Answers
The expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is an algebraic expression, and the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1
How to simplify the expression?The expression is given as:
[tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]
Apply the power rule of indices
[tex](x^{a-b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]
Expand the exponents of the expression
[tex]x^{a^2-b^2} \cdot x^{b^2 - c^2} \cdot x^{c^2 - a^2[/tex]
Apply the product rule of indices
[tex]x^{a^2-b^2+b^2 - c^2+c^2 - a^2[/tex]
Collect like terms
[tex]x^{a^2- a^2-b^2+b^2 - c^2+c^2[/tex]
Evaluate the differences
[tex]x^{0-0 - 0[/tex]
This gives
[tex]x^{0[/tex]
Evaluate the exponent
1
Hence, the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1
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Related Questions
Can someone please show step by step to this problem? Find the area of the following figure.
Answers
Answer:
20 x 12=240
Step-by-step explanation:
A certain flight arrives on time 80
percent of the time. Suppose 131
flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that
(a) exactly 103
flights are on time.
(b) at least 103
flights are on time.
(c) fewer than 98
flights are on time.
(d) between 98
and 117
,
inclusive are on time.
Answers
Answer:
B at least 103 flights are on time. :)
Step-by-step explanation:
First we need to turn the percentage into a decimal :)
131 x 0.80 = 104.8
The answer should be B at least 103 flights are on time.
Have an amazing day!!
Please rate and mark brainliest!!
Pythagorean Theorem
solve for the missing side . Round to the nearest 10th
I NEED HELP ASAP I WILL MARK BRAINLIEST IF ANSWERED CORRECTLY NO LINKS IF YOU DO NOT KNOW THE ANSWER DONT COMMENT ON THIS THREAD
Answers
Answer:
\sqrt{45}
Step-by-step explanation:
A^2+B^2=C^2
36+?=81
81-36=45
[tex]\sqrt{45}[/tex]=
Answer:
6.7 mmStep-by-step explanation:
Pythagorean Theorem
a² + b² = c²Here, we are missing one of the altitudes, so we can arrange the equation to form :
a² = c² - b²Solving
UW² = VW² - UV²UW² = (9)² - (6)²UW² = 81 - 36UW² = 45UW = √45UW = 6.7 mmFind the area of the shaded shape. Write the area in square units
Answers
Answer:
length times width equals area LxW=Area
Step-by-step explanation:
so,
4 times 4= 26 yards
1=4 square yards
then 26X4 = 104 square yards
Answer:
Step-by-step explanation:
What is the exact value of cos(-60°)?
V3
2
Ni-
을
V3
2
Answers
Applying the cosine ratio of trigonometry, the exact value of cos(-60°) which equals cos (π/3) is: C. 1/2.
What is the Cosine Ratio?In trigonometry, the vaue of the cosine ratio is the cosine of the reference angle which equals the ratio of the adjcent side over the hypotenuse.
To get the exact value of cos(-60°), convert 60 to radians.
π radian = 180
60° = (π/3) radians
Note: cos (-θ) = cos θ
Therefore, cos (-π/3) = cos (π/3)
cos (π/3) = 1/2
The exact value of cos(-60°) = 1/2 (option C).
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Compute the value of the discriminant and give the number of real solutions of the quadratic equation. -9x to the second power-6x-1=0
Answers
discriminant=0
Number of real solutions=1
Step-by-step explanation:
Given the equation:
-9x^2-6x-1=0
Let a: coefficient of x^2
Let b: coefficient of x
Let c: constant
a=-9
b=-6
c=-1
The formula of the discriminant is given by:
discriminant= b^2 - 4ac
discriminant= (-6)^2 - 4(-9)(-1)
= 36 - 36 = 0
We know that:
If discriminant<0 then the equation has no real root
If discriminant=0 the equation has one real root
If discriminant>0 the equation has 2 real roots
Here we got discriminant=0 so the quadratic equation has 1 real root.
What is x?
ONLY WRITE A NUMBER FOR YOUR ANSWER
If you need to round, round to the nearest tenth (one decimal place).
Please help, thank you!
Answers
Answer:
15
Step-by-step explanation:
to get from 10 to 25 you time by 2½
so then times 6 by 2½ and the answer is 15
Which prism has a greater volume?
