Plzzzz help its urgent i will mark u as brainiest i cant find it help
here

To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, both to find the needed time and to find the inverse function. From this, we get that:

Number of trees infected after t years:

The number of trees infected after t years is given by:

[tex]f(t) = e^{0.4t}[/tex]

Question 1:

We have to find the number of years it takes to have 21 trees infected, that is, t for which:

[tex]f(t) = 21[/tex]

Thus:

[tex]e^{0.4t} = 21[/tex]

To isolate t, we apply the natural logarithm to both sides of the equation, and thus:

[tex]\ln{e^{0.4t}} = \ln{21}[/tex]

[tex]0.4t = \ln{21}[/tex]

[tex]t = \frac{\ln{21}}{0.4}[/tex]

[tex]t = 7.6[/tex]

Thus, it will take 7.6 years for 21 of the trees to become infected.

Question 2:

We have to find the inverse function, that is, first we exchange y and x, then isolate x. So

[tex]f(x) = y = e^{0.4x}[/tex]

[tex]e^{0.4y} = x[/tex]

Again, we apply the natural logarithm to both sides of the equation, so:

[tex]\ln{e^{0.4y}} = \ln{x}[/tex]

[tex]0.4y = \ln{x}[/tex]

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

Thus, the logarithmic model is:

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

For an example of a problem that uses exponential functions and logarithms, you can take a look at https://brainly.com/question/13812761

Answer:

29.83 ft

Step-by-step explanation:

First, you find the square root of 445, which is 21.09.

Then you use the Pythagorean theorem, which is a^2 + b^2 = c^2

because a and b are the same value you plug it in

21.09^2+21.09^2 = c^2

You end up getting:

c^2=889/5762

You then square root both sides to get:

c = 29.83, which is option 3

Answer:

-48/165

Step-by-step explanation:

Answer:

y = 2/5x +24/5

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 2/5 x +b

Substitute the point into the equation and solve for b

4 = 2/5(-2)+b

4 = -4/5 +b

Add 4/5 to each side

20/5 +4/5 = b

24/5 = b

y = 2/5x +24/5

below

Step-by-step explanation:

all real numbers

[0,∞]

increasing

decreasing

Answer:

XN = 22

Step-by-step explanation:

Recall: the Centroid theorem states that the Centroid of a triangle is ⅔ of the distance any vertex of the triangle to the midpoint of the side opposite to it.

This implies that:

XN = ⅔(XG)

XG = 33

Substitute

XN = ⅔(33)

XN = 2*11

XN = 22

Answer:

$0.5

Step-by-step explanation:

A + B = 1.10

A=1 +B

now A + B = 1.10

A - B = 1 (B cancels out)

2A = 2.10

A= 1.05

A + B = 1.10

substitute A value

1.05 + B = 1.10

B= 1.10-1.05

B=$ 0.5

Answer:

Step-by-step explanation:

te da x<3/2 y x<2, pero la segunda solucion abarca la primera. Por lo tanto creo q seria x<2

Answer:

-5/2

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -12 - 3)/(4 - -2)

   = (-12-3)/(4+2)

   -15/6

  -5/2

Answer:

-5/2

Step-by-step explanation:

(y2-y1)/(x2-x1) = -15/6 = -5/2

Answer:

f(x) = x² + 2x + 1

Step-by-step explanation:

you know how to multiply 2 expressions ?

let's say in general we have

(a + b)(c + d)

you take one part of one expression and multiply it with all parts of the other expression, then you take the second part of the first expression and multiply it with all parts of the other expression, then a potential third part, then a fourth part and so on, and you add all these things together (well, depending on the actual signs, of course).

so, we get for this simple generic example

a×c + b×c + a×d + b×d

now we use that understanding for our question here.

(x+1)(x+1) = x×x + 1×x + x×1 + 1×1 = x² + x + x + 1 = x² + 2x + 1

Answer:

It's A

Step-by-step explanation:

DO FOIL

-10d^4+(5+12)d^2s-6s^2=-10d^4+17d^2s-6s^2

Answer:

the first answer: -10a^4 + 17a^2s-6s^2

Step-by-step explanation:

Answer:

(2,-2) --> (-1, 3)

(8,-2) --> (5, 3)

(8,-5) --> (5, 0)

(2,-5) --> (-1, 0)

Answer:

6%.

Step-by-step explanation:

For arguments sake lets assume each fruit cost $1.

He spent $50 for the fruit.

His income from the 30 kg he sold was $35.

His income from  the remaining 20Kg  was $18.

Total income = $35 + $18 = $53

So his profit was  53 - 50 = $3.

= (3/50) * 100

= 6%

Answer:

It is c

Step-by-step explanation:

Answer:

(- 8, 8 ) and (- 4, 1 )

Step-by-step explanation:

The solution to a system of equations given graphically is at the points of intersection of the two

They intersect at (- 8, 8 ) and (- 4, 1 ) ← solutions

Answer:

The center is (0,0) and the radius is 2

Step-by-step explanation:

The equation of a circle is

(x-h)^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

x^2+y^2=4

(x-0)^2 + (y-0)^2 = 2^2

The center is (0,0) and the radius is 2

18.75%

Step-by-step explanation:

600÷3200=0.1875

0.1875=18.75%

Answer:

18.75%

Step-by-step explanation:

Answer:

First choice

Step-by-step explanation:

It gives you the endpoints of the included side, F and R. Therefore, the side is FR or RF.

Answer:

D

Step-by-step explanation:

Shawn

Let the number of weeks = w

The beginning amount = 16 dollars

The amount per week is 10 dollars

The number of weeks is 10x

Equation

Savings = 16 + 10x

Mark

Let the number of weeks = w

The beginning amount = 22 dollars

The amount per week is 7 dollars

The number of weeks is 7x

Equation

savings = 22 + 7x

But they are working together so their separate equations must be added.

Total Savings= 16 + 10x + 22 + 7x = 38 + 17x

Answer: 17x + 38 = 225

Answer: [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

Use trigonometry (shown in image below) to find the 3 side-lengths:

According to right triangle trigonometry:

cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Substitute in the values:

cos θ = [tex]\frac{11}{12}[/tex]

Answer:

I'm pretty sure you are intended to pick AAS.

Step-by-step explanation:

As it stands, AAS. But this can be an unreliable theorem. If you show that the third angles are equal (which they are) using the fact that if two angles of a triangle are equal to the corresponding angles of another triangle, then the third angle is as well. That means that you can use the much more reliable ASA.

Answer:

Step-by-step explanation:

  Number               Estimate using a single digit and power of 10  

23,898,497                      2 × 10⁷          

0.000136                          1 × 10⁻⁴

26,857                              3 × 10⁴

0.0302                             3 × 10⁻²

Factorize the numerator:

4r + 20 = 4r + 4×5 = 4 (r + 5)

I think you meant to say r ≠ -5, which means r + 5 ≠ 0, so that the denominator is never zero and so the expression is defined (no division by zero). This lets you cancel the factor of r + 5 in the numerator with the one in the denominator:

(4r + 20)/(r + 5) = 4 (r + 5)/(r + 5) = 4

Answer:

the total amount of change she should receive is $1.50

Step-by-step explanation:

$7.25+$7.25= $14.50

$20.00-$14.50=$5.50

$5.50-$4.00= $1.50

Answer:

7/504

Step-by-step explanation:

there are 504 possibilities of your mom winning and 7 out of tjose are the odds of her winning.

Answer:

y = 6

Step-by-step explanation:

If x = 1, then: 3 x 1 + y = 9 (first equation)

3 x 1 + y = 9

3 + y = 9

y = 9 - 3

y = 6

Answer:

Yes

Step-by-step explanation:

Answer:

[tex]\approx 13.0[/tex]

Step-by-step explanation:

The Pythagorean theorem is a formula that relates the sides of a right triangle. This formula states the following:

[tex]a^2+b^2=c^2[/tex]

Where (a) and (b) are the legs or the sides adjacent to the triangle angle of the right triangle. Parameter (c) represents the hypotenuse or the side opposite the right angle of the right triangle. Substitute the given values into the formula and solve for the unknown:

[tex]a = 7\\b = 11[/tex]

[tex]a^2+b^2=c^2[/tex]

[tex]7^2+11^2=c^2[/tex]

Simplify,

[tex]7^2+11^2=c^2\\\\49 + 121= c^2\\\\170=c^2[/tex]

Inverse operations,

[tex]170=c^2\\\\\sqrt{170}=c\\\\\\c \approx 13.0384[/tex]

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as some coordinates to transform are not given.

I will, however, give a general explanation.

Rotate circle 270 degrees counterclockwise

This implies that, we rotate the center of the circle and the rule of this rotation is:

[tex](x,y) \to (y,-x)[/tex]

Assume the center is: (5,3), the new center will be: (3,-5)

Reflect square across y-axis

The rule is:

[tex](x,y) \to (-x,y)[/tex]

If the square has (3,5) as one of its vertices before rotation, the new point will be (-3,5).

Reflect triangle across y-axis, then 3 units up and 2 units left

The rule of reflection is:

[tex](x,y) \to (-x,y)[/tex]

If the triangle has (3,5) as one of its vertices before rotation, the new point will be (-3,5).

The rule of translating a point up is:

[tex](x,y) \to (x,y+h)[/tex] where h is the unit of translation

In this case, h = 3; So, we have:

[tex](-3,5) \to (-3,5+3)[/tex]

[tex](-3,5) \to (-3,8)[/tex]

The rule of translating a point left is:

[tex](x,y) \to (x-b,y)[/tex] where b is the unit of translation

In this case, b = 2; So, we have:

[tex](-3,8) \to (-3+2,8)[/tex]

[tex](-3,8) \to (-1,8)[/tex]

The L shape

[tex]A = (3, 8)[/tex]       [tex]A" = (-3, 1)[/tex]

[tex]B = (6, 8)[/tex]       [tex]B"= (-6, 1)[/tex]

[tex]C = (6, 3)[/tex]       [tex]C" = (-6, -4)[/tex]

[tex]D = (5, 3)[/tex]       [tex]D" = (-5, -4)[/tex]

Required

The transformation from ABCD to A"B"C"D"

First, ABCD is reflected across the y-axis.

The rule is:

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]A' = (-3,8)[/tex]

[tex]B' = (-6,8)[/tex]

[tex]C' = (-6,3)[/tex]

[tex]D' = (-5,3)[/tex]

Next A'B'C'D' is translated 7 units down

The rule is:

[tex](x,y) \to (x,y-7)[/tex]

So, we have:

[tex]A"= (-3,8-7) = (-3,1)[/tex]

[tex]B"= (-6,8-7) = (-6,1)[/tex]

[tex]C"= (-6,3-7) = (-6,-4)[/tex]

[tex]D"= (-5,3-7) = (-5,-4)[/tex]

3/z when z = 2

= 3/2

= 1.5

This is the answer

Answer:

[tex]3/z\: when\:z=2[/tex]

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

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

[tex]2z=3[/tex]

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

[tex]z=1.5\right[/tex]

OAmalOHopeO