Determine the vertex form of g(x) = x^2 + 2x – 1. Which graph represents g(x)?

Answer:

(2, 5)

Step-by-step explanation:

Given:

To find the components of [tex]\overrightarrow{RS}[/tex] we need to go from R to O and then O to S.  Remember that [tex]\overrightarrow{RO}[/tex] is the negative of [tex]\overrightarrow{OR}[/tex].  Therefore:

[tex]\begin{aligned} \displaystyle \overrightarrow{RS} & =\overrightarrow{RO}+\overrightarrow{OS}\\& = \overrightarrow{OS}-\overrightarrow{OR}\\& =\binom{-2}{12}-\binom{-4}{7}\\& =\binom{2}{5}\end{aligned}[/tex]

Therefore, the component form (x, y) of the vector [tex]\overrightarrow{RS}[/tex] is (2, 5)

a. A critical point at x = 25 would mean f'(25) = 0 or doesn't exist. We have derivative

[tex]f(x) = x - k \sqrt x \implies f'(x) = 1 - \dfrac k{2\sqrt x}[/tex]

so that

[tex]f'(25) = 1 - \dfrac k{2\sqrt{25}} = 1 - \dfrac k{10} = 0 \implies \boxed{k=10}[/tex]

b. Taking the second derivative, we get

[tex]f''(x) = \dfrac k{4 x^{3/2}} = \dfrac5{2 x^{3/2}}[/tex]

At x = 25, the second derivative has a positive sign,

[tex]f''(25) = \dfrac 5{2 \times 25^{3/2}} = \dfrac 5{2\times5^3} = \dfrac1{50} > 0[/tex]

which means f(x) is concave upward around x = 25, so this critical point is a local minimum.

Answer:

see the attachment photo!

Answer:

see the attachment photo!

Answer: The correct answer is 135 in².

Step-by-step explanation: An area of a polygon is this:

Area = (number of sides × length of one side × apothem)/2

(5 x 6 x 9) / 2 = 135

Answer:

i think the answer is 278.75

Area of the plot = 193 sq.yd.  , Option B is the correct answer.

Area is the space occupied by a flat surface or an object .

It is measured in square units

It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.

It is given that

A developer buys an empty lot to build a small house.

area of the lot = ?

The figure is incomplete and the complete figure is attached with the answer.

To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure

Area of the first triangle = (1/2) * base * height

By Calculation

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5

=85 sq.unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq.unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

The area of the plot = 85+36+63+9

Area of the plot = 193 sq.yd.

Therefore , Option B is the correct answer.

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Answer:

Step-by-step explanation:

Area of the plot = 193 sq.yd.  , Option B is the correct answer.

What is Area ?

Area is the space occupied by a flat surface or an object .

It is measured in square units

It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.

It is given that

A developer buys an empty lot to build a small house.

area of the lot = ?

The figure is incomplete and the complete figure is attached with the answer.

To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure

Area of the first triangle = (1/2) * base * height

By Calculation

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5

=85 sq.unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq.unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

The area of the plot = 85+36+63+9

Area of the plot = 193 sq.yd.

Therefore , Option B is the correct answer.

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The  equation  that can be used to find how many nickels logan uses is: 50÷5.

Given:

Total pennies=50

Logan got a nickel of 5 pennies=1

Hence:

Number of nickels=1÷5×50

Number of nickels=50÷5

Number of nickels=10 nickels

Therefore the  equation  that can be used to find how many nickels logan uses is: 50÷5.

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Answer:

-50

Step-by-step explanation:

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100

just means,

1 - 2 = -1

3 - 4 = -1

5 - 6 = - 1

7 - 8 = - 1

99 - 100 = -1

basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1

[tex](-1)^{n}[/tex]

Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:

S = 1 − 1 − 1 + ..., so

1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S

1 - S = S

1 = 2*S

resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1

1/2 of the last term is 100 x 1/2 = 50

This because you are using 2 numbers per -1

example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted

Answer:

2 up 3 run

Step-by-step explanation:

just count the squares until u reach a part where the line touches again

Answer:

[tex]\boxed{ \rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3} } \rm (rounded \: to \: nearest \: tenth)[/tex]

Step-by-step explanation:

Given dimensions:

Given value of π :

To find:

Solution:

Here, we'll need to use the formulae of the volume of cylinder,to find it's volume.Its actually like a savior while solving these type of questions.

[tex] \pink{\star}\boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}\pink{\star}[/tex]

where,

Plug/substitute them onto the formulae,then simplify it using PEMDAS.

[tex] \rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} \times 3[/tex]

[tex] \rm \: Volume_{(Cylinder)} = \pi(49)(3)[/tex]

[tex] \rm \: Volume_{(Cylinder)} = 147\pi \: [/tex]

[tex] \rm \: Volume_{(Cylinder)} = 147 \times 3.14[/tex]

[tex] \rm \: Volume_{(Cylinder)} = 461.58 \: {m}^{3} [/tex]

[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3}} \rm (rounded \: to \: nearest \: tenth) \: [/tex]

Hence, we can conclude that:

The volume of the cylinder is approximately

461.6 m³.

[tex] \rule{225pt}{2pt}[/tex]

Answer:

X=-1

Y=1

Step-by-step explanation:

6x-12y

-18

) 6x + 4y

-

-2

Subtract the two equations

6x - 12y - (6x + 4y) = -18 - (-2)

Determine the sign

6x- 12y - 6x- 4y

=-18 + 2

Simplify

-12y

- Ay

=-18 + 2

Solve the equation

Substitute

6×+4

-2

Solve the equation

X=

The true solution to the system of inequities shown is B; All values that satisfy  [tex]y \leq \dfrac{ 1}{3}x - 3[/tex] are solutions.

When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalities.

A collection of inequalities for which we consider a common solution for all inequalities is called a system of inequalities.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true.

A set of such values is called a solution set to the considered equation or inequality.

The true solution to the system of inequities shown is B;

All values that satisfy  [tex]y \leq \dfrac{ 1}{3}x - 3[/tex] are solutions.

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Answer:

The bottom right line plot.

Step-by-step explanation:

In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.

Let's first consider: the fact that a new computer loses 1/2 of its value

 ⇒ third choice and fourth choice are eliminated

    ⇒ because of the graph project the computer's value as growing over  

         years

Now let's try to set up an equation:

After 1st year ⇒ Computer's value = [tex]total_.value*\frac{1}{2}[/tex]

After 2nd year ⇒ Computer's value = [tex]total_.value*\frac{1}{2}*\frac{1}{2}=total_.value*(\frac{1}{2} )^2[/tex]

After 3rd year ⇒ Computer's value =[tex]total_.value*\frac{1}{2}*\frac{1}{2}* \frac{1}{2}=total_.value*(\frac{1}{2})^3[/tex]

 ..... (Hopefully you see a pattern)

After x year ⇒ Computer's value = [tex]total_.value*(\frac{1}{2})^x[/tex]

Therefore, the equation is: [tex]total_.value*(\frac{1}{2})^x[/tex]

  ⇒that means the graph has to exponentially decreasing as it has

     an exponent (meaning the function is exponential) and a base less

     than 1 (meaning that the function is decreasing)

Answer: Choice (1)

Hope that helps!

Answer:

A

Step-by-step explanation:

After x year, computer's value will be (1/2)^x

So the graph has to exponentially decreasing.

Both A and B show decreasing value but B is linear. So B is incorrect

C and D show increasing value so they are both incorrect.

Answer:

  (1/4, 5 7/8)

Step-by-step explanation:

The vertex is the extreme point of the graph. Here, it is a minimum.

For this quadratic function, a graphing calculator can tell you exactly what the vertex is. (No approximation is required.)

__

The graphing calculator in the attachment shows the vertex is ...

