f(x) = x ^ 2 + 6x - 4 in vertex form

Answer:

False

Step-by-step explanation:

numbers are integers, the integers are negative, zero and positive, 

while natural numbers are only positive, 

therefore the statement is false

 . False. Integers comprise negative and positive numbers (...- 3, -2, -1, 0, 1, 2, 3 ...) and natural numbers only comprise positive integers (0, 1, 2, 3 ...)  

Answer:

you should drag to x axis #3

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

[tex]y=x\,(10-x)=10x-x^2[/tex]

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

[tex]y=ax^2+bx+c[/tex]

is given by the formula:

[tex]x_{vertex}=-\frac{b}{2\,a}[/tex]

which in our case gives:

[tex]x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5[/tex]

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

[tex]y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25[/tex]

Answer:

4.8

Step-by-step explanation:

Multiply the Price Percentage by the Original Price

Multiply the original price and the percentage that represents the sale price; the result is the sale price of the blazer in dollars: $90 × 0.7 = $63. So if the blazer is on sale for 30 percent off, you'll pay the remaining 70 percent of the price, which is $63.

Answer:

third function: first domain

first function: second domain

last function: third domain

second function: last domain

Answer:

1) Step 1- Question. The "thing" that you want to know. ...

Step 2-Research. Conduct research. ...

Step 3-Hypothesis. Educated guess or prediction of the outcome experiment.

Step 4-Experiment. Test the hypothesis.

Step 5-Observations.

Step 6-Results/Conclusion. Determine if your hypothesis was correct or not.

Step 7- Communicate.

2) Being able to communicate the relevance and impact of their ideas and discoveries can enhance scientists' ability to secure funding or find a job. It allows them to write better and more comprehensible research papers.

3) 1) People should be treated as autonomous.

   2) People with diminished autonomy should be protected.

    3) Do no harm.

     4) Maximize benefits for participants and minimize risks for participants.

Step-by-step explanation:

Answer:

True, r represents the distance from a point to the pole when plotting that point in polar coordinates.

Step-by-step explanation:

Given: The statement '' The value of r represents the distance from a point to the pole when plotting that point in polar coordinates ''

To state: whether the given statement is true or false

Solution:

In the cartesian coordinate system, any point is represented by the coordinates  [tex](x,y)[/tex]

In polar-coordinates system, distance of the point from the origin (pole)(r) and the angle [tex](\theta)[/tex] that the line joining the point to the origin makes with the positive  x -axis are used as polar coordinates. Polar coordinates are of form [tex](r,\theta)[/tex]

True, r represents the distance from a point to the pole when plotting that point in polar coordinates.

Answer:

true

Step-by-step explanation:

trust

Answer:   [tex]\bold{y=7cos\bigg(\dfrac{2\pi}{7}x\bigg)}[/tex]

Step-by-step explanation:

y = A cos (Bx - C) + D

The minimum is -7 and the max is 7 so A = 7 and D = 0

Period is 7.  Since P = 2π/B then 7 = 2π/B --> B = 2π/7

Nothing was stated about a phase shift so you can use any value for C. I chose C = 0.

Now, input A = 7, B = 2π/7, C = 0, & D = 0 into the equation

[tex]y=7\cos\bigg(\dfrac{2\pi}{7}x-0\bigg)+0\\\\\\\text{Simplify}:\\y=7\cos\bigg(\dfrac{2\pi}{7}x\bigg)[/tex]

Answer:

200

Step-by-step explanation:

[tex]\dfrac{(6.6\times 10^{-2})}{(3.3\times 10^{-4})}= \\\\\\\dfrac{6.6}{3.3}\times \dfrac{10^{-2}}{10^{-4}}=\\\\\\2\times 10^{-2-(-4)}= \\\\2\times 10^2=\\\\200[/tex]

Hope this helps!

Answer:

6.

Step-by-step explanation:

Both of the arcs that subtend the segments are congruent. By definition, both segments are congruent as well.

Since the length of segment EG is 6, the length of segment FG must be 6.

I hope this helps!

Answer:

f(x) = x^2 + 11x + 18.

Step-by-step explanation:

As the zeroes are -2 and -9 the factored form  is

f(x) = a(x - (-2))(x -  (-9))   where a is some constant.

As we want any quadratic function with theses zeros we  can let a = 1 so:

f(x) = (x + 2)(x + 9)

f(x) = x^2 + 2x + 9x + 18

f(x) = x^2 + 11x + 18.

The required quadratic function is given as x²+11x+18 = 0,

Given that,
To write a quadratic function f whose zeros are -2 and -9

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
x = -2 and x = -9
x  2 = 0  and x + 9 = 0
The function is given as,
(x + 2)(x + 9) = 0
x²+11x+18 = 0,

Thus, the required quadratic function is given as x²+11x+18 = 0,

learn more about function here:

brainly.com/question/21145944

#SPJ2

Answer:

the value of  line ST is 6 centimeters long

Step-by-step explanation:

The attached image in conjunction with the question is shown in the file below.

