New grass seeds grow rapidly. A grass seed has grown to 12 millimeters tall. tomorrow it will be 23 millimeters tall, the next day it will be 24 millimeters tall. and on the next day it will be 45 millimeters tall. write a rule to represent the height of the bean plant as an arithmetic sequence. how tall will the plant be in 15 days?

A) A(n) = 16 + (n-1) 11: 194 millimeters
B) A(n) = 12 + (n-1) 11: 166 millimeters
C) A(n) = 13n: 195 millimeters
D) A(n) = 12n; 180 millimeters

Answers

Answer 1

Assuming that the second day the plant was 34 mm tall, B would be the correct answer.
B) A(n) = 12 + (n-1) 11: 166 millimeters

Related Questions

A cable hangs between two poles of equal height and 30 feet apart. set up a coordinate system where the poles are placed at x=−15 and x=15, where x is measured in feet. the height (in feet) of the cable at position x i

Answers

The length of the cable is the number of units on it.

The cable is 35.26 feet long

How to determine the cable length

The function is given as:

[tex]h(x) = 15\cos(x/15)[/tex]

For all the lengths, we have the following differential equation

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (\frac{dy}{dx})^2} \, dx[/tex]

So, we have:

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (15 * \frac{1}{15} * \tanh^2(\frac{x}{15}))} \, dx[/tex]

Evaluate

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + \tanh^2(\frac{x}{15})} \, dx[/tex]

This gives

[tex]Length = \int\limits^{15}_{-15} {\sqrt{cosh^2(\frac{x}{15})} \, dx[/tex]

Evaluate the exponents

[tex]Length = \int\limits^{15}_{-15} {cosh(\frac{x}{15}) \, dx[/tex]

The above function is an even function.

So, we have:

[tex]Length = 2\int\limits^{15}_{0} {cosh(\frac{x}{15}) \, dx[/tex]

Integrate

[tex]Length = 2 * [\frac{sinh(\frac{x}{15})}{1/15}]|\limits^{15}_{0}[/tex]

Simplify

[tex]Length = 30 * [\sinh(\frac{x}{15})]|\limits^{15}_{0}[/tex]

Expand

[tex]Length = 30 * [\sinh(\frac{15}{15}) - \sinh(\frac{0}{15})][/tex]

Solve

[tex]Length = 35.26[/tex]

Hence, the length of the cable is 35.26 feet

Answers

A, you need to figure out what the companies use per week. A does that. Good luck with further math

Answer:

A if you look close at the story you will learn alot! hope this helps!

Look at the figure. How can you prove ∆ABD and ∆ACD are congruent?

A. ∆ABD ≅ ∆ACD by the SAS Postulate.

B. It is not possible to determine if the triangles are congruent.

C. ∆ABD ≅ ∆ACD by the SSS Postulate.

Answers

I think its A. what does everybody else think?

Answer: The correct option is (B). It is not possible to determine if the triangles are congruent.

Step-by-step explanation: We are given to select the correct option by which we can prove that ∆ABD and ∆ACD are congruent.

As shown in the figure,

In ∆ABD and ∆ACD, we have

∠ADB = ∠ADC = 90°,

AD is the common side.

So, one angle and the adjacent side of one triangle are congruent to the corresponding angle and the adjacent side of the other triangle.

That is, to prove that the two triangles are congruent, we need one of the following two conditions:

(i) BD = CD

(ii) ∠BAD = ∠CAD.

Since none of these two are given, so we cannot determine the congruence of the two triangles.

Therefore, it is not possible to determine if the triangles are congruent.

Thus, option (B) is correct.

Find the inverse of this 3x3 matrix. [1 5 2]
[ 1 1 7]
[0 -3 7]

Answers

Lets say the 3x3 Matrix is

M = [1 5 2 ]
[1 1 7 ]
[0 -3 7 ]

We apply the Gauss-Jordan elimination method (Procedure and result shown in the image below)

Answer:

Step-by-step explanation:

⎡−25 26 −33⎤

⎥ 4 −4 5 ⎥

⎥ 3 −3 4 ⎦

How much would $500 invested at 7% interest compounded annually be worth after 5 years?

