Answers
Answer:
[tex]a^{-51} = \frac1{a^{51}}[/tex]
Step-by-step explanation:
When you're multiplying two powers with the same base (in our case, a) you add together the exponents.
[tex](\frac{a^1^4\cdot a^-^6}{a^{25}})^3 =\\(\frac {a^{14+(-5)}}{a^2^5})^3= (\frac {a^{14-6}}{a^2^5})^3 = (\frac {a^{8}}{a^2^5})^3[/tex]
Now, when you are dividing two powers with the same base (in our case, a again) you subtract the exponents:
[tex]= (a^{8-25})^3 = (a^{-17})^3[/tex]
Finally, when you're calculating the power of a power, you multiply the exponents together:
[tex]a^{-17\cdot 3} = a^{-51} = \frac1{a^{51}}[/tex]
At this point you just have to choose - or check with your book/teacher if you prefer a negative exponent, or a fraction.
Related Questions
Solve the equation for z.
-2z + b = h
Answers
Answer:
z= - 1/2h + 1/2b
Step-by-step explanation:
-2z + b = h
-2z = h - b
z= - 1/2h + 1/2b
And angle measure 88. 2 more than a measure of is complimentary angle what is the measure of each angle
Answers
Answer: 90 degrees
Step-by-step explanation: ez
A Ferris wheel at Kone Island has a diameter of 63 feet.
Which equation can be used to find its circumference, Cin feet?
diameter 63 feet
O C = 63 x II
O C = 31 x II
O C = 2 x II x 63
O C = 2 x II x 31
Answers
The circumference of the Ferris wheel is the product of the diameter and [tex]\pi[/tex]
The circumference equation of the Ferris wheel is C =63 * [tex]\pi[/tex]
How to determine the circumference equationThe circumference of a circle, when the diameter is given is calculated using the following equation
C = [tex]\pi[/tex]d
The diameter of the Ferris wheel is given as:
d = 63 feet.
So, we have;
C = [tex]\pi[/tex] * 63
Rewrite as:
C =63 * [tex]\pi[/tex]
Hence, the circumference equation of the Ferris wheel is C =63 * [tex]\pi[/tex]
Read more about circumference at:
https://brainly.com/question/10921927
The first term of an arithmetic sequence is 1, another term of the sequence is 91 and all of the terms of the sequence are integers. How many distinct arithmetic sequences meet these three conditions?
Answers
Answer:
108r4
Step-by-step explanation:
91+16 yea go install senebratic
Answer:
It has been answered and I need some point so I hope you don't mind lol
Step-by-step explanation:
Someone pls help????????????????
Answers
Answer:
18
Step-by-step explanation:
perimeter = sum of the lengths of the sides
perimeter = 5 m + 5 m + 2 m + 5 m + 1 m
perimeter = 18 m
Due to the math
I’ve done this before so it should be 18cm
⚠️ ⚠️⚠️⚠️PLEASE HELP ⚠️⚠️⚠️⚠️
Answers
Answer:
PLz give brainliest
Step-by-step explanation:
Y=60
x=33
Complete the square
[tex]2x^2+16x-7[/tex]
Answers
Hey there!
[tex]\fbox{2x²+16x-7}[/tex]
[tex]\fbox{2(x + 4)² - 39}[/tex]
A 499
B 498
C 898
D 500
Answers
Answer:
498
Step-by-step explanation:
We will need to use the Pythagorean Theorem.
A^2 + B^2 = C^2
45^2 + B^2 = 500^2
Subtract 45^2
B^2 = 500^2 - 45^2
Simplify
B^2 = 247,975
Take square root so B is alone
B = 497.9708
Round
B = 498
What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table to help answer the question. A normal curve with a peak at 0 is shown. The area under the curve shaded is negative 1 to positive 2. Z Probability 0. 00 0. 5000 1. 00 0. 8413 2. 00 0. 9772 3. 00 0. 9987 0. 16 0. 68 0. 81 0. 84.
Answers
The area under the curve shaded is -1 to 2 is 13.59%.
The z score is a measure used in statistic to determine by how much standard deviations the raw score is above or below the mean.
If the raw score is greater than the mean then the z score is positive but if the raw score is less than the mean then the z score is negative.
What is the formula for the z score?
The formula of z score
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]\mu=mean[/tex]
[tex]\sigma=standard deviation[/tex]
x=raw score
From the normal distribution table,
Area between z = -2 and z =-1 is given by
P(-2 < z < -1) implies that P(z < -2) - P(z < -1) that is
P(z < -2) - P(z < -1) = 0.1587 - 0.0228
P(z < -2) - P(z < -1) = 0.1359
P(z < -2) - P(z < -1) = 13.59%
Therefore we get the area under the curve shaded is -1 to 2 is 13.59%.
