Find the exponential function that passes through the points (1, 3) and (2, 9). A) y = 12x B) y = 9x C) y = 6x D) y = 3x

Answers

Answer 1

Answer:

D

Step-by-step explanation:

An exponential function which crosses through (1,3) and (2,9) will have a base of 3 since the y values are multiples of 3.

3^1 = 3

3^2 = 9

This means that the function is y = 3^x.

Answer 2

y = 3x

Substitute the two points into the equation y = abx, giving 3 = ab1 and 9 = ab2.

Since a = a, then  

3

b1

=  

9

b2

, rearranged yields 3b2 = 9b1 → 3b2 − 9b = 0 → b(3b − 9) = 0

Thus, b = 0 or b = 3.

A curve of exponential function never drop below the x-axis, ignore any values of b that are less than or equal to zero.

Therefore, insert b = 3 into  

3

b1

= a and  

9

b2

= a → a = 1 for both equations.

y = abx

y = (1)(3x)

y = 3x


Related Questions

Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent. Continent Number of cities Europe 10 Asia 888 Africa 4 Australia 3 How many different combinations of cities does Elyse have to choose from?

Answers

Answer:

960

Step-by-step explanation:

10 x 8 x 4 x 3

Hope This Helped

Regards Jaygtgajm11

Disclaimer: The number of cities in Asia will be 8 and not 888.

Elyse can choose from 960 different combinations of cities.

What are permutations and combinations?

The different ways in which objects from a set can be picked, often without replacement, to produce subsets are known as permutations and combinations. When the order of selection is a factor, this selection of subsets is termed a permutation; when order is not a factor, it is called a combination.

How do we solve the given question?

We are given 4 continents, with a number of cities to choose from for Elyse to visit.

The table is like this:

Continent                          Number of cities

Europe                                           10

Asia                                                8

Africa                                              4

Australia                                         3

We use permutations and combinations to find the number of combinations Elyse will have to choose from.

We can say that for every 10 cities in Europe, she can choose any of the 8 cities in Asia. Similarly, for every 8 cities in Asia, she can choose any of the 4 cities in Africa. And similar is the case for Africa and Australia.

∴ Elyse can choose from a combination of 10*8*4*3 cities,

or, Elyse can choose from a combination of 960 cities.

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If ec bisects are congruent to bed find m bed ..??

Answers

Answer:

m<BED = 136 deg

Step-by-step explanation:

Since ray EC bisects <BED, angles BEC and CED are congruent. That means their measures are equal. Set the measures equal to each other, and solve for x.

11x + 2 = 8x + 20

Subtract 8x from both sides.

3x + 2 = 20

Subtract 2 from both sides.

3x = 18

Divide both sides by 3.

x = 6

Now we use the value of x to find the measure of angle BED.

The measure of angle BED is twice the measure of angle BEC. We know that x = 6.

m<BED = 2m<BEC = 2(11x + 2) = 2(11 * 6 + 2) = 2(66 + 2) = 2(68) = 136

An element has half life of about 20 days. How much of 3000 gram sample is left after 100 days?

Answers

t=100

p=3000

t 1/2 = 20

Try inserting the numbers in the half-life formula.

Answer:

93.75 gm.

Step-by-step explanation:

We have been given that an element has half life of about 20 days. We are asked to find the amount of 3000 gm sample left after 100 days.

We will use half-life formula to solve our given problem.

[tex]A=a\cdot (\frac{1}{2})^{\frac{t}{h}}[/tex], where,

A = Amount left after t units of time,

t = Time,

a = Initial amount,

h = Half-life.

Upon substituting our given values in above formula, we will get:

[tex]A=3000\cdot (\frac{1}{2})^{\frac{100}{20}}[/tex]

[tex]A=3000\cdot (0.5)^{5}[/tex]

[tex]A=3000\cdot 0.03125[/tex]

[tex]A=93.75[/tex]

Therefore, 93.75 gm of sample is left after 100 days.

Two points are 10 units apart on the coordinate plane. If
an ant were to walk between the 2 points moving only
vertically and horizontally, it would have to walk 6 horizontal
units. How many vertical units would the ant have to walk?

Answers

Answer:

The vertical distance the ant have to walk is 8 units

Step-by-step explanation:

∵ The ant must be walk vertically and horizontally

∴ The distance from start point to end point will be as

   a hypotenuse of a right angle triangle

∵ The ant would have to walk 6 units horizontally that

   means one side of the right angle is 6 units

∵ The two points are apart by 10 units that means

   the length of the hypotenuse is 10 units

∴ The vertical distance the ant would have to walk is

   the length of the second side of the right angle

* By using Pythagoras Theorem:

∵ (hypotenuse)² = (horizontal leg)² + (vertical leg)²

∴ 10² = 6² + (vertical leg)²

∵ (vertical leg)² = 100 - 36 = 64

∴ Vertical leg  = √64 = 8 units

∴ The vertical distance the ant have to walk is 8 units

The volume is a rectangle prism is ( x^4+4x^3+8x+4) and the area of its base is (x^3+3x^2+8) if the volume of a rectangle prism is the product of its base area and height what is the height of the of the prism

Answers

Answer:

[tex]h=(x^{4}+4x^{3}+8x+4)/(x^{3}+3x^{2}+8)[/tex]

Step-by-step explanation:

Let

h------> the height of the prism

we know that

The volume of the prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

In this problem we have

[tex]V=x^{4}+4x^{3}+8x+4[/tex]

[tex]B=x^{3}+3x^{2}+8[/tex]

substitute and solve for h

[tex]x^{4}+4x^{3}+8x+4=(x^{3}+3x^{2}+8)h[/tex]

[tex]h=(x^{4}+4x^{3}+8x+4)/(x^{3}+3x^{2}+8)[/tex]

524.95 to the nearest ten

Answers

525

Because the nearest tenth is the number after the decimal point but then nine rounds up. If you don’t want the nine rounded up leave it as 524.9

In given number 524.95, place value of 9 is tenth. So, the nearest ten is 525.0

What is place value?

The place value is the position of each digit in a number.

The nearest tenth is the number after the decimal point but then nine rounds up. If you don’t want the nine rounded up leave it as 524.9

524.9 = 525.0

Therefore, the answer is 525.0

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[tex]xy + x + y = 11 \\ x {}^{2}y + xy {}^{2} = 30[/tex]
find x & y​

Answers

I think the answer is 2 and 3.

Answer:

x=1,2,3,5

y=5,3,2,1

Step-by-step explanation:

see the image

Find the unknown measure

Answers

The two little lines through the two sides of the triangle mean that they are the same length.

When two sides of a triangle are the same, the two lower inside angles are also the same.

Angle A is given as 50 degrees, so angle C is also 50 degrees.

The sum of the three inside angles need to equal 180 degrees, so angle B would equal 180 - 50 - 50 = 80 degrees.

Angle B = 80

Angle C = 50

if you subtract 8 from 7 times a certain number, you end up with 34. what is the number?​

Answers

If we call the unknown number x, we have:

7 times a certain number is [tex]7x[/tex]If we subtract 8, we have [tex]7x-8[/tex]

If this equals 34, we have

[tex]7x-8=34[/tex]

Add 8 to both sides:

[tex]7x=42[/tex]

Divide both sides by 7:

[tex]x=6[/tex]

Which complex number has a distance of (squareroot) of 17)) from the origin on the complex plane?

2 + 15i
17 + i
20 – 3i
4 – i

Answers

Answer:

[tex]4-i[/tex]

Step-by-step explanation:

The distance of a complex number

[tex]z=a+bi[/tex]

from the origin is given by:

[tex]|z|=\sqrt{(a-0)^2+(b-0)^2}[/tex]

[tex]|z|=\sqrt{a^2+b^2}[/tex]

The length of  [tex]2+15i[/tex] is;

[tex]=\sqrt{2^2+15^2}[/tex]

[tex]=\sqrt{4+225}[/tex]

[tex]=\sqrt{229}[/tex]

The length of  [tex]17+i[/tex] is;

[tex]=\sqrt{17^2+1^2}[/tex]

[tex]=\sqrt{289+1}[/tex]

[tex]=\sqrt{290}[/tex]

The length of  [tex]20-3i[/tex] is;

[tex]=\sqrt{20^2+3^2}[/tex]

[tex]=\sqrt{400+9}[/tex]

[tex]=\sqrt{409}[/tex]

The length of  [tex]4-i[/tex] is;

[tex]=\sqrt{4^2+1^2}[/tex]

[tex]=\sqrt{16+1}[/tex]

[tex]=\sqrt{17}[/tex]

The correct choice is D

Write the following coordinates where they belong in the line segments below. Consider the graph below. Which of the following coordinates belong in the box?