Answers
for B, the volume is 3 x 3 x 2 = 18
so B has a greater volume
please give brainliest! thanks, :D
Figure B is a scale image of Figure A, as shown. Enter the scale factor applied to Figure A to produce Figure B.
Answers
Given two side lengths of a triangle (4cm and 17cm), find a range of possible lengths for the third side.
Answers
Check the picture below.
so notice the top part of the picture
if we move the "4" and "17" sides close to each other, till one is on top of the other, the side in red, can never be less than 17 - 4, or 13, it cannot be 13 either, because then both lines will be on on top and we wouldn't have a triangle just a flat-line, so whatever the red line is, it must be more than 13.
notice the bottom part of the picture
if we separate the "4" and "17" sides, and lay them flat, the most the red side can be is 4 + 17 or 21, it can never be greater than 21, it can't be 21 either because if we lay "4" and "17" flat, we lose the triangle and all we'd have is a flat-line. So whatever the red side is, must be less than 21.
What is the surface area?
5 mm
5 mm
5 mm
square millimeter
Answers
= #7 i
In the diagram, ARST ~ AXYZ . Find the scale factor from
ARST to AXYZ. Write your answer in simplest form.
S
Y
CO
3
R 4
T
21
10.5
Х
14
Z
Answers
Answer:
b
Step-by-step explanation:
what is 7/8 - 1/2 = in simplest form
Answers
Answer:
[tex] \frac{7}{8} - \frac{1}{2} = \frac{7 - 4}{8} = \frac{3}{8} [/tex]
Step-by-step explanation:
I hope I helped you! :)
Which point is a point where the graph of [tex]y=(x-5)(x^2-7x+12)[/tex] crosses the x-axis?
Answers
Answer: C. (4, 0)
Step-by-step explanation:
We can graph the equation given to solve. See attached.
The answer to this question is C. (4, 0)
-y + 2y = what ? Please help and why is it negative or positive ?
Answers
Step-by-step explanation:
-y is the same as writing -1y. if we forget about the y’s, -1 + 2 = 1. so -1y + 2y = 1y, or just y to be simpler :)
i hope this helps :)
[tex]-y+2y=2y-y=(2-1)y=y[/tex]
It is positive because the coefficient is positive.
I need help with this question
Answers
A builder wants to install a triangular window with the angles shown in the illustration. What angles will he have to cut to make the window fit? (Hint: The sum of the angles in a triangle equals 180°.)
x° =
°
(x + 30)° =
°
Answers
Answer:
X=40°
Step-by-step explanation:
40+30=70
40+30=70
70+70=140
140+40=180
The angles will builder has to cut to make the window fit is 40°, 70° and 70°.
Given that, the measures of the three angles of a triangle are x°, (x+30)° and (x+30)°.
What is the angle sum property of a triangle?The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.
Now, x°+(x+30)°+(x+30)°= 180°
⇒3x+60°=180°
⇒3x=180°-60°
⇒3x=120°
⇒x=40°
So, x°=40°, (x+30)°= 70°
Therefore, the angles will builder has to cut to make the window fit is 40°, 70° and 70°.
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BRAINLIEST + STARSS!!
In this diagram, x || y || z and m<9 = 93°.
What is the measure of each angle?
Drag and drop the correct measurements into the boxes to
match each angle.
m<2
m<4
m<7
89° 91 ° 93 ° 87°
Answers
Which is more, 1 pound or 22 ounces?
Answers
Answer:
22 ounces is more
Step-by-step explanation:
1 pound is equal to 16 ounces
Answer:
1 pound
Step-by-step explanation:
1pound=16oz 22oz= 1.375pound
Please solve the following thank you so much math experts
Answers
Answer:
4) 97%
6) 13%
Step-by-step explanation:
4) We are given that 3% for 250 million are diesel.
100% - 3% = 97% NON DIESEL cars
97% of 250 million is 242.45 million.
______________________________
6) We know that 17% (buses) and 70% (cars) are part of that total.
We also know that the total needs to be 100%
So, we simply do this:
100 - (17+70) = 13 (%)
So, 13% of the survey participants had bikes
what is 2/3 - 1/2 = in simplest form
Answers
Answer:
1/3
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
2/3-1/2 = find the denominator 3×2=6
4/6-3/6 = rewrite with a denominator of 6
(4-3)/6 = 1/6 subtract numerators
PLEASE HURRY!!!
