A radical expression can always be rewritten using a rational exponent .
Radicals : The expressions which include a root ( [tex]\sqrt[n]{x}[/tex] ) are called radicals . For ex . [tex]\sqrt{2}[/tex] , [tex]\sqrt[3]{3}[/tex] , [tex]\sqrt[7]{5}[/tex] , and so on .
Rational Exponent : Numbers of the form ( [tex]a^{m}[/tex] ) are called rational exponents . For ex . [tex]7^{2}[/tex] , [tex]11^{3}[/tex] , [tex]5^{5}[/tex] and so on .
A radical can be converted into a rational exponent . This can be done by keeping the no . inside root as it is and reciprocating the index and raising it to the power of exponent .
( [tex]\sqrt[n]{x}[/tex] ) = ( [tex]x^{1/n}[/tex] ) where x is the base and 1 / x is the power of the exponent .
Hence , a radical expression can always be rewritten using a rational exponent .
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Help! I know its simple but who is X in X-11=79
Answer:
x = 90
Step-by-step explanation:
x - 11 = 79 ( isolate x by adding 11 to both sides )
x = 79 + 11 = 90
In the past month, Josh rented 6 video games and 4 DVDs. The rental price for each video game was $2.60. The rental price for each DVD was $3.80. What is the total amount that Josh spent on video game and DVD rentals in the past month?
Answer:
$30.80
Step-by-step explanation:
v = the price of each video game = 2.6
d = the price of each DVD = 3.8
x = the total amount Josh spent
6v + 4d = x
Substitute the values for v and d into the equation.
6 (2.6) + 4 (3.8) = x
15.6 + 15.2 = 30.8
Josh spent $30.80 on video game and DVD rentals in the past month.
The scale drawing is a map of the campus of Central Middle School. The school board needs to know
the distance from the art room to the gym in order to build a walkway.
What is the scale factor from the map to the
actual school?
scale factor =?
Answer:Scale factor is 10 , the second part is 50
Step-by-step explanation:
check if each of the following equalities is true for all value of the variables (1-2b)(1-5b+b^2)+(2b-1)(1-6b+b^2)=b(1-2b)
The check done confirmed that the equality is true since the value arrived at while solving the expression is same as the given value
How to check if the equalities is true for all value of the variablesGiven data
[tex](1-2b)(1-5b+b^{2} )+(2b-1)(1-6b+b^{2} )=b(1-2b)[/tex]
breaking the expansion into 2 we have
[tex]=(1-2b)(1-5b+b^{2} )[/tex]
[tex]=(1)(1)+(1)(-5b)+(1)(b^2)+(-2b)(1)+(-2b)(-5b)+(-2b)(b^2)[/tex]
[tex]=1-5b+b^2-2b+10b^2-2b^3[/tex]
[tex]=-2b^3+11b^2-7b+1[/tex]
expanding this [tex](2b-1)(1-6b+b^2)[/tex] gives:
[tex]=2b^3-13b^2+8b-1[/tex]
adding both equation gives
[tex]= -2b^3+11b^2-7b+1 + 2b^3-13b^2+8b-1[/tex]
[tex]= -2b^2 + b[/tex]
[tex]= b - 2b^2[/tex]
[tex]= b (1 - 2b)[/tex]
Since the expansion gave same value we can say that the equality is true
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mixing alcohol solutions a pharmacist needs to obtain a 70% alcohol solution. how many ounces of a 30% alcohol solution must be mixed with 40 ounces of an 80% alcohol solution to obtain a 70% alcohol solution? hint add x ounces of 30% solution to 40 ounces of 80% solution to get x 40 ounces of 70% solution.
10 Ounces of 30% alcohol solution must be mixed.
Let the amount of 30% solution to be added = x ounces
So , total solution is (40+x) ounces.
we know that 30%=0.30 , 80%=0.80 , 70%=0.70
According to the question
x ounces of 30% alcohol solution + 40 ounces of 80% alcohol solution = (40+x)ounces of 70% alcohol solution.
x*(0.30)+40(0.80)=(40+x)*0.70
0.30x+32=40*0.70+0.70x
0.30x+32=28+0.70x
Rearranging the terms we get
0.70x-0.30x=32-28
0.40x=4
x=4/0.40
x=10
Therefore , 10 ounces of 30% alcohol solution must be mixed with 40 ounces of an 80% alcohol solution to obtain a 70% alcohol solution.