A.(4 3/4,-3 3/4)
B.(4 5/8,-2 3/4)
C.(4 1/4,-5 1/2)
D.(4 1/8,-2 3/5)

Answers

Answer:

The option B (4 5/8,-2 3/4)  = (4.6 , -2.75) will be the coordinates belonging in the box.

Step-by-step explanation:

A.(4 3/4,-3 3/4) = (4.75,-3.75)

B.(4 5/8,-2 3/4)  = (4.6 , -2.75)

C.(4 1/4,-5 1/2)  = (4.25, -5.5)

D.(4 1/8,-2 3/5) = (4.125, -2.6)

The first point of line segment is: (5.5, -4.25)

second will be (4.75,-3.75)

third will be (4.6 , -2.75)

fourth will be (4.125, -2.6)

and fifth is  (3.75,-1.25)

The option C is not correct i.e not included in line segment.

The option B will be the coordinates belonging in the box.

Please help I need help with this ASAP please

please i really need help

Answers

Answer:

D

Step-by-step explanation:

Two events are independent if the intersection of the two events is the same as multiplying each events probability.

P (Texas) = 125/ 275 = 0.45

P (Brand A) = 176/275 = 0.64

0.45 * 0.64 = 0.29

P (Texas ∩ Brand A) = 0.29

So to find P (Texas | Brand A) = 0.29 / 0.64 = 0.45

Answer choice D makes the best choice.

Determine the value of base b if (152)b = 0x6A. Please show all steps.

Answers

Assuming 0x6A is given in base 16, first convert [tex]152_b[/tex] and [tex]6A_{16}[/tex] to a common base, say base 10:

[tex]152_b=1\cdot b^2+5\cdot b^1+2\cdot b^0=(b^2+5b+2)_{10}[/tex]

[tex]6A_{16}=6\cdot16^1+10\cdot16^0=106_{10}[/tex]

Then

[tex]b^2+5b+2=106[/tex]

[tex]b^2+5b-104=(b-13)(b+8)=0[/tex]

[tex]\implies b=13[/tex]

Answer:

The value of b is, 8

Step-by-step explanation:

Determine the value of b;

Given:

[tex](152)_b = 0x6A[/tex]             ....[1]

Since, 0x6A represents the hexadecimal form.

First convert this hexadecimal form into decimal form:

[tex](6A) = (6 \times 16^1)+(A \times 16^0) = (96)+(10 \times 1) = 96+10 = 106[/tex]

⇒[tex]0x6A = 106[/tex] (decimal form)

Now we have to convert this decimal form into octal

8  |  106

8   |  13   | 2

     |   1    | 5

          1

Then, the octal form we get, [tex](152)_8[/tex]

Substitute these in [1] we have;

[tex](152)_b=(152)_8[/tex]  

On comparing both sides we get;

b = 8

Therefore, the value of b is, 8

Toms Toy car went 2 meters without stopping Roberts went 145 centimeters whose car went farther

Answers

Answer:

Tom's car went further

Step-by-step explanation:

Since there are 100 centimeters in 1 meter - Roberts car went nearly 1 and a half meters or Tom's car went 200 centimeters.

toms car went farther

Kyra was building a bed for her dollhouse. She used her bed, which is 4 feet × 5 feet, as a guide. She scaled down the dimensions of her bed by a factor 1 over 5. What are the dimensions of the model bed she built?

0.08 foot × 0.10 foot
0.40 foot × 0.50 foot
0.80 foot × 1.00 foot
0.04 foot × 0.05 foot

Answers

Answer: third option

Step-by-step explanation:

You have the following information given in the problem:

- The dimensions of Kyra's bed is:

[tex]4feet*5feet[/tex]

- The scale factor she used was: [tex]\frac{1}{5}[/tex]

Therefore, keeping the above on mind, you can find the the dimensions of the model bed she built by multipliying the dimensions of her bed by the scale factor:

[tex]\frac{1}{5}*4ft=0.80ft\\\\\frac{1}{5}*5ft=1.00ft[/tex]

Then, the answer is:

[tex]0.80ft*1.00ft[/tex]

Olivia is cutting 1 1/2 m by 3/4 m pieces of rectangular paper in the two pieces along its diagonal What is the area of each of the pieces

Answers

Answer: 2 1/4

Step-by-step explanation:

Convert both to same denominators and mixed numbers

1 1/2 = 1 2/4 = 6/4

3/4 = 3/4

3/4*6/4 = 18/16

Simplify: 9/4 = 2 1/4

what does x in this equation
2x-3=6​

Answers

Answer:

x=4.5

Step-by-step explanation:

Answer:

[tex]x = 4.5[/tex]

Step-by-step explanation:

[tex]2x - 3 = 6 \\ 2x = 6 + 3 \\ 2x = 9 \\ \frac{2x}{2} = \frac{9}{2} \\ x = 4.5[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

7814/12 in a mixed number

Answers

Here is your answer 651 2/12

hope this helps.

Please mark me as brainliest.

Answer:

651  2/12

Step-by-step explanation:

In a sample of 32 city residence, 24 reported that they take vitamin C supplement daily. There are 46,480 residence in the city. Which estimate represents the number of city residents who take vitamin C supplement daily?

Answers

Answer:

34,860

Step-by-step explanation:

In a sample of 32 residence, 24 take Vitamin C. From here we can get the proportion of residents who take Vitamin C, which is 24/32 = 3/4 = 0.75

0.75 in  percentage is 75%. This means 75% of the residents in sample take Vitamin C.

We can expect the same percentage of people in entire population to take Vitamin C.

Total population of city = 46480

Expected number of residents who take vitamin C in the city = 75% of 46480

= 0.75 x 46480

= 34860

This means, 34860 is an estimate of number of city residents who take Vitamin C supplement daily.

Final answer:

Based on the sample study and assuming its representativeness of the general population, it is estimated that approximately 34,860 residents of the city take a vitamin C supplement daily.

Explanation:

In the sample study, the proportion of residents who take vitamin C supplements daily is calculated by dividing the number of individuals who reported taking the supplement (24) by the total number of individuals in the sample (32). This yields a proportion of 0.75, or 75%. Then, we can apply this proportion to the total population of the city to estimate the number of residents who take vitamin C daily. Therefore, the estimated number is 0.75 * 46,480 = 34,860.

In conclusion, assuming that the small sample is representative of the larger population, we would estimate that "approximately 34,860" city residents take a vitamin C supplement daily.

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At a sporting event, the price of 3 cheeseburgers and 2 cups of lemonade is $14 and the price for 2 cheeseburgers and 4 cups of lemonade is $12. How much does it cost for 1 cheeseburger and 2 cups lemonade?

Show Work Please Please Help Imediatly

Answers

Answer: $2

Step-by-step explanation: this is only if everything is the same price.

Mario simplified the expression as shown.



Which statement explains Mario’s error?

Answers

Answer: Last option

Step-by-step explanation:

1. According to the properties of exponents, you have that:

[tex]a^{-n}=\frac{1}{a^n}\\\\(a^n)^m=a^{mn}[/tex]

2. Then, he must simplify the expression as following:

[tex](4z^8)^{-3}={4^{-3}z^{8(-3)}=\frac{1}{64z^{24}}[/tex]

3. Therefore, as you can see, should have also applied the negative exponent to 4 to get [tex](4z^8)^{-3}={4^{-3}z^{8(-3)}=\frac{1}{64z^{24}}[/tex]

Answer:

The correct answer option is He should have also applied the exponent -3 to 4 to get [tex]4^{-3}z^{8 \cdot(-3)} = 4^{-3}z^{-24} = \frac{1}{64z^{24}}[/tex].

Step-by-step explanation:

The following expression was to be simplified by Mario:

[tex] (4z^8)^-3 [/tex]

Given this expression, we need to apply this rule on it in order to simplify:

[tex] (a b)^m = a^m \cdot b^m [/tex]

So we would get:

[tex] (4z^8)^-3 [/tex]

[tex]4^{-3} \cdot (z^8)^{-3}[/tex]

[tex]\frac{1}{4^3} \cdot z^{-24}[/tex]

[tex]\frac{1}{64z^{24}}[/tex]

This would be the right simplification for the given expression but by looking at Mario's work shown, we can conclude that:

He should have also applied the exponent -3 to 4 to get [tex]4^{-3}z^{8 \cdot(-3)} = 4^{-3}z^{-24} = \frac{1}{64z^{24}}[/tex].

