Answers
Answer:
Here we will use the relationships:
[tex]a^n*a^m = a^{n + m}[/tex]
[tex](a^n)^m = a^{n*m}[/tex]
[tex]\frac{a^n}{a^m} = a^{n - m}[/tex]
And a number:
[tex]a^n[/tex]
is between 0 and 1 if a is positive and larger than 1, and n is negative.
if a is positive and 0 < a < 1, then we need to have n positive such that:
0 < a^n < 1
A) [tex]5^3*5^{-4} = 5^{3 + (-4)} = 5^{-1}[/tex]
This is between zero and 1,
B) [tex]\frac{3^5}{3^{-6}} = 3^{5 - (-6)} = 3^{11}[/tex]
This is greater than 1, because the exponent is positive.
C) [tex](\frac{1}{4})^3*( \frac{1}{4})^2 = (\frac{1}{4})^{2 + 3} = (\frac{1}{4})^5[/tex]
Because a is smaller than 1, and the exponent is positive, then the expression is between 0 and 1.
D) [tex]\frac{(-7)^5}{(-7)^7} = (-7)^{5 - 7} = -7^{-2}[/tex]
The exponent is negative (and pair) then the expression is between 0 and 1.
Remember that when the exponent is pair, we always have that:
(-N)^m = (N)^m
So (-7)^-2 = 7^-2
Related Questions
a square has an area of 90cm^2
work out the length of one side of the square
Give your answer to 1 decimal space
Answers
Step-by-step explanation:
area of square= a^2
[tex]90 = {a}^{2} \\ a = \sqrt{90} \\ a = 9.48683298 \\ a= 9.5[/tex]
3x+4(x-4) I ahve been having trouble with this and i cant wrap my finger around it to figure this out please help.
Answers
PLEASE HELP
6x+2+3x+7
Answers
Beth walked 10 7/8 miles one week. she walked 2 1/4 fewer miles the following week. About how many miles did she walk the second week round each mixed number to the nearest whole number.
Answers
Answer:
8 and 5/8 miles
Step-by-step explanation:
A circle is represented by the equation below: (x + 8)2 + (y − 3)2 = 100 Which statement is true?
The circle is centered at (−8, 3) and has a radius of 20.
The circle is centered at (8, −3) and has a diameter of 20.
The circle is centered at (8, −3) and has a radius of 20.
The circle is centered at (−8, 3) and has a diameter of 20.
Answers
Answer:
D) The circle is centred at (-8,3) and has a diameter 20
Step-by-step explanation:
Explanation:-
Given that the circle
( x + 8)² +( y-3)² = 100
⇒ ( x + 8)² +( y-3)² = 10²
Standard form of the circle ( x-h)² +(y-k)² = r²
Centre of the circle (h , k) = (-8 , 3)
Radius of the circle r = 10
Diameter of the circle 'd' = 2r = 2(10) =20
Final answer:-
The circle is centred at (-8,3) and has a diameter 20
Answer:
The circle is centered at (−8, 3) and has a diameter of 20.
Step-by-step explanation:
Hope this helps :)
A quadrilateral is a four-sided polygon. True or false?
Answers
Answer:
True
Step-by-step explanation:
Four-sided polygons are usually referred to as quadrilaterals, quadrangles or sometimes tetragons. In geometry the term quadrilateral is commonly used.
Answer: True
Step-by-step explanation: :D
10) The scale of a map is 1 inch represents 4 miles. How many miles does 0.5 inches represent?
Answers
Answer:
2 miles
Step-by-step explanation:
1 in=4miles
0.5 in=2miles
so divide by two on each side
We know that 1/0.5 = 2
We divide 4/2 = 2
0.5 inches = 2 miles
Help please !!!
A: 35
B: 105
C: 40
D: 60
Answers
Answer:
105 degerees
Step-by-step explanation:
Answer:
D) 60°
Step-by-step explanation:
360-40-105-155=60°
will give brainlest if you give all answers its due in 10 minutes !!!!! pls hurry :((((
Answers
Answer:
8. 7x/2 + 2
9. 4y + 2
10. 7x
11. 6y
Step-by-step explanation:
There i did it all.
maddie help please ee
Answers
Answer:
x+11/x+9
Step-by-step explanation:
Just Cancel the common factor of x-4
The house was bought for $125,000 in 1990, the overage rate is 7.85%, what year will the purchase of the house be worth 3 times the purchase price?
