Answers
Answer:
1) [tex]9^{2}=81[/tex]
2) [tex]7=log_{2}(128)[/tex]
Step-by-step explanation:
1)
We need to use the property of power and logarithms, particularly this:
[tex]a=x^{log_{x}(a)}[/tex] (1)
So, let's take take the exponent:
[tex]9^{log_{9}}(\frac{1}{81})=9^{-2}[/tex]
[tex]\frac{1}{81}=9^{-2}[/tex]
now, we can write the negavitve power as:
[tex]\frac{1}{81}=\frac{1}{9^{2}}[/tex]
So, the aswer will be:
[tex]9^{2}=81[/tex]
2)
Applying equation 1, let's take log in base 2 on each side of the equation
[tex]log_{2}(2^{7})=log_{2}(128)[/tex]
using the power definition in log, we have:
[tex]7log_{2}(2)=log_{2}(128)[/tex]
Therefore, the answer is:
[tex]7=log_{2}(128)[/tex]
I hope it helps you!
Related Questions
warm up !!!!!!!!!!!!
Answers
Answer:
Option C. Rational numbers can be written as a fraction where denominator is not zero.
Answer:
B
Step-by-step explanation:
Hope this helps D:
I need help I am lost please help me
Answers
Answer:
6
Step-by-step explanation:
Because 6 is 6 times as 1, 12 is 6 times as 2, 18 is 6 times as 3 and so on.
Cuánto tiempo debe transcurrir para que un capital de $3,000.00 alcance un monto de $7,000.00, si la inversión se hizo con 5% de interés simple mensual?
Answers
Answer:
27 years approx
Step-by-step explanation:
Given data
Principal P= $ 3,000
Final amount A= $ 7000
Rate r= 5%
The simple interest expression is
A=P(1+rt)
substitute and solve for t
7000=3000(1+0.05t)
7000=3000+150r
7000-3000=150r
4000=150t
t= 4000/150
t= 26.66
Hence, the time is 27 years approx
A standard deck of playing cards contains 52 cards, equally divided among four suits(hearts, diamonds, clubs, and spades). Each suit has the cards 2 through 10, as well as a jack, a queen, a kind, and an ace.
If the 3 of spades card is drawn from a standard deck and is not replaced, what is the probability that the next card drawn is a spade OR a kind?
A) [tex]\frac{1}{17}[/tex]
B) [tex]\frac{16}{51}[/tex]
C) [tex]\frac{4}{17}[/tex]
D) [tex]\frac{5}{17}[/tex]
Answers
Answer:
4/17
Step-by-step explanation:
Qual a resposta da seguinte equação (x-3)(x-1)=0
Answers
Answer:
(x-3)(x-1) =0
x-3=0 or x-1=0
x=3 or x=1
A rectangle has a perimeter of 24 ft. Following a dilation, the new perimeter of the
rectangle is 36 ft.
Determine the scale factor of the dilation.
Answers
Answer:
it has increased by 1/2 so the scale factor would either be 3/2 or 1.5 or something
Step-by-step explanation:
Jim borrows $210 from his sister at an 8% interest for seven years. How much interest does Jim have to pay?
Answers
Answer:
$117.6
Step-by-step explanation:
Formula:
I = Prt
Given:
P = 210
r = 8% = 0.08
t = 7
Work:
I = Prt
I = (210)(0.08)(7)
I = 117.6
Answer:
Step-by-step explanation:
So with 8% interest, Jim will have to pay 8% more each year. For the first year we need to multiply 210 with 1.08 to find the amount that Jim would have had to pay to his sister if he had gotten an 8% interest for 1 year. Every time the year increases we need to multiply the previous number with 1.08 because we are looking for the 8% increased value of the previous one, therefore our equation is:
P(t) = 210*(1.08)^t --> (t=time in years, P(t)=amount of money Jim need to pay back with respect to time)
Since Jim gets an 8% interest for 7 years we have to put in 7 for t.
P(7)=210*(1.08)^7
which is approximately $359.903
Camille buys a cake for $24.99 . She also buys 12 brownies. Each brownie costs the same amount. She spends $39.99 on the cake and the brownies. Camille finds the cost of each brownie by calculating (39.99 - 24.99) *12 . Tanya finds the cost of each brownie by solving the equation $39.99 + 12b = 24.99 , where b is the cost of each brownie. Which approach uses the sequence of operations necessary to find the cost of each brownie: Camille’s, Tanya’s, both, or neither?
Answers
Answer:
hi
didn't get it
Step-by-step explanation:
.....
....
Answer:
sorry
Step-by-step explanation:
Which expression has the greatest value?
Answers
Answer:
the last one
Step-by-step explanation:
[tex]\sqrt[3]{64}[/tex] and [tex]16^{3/2}[/tex] expressions have the greatest value.
What is square root and cube root of a number?
Square root of a number results a number that when square, gives us the previous number.
Similarly, cube root of a number results a number that when cubed, gives us the previous number.
Here, [tex]\sqrt[3]{64}[/tex]² = ∛(64 × 64) = ∛(8 × 8 × 8 × 8 × 8 × 8) = 8 × 8 = 64
[tex]16^{3/2}[/tex] = 4³ = 64
[tex]\sqrt[3]{8^{4} }[/tex] = ∛(8 × 8 × 8 × 8) = ∛(64 × 64) = ∛(4 × 4 × 4 × 4 × 4 × 4) = 4 × 4 = 16
√(16²) = √(16 × 16) = 16
Therefore, [tex]\sqrt[3]{64}[/tex]² and [tex]16^{3/2}[/tex] have the greatest value.
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I will mark branliest!
Find the area of the circle below, rounding your answer to the nearest tenth.
Answers
Answer:
sorry it blurry the answer is 154cm²
hope that helps
please make it correct
Answers
Answer:
"The drone is at the surface of the water at both 4 and 7 seconds into the observation."
Have a good day! :>
Answer:
B
Step-by-step explanation:
0 = t^2 - 11t + 28
0 = (t-4) x (t-7)
so it is at the surface at seconds 4, 7
A researcher is interested in the effect of alcohol consumption on reaction times. Participants are assigned to one of three possible conditions: nonalcoholic beer group, 1 beer group, 2 beer group. After drinking, each participant is run through a driving simulator that measures their reaction time to unexpected obstacles (e.g., a child running into the street after a ball) that randomly appear during the simulation. In this example, what is the independent variable
Answers
Answer:
The three different possible conditions ;
nonalcoholic beer group, 1 beer group, 2 beer group
Step-by-step explanation:
The Independent variable, also known as the predictor variable are variables used to influence and check changes in the dependent or predicted variable as subjects are exposed to the different types or levels of independent variable used in the study.
In the scenario described above, the predictor or independent variables which are used to measure the reaction times of participants to unexpected variables is the independent variable, beacuse these different variables ; nonalcoholic beer, 2 beer will probably affect the response time of the participants which is the dependent variable.
The length of a rectangular courtyard can be represented by (4x +3) and the width by (3x– 7). What is
the area of the courtyard?
Answers
John buys a bag containing 3 pounds of flour. He uses 12 ounces of the flour for a craft project. How much flour is left in the bag?
PLEASE ASAP
Answers
Answer:
36 ounces
Step-by-step explanation:
3 pounds is 48 ounces - 12 pounds used gives you 36 ounces which is 2 pounds and a quarter ( 2 1/4)
Sally flipped a penny 25 times and landed on heads 16 out of the 25 times. If she plans to flip the coin 100 times,
how many times can she expect to land on heads?
Answers
Answer:
50 times
Step-by-step explanation:
Since the odds of her getting a heads is 50% (1/2) every time she flips the coin. So she should expect to get 50 heads. However this number varies practically because in every single flip there is a 50-50 chance. If she had flipped it infinitely many times then it would be exactly 50%
Help please! What part of the model represents "n" in the
equation?
Answers
I need answers ASAP!
Answers
Answer:
x>2
Step-by-step explanation:
im the same guy who wrote the comment. I just want points lol
What is the surface area of this triangular pyramid?
Answers
Answer:
48.25
Step-by-step explanation:
This is because when finding the area of a triangle it is known as base times height then divide by 2 and since the base is a triangle, multiply 4.3 times 5 which is 21.5 and divide by 2 which is 10.75 and for the top since its also a triangle multply 5x5 which is 25 divide by 2 whicih is 12.5, but there is 3 of them so multiply by 3 and you get 37.5, then add 37.5+10.75 to get 48.25 cm^2
What expression is equivalent to 4 + 2(3 + 5 exponent 2 - 6)?
Answers
Answer:
A. 48
Step-by-step explanation:
4 + 2(3 + 25 - 6) =
4 + 2(28 - 6) =
4 + 2 x 22 =
4 + 44 =
48
Hope that helps!
what is the slope of this line?
Answers
Answer:
-1/200
Step-by-step explanation:
To get from one point to the other you rise (go down in this case since the slope is negative) $1 every time you make 200 more scarves.
One pound of pasta noodles can be made using the ingredients shown in the recipe below. A chef uses 166 1/4 cups of flour each week to make noodles. How many pounds of noodles does the chef make each week?
Answers
Answer:
Pounds of noodles made per week = 47 1/2 pounds
Step-by-step explanation:
One pound of pasta noodles can be made using the ingredients shown in the recipe below.
Recipe for Pasta Noodles
Ingredients
3 1/2 cups of flour
4 large eggs
2 teaspoons of olive oil
A chef uses 166 1/4 cups of flour each week to make noodles. How many pounds of noodles does the chef make each week?
