Suppose an investor builds a stock portfolio with a variety of shares in various high tech companies. The value of the stock portfolio is modeled by the function y = 2x^2 - 20x + 100, where y is the value of the portfolio in hundreds of dollars, and x is the time in months.

a) Find the x-coordinate of the vertex. Show all work leading to your answer and write the answer in simplest form.

b) Find the y-coordinate of the vertex. Show all work leading to your answer and write the answer in simplest form.

c) What does the vertex represent for this situation? Write 1 - 2 sentences to explain your answer.

Answer:

1000 cubic feet

Step-by-step explanation:

1000 cubic feet because you have to find the volume of the small cube on the bottom right which is 5x5x5=125, volume of the middle right rectangular prism is 20x5x5=500, and volume of the right side rectangular prism is 15x5x5=375. 125+550+375= 1000 cubic feet.

270,000

The ten-thousandths place is the fifth digit to the left of the decimal point, which is a 7 in this case.

The next number to the right of the 7 is a 4, which is 4 or less, so you don't need to round up the 7.  This means we can just replace the 4 and everything to the right of it with 0s.

If the 4 were 5 or more instead, you would turn the 7 into an 8 and then turn everything after it into 0s.

Answer:

15x - 21x² + 12

Step-by-step explanation:

(3x - 6)(2 X 2 - 7x + 1) = (3x - 6)(4 - 7x + 1)

                                  = (3x - 6)(5 - 7x)

                                  = (3x X 5) + (3x X -7x) + (-6 X 5) + (-6 X -7)

                                  = 15x - 21x² - 30 + 42

                                  = 15x - 21x² + 12

Answer:

(3x-6)(2x² -7x+1)

= 6x³ - 33x² + 45x - 6

Step-by-step explanation:

(3x-6)(2x² -7x+1)

To find the product of this we will expand the equation by multiplying each element in one bracket with the other bracket.

(3x-6)(2x² -7x+1)

Expand

(3x)(2x² - 7x + 1) (-6)(2x² - 7x + 1)

Opening the bracket (multiple)

6x³ - 21x² + 3x - 12x² + 42x - 6

Collect like terms

= 6x³ - 21x² - 12x² + 3x + 42x - 6

= 6x³ - 33x² + 45x - 6

Answer:

She should cut each diagonal piece 10 ft long.

Step-by-step explanation:

The bottom face of the box is a rectangle 8 ft by 6 ft.

A diagonal of a rectangle divides the rectangle into two congruent right triangles. With a right triangle you can use the Pythagorean theorem.

a = length of rectangle = leg of right triangle

b = width of rectangle = other leg of right triangle

c = diagonal of rectangle = hypotenuse of right triangle

a^2 + b^2 = c^2

(8 ft)^2 + (6 ft)^2 = c^2

64 ft^2 + 36 ft^2 = c^2

c^2 = 100 ft^2

Take the square root of each side.

c = 10 ft

Answer: She should cut each diagonal piece 10 ft long.

Answer:

The diagonal piece of wood should be 10 feet long.

Step-by-step explanation:

The diagonal piece of wood will form a right-angled triangle with the width and length  of the box. By the Pythagoras Theorem:

x^2 = 6^2 + 8^2   where x is the  length of the diagonal.

x^2 = 36 + 64

x^2 = 100

x = 10 feet.

In a normal distribution, 99.7% of the data falls within three standard deviations from the mean. Given the mean of 68 and standard deviation of 4, 99.7% of the heights would range from 56 to 80 inches. Therefore, the answer is option A.

The question is about the normal distribution, a key concept in statistics. In a normal distribution, about 68% of the values fall within one standard deviation around the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations. Since the mean height of the population is 68 inches and the standard deviation is 4 inches, three standard deviations from the mean would be 12 inches above and below the mean. Hence, 99.7% of the population's height would fall within the range of 68 inches - 12 = 56 inches and 68 inches + 12 = 80 inches.