To learn more about the area under the curve visit:
https://brainly.com/question/6758792
Triangle XYZ with vertices X(-2, 12), Y(6, 4), and Z(-6,-4): scale factor = 3/4, centered at (-2, 8)
Answers
Given that the points on triangle XYZ are, (-2, 12), (6, 4), (-6, -4), and the scale factor and center of dilation are 3/4, and (-2, 8), the coordinates of triangle X'Y'Z' are;
X'(-2, 11), Y'(4, 5), Z'(-5, -1)How can the image of the triangle be found?The coordinates of the vertices of the triangle are;
X(-2, 12), Y(6, 4), Z(-6, -4)
The center of dilation = (-2, 8)
The scale factor of the dilation = 3/4
The coordinates of the required image following the dilation are;
(-2 + (3/4) × ((-2 - (-2)), 8 + (3/4) × (12 - 8))
The coordinates of X' = (-2, 11)
The coordinates of Y' are found as follows; (-2 + (3/4) × ((6 - (-2)), 8 + (3/4) × (4 - 8))
The coordinates of Y' = (4, 5)
The coordinates of Z' are found as follows; (-2 + (3/4) × ((-6 - (-2)), 8 + (3/4) × (-4 - 8))
The coordinates of Z' = (-5, -1)
The coordinates of the vertices of the triangle XYZ following a dilation by a scale factor of (3/4) are;
X'(-2, 11), Y'(4, 5), Z'(-5, -1)Learn more about dilation transformation here:
https://brainly.com/question/4280198
Choose the option that best completes the following statement.
If two polygons ___________, then they have the same area.
are congruent
have the same number of sides
have the same number of angles
are similar
Answers
Answer:
are congruent
Step-by-step explanation:
If two polygons are congruent, then they have the same area.
Two polygons are congruent if their corresponding sides and angles are congruent. Note: Two sides are congruent if they have the same length and angles are congruent if they have the same measure. We indicate that angles are congruent by putting the same number of slash marks through each angle.
What are the answers to number 12 and 14? Pls help!!!! 15 points :)
Answers
14. A
I hope it's right
Explain how to find 19+6 use equations to show your thinking
Answers
Answer:
1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=25
Step-by-step explanation:
mafs
19+6
(19+1)+(6-1) adding 1 to 1 number and subtracting 1 from the other
20+5 simplifying
25 now it's just adding 20 + 0 + 5 = 25
This problem is a little abstract, but I hope it helped. Happy mathing!
Can a triangle have sides with the given lengths?
2 yd, 9 yd, 10 yd
Answers
Answer: Yes
Step-by-step explanation: The sum of the length of the 2 smaller side must be greater than the biggest side (hypotneus) So yes, 9+2=11 which is greater than 10.
order the numbers from least to greatest 8.062, 8.26, 8.026, 8.6
Answers
Describe and correct the error a student made in identifying the common difference of the following sequence.
29, 22, 15, 8, 1, ...
Answers
Given:
The sequence is 29, 22, 15, 8, 1, ...
To find:
The common difference.
Solution:
We have,
29, 22, 15, 8, 1, ...
It is an AP.
First term : [tex]a_1=29[/tex]
Second term : [tex]a_2=22[/tex]
Now,
Common difference : [tex]d=a_2-a_1[/tex]
[tex]d=22-29[/tex]
[tex]d=-7[/tex]
Therefore, the correct common difference is -7.
Note: Here calculation by student is not given, so we cannot find the error of the student.
At a car rental office, 63% of the customers are men and 37% are women. If 25% of people request a compact car, 37% request a full-sized, 10% request a convertible,16% request an SUV, and 12% request a luxury car, what is the probability that the next customer will be a woman who requests a convertible?
Answers
Answer:
3.7%Step-by-step explanation:
As per given
P(woman)= 37%P(convertible) = 10%So combined probability is:
P = 37%*10% = 37%*0.1 = 3.7%the area of trapezium is 40cm parallel sides is 12 cm and 8cm the distence between the parallel sides are
Answers
Step-by-step explanation:
Area of trapezium= 40cm²
½ h(b1+b2)=40
½ h (12+8)=40
½h (20)=40
h=40×2/20
h=4cm
Find the value of two numbers if their sum is 12 and their difference is four.
Answers
Answer:
8 and 4 is the answer!
x= 4+ y
4+y+y=12
y = 4
x = 8
So , 4 and 8
Good Luck.
Starting from the same place, Ryu walks due west and Samantha walks due east.
On the number line, 0 represents their starting point, negative values represent the distance traveled west and positive values represent the distance traveled east. All values are given in feet.
A number line ranging from minus 660 to plus 660. Tick marks are every 60 units. A point labeled Samantha is located at two tick marks to the right of zero. A point labeled Ryu is located at 8 tick marks to the left of zero.
How many feet apart are Ryu and Samantha on the number line?
Enter your answer in the box.
Answers
For Samantha, 2 tick marks east is 120 units east because 1 tick is 60 units.
For Ryu, 8 tick marks west is 480 units west because 1 tick is 60 units.
They are walking to form a line. Just add their distances from 0.
120 + 480 = 600.
--------------------------0----------------------------
Ryu: 480 Samantha: 120
480 + 120 = 600.
600 units, or feet.