  (0.25, 5.875) = (1/4, 5 7/8)

Answer:

b ≈ 7.8

Step-by-step explanation:

using the law of sines

∠ A = 180° - 105° - 40° = 180° - 145° = 35° , then

[tex]\frac{b}{sin40}[/tex] = [tex]\frac{7}{sin35}[/tex] ( cross- multiply )

b × sin35° = 7 × sin40° ( divide both sides by sin35° )

b = [tex]\frac{7sin40}{sin35}[/tex] ≈ 7.8 ( to the nearest tenth )

The simplified expression is [tex]\frac{-1}{9x} -9x - 10[/tex].

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

Here, the given expression

           [tex]\frac{1}{x}+\frac{-10x/9}{x^2}-9x-10[/tex]

            [tex]\frac{1}{x}+\frac{-10}{9x}-9x-10[/tex]

             [tex]\frac{9-10}{9x} -9x -10[/tex]

                 [tex]\frac{-1}{9x} -9x - 10[/tex]

Thus, the simplified expression is [tex]\frac{-1}{9x} -9x - 10[/tex].

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△STU is mapped to △PQR with center of dilation (-1.5, -1.5) and a scale factor of 2 and reflected about the x-axis.

From the given graph, we can see that;

SU is 1.5 units and the corresponding side of the dilated figure is 3 units. Thus, the scale factor of dilation is; 3/1.5 = 2

Now, we can see clearly that it is reflected about the x-axis as the x-values remain negative in △STU while the y-values are now positive in △PQR.

Lastly, we can see the dilation was with center (-1.5, -1.5)

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The sequence is an arithmetic sequence and the expression used to find the nth term would be 3n option fourth I and II is correct.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a sequence:

3, 6, 9, 12…

First term a  = 3

Common difference d = 6 - 3 = 3

This is an arithmetic sequence.

nth term of the arithmetic sequence:

a(n) = 3 + (n-1)(3)

a(n) = 3n

Plug n = 5

a(5) = 3(5) = 15

Thus, the sequence is an arithmetic sequence and the expression used to find the nth term would be 3n option fourth I and II is correct.

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A ratio shows us the number of times a number contains another number. The number of baskets Jasmine made is 24.

A ratio shows us the number of times a number contains another number.

The ratio of the number of baskets she missed during the tournament to the number of baskets she made is 3:8. Therefore, we can write,

(Number of baskets Missed)/ (Number of baskets made) = 3/8

If Jasmine missed 9 baskets during the tournament, then the ratio can be rewritten as,

(Number of baskets Missed)/ (Number of baskets made) = 3/8

9 / (Number of baskets made) = 3/8

(9×8)/3 = (Number of baskets made)

Number of baskets made = 24 baskets

Hence, the number of baskets Jasmine made is 24.

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The function g(x) = √(x - 8) represents a horizontal shift of the square root parent function f(x) = √x, to the right by eight units. Option B.

To horizontally shift the square root parent function, f(x) = √x, right eight units, we need to replace x with (x - 8) in the function. This shift will move the entire graph eight units to the right.

So, the equation of the new function, let's call it g(x), will be:

g(x) = √(x - 8)

Therefore, the correct choice is  g(x) = √(x - 8).

This means that for any given value of x, we substitute (x - 8) in the original square root function. The effect of this shift is that all x-values on the graph of g(x) will be eight units greater than their corresponding x-values on the graph of f(x).

For example, if we consider the point (8, 2) on the graph of f(x), after the horizontal shift, it will be located at (16, 2) on the graph of g(x). Similarly, the point (0, 0) on the graph of f(x) will shift to (8, 0) on the graph of g(x).

The function g(x) = √(x - 8) represents a horizontal shift of the square root parent function f(x) = √x, to the right by eight units. This transformation allows us to analyze and understand how the graph of the square root function is affected by horizontal shifts. SO Option B is correct.

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Answer:

y-intercept = 1, x-intercept= -1/4

Step-by-step explanation:

Default equation of line:

y = mx+c , where m is the slope and c is the y-intercept.

So first we will find the slope from the values given in the table.

slope of line  [tex]\frac{y1-y2}{x1-x2}\\= \frac{9-5}{2-1} \\= \frac{4}{1}\\ =4[/tex]

So take 1 random value of x and y from the table,

x =1 , y=5

5 = 4(1)+c

c = 5-4 = 1

so equation of line is y = 4x+1

and y intercept = 1

x intercept is the value of x when y = 0.

so given

y = 4x+1

0 = 4x+1

4x = -1

x = [tex]-\frac{1}{4}[/tex]

therefore x intercept = -1/4

Answer:

381

Step-by-step explanation:

232 + 88 = 320

320 + 61 = 381

Hope this helped and brainliest please

The graphed cosine function can either be:

cos(x + pi) or cos(x - pi).

We know that this function is a cosine function with a phase shift, so the general form is:

f(x) = cos(x + P).

Where P is the phase shift.

In the graph we can see that when x = 0, f(0) = -1

And we know that cos(pi) = -1 = cos(-pi)

Then we must have that:

f(0) = cos(P) = -1

By what we wrote above, we know that P can be either -pi or pi (because of the parity of the cosine). Let's say that P = pi, then the cosine function is:

f(x) = cos(x + pi).

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Answer:

⇒8(x−1)=5x

⇒8x−x=5x

⇒8x−5x=8

⇒3x=8

⇒x=

3

8

Answer:

The 6 names to circle are:

The underlined letters from those circled names are:

The letters form the phrase [tex]\underline{\text{WR}}\ \underline{\text{ON}} \ \underline{\text{G}} \ \ \ \ \ \ \underline{\text{TU}} \ \underline{\text{RN}}[/tex]  or "wrong turn". The spacing is done like that in the first version to show the various subgroups of letters.

Unfortunately the mentioned riddle at the bottom is cut off, so I don't know what the riddle is.

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

Explanation:

Here's a summary table:

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Student} & \text{Are They Correct?}\\\cline{1-2}\text{Laverna} & \textbf{Yes}\\\cline{1-2}\text{Alfonso} & \textbf{Yes}\\\cline{1-2}\text{Autumn} & \textbf{Yes}\\\cline{1-2}\text{Willa} & \text{No}\\\cline{1-2}\text{Ignacio} & \textbf{Yes}\\\cline{1-2}\text{Napoleon} & \text{No}\\\cline{1-2}\text{Kathyrn} & \textbf{Yes}\\\cline{1-2}\text{Titus} & \text{No}\\\cline{1-2}\text{Lawrence} & \textbf{Yes}\\\cline{1-2}\end{array}[/tex]

Put another way, here are the people to circle (i.e. the people who made true statements):

In the order presented above, the letters underlined are:

Through a bit of trial and error, the letters make the phrase of:

[tex]\underline{\text{WR}}\ \underline{\text{ON}} \ \underline{\text{G}} \ \ \ \ \ \ \underline{\text{TU}} \ \underline{\text{RN}}[/tex]

I'm not sure what to do with the extra "RN". It might be a typo, or it might be the case your teacher wants you to ignore repeats like this.

Answer:

1218 inches

Step-by-step explanation:

First, let's make our numbers equivalent to a certain unit. Preferably inches, since we can't turn inches into yards or feet, but we can turn yards and feet into inches.

3 yards is 9 feet, which when multiplied by 12 (12 inches in a foot) is 108.

5 feet times 12 is 60 inches.

6 inches is 6 inches.

108+60+6 is 174

Multiply all that by 7 and you get your answer of 1218 inches.

Hope this helps!

Answer: not a triangle

Step-by-step explanation:

If this were to be a triangle, the shorter sides would be 11 and 4 and the longest side would be 16.

First, we should determine if it is a triangle.

Answer:

26x^6 sqrt 23x

Step-by-step explanation: