Step-by-step explanation:
[tex]\text{Use:}\\\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\(a^n)^m=a^{nm}\\\\a^{-n}=\left(\dfrac{1}{a}\right)^n\\\\=============================[/tex]
[tex]A.\ \dfrac{5^3}{5^6}=5^{3-6}=5^{-3}=\left(\dfrac{1}{5}\right)^3\\\\B.\ (14^3)^6=14^{3\cdot6}=14^{18}\\\\C.\ 8^3\cdot8^6=8^{3+6}=8^9\\\\D.\ \dfrac{16^6}{16^3}=16^{6-3}=16^3\\\\E.\ (21^3)^{-6}=21^{3\cdot(-6)}=21^{-18}=\left(\dfrac{1}{21}\right)^{18}\\\\F.\ 100^0=1\\\\G.\ \dfrac{\left(\frac{2}{5}\right)^8}{\left(\frac{2}{5}\right)^6}=\left(\dfrac{2}{5}\right)^{8-6}=\left(\dfrac{2}{5}\right)^2\\\\H.\ (0.15)^{-2}\cdot(0.15)^4=(0.15)^{-2+4}=(0.15)^2\\\\I.\ 7^{-5}=\left(\dfrac{1}{7}\right)^5[/tex]
[tex]J.\ 4\cdot4^3=4^{1+3}=4^4[/tex]
Find the greatest common factor of 28a^3 , 12a^4 and 26a^5
Answer:
2a³
Step-by-step explanation:
2a³ can divide all these without living a remainder
Help please! Someone!
Answer:
8
Step-by-step explanation:
Since AB is tangent to the circle, ABC is a 90 degree angle. Using either knowledge about special triangles (3-4-5) or the Pythagorean theorem, BC will equal 8.
Hope this helped.
A group of 35 team members needs to be divided into smaller workgroups. If each group is to contain two, three, or four people, what is the smallest number of groups possible?
Answer:
9
Step-by-step explanation:
Since we want the fewest number of groups possible, we need to maximize the number of people in each group. Since there can be a maximum of four people in each group, we can have a maximum of [tex]\left\lfloor \frac{35}{4}\right \rfloor=8[/tex] groups of four. The final three students can form the last group, hence the smallest number of groups possible is [tex]8+1=\boxed{9}[/tex]
A plant 3 inches tall grows an average of 0.5 inches each month. Which equation models the heigh h after x months
Answer:H = 3 + 0.5x
Step-by-step explanation:
This would be H = 3 + 0.5x
Two vertices of a right triangle have the coordinates (-2, 5) and (9, 5). What is the length of the side formed by these vertices?
Answer:
11 unit
Step-by-step explanation:
Applying,
s = √[(y₂-y₁)²+(x₂-x₁)²]...................... Equation 1
Where s = length of the side formed.
From the question,
Given: x₁ = -2, x₂ = 9, y₁ = 5, y₂ = 5
Substitute these values into equation 1
s = √[(9+2)²+(5-5)²]
s = √(11²)
s = 11 unit.
Hence the length of the side formed by the vertices is 11 unit
can you solve this problem please
Answer:
k = 11
Step-by-step explanation:
Given the points are collinear then the slopes between consecutive points are equal.
Using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)
m = [tex]\frac{-1-1}{1-5}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]
Repeat with another 2 points and equate to [tex]\frac{1}{2}[/tex]
with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (k, 4)
m = [tex]\frac{4+1}{k-1}[/tex] , then
[tex]\frac{5}{k-1}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
k - 1 = 10 ( add 1 to both sides )
k = 11
pleaaseee explain !!
