The required simplified form of the expression 12x⁵/6x² is 2x³.
What are exponential expressions?Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. To answer the exponential expressions, we may need to apply the relationship between exponents and logarithms.
The exponential expression is given in the question as:
12x⁵/6x²
To simplify the expression 12x⁵/6x², we can start by dividing 12 by 6 to get:
12x⁵/6x² = (12/6)x⁵/x² = 2x⁵/x²
Then, we can use the quotient of powers rule, which states that when we divide two powers with the same base, we can subtract the exponents to get:
2x⁵/x² = 2x⁵⁻² = 2x³
Therefore, the expression is 2x³ equivalent to the given expression 12x⁵/6x².
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A wildlife biologist catches and releases 20 fish from two different lakes at random locations. he catches 10 fish at lake palmer and 10 fish at lake dalton. he measures the length of each fish to the nearest quarter of an inch. palmer dalton first quartile 6.75 5.5 second quartile (median) 10.25 6.75 third quartile 13 7.5 based on the samples, what generalization can be made? at least 25 percent of the fish in both lakes are no longer than 6 inches. the interquartile range for lake dalton is 2 inches greater than the interquartile range for lake palmer. the first quartile value at lake palmer is 1.25 inches longer than the first quartile value at lake dalton. not enough information is provided to draw any of these conclusions.
Answer:
The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton.
Step-by-step explanation:
twenty-four players divided into three teams?
What is the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4) ?
y−4=−911(x+8)
y+4=−911(x−8)
y−4=−15(x+8)
y+4=−15(x−8)
plzzz helppppppp meeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the line is y - 4 = (-9/11)[x + 8] which passes through the points (3, −5) and (−8, 4) option (A) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The two points are: (3, −5) and (−8, 4)
As we know,
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
The equation of the line:
y - 4 = (4+5)/(-8-3)[x + 8]
y - 4 = (-9/11)[x + 8]
Thus, the equation of the line is y - 4 = (-9/11)[x + 8] which passes through the points (3, −5) and (−8, 4) option (A) is correct.
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When h has the value of 5 calculate 6h +9
25% of what number is 9
can you explain how you got your answer and show your answer too.
Thank You
Solve for x.
−1/3x≤−6
Answer:
x ≥ 18
hope this helps! <3
The solution of the inequality is x ≥ 18.
What is Inequality?Inequalities are mathematical formulas in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is substituted by a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
We have −1/3x≤−6
Now, Multiply the inequality 3 from both side
-3x /3 ≤ -6 x 3
-x ≤ -18
Multiply (-1) to both side as
x ≥ 18.
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What adds together to equal -7
1) AB¯≅AD¯ Given
2)∠ACD is a right angle.- Given
3) m∠ACD=90° -Definition of right angle
4) m∠ACB=90° -Given
5) m∠ACB=m∠ACD -Transitive Property of Equality
6) ∠ACB≅∠ACD Definition of congruent angles
7) C is the midpoint of BD¯ Given
8)C bisects BD¯ ?
9) BC¯≅CD¯ Definition of bisect
10) AC¯≅AC¯ Reflexive Property of Congruence
11) △ABC≅△ADC -SAS Congruence Postulate
What is the correct reason for Statement 8?
Given
Definition of bisect
Definition of congruent segments
Definition of midpoint
Answer:
By definition of midpoint.
Step-by-step explanation:
proof:
1.Statement: [tex]\overline{AB}\cong \overline{AD}[/tex].
Reason: Given.
2.Statement: [tex]\angleACD[/tex] is a right angle.
Reason:Given.
3.Statement:[tex]m\angle ACD=90^{\circ}[/tex].
Reason: By definition of right angle.
4.Statement: [tex]m\angle ACB=90^{\circ}[/tex].
Reason: Given.
5.Statement: [tex]m\angle ACB=m\angle ACD[/tex]
Reason: Transitive property of equality.
6. Statement:[tex] m\angle ACB\cong m\angle ACD[/tex].
Reason: By definition of congruent triangles.
7.C is the midpoint of [tex]\overline {BD}[/tex].
Reason: Given.
8.Statement: C bisect [tex]\overline{BD}[/tex]
Reason: By definition of midpoint.
9.Statement:[tex]\overline{BC}\cong \overline{CD}[/tex]
Reason: By definition of bisect.
10.Statement:[tex]\overline{AC}\cong\overline{AC}[/tex]
Reason: By reflexive property of congruence.
11.Statement:[tex]\triangle ABC\cong \triangle ADC[/tex].
Reason: SAS congruence postulate.
The volume of a can (right circular cylinder) is 10 cubic feet. the curved surface area is the area of the side. write the curved surface area s as a function of the radius r. s =
The volume formula of a cylinder is given as:
V = π r^2 h
So plugging in the value of the volume:
10 ft^3 = π r^2 h
h = 10 / (π r^2) ---> eqtn 1
The formula for the surface area of cylinder is:
s = 2 π r h + 2 π r^2
plugging in eqtn 1:
s = 2 π r [10 / (π r^2)] + 2 π r^2
s = (20 / r) + 2 π r^2 (ANSWER)
what is the value of x (I will give 20 points to best answer)
Answer options
61
37
85
122
The value of x is 61 after using the concept of vertically opposite angles option (A) 61 is correct.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
It is given that:
The angles are shown in the picture.
As we know, from the definition of vertically opposite angles, the angles when two lines intersect each other and at the intersecting point.