28 1/2
47 1/2
53 1/4
55 1/2
Pounds of noodles made per week = Total cups of flour used each week / flour used per pound
= 166 1/4 ÷ 3 1/2
= 665/4 ÷ 7/2
= 665/4 ÷ 2/7
= (665*2)/(4*7)
= 1330/28
= 47.5 pounds
Pounds of noodles made per week = 47 1/2 pounds
solve 2x + -3 = -23 algebraically
Answers
Answer:
x = -10
Step-by-step explanation:
Answer:
x = -10
Step-by-step explanation:
Hope this helps!
Have a nice day <3
help! parallel, perpendicular, or neither?
Answers
Answer:
parallel
Step-by-step explanation:
Because a is pependicular to k
Hope that’s helpful :)
Your parents are buying a new car for $15,000. They pay 6.25% sales tax . How much do they pay for the car including tax
Answers
Answer:
$15,937.50
Step-by-step explanation:
15000 × 1.0625 = 15937.5
Can someone pleaseee help me
Answers
Answer:6
Step-by-step explanation:
Vertical angle proof. 4x is equal to 24 so 24/4=6 and x is 6
what is the distance between the points (-5,-4) and (3,-3) on a coordinate plane
Answers
Answer:
18
Step-by-step explanation:
if you were to plug the coordinates into a graph, (-5,-4) would be 16 blocks to the right and two blocks up making it a total of 18
Hope this helps!
The distance between the points P ( -5 , 4 ) and Q ( 3 , -3 ) on the plane is given by D = 8.06 units
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the first point be P = P ( -5 , -4 )
Let the second point be Q = Q ( 3 , -3 )
Now , distance between P and Q is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
D = √ ( -5 - 3 )² + ( -4 - ( -3 ) )²
D = √ ( 64 + 1 )
D = √65 units
D = 8.06 units
Hence , the distance is 8.06 units
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If an object is moving at 8m/s and slows down to a stop in 2 seconds. What is the objects acceleration
Answers
Answer:
-4m/s
Step-by-step explanation:
2)
g(x) = 2x-1
h(x) = 1 - g(x)
The functions g and h are defined above. What is the
value of h(0) ?
A) - 2
B)+
0
1
C)
D)
2.
Answers
Answer:
h(0) = -2x
Step-by-step explanation:
Choose the expression that shows P(X) = x3 + 5x2 + 11x + 10 as a product of two factors.
A. 2x(x2 + 3x + 3)
B. (x + 1)(2x2 + 3x + 6)
C. (2x + 3)(x2 + x + 2)
OD. (X + 2)(x2 + 3x + 5)
Answers
Answer:
D
Step-by-step explanation:
X3+3x2+5x+2x2+6x+10
Collect like terms
X3+5x2+11x+10
The correct expression that shows the P(X) = x³ + 5x² + 11x + 10 as a product of two factors will be;
⇒ (x + 2) (x² + 3x + 5)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ P(X) = x³ + 5x² + 11x + 10
Now,
Solve the expression for the factors as;
The expression is,
⇒ P(X) = x³ + 5x² + 11x + 10
Since, -2 is the solution of the expression.
Hence, (x + 2) is one of the factor of the expression.
So, Find the second factor by dividing the expression (x³ + 5x² + 11x + 10)
by (x + 2), we get;
x + 2 ) x³ + 5x² + 11x + 10 (x² + 3x + 5
x³ + 2x²
--------------
3x² + 11x
3x² + 6x
------------------
5x + 10
5x + 10
--------------------
0
Thus, The second factor = (x² + 3x + 5)
Therefore,
x³ + 5x² + 11x + 10 = (x + 2) (x² + 3x + 5)
Thus, The correct expression that shows the P(X) = x³ + 5x² + 11x + 10 as a product of two factors will be;
⇒ (x + 2) (x² + 3x + 5)
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Joseph flew home from vacation with a heavy bag. With the first airline he flew, Joseph had to pay $27 to check his bag, plus $24 for every kilogram that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Joseph had to pay $25 per kilogram that his bag was over the weight limit, in addition to the checked bag fee of $16. By coincidence, the fees ended up being the same with both airlines. How far over the weight limit was the bag
Answers
Answer:
Step-by-step explanation:
Flight A :
Checked bag fee = $27
Additional fee per overweight limit = $24
Flight B:
Checked bag fee = $16
Additional fee per overweight limit = $25
Since, the total amount paid for the package on both flights are the same ;
Let x = mass of bag above the weight limit.
Hence, Mathematically ;
27 + 24x = 16 + 25x
24x - 25x = 16 - 27
-x = -11
x = 11
Hence. The bag was s 11kg over the weight limit.