Answers

interest compound= p(r+1)^t A=interest compound

7%= 7/100=0.07
A=500(0.07+1)^5
A=701.28

Please try this, I forget absolutely everything about rhombuses. Thanks for all the help, shouldn't be too hard

Answers

so, check the picture below. It has four sections.

the volume of a pyramid is, 1/3 ( base area)(height).

well, we know the base is a rhombus, and rhombuses diagonals meet at right-angles, therefore the center O has 4 right-angles where they meet.

since we know the angle at A, 50°, and since rhombuses are quadrilaterals with all equal sides, we know all the sides are 6 long, and the angle at C is 50° as well, and the remaining angles are 130°, as shown there.

now, if we tease out one of those triangles from the rhombus, as shown on the 1st section in the picture, we can say use the angle of 65° to get "x" and "y" lengths

[tex]\bf cos(65^o)=\cfrac{x}{6}\implies 6cos(65^o)=x \\\\\\ sin(65^o)=\cfrac{y}{6}\implies 6sin(65^o)=y[/tex]

now, we'll use those to get the area of the rhombic base.

and then onto the second section

is a right-triangle with a perpendicular line through it, which creates 3 similar triangles, by using the "geometric mean" of "w" there.

anyhow, we used the medium-sized and large-sized triangles there, to draw proportions and get what the "w" distance is, and you can see there what "w" is.

and onto the 3rd section

now that we know how long "w" is, we can use the triangle containing the 40° angle, in order to get the pyramid's height of "h", by using the tangent function, as you see there.

and we also use the same triangle, to get the "z" distance, which is namely the slant-height of the pyramid, however, is also the "altitude" of the triangular faces.

and onto the 4 and last section in the picture

that's a triangular face by herself, it has a base of 6, and an altitude of "z".

now, all that said, let's plug those values to get the volume, and then the surface area, keeping in mind the surface area is just the area of the rhombus plus the area of all four triangles.

[tex]\bf V=\cfrac{1}{3}\left[ \stackrel{\textit{area of the rhombic base}}{4\left( \frac{1}{2}xy \right)} \right](h) \\\\\\ SA=\left[ \stackrel{\textit{area of the rhombic base}}{4\left( \frac{1}{2}xy \right)} \right]~~+~~\left[ \stackrel{\textit{area of the four triangles}}{4\left[ \frac{1}{2}(6)(z) \right]} \right][/tex]

x ≈ 2.54 y ≈ 5.44 w ≈ 2.298 h ≈ 1.93 z = 3

V ≈ 17.7265 SA ≈ 63.58

how many rootes are in f(x)=(x^2-3x+1)^2
2
5
6
9

Answers

Since there is an x^2 inside the parenthesis, there will be only 2 roots. so A

Gas prices in Cook county are at $3.30 per gallon. If a market scientist predicts a 20% increase in the price of gas in the coming month, what will the price of gas be?

Answers

3.30*1.2=3.96
$3.96 will be the new price of gas

The price of the gas is $3.96.

What is a percentage?

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Gas prices in Cook-County are at $3.30 per gallon.

If a market scientist predicts a 20% increase in the price of gas in the coming month,

that means,

100 + 20% = 120% increase = 1.2 in decimals.

The price of gas,

= 3.30 + 3.30 x 1.2

= 3.96

Therefore, the new price is $3.96.

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Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx

Answers

Okay, so we have

[tex] \int\limits { \dfrac{7ln(x)}{x \sqrt{5+ln(x)^2}}} \, dx [/tex].

Substitute [tex]u=ln(x)^2+5[/tex] and differentiate.
[tex]dx= \dfrac{x}{2ln(x)}du[/tex]
[tex] \dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}}} \, du [/tex]

[tex]\int\limits { \dfrac{1}{ \sqrt{u}}} \, du = 2 \sqrt{u} [/tex]

[tex] \dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}} } \, du = 7 \sqrt{ln(x)^2+5}+C [/tex]

The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

Given an integral expression:

[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

This can be written as:

[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

It is required to find the integral value.

Let u = 5 + (ln (x))²

Differentiate.

[tex]du=2ln(x)*\frac{1}{x} dx[/tex]

Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]

Substitute the values.

[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]

[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]

[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]

Substitute back the value of u.

[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]

Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

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For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?

Answers

for the graph to cross the x axis twice, b²-4ac needs to be larger than 0
b=-k, a=1, c=k²
b²-4ac=k²-4k²=-3k²
-3k² will never be larger than 0.

Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A? Enter your answer in the box. m∠A= ° A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 3 x plus 6 right parenthesis degrees. The angle C is labeled as left parenthesis x plus 2 right parenthesis degrees.

