to find the height of a tree, a group of students devised the following method. A girl walks toward the tree along it's shadow until the shadow of the top of her head coincide with the shadow of the top of the tree. if the girl is 150 cm tall, her distance to the foot of the tree is 13 meters, and the length of her shadow is 3 m, how tall is the tree?

The given points are A(-3, 1), B(2, 1), C(2, 4), D(-3, 4).

The image below shows the figure formed by these points.

As you can observe, the shape formed by the given points is a rectangle with dimensions 5 times 3.

In the  Polynomial  function  f(x)= [tex]2x^{3} -11x^{2} -12x+36 =0 then[/tex]

So all the zeros of f(x) algebraically

[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex].

Step: 1

Given[tex]$f(x)=2 x^3-11 x^2-12 x+36$and $f(6)=0 \Rightarrow(x-6)$ is factor of $f(x)$now $f(x)=2 x^3-11 x^2-12 x+36$$$[/tex]

[tex]\begin{aligned}&\Rightarrow \mathrm{f}(\mathrm{x})=\left(2 \mathrm{x}^2-12 \mathrm{x}^2\right)+\left(\mathrm{x}^2-\right. \\&\Rightarrow \mathrm{f}(\mathrm{x})=2 \mathrm{x}^2(\mathrm{x}-6)+(\mathrm{x}-6)^2 \\&\Rightarrow \mathrm{f}(\mathrm{x})=(\mathrm{x}-6)\left(2 \mathrm{x}^2+\mathrm{x}-6\right)\end{aligned}$$[/tex]

Step: 2

Now consider [tex]$2 x^2+x-6=2 x^2+4 x-3 x-6$$$\begin{aligned}&\Rightarrow 2 x(x+2)-3(x+2) \\&\Rightarrow 2 x^2+x-6=(2 x-3)(x+2)\end{aligned}$$[/tex]

[tex]$5 \circ f(x)=(x-6)\left(2 x^2+x-6\right)$$$\Rightarrow \mathrm{f}(\mathrm{x})=(x-6)(2 \mathrm{x}-3)(\mathrm{x}+2)$$[/tex]

Step: 3

so for finding zeros of

[tex]$f(x) \rightarrow f(x)=0$$$\Rightarrow(x-6)(2 x-3)(x+2)=0$$$$\Rightarrow(x-6)=0 ;(2 x-3)=0 ;(x+2)=0$$[/tex]

[tex]$$\Rightarrow x=6, x=\frac{3}{2} ; x=-2$$[/tex]

Explanation: Please refer to solution in this step.

Answer:

So required zeros of

[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex]

A polynomial consists of two words, poly and nominal. "Poly" means many and "nomial" means  term, and so when  combined, polynomials can be said to be "algebraic expressions with many terms." Let's go ahead and start by defining polynomial functions and their types.

The polynomial function in standard form is:

f(x) =  [tex]a_{n}x^{n} +a_{n-1} x^{n-1} +.....a_{2} x^{2} +a_{1} x+a0[/tex]

This algebraic expression is called a polynomial function of the variable x. The name of a polynomial is determined by the number of terms it contains.

The three most common polynomials we usually encounter are

To learn more about polynomial function, refer;

https://brainly.com/question/12976257

#SPJ13

Two plants

Spider plant 4 days

Cactus plant 6 days

Then find when

4X = 6Y

find m.c.m (minimum common multiple) of 4 and 6

m.c.m (4,6) = 12

SO therefore, if both plants were watered November 30, then

add 12 days to Nov 30

12 days after Nov 30 = December 12

The expression (−1/2x + 7/10) − (−3/4x − 1/5) has a value of  1/4x + 9/10 when simplified

From the question, the expression is given as

(−1/2x+7/10)−(−3/4x−1/5)

Rewrite the expression properly to  make it legible

So, we have

(−1/2x + 7/10) − (−3/4x − 1/5)

Expression the above parameter as an equation

This is represented as

(−1/2x + 7/10) − (−3/4x − 1/5) = (−1/2x + 7/10) − (−3/4x − 1/5)

Open the brackets

So, we have the following equation

(−1/2x + 7/10) − (−3/4x − 1/5) = −1/2x + 7/10 + 3/4x + 1/5

Collect the like terms in the equation

(−1/2x + 7/10) − (−3/4x − 1/5) = 3/4x − 1/2x + 7/10  + 1/5

Evaluate

(−1/2x + 7/10) − (−3/4x − 1/5) = 1/4x + 9/10

The expression cannot be further simplified

Hence, the solution to the expression (−1/2x + 7/10) − (−3/4x − 1/5) is 1/4x + 9/10

Read more about expression at

https://brainly.com/question/723406

#SPJ1

Solution:

Given that the initial cost price of the jewelry is $2,200.

The rate at which it decreases each year is 12%.

Thus, the exponential decay function is;

The graph of the function is;

From the graph;

CORRECT OPTION:

Based on the half-life, 35.36 mg will remain at 6:00P PM in the body

The details that complete the question are added as an attachment

From the question, we have

Initial dosage = 200 mg

This means that

M = 200

Also, we have

Initial time =1 : 00 pm

This means that the number of hours, is

n = 6pm - 1pm

n = 5

Recall that the function is given as

R = M(0.5)ⁿ/²

So, we have the following equation

R = 200 x (0.5)⁵/²

Evaluate the quotient of the exponents

So, we have the following equation

R = 200 x (0.5)².⁵

Evaluate the products

R = 35.36 mg

Using the above computation as a guide, we have the remaining amount to be 35.36 mg

Hence, the amount of the medication that will remain at 6:00P PM is 35.36 mg

Read more about half life at

https://brainly.com/question/14407764

#SPJ1

Given

n= 5

p = 0.7

Find:

a. mean

b. variance

sol:

Mean d

Given a principal P, compounded anually at r% for t years. Then the

Step-by-step explanation:

i think it will satisfied you

please mark me as brainlist

The values of the variables are x = 2, y = -2 and z =0

From the question, the system of equations is given as

x – y - 3z = 4

2x + 3y – 3z = -2

x + 3y – 2z = -4

Subtract the second equation from the third

This action will eliminate (y)

So, we have

x + 3y – 2z = -4 - (2x + 3y – 3z = -2)

Evaluate

-x + z = -2

Make x the subject

x = z + 2

Substitute x = z + 2 in x – y - 3z = 4 and x + 3y – 2z = -4

z + 2 – y - 3z = 4

z + 2 + 3y – 2z = -4

Evaluate

-2z - y = 2

-z + 3y = -6

Double -z + 3y = -6

-2z + 6y = -12

Subtract -2z + 6y = -12 from -2z - y = 2 to eliminate z

7y = -14

Divide

y = -2

Substitute y = -2 in -z + 3y = -6

-z + 3(-2) = -6

Evaluate

-z - 6 = -6

Evaluate

z = 0

Recall that x – y - 3z = 4

So, we have

x + 2 - 3(0) = 4

Evaluate

x = 2

Hence, the solution is x = 2, y = -2 and z =0

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

ANSWER

x = 10.2

EXPLANATION

In this problem, we are given a right triangle: one of its non-right interior angles measures 22°. We know that the length of the hypotenuse is 11 units long and we have to find the length of the side adjacent to the given angle, x.

With the given information, we can use the cosine of the angle to find the missing value,

In this problem,

Solving for x,

Hence, the value of x is 10.2, rounded to the nearest tenth.

Observe that the triangles have one pair of congruent angles, and two pair of congruent sides. This means we can demonstrate the congruence using SAS postulate, that is, Side-Angle-Side.

Therefore, the answer is the first option.

Answer:

-7

Step-by-step explanation:

Tiger Woods was 15 under par after the third round of a golf tournament, but was 8 over par for the fourth round. So, his score for the entire tournament was -15 + 8 = -7 (That is, 7 under par).

Using percentages we can conclude that 50.2% of students are taking a computer class.

So, the percentage of students taking computer classes:

Now, calculate as follows:

Therefore, using percentages we can conclude that 50.2% of students are taking a computer class.

Know more about percentages here:

https://brainly.com/question/9553743

#SPJ13

We must solve the following equation for x:

We can square both sides of the equation so we can get rid of the radical:

We expand the squared binomial on the left:

Then we substract (3-x) from both sides:

Then we have to find the solutions to this last equation. Remember that the solutions to an equation of the form ax²+bx+c have the form:

In our case a=1, b=7 and c=6 so we get:

So we have two potential solutions x=-1 and x=-6. However we should note something important, in the original equation we have the term:

Remember that the result of the square root is always positive. Then the term in the left of the expression has to be positive or 0. Then we impose a restriction in the value of x:

From the two possible solutions only x=-1 is greater than or equal to -3 so this is the correct one.

Then the answer is option A.

Initial distance: 108 miles

We know that they start riding toward each other, and one of them is 2 times as fast as the other. Then, if the speed of the slowest is v, the speed of the faster cyclist is 2v. The combined speed is:

The speed and the distance are related by the equation:

They meet 4 hours later, thus:

Finally, using the previous equation:

The speed of the faster cyclist (2v) is 18 mi/h.

Given the expression:

Let's simplify the expression and convert its decimal form to get its approximation.

We get,

In decimal form:

Therefore, the approximate equivalent of 3√200 is 5.8.

Question:

Find a volume of a cylinder:

Solution:

Remember that the volume of the cylinder with radius r and height h is given by the following formula:

then, replacing the data of the problem into the previous equation, we get:

thus, we can conclude that the correct answer is:

The given equation is

Where a = 2, b = 8, and c = 8.

The discriminant formula is

Let's replace the values

x = 8, y = 21

The given equation is:

y = 4x - 11 = x + 13

This can be splitted into two equations as:

y = 4x - 11..........(1)

y = x + 13..........(2)

Substitute equation (1) into equation (2)

4x - 11 = x + 13

4x - x = 13 + 11

3x = 24

x = 24/3

x = 8

Substitute the value of x into equation (1)

y = 4x - 11

y = 4(8) - 11

y = 32 - 11

y = 21

x = 8, y = 21

Solution

The volume for a triangular pyramid is given by:

And the Base is given by:

And since h= 1.5 ft we have this:

And then we can find the total cost like this:

Then the final answer would be 12$

Those angles are complementary, therefore, we can conclude:

Answer:

x = 18

Answer: 14

Step-by-step explanation:

1/4 of a pumpkin is required to make a pie. The easiest way to complete this is to convert 3.5 pumpkins into the same fraction.

1 pumpkin = 4/4

3.5 pumpkins = 14/4

If only 1/4 of a pumpkin is required to make a pie and we have 14/4 then we can make 14 pumpkin pies.

The likelihood of the following situations:

1. rolling an even number is likely.

2. rolling a 7 is impossible.

3. rolling a number greater than 0 is certain.

4. rolling a number that is greater than 2 is likely.

5. rolling a 2 or 3 is equally likely

The volume from tanks A and B are taken as 3 and 5 gallons respectively.

Here,
Let the volume taken from tank A and tank B be x and y.
According to the question,
x + y = 8 - - - - - (1)
And
Composition of the alcohol in Tank A = 1/3
Composition of the alcohol in tank B =  1 /5
x / 3 + y / 5 = 8 / 4
5x + 3y = 30
From equation 1
5(y8 - y) + 3y = 30
-5y + 40  + 3y = 30
-2y = -10
y = 5
Now, put y in equation 1
x = 8 - 5
x = 3

Thus, the Volume from tanks A and B are taken as 3 and 5 gallons respectively.

Learn more about Volume here:

https://brainly.com/question/1578538

#SPJ1

Let's begin by identifying key information given to us:

Thale's method shows that angles in a triangle opposite two sides of equal length are equal

As such, the answer is A (The distance between points A and Z is the same as the distance between X and Z)

The given quadratic equation is

y = - x^2 + 25

a) The leading coeffiecient is the coefficient of the term with the highest exponent. Thus, the leading coefficient is the coefficient of x^2.

Leading coefficient = - 1

Since the leading coefficient is negative, the graph would open downwards. Thus, the correct option is

Down

b) The standard form of a quadratic equation is

y = ax^2 + bx + c

By comparing both equations,

a = - 1

b = 0

c = 25

The formula for calculating the x coordinate of the vertex of the graph is

x = - b/2a

By substituting the given values,

x = - 0/2 * - 1 = 0

We would calculate the y coordinate of the vertex by substituting x = 0 into the original equation. We have

y = - 0^2 + 25

y = 25

The coordinate of the vertex is (0, 25)

c) To find the x intercepts, we would equate the original equation to zero and solve for x. We have

- x^2 + 25 = 0

x^2 = 25

Taking the square root of both sides,

x = square root of 25

x = ± 5

Thus, the x intercepts are

(5, - 5)

d) The y intercept is the value of y when x = 0

Substituting x = 0 into the orignal equation,

y = - 0^2 + 25

y = 25

y intercept = (0, 25)

e) We would find another point on the graph. Let us substitute x = 6 into the equation. We have

y = - (6)^2 + 25 = - 36 + 25

y = - 11

We would plot (6, - 11) and (0, 25) on the graph. The graph is shown below

Answer:

answer is -0.8333

round about -0.834

Step-by-step explanation: I hope this helps.

Answer:

Part B

Remember that

z =(x - μ)/(σ/√n)

where

n=21

we have

μ=1,700

σ=200

For X=1,500

Find out the value of Z1

Z1=(1,500-1,700)/(200/√21)

Z1=-4.5826

For X=1,900

Z2=(1,900-1,700)//(200/√21)

Z2=4.5826

Using a z-score table value

P(1,500therefore

The answer is 21 out of 21

To determine the fraction of cousins, you have to divide the number of cousins she invited by the total number of guests.

She invited 12 cousins, 6 aunts, 4 brothers, and 2 sisters, a total of 24 guests.

Then:

Both, 12 and 24 are divisible by 12, to simplify the fraction, divide the numerator and denominator by 12

The fraction