Answer:
64
Step-by-step explanation:13+51=64
Solve:
[tex] \frac{dy}{dx} = {x}^{3} + 5x - 18[/tex]
[tex]y = \frac{1}{4} {x}^{4} + \frac{5}{2} {x}^{2} - 18x + k[/tex]
Step-by-step explanation:
[tex]dy = ( {x}^{3} + 5x - 18)dx[/tex]
Integrating the above expression, we get
[tex]y = \int( {x}^{3} + 5x - 18)dx[/tex]
[tex] = \frac{1}{4} {x}^{4} + \frac{5}{2} {x}^{2} - 18x + k[/tex]
where k is the constant of integration
The total resistance in a circuit with two parallel resistors is 2 ohms and R1 is 6 ohms. Using the equation for R2, in terms of RT and R1, what is R2 R2 blank is ohms
[tex]R_2[/tex] is 3 ohms
Step-by-step explanation:In a circuit containing two resistors [tex]R_1[/tex] and [tex]R_2[/tex] connected together in parallel, the total resistance [tex]R_T[/tex] is given by;
[tex]\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}[/tex] ---------(i)
Make [tex]R_2[/tex] subject of the formula;
=> [tex]\frac{1}{R_2} = \frac{1}{R_T} - \frac{1}{R_1}[/tex]
=> [tex]\frac{1}{R_2} = \frac{R_1 - R_T}{R_TR_1}[/tex]
=> [tex]{R_2} = \frac{R_TR_1}{R_1 - R_T}[/tex] ---------------(ii)
From the question,
[tex]R_1[/tex] = 6Ω
[tex]R_T[/tex] = 2Ω
Substitute these values into equation (ii) as follows;
=> [tex]{R_2} = \frac{2*6}{6 - 2}[/tex]
[tex]{R_2} = \frac{12}{4}[/tex]
[tex]R_2[/tex] = 3Ω
Therefore, the value of [tex]R_2[/tex] = 3 ohms or [tex]R_2[/tex] = 3Ω
Answer: is 3 ohms.
Explanation: edmentum/plato :)
If mABC=125 and mABD=94 then m DBC, somebody help!
Answer:
31 degrees
Step-by-step explanation:
Subtract 94 from 125 to get the measure of angle DBC.
can you slve fasssst pls
Step-by-step explanation:
the value of x is 18 degree and the value of Y is 15 degree
Can someone help me
Step-by-step explanation:
the answer is in the above image
Answer:
[tex]-12^{2}[/tex] + 9a - 5
Step-by-step explanation:
combine like terms :
-7[tex]a^{2}[/tex] - 5[tex]a^{2}[/tex] = -12[tex]a^{2}[/tex]
+3a - (-6a) = 9a
-9 - (-4) = -5
Which is equivalent to7^(3/2) over 7^(1/2)?
A. 7^(1/3)
B. 7^(3/4)
C. 7^1
D. 7^2
E. 7^3
Given the expression below:
[tex] \large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } }[/tex]
Use the following property:
[tex] \large \boxed{ {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } }[/tex]
Therefore:
[tex] \large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } = \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } } \\ \large{ \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } = \frac{ \sqrt{7 \times 7 \times 7} }{ \sqrt{7} } \longrightarrow \frac{7 \sqrt{7} }{ \sqrt{7} } } \\ \large{ \frac{7 \cancel{ \sqrt{7} }}{ \cancel{ \sqrt{7} }} = 7}[/tex]
Note that a¹ = a. Therefore, 7¹ = 7.
Answer
7¹ or 7.what number represents the same amount as 4 tens+0 ones
?????????????????????
Answer:
[tex]\sqrt{x+6}[/tex]
Step-by-step explanation:
So, there are a few things we need to go over to graph a function,
When a number is outside of a root, it changes the y value. For example:
y=[tex]\sqrt{x}+6[/tex]
With the +6, y will always be 6 higher than normal.
If it was -6, then y will always be 6 lower than normal.
What if the number is inside the root? Well, it works a little differently.
Instead of changing the y value, it changes the x value. For example:
y=[tex]\sqrt{x+6}[/tex]
So if you put a number in for x, lets say -6, wht would you get?
You would get -6+6=0
The square root of 0 is 0, so when x=-6, y=0
Normally, x would have to equal 0 for the y value to be 0.
So basically, when we see the number isnide of the root, we can think the our x coordinate being subtracted by that number.