A bag contains 4 red pencils, 6 blue pencils, and 5 green pencils. A pencil is randomly selected, its color is recorded, and it is returned to the bag. This is repeated 1350 times. How many times is it expected that a green pencil will be selected?
A. approximately 360 times
B. approximately 450 times
C. approximately 540 times
D. approximately 900 times
Answers
Answer:
450
Step-by-step explanation:
1. Based on the given conditions, formulate:
1350 x 5 ÷ (5 + 4 + 6)
2. Calculate
[tex]\frac{1350x5}{5 + 4 + 6}[/tex] The numerator is 1350 multiply by 5
[tex]\frac{6750}{5 + 4 + 6}[/tex]
[tex]\frac{6750}{15}[/tex]
Answer: 450
I need help solving please do not report this question I need the answer I will give 30 points a heart 5.0 stars and brainlest
Answers
Answer:
280 m³
Step-by-step explanation:
Volume of a Triangular Prism
V = 1/2BHLSolving
V = 1/2 x 7 x 8 x 10V = 7 x 10 x 4V = 280 m³Answer:
280
Step-by-step explanation:
So first lets establish the formula for a Triangular Prism :
1/2 * b * h * l
now lets use the mesurements given to substitute into the formula :
1/2 * 7 * 8 * 10
now lets solve it by first multiplying all the whole numbers together!
7 * 8 = 56
56 * 10 = 560
Finally lets multiply 560 by 1/2 or in other words, divide 560 by 2 :
560/2 = 280
Explain why it is important to have a good credit history.
Answers
Answer:
A good credit score is used for more than just getting a credit card or a loan. Credit scores demonstrate your history of paying your debts to entities that loan you money. Due to extending themselves beyond their means, many people are not able to pay their debts
Find the perimeter of the figure.
6 meters
2y meters
2y
meters
4y meters
16 meters
4y meters
Answers
Answer:
34
Step-by-step explanation:
Usually when finding the perimeter all you have to do is add the sides.
What is the equation in standard
form of a circle with the
equation x^2+ y^2 + 14y – 1 = 0?
Answers
Answer:
(x-2)²+(y+7)² = 25Step-by-step explanation:
The general standard form of an equation is written in expressed as shown;
(x-a)²+(y-b)² = r²
(a,b) is the centre of the circle and r is the radius
Given the equation of the circle x^2 + y^2 - 4x + 14y +28 =0, we need to find the centre of the circle and its radius.
comparing the equation given with x²+y²+2gx+2fy+c =0
(-g, -f) is the centre
radius = √g²+f²-c
On comparison,
2gx = - 4x
g = -4/2
g = -2
2fy = 14y
f = 14/2
f = 7
c = 28
r = √(-2)²+7²-28
r = √4+49-28
r = √25
r = 5
comparing centre (a,b) to (-g, -f)
a = -g = -(-2)
a = 2
b = -f = -7
b = -7
substituting the centre (a, b) and the radius r into the equation
(x-a)²+(y-b)² = r²
The required equation will be (x-2)²+(y+7)² = 5²
(x-2)²+(y+7)² = 25
Brain teaser what is two plus two minus two plus four divided by two?
Answers
Answer:
4
Step-by-step explanation:
2+2-2+4÷2
we go through
P- parentheses
E- exponents
M- multiplication
D- division
A- addition
S- subtraction
also note that we read it from left to right becaue × is not more important than ÷ and same goes to + and -
First step
2+2-2+(4÷2) --> 2+2-2+2
then
2+2-2+2 --> 4-2+2
then
4-2+2 --> 2+2
finally
2+2=4
Answer:
4
Step-by-step explanation:
Having trouble with this, help please?
Answers
Answer:
a) [tex]7x-15=20[/tex]
b) [tex]\frac{20+15}{7}[/tex]
c) [tex]5[/tex]
Step-by-step explanation:
Make a stem-and-leaf plot of the data values 14, 22, 9, 13, 30, 8, 25, and 29.
Stem Leaf
89
1 3
22
0
Key: 1 | 3 =
Previous
H
9
2
3
SO
Answers
Answer:
Step-by-step explanation:
The speed of the jet Alyssa flew on from Boston to London was 480 mph. On her return flight, the speed of the jet was 600 mph with a tail wind. What was Alyssa's average speed on the round trip? Round your answer to one decimal place.
Answers
Answer:
540
Step-by-step explanation:
Answer:
533.3mph
Step-by-step explanation: