Answer:
[tex]\displaystyle \frac{3^5}{3^{-6}}=3^{11}[/tex]
Step-by-step explanation:
Properties of Exponents
They can be used to simplify expressions of the form
[tex]b^x\cdot b^y=b^{x+y}[/tex]
[tex]\displaystyle \frac{b^x}{b^y}=b^{x-y}[/tex]
The last property will be used to simplify:
[tex]\displaystyle \frac{3^5}{3^{-6}}=3^{5-(-6)}=3^{5+6}=3^{11}[/tex]
[tex]\mathbf{\displaystyle \frac{3^5}{3^{-6}}=3^{11}}[/tex]
The length l of a rectangle is decreasing at a rate of 3 cm/sec while the width w is increasing at a rate of 3 cm/sec. When l=5 cm and w=12 cm, find the rates of change of the area, the perimeter, and the lengths of the diagonals of the rectangle. Determine which of these quantities are increasing, decreasing, or constant.
a) The rate of changes of the area of the rectangle is _______ cm^2/sec
Is the area increasing, decreasing, or constant?
b) The rate of change of the perimeter of the rectangle is ____ cm/sec.
Is the perimeter increasing, decreasing, or constant?
c) The rate of change of the length of the diagonals of the rectangle is ____ cm/sec.
Is the length of the diagonals increasing, decreasing, or constant.
Answer:
1) dA/dt = -21 cm²/s and Area is decreasing
2)dP/dt = 0 and perimeter is constant
3) dD/dt = 21/13 cm/s and diagonal is increasing
Step-by-step explanation:
We are given that;
length l of a rectangle is decreasing at a rate of 3 cm/sec.
Thus, dl/dt = -3 cm/sec
Also, the width w is increasing at a rate of 3 cm/sec. Thus;
dw/dt = 3 cm/sec
When l=5 cm and w=12 cm;
A) Area is given by the formula;
A = lw
The rate at which area is increasing is;
dA/dt = l(dw/dt) + w(dl/dt)
Plugging in the relevant values;
dA/dt = 5(3) + 12(-3)
dA/dt = 15 - 36
dA/dt = -21 cm²/s
This is less than 0.thus, A is decreasing.
B) Formula for perimeter is;
P = 2l + 2w
rate of change of perimeter is;
dP/dt = 2(dw/dt) + 2(dl/dt)
Plugging in the relevant values, we have;
dP/dt = 2(-3) + 2(3)
dP/dt = 0
Thus,Perimeter is constant
C) the length of the diagonal of a rectangle is given by;
D = √(w² + l²)
Rate of change of diagonal is;
dD/dt = [2w(dw/dt) + 2l(dl/dt)]/(2√(w² + l²))
2 will cancel out in numerator and denominator to give;
dD/dt = [w(dw/dt) + l(dl/dt)]/(√(w² + l²))
Plugging in the relevant values gives;
dD/dt = [12(3) + 5(-3)]/(√(12² + 5²))
dD/dt = (36 - 15)/13
dD/dt = 21/13 cm/s
This is greater than 0.
Thus, diagonal is increasing.
Determine a constant in 9x + 4y -13.
A) -13
B) 9x
C) 4y
A wizard-in-training has 300 grams of 20% liquid-gold solution. He wishes to drain some and replace it with an 80% solution, so that he gets 300 grams of 35% solution. How many grams should the wizard drain and replace with 80% solution?
Answer:
it would take 4 grams. I hope this helps
Answer:
75 grams! hope this helps :3
Rosalita is making chocolate chip cookies. She needs 20 ounces of
chocolate chips. She has
2 1/4 pounds of chocolate chips. There are 16 ounces in 1 pound. How
many ounces of chocolate chips will Rosalita have left after she makes her
cookies?
A customer at a store paid $96 for 5 large candles and 7 small candles. At the same store a second customer paid $8 less than the first customer for 4 large candles and 8 smal candies Write a system that could be used find the price in dollars of each large candle, x, and each small candle, Y
Answer:
The system that could be used find the price in dollars of each large candle, x, and each small candle, Y is given as:
5x + 7y = 96...... Equation 1
4x + 8y = 88..... Equation 2
Step-by-step explanation:
From the question:
Let cost of:
large candles = x
Small candles = y
A customer at a store paid $96 for 5 large candles and 7 small candles.
Hence:
5x + 7y = 96...... Equation 1
At the same store a second customer paid $8 less than the first customer for 4 large candles and 8 smal candies
Hence:
4x + 8y = $96 - $8
4x + 8y = 88..... Equation 2
The system that could be used find the price in dollars of each large candle, x, and each small candle, Y is given as:
5x + 7y = 96...... Equation 1
4x + 8y = 88..... Equation 2
part two thinking a number between 1 and 10 but doble the money!