(x ________ )(x ________) = x^2−4x−32

what numbers/variables can fill in the blanks?
SOMEBODY PLZZZ HELPPPPPPP!!!!!

Answers

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

You have to find two values that will multiply to give -32 and add to give -4

Through trial and error, you will find that the two values are -8 and +4

Place these in:

(x + 4)(x - 8)

Hope This Helps You!

Good Luck (:

Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ

how i solve that please

Answers

Answer:

i cant see the picture

Step-by-step explanation:

Solve: 25x^2 - 36 = 0
A.) x = 6, 5
B.) x = -6, -5
C.) x = 36/25, x = -36/25
D.) x = 6/5, x = -6/5

Answers

Answer: 6/5 and -6/5

Step-by-step explanation: In order to solve this problem, we want to get the variable on one side. In order to do that, we must do the following:

Add 36 on Both Sides:

[tex]25x^2 - 36+36 = 0+36[/tex]

Divide 25 on Both Sides:

[tex]\frac{25x^2}{25}= \frac{36}{25}[/tex]

Take the square root of Both Sides:

[tex]\sqrt{x^2} = \sqrt{\frac{36}{25} }[/tex]

That means your answer is:

[tex]x = \frac {6}{5}[/tex], or [tex] -\frac {6}{5} [/tex]


If CDEF ≅ MNPQ, then ∠N ≅ _____


∠E.


∠D.


∠F.


∠C.

Answers

Answer: ∠D.

Step-by-step explanation:

because they are in the same position (2nd letter placement)

If quadrilaterals CDEF ≅ MNPQ, then it follows that ∠N ≅ ∠D.

Hence ∠D is correct.

If CDEF and MNPQ are congruent,

Then it means they have the same shape and size.

In other words, all of their corresponding angles and sides are equal.

Therefore, if ∠C is congruent to ∠M,

∠D is congruent to ∠N,

∠E is congruent to ∠P, and

∠F is congruent to ∠Q.

This is because congruence is a relation of equality between two geometric figures.

So, if two triangles (or any other polygons) are congruent,

Then all of their corresponding angles and sides are equal.

Therefore, if CDEF ≅ MNPQ, then it follows that ∠N ≅ ∠D.

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The value of y varies directly with x.when y =150,x=1/3.what is the value of y when x is 16/6.

Answers

maybe 1200 because you multiply by 8 or 16/2

4/3x -3 ≤ -11

Please show how you got your answer!!

Answers

Answer:

-11+3=-8

-8=4/3x

-8/(4/3)=x

x=6

What are the coordinates of the midpoint of the segment whose endpoints are J(3, -1) and K(9, 5)?

A. (1, 2)
B. (3, 2)
C. (3, 3)
D. (6, 2)

Answers

Answer:

Option D. (6, 2)

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute

[tex]M(\frac{3+9}{2},\frac{-1+5}{2})[/tex]

[tex]M(\frac{12}{2},\frac{4}{2})[/tex]

[tex]M(6,2)[/tex]

Water has a density of about 0.0361 pounds/cubic inch. You might know that wood floats on water. What can you conclude about the densities of objects that float and the densities of objects that do not?

Answers

Answer:

Step-by-step explanation:

Objects that float on water have densities less than the density of water; those that do not float on water have densisties greater than the density of water:

Float on water:  d < 0.0361 lb/in³ (where d denotes denisity)

Do not float on water:  d > 0.0361 lb/in³

The densities of objects that float on water are lower than those of objects that don't float.

What is density?

It is defined as the mass-to-volume ratio. The density indicates the object's density and is represented by the symbol. The density is measured in kilograms per cubic meter.

We have:

Water has a density of about 0.0361 pounds/cubic inch.

Let d be the density:

Float on water:  d < 0.0361 lb/in³

Do not float on water:  d > 0.0361 lb/in³

The densities of objects that float on water are lower than those of objects that don't, which have densities higher than those of water.

Thus, the densities of objects that float on water are lower than those of objects that don't float.

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I need help please????

Answers

Answer:

The correct one is b nice you chose the right one!

Step-by-step explanation:

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