Which is equivalent to 2^5?

Answer:

[tex]f(n) = \frac{32}{3}(\frac{3}{2})^n[/tex]

Step-by-step explanation:

Given

[tex]r = \frac{3}{2}[/tex]

[tex]f(5) = 81[/tex]

Required

The geometric sequence

A geometric sequence is represented as:

[tex]f(n) = ar^{n-1}[/tex]

Replace n with 5

[tex]f(5) = ar^{5-1}[/tex]

[tex]f(5) = ar^4[/tex]

Substitute values for f(5) and r

[tex]81 = a* (\frac{3}{2})^4[/tex]

Open bracket

[tex]81 = a* \frac{81}{16}[/tex]

Make a the subject

[tex]a = \frac{81 * 16}{81}[/tex]

[tex]a = 16[/tex]

So, the explicit function is:

[tex]f(n) = ar^{n-1}[/tex]

[tex]f(n) = 16 * (\frac{3}{2})^{n-1}[/tex]

Split

[tex]f(n) = 16 * (\frac{3}{2})^n \div (\frac{3}{2})[/tex]

Convert to multiplication

[tex]f(n) = 16 * (\frac{3}{2})^n * \frac{2}{3}[/tex]

[tex]f(n) = \frac{32}{3}(\frac{3}{2})^n[/tex]

Answer:

f(x) = 16*(3/2)^(x-1)

Step-by-step explanation:

right on edge

Answer:basically if what they want you to prove is correct say it is correct and why is it correct

Step-by-step explanation:

Answer: Choice A

L = 65 - 15d; discrete

===============================================

Explanation:

He starts with 65 cm of bread. After the first day he has 65-15 = 50 cm left over. After the second day he has 65-15*2 = 35 cm left over, and so on.

In general, he has 65-15d centimeters left over after d number of days have elapsed. For example, if d = 3 days pass by, then he has 65-15d = 65-15*3 = 65-45 = 20 cm left over.

So that's why the equation we're after is L = 65-15d where d is the number of days, and L is the amount left over in cm.

The number of days is discrete because we're dealing with the set of nonnegative numbers {0,1,2,3,4,...}. We can't have d = 2.5 for instance.

Because the input variable d is discrete, this automatically means L is discrete as well. Consider a finite domain such as {0,1,2,3}. This finite domain would map to the finite range {65,50,35,20}. These two finite sets are sufficient to say we have a discrete function.

A discrete function leads to a discrete graph which is simply a set of points. You would not connect the dots to form a straight line (simply leave the points as separate islands).

Answer:

{5,7,8}

Step-by-step explanation:

A-B = {2,4,6} => A={2,4,6}

B - A = {0,1,3} => B= {0,1,3}

A∪B = {0,1,2,3,4,5,6,7,8}

=> A = {2,4,5,6,7,8}

B= {0,1,3,5,7,8}

=> A∩B = {5,7,8}

Answer:

4 number

Step-by-step explanation:

16p+32q=1,280

Step-by-step explanation:

Only 1 number works. 1 will make 819 which is divisible by 9.

Since it is 1 of ten numbers can go in the blank, the answer is 1/10 which is 0.1

The 10 number choices are

0,1,2,3,4,5,6,7,8,9

The only one that works is 1 as I've stated.

Answer:

4a 2/7.

I could solve just this

Answer:

For #3b, shade in 1 1/2 bars

For 4a, i think it is 3/7

4b is prob 43%

5 i think is abt 0.2 miles

Answer:

Step-by-step explanation:

Answer:

library 2,3

park 8,2

market 3,7

red centers 4,10

pool 6,6

movie theater 9,9

ice cream shop 5,4

Answer:

C

Step-by-step explanation:

its asking for y, on the graph, the line is placed on point 4

Answer:

slope= -8/1

y-intercept= 0,0

Answer:

m = -8

c = 0

Step-by-step explanation:

The given equation of the line is ,

[tex]\implies y = -8x[/tex]

We know that the Standard equation of Slope Intercept Form of the line is,

[tex]\implies y = mx + c[/tex]

Where ,

On comparing to the Standard form of the line we get ,

[tex]\implies Slope = -8 [/tex]

[tex]\implies y - intercept= 0 [/tex]

Answer:

y=0.3x-2

Step-by-step explanation:

first find the gradient

m=y2-y1/x2-x1

m=0-(-2)/6-0

m=0.3

then use this equation

y-y1=m(x-x1)

y-(-2)=0.3(x-0)

y+2=0.3x-0

y=0.3x-2

Answer:

B

Step-by-step explanation:

[tex]y = \sqrt{x } - 4 \\ \sqrt{x} = y + 4 \\ x = (y + 4) {}^{2} \\ [/tex]

Domain of inverse = Range of f = x>-4

Hence B

The correct option is B which is f⁻¹(x) = ( x + 4 )² and x ≥ -4.

The inverse function of a function f in mathematics is a function that reverses the operation of f. If and only if f is bijective, the inverse of f is true.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The given function is f(x) = √x - 4. The inverse function will be calculated as:-

y = √x - 4

√x = y + 4

Squaring on both sides.

x = ( y + 4 )²

Replace x with y.

y = ( x + 4 )²

The range of the function is x ≥ -4.

Therefore, the correct option is B which is f⁻¹(x) = ( x + 4 )² and x ≥ -4.

To know more about an inverse function follow

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Answer:

2.4cm

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

that means two lengths of the triangle have to be multiplied.

and to have 2 similar triangles means that all lengths inside one triangle are the corresponding lengths inside the other triangle multiplied by the scaling factor f.

multiplying 2 if these lengths with each other means also including the square of the scaling factor (multiplying with the scaling factor twice).

so, if the area of triangle 1 is

"baseline 1" × "height 1" / 2 = 45 cm²

then the area of triangle 2 is

"baseline 2" × "height 2" / 2 =

= "baseline 1"×f × "height 1"×f /2 =

= "baseline 1" × "height 1" × f² / 2 =

= ("baseline 1" × "height 1" / 2) × f² =

= 45 × f² = 20 cm²

f² = 20/45 = 4/9

f = 2/3

so, for a side of ABC being 3.6cm long, that means the corresponding side in DEF is

3.6 × f = 3.6 × 2/3 = 7.2/3 = 2.4cm

Answer:

C

Step-by-step explanation:

The vertex is the point where the 2 lines meet on the V shape

The vertex is at (3, 2 ) → C

Answer:

Option c is the answer I think so if the answer is correct plz mark me as brainliest

Answer:

First answer choice: [tex]y=\sqrt{x}[/tex] shifted right 6 units and down 2 units.

Step-by-step explanation:

Graph

Answer:

(7x + 2)(x - 2)(x + 2)

Step-by-step explanation:

Given

7x³ + 2x² - 28x - 8 ( factor the first/second and third/fourth terms )

= x²(7x + 2) - 4(7x + 2) ← factor out (7x + 2) from each term

= (7x + 2)(x² - 4) ← x² - 4 is a difference of squares

= (7x + 2)(x - 2)(x + 2)

Answer:

17253.52

Step-by-step explanation:

100-9.5=90.5

19064.67*0.905=17253.52

Answer:

x is ( -∞, 6-√(33) ) U ( 6+√(33) , -∞ )

Step-by-step explanation:

I have attached the explanation on the image above, hopefully this help

Hello,

I am going to calculate all the surface areas of the prism:

1) the bases: 2*(6*9)/2=64 (cm²)

2) perimeter of the base: 7+9+7=23 (cm)

3 lateral area: 23*5=115 (cm²)

All surface areas= 64+115=179 (cm²)

What does it means sq ? (for a foreigner) ?

All surface areas= 64+115=179 (cm²)

A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry. If the sides of a right triangular prism are not rectangular, the prism is oblique.