This makes since, because if we subtract the +6 from x:
x-(+6)= x-6, and -6 is our x coordinate.
If it was -6 at the start, this would also work:
x-(-6)= x+6. So our x coordinate would start at 6.
Now, lets look at our graph.
As we can see, the x values start at -6, and the y values starts at 0.
This eliminates A and D, since the +6 would change the y value, not the x.
Remember that x-6 would make x a postive 6.
x+6 however, would make x a negative 6.
So we need x+6 in a square root.
This eliminates B, since it has a x-6, making the x coordinate postive 6, not negative 6.
So c is our answer.
Hope this helps!
Type the equation for the graph below.
please help!!!
Answer:
y = 1sin(3x)
Step-by-step explanation:
y = A sin( (2π/ω)x )
A is amplitude = 1
ω is period = 2π/3
------------------------------
y = 1sin( 2π / (2π/3) x)
y = 1sin(3x)
The equation for the graph with a sinusoidal wave, given an amplitude of 1, a period of 2π/3, and a phase shift of 0, is y = sin((2π/3)x).
The equation for a sinusoidal wave can be written as:
y = A * sin(ωx + φ)
In this case, we are given the values of amplitude (A = 1), period (ω = 2π/3), and phase shift (φ = 0).
The amplitude (A) represents the maximum displacement or height of the wave from the center line. In this case, it is 1.
The period (ω) represents the length of one complete cycle of the wave. The period is the reciprocal of the frequency, and in this case, it is 2π/3.
The phase shift (φ) represents any horizontal displacement of the wave. In this case, the phase shift is 0, indicating that the wave starts at its equilibrium position.
Using these values, the equation for the given graph would be:
y = 1 * sin((2π/3)x + 0)
Simplifying it further:
y = sin((2π/3)x)
To learn more about equation click on,
https://brainly.com/question/30509851
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find the area of the figure below
A.832in^2
B.768^2
C.416^2
D.384in^2
The adjacent sides of a rectangle are (2x – 1) and (x + 5). Find its area.
Answer:
2x²+9x-5
Step-by-step explanation:
Area of a rectangle = Length * Width
If the adjacent sides are 2x – 1) and (x + 5), the area is calculated as;
A = (2x – 1) * (x + 5).
A = 2x²+10x-x-5
A = 2x²+9x-5
Hence the area of the rectangle with the adjacent sides is 2x²+9x-5
What is the value of this expression when a = 7 and b = -4? 1201 - 6 3 OA. -6 OB. - 31 Oc. 37 D. 6
Answer:
OA . -6
Step-by-step explanation:
correct me if I'm wrong
Help me pls
this is very important
Answer:
C/3rd one. (y=2x+4)
Step-by-step explanation:
In the equation y=mx+b, m=slope of the line and b=y-intercept. From the graph, we know the y-intercept is 4 so we can write y=mx+4. To find the slope: (0-4)/(-2-0) = (-4)/(-2) = 2. We can replace the m with 2 to get the final equation of y=2x+4 which is also the third answer.
WILL GIVE BRAINLIEST!
3 Using SOH CAH TOA!
1 point
Find the missing side length,
1
16
23°
2
х
Type your answer...
Previous
Find the sum.
b/ b^2+4b+4 + 9/b^2+7b+10
Answer:
11b^3+14b^2+b+9
---------------------------
b2
Step-by-step explanation:
help me please i need help on this
Answer:
CE = 20
Step-by-step explanation:
Given a line parallel to a side of a triangle and intersecting the other 2 sides then it divides those sides proportionally, that is
[tex]\frac{6}{8}[/tex] = [tex]\frac{15}{CE}[/tex] ( cross- multiply )
6 CE = 120 ( divide both sides by 6 )
CE = 20
Find the y-intercept of the quadratic function: g(x) = 5х2 + 9x + 4 о (0, 18) (4.0) ООО (0.4) (0,5)
Answer:
(0,4)
Step-by-step explanation:
Here, we want to find the y-intercept of the quadratic function
g(x) = 5x^2 + 9x + 4
Mathematically, we know that the y-intercept is the position on the graph where we have x = 0
so, to find the y-intercept value, we have to find g(0)
simply put, we have to substitute the value of 0 for x
Mathematically, we have this as;
g(0) = 5(0)^2 + 9(0) + 4
g(0) = 0 + 0 + 4
g(0) = 4
thus, we have the y-intercept point as (0,4)
f(x)=-3x^2-20
find f(-9)
Answer: go to symbolab i swear it will help if not apologies
Step-by-step explanation:
A rectangular garden has a length that is modeled by the expression2X -7 and a width of 3X^2+4x. What is the area of the garden?