So, the correct answer to this question is option A: 56 inches to 80 inches.

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The range within which 99.7% of the population will have a height can be found using z-scores. The correct answer is option A. 56 inches to 80 inches

To find the range within which 99.7% of the population will have a height, we need to use the concept of z-scores.

The range is usually defined as the mean plus or minus a certain number of standard deviations.

In this case, 99.7% of the population would fall within three standard deviations of the mean.

So, the range would be 68 - (3 * 4) = 56 inches to 68 + (3 * 4) = 80 inches.

Therefore, the correct answer is A. 56 inches to 80 inches.

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The quadratic formula is:

[tex]ax^{2} + bx + c = 0[/tex]

This means that

3 is a

-5 is b (this would be negative 5 not positive because it is being subtracted in the equation)

5 is c

This would make letter B correct!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The correct option is B.

Step-by-step explanation:

Solution:

The shortest on map is 7cm  

The longest on map is 14 cm  

The shortest in real life is 120 km  

Let the longest in real life is x km  

So,

The ratio is:

7/120 = 14/x  

x = 120*(14) / 7

x=1,680/7

x= 240 km

The longest in real-life is 240 km

Thus the correct option is B....

Answer:

B. x > 5

Step-by-step explanation:

Simply combine all like-terms on the left side of the inequality symbol, then evaluate to arrive at your answer.

Check the picture below.

Answer:

The positive difference between the a values is 0.5

Step-by-step explanation:

we know that

Both parabolas cross the x axis at (-4,0) and (6,0)

so

The general equation is

[tex]y=a(x+4)(x-6)[/tex]

Find the value of a in the first parabola

The y-intercept is (0,-12)

so

For [tex]x=0, y=-12[/tex]

substitute

[tex]y=a(x+4)(x-6)[/tex]

[tex]-12=a(0+4)(0-6)[/tex]

[tex]-12=a(-24)[/tex]

[tex]a=0.5[/tex]

Find the value of a in the second parabola

The y-intercept is (0,-24)

so

For [tex]x=0, y=-24[/tex]

substitute

[tex]y=a(x+4)(x-6)[/tex]

[tex]-24=a(0+4)(0-6)[/tex]

[tex]-24=a(-24)[/tex]

[tex]a=1[/tex]

Find the positive difference between the a values for the two functions

so

[tex]1-0.5=0.5[/tex]

0.5

Step-by-step explanation:

Answer:

A) 5/2 is greater than 3/2

Step-by-step explanation:

Konichiwa~! My name is Zalgo and I am here to be of assistance to you today. The answer to your question would be Answer Choice 1/A;5/2>3/2. The reason it is the 1st answer choice is because 5/2 turned into a decimal is 2.5, but 3/2 turned into a decimal is 1.5, so since 2.5 is greater than 1.5, that would be the evidence that the 1st answer choice is correct!

I hope that this helps! :3

"Stay Brainly and stay proud!" - Zalgo

(By the way, do mind marking me as Brainliest? I'd greatly appreciate it! Arigato~!)

Answer:

45

Step-by-step explanation:

Hope this helps!

Answer:

that graph will feature an area delimited by a line of slope m passing through the origin (0,0).

Since m>0 the slope is positive, meaning the line goes up.

Since the equation is y > mx, the inequality sign being >, that means the area represented will be ABOVE the line drawn.  

So it will for sure include ALL quadrant II (with -x and +y values) and NONE of the quadrant IV (with +x and -y values) since the line is passing through the origin (0,0).

Answer:

The graph of y > mx, where m > 0, consists of a dashed line and a shaded half plane. The line has a positive slope and passes through the origin. The shaded half plane is above the line.

