Answer:
2^0
Step-by-step explanation:
When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.
There are two ways to go about this problem.
The first way, the generic way, is to know that,
[tex]\frac{a^n}{a^m}=a^{n-m},a\neq0[/tex].
So,
[tex]\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}[/tex].
The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,
[tex]\frac{a}{a}=1, a\neq0[/tex]
And 1 equals to any number raised to the power of zero,
[tex]a^0=1,a\neq0[/tex]
So we just have to say that the 1 we got is rewritten as some base to the power of zero.
Since our base needs to be 2, we just simply say,
[tex]2^0[/tex].
Et Viola.
Hope this helps.
Conjugate/Rational Number?
Please include a detailed explanation so I can learn to do it by myself, Thank you!
Answer:
1) [tex]\dfrac{2}{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}[/tex]
2) [tex]-\dfrac{5}{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}[/tex]
3) [tex]\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} } =\dfrac{\sqrt{5} }{5} + \dfrac{ \sqrt{2} }{2}[/tex]
4) [tex]\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \sqrt{3} + \dfrac{\sqrt{6} }{3}[/tex]
5) [tex]\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} }= \dfrac{\sqrt{15} - \sqrt{6} }{3}[/tex]
Step-by-step explanation:
The rationalization of the denominator of the surds are found as follows;
1) [tex]\dfrac{2}{\sqrt{5} }[/tex]
[tex]\dfrac{2}{\sqrt{5} } \times \dfrac{\sqrt{5} }{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}[/tex]
[tex]\dfrac{2}{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}[/tex]
2) [tex]-\dfrac{5}{\sqrt{3} }[/tex]
[tex]-\dfrac{5}{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}[/tex]
[tex]-\dfrac{5}{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}[/tex]
3) [tex]\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} }[/tex]
[tex]\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} } \times \dfrac{ \sqrt{10} }{\sqrt{10} } = \dfrac{\sqrt{20} + \sqrt{50} }{10 } = \dfrac{2\cdot \sqrt{5} + 5 \cdot \sqrt{2} }{10} = \dfrac{\sqrt{5} }{5} + \dfrac{ \sqrt{2} }{2}[/tex]
[tex]\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} } =\dfrac{\sqrt{5} }{5} + \dfrac{ \sqrt{2} }{2}[/tex]
4) [tex]\dfrac{3 + \sqrt{2} }{\sqrt{3} }[/tex]
[tex]\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \dfrac{3 \cdot \sqrt{3}+\sqrt{6} }{3 } = \sqrt{3} + \dfrac{\sqrt{6} }{3}[/tex]
[tex]\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \sqrt{3} + \dfrac{\sqrt{6} }{3}[/tex]
5) [tex]\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} }[/tex]
[tex]\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} } = \dfrac{\sqrt{5} - \sqrt{2} }{\sqrt{5} - \sqrt{2} } = \dfrac{\sqrt{15} -\sqrt{6} }{5 - 2} = \dfrac{\sqrt{15} - \sqrt{6} }{3}[/tex]
[tex]\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} }= \dfrac{\sqrt{15} - \sqrt{6} }{3}[/tex]
6) [tex]\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5} }[/tex]
[tex]\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5} } \times \dfrac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} = \dfrac{\sqrt{21} + \sqrt{35}}{{3} + {5}} = \dfrac{\sqrt{21} + \sqrt{35}}{8}[/tex]
[tex]\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5} } \times \dfrac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} =\dfrac{\sqrt{21} + \sqrt{35}}{8}[/tex]
Which number line plots the integers –6, –2, and 5?
A number line going from negative 6 to positive 6. Points are at negative 6, negative 5, negative 2.
A number line going from negative 6 to positive 6. Points are at 2, 5, 6.
A number line going from negative 6 to positive 6. Points are at negative 5, 2, 6.
A number line going from negative 6 to positive 6. Points are at negative 6, negative 2, 5.
Answer:
Một trục số đi từ âm 6 đến dương 6. Các điểm ở âm 6, âm 2, 5.
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
which one is the correct answer
Answer:
B.
Step-by-step explanation:
2x - 31 = - 2x - 314x = 0x = 0Other equations don't have any value of x.
Answer:
[tex]2x-31=-2x-31[/tex]Because if you see.. The component of x will get canceled in each of the other 3 options.. ( 2x - 2x) which means no solution.. In option B.. 2x + 2x will give 4x..= 31-31 = 0..
-------------------------
Hope it helps...
Have a great day!!
Work out the mean for the data set below:
603,607
The function f(x) is shown on the graph.
What is f(0)?