Some plz help it’s for all of them
Answer:
a is 0,4
Step-by-step explanation:
Answer:
A) 4,0
G) 1,4
Q) 0,-4
N) -4,-3
helpppppppp meeeeeeee
Answer:A
Step-by-step explanation:
Write an integer for: A bank deposit of $175
Answer:
175
Step-by-step explanation:
A deposit is adding money to the bank, so the integer will be positive.
That makes our integer: 175
Muffins are sold in packages of 18. Select the expressions that can represent the total number of muffins in p packages of muffins.
A. 18 + p
B. 18 × p
C. 18 – p
D. 18 ÷ p
E. 18p
There is a proportional relationship between time in hours and time in days.
A. What is the constant of proportionality?
B. what equation describes this relationship?
Of the proportional relationship between time in hours and time in days, we have that:
a) The constant of proportionality is 24.
b) The equation is [tex]h = 24d[/tex].
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:[tex]y = kx[/tex]
In which k is the constant of proportionality.Item a:
A day has 24 hours, hence the constant of proportionality is 24.
Item b:
Considering the time in hours as the output and the time in days as the input, the equation is:
[tex]h = 24d[/tex]
You can learn more about proportional relationships at https://brainly.com/question/25815502
I need help for math plz :(
Answer:
Option D
Step-by-step explanation:
Set of data in terms of ordered pairs represents a function when output value of each input value is different.
Option A
Since, for every value of x there is a different value of y, it's a function.
Option B
In each ordered pair, for every value of x there is a different value of y.
Therefore, it's a function.
Option C
From the given graph, for every value of x there is a different value of y.
Therefore, it's a function.
Option D
From the given set of ordered pairs we find for x = 1 there are two values of y (y = 4 and 3).
Therefore, the given set of ordered pairs doesn't represent a function.
Option D is the answer.
"Individuals, cultures, societies, and the world change through times of conflict and cooperation."
The statement above exemplifies the era of global expansion and encounter. What other word also reflects this theme?
Technology
Trade
Monopoly
Hegemony
A card is randomly selected out of a standard 52 deck of cards. What is the probability of selecting a queen or a
heart?
Leave your answer as a fraction in lowest terms
Express (x+9)^2(x+9)
2
as a trinomial in standard form.
Given:
[tex](x+9)^2[/tex]
To find:
The given expression as a trinomial in standard form.
Solution:
We have,
[tex](x+9)^2[/tex]
Using the formula, [tex](a+b)^2=a^2+2ab+b^2[/tex], we get
[tex](x+9)^2=x^2+2(x)(9)+(9)^2[/tex]
[tex](x+9)^2=x^2+18x+81[/tex]
Standard form a trinomial is [tex]ax^2+bx+c[/tex].
[tex]x^2+18x+81[/tex] is in the standard form.
Therefore, the required expression is [tex]x^2+18x+81[/tex].
What is the slope of the function f(x) = 6x + 10 *
1
10
6
16
Other:
Answer:
6
Step-by-step explanation:
6 is the slope of the function
Lisa has scored 24, 21, and 20 points in her three basketball games so far. How many points does she need to score in her next game so that her average
(mean) is 21 points per game?
Explanation
Check
She needs to score AT LEAST 19 points
Step-by-step explanation:
24 + 21 + 20 + 19 = 84
84 ÷ 2 = 21
Solve the system by graphing 3x+y=4 and x-y=4
multiple of 3 and 5 less than 47 but greater than 42....
Answer:
45
Step-by-step explanation:
45 > 42 but < 47 and it's a multiple of 3 and 5
EC - The ratio of three numbers is 2:7:1.
The sum of the numbers is 30. What are the
three numbers?
