Answer: Q(t) = 410*(5)^(2t) = 410*(5^2)^t = 410*(25)^t
Step-by-step explanation:
We start with the equation:
Q(t) = 410*(5)^(2t)
And we want to rewrite this in the form:
Q(t) = a*b^t
To do this, we need to use the property:
(a^x)^y = a^(x*y)
Using this, we can rewrite:
Q(t) = 410*(5)^(2t) = 410*(5^2)^t = 410*(25)^t
And this is the form that we wanted:
Answer:
13120(16)^t
Step-by-step explanation:
The number of views on a viral video can be modeled by the function Q(t)=820(4)^{2t+2}.Q(t)=820(4)
2t+2
. Write an equivalent function of the form Q(t)=ab^t.Q(t)=ab
t
.
Q(t)=
Q(t)=
\,\,820(4)^{2t+2}
820(4)
2t+2
Q(t)=
Q(t)=
\,\,820\cdot\color{steelblue}{4^{2t+2}}
820⋅4
2t+2
Q(t)=
Q(t)=
\,\,820\cdot\color{steelblue}{4^{2t}\cdot 4^{2}}
820⋅4
2t
⋅4
2
\small 4^a\cdot4^b \rightarrow 4^{a+b},4
a
⋅4
b
→4
a+b
, but going backwards \small 4^{a+b}\rightarrow 4^a\cdot 4^b4
a+b
→4
a
⋅4
b
Q(t)=
Q(t)=
\,\,820\cdot\color{steelblue}{4^{2}\cdot 4^{2t}}
820⋅4
2
⋅4
2t
Switch order of multiplication
Q(t)=
Q(t)=
\,\,(820\cdot\color{steelblue}{16})\cdot \color{steelblue}{4^{2t}}
(820⋅16)⋅4
2t
Evaluate \color{steelblue}{4^{2}=16}4
2
=16
Q(t)=
Q(t)=
\,\,13120(4)^{2t}
13120(4)
2t
Multiply 820\cdot 16=820⋅16=1312013120
Q(t)=
Q(t)=
\,\,13120(4^{2})^{t}
13120(4
2
)
t
Since (4^a)^b\rightarrow 4^{ab},(4
a
)
b
→4
ab
, we can go backwards 4^{ab}\rightarrow (4^a)^b4
ab
→(4
a
)
b
Q(t)=
Q(t)=
\,\,13120(16)^{t}
13120(16)
t
Evaluate 4^{2}=164
2
=16
The selling price of a television in a retail store is $66 less than 3 times the wholesale price. If the selling price
of a television is $948. How much is the wholesale price of the tv?
Answer:
899 + 66 = 3*X, X being the wholesale price.
965 = 3*x -> x = 965/3 -> x = 321.66 (and 2/3 of a cent)
Step-by-step explanation:
write the equation of each line in slope-intercept form slope=4 y-intercept=-5
Answer:
Y=4X-5
Step-by-step explanation:
The Slope is a positive 4 so you will already have the equation Y=4X and the y-intercept is the Y when X is at the origin. Since the y-intercept is negative you have to subtract from the slope instead of adding. Then you get Y=4X-5.
Solve: x2 + 5x - 6= 0
A. -1, 6
B. 1, -6
C. -2, -3
D. 1,5
Answer:
Assuming that the x2 is x squared, B
Step-by-step explanation:
(1)(1) + 5(1) - 6 = 1 + 5 - 6 = 6 - 6 = 0
(-6)(-6) + 5(-6) - 6 = 36 - 30 - 6 = 6 - 6 = 0
Answer:
B
Step-by-step explanation:
Let's solve using factoring.
x²+5x-6=0
5 is the sum of the numbers, while -6 is their product.
Think: which two numbers add up to 5, but when multiplied, equal -6?
Those numbers are -1 and 6.
Now factor the polynomial:
(x-1)(x+6)=0
split into parts:
(x-1)=0
x-1=0
x=1
(x+6)=0
x+6=0
x=-6
So B
Hope this helps!
