Which exponential function is represented by the graph?

A) f(x) = 2(3^x)
B) f(x) = 3(3^x)
C) f(x) = 3(2^x)
D) f(x) = 2(2^x)

The value of money that you save increases over time is the right answer

Answer:

Perimeter of triangle = 71.72 unit.

Area of triangle = 149.44 unit²

Explanation:

 Distance between (a,b) and (c,d) = [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex].

 So we have  SB = [tex]\sqrt{(-2-15)^2+(21-(-8))^2}=\sqrt{1130} =33.62[/tex]unit

                       BA = [tex]\sqrt{(0-(-2))^2+(0-21^2)}=\sqrt{445} =21.10[/tex]unit

                       AS = [tex]\sqrt{(15-0)^2+(-8-0)}=\sqrt{289} =17[/tex]unit

 So perimeter of triangle = 33.62 + 21.10 + 17 = 71.72 unit.

  We have SB = Base = 33.62 unit and Perpendicular height = 8.89 units.

  Area = 0.5 x Base x Perpendicular height.

           = 0.5 x 33.62 x 8.89 = 149.44 unit²

The perimeter of the triangle SBA is approximately 66.91 units and the area is approximately 131.06 square units.

To find the perimeter of triangle SBA, we need to find the lengths of the three sides first. We can use the distance formula to calculate the length of each side. Using the coordinates of S(15,-8), B(-2,21), and A(0,0), we find that SB ≈ 29.47 units, BA ≈ 18.19 units, and AS ≈ 19.25 units. The perimeter is the sum of these three lengths, which is approximately 66.91 units.

To find the area of triangle SBA, we can use the formula: area = 1/2 * base * height. The base is the length of SB, which is approximately 29.47 units, and the height is given as 8.89 units. Plugging these values into the formula, we get the area ≈ 131.06 square units.

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Answer:

4.2*10^7

Step-by-step explanation:

Khan Academy

The human heart beats approximately 4.2 ⋅ 10^7 times in one year.

To calculate the number of times the human heart beats in one year, we need to multiply the average number of beats per day by the number of days in a year. The average human heart beats 1.15 ⋅ 105 times per day, and there are 3.65 ⋅ 102 days in one year. So, the number of times the heart beats in one year is:

1.15 ⋅ 105 times/day ⋅ 3.65 ⋅ 102 days/year = 4.1975 ⋅ 107 times/year

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Answer:

The required answer is shown below:

Step-by-step explanation:

Consider the provided equation.

   Statement                   Reason

1. [tex]5(x+6)=x+38[/tex]    Given

2. [tex]\bold{5x+30=x+38}[/tex]    Distributive property

3. [tex]5x+30-30=x+38-30[/tex]    Subtraction property of equality

4. [tex]\bold{5x=x+8}[/tex]         Simplifying

5. [tex]\bold{5x-x=x+8-x}[/tex]         Subtraction property of equality

6. [tex]\bold{4x=8}[/tex]            Simplifying

7. [tex]\frac{4x}{4}=\frac{8}{4}[/tex]            Division property of equality

8. [tex]x=2[/tex]            Simplifying

Hence the required answer is shown above.

ANSWER

[tex]-\frac{2}{3}(2x-\frac{1}{2})\le \frac{1}{5}x-1[/tex]

Multiply through by LCM of 15

[tex](15) \times -\frac{2}{3}(2x-\frac{1}{2})\le 15(\frac{1}{5}x-1)[/tex]

[tex] -10(2x-\frac{1}{2})\le 3x-15[/tex]

Expand brackets to obtain,

[tex] -20x+5\le 3x-15[/tex]

Group like terms

[tex] 15+5\le 20x+3x[/tex]

[tex] 20\le 23x[/tex]

[tex] \frac{20}{23}\le x[/tex]

[tex]x\ge \frac{20}{23}[/tex]

In interval form it is written as

[tex] [\frac{20}{23}, \infty)[/tex]

The correct solution to the inequality is x ≥ 20/23, written in interval notation as: [20/23, +Infinity).

In this mathematical inequality problem, your steps are correct until you get to -2/3(2x - 1/2) ≤ 1/5x - 1. Thereafter, however, your proceedings seem to be erroneous. Let's correct the steps:

So the solution to the inequality is x ≥ 20/23, which in interval notation would be written as: [20/23, +Infinity).

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Answer:

Intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

Step-by-step explanation:

Required vector is consists of the two components

vx= 2+4=6 units  and vy= 1 unit and vx ⊥ vy

We will use Pythagorian theorem to find intensity of the vector v

v∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 units

The angle ∡α between vector and east direction we wil find with tanα

tanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

Good luck!!!

Answer:

The vector that describes their hike from their starting position to their final destination is  < 6, 1 >

The answer would be the bottom left. You can't fold it in half and have it match up with the other side.

Answer:its correct got a 100

Step-by-step explanation:

Circumference varies directly with radius means:

[tex]\frac{C}{r} = k[/tex]

[tex]\frac{9.42}{1.5} = k[/tex]

6.28 = k

So, the new equation is:

[tex]\frac{C}{r} = 6.28[/tex]

[tex]\frac{C}{9} = 6.28[/tex]

[tex](9)\frac{C}{9} = (9)6.28[/tex]

C = 56.52

****************************************

paycheck varies directly with hours means:

[tex]\frac{P}{h} = k[/tex]

[tex]\frac{52.50}{6} = k[/tex]

8.75 = k

So, the new equation is:

[tex]\frac{P}{h} = 8.75[/tex]

[tex]\frac{P}{11} = 8.75[/tex]

[tex](11)\frac{P}{11} = (11)8.75[/tex]

P = $96.25

Simplify: 12 + 10i +14i = 12 +24i

answer

B) 12 +24i

24i+12 thats pretty basic though

1. Culture A.

Since the number of cells increases by 200 each day and every day thereafter, then after seven days the number of cells will increase by

[tex]200\cdot 7=1,400.[/tex]

2. Culture B.

The initial number of cells was 1,000. Since the number of cells increases 8% each day and every day thereafter, then after seven days the number of cells will be

[tex]1,000\cdot (1.08)^7\approx 1,713.[/tex]

The number of cells that have grown by the end of the seventh day is

1,713-1,000=713.

Answer: option A -- Culture A: 1400 cells Culture B: 713 cells

Answer:

A is correct: Culture A: 1400 cells

                    Culture B: 713 cells

Step-by-step explanation:

Correct on Edge 2020 Quiz

Answer:

There are two discontinuities, one in the point (-2,2) and another on (-1,3).

Step-by-step explanation:

The discontinuity in (-2,2) is referred to as a removable discontinuity because this point is defined elsewhere.

The discontinuity in (-1,3) is called a jump discontinuity because it seems to "jump" from one point and continue at another.

Answer:

5.23 years, the time at which the coin has increased in value to $150.

Step-by-step explanation:

Use the exponential function f(t) = 4*2^t.

Substitute $150 for f(t):  $150 = 4*2^t.

Simplify this by dividing both sides by 4:  $150/4 = 2^t, or $37.50 = 2^t.

Next, solve for the value of t.  To do this, take the common log of both sides, obtaining:

log 37.50 = t*log 2.  Thus, t = [log 37.50] / [log 2].  Evaluate this using a calculator:

t = 1.57403 / 0.30103 = 5.23 time units.  For example, this could be 5.23 years.

Answer:

It will take about 17.7 years, or almost 18 years, for the coin to be worth $150.

Because the initial year was 2016, the coin is predicted to be worth $150 in 2034.

Step-by-step explanation:

Answer:

  43.6°, 46.4°

Step-by-step explanation:

Let x represent the smaller angle. Then the complementary angle is (90°-x). The problem statement tells us the relation is ...

  x = (90°-x) -2.8°

  2x = 87.2° . . . . . add x, collect terms

  x = 43.6° . . . . . . divide by 2

Then the complementary angle is ...

  90°-x = 46.4°

The measures of the angles are 43.6° and 46.4°.

We know that

when we start exercise our hear beats starts increasing gradually

because blood flowing rate becomes higher

and it keeps increasing upto a certain limit

because for normal human beings maximum heart rate is 135 beats per minute

and it remains constant there for few minutes

and as we slow down slowly

It will start decreasing  gradually and then becomes normal

we can see the graph

so,

The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes..........Answer

Answer:The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes. Positive

Step-by-step explanation:

Answer: Upper right corner

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

How I got that answer:

The line y = x goes through (0,0) and (1,1). You would normally extend this line out as far as you can in both directions. However, the inequality x < -1 says you can only graph this if x is less than -1. We will not graph any part of the graph that is beyond x = -1 to the right. So we only have a small piece of it. The left piece of y = x. There is an open hole at the endpoint.

Similarly, y = -x is only graphed if x >= -1. We have a closed endpoint here. This graph goes through (0,0) and (1,-1). We erase the portion that is to the left of x = -1.

Doing all this leads to the upper right corner choice as our answer. The bottom right corner is close to the answer, but the open and closed endpoints are in the wrong spots.

Answer: The mouse can travel 2.045 miles .

Step-by-step explanation:

Speed of mouse = 2.0 feet per second.

Time traveled by mouse = 1.5 hours = 1.5 × 3600 seconds [ as 1 hour = 3600 seconds]

Distance traveled by mouse in 1.5 hours = speed × time

= 2.0 × 1.5 × 3600 = 10800 feet.

We know that

1 mile = 5280 feet

then 1 foot = 1/5280 miles

Distance in miles = [tex]10800\times \frac{1}{5280} miles=2.045miles[/tex]

Given

A mouse scurries across your kitchen floor at 2.0 feet per second.

Find out the mouse travel in 1.5 hours.

To proof

FORMULA

Distance = speed × time

[tex]1foot = \frac{1}{5280} miles[/tex]

Convert feet per second into miles per second

[tex]= \frac{2.0}{5280}[/tex]

As given in the question

Time = 1.5 hours

1 hours = 3600 second

Time convert in the second

Time = 1.5 × 3600 second

       = 5400 second

put all these value in the above formula

we get

[tex]Distance= \frac{2.0\times 1.5 \times 3600}{5280}[/tex]

[tex]Distance= \frac{10800}{5280}[/tex]

= 2.04 (approx) miles

= 2.0 miles

Hence proved

((V/π)(3/4))1/3 = R so I would say possibly the second one

Answer:

D

Step-by-step explanation:

hello!!! the correct answer for this problem is D

Answer:

D. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 5

and translated up 5 units.

Step-by-step explanation:

First answer, this is because if you were to substitute the x and y variables which are the height and days the plant grew, then the 1st answer would be the answer

Answer:

12.68%

Step-by-step explanation:

To calculate effective annual interest rate we need to use the following formula:

[tex]i=(1+\frac{r}{m})^m-1[/tex]

Where, 'i' is the effective annual interest rate

'r' is the annual rate of interest

'm' is the frequency of compounding.

When there is continuous compounding the effective annual rate uses the following formula:

[tex]i=e^r-1[/tex]

In our case we would are assume that there is continuous compounding since no information regarding the frequency of compounding is given:  

Plugging r=12%=0.12, we get:

[tex]i=e^{0.12}-1[/tex]

[tex]i=1.1274-1=0.1274[/tex]

[tex]i=0.1274[/tex]

[tex]i=12.74\%[/tex]

Therefore, the effective annual interest rate is 12.74%.

Answer:

13.2

Step-by-step explanation:

Answer:

The value of f(2)≈1.57

The time it takes an object to fall 2 feet is 1.57 seconds.

Step-by-step explanation:

Consider the provided function.

[tex]f(d) = 1.11\sqrt{d}[/tex]

It takes for an object to fall a distance, d, in feet,

We need to determine f(2).

Substitute the value d = 2 in the above function.

[tex]f(2) = 1.11\sqrt{2}[/tex]

[tex]f(2)\approx 1.57[/tex]

The value of f(2)≈1.57

The time it takes an object to fall 2 feet is 1.57 seconds.

[tex](0,\ 2);\ \left(\dfrac{\pi}{2},\ 0\right);\ (\pi,\ -2);\ \left(\dfrac{3\pi}{2},\ 0\right);\ (2\pi,\ 2);\ \left(\dfrac{5\pi}{2},\ 0\right);\ (3\pi,\ -2)\\\\\text{Look at the picture}\\\\Answer:\ \boxed{y=2\cos(x)}[/tex]

Graph of f(x)=ln(x) is missing but we can still answer this problem.

We just have to explain about what will happen if f(x)=ln(x) changes into g(x)=1/3 ln(x)

To find that compare both functions.

We see that ln(x) gets multiplied by 1/3 to produce graph of 1/3ln(x)

there multiplifaction factor 1/3 lies between 0 and 1.

Hence graph of f(x) will compress vertically by factor of 1/3 to produce graph of g(x).

So for the final answer we will write f(x) compress vertically by factor of 1/3 to produce graph of g(x)=1/3 ln(x)

You can check attached file for more related rules

Answer:

compress vertically by factor of 1/3 to produce graph of g(x)=1/3 ln(x)

Step-by-step explanation:

22.5

note that the difference (d ) between each term is

d = 9 - 4.5 = 13.5 - 9 = 18 - 13.5 = 4.5

to obtain the next term add 4.5

next term = 18 + 4.5 = 22.5

The next term in the pattern is 22.5.

To find the next term in the pattern, it's essential to identify the underlying rule or mathematical operation that governs the progression of the given numbers.

In this case, we can observe that the sequence is increasing by a consistent difference of 4.5 between each consecutive term.

Starting from 4.5 and adding 4.5 successively, we get:

4.5 + 4.5 = 9

9 + 4.5 = 13.5

13.5 + 4.5 = 18

The next term would be:

18 + 4.5 = 22.5

So, the next term in the pattern is 22.5.

In this sequence, each term is obtained by adding 4.5 to the previous term, resulting in an arithmetic progression.

If you continue this pattern, you will keep adding 4.5 to each subsequent term to find the following numbers in the sequence.

For similar question on pattern.

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direct linear variation is a straight line in which the y intercept is 0

a- wrong because it is quadratic, not linear.

b- correct, linear with a y intercept of 0

c- wrong because its exponential

d- wrong, its linear but the y intercept is 3, not 0

You would use PEMDAS to solve this:

0.8 x 1.5 = 1.2

4 + 1.2 - 3

5.2 - 3

2.2 is your answer

Answer:

the answer is 2.2