• 12 only
• -2 and 3 only
• -2, -1, 1, and 2 only
• -2, -1, 1, 2 and 12
compare the slopes and y intercepts of the graphs of the equations in the linear system 8x + 4y =12 and 3y = -6x -15 to determine whether the system has one solution no solutions or infinitely many solutions explain
Answer:
No solutions
Step-by-step explanation:
Convert both equations into y = mx + b form, where m is the slope and b is the y intercept.
8x + 4y = 12
4y = -8x + 12
y = -2x + 3
Rearrange the other equation:
3y = -6x - 15
y = -2x - 5
So, both equations have a slope of -2. But, one has a y intercept of 3 and the other has a y intercept of -5.
Because the lines have the same slope but different y intercepts, the lines are parallel.
Parallel lines have no solutions, because they will never intersect.
So, the system has no solutions.
You are picking out an outfit. Which of the following options shows a closet with 24 different possible combinations of outfits? Select all that apply.
A) 6 shirts, 2 shorts, 3 hats
B) 12 shirts, 2 shorts, 2 hats
C) 3 shirts, 4 jeans, 2 hats
D) 6 shirts, 2 jeans, 2 hats
E) 12 shirts, 2 jeans, 1 hat
Answer:
C, D, E
Step-by-step explanation:
You just need to multiply the numbers together. Whichever choice is equal to 24, is your answer
So when you multiply for each one...
A is 36
B is 48
C is 24
D is 24
E is 24
So since C, D, E multiply to 24, they are the correct answers.
Find the area of the sector. Round the answer to the nearest tenth.
Answer:
63.4
Step-by-step explanation:
Area of arc is (pi*(11)^2*(60/360))=63.4
only answer mean with explanation please
Answer:
Hello,
3.85
Step-by-step explanation:
[tex]Number\ of\ customers=3+0+5+3+7+2=20\\\\mean=\dfrac{1*3+2*0+3*5+4*3+5*7+6*2}{20} =\dfrac{77}{20} =3.75[/tex]
Question 2 of 10
Which of the following can you determine, when you use deduction and start
from a given set of rules and conditions?
A. None of these
B. What may be true
C. What may be false
D. What must be true
SUBMIT
help on this question please! also if you can kindly explain it would be very much appreciated!!
Answer:
D. 50°
Step-by-step explanation:
We know that there are 3 line segments that are forming the angles. Based on that, we can safely say that each line segment is 180°. Given that, we can find the other 2 interior angles of the triangle. We know that one of the exterior angles is 90° so that interior angle also has to be 90° because both angles have to sum to 180. The 2nd exterior angle that we know is 140, so 180-140 = 40°. Since we know the other 2 angles of the triangle now and we know that all the angles of a triangle must sum to 180°, we add 90 and 40 to get 130 and then subtract that from 180 to get 50°. That would look something like this: 180-(90+40) = 180 - 130 = 50°. Hope this helps!
Answer
The measure of p is 50 degrees.
Explanation
You can see that p is located in a triangle.
The interior angles of a triangle always add up to 180 degrees.
So, to solve this problem, you can find the other interior angles, then subtract those from 180 to find p.
The exterior angles are 140 and 90 degrees. To find the measure of the interior angles, you subtract them from 180, (because the exterior angles and interior angles add up to 180).
The measure of the interior angles are 40 and 90 degrees; 180-140=40 and 180-90=90.
Now you can subtract the measure of the two interior angles from 180 to find p; 180-40-90=50.
Which of the following statements follows from (x - 3)2 = 7?
Answer:
x = 17
Step-by-step explanation:
(x-3)2 = 7
Divide both sides by two
(x-3)2 = 7
2 2
x-3= 31/2
x= 31/2-3
x= 1/2 or 0.5
in a shipment of 10,000 headlights, 5% are defective. what is the ratio of defective headlights to non-defective headlights
Answer:
19:1
Step-by-step explanation:
There are 10000 headlights. If 5% are defective, then 500 are defective. Since we took that 500 out, we get 9500 good headlights. The ratio is 9500:500 or 19:1
The ratio of defective headlights to non-defective headlights will be 19:1.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
There are 10000 headlights. If 5% are defective, then 500 are defective. Since we took that 500 out, we get 9500 good headlights.
The ratio will be calculated as below:-
Ratio = 9500:500
Ratio = 19:1
Therefore, the ratio of defective headlights to non-defective headlights will be 19:1.
To know more about percentages follow
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Proving That Congruent Central Angles Have Congruent Chords
Given: ⊙O with central angles ∠AOC ≅ ∠BOD
Prove: AC ≅ BD
Circle O is shown. Line segments O A, O C, O B, and O D are radii. Line segments connect points A and C and points B and D to form 2 triangles inside of the circle. Angles A O C and B O D are congruent.
Complete the missing parts of the paragraph proof.