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first to answer gets +10 points and brainliest need help please
The dimensions of the shape allow us to find the length of PR to be 19.8 units.
What is the length of PR?The shape that is given is an equilateral triangle. This allows us to know that all the sides of the shape are equal.
This means that PR and QR are the same:
PR = QR
Equate both formulas as:
2n + 9 = 7n - 18
You can then solve for the value of n:
7n - 2n = 18 + 9
5n = 27
n = 5.4
The length of PR is therefore:
= 2n + 9
= 2 (5.4) + 9
= 19.8 units
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Write each expression as a single logarithm. Identify any properties used. log 5-2 log x
According to the given statement The single form of the given logarithm log 5-2 log x is log₁₀(5/x²).
What is logarithm property?The features of log are utilized to expand (or compress) a single logarithm across numerous logarithms. A logarithm is simply another way of expressing exponents. Thus, logarithmic features are derived from exponentiation qualities.
According to the given data:log 5-2 log x
This can be written as:
log₁₀ (5) - 2log₁₀(x)
Apply log rule (b logₐ (c) = logₐ(cᵇ)):
2log₁₀(x) = log₁₀(x²)
= log₁₀(5) - log₁₀(x²)
Applying log rule (logₐ (b) - logₐ (c) = logₐ(c/b)):
log₁₀(5) - log₁₀(x²) = log₁₀(5/x²)
The single form of the given logarithm log 5-2 log x is log₁₀(5/x²).
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Are the ones with answers correct? I just want to make sure I’m right
Answer:
yes just make sure to pay close attention
m∠PQS=(3x−3)° and m∠RQS=(x+19)°. Find the value of x.
The figure shows straight angle P Q R that consists of two smaller angles, P Q S and R Q S.
34
41
21
56
The value of x is 41 . Option B
How to determine the angleIt is important to note that angles on a straight line are known to be supplementary.
Supplementary angles are defined as angles that sum up to 180 degrees.
From the information given, we have that;
m∠PQS=(3x−3)° m∠RQS=(x+19)Since angles on a straight line sum up to 180 degrees, we have that;
m∠PQS + m∠RQS = 180°
Substitute the values into the equation
3x - 3 + x + 19 = 180°
collect like terms
4x = 180 - 16
4x = 164
Make 'x' the subject of formula
x = 164/4
x = 41
Thus, the value of x is 41 . Option B
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round up 1.237 to the nearest hundredths
Answer:
1.24
Step-by-step explanation:
To round 1.237 to the nearest 100th ( you have to know the thousandth one. which the value is 1.237, ) which is 7 and equal to or more than 5. Therefore, the hundredths value of 1.237
Math on the Spot The Hungarian club needs to earn at least from a bake sale to fund their Goulash Festival. They are selling croissants for each and loaves of French bread for each. Write a linear inequality to describe the situation and graph the solutions.
Answer:
2x +5y ≥ 175 is required inequality
Step-by-step explanation:
If x and y vary directly and y is 40 when x is 5, find y when x is 6.
The area of the rectangular arena can be represented as A = (8y2 - 18y) square feet.
Here, we are given the dimensions of a rectangular arena, which are as follows-
Length = 4y - 9 feet
width = 2y feet
The area of a rectangle is given by the formula-
Area of a rectangle = length x breadth
Thus, in this case, area (A) can be calculated as follows
A = (4y - 9) * 2y
Now, we simplify the equation-
A = (4y)(2y) - 9(2y)
A = 8[tex]y^{2}[/tex] - 18y
Thus, the area of the rectangular arena can be represented by the following equation- A = (8[tex]y^{2}[/tex] - 18y) square feet.
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I’m slow asl bro istg help
Answer:
Area = 1725 ft²
Step-by-step explanation:
In this question, we have to calculate the area of the trapezoid. As mentioned in the hint, the formula for the area of a trapezoid is:
[tex]\boxed{\mathrm{Area = \frac{b_1 + b_2}{2} \times h}}[/tex],
where [tex]\mathrm {b_1}[/tex] and [tex]\mathrm {b_2}[/tex] are the two parallel bases of the trapezoid, and h is the height of the trapezoid.
As we can see in the diagram the two bases are 50 ft and 65 ft respectively, and the height is 30 ft. Using this information and the formula above, we can calculate the formula of the trapezoid:
[tex]\mathrm{Area = \frac{(50 + 65)\: \mathrm{ft}}{2} \times 30 \: \mathrm{ft}}[/tex]
[tex]= \frac{115 \: \mathrm {ft}}{2} \times 30 \: \mathrm{ft}[/tex]
[tex]= \bf 1725 \: ft^2[/tex]
Therefore, the area of the lawn is 1725 ft².
Write An expression that represents the phrase "one third the difference of 15 and a number."
answer:
(15-x)/3
"one third the difference of 15 and a number."
I need help with c and 3. I’ll give brainliest.
Answer:
This might help
Step-by-step explanation:
for C-The number of lines of symmetry in a regular polygon is equal to the number of sides.
for 3 I’m not as sure but all I know is that Y is greater than 90 degrees and x is also greater than 90 degrees
Evaluate a2b2c2 for a = 2, b = 3, and c = 4.
Hey there!
a^2 * b^2 * c^2
= 2^2 * 3^2 * 4^2
= 2 * 2 * 3 * 3 * 4 * 4
= 4 * 9 * 16
= 36 * 16
= 576
Therefore, your answer should be:
576
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Brandon has a jar of quarters and dimes with a total value of $5.95. The number of quarters is 5 less than twice the number of dimes. How many quarters and how many dimes does Brandon have?
The quarters and dimes that Brandon have will be 13 quarters and 9 dimes.
How to illustrate the information?Based on the information given, the appropriate equation will be:
0.25q + 0.10d = 5.95 .... i
q = 2d - 5 .....
q = quarter
d = dime
From equation i, multiply through by 100
25q + 10 = 595
Put equation ii into i
25q + 10d = 595
25(2d - 5) + 10d = 595
50d - 125 + 10d = 595
Collect like terms
60d = 595 + 125
60d = 720
Divide
d = 720/60
d = 9
q = 2d - 5
q = 2(9) - 5
q = 18 - 5 = 13
Therefore, the quarters and dimes that Brandon have will be 13 quarters and 9 dimes.
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Let f(x)=2x-3. Write a function g whose graph is a reflection in the y axis of the graph of f
Write an expression for the perimeter of the figure below.
From the diagram shown, the algebraic expression representing the perimeter of the shape is 12x - 10
This is determined by substituting the values into the formula for perimeter.
How to determine the perimeterThe formula for determining the perimeter of an isosceles trapezoid is expressed as;
Perimeter = a + b + c + d
Note that none of the sides of an isosceles trapezoid are equal
Where;
a = xb = side length = 2x + 5c = side length = 3x + 2d = base length = 6x - 17Now, let's substitute the values into the formula for perimeter of an isosceles trapezoid
Perimeter = x + (2x + 5) + ( 3x + 2) + (6x - 17)
Now, expand the bracket
Perimeter = x + 2x + 5 + 3x + 2 + 6x - 17
collect like terms
We have;
Perimeter = x + 2x + 3x + 6x + 5 + 2 - 17
Add like terms
Perimeter = 12x + 7 - 17
Perimeter = 12x - 10
Thus, the algebraic expression representing the perimeter of the shape is 12x - 10
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Dylan prepared 49 kilograms of dough after working 7 hours. How many hours did Dylan work if he prepared 70 kilograms of dough? Solve using unit rates.
Answer:
10 hours
Step-by-step explanation:
49kilograms/7hours = 7 kilograms per hour
70 kilograms ÷ 7 kilograms per hour = 10 hours
FCP#1. If your teacher has three dogs named Gabby, Ranger, and Rico, how many different ways can the dogs be lined up for their
photograph?
If teacher has three dogs named Gabby, Ranger, and Rico then in 6 different ways can the dogs be lined up for their photograph.
What is Permutation?
The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.
If teacher has three dogs named Gabby, Ranger, and Rico.
We can lineup 3 dogs in 3! ways.
3!=3*2=6 different way.
Gabby, Ranger, Rico
Ranger, Rico, Gabby
Rico, Gabby, Ranger
Ranger, Gabby, Rico
Rico, Ranger, Gabby
Gabby, Rico, Ranger.
Therefore in 6 different ways can the dogs be lined up for their
photograph.
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if the mass is 12g and the volume is 13cm3 what is the density
[tex] \rho = \frac{mass}{volume} = \frac{12}{13} \approx0.923 \: g.cm {}^{ - 3} [/tex]
Rewrite 50,800,000 in scientific notation.
Question:
Rewrite 50,800,000 in scientific notation.
Answer:
5.08 x 10 to the power 7
Step-by-step explanation:
To get the answer you would first need to change the number into a decimal which would be 50800000.0 then you count the number of zeros in this case there is 7 but then number is not 1-10 so you could use the bumps to make it a decimal which is 5.08
I hope it helps you!
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#Learn with Brainly
Answer:
5.08 times 10, to the power of 7
Step-by-step explanation:
Have a great rest of your day
The one and only
Mr. Universe
Reasoning At a butcher shop, Hilda
bought beef and pork. She left with
18 8/25 pounds of meat. Express the
number of pounds of pork she bought
using a decimal.
Reasoning At a butcher shop, Hilda bought beef and pork. She left with 18 8/25 pounds of meat. Express the number of pounds of pork she bought using a decimal.
Hilda bought 18.32 pounds of pork.
Hilda purchased 18.32 pounds of pork, which is a terminating decimal, according to the conversion of an improper fraction to a decimal.
She left behind, in pounds, the following amount of meat:
[tex]18 \frac{8}{25}[/tex]
Now we have to convert the improper fraction to decimal, which is made adding the decimal fraction to the integer part, that is:
[tex]18 \frac{8}{25} =18+\frac{8}{25} = 18+0.32 = 18.32[/tex]
Therefore, the number of pounds of pork Hilda bought using a decimal number is 18.32.
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a bull weighs 1,700 pounds. Is it more appropriate to express the bull's weight as 1,700 pounds or 2.72 x 10 to the 4th power onces? explain your reasoning
It is better to express the bull's weight as 1,700 pounds.
How to calculate the value?It should be noted that from the information given, the bull weighs 1,700 pounds.
It should be noted scientific notation isn't required in all situation.
In this case, it's better to express the bull's weight as 1,700 pounds. This aligns better with the weight.
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Meredith lives 24blocks from her friend's house. if she travels 1block every minute, how many minutes will it take her to reach her friend's house? what if she travels 2blocks every minute? show how you calculate each answer.
Answer:
1 block per minute: 24 minutes. 2 blocks per minute: 12 minutes.
Step-by-step explanation:
For the 2 blocks per minute one, it would just be 24/2 because she is going 2 blocks per minute, equaling 12.
Thirteen less than triple n is negative ten
Answer:
n = 1
Step-by-step explanation:
triple n is 3 times n = 3n , then
3n - 13 = - 10 ( add 13 to both sides )
3n = 3 ( divide both sides by 3 )
n = 1
I need help, please help!
Answer:
d because every number power of zero is one ande the negative exponent defines to 1/that number
f(x)=x^2+8x+6 what is the value of f (4)
Answer: the answer would be 54
Step-by-step explanation:
4 x 4 = 16
8 x 4 = 32
16 + 32 + 6 = 54
EXTRA POINTS FOR A CORRECT AND SURE ANSWER
Answer: The equivalent decimal is 0.5
Step-by-step explanation: Ok, so 4/8 is a equivalent fraction to 1/2.
0.5 is the decimal form for one half.
I am also 100% sure I am right, so you have no worries :D
Answer: the answer is 0.5
Step-by-step explanation: