Answer:
[tex]y = 4^x[/tex]
Step-by-step explanation:
Given
[tex](2,16)[/tex]
[tex](5,1,024)[/tex]
Required
Determine the exponential function [tex]y = a.b^x[/tex]
In [tex](2,16)[/tex]
[tex]x=2[/tex] and [tex]y = 16[/tex]
Substitute these values in [tex]y = a.b^x[/tex]
[tex]16 = a.b^2[/tex] --- (1)
In [tex](5,1,024)[/tex]
[tex]x = 5[/tex] and [tex]y = 1024[/tex]
Substitute these values in [tex]y = a.b^x[/tex]
[tex]1024 = a.b^5[/tex] --- (2)
Divide (2) by (1)
[tex]\frac{1024}{16} = \frac{a.b^5}{a.b^2}[/tex]
[tex]\frac{1024}{16} = \frac{b^5}{b^2}[/tex]
[tex]64 = \frac{b^5}{b^2}[/tex]
Apply second law of indices
[tex]64 = b^{5-2[/tex]
[tex]64 = b^3[/tex]
Express 64 as an exponent of 3
[tex]4^3 = b^3[/tex]
[tex]4 = b[/tex]
[tex]b = 4[/tex]
Substitute 4 for b in (1)
[tex]16 = a.b^2[/tex]
[tex]16 = a * 4^2[/tex]
[tex]16 = a * 16[/tex]
[tex]16 = 16a[/tex]
Solve for a
[tex]a=\frac{16}{16}[/tex]
[tex]a = 1[/tex]
Substitute 1 for a and 4 for b in [tex]y = a.b^x[/tex]
[tex]y = 1 * 4^x[/tex]
[tex]y = 4^x[/tex]
The exponential function is given by y = 100(0.4)ˣ
An exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the factor.
At point (2, 16):
16 = ab² (1)
At point (5, 1.024):
1.024 = ab⁵ (2)
Dividing equation 2 by equation 1:
b³ = 0.064
b = 0.4
16 = a(0.4)²
a = 100
The exponential function is given by: y = 100(0.4)ˣ
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Selina walked 2 1/2 miles in 2/3 hour. Dennis 6 3/4 miles in 1 1/2 hours. Who walked faster and how much faster?
Answer:
Dennis walked faster by 0.75 miles/hr
Step-by-step explanation:
a)Selina's speed
speed= distance
time
= 2.5 miles = 3.75 miles/hr = the slower
2/3 hrs
b) Dennis' speed
speed = distance
time
= 6.75 miles = 4.5 miles/hr = the faster
1.5 hrs
difference in speed:
faster - slower
4.5 - 3.75
=0.75 miles/hr
Dennis walked 0.75 miles per hour faster than Selina's speed.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
To determine Selina's speed
speed = distance/time
speed = 2.5 miles/(2/3) hour
speed = 3.75 miles/hour
To determine Dennis' speed
speed = distance/time
speed = 6.75 miles/(1.5) hour
speed = 4.5 miles/hour
Here Dennis' speed is greater than Selina's speed which means Dennis walked faster.
So the difference in speed = Dennis' speed - Selina's speed
The difference in speed = 4.5 miles/hour - 3.75 miles/hour
The difference in speed = 0.75 miles/hr
Thus, Dennis walked 0.75 miles per hour faster than Selina's speed.
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-0+2
Ezzzzzzzzzzzzzzzzzzzzzzzz
Bob is having a cookout. He bought 6 liters of seltzer water. How many full 1-pint servings of seltzer can he pour?
(1 L = 2.11 pt)
a. 6
c. 18
b. 12
d. 21
Answer:
B
Step-by-step explanation:
6 x 2.11 = 12.66
The value of a 1-pint serving of shelter will be 12.66 liters. The correct option is b.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also represent the logical syntax's operation order and other properties.
Given that Bob is having a cookout. He bought 6 litres of seltzer water. The quantity of water for 1 point of serving is,
Quantity = 6 x 2.11
Quantity = 12.66
The quantity will be equal to 12.66 pints.
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How to solve 9(-4k+8b) b=-9 k=4
Answer:
504
Step-by-step explanation:
I hope this helps you out!
Three friends each have some ribbon. Carol has 42 inches of ribbon, Tino has 2.5 feet of ribbon, and Baxter has 1.5 yards of ribbon. Who has the most ribbon? How do you know?
Answer: Baxter
Step-by-step explanation:
To solve this question, we need to know that:
12 inches = 1 foot
36 inches = 1 yard
The number of ribbon for each person will be:
Carol = 42 ribbons
Tino = 2.5 feet = 2.5 × 12 = 30 ribbons
Baxter = 1.5 yard = 1.5 × 36 = 54 ribbons
Therefore, Baxter has the most ribbon
I need help with all of these questions, I would really appreciate it if you would help me, thank you! Also if you would like to send the answers on Instagram my account name is habibamalikkk
Answer: 10. Answer is -3
Step-by-step explanation:
Whats the constant of proportinality?