Answer:
A = 6x³ - 13x² - 28xStep-by-step explanation:
Area of rectangle:
A = lwGiven:
l = 2x - 7w = 3x² + 4xThe area is:
A = (2x - 7)(3x² + 4x) =
2x(3x² + 4x) - 7(3x² + 4x) =
6x³ + 8x² - 21x² - 28x =
6x³ - 13x² - 28x
Answer:
Area of rectangle = 6 x ³ - 13 x ² + 28
step by step explanation
Given That :-
Length of rectangle = 2 x - 7Width of rectangle = 3 x ²+ 4 xTo Find :-
Area of rectangleFormula Used :-Area of rectangle = Length × Width
Solution : -Using Formula
Area of rectangle = Length × Width
substitute the values.
Area of rectangle = ( 2 x - 7 ) × ( 3 x ² + 4 )
= 2 x ( 3 x ² + 4 ) - 7 ( 3 x ² + 4 )
= 6 x ³ + 8 x - 21 x ² + 28
= 6 x ³ - 13 x ² + 28
I NEED HELP PLEASE UHHH PLEASE I NEED HELP UUUUHHHHHHH
Sulio wants to build a wooden fence to enclose his vegetable garden. Determine the amount of fencing he needs by finding the perimeter of the garden.
Perimeter = 2 times length + 2 times width. The length of a garden is 8 feet and the width is 6 feet.
Evaluate the formula for the perimeter of a parallelogram to solve the problem. Then check all that apply.
First, write the formula for the perimeter of a parallelogram, P = 2l + 2w.
Next, use parentheses when you substitute 8 for l and 6 for w.
After multiplying, add 16 and 12.
Sulio needs 28 feet of fencing.
Sulio needs 48 feet of fencing.
Answer:
Sulio needs 28 feet of fencing.
Step-by-step explanation:
P = 2l + 2w
P = 2(8) + 2(6)
P = 16 + 12
P = 28
Answer:
The answer is
First, write the formula for the perimeter of a parallelogram, P = 2l + 2w.
Next, use parentheses when you substitute 8 for l and 6 for w.
After multiplying, add 16 and 12.
Sulio needs 28 feet of fencing.
Step-by-step explanation:
this is your answer
Find the value of angle y
Answer:
116
Step-by-step explanation:
116 is parallel to y so that are the same its called corresponding angles
When a transversal cuts two parallel lines, the corresponding angles are equal.
In the given figure, the corresponding angles are 116° and y
So, they are equal
⇒ y = 116°
I need helped really need this question to be answer!
Answer:
the answer for your question is b
The length of a rectangle is the same as its width. If its perimeter is 32 meters, what is its area? 15points- HELP ME PLLLLLLLEEEEAAASSSEE
32 m ^2
64 m ^2
81 m ^2
16 m ^2
Answer:
64
Step-by-step explanation:
a rectangle with length and width equal is a square.
32/4 sides
equals 8 for each side.
l x w = A
8 x 8 = 64
Answer: 64 m ^2
Step-by-step explanation:
Ok well if it's length is the same as the width then we can divide the perimeter by 4 to see the length of each side
[tex]\frac{32}{4} =8[/tex]
Each side is 8m long so it's an 8x8 rectangle. Now we can find the area.
8x8=64
The area is 64 meters squared