Answer: 6, 21, 3
Step-by-step explanation:
2:7:1
Also, 2x 7x and 1x or just x
2x+7x+x = 30
10x = 30
x=3
So the three numbers: 2(3):7(3):1(3) OR 6:21:3
4x + 2y = 32
5x - 2y = 31
Answer:
Step-by-step explanation:
-8x-y=16;3x-y=5 | | x-y=11;2x+y=4 | | -8x-8=-40y;50y-10=10x | | 0=-11y+8x+33;-1+4/9x+1/3y=0 | | 0=-16+4x+4y;0=28-7y+7x | | 3x-y=9;-3x+y=-9 | | -4x+y=8;4x-y=8 | | x=2y-8;-2x+3y=14 | | y=2x;y=2x-3 | | x-3y=2;7x+y=36 | | 2x+5y=16;2x+3y=8 | | 2c+5p=16;2c+3p=8 | | x/5;7/4 | | -(x-2)=3(y+1);2x+3=4y-1 | | 4x-12y=17;2x+6y=1 | | 1A+4C=85;3A+2C=105 | | 2x-11y=7;3x-9y=7 | | 40-2x;X=3 | | x+y=220;2x+4y=520 | | 3p+2b=29;5p+3b=47.50 | | 4x+2y=23.50;2x+4y=18.50 | | t=2r+3;5r-4t=6 | | x+y=5157.50;y-x=917.50 | | x+y=177;x=97 | | x+y=55;x+10=181 | | x+y=10;x-y=4 | | 1/5x+1/3y=14/15;1/5x+4y=78/5 | | 8x+16y=3520;-8x-8y=2560 | | 1/25x-1/100y=7/5;1/4x+4/25y=66/5 | | -2x+5y=5;-4x+10y=0 | | 1/2x+1/3y=-5/3;1/2x+4y=2 |
| 3x+2y=-3;x=21-8y | | 5x-y=27;x+y=9 | | 36x-4y=16;y=9x+4 | | -15x-10y=1;15y=1+10x | | 3x+7y=9;x=2-2y | | 2x+y=8;y=2x | | x-2y=10;x | | x+y=2;x-y=2 | | 7x-y=27;9x-4y=3 | | x+y=480;x-y=400 | | 3x+2y=78.39;2x+3y=74.61 | | 11x+15y=6912;-11x-11y=-6336 | | 1.6x+1.6y=160;x-y=10 | | y=-1/2x-5;6x-2y=24 | | x+y=4;y-x=4 | | 5x=22-y;7x=35+2y | | 3x=12+2y;-6/5x+y=-9/5 | | 3x+2y=0;12x+2=6y | | 2x-5y=-9;5x+2y=50 | | x+y=4;x+y=-2 | | 7x-y=41;x+5y=47 | | 2x-y=7;9y=2x-31 | | x+y=11;6x-y=10 | | 0.1x+0.5y=-0.8;0.8x-0.6y=7.4 | | 1/3x+1/2y=1/6;1/3x+2y=5/3 | | 16x-10y=4;8x=5y+2 | | 15x-20y=7;10y=-3+5x | | x=5y-5;-2x+10y=10 | | 5x-27=-y;4x-y=0 | | 5x-27=-1y;4x-1y=0 | | 4x+5y=3;x=3-2y | | 6x+2y=10;12x+4y=21 | | x+y=5;3x+2y=10 | | -12x+14z=-14;-14x-14z=98 |
A box of 6 glue sticks costs $8.95. How much will it cost to buy 5 glue sticks?
Carly earned some money doing odd jobs last summer and put it in a savings account that earns 5% interest compounded quarterly. After 2 years, there is $400.00 in the account. How much did Carly earn doing odd jobs? * A. 155.90 B. 441.79 C. 390.18 D. 362.16
Can anyone solve this? If so tell me and make sure u know what ur doing please
Answer:
-2
Step-by-step explanation:
To find the slope of a line, you need to find the [tex]\frac{rise}{run}[/tex] between two points. I will be using the points (-3, 2) and (-1, -2).
[tex]\frac{rise}{run}[/tex] = [tex]\frac{-2-2}{-1-(-3)}[/tex]
= [tex]\frac{-2-2}{-1+3}[/tex]
= [tex]\frac{-4}{2}[/tex]
= -2
Identify a diameter of circle E.
Answer: B) HI
Step-by-step explanation:
what is the midpoint of the segment shown below ?
g If the p-value for your test statistic in a test of hypothesis (for example, a t-test, one-tail) is 0.07 and the significance level alpha is set at 0.05, you conclude that: Both hypotheses H0 and H1 can be accepted The null hypothesis H0 cannot be rejected The null hypothesis H0 can be rejected The research hypothesis H1 can be accepted
Complete Question
If the p-value for your test statistic in a test of hypothesis (for example, a t-test, one-tail) is 0.07 and the significance level alpha is set at 0.05, you conclude that:
A
Both hypotheses H0 and H1 can be accepted
B
The null hypothesis H0 cannot be rejected
C
The null hypothesis H0 can be rejected
D
The research hypothesis H1 can be accepted
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The p-value is [tex]p-value = 0.07[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Generally given that it is a one tail test then the possible value of
The null hypothesis is [tex]H_o : \mu = x[/tex]
Here [tex]\mu[/tex] is the mean and x is the value
the possible values of the alternative hypothesis is [tex]\mu > x \ \ or \ \ \mu < x[/tex]
Now from the value given we see that the [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The point (-3, 8) is translated using the rule (x + 5, y - 7). The new point is (____).
O (2, 1)
O (8,1)
O (-2, 15)
0 (-8, 1)
Answer:
(2, 1)
Step-by-step explanation:
You add 5 to the x coordinate, which is -3 and you get 2. Then add -7 to the y coordinate, which is 8 and get 1
Answer:
(2, 1)
Step-by-step explanation:
(x + 5, y - 7), (-3, 8)
(- 3 + 5, 8 - 7) = (2 + 1)
Thus, The new point is (2 + 1).
-TheUnknownScientist
please help me thanks
Help me please i beed this now
Answer:
well 5% of 600 is 30. so if you make 600 phone calls and an average of 5% of those calls are people signing up, then that would be 30.