-3 represents the distance from a stage to the floor below. 3 represents the distance from the stage to the top of a bookcase. What dose zero represent in this situation?
Answer:
the distance from the floor below to the top of the bookcase
Step-by-step explanation:
From the question we are given the following
distance from a stage to the floor below = -3
distance from the stage to the top of a bookcase = 3
The distance from the floor below to the top of the bookcase = distance from a stage to the floor below + distance from the stage to the top of a bookcase
The distance from the floor below to the top of the bookcase = -3 + 3
The distance from the floor below to the top of the bookcase = 0
Hence zero represents the distance from the floor below to the top of the bookcase
Find the area of the parallelogram.
Question 16 options:
*the bottom is 5.8 inches.
A)
29 square units
B)
37.12 square units
C)
14.5 square units
D)
32 square units
PLEASE HELP ASAP
Answer:
B
Step-by-step explanation:
At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are the cost, y, in dollars and the amount of yogurt, x, proportional? Explain. Write an equation to represent this relationship.
Answer:
Yes, the cost y in dollars and the amount of yogurt are proportional.
The equation is: y = 0.08x
Step-by-step explanation:
1. If y varies directly as x, you can write it as following: y = kx
Where k is the constant of proportionality.
2. Let's calculate the value of the constant of proportionality. If y = 2.56 and x = 32, you have:
y = kx
k = y/x
k = 2.56/32
k = 0.08
3. Then, the equation is: y = 0.08
4. Let's verify if they are directly proportional. Substitute which is the amount of yogurt bought by Jonah. The result must be $0,48:
y = 0.08 (6)
y = 0.48
5. They are directly proportional.
a. Identify all pairs of congruent angles in the diagram.
b. In the diagram, the measure of angle PQR = 130°, the measure of angle RQS = 84°, and the measure of angle TSR = 121°. Find the other angle measures in the diagram.
First off, we can see already that there are congruent symbols in the diagram (the single and double red lines correspond to the other one that looks alike to it)
Measure QRS is like measure QPT and since QRS = 84°, then QPT also equals 84°
Measure TSR is like measure STP and since TSR = 121°, then STP also equals 121°
A company offers premium cable for 39.95 per month plus a one time setup fee. The total cost of 6 months of service is 264.70. Write and solve a linear equation to find the total cost for 2 years of service
Answer:
Total cost = 983.8
Step-by-step explanation:
Monthly charge = 39.95
One time set up fee = x
Number of months = y
Total cost = x + 39.95y
The total cost of 6 months of service is 264.70.
264.70 = x + 39.95(6)
264.70 = x + 239.7
264.70 - 239.7 = x
x = 25
Total cost = 25 + 39.95y
Write and solve a linear equation to find the total cost for 2 years of service
2 years = 24 months
Total cost = 25 + 39.95y
= 25 + 39.95(24)
= 25 + 958.8
= 983.8
Total cost = 983.8
PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Answer:
x= -3
y=2
Step-by-step explanation:
How does graphing help you solve a system of linear equations? i need the answer asap please
III. Round each decimal to the indicated place,
Nearest Hundredths
Nearest Thousandths
Decimal Number
98.9834
45,4536
3 65.1263
4 76.1267
12.4519
Answer:
See rounded numbers below
Step-by-step explanation:
Number | Nearest Thousandths | Nearest Hundredths | Decimal Number
98.9834 | 98.983 | 98.98 | 98.9
45.4536 | 45.454 | 45.45 | 45.5 |
3 65.1263 | 365.126 | 365.13 | 365.1
4 76.1267 | 476.127 | 476.13 | 476.1
12.4519 | 12.452 | 12.45 | 12.5
PLEASE PLEASE SOMEONE HELP. ILL MARK YOU BRAINLY ANSWER ASAP
Answer:
ngl ion even know
Step-by-step explanation:
PLS HELP WITH THESE ASAP
Step-by-step explanation:
For a
the solution is x>-17
For b
the solution is x<-1
For c
solve by adding 5.5 to each side
For d
solve by dividing each side by 2.5
is o.16 in root a rational or irrational
Answer:
[tex]\sqrt{0.16}[/tex] is a rational number
Step-by-step explanation:
[tex]\sqrt{0.16}=\sqrt{\frac{16}{100}}=\frac{4}{10}=0.4[/tex]
It is a perfect square. so, it is a rational number
-2(3b - 8) + 12b
Please answer
Answer:6b+16
Step-by-step explanation:
Answer:
6b + 16
Step-by-step explanation:
-2(3b - 8) + 12b --> Question
-6b + 16 + 12b --> Distributed -2 to the parenthesis
(-6b + 12b) + 16 --> Combined Like Terms
6b + 16 --> Simplified
Hope this answered your question! <3
After making 20 servings of pasta, a chef has used 30 cloves of garlic. The chef used 6 cloves to make the first 4 servings. How many cloves of garlic are used to make 10 servings?