Answers
Answer: 2005
Step-by-step explanation:
Exponential function to determine the value of item after t years,
[tex]f(x)=A(1+r)^t[/tex] , where r= rate of growth, A=Initial value.
As per given , A = 7.85% = 0.0785
A = $125,000
Substitute all values in function, we get
[tex]f(x)=125000(1+0.785)^t[/tex]
When f(x)= 3A , then
[tex]3A=A(1.0785)^t\\\\\Rightarrow\ 3=(1.0785)^t[/tex]
Taking tog on both sides , we get
[tex]\ln 3=t\ln 1.0785\\\\\Rightarrow\ t=\dfrac{\ln 3}{\ln 1.0785}\\\\\Rightarrow t=\dfrac{1.09861228867}{0.0755711868471}\approx15[/tex]
The year will be 1990+15= 2005
Hence, the required year = 2005
Which of the following relations is a function?
O A
{(-1, - 4), (-1,0), (- 1,5), (- 1, 7), (-1,9)
B.
{(-2, - 4), (-1,7), (1, - 1), (1, 1), (3,9)}
о
C.
{(-4,9), (- 3, 1), (- 2, 3), (- 2, 12), (0, 6) }
D.
{(0, - 4), (1, - 4), (2, 4), (3, 4), (4, - 4)}
О O
Answers
Answer: D. {(0, - 4), (1, - 4), (2, 4), (3, 4), (4, - 4)}
Step-by-step explanation:
A relation R is said to be a function if for each input value there exists only one unique output value.In (x,y) , x= Input value , y= output value.
A. {(-1, - 4), (-1,0), (- 1,5), (- 1, 7), (-1,9)}
Here, -1 has two output values -4 and 0.
So it is not a function.
B. (-2, - 4), (-1,7), (1, - 1), (1, 1), (3,9)}
Here, 1 has two output values -1 and 1.
So it is not a function.
C. {(-4,9), (- 3, 1), (- 2, 3), (- 2, 12), (0, 6) }
Here, -2 has two output values 3 and 12.
So it is not a function.
D. {(0, - 4), (1, - 4), (2, 4), (3, 4), (4, - 4)}
here, each input value has an unique output value.
Hence, D. option is correct.
James and Martina each read
74 books last summer. How
many books altogether did
they read?
3
books
90
Answers
Answer:
148 books
Step-by-step explanation:
Answer:
148 books all together
PLS HELP WILL MARK BRAINIEST
Answers
need help plz help me
Answers
Answer:
The last one t/5-6=-3
Step-by-step explanation:
All you have to do is plug in 15 to each equation, knowing this if you add 15 into this equation you would get 15/5-6=-3 and this is true because 15/5=3, 3-6=-3!
I hope this helps and have a great day!
i never understood this!who ever gives me a answer i'll give em 5 stars and a thanks
Answers
will make brainliest with correct answer
Answers
Answer:
10
Step-by-step explanation:
8² = 64
6² = 36
64 + 36 = 100
√100 = 10
solve the equation by factoring plssss help ASAPPPP
4x^{2}-20x=0
Thanks UwU
Answers
Answer:
x = 0 and 5
Step-by-step explanation:
4x^2 - 20x = 0
Factor 4x
4x(x - 5) = 0
4x = 0 = > x = 0
x- 5 = 0 = > x = 5
p - 5.89 = –1.2
How can I do this?
Answers
Answer:
p=4.69
Step-by-step explanation:
Move all terms not containing
p
to the right side of the equation.
Answer: p=4.69
Step-by-step explanation:
Step 1: Add 5.89 to both sides.
p−5.89+5.89=−1.2+5.89
p=4.69
John placed $5000 in an account that earns interest compounded annually. His interest rate is 8.2%. If John leaves his money in the account for 10 years, what is the balance of his account? Round your answer to the nearest dollar.
Answers
I multiplied 5000 x .082 and got 410
then i multiplied 410 x 10 and got 4,100
then i added 5000 + 4100 to get $9,100.