Answer:
1.5
Step-by-step explanation:
3÷2= 1.5
6÷4=1.5
12÷8= 1.5
A number divided by three less two is at most two
Answer:
6
Step-by-step explanation:
6/3 = 2
Can someone help me with that pls
Answer:
area = length x width or LW
Step-by-step explanation:
the answer is 6 1/15
i need help it's 10th grade (sophomore) geometry
Answer:
1. 27
2. 1 and 2 = 17
3. 55
4. 55
5. 70
6. 125
7. 55
8. 95
9. 140
10. 40
11. 65
12. 75
13. 115
14. 27
15. 27
Step-by-step explanation:
question 8 pls help me please
Answer:
B
Step-by-step explanation:
A is Standard Intercept Form
B is Point Slope Form
The rest are used for other problems I'm unsure of
If 3a - 2 = 10, what is the value of 8a + 1?
Answer:
8a+1=33
Step-by-step explanation:
you can solve 3a-2=10 by simplifying to 3a=12, so a=4. Then you replace the a in 8a+1 with 4 to get 32+1, which is 33
Answer:
33
Step-by-step explanation:
3a-2= 10
3a=12
a=4
in this equation a=4 so you substitute that value into the other equation
8(4) +1=33
Boadu and Ansah formed a company and agreed that their annual profit will be shared in the ratio 4:5 respectively. If at the end of the year. Ansah received Gh€ 5.000.00 more than boadu how much was boadu shared?
Answer:
Step-by-step explanation:
The share of Boadu is Gh€ 222,222.22 if Boadu and Ansah formed a company and agreed that their annual profit will be shared in the ratio 4:5 respectively.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
Boadu and Ansah formed a company and agreed that their annual profit will be shared in the ratio 4:5 respectively.
Let 4x be the share of Boadu and 5x be the share of Ansah
4x + 5x = 5,000,00
9x = 5,000,00
x = 55555.55
The share of Boadu = 4x = 4(55555.55) = 222,222.22
Thus, the share of Boadu is Gh€ 222,222.22 if Boadu and Ansah formed a company and agreed that their annual profit will be shared in the ratio 4:5 respectively.
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WILL GIVE BRAINLIEST!!!!!!
Answer:
17.738
Step-by-step explanation:
to find x we’ll use sine
sin69=x/19
(remember that sine = opposite/hypotenuse)
so x = 19sin69
when typing this in your calculator you might need to change from radian to degree mode
Gloria’s washing machine is broken. Since her machine is pretty old, she doesn’t want to spend more than $100 for repairs. A service call will cost $35 and the labor will be an additional $20 per hour. There are no other charges. What is the maximum number of hours that the repair person can work without the total cost exceeding $100?
Answer:
The actual answer is 3.25
Step-by-step explanation:
I just took the test
the maximum number of hours that the repair person can work is 3.5 hours
Given :
Gloria doesn’t want to spend more than $100.
A service call will cost $35 and the labor will be an additional $20 per hour
Let 'h' be the maximum number of hours the repair can take.
Lets find out the total cost for 'h' hours
35+ additional 20 per hour
[tex]35+20h[/tex]
The total cost should not exceed 100
[tex]35+20h \leq 100\\20h \leq 100-35\\20h\leq 65\\Divide \; by \; 20\\h\leq 3.5[/tex]
So , the maximum number of hours that the repair person can work is 3.5 hours
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mia uses triangle A and says the slope of this line is 6/4.Elena use triangle B and say no,the slope is 1.5
Incomplete question.
A Sub
sentence.
DVD Deals
Anthony and Miguel go to the store to purchase some new DVDs. An
advertisement in the window catches their attention.
DVD
T
Deals!
3 for $22,50
5 for $37.50
응
.
Part A (2 points)
Does the information on the sign represent a proportional relationship?
Explain how you know.
6
Answer: Yes. There's a proportional relationship
Step-by-step explanation:
We are told that Anthony and Miguel go to the store to purchase some new DVDs and that an advertisement in the window catches their attention as they saw that:
3 DVDs cost $22,50. This means the price of one will be:
= $22.50 / 3
= $7.50
5 DVDs cost $37.50. This means that the price for one will be:
= $37.50 / 5
= $7.50
Since the price of a DVD both cost $7.50, it means that the information on the sign represent a proportional relationship.
If M(2,3) is reflected in the line y=4, then M' is (6,3)
TRUE OR FALSE???