Tim rolls a number cube labeled 1 through 6 and flips a coin. Which is the
probability that Tim rolls a number greater than 3 and flips tails?
There are 3 numbers on the cube greater than 3 ( 4, 5, & 6)
This means he has a 3/6 = 1/2 chance of doing that.
He has a 1/2 chance of getting tails on the coin.
The probability of doing both would be the probability of the cube roll x the probability of the coin toss:
1/2 x 1/2= 1/4
The answer is 1/4
PLEASE HElp with math ... please and thank you
Answer:
y = -1/5x + 2
Step-by-step explanation:
y = mx + b
m (slope) = -1/5
b (y-intercept) = 2
y = -1/5x + 2
if you ate 56 hotdogs in 7 minutes how much would you eat per minute
Answer:
8 hot dogs
Step-by-step explanation:
[tex]8*7=56\\[/tex]
Answer:
You could Eat 8 in a minute.
Step-by-step explanation:
divide 56 by 7.
Feels impossible to be honest. I have no idea.
A square has an area of approximately 750 square feet. Which of the following would be the most reasonable estimate of the length of a side of the square?
A.between 20 and 21 feet
B.between 24 and 25 feet
C.between 27 and 28 feet
D.between 30 and 31 feet
Answer:
c
Step-by-step explanation:
hi yeeeeeeeeeeeeeeeeeettttttttttttt
Answer:
C
Step-by-step explanation:
A= l x w
A = 27 x 27 = 729
A = 28 x 28 = 784
so C is the answer
hope this helps if it is wrong i apologize
help :(
14/21 = 14•2/21•2 = ?
14/21= 14/21 divided by ?/?=?/?
Answer:
divide both by 7
2/3
I hope I'm correct
Answer:
the top is 28/42
Step-by-step explanation:
Phil Lanthropist won a great deal of money in a contest. He gave 20% of his winnings to his parents, 25% of the remaining money to his children, and the remaining $900,000 to his favorite charity. What was the total number of dollars that Phil won?
Answer:
$1,636,363.64
Step-by-step explanation:
let x = total amount of money received
the total amount he received is 100%
Percent remaining after giving a percent of the money to family = 100% - 20% - 25% = 55%
This means that 55% of x = $900,000
To find the value of x, divide both sides by 55% or 0.55
x = $900,000 / 0.55 = $1,636,363.64
A random sample of 50 bottles is selected from the production line of a large manufacturing company. The mean weight of the contents of the 50 bottles is 20.25 ounces. The manager of the company requests that the machines be recalibrated because bottles coming off the production line are supposed to contain 20 ounces. Which of the following statements is true?
The population is the production line that needs to be recalibrated and the sample is all production lines.
The population is all production lines and the sample is the production line that needs to be recalibrated.
The population is all bottles in the production line and the sample is the 50 bottles that were selected.
The population is the 50 bottles that were selected and the population is all bottles in the production line.
Answer:
The population is all bottles in the production line and the sample is the 50 bottles that were selected.
