Answers
We will be using division property of exponents.
The property is as follows:
[tex] \frac{x^{a}}{x^{b}} =x^{a-b} [/tex]
This means if we have same base in both numerator and denominator, the exponents will get subtracted.
In our question we have
[tex] \frac{4^{1}}{4^{3} } =4^{1-3} [/tex]
[tex] \frac{4^{1}}{4^{3} } =4^{-2} [/tex]
Now we will use another property of exponents here:
[tex] x^{-a} =\frac{1}{x^{a} } [/tex]
So if we take reciprocal of the above expression we will get,
[tex] 4^{-2} =\frac{1}{4^{2} } [/tex]
Rewriting the final answer:
[tex] \frac{6^{3} }{4^{2} } [/tex]
Related Questions
What situation could this diagram represent?
Answers
Answer: B- Flipping two coins once
Step-by-step explanation:
B. Tossing Two Coins Once
I Got it Right i Promise
-(m-6)=3m+14 what is m
Answers
[tex] - m + 6 = 3m + 14[/tex]
[tex] - 4m = 8[/tex]
[tex]m = - 2[/tex]
Simplify each expression. Select the correct answer from the drop-down menu.
−6(3i)(−2i) =
2(3 − i)(−2 + 4i) =
Answers
2(3-I)(-2+4i)= -4 + 28i
the answer is:
−6(3i)(−2i) = -36
2(3 − i)(−2 + 4i) = -4+28i
2i(4 − 5i) = 10+8i
hope this helps! :o)
It is given that y varies directly as x. If y = 5 when x = 4 determine the constant of variation.
A) -4/5
B) 4
C) 5
D) 5/4
Answers
use the x,y values to find k
5 = 4k
5/4 = k
answer is D
Write an equition that expresses y in terms of x
Answers
y on the left side is expressed in terms of x on the right side.
You and your friend are standing back to back. Your friend runs 20 feet forward and then 15 feet right. At the same time, you run 12 feet forward and then 9 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball
Answers
Evaluate. 6+5|4-3^2| A. -19 C. 31 D. 55
Answers
Answer:
6 + 5|4 - 3²| =
6 + 5|4 - 9| =
6 + 5|-5| =
6 + 5(5) =
6 + 25 = 31
The correct answer is C.
Jeremiah built a box that was 5 inches long by 6 inches wide by 7 inches high .he started filling it up with 1 cube.he realized quickly that he did not have nearly enough cubes to fill the box .can he still figure out how many cubes it will hold?
Answers
PLEASE HELP!!!! SOLVE: |2x+1|+|3x−4|=5
Answers
5x-3=5 Group like terms
5x=8 Add 3 to the end to isolate x
x=1.6 Divide 8 by 5
Hope this helped
A function is a relationship that maps__.
A) many inputs to many outputs or one input to one output
B) many inputs to many outputs or many inputs to one output
C) one input to many outputs or one input to one output
D) one input to one output or many inputs to one output
Answers
Solution:
A function is always a relation but a relation is not always a fucntion.
For example
we can make a realtion of student roll number and their marks obtained in mathematics.
So we can have pairs like (a,b), (c,d)..etc.
Its a realtion but it may not be function. Because function follows that for same input there should not be diffrent output, aslo there could be many inputs to one output in the case of constant function . But this doesn't holds a necessary condition in case of relation.
Because two diffrent students with two diffrent Roll number may have same marks.
Hence the foolowing options holds True in case of a function.
A) many inputs to many outputs or one input to one output.
D) one input to one output or many inputs to one output.
Answer:
The correct answer is D. A function is when an input has one output. An input can only have one output but an output can have multiple inputs. Hope this helps!
an art easel with equal sides are opened and placed on a desk, classify the type of triangle formed by the easel and the desk
Answers
PLZ HELP!
at the apple orchard workers were asked to put 100 apples in barrels. the following five were filled incorrectly. if the supervisor wrote +5 above a barrel, it meant that the barrel was 5 apples over, -5 meant that a barrel was 5 apples less than 100.
How many TOTAL apples are i the five barrels?
a -480 apples
b 498 apples
c 500 apples
d 520 apples
Answers
Two sides of a triangle measure 20 cm and 30cm. What is the third side?
Answers
It depends on what angles there are, and how many degrees are in each angle. In order to figure this problem out, you need to know at least one angle ;)
Hope this helps!
Hope this helped☺☺
If a(x) is a polynomial function and b(x) is a polynomial function, then which of the following could be the sum of a(x) + b(x)?
A. ex + 2
B. x2 + 2x − log(x)
C. x6 − x4 + 9x
D. 5x² − 3x
Answers
The formatting is not proper in the options C and D. Only 1 option can be the correct answer.
If the options are:
[tex]C) x^{6} - x^{4} +9x \\ \\ D) 5x^{2} -3^{x} [/tex]
Then option C would be the correct answer as in option D variable is in the exponent which is against the definition of polynomial function.