The first angle = 2x + 24
The second angle = 146
Equating both the angles:
2x + 24 = 146
2x = 146 - 24
2x = 122
x = 122/2
x = 61
Thus, the value of x is 61 after using the concept of vertically opposite angles option (A) 61 is correct.
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concert tickets cost $15 for general admission, but only $9 with a student ID. ticket sales total $4500. wirte and graph ab equation that models this situation. explain how to use your graph to find how many student tickets were sold if 200 general admission tickets were sold
The equation is given as 15x + 9y = 4500
The tickets sold when 200 are sold is y = 166.7
How to model the equation
The equation that models this would be
$15x + $9y = $4500
15x + 9y = 4500
If 200 admission tickets were sold we would have
15 * 200 + 9y = 4500
3000 + 9y = 4500
9y = 4500 - 3000
9y = 1500
y = 166.7 please approximate because tickets number has to be whole
The approximated total tickets that were sold is given as 167
Use your graph to check for the value of the corresponding y side if 200 tickets are sold
solve the system by substitution. -4.5-2y=-12.5 , 3.35x-y=-0.75
For f(x)=4x squared -3 and g(x)=x +1 find (f - g)(x) PLEASE HELPP
Which of the following represents ninth root of x to the seventh power in exponential form?
Answer:
[tex]x^{\frac{7}{9}}[/tex]
Step-by-step explanation:
write ninth root of x to the seventh power in exponential form
[tex]\sqrt[9]{x^7}[/tex]
To write the radical in exponential form we use the below property
[tex]\sqrt[n]{x^a} = x^{\frac{a}{n}}[/tex]
The radical becomes the base of the fraction
[tex]\sqrt[9]{x^7}=x^{\frac{7}{9}}[/tex]
we cannot simplify the fraction.
The given expression in exponential form is
[tex]x^{\frac{7}{9}}[/tex]
A function is given. Determine the average rate of change of the function between the given values of the variable: f(x)= 4x^2; x=3, x=3+h
Michael has $1.95 in his collection, consisting of nickels and quarters. the number of nickels is three more than the number of quarters. how many nickels and quarters does michael have
One hundred percent of the fish in a pond are goldfish. i take 10$\%$ of the goldfish out of the pond. what percentage of goldfish does the pond now contain?
karen says that 6 is a common factor of 2 and 3 ken says that 6 is a common multiple of 2 and 3 who is correct
What is the product of 6+5i and 4+7i?
Answer:
-11+62i
Step-by-step explanation:
(6+5i)(4+7i)
Use the Distributive Property
24 + 42i + 20i + 35i²
Combine like terms
24+62i+35i^2
i^2 = -1
24+62i+35(-1)
24+62i+(-35)
24+(-35)= -11
-11+62i
The students at Campbell High School have been planting trees as part of an ongoing service project. This month, they averaged 15 trees per participant. That is 150% more trees than their average the last time they did it. What was their average last time?
___ trees
Final answer:
The average number of trees planted by participants last time was 10 trees, calculated by understanding the percentage increase and using basic arithmetic.
Explanation:
The average number of trees planted by participants last time was 10 trees.
To solve this, we know that the current average is 15 trees per participant, which is 150% more than the last average. This means the current average is 250% of the last average. To find the last average, you divide the current average by 2.5 (250%), giving you 6. Then, you calculate 150% of 6, which equals 9. Adding 6 and 9 together gets you 15 trees, the current average, confirming the last average was 10 trees.
Dana was picking strawberries to sell and placing them in baskets on a table. the number of strawberries in the basket is 4 more than the number of baskets on a table. if b represents the number of baskets on each table, which expression can be used to represent the number of strawberries on 5 tables? 5b4 5(b + 4) 5b(b + 4) 5b + 4
Add.
(−8x4+x3+2x2+2)+(−x4+5x3−x2+5x)
Enter your answer, in standard form, in the box.
Help please!! Find domain and range for 20 points
You flip a coin and then roll a fair six sided die. Then the coin lands heads up and the die shows a one
What is the percent increase modeled in the function f(x)=30(1.25)*
A. 30%
B. 1.25%
C. 25%
D. 75%
the increase would be 1.25-1 = 0.25 = 25%
Answer is C
12x^2 −75=3(2x+?)(2x−5)
What is the missing term in the factorization
To find the missing term in the factorization, we rewrite the equation in the form of ax^2 + bx + c = 0, equate the coefficients and solve for the term. The missing term is -25.
Explanation:
To find the missing term in the factorization, we can rewrite the given equation in a general form of the quadratic equation like ax^2 + bx + c. In our case, this would be:12x^2 - 3(4x^2 - 10x + ?) = −75. Here, 'a' has a coefficient of 12, 'b' is -10 multiplied by 3 (the '3' outside the brackets), and 'c' is ? multiplied by 3. By equating the coefficients on both sides of the equation, we can solve for the missing term '?'. Therefore, the missing term is '? = -75 / 3' or '? = -25'.
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suppose a research team takes a simple random sample of 100 parma wallabies. in this sample, the tails of the wallabies have a mean length of 46 centimeters and a standard deviation of 2.6 centimeters.
What percent of the time could a simple random of 100 parma wallabies have a sample mean that is not in the 95% confidence interval?
5%
0%
2.5%
20%
If it starts out at -10 degrees, what will the temperature be if it rises 30 degrees?
A.10 degrees
B.20 degrees
C.30 degrees
D.40 degrees
add 30 to -10:
-10 + 30 = 20
Answer is B.
help me and show how you got it please
Under which condition does a country with a small GDP have a large per capita income?