Answer:
It is false
Step-by-step explanation:
It's false since M' should be (2,5)
(6,3) is point M reflected about the axis or line: x = 4.
can someone help me please. thanks!
Is this for a test or something?
Given the general identity tan X = , which equation relating the acute angles, A and C, of a right ∆ABC is true?
Answer:
A. tan A = sin A / sin C
Step-by-step explanation:
Answer:
tan A = sin A / sin C
Step-by-step explanation:
Angles A and B are supplementary angles. The mZA = (9x - 12) and the mZB = (24x + 60).
Answer:
/ A = 24°
/ B = 156°
Step-by-step explanation:
Supplementary angles add up to 180°.
_________________________________
Therefore, / A + / B = 180
(9x - 12) + (24x + 60) = 180
9x - 12 + 24x + 60 = 180
33x + 48 = 180
33x = 180 - 48
33x = 132
x = 132/33
x = 12/3
x = 4
_________________________________
/ A = (9x - 12)
= (9(4) - 12)
= (36 - 12)
= 24°
/ B = (24x + 60)
= (24(4) + 60)
= (96 + 60)
= 156°
_________________________________
#teamtrees#WAP
pls help!!! look at picture
Answer:
8.5 hours
Step-by-step explanation:
a). 10h + 45 = 130
b). 10h = 130 - 45 ⇒ h = 8.5 hours
2. Find the measure of the missing angle.
Help me plzzzzzzz I need it!!!
Answer:
84°
Step-by-step explanation:
Alternating interior angles are congruent.
MATH HELP ASAP! MARKING BRAINLIST!!!!!! maTH haLLP
It is a 75% increase
Answer:
75%?? im unsure
Step-by-step explanation:
Nell made a pizza.She cut the pizza into fourths.Then she cut each fourth into four pieces.Nell and her friends ate 6 of the smaller pieces of the pizza. What fraction of the pizza did Nell and her friends NOT eat?
Answer:
5/8
Step-by-step explanation:
They ate 6/16 which the left is 10/16 is 5/8
What is $500= blank+ $600
Answer:
-100$
Step-by-step explanation:
Adding a negitive number to a positive number is basically subtracting it, and since 600-100 is 500 that means 600 + -100 is also 500.
Mrs.Johnsons new car has an 18 gallon gas tank. If she can travel 400 miles on one tank of gasoline, what is her miles per gallon rate to the nearest whole number
Answer:
22
Step-by-step explanation:
400/18=22.222222222
Round to 22
A seventh-grade class is playing the Integer Game modified to include rational numbers. Write a multiplication or division equation to answer the following questions with reference to the Integer Game. Show all of your work.
a. Tobias removes three —3.25 cards from his hand. How does this affect the overall point value of the cards in his hand?
The point value of the cards in Tobias' hand will increase.
The point value of the cards in Tobias' hand will decrease.
b. The cards in Iman's hand had a value of 2.75, but then she added five -1.5 cards to her hand. What is the new value of the cards in her hand?
A passenger on a stranded lifeboat shoots two distress flares into the air. The first flare travels a maximum height 196 feet and lands in the water after 7 seconds. The height (feet) of the second flare above the water is given by f(t) = -16t(t-8), where t is time (seconds) since the flare was shot. Which flare travels higher? Which remains in the air longer?
Answer:
The second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare
Step-by-step explanation:
The given parameters are;
The height of the first flare = 196 feet
The duration the first flare spends in the air = 7 seconds
The function representing the height of the second flair is f(t) = -16t(t - 8)
Where;
t = The time since the passenger shot the second flare
The time the flair stays i the air is given by the time it takes for the height, f(t), to be 0 as follows;
f(t) = 0 = -16t(t - 8)
-16t(t - 8) = 0
t = 0, or t = 8
The time the second flare stays in the air = 8 seconds
The maximum height reached by the second flair is given by the finding the maximum point of the curve of the function as follows;
d(f(t))/dt = 0 = d(-16t(t - 8))/dt = -32t + 128 at the maximum point (the coefficient of t² is negative in the quadratic equation)
-32t + 128 = 0
128 = 32t
32t = 128
t = 128/32 = 4
t = 4 at maximum height and f(4) = -16 × 4 × (4 - 8) = 256 feet
The maximum height reached by the second flare f(4) = -16 × 4 × (4 - 8) = 256 feet.
Therefore, the second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare, with maximum height of 196 feet, and time in the air of 7 seconds.
I’m honestly so dumb can someone help me?
Answer: Hope it helps, have a nice day :)
A: 0.3
A: 3/10
B: 0.6
B: 6/10 (3/5 if simplified)
C: 1.4
C: 1 4/10
D: 1.9
D: 1 9/10
Step-by-step explanation:
The first letter is decimal and the second is fractions- just likes yours