Answers

Since the quadrilateral is inscribed in the circle, the two angles add to a 180 degrees angle.
We deduce the following equation:
[tex](3x+6)+(x+2)=180[/tex]
Solve for x like this:
[tex](3x+x)+(6+2)=180\\4x=180-8\\4x=172\\x=43.[/tex]

Now we deduce the measure of A:
[tex]A=3x+6=3\times(43)+6=135[/tex]

Final answer:

The measure of angle A in a cyclic quadrilateral ABCD, where the measure of angle A is (3x + 6) degrees and the measure of angle C is (x + 2) degrees, is determined to be 135 degrees.

Explanation:

Given that quadrilateral ABCD is inscribed in a circle, it follows from the properties of cyclic quadrilaterals that the sum of the opposite angles of such a quadrilateral is always 180 degrees. Therefore, if the measure of angle A is represented by the expression (3x + 6) degrees and the measure of angle C is represented by the expression (x + 2) degrees, then we can set up an equation that (3x + 6) + (x + 2) = 180. Solving this equation gives x = 43. Using x = 43, substitute it into 3x + 6 to get the value of angle A, which is equal to 135 degrees.

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Select two rations that are equivalent to 3: 12.

Answers

1 over 4 and 2 over 8. I just multiplied both sides of the ration to get this answer.

226Ra has a half-life of 1599 years. How much is left after 1000 years if the initial amount was 10 g?

Answers

[tex]\bf \textit{Amount for Exponential Decay using Half-Life}\\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &10\\ t=\textit{elapsed time}\to &1000\\ h=\textit{half-life}\to &1599 \end{cases} \\\\\\ A=10\left( \frac{1}{2} \right)^{\frac{1000}{1599}}[/tex]

The formula for the volume of a cube is V(s) = s3 where s is the side length of the cube. In which quadrant(s) is the graph of the function V(s)?

Answers

For this case what you should know is that we are in the presence of a cubic function that could take both positive and negative values.
However, when talking about the volume of a figure, a cube specifically, so that there is a physical sense, it must be fulfilled:
s> 0
Thus:
V (s)> 0
Thus, the function V (s) = s3 belongs to the first quadrant.
Answer:
the graph of the function V (s) is in the first quadrant.

Answer:

The answer is A: Quadrant 1

Step-by-step explanation:

On Edge :)

Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.4, and 0.4, respectively. what is the expected number of books a customer will purchase? the standard deviation of the customer's book purchases is

Answers

Porobability distribution of X
x P(x)
0 0.2
1 0.4
2 0.4
Total .1.0
i] Expectation
Mean=Σxp
Variance=x²p-(∑xp)²
thus:
Mean=(0*0.2)+(1*0.4)+(2*0.4)
=0+0.4+0.8
=1.2

ii] Variance
Variance=[(0²*0.2)+(1²*0.4)+(2²*0.4)]-(1.2)²
=[0+0.4+1.6]-1.44
=0.56
hence:
standard deviation=sqrt(0.56)=0.74833

The expected number of books a customer will purchase is 1.2 books, and the standard deviation of their book purchases is approximately 0.78 books.

To find the expected number of books a customer will purchase,

use the formula for the expected value (also known as the mean) of a random variable:

Expected Value (μ) = Σ (x × P(x))

Where:

μ is the expected value.

x represents the possible values of the random variable (in this case, 0, 1, and 2).

P(x) is the probability associated with each value of x.

Probability of purchasing 0 books (P(0)) = 0.2

Probability of purchasing 1 book (P(1)) = 0.4

Probability of purchasing 2 books (P(2)) = 0.4

Now, calculate the expected value:

μ = (0 × 0.2) + (1 ×0.4) + (2 × 0.4)

μ = 0 + 0.4 + 0.8

μ = 1.2

To find the standard deviation (σ) of the customer's book purchases,

use the formula for the standard deviation of a discrete random variable:

Standard Deviation (σ) = √[Σ((x - μ)² × P(x))]

Where:

σ is the standard deviation.

x represents the possible values of the random variable.

μ is the expected value.

P(x) is the probability associated with each value of x.

In this case, you already calculated μ as 1.2, and you have the probabilities P(0), P(1), and P(2).

Now, calculate the standard deviation:

σ = √[((0 - 1.2)² × 0.2) + ((1 - 1.2)² × 0.4) + ((2 - 1.2)² × 0.4)]

σ = √[(1.44 ×0.2) + (0.16 × 0.4) + (0.64 × 0.4)]

σ = √[0.288 + 0.064 + 0.256]

σ = √0.608

σ ≈ 0.78

Therefore, the expected number and the standard deviation of books a customer will purchase is 1.2 books and approximately 0.78 books respectively.

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J is 25 more than 3 help???

Answers

j would equal 28!!!!!!!!!!!!!!!!!!!

I think the answer would be 28

tickets for a football match are sold at $30 for adults and $15 for children a company bought 28 tickets if x of these tickets were for adults, write in terms of x a. the number of tickets for children b. the amount spent on tickets for adults c. the amount spent on tickets ...

Answers

Final answer:

The number of tickets for children is represented by '28-x' and the amount spent on tickets for adults is '$30x'. The amount spent on tickets for children is '$15*(28-x)'.

Explanation:

We will use the concept of algebraic expressions to solve this question. If we represent the number of adult tickets as x, we know that the total number of tickets is 28. Hence, the number of children tickets can be represented as 28-x. The cost of a ticket for adults is $30, so the amount spent on adult tickets can be represented as $30x. Similarly, as the cost of a ticket for children is $15, the amount spent on children tickets can be represented as $15*(28-x).

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Final answer:

The number of ticket for children is (28 - x), the amount spent on tickets for adults would be $30x, and the total amount spent on tickets would be $30x + $15(28 - x).

Explanation:

If a company bought 28 tickets and x of these tickets were for adults, then:

a. The number of tickets for children would be 28 - x. This is because from the total number of tickets purchased, we subtract the number of adult tickets to find the number of children's tickets.

b. The amount spent on tickets for adults would be $30x. This is because each adult ticket costs $30 and there are x number of adults.

c. To find out the total amount spent by the company, we will multiply the number of adult tickets by the price of an adult ticket ($30x) and add this to the product of the number of children tickets (28 - x) and the price of a child's ticket ($15). Therefore, the total spent would be $30x + $15(28 - x).

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Kelly is having a party. She wants to make punch. The recipe for punch uses 3 pints of pineapple juice, 5 cups or orange juice, 1/4 gallon of lemonade, and 1 quart of apricot nectar. Kelly says her recipe will make 20 cups of punch. Is Kelly correct? Explain your answer. How does one arrive at the answer? Are all the ingredients added? Is anything multiplied?

Answers

First convert all the ingredients into cups.
3 pints = 6 cups
5 cups = 5 cups
1/4 gallon = 4 cups
1 quart = 4 cups

Add all the ingredients.
6 + 5 + 4 + 4 = 19 cups

Therefore, Kelly does not make 20 cups of punch because her recipe is enough for only 19 cups of punch. All the ingredients are added and noting is multiplied.

given right triangle XYZ what is the value of tan 60°

Answers

I have attached the image associated with this question

Answer:
tan (60) = √3

Explanation:
The given triangle is right-angled triangle, therefore, we will use Pythagorean theorem to get the length of the third side.
third side = sqrt [(hypotenuse)^2 + (second side)^2]
third side = 21√3 units

Since the given triangle is a right-angled triangle, we can apply the special trigonometric identities.
Therefore:
tan θ = opposite / adjacent
In the given triangle:
θ = 60°
The opposite side = 21√3
The adjacent side = 21

Substitute in the above equation to get tan 60 as follows:
tan (60) = (21√3) / (21) = √3

Hope this helps :)

Answer:

√3

Step-by-step explanation:

got 100%

Write the explicit formula for the geometric sequence.

64, 32, 16, 8, ...
A) an = 8 · 4n-1
B) an = 8 · 2n-1
C) an = 32 · 0.5n-1
D) an = 64 · 0.5n-1

Answers

Answer:

D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

The answer is D because it is the only answer that has an=64 and a decimal, 64 is your first term and the sequence is getting smaller

AND OR

Answer:

D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

Explicit Formula: an = a1 · dn-1

a1 = 64, d = 0.5

an = 64 · 0.5n-1

The cylinder shown has a volume of π in3. Find the volume of a cone with the same base and height as the cylinder.

Answers

The volume of a cylinder is 3 times larger than a cylinder. So find your answer for the cylinder and multiply it by 1/3 to get your answer. Hope this helps! Study on!

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the height of cylinder is h and radius of base is r.

The volume of cylinder will be : [tex]\pi r^2h[/tex]

The cone is of same height means h and same base means radius will be r.

The formula of volume of cone is : [tex]\frac{1}{3} \pi r^2h[/tex]

It means the volume of cone is one third of the volume of cylinder.

The volume of cylinder is given as π.

So, the volume of cone will be : [tex]\frac{\pi }{3}[/tex] : Answer

Hope it will help :)

Treys online music club charges a monthly rate of $20 plus $0.80 per song download. Debs online music club charges a monthly rate of $21 plus $0.60 per song download. For what number of songs will the monthly charge be the same for both clubs? How much will it cost?

Answers

For this case, the first thing we must do is define variables.
We have then:
x: number of songs.
y: total charge
For Treys online music club:
[tex]y = 0.80x + 20 [/tex]
For Debs online music club:
[tex]y = 0.60x + 21 [/tex]
Equaling both equations we have:
[tex]0.80x + 20 = 0.60x + 21 [/tex]
Clearing x we have:
[tex]0.80x - 0.60x = 21 - 20 0.20x = 1 x = 1 / 0.20 x = 5 songs[/tex]
Substituting the value of x for any of the equations we have:
[tex]y = 0.60 (5) + 21 y = 3 + 21 y = 24 $[/tex]
Answer:
The monthly charge will be the same for 5 songs in both clubs.
the cost will be $ 24

Answer:

For 5 songs the monthly charge be the same for both clubs.

It will cost $ 24.

Step-by-step explanation:

Let, for x songs, the monthly charges are same for both clubs,

Given,

For Treys online music club,

Monthly rate = $ 20,

Additional Charges for a song = $ 0.80,

⇒ Additional Charges for x song = $ 0.80x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 20 + 0.80x

Now, for Debs online music club,

Monthly rate = $ 21,

Additional Charges for a song = $ 0.60,

⇒ Additional Charges for x song = $ 0.60x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 21 + 0.60x

Hence, we can write,

[tex]20 + 0.80x = 21 + 0.60x[/tex]

[tex]0.80x - 0.60x = 21 - 20[/tex]

[tex]0.20x = 1[/tex]

[tex]\implies x = \frac{1}{0.20}=5[/tex]

Hence, for 5 songs the monthly charge be the same for both clubs.

Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24

A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone?
A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm

Answers

Try this option:

[tex]if \ the \ volume \ of \ the \ sphere \ is \ the \ same \ one \ as \ a \ cone, \ then \ V_s=V_c; \ <=> \ \frac{4 \pi}{3}*3^3=\frac{1}{3} \pi*6^2*h_c; \ => \ h_c=3(cm)[/tex]

answer: B

B) 3 cm

Vsphere = [tex]\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi(3)^{3} = 36\pi[/tex]

Vcone =

πr2h

36π =

π(6)2h

36π = 12πh

h = 3

Thus, the height is 3 cm.

Alternatively, the two equations could be set equal to each other and solved for the unknown height of the cone.

Form a seven-letter word by mixing up the letters in the word FIXTURE.
How many ways can you do this if no vowel is isolated between two consonants?

Answers

There are 4 consonants and 3 vowels. If the vowels can't be isolated between two consonants then the vowels would have to be right next to each other. Let's consider the vowels as a group so that they can be arranged in 3!=6 ways and the consonants 4!=24 ways. So:
6x24=144ways

You have the main rule: no vowel is isolated between two consonants.

The word FIXTURE consists of 4 consonants and 3 vowels.

There are such possible cases:

1. Formed word begins with three vowels and ends with 4 consonants.

The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]

2. Formed word begins with two vowels and ends with one vowel (between them stand all consonants).

The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]

3. Formed word begins with one vowel and ends with two vowels (between them stand all consonants).

The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]

4. Formed word begins with with 4 consonants and ends with 3 vowels.

The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]

5. In total 144+144+144+144=576 different words.

The goal of an optimization problem is to find the maximum or minimum value of the

Answers

to complete your statement: function. optimization is a very useful tool in calculus to calculate extremi of functions

An optimization problem seeks to maximize or minimize an objective function, involving endogenous and exogenous variables and is widely used in various fields. Linear optimization uses linear equations and can often be solved with gradient-based techniques in software like MS Excel.

The goal of an optimization problem is to find the maximum or minimum value of a specific function, which is known as the objective function. This function typically represents a scenario such as profit maximization or cost minimization in different fields such as business, economics, and engineering. In an optimization model, there are typically three components: the goal (e.g., maximize profits), the endogenous variables (e.g., the amount of goods produced or the number of hours worked), and the exogenous variables (e.g., price of the goods, wage rates). Linear optimization problems, in particular, represent the objective function and constraints as linear equations and are solved using various mathematical techniques.

Most optimization techniques, such as those used in MS Excel, are gradient-based and offer a systematic approach for finding the optimal solution that either maximizes or minimizes the objective function while satisfying a set of constraints. Whether the objective is to maximize utility or minimize costs, similar approaches can be applied, and sometimes the objective function can be stated in the minimization form in any linear optimization problem by using a transformation.

if x2 = 49 the only possible answer for x is 7

Answers

Solve for x over the real numbers:
x^2 = 49

Take the square root of both sides:
Answer: x = 7 or x = -7

While the equation x² = 49 suggests that x = 7, it also has a negative solution, x = -7. Both solutions can be verified by substitution into the original equation, proving they are correct through resulting identities.

The equation x² = 49 has two solutions in the realm of real numbers, not just x = 7. To find the values of x that satisfy the equation, we take the square root of both sides. Since the square root of a number has both a positive and a negative value, the solutions are x = 7 and x = -7. To verify these solutions, we can substitute them back into the original equation to confirm that they work, demonstrating identities such as 7² = 49 and (-7)² = 49.

How many triangles are with two sides each 6 inches long and one angle measure of 90°.

Answers

A Right triangle is a type of triangle is the only type of triangle that should contain a right angle. If there are 2 equal sides it must be an isosceles triangle.
So the triangle is a Right Isosceles triangle

The description relates to an isosceles right triangle.

An isosceles right triangle can be described as the triangle that has two sides that are both equal while it also has an angle that will be 90° which is the right angle.

In this case, the two equal sides are given as 6 inches while it also has an angle of 90°. Therefore, it's an isosceles right triangle.

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Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal.

Answers

y = 2x^3 + 3x^2 − 12x + 9
y' = 6x^2 + 6x − 12

tangent line is horizontal y'=0
6x^2 + 6x − 12=0
x^2+x-2=0
(x+2)(x-1)=0
x=-2 or x=1
when x=-2, y=2x^3 + 3x^2 − 12x + 9 = -16 + 12 + 24 + 9 =29
when x=1, y=2x^3 + 3x^2 − 12x + 9 = 2 +3 -12 +9 =2
two points (-2,29),(1,2)

2). y = 2x^3 + 3x^2 − 12x + 9

slope of horizontal-tangent-line, y' = 6x^2+6x-12 = 0
SO,
6(x+2)(x-1) = 0,
x=1, and x=-2,
SO, for, x= 1, y= 2+3-12+9 = 2,
Hence,
the 1st. point is : Answer (1, 2)

and, for, x=-2,
y = 2(-2)^3 +3(-2)^2 -12(-2) +9 = -16+12+24+9 = 29
Hence,
the 2nd-point is : Answer (-2, 29)

the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.

Given :

The equation of the curve is [tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9[/tex]

Given tangent line is horizontal . Tangent line is horizontal when slope =0

Slope is nothing but the derivative.

So we find out x values where derivative =0

Lets take derivative for the given curve y

[tex]y=2x^3+3x^2-12x+9\\y'=2(3x^2)+3(2x)-12\\y'=6x^2+6x-12[/tex]

Now we set the derivative =0 and solve for

[tex]6x^2+6x-12=0\\Divide\; whole \; equation \; by \; 6\\x^2+x-2=0\\(x+2)(x-1)=0\\x+2=0, x=-2\\\\x-1=0, x=1[/tex]

So , the slope =0 when x=1 and x=-2

Now we find out the points . Use the original function

[tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9\\x=-2\\2\left(-2\right)^3+3\left(-2\right)^2-12\left(-2\right)+9=29\\(-2,29)\\\\x=1\\2\left(1\right)^3+3\left(1\right)^2-12\left(1\right)+9=2\\(1,2)[/tex]

the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.

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Solve for C. See photo

Answers

[tex]F = \frac{9}{5} C+32 \\ F - 32 = \frac{9}{5} C \\ \frac{5}{9} (F -32)=C[/tex]

Milli plans to rent a room for her birthday party for $40. The catering charge is $12 per person but there is no charge for Milli's meal since she is the guest of honor. If Milli has $100 to spend on her birthday party, what is the maximum number of friends Milli can invite?

Answers

The answer is (5 guest) hope it helps and have a good one!

5 is the maximum number of friends that Milli can invite because she has a budget of $100. 100-40 (the required cost to rent the room) =60. 60/12 (the catering charge per person, excluding Milli) =5. Hope this helps

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