We can see from the RT segment that the equation given can be expressed as:

[tex]\mathbf{2x+3x = 10}[/tex]

so; if we solve for x ; we have ;

[tex]\mathbf{5x= 10}[/tex]

divide both sides by 5 ; we have:

[tex]\mathbf{\dfrac{5x}{5}= \dfrac{10}{5}}[/tex]

[tex]\mathbf{x=2}[/tex]

However ; the value of ST is represent by the information:

[tex]\mathbf{ ST = 3x}[/tex]

replcaing the value for x; we have :

[tex]\mathbf{ ST = 3*2}[/tex]

[tex]\mathbf{ ST = 6}[/tex]

Thus, the value of  line ST is 6 centimeters long

Answer:

C. 6 centimeters

May I have brainliest please? :)

Answer: y-2=2/5(x-17), y=1/3x-2/5

Step-by-step explanation:

Answer:

1.)y+6=2/5(x+3)

2.)y=1/3x-2/5

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

1 1/2 = 3/2

3/2 / 1/4 = 3/2 * 4 = 12 / 2 = 6

Answer:

6

Step-by-step explanation:

One recipe uses 1/4 cup of red onions.

They have 1 1/2 cups of red onions.

We need to divide 1 1/2 by 1/4.

First, we convert the mixed numeral into a fraction. Then, to divide by a fraction, we multiply by the reciprocal of the fraction.

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

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

[tex] = \dfrac{3}{2} \times \dfrac{4}{1} [/tex]

[tex] = \dfrac{12}{2} [/tex]

[tex] = 6 [/tex]

Answer:

i think its A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

they share the same min of -3

Answer:

The minimum values are equal

Step-by-step explanation:

The minimum for f(x) = (4,-3)  since the parabola is written in vertex form

y = a(x-h)^2 +k

The minimum is at x=4 the the y value is -3

Looking at the graph for g(x) the minimum is at x=-3 y = -3

Since the y values are equal

The minimum values are equal

Answer:

The step to take to avoid fraction is to solve for y in equation 2

Step-by-step explanation:

Given

-9x+ 4y =- 10

-9x+ 3y = 3

Required:

Step for solving using substitution (avoiding fraction)

Let -9x+ 4y =- 10  represent equation 1

and -9x+ 3y = 3 represent equation 2

The following points are to be noted

Having said that, the step to take to avoid fraction is to solve for y in equation 2

Check

[tex]-9x+ 3y = 3[/tex]

Add 9x to both sides

[tex]9x-9x+ 3y = 3 + 9x[/tex]

[tex]3y = 3 + 9x[/tex]

Divide through by 3

[tex]\frac{3y}{3} = \frac{3 + 9x}{3}[/tex]

[tex]y = \frac{3 + 9x}{3}[/tex]

Split fraction

[tex]y = \frac{3}{3} + \frac{9x}{3}[/tex]

[tex]y = 1 + 3x[/tex]

At the point, the expression of y can then be substituted in equation 1

Answer: solve for y in the second equation

Step-by-step explanation:

I got it right on edenuity

Answer:

{ 2 , 4 , 9 , 16 }

Step-by-step explanation:

Answer:

range ={ 2,4,9,16}

Step-by-step explanation:

range is  related to y coordinate of the points

Add 1 to both sides

Multiply both sides by 4

Take the square root of both sides

Subtract 5 from both sides

In this problem, you are trying to isolate the x. In order to do that you have to get rid of all the other numbers surrounding it. The first thing you're going to do is move the 1. To get rid of the -1 you have to do a +1. What you do to one side you have to do to the other. Therefore, you have to add +1. Next, you will move the 1/4 by multiplying by the reciprocal which is 4 (because 1/4 x 4 = 1, this gets rid of the 1/4 on the left side). After that you will do the opposite of square, which is to take the square root. Lastly, you will subtract the five for the same reason you added the 1.

Answer:

x = 50

Step-by-step explanation:

Let x be the original number.

This question can be expressed as:

0.4x = 20

0.4 of the original number is 20.

Now, we can directly solve for x:

4x = 200

x = 50

Answer:

8

Step-by-step explanation:

40 times 0.20 is 8.

You can also use 40 percent of 20, which is also 8, but the original is easier to comprehend.

Answer:

ok

Step-by-step explanation:

Answer:

3x-3y=-4 and y+2=3/4x+4

Step-by-step explanation:

parallel line equations have the same slope. just find the equation that also has positive 3 in this problem

Answer:

B & D

Step-by-step explanation:

Answer:

WALK=9 PUPILS

BUS=12 PUPILS

CAR=4 PUPILS

BIKE=4 PUPILS

Step-by-step explanation:

TOTAL=360/10 = 36                          120+90=210

BUS=120/10=12                                  360-210=75/2=37.5

WALK=90/10=9

CAR=37.5/10=3.75=4

BIKE=37.5/10=3.75=4

Answer: VA: x = {-5, 5), HA: y = 0, Zeros: x = 0

Step-by-step explanation:

[tex]f(x) = \dfrac{5x}{x^2-25}[/tex]

Vertical asymptotes: The denominator cannot equal zero.

x² - 25 = 0  

(x - 5)(x + 5) = 0

x = 5, x = -5

Horizontal Asymptote: Let m represent degree of numerator and n represent the degree of the denominator.