Given

the bases: 2*(6*9)/2=64 (cm²)

perimeter of the base: 7+9+7=23 (cm)

3 lateral area: 23*5=115 (cm²)

All surface areas= 64+115=179 (cm²)

To know more about triangular prisms refer to:

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Answer:

The friend would pay $100

Step-by-step explanation:

The price of the card was $20 when Daniel bought it, it gained a value of $10 every year,

since Daniel bought it 3 years ago we will add $30 to $20 as the value increased by $10/year

so the price becomes $50, but his friend says he'll pay twice the value so,

$50×2= $100

Answer:

See Explanation

Step-by-step explanation:

Given

Let

[tex]S \to[/tex] Strawberry

[tex]B \to[/tex] Banana

[tex]S : B = 2 : 3[/tex]

Solving (a):

Complete the table

The table, to be complete, is not given; so, I will generate one myself.

[tex]\begin{array}{cccccc}S & {2} & {3} & {4} & {5} & {6} \ \\ {B} & {3} & {4.5} & {6} & {7.5} & {9} \ \end{array}[/tex]

The table is generated as follows:

[tex]S : B = 2 : 3[/tex]

Multiply by 1.5

[tex]S : B = 2 * 1.5 : 3 * 1.5[/tex]

[tex]S : B = 3 : 4.5[/tex]

Multiply by 2

[tex]S : B = 2*2 : 3*2[/tex]

[tex]S : B = 4 : 6[/tex]

And so on....

In summary, whatever factor is multiplied to S must be multiplied to B; in order to keep the ratio constant

Solving (b): Why the amount are proportion

Because the ratio is constant and it remains unchanged all through.

Answer:

3/10

Step-by-step explanation:

The question asks for the probability of finding 4 or more, so first, you must add up all of the teenagers that have 4 or more shoes. Both the 4 and 5 categories fit, so add 20 and 10. Then, find the total number of people in the sample size. Overall, 100 teenagers are represented. Finally, put the number of people that have 4 or more shoes, 30, over the sample size, 100. This equals 30/100 which should be simplified to 3/10.

99 boys and 1 girl makes 99 percent of boys. To make it 98%, 50 boys must leave the theatre, so there are 49 boys and 1 girl, making 98% of boys.

Answer:

hi, it's 16 because:

[tex]ab = bc \\ ab = 8 \\ ac = 2 \times 8 = 16 \\ ac = 16[/tex]

Answer:

16

Step-by-step explanation:

Theorem: In a circle, if a radius is perpendicular to a chord, then the radius is the perpendicular bisector of the chord.

In this case, the radius containing points O and B is perpendicular to chord AC, so the radius bisects chord AC making AB = BC.

Also,

AB + BC = AC

By substitution, we have

AB + AB = AC

AC = 2AB

AC = 2(8)

AC = 16

Answer:

[tex]f) \: r2 \div r1 \: = 5 \div 1[/tex]

Step-by-step explanation:

[tex] \frac{a1}{a2} = \frac{1}{25} = \frac{\pi \times (r1)^{2} }{\pi \times (r2)^{2}} [/tex]

[tex] {(\frac{r2}{r1})}^{2} = 25[/tex]

[tex] \frac{r2}{r1} = 5[/tex]

Answer:

α = 0.63 radians

Step-by-step explanation:

We are given;

Length of arc; L = 1.6 mm

Radius; r = 2.54 mm

The arc length equation is given by;

L = αr

Where;

L is length of arc

r is radius

α is angle in radians

Thus;

α = L/r

α = 1.6/2.54

α = 0.63 radians

Answer:40

step by step explanation

3*23÷46=6

46-6=40

there are 40 pies in each plate

Answer:

Answer: 10 pies on each plate.

Step-by-step explanation:

Okay, to solve this problem we first need to find 3/23 of 46.

But before we do that, we need to know 1/23 of 46.

To solve this, we do 64 divided by 23 which equals 2.

then we multiple 2 by 3 to get 3/23 of 46 and that equals 6.

To find out how many pies remain, we subtract 6 pies from 46 pies, which gives us 40 pies. Then we divide 40 by 4, which is 10.

Step-by-step explanation:

simply take the average of the x and y coordinates