Step-by-step explanation:

Answer:

[tex]\large\boxed{\bold{No\ real\ solutio}\\\boxed{\dfrac{3}{2}\pm\dfrac{1}{2}i}[/tex]

Step-by-step explanation:

[tex]2x^2=6x-5\qquad\text{subtract}\ 2x^2\ \text{from both sides}\\\\0=-2x^2+6x-5\qquad\text{change the signs}\\\\0=2x^2-6x+5\\\\2x^2-6x+5=0\\\\\text{use the quadratic formula:}\\\\ax^2+bx+c=0\\\\if\ b^2-4ac<0,\ then\ the\ equation\ has\ no\ real\ solution\\\\if\ b^2-4ac=0,\ then\ the\ equation\ has\ one\ solution\ x=\dfrac{-b}{2a}\\\\if\ b^2-4ac>0,\ then\ the\ equation\ has\ two\ solutions\ x=\dfrac{-b\pm\sart{b^2-4ac}}{2a}[/tex]

[tex]2x^2-6x+5=0\\\\a=2,\ b=-6,\ c=5\\\\b^2-4ac=(-6)^2-4(2)(5)=36-40=-4<0\\\\\bold{No\ real\ solution}\\\\\text{If yo want the complex solution, then:}\\\\i=\sqrt{-1}\to\sqrt{-4}=\sqrt{4}\cdot\sqrt{-1}=2i\\\\x=\dfrac{-(-6)\pm2i}{2(2)}=\dfrac{6\pm2i}{4}=\dfrac{3\pm i}{2}=\dfrac{3}{2}\pm\dfrac{1}{2}i[/tex]

Answer:

D. -5x² - 25x - 3

Step-by-step explanation:

Simply distribute where needed, evaluate the distribution, then combine like-terms to arrive at your answer.

The required solution of the given algebraic expression is -5x² − 25x + 3.

Given that,
The simplest form of the expression 2x(x − 6) − 7x² − (13x − 3) is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Simplify the given expression,
= 2x(x − 6) − 7x² − (13x −3)
= 2x² -12x - 7x² -13x + 3
Associate the alike terms,
= -5x² -25x + 3

Thus, the required solution of the given algebraic expression is -5x² − 25x + 3.

Learn more about simplification here:

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Answer:

Step-by-step explanation:

1. f(x) < 0

Interval of the domain where the graph is below the x-axis

because the negative regions of a function compromises those intervals where the function lies below the x-axis

2. x-intercept

Location on graph where output is zero

because when we find x-intercept we put y=0

3. y-intercept

Location on graph where input is zero

because when we find y-intercept we put x=0

4. f(x) > 0

Interval of the domain where the graph is above the x-axis

because the positive regions of a function compromises those intervals where the function lies above the x-axis

[tex]A=68units^2[/tex]

First of all, let's plot all the points, so we get the first figure below. Since a Polygon is a shape with straight sides and closed, then if we draw lines in order for the shape to be closed, we get the shape as shown in the second figure. This polygon is a trapezoid because at least one pair of opposite sides are parallel. To get the area, we know the formula:

[tex]For \ any \ trapezoid: \\ \\ A=\frac{(b_{1}+b_{2})h}{2} \\ \\ b_{1} \ and \ b_{2} \ are \ the \ two \ parallel \ bases \\ \\ h \ is \ the \ height[/tex]

From the second figure, we know:

[tex]b_{1}=6 \\ \\ b_{2}=11 \\ \\ h=8 \\ \\ Then: \\ \\ A=\frac{(6+11)\times 8}{2} \\ \\ \boxed{A=68units^2}[/tex]

Answer:

Part 1) The expression is [tex]24n[/tex]

Part 2) The value is [tex]115.2[/tex]

Step-by-step explanation:

Part 1) Find the expression

Let

n -----> the number

we know that

The algebraic expression of the phrase "The product of 24 and a number"  is equal to multiply the number by 24

so

[tex]24n[/tex]

Part 2) Find the value of the product when n=4.8  

substitute the value of n in the algebraic expression

[tex]24(4.8)=115.2[/tex]

Answer: It's C i got it right on edge

Step-by-step explanation:

By factorising a function, you can find the value of x-intercepts by substituting f(x)=0

By plotting a graph, you can check the values of x-intercepts

A function graph can be used to verify if a function is factored correctly by comparing the x-intercepts on the graph to the solutions of the factored function.

A function graph can be used to help verify that a function is factored correctly by examining its x-intercepts. When a function is factored correctly, the x-intercepts represent the values of x for which the function equals zero. In other words, they are the solutions to the equation f(x) = 0. By plotting the function and identifying the x-intercepts on the graph, we can compare them to the solutions of the factored function to determine if they match.

For example, let's say we have a function f(x) = (x+2)(x-3). The factored form suggests that the x-intercepts should occur at x = -2 and x = 3. By graphing the function and observing where it crosses the x-axis, we can confirm if these values are indeed the x-intercepts.

If the x-intercepts on the graph match the solutions of the factored function, it indicates that the function is correctly factored. However, if they do not match, it suggests an error in the factoring process.

Answer:

55

Step-by-step explanation:

Assuming she deposited the same amount each month.

Total ÷ Months = Amount Deposited Each Month

1,320 ÷ 24 = 55

Answer:

(6, ∞)

(-∞, 6)

Step-by-step explanation:

x^2 + 36 > 12x

Subtract 12 x from each side

x^2 -12 x+ 36 > 12x-12x

x^2 -12 x+ 36 > 0

Factor

What 2 numbers multiply together to give us 36 and add together to give us 12

-6*-6 = 36

-6+-6 = 12

(x-6) ^2 > 0

Take the square root of each side

x-6 >0   or  x-6 <0

x>6     or   x < 6

Answer:

c. and second one is B

Step-by-step explanation:

[tex]\bf \cfrac{18x^4+27x^3-36x^2}{9x^2}\implies \stackrel{\textit{distributing the denominator}}{\cfrac{18x^4}{9x^2}+\cfrac{27x^3}{9x^2}-\cfrac{36x^2}{9x^2}} \\\\\\ \cfrac{18x^4x^{-2}}{9}+\cfrac{27x^3x^{-2}}{9}-\cfrac{36x^2x^{-2}}{9}\implies \cfrac{18x^{4-2}}{9}+\cfrac{27x^{3-2}}{9}-\cfrac{36x^2x^{-2}}{9} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 2x^2+3x-4~\hfill[/tex]

Answer:

Events D and C are mutually exclusive.

Step-by-step explanation:

Two events D and C are mutually exclusive if

[tex]Pr(D\cup C)=Pr(D)+Pr(C)[/tex]

Find these probabilities. In a standard deck of 52 playing cards there are 13 diamond cards and 13 club cards.

The probabilty of chosing diamond is

[tex]Pr(D)=\dfrac{13}{52}=\dfrac{1}{4}[/tex]

The probabilty of chosing club is

[tex]Pr(C)=\dfrac{13}{52}=\dfrac{1}{4}[/tex]

The probabilty of chosing diamond or club is

[tex]Pr(D\cup C)=\dfrac{13+13}{52}=\dfrac{1}{2}[/tex]

Since

[tex]\dfrac{1}{2}=\dfrac{1}{4}+\dfrac{1}{4},[/tex]

events D and C are mutually exclusive.

Final answer:

In the context of a standard deck of 52 playing cards, the events representing diamonds (D) and clubs (C) are mutually exclusive events because a single card cannot be both a diamond and a club at the same time.

Explanation:

The question asks about the concept of mutually exclusive events in probability, using the context of a standard deck of playing cards. In a standard deck, there are four suits: spades, hearts, diamonds, and clubs. Diamonds (D) and clubs (C) are two different suits of cards, and so they are mutually exclusive events because the same card cannot be both a diamond and a club at the same time.

In reference to a standard deck of 52 cards which contains clubs, diamonds, hearts, and spades, each suit has 13 cards - A (ace), 2 through 10, J (jack), Q (queen), and K (king). Therefore, seeing as how a card from a deck cannot belong to two different suits, D and C are mutually exclusive events; there is no overlap between these two groups of cards.

Perimeter=120

ED=x (length)

FE=4x (breadth)

Perimeter of rectangle= 2(l+b)

Given,

2(x+4x)=120

2x+8x=120

10x=120

x=120÷10

x=12

Therefore, value of x is 12

Answer: 12

Step-by-step explanation:

You are given that perimeter = 120, length (FE) = 4x, and width (ED) = x

 P  =    2L  + 2w    (P = perimeter, L = length, w = width)

120 = 2(4x) + 2(x)

120 =   8x   +  2x

120 =       10x

÷10       ÷10    

12  =          x

Answer:

Straight edge, and compass.

Step-by-step explanation:

Greeks used very simple tools for geometric construction. They did not used advanced tools that we are using today.

Please mark brainliest and have a great day!

Answer:

The Greeks did not use ruler and tracing paper.

Step-by-step explanation:

Compass and straight edge were the tools that were used by Greeks in their formal geometric construction.

During earlier Greek times, simple geometric tools were used like compass and straight edge to draw something. Rulers and other tools came to use much later in time.

ANSWER

b=11

EXPLANATION

The given quadratic equation is

[tex](2x - 1)(x + 6) = 0[/tex]

We expand to get:

[tex]2 {x}^{2} + 12x - x - 6 = 0[/tex]

We simplify further by combining the x terms.

[tex]2 {x}^{2} + 11x - 6 = 0[/tex]

This is the standard form.

Comparing to

[tex]a{x}^{2} + bx + c= 0[/tex]

We have b=11

Answer:

b

Step-by-step explanation:

they will be parallel same slope jujst different start points

Answer:

Option A: 15 square inches

Step-by-step explanation:

Given

[tex]Base = 10 inches\\Height = 3 inches[/tex]

We know that the formula for the area of triangle is:

[tex]Area=\frac{1}{2}*base*height\\ = 0.5*10*3\\= 15[/tex]

So the area is 15 square inches.

We can conclude that option A: 15 square inches is the correct answer ..

Answer:

The correct answer is option A.  15 square inches

Step-by-step explanation:

Points to remember

Area of triangle = bh/2

b - Base of triangle

h - Height of triangle

To find the area of triangle

Here base b = 10 inches and

height h = 3 inches

Area = bh/2

 = (10 * 3)/2

 = 30/2 = 15 square inches

The correct answer is option A.  15 square inches

Answer:

Sara is 4 ft tall

Step-by-step explanation:

Let

x ----> the height of Sarah

using proportion

[tex]\frac{50}{75}=\frac{x}{6} \\ \\x=6*50/75\\ \\x= 4\ ft[/tex]

Final answer:

Using the properties of similar triangles, the height of Sarah is found to be 4 feet tall, given the proportions between the building's height and shadow and Sarah's shadow.

Explanation:

The question requires us to use the properties of similar triangles to find the height of Sarah given that a building 50ft high casts a 75ft shadow and Sarah casts a 6ft shadow. Since the triangles are similar, their sides are in proportion.

To find Sarah's height, we can set up a proportion using the corresponding sides of the similar triangles:

Building's height / Building's shadow = Sarah's height / Sarah's shadow

50ft / 75ft = Sarah's height / 6ft

To solve for Sarah's height, we can cross-multiply and divide:

(50ft × 6ft) / 75ft = Sarah's height

300ft² / 75ft = 4ft

Therefore, Sarah is 4 feet tall.

Answer:

(6,-31)

Step-by-step explanation:

f(x) = (x-6)^2 -31

This is in the form

f(x) = (x-h)^2 +k

where (h,k) is the vertex

(6,-31) is the vertex of the parabola