expression of the function.
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Divide and simplify. √36 x⁴ / √9 x⁶
The divide and simplify of the equation √36 x⁴ / √9 x⁶ will result to [tex]\frac{2}{x^{2} }[/tex]
Let's begin by simplifying the equation;
Simplify the equation by finding the square root of both 36 and 9
The square root of 36= 6
The square root of 9= 3
= [tex]\frac{6x^{4} }{3x^{6} }[/tex]
The above equation can also be written as;
= [tex]6x^{4} * 3x^{-6}[/tex]
The next step is to solve the powers, that is,
= [tex]\frac{6x^{4} }{3x^{6} }[/tex]
Cancel out 6 by 3 and get 2
The result is,
= [tex]\frac{2}{x^{6-4} }[/tex]
The final submission result is,
= [tex]\frac{2}{x^{2} }[/tex]
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2) The area of my best friend's pool is 121ft2. What is the width of the pool if the length is 12ft?
Answer:
10.083333...ft
Step-by-step explanation:
length = 12ft
area = 121sqft
area = length * width
121sqft = 12ft * width
width = 121sqft / 12ft
[tex]width = 10\frac{1}{12}\mathrm{ft}[/tex]
width = 10.08(3)ft
what is the gradient
pls help giving brainliest answers!! :)
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{d}{dx}\left(\frac{x}{2}-\frac{1}{3}\right)[/tex]
= [tex]\frac{d}{dx}\left(\frac{x}{2}\right)-\frac{d}{dx}\left(\frac{1}{3}\right)[/tex]
=[tex]\frac{1}{2}\frac{d}{dx}\left(x\right) - 0[/tex]
= [tex]\frac{1}{2} - 0[/tex]
= [tex]\frac{1}{2}[/tex]
Hope this helps! :) please leave a rating and brainliest if this was useful!
What would you do if when you okay so he said yes would go??
Aidan is doing a multiple choice test with 20 questions he scores 3 marks for a correct answer and loses 1 mark if the answer is incorrect he answered all questions and scored 40 marks how many we questions were correct
Answer: 10 answers correct and 10 answers incorrect
Step-by-step explanation:
60 is the highest total assuming every one was correct
20 is the lowest total assuming every one was incorrect
40 is the middle meaning he got half write half wrong
Half of 20 is (10) (10 x 3 = 30 ) + ( 10 x 1 = 10 ) 30 + 10 = 40
Answer: 13.3 repeating is what I got see if it make sense according to my work
Step-by-step explanation: 20x3=60, and one mark per wrong answer, so 60-40=20 wrong. So, 40 divided by 3=13.3 repeating
10.
Ginnie and her cousin went to a restaurant for dinner. Ginnie dinner cost
$15 more than her cousin's. If their combined bill was under $65, which
inequality best describes the cost of their dinners?
The cost of the Ginnie's dinner is a $40 and the cost of his cousin's dinner is $25.
According to the statement
We have to find that the cost of their dinners.
So, For this purpose, we all know that the
The cost function may be wont to find the common cost, which is that the average amount of cash it costs to provide a unit.
From the given information:
Ginnie dinner cost $15 over her cousin's. If their combined bill was under $65.
Then
Let Ginnie dinner is x and his cousin's be y.
Then
x+y = 65 And x = y+15
Then
Substitute the values then y+15+y = 652
y+15 = 652
y = 65-152
y = 50
[tex]y = \frac{50}{2}[/tex]
y = 25.
Then x = y+15
x = 25+15
x = 40.
So, The cost of the Ginnie's dinner is a $40 and the cost of his cousin's dinner is $25.
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pls help and show ur work
Is y=e (x+7) a natural base exponential function?
We need to know about natural exponential function to solve the problem. The given function is a natural base exponential function.
An exponential function is a function in which x is an exponent. An exponential function has an exponential graph that keeps growing. A natural base exponential function is one where the base of the function is e which is a mathematical constant and is approximately equal to 2.71828. The inverse of a natural exponential function is a logarithmic function. An exponential function is of the form y=[tex]b^{x}[/tex] where b is the base, in a natural base exponential function, the b is replaced by e which means y=[tex]e^{x}[/tex]. In the given question y=[tex]e^{x+7}[/tex] is a natural base exponential function since the base is the natural base.
Therefore we found that the given function is a natural base exponential function.
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There are between 50and 60 eggs in a basket when mohammed counts by 3's,there are 2egg left left over when he counts by 5's there are 4 left over how many eggs are there in the basket
Answer: 59 eggs
Step-by-step explanation: Dividing 3 will get you 19 eggs with 2 left over. Dividing 59 by 5 will get you 11 eggs and 4 left over
Solve. Check for extraneous solutions. √-3 x-5=x+3
-7 = extraneous solution
The equation is
[tex]\sqrt{-3x - 5}[/tex] = x + 3
To find the value of x we need to square both sides of the equation
[tex](\sqrt{-3x - 5})^{2}[/tex] = [tex](x + 3)^{2}[/tex]
- 3x -5 = [tex]x^{2}[/tex] + 6x + 9
[tex]x^{2}[/tex] + 9x + 14 = 0
[tex]x^{2}[/tex] + 7x + 2x + 14 =0
x( x + 7) + 2( x + 7) = 0
(x + 7) (x + 2 ) = 0
x = -2, -7
To find the extraneous solution we have to put both the value of x in the equation.
x=-2
[tex]\sqrt{(-3 * -2) - 5}[/tex] = -2 +3
[tex]\sqrt{1}[/tex] = 1
1 = 1
x = -7
[tex]\sqrt{(-3 * -7) - 5}[/tex] = -7 +3
[tex]\sqrt{16}[/tex] = -4
4 = -4
The extraneous solution of the equation is -7 and -2 is the solution of the equation
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PLEASE HELP QUICK TYSM
Answer:
Step-by-step explanation:oooooooooooooooooooooooooooooooooooooo
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Maxwell drives 45 miles/hour for 0.4 hours. Bianca drives 65 miles/hour for 0.25 hours.
Who drove farther?
Answer:
D Maxwell drove further. He drove 18 miles.
Step-by-step explanation:
Distance = Speed × Time
Maxwell:
Distance = 45 × 0.4
Distance = 18 miles
Bianca:
Distance = 65 ×0.25
Distance = 16.25 miles
18 > 16.25
Maxwell drove further. He drove 18 miles.
Answer:
D. Maxwell. He drove 18 miles,
Step-by-step explanation:
Distance = speed * time
Maxwell drives:
45 * 0.4 = 18 miles.
Bianca drove:
65 * 0.25 = 16.25 miles.
4/15+1/2?????????????????????????????????????????????????????????????????????????????????????????
Answer:
23/30
Step-by-step explanation:
4/15= 8/30
1/2= 15/30
8/30+15/30= 23/30
Im not sure how to do this one
Answer:
B
Step-by-step explanation:
6x - 8x - 4 = - 2x - 2 , that is
- 2x - 4 = - 2x - 2 ( add 4 to both sides )
- 2x = - 2x + 2 ( add 2x to both sides )
0 = 2 ← not possible
this indicates the equation has no solution
Answer:
6x-8x-4=-2x-2 (group the like terms)
6x-8x+2x= 4-2 (-8x+2x= -6x and 6x-6x=0) (4-2=2)
answer= 0=2
,therefore: it has no solution
Step-by-step explanation:
the answer is 0=2 which mean there is nothing that 2 is equivalent to because when you group the like terms and work out the answer the x in the equation will be canceled.