Step-by-step explanation:
Edge 2020
P.S. im on unit 7 test i believe you are still in unit 6 I can help you *wink wink with the assignments and quizs
Find the diagonal of a rectangular solid if the length is 44 inches, the width is 32 inches, and the height is 26 inches.
Answer:
d≈60.3
Step-by-step explanation:
I answered wrong what’s the right answer?
On a softball field, home plate is 43 feet from the pitcher's mound. A ball is hit at an angle of 27° east of the pitcher's mound. The ball travels 162 feet before it is caught by an outfielder. A triangle is drawn on a baseball field. A point is at home plate, another point is at the pitcher apostrophe s mound, and another point is at an outfielder. The distance from home plate to the pitcher is 43 feet. The distance from home plate to the outfielder is 162 feet. The angle between the 2 sides is 27 degrees. Law of cosines: How far must the outfielder throw the ball to return it to the pitcher? Round to the nearest foot. 112 feet 125 feet 145 feet 156 feet
Answer:
c = 125 f
Step-by-step explanation:
Let´s call points A ( home plate ) B (pitcher´s place ) and C ( outfielder place)
these three points form a triangle in which according to cosine law, one side of a triangle c can be calculated by the equation:
c² = a² + b² - 2a*b*cos∡a,b
a and b are the other sides of the triangle and ∡a,b is the angle between sides a and b
All distances are in feet then the distance between outfielder and pitcher (c) is in feet:
c² = (43)² + ( 162)² - 2*(43)*(162)*cos 27° cos 27° = 0,891
c² = 1849 + 26244 - 12413,4
c² = 15679,6
c = √15679,6
c = 125 f
how much money would you have if you deposited $100.00 in an account that earned 8% interest after 40 years?
Answer:
$ 420
Step-by-step explanation:
Principal is $ 100 and interest is $ 320
Yvonne is interested in testing the effectiveness of a new flea medication on dogs, so she divided some dogs with fleas into two groups, group A and group B. She gave group A the flea medication. Should she also give group B the flea medication?
Answer:
a is the correct answer i just took the test
Answer: No, because group B should be rhe control group
Step-by-step explanation:
Can somebody please help me here is the question
Pleasee help me !!!92. Find the measures of the numbered angles in the kite shown to the right.
m∠1 = m∠6 =
m∠2 = m∠7 =
m∠3 = m∠8 =
m∠4 = m∠9 =
Answer:
See below
Step-by-step explanation:
Kites have perpendicular diagonals, two pairs of congruent angles and sides.
Angles 1, 2, 3, 4 are all right angles∠6 and 37 are congruent, ∠5 and 43 are congruent, ∠7 and ∠9 congruent, ∠8 and ∠10 are congruentRequired measures:
m∠1 = 90 ° m∠6 = 37°m∠2 = 90 ° m∠7 = 90° - 37° = 53° m∠3 = 90 ° m∠8 = 90° - 43° = 47 ° m∠4 = 90 ° m∠9 = 53°m∠5 = 43 ° m∠10 = 47 °The angles are m∠1 =m∠2 =m∠3 =m∠4 = 90 degrees.
m∠9=m∠7 =m∠8= m∠10 = 53 degrees.
m∠5 = m∠6 =37 degrees
Let us find the angles.
m∠1 , m∠2, m∠3 and m∠4 are right angles.
m∠1 =m∠2 =m∠3 =m∠4 = 90 degrees.
Now let us find m∠9.
By angle sum property, the sum of three angles is 180 degrees.
m∠1 + 37 + m∠9 =180
37+90+m∠9=180
127+m∠9=180
m∠9=180-127
m∠9=53
m∠9=m∠7 = 53 degrees.
Now let us find m∠6.
53+90+m∠6=180
143+m∠6=180
m∠6=37 degrees.
m∠5 = 37 degrees as it is congruent to m∠6.
Now let us find m∠8.
m∠8 + 90+ 37=180
m∠8 +127=180
m∠8 =53 degrees.
m∠10 = 53 degrees.
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