Proof:
We know that central angles
are congruent, because it is given. We can say that segments AO, CO, BO, and DO are congruent because
. Then by the
congruency theorem, we know that triangle AOC is congruent to triangle BOD. Finally, we can conclude that chord AC is congruent to chord BD because
.
Answer:
1. AOC and BOD.
2. all radii of a circle are congruent
3. SAS
4. CPCTC
Step-by-step explanation:
I did it on edge. ALSO PLS GIVE ME BRAINLIEST
Answer:
1. AOC and BOD.
2. all radii of a circle are congruent
3. SAS
4. CPCTC
Step-by-step explanation:
i need helpppppp it’s urgentttttt!!!!
I need help I don't understand it at all
Answer:
x = 9
Step-by-step explanation:
Given
5x - 31 = 23 - x ( add x to both sides )
6x - 31 = 23 ( add 31 to both sides )
6x = 54 ( divide both sides by 6 )
x = 9
Answer: X = 9
Step-by-step explanation: basically you solve it just like any other algebra equation. The only difference is that you have x’s on both sides. You have to move one of them over. I move the x to the right and I added it to the left side. 5x plus x is 6x. ( in case you didn’t already know an x never stands alone when you see one alone it always has an imaginary 1 beside it.) after I did that I tried to isolate 6x so I added 31 to 23. 31 plus 23 equals 54. I then had the equation 6x=54. The next thing I wanted to do was to isolate the x. I then dived 6 on both sides and got x= 9
Please help! The answer isn’t 36!
Find the value of the expression:
Answer:
3.6
Step-by-step explanation:
Hi there!
We are given this expression:
.6√36 (.6*√36)
And we want to find the value of it
.6 can be re-written as 0.6
In that case,
0.6*√36
First, simplify what's under the radical: √36, which is equal to 6 (6*6=36)
The expression then becomes:
0.6*6
Multiply those numbers together
0.6*6=3.6
Hope this helps!
What are the factors of the quadratic function represented by this graph?
A (x - 1) and (x - 5)
B. (-x-1) and (x + 5)
C. (x-1) and (x + 5)
D (-x + 1) and (x-5)
Answer:
I think it is AStep-by-step explanation:
[tex](x - 1) \: and \: (x - 5)[/tex]
I hope that is useful for you :)
The factors of the quadratic function whose graph is given are (-x -1) and ( x-5).
What is the factor of a quadratic equation?Factor of a quadratic equation is any monomial or binomial which divides the quadratic equation without leaving any remainder.
What is factorization of quadratic equation?Factoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.
What is solution to the quadratic equation?The solutions of a quadratic equation represent the values of x that make the equation true. And the solutions to any equation are the x-intercepts of that equation.
According to the given question
We have a graph of a quadratic equation and x intercepts -1 and -5.
⇒ we have two points (-1,0) and (-5,0)
⇒ -1 and -5 will be the solution of the quadratic function.
⇒ x = -1 and x = -5
⇒ x+ 1= 0 and x + 5 = 0
or -x -1 = 0 and x+5 = 0
Therefore, the factors of the quadratic function whose graph is given are (-x -1) and ( x-5).
Learn more about the factors of a quadratic function here:
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Which values of a and b in the exponential function y = a times b Superscript x would result in the following graph? On a coordinate plane, a curve approaches the x-axis in quadrant 3 and then decreases down through (0, negative 3) to quadrant 4. a. a = -3, b = 2 c. a = 3, b = 2 b. a = -1, b = 3 d. a = 2, b = -3 Please select the best answer from the choices provided A B C D
Answer:
[tex]a =-3[/tex] [tex]b =2[/tex]
Step-by-step explanation:
Given
[tex]y = ab^x[/tex]
[tex](x_1,y_1) = (0,-3)[/tex]
Required
Find a and b
Substitute [tex](x_1,y_1) = (0,-3)[/tex] for x and y in [tex]y = ab^x[/tex]
[tex]-3 = ab^0[/tex]
[tex]-3 = a * 1[/tex]
[tex]-3 = a[/tex]
Rewrite as:
[tex]a =-3[/tex]
The above implies that (a) is correct;
Hence:
[tex]a =-3[/tex] [tex]b =2[/tex]
So, the equation is:
[tex]y = -3(2)^x[/tex]
Answer: a=-3 b=2
Step-by-step explanation:
Simplify -1/2x3/5÷(-59/40)
Answer:
12/59
Step-by-step explanation:
-1/2x3/5÷(-59/40)
-3/10÷(-59/40)
-3/10*-(40/59)
120/590
12/59
please help!!!!!!!!!!!
X + 1 by X is polymer or not, polymer means ,write its degrees?
1. Take a look at the steps below for solving the
equation 4(3 - 2x) = -20.