2/5x + 4 = 1/5x + 8 what does x equal
Answers
Answer:
x=20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
2/5x + 4 = 1/5x + 8
(subtract 1/5x from both sides)
1/5x + 4 = 8
(subtract 4 from sides)
1/5x = 4
(multiply by 5 from both sides of the equation to isolate x)
x = 20
Jake has a container in the shape of a rectangular prism. The base of the container is 30 centimeters long and 20 centimeters wide. Jake pours 0.5 gallons of water into the container. How high, in centimeters, will the water reach in the container? Note that 1 gallon is approximately equal to 3.8 liters and 1cm3 of volume can hold 1 milliliter of water.
Answers
Answer:
3.16cmStep-by-step explanation:
Given that
1gallon=3.8liters
0.5gallon=x
x=0.5*3.8
x=1.9liters
we know that 1liter is 1000cm^3
1.9liter is x
x=1900cm^3
Now we have the volume of water poured in cm^3
the volume of a rectangular prism is
volume=l*w*h
1900=30*20*h
1900=600h
h=1900/600
h= 3.16cm
Kaya rented a limousine for prom. There was one-time charge of $100, plus an hourly rate of $45. Her total cost for the night was $347.50. How many hours did Kaya rent the limo for?
Answers
Answer:
5 and a half hours
Step-by-step explanation:
347.5-100=247.5
247.5/45=5.5
Answer:
Kaya rented the limo for about 5 and a half hours
Hope this helps! good luck :)
Stuffed animals each weighing 1 over 4 pound are on a scale. The scale shows 1 1 over 2 pounds. How many stuffed animals are on the scale?
Answers
Answer:
6 stuffed animals
Step-by-step explanation:
if 1/4= 1 then 1x6= 1 1/2
Answer: The answer is: 6
Step-by-step explanation: I have my ways ;>
Have a nice day!
-Sunny
What is the result of the construction shown?
A. Angle bisector
B. Copying an angle
C. Copying a line segment
D. Perpendicular bisector
Answers
Answer:
Option C: Copying an angle
Step-by-step explanation:
Angle bisector is a line through an angle that will split that angle to 2 equal angles. Thus, option A is wrong as no angle is being split.
Copying an angle involves reproducing a particular angle in another construction. The image shows us that there is an attempt to reproduce the perpendicular angle of 90°. Thus, option B is correct.
Copying a line segment involves creating the exact size of line in another construction. The image doesn't depict that. Thus option C is wrong.
Perpendicular bisector is when we draw a perpendicular line through a horizontal one to divide it into 2 equal parts. This is not the case here. Thus, option D is wrong.
plsss I'll mark Brainlest
Answers
Answer:
For class A, the test scores were closer togther so that means more students most likely scored the smae score mutiple times. I think this because the box on the box plot is not spread out like class B.
For class B, the scores varied more so the box plot has to be spread out over more values. Because of the box plot, we can see that Class B had the highest test score compared to class A.
Have an amazing day!!
Please rate and mark brainliest!!
What are all the things dilations do in geometry?
Answers
Answer:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation that creates a larger image is called an enlargement. A dilation that creates a smaller image is called a reduction. A dilation stretches or shrinks the original figure.
PLEASE HELP!!!
A school has 3 tons of gravel to be
spread over the playground. The
members of the landscaping crew
can move 80 pounds of gravel in each
wheelbarrow load.
How many wheelbarrow loads will it take to move all the gravel?
Answers
Using proportions, it is found that it will take 75 loads to move all the gravel.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In one load, they mode 80 pounds. How many loads are needed to move 3 tons = 3 x 2000 = 6000 pounds? The rule of three is given as follows:
1 load - 80 pounds
x loads - 6000 pounds
Applying cross multiplication:
80x = 6000
x = 6000/80
x = 75.
It will take 75 loads to move all the gravel.
More can be learned about proportions at https://brainly.com/question/24372153
Write the equation of a line through points (5, 5) and (1, 0) in point-slope form.
Help soon pls :)
Answers
Answer:
Step-by-step explanation:
Find the slope of the line between (5,5)and (1,0) using m=(y2-y1)/(x2-x1)
which is the change of y over the change of x.
m=5/4
Use the slope 5/4 and a given point (5,5) to substitute for x1 and y1 in the point-slope form y−y1=m(x−x1), which is derived from the slope equation m=(y2-y1)/(x2-x1)
y-5=5/4*(x-5)
Simplify the equation and keep it in point-slope form y-5=5/4*(x-5)
Solve for y.
y=5x/4-5/4
Reorder terms.
y=5/4 x-5/4
List the equation in different forms.
Slope-intercept form: y=5/4 x-5/4
Point-slope form: y-5=5/4*(x-5)
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
E, 3/2
Step-by-step explanation:
First, say that the numerator is 2^2001 * 3^2001 * 3^2, so that the powers will align. Then, we can combine 2^2001 and 3^2001 for 6^2001. If we ignore the 3^2, we get 6^2001/6^2002, which simplifies to 1/6. If we multiply 9 (which is 3^2) to 1/6, we get 9/6=3/2. This is a pretty tough question. Hopefully this helps!