If the options are:
[tex]C) x^{6} - x^{4} +9^{x} \\ \\ D) 5x^{2} -3x[/tex]
Then option D would be the correct answer as in option C variable is in the exponent which is against the definition of polynomial function.
Options C and D are correct
Explanation:
We are given that both functions a(x) and b(x) are polynomial.
This means that adding them will also produce a polynomial function
polynomial a(x) + polynomial b(x) = polynomial c(x)
Now, let's check the given options:
Option A:
e² + 2
This is a exponential function. An exponential function is not a polynomial. Therefore, this option is incorrect
Option B:
x² + 2x - log(x)
This is a logarithmic function. A logarithmic function is not a polynomila.
Therefore, this option is incorrect
Option C:
x⁶ - x⁴ + 9x
This is a polynomial of the 6th degree.
Therefore, this option is correct
Option D:
5x² - 3x
This is a polynomial of the second degree.
Therefore, this option is correct
Based on the above, options C and D are both correct options
Hope this helps :)
Bill says that he can add 23 and 40 without regrouping. Is bill correct? How do you know?
Answers
Hope this helped☺☺
write the equation of the parabola below
Answers
Equation is: y = 0.5x² + 0.5x - 3
Explanation:
general form of the parabola is:
y = ax² + bx + c
Now, we will need to solve for a, b and c.
To do this, we will simply get points from the graph, substitute in the general equation and solve for the missing coefficients.
First point that we will use is (0,-3).
y = y = ax² + bx + c
-3 = a(0)² + b(0) + c
c = -3
The equation now becomes:
y = ax² + bx - 3
The second point that we will use is (2,0):
y = ax² + bx - 3
0 = a(2)² + b(2) - 3
0 = 4a + 2b -3
4a + 2b = 3
This means that:
2b = 3 - 4a
b = 1.5 - 2a ...........> I
The third point that we will use is (-3,0):
y = ax² + bx - 3
0 = a(-3)² + b(-3) - 3
0 = 9a - 3b - 3
9a - 3b = 3 ...........> II
Substitute with I in II and solve for a as follows:
9a - 3b = 3
9a - 3(1.5 - 2a) = 3
9a - 4.5 + 6a = 3
15a = 7.5
a = 7.5 / 15
a = 0.5
Substitute with the value of a in equation I to get b as follows:
b = 1.5 - 2a
b = 1.5 - 2(0.5)
b = 0.5
Substitute with a and b in the equation as follows:
y = 0.5x² + 0.5x - 3
Hope this helps :)
What is the area of the triangle in this coordinate plane? 9.0 units² 14.0 units² 16.5 units² 24.5 units² A graph with a triangle drawn on it
Answers
In a dog show, there will be a gold, a silver, and a bronze medal awarded. There are
5 finalists. In how many different ways can the 3 medals be awarded?
Answers
60 ways
Explanation
In permutation the order really matters unlike combination where order does not matter.
The question wants you to find how many time you can choose 3 out of 5 with order.
This means we should find 5 permutation 3.
5P3=5!/3!
=(5×4×3×2×1)/(3×2×1)=5×4
=60
Answer:
60 ways
Step-by-step explanation:
There are five finalist and 3 medals.
For getting the first medal, there are 5 choices, any of the finalist can get that.
For getting the second medal, we are left with 4 choices.
For getting the third medal we are left with 3 choices.
Hence, the number of ways 3 medals can be awarded are:
5×4×3=60 ways
Solve each equation. Factor and use the zero product property to solve. Show all work algebraically.
Answers
5n^2 = 4n^2 - 4n
n^2 + 4n = 0
n(n + 4) = 0
n = 0 or n + 4 = 0
n = 0 or n = -4
24.
d^2 - 4d = 3d
d^2 - 7d = 0
d(d - 7) = 0
d = 0 or d - 7 = 0
d = 0 or d = 7
25.
3 - 13h = 3 - 8h + h^2
Subtract 3 from both sides.
-13h = -8h + h^2
Add 13h to both sides.
0 = 5h + h^2
0 = h(5 + h)
h = 0 or 5 + h = 0
h = 0 or h = -5
round 49,953 to the nearest hundred
Answers
PLEASE NEED HELP WITH A-D
Answers
4(d+3c)
b.
6(3x+5y)
c.
7(3a+4y)
d.
8(3f + 7g)
a. 4(a + 3e)
b. 6(3x + 5y)
c. 7(3a + 4y)
d. 8(3f + 7g)
Going against the current, a boat takes 7 hours to make a 120 mile trip. When the boat travels with the current on the return trip, it takes 4.5 hours. If x is the speed of the boat is still water and y is the speed of the current, which of the following system of equations could be used to solve the problem?
Answers
The system of equations that could be used to solve the problem is 7(x - y) = 120; 4.5(x + y) = 120. option A
which of the following system of equations could be used to solve the problem?
If
x is the speed of the boat is still water
y is the speed of the current
7(x - y) = 120
4.5(x + y) = 120
Therefore, the system of equation can be rewritten as;
7x - 7y = 120
4.5x + 4.5y = 120
Complete question:
Going against the current, a boat takes 7 hours to make a 120 mile trip. When the boat travels with the current on the return trip, it takes 4.5 hours. If x is the speed of the boat is still water and y is the speed of the current, which of the following system of equations could be used to solve the problem?
A. 7(x - y) = 120; 4.5(x + y) = 120
B. 7(x + y) = 120; 4.5(x + y) = 120
C. 7(x - y) = 120; 4.5(x - y) = 120
D. 7(x + y) = 120; 4.5(x + y) = 120
A cake recipe requires 1 2/3 cups of milk how many cups altogether are necessary to make 4 cakes
Answers
6 and 2/3
5/3*4=
20/3=
6 2/3.
Hope this helped☺☺
if a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 ft, what is the volume of the hole? use 22/7 for pi
Answers
You will first need to find the radius by using the information given about the circumference and the circumference formula.
C = pi x d
44 = 22/7 d
d = 14 feet.
Then use the diameter to find the radius of 7 feet.
V = 1/3 x r^2 x h
1/3 x 7^2 x 3
V = 49 cubic feet
Final answer:
To find the volume of a cone-shaped hole with a depth of 3 feet and a base circumference of 44 ft, calculate the radius using the circumference formula, then plug the radius and height into the volume formula to get 154 cubic feet.
Explanation:
The volume of a cone-shaped hole can be calculated using the formula V = (1/3) × π × r² × h, where r is the radius of the base and h is the height of the cone. In this case, the circumference of the base, 44 ft, can be used to find the radius. Given that the radius is 14 ft, and the height is 3 ft, you can substitute these values into the formula to find the volume of the hole.
Calculate the radius: Circumference = 2πr, so r = Circumference / 2π = 44 / 2π = 7 ft.
Calculate the volume: V = (1/3) × 22/7 × 7² × 3 = 154 ft³.
What is the volume of this right triangular prism?
A.)144.2 cm3
B.)164.8 cm3
C.) 288.4 cm3
D.) 1153.6 cm3
Answers
Hope this helps:)
= 0.5* 7 *4* 10.3 =144.2 cm3
A bag of fruit contains 3 apples, 2 oranges, 1 banana and 4 pears. What is the probability that I will pull out a banana first and a pear second?
Answers
In which quadrant of the coordinate graph does point F lie? Quadrant I Quadrant II Quadrant III Quadrant IV
Answers
But, Quadrant 1 is the top right corner, Quadrant 2 is the top left, and it continues like that in a counterclockwise way.
The quadrant of the coordinate graph does point F lie in quadrant IV.
What is Quadrant in Graph?The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant.
The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes.
The sign notations for four Quadrants is as follows:
Quadrant I :
both x and y positive.
Quadrant II :
x negative and y positive
Quadrant III:
x and y both negative.
Quadrant IV:
x positive and y negative.
As, the point F has coordinates (1,-5) which shows x is positive and y is negative.
So, point F is in quadrant IV.
Learn more about Quadrant here:
https://brainly.com/question/9182164
#SPJ5
What is the value of G in the center and how do you solve it?
Answers
7 + 3c = -11 --> c = -6
-9 - a/4 = 5 --> a = -56
b/5 +9 = 6 --> b = 75
second, solve:
a/f = -7 --> substitute -56 in for a --> -56/f = -7 --> f = 8
b/e = 3 --> substitute 75 in for b --> 75/e = 3 --> e = 25
3 = c/d --> substitutie -6 in for c --> 3 = -6/d --> d = -2
third solve:
g = d+e+f --> substitute -2 in for d, 25 in for e, and 8 in for f.
g = -2 + 25+8
g = 31
3 = c/d => d = c/3
7+3c = -11 => 3c = -11 - 7 => 3c = -18 => c = -18/3 => c = -6.
Now d = c/3 => d = -6/3 => d = -2.
Lets now find out e:
b/e = 3 => e = b/3
b/5 + 9 = 6 => b = (6-9)*5 => b = -15
Now e = b/3 => e = -15/3 = -5
Now we need to find f:
a/f = -7 => f = a/-7
-9 - a/4 =5 => a= (-9-5)*4 = -56
Now f = a/-7 => f = -56 / -7 = 8
So g = d + e + f
= (-2) + (-5) + 8
= 1
Therefore g = 1
Last year, there were 80 students in the orchestra. This year there are 100 students in the orchestra. Determine the percent of increase in the number of students taking orchestra from last year to this year.
A 25%, because 100-80/80= 25%
B 20%, because 100-80/100= 20%
C 80%, because 80/100= 80%
D 125%, because 100/80= 125%
Answers
The answer is A.
To find the percent increase, you need to 1. Find the difference between the two numbers, and 2. Divide it by the original number.
100-80/80 = 25%
Hope this helps!
if a line is tangent to a circle at how many points does it interest the circle?