Step 1: 4(3 - 2x) = -20
Step 2: 12 - 8x = -20
Step 3: 12-8x - 12 = -20 - 12
Step 4: - 8x + 0 = -32
Step 5:
- 8x = -32
1
Step 6. - 8x
-1
8
8
Step 7:
x = 4
1
= -32
Which property justifies the work between ...
A. Step 1 and Step 2?
B. Step 2 and Step 3?
C. Step 3 and Step 4?
D. Step 4 and Step 5?
E. Step 5 and Step 6?
F. Step 6 and Step 7?
Answer:
x= 1
Step-by-step explanation:
Work is shown in the picture
What is the equation of this circle?
Answer:
(x-3)^2+y^2=8
Step-by-step explanation:
I'm going to go ahead and assume the center is (3,0). The radius can be found by computing the distance from the center, (3,0), to a point on the circle, (5,-2).
The distance between two points is calculated by doing sqrt((distance between x's)^2+(distance between y's)^2).
The distance between our x's is 2.
The distance between our y's is 2.
The square of each then is 4 and 4 respectively.
So we have the distance is sqrt(4+4)=sqrt(8).
The radius is sqrt(8).
The equation of a circle is (x-h)^2+(y-k)^2=r^2 where (h,k) is center and r is radius.
If r=sqrt(8), then r^2=8.
(h,k)=(3,0)
(x-h)^2+(y-k)^2=r^2
(x-3)^2+(y-0)^2=8
(x-3)^2+y^2=8
If m angle PQR = 141", find each measure.
Answer:
x=6
pqs=82
sqr=59
Step-by-step explanation:
13x + 4 + 10x - 1 = 141
23x + 3= 141
23x = 136
x = 136/23 = 6
~~~~~~~~~~~~~~~
pqs = 13x + 4 = 13(6) + 4 = 78+4 = 82
sqr = 10x - 1 = 10(6)-1 = 60 - 1 = 59
Answer:
x = 6
Angle PQS is 82
Angle SQR is 59
Step-by-step explanation:
13x + 4 + 10x - 1 = 141
Group like terms : 23x + 3 = 141
Subtract 3 from both sides to get 23x = 138
Divide both sides by 23 to get x = 6
Angle PQS: Plug 6 into x for 13x + 4 = 13 (6) + 4 = 82
Angle SQR: Plug 6 into x for 10x - 1 = 10 (6) -1 = 59
how much balance we have to save to get Rs 120 interest on 3 years by 2% weight for Annum
Answer:
Principal, P = Rs. 2000
Step-by-step explanation:
Given the following data;
Simple interest (S.I) = Rs. 120Interest rate, R = 2%Time, T = 3 yearsTo find how much balance (principal) is to be saved, we would use the formula;
[tex] S.I = \frac {PRT}{100} [/tex]
Where;
S.I is the simple interest.P is the principal.R is the interest rate.T is the time measured in years.Making "P" the subject of formula, we have;
[tex] P = \frac {100S.I}{RT} [/tex]
Substituting the values into the formula, we have;
[tex] P = \frac {100 * 120}{2 * 3} [/tex]
[tex] P = \frac {12000}{6} [/tex]
Principal, P = Rs. 2000
Therefore, you'll have to save up to Rs. 2000.
if triangle ABC = triangle DBC, AB = 10, AC = 7, DC = ?
Answer:
DC =7
Step-by-step explanation:
if ΔABC ≅ΔDBC then the corresponding sides are
AB = DB = 10
AC = DC = 7
See attachment
10. Find the mean, median of the following data.
5,3, 2, 6, 5, 2,5
a. 5,4
b. 6,8
c. 28,7
d. 4,5
Answer:
A
Step-by-step explanation:
You find the mean by adding all the values then dividing that sum by the amount of values
You find the median by putting the numbers in order from least to greatest and then find the middle number.
Helpppp
Graph the quadratic function y 9x Ox 140. What are the solutions of the quadratic equation 0 - 0 - 6x
140?
Answer:
Answer:bf
Step-by-step explanation:
Solve for: X=____ Y=____
Round to the nearest tenth.
X= 60°
Y=30°
X=22.6°
Y=67.4°
X=30°
Y=60°
X=67.4°
Y=22.6°
Answer:
D
Step-by-step explanation:
These diagrams can drive you crazy. The only way you can do this question is to ASSUME that the angle that looks like it is 90 really is 90. That is a very dangerous assumption.
Solution for y
cos(y) = adjacent / hypotenuse
adjacent = 12
hypotenuse = 13
Cos(y) = 12 / 13
Cos(y) = 0.92308
y = cos-1 (0.92308)
y = 22.6
Solution for x
x does not need trig to solve.
x = 180 - 90 - 22.6
x = 67. 4
So that's D