Angle X and Angle Y are complementary angles. Angle X is eight times larger than Angle Y. What are the
measures of Angle X and Angle Y?
Answers
Answer:
If you know that Angle X and Angle Y are complementary angles, X+Y = 90
Then we translate the sentence "angle x is 8 times larger than angle Y" into mathematical terms. is means equal, and 8 times means multiplication. This gives us our second equation
X = 8Y
We then use the property of substitution to combine the equations into a solvable system. if X = 8Y and X + Y = 90, we can say that 8Y + Y = 90.
combining like terms, we have 9Y = 90. Y then equals 10.
We then substitute back into the original X = 8Y to get X = 8*10. X = 80.
The final answer is X = 80 degrees and Y equals 10 degrees
Step-by-step explanation:
is y=x^8 an exponential function
Answers
Tyler brother works in a shoe store and the store brought a pair of shoes for $50 and sold it for $80 what percentage was the markup?
Answers
Answer:
$60.
Step-by-step explanation:
Cost price= $50
Selling price = $80
Percentage markup = Gain/Cost price x 100%
=30/50x100
=$60.
Question 15 (5 points)
5
6
(2) There are two paths that one can choose to go from
Sarah's house to James house. One way is to take C street,
and the other way requires to take A street and then B
street. How much shorter is the direct path along C street?
(Using figure).
3
9
12
Sarah
house TTT
15
James
house
B Street
1.5 miles
C Street
A Street
2 miles
Answers
What is the area of the arrow
Answers
Answer:
14 in
Step-by-step explanation:
4+12+4+4+4=28/2= 14
The solution to 9-2w≤11-10w is: 1.w≥1/4 2.w≤1/4 3.w≥5/2 4.w≤5/2
Answers
Answer:
[tex]w \le \frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]9-2w \le 11-10w[/tex]
Required
Solve
[tex]9-2w \le 11-10w[/tex]
Collect like terms
[tex]-2w + 10w \le 11 - 9[/tex]
[tex]8w \le 2[/tex]
Make w the subject
[tex]w \le \frac{2}{8}[/tex]
[tex]w \le \frac{1}{4}[/tex]
There are 15 students not going on the field trip. That is 6% of all
of the 6th graders, How many 6th graders are there?
Answers
Answer:
250
Step-by-step explanation:
15=6%
?=1%
15/6=2.5
2.5=1%
1%=1/100
2.5 x 100=
250
A car travels 110km on 8 litres of petrol. How far will it travel on 20 litres?
Answers
Answer:
2e-11
Step-by-step explanation:
Answer:
110/8 13.75 for 1 litres 13.75*20 275
it travels 275 km on 20 litres
You drop a ball from a height of 98 feet. At the same time, your friend throws a ball upward. The polynomials represent the heights (in feet) of the balls after t seconds. At what time do the balls reach the same height?
Answers
Answer: The polynomial is 92 - 46t
92,92,-46,46
Step-by-step explanation:
The polynomial represent the heights (in feet) of the balls after t seconds is : -46t+92
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
The motion of both balls is a free-fall motion which means that the ball is acted upon the force of gravity only.
Therefore, the motion of the ball is a uniformly accelerated motion, with constant acceleration equal to the acceleration of gravity:
g = 32 ft / sec sq.
The ball which is thrown upward from the ground instead is fired with an initial vertical velocity , and its starting height is zero, so its position at time t is given as;
h(t) = ut - 1/2 gt²
Therefore, the polynomial that represents the distance between the two balls is -46t+92
Learn more about polynomials here:
https://brainly.com/question/27343162
#SPJ2
What is the equation of a line that is perpendicular to a line with a slope of 2 and passes
through the point (-2, 0)?
Answers
To find the equation of a perpendicular line, you first need to find the negative reciprocal of the slope given. The slope is -1/3, so the slope of the perpendicular line will be 3
Now we just need to find the y intercept using the point (3, 2) and you can plug the coordinates in and then solve for b. Let's see what that looks like.
y=3x+b
2=3*(3)+b
2=9+b
-7=b So now we know the y-intercept and slope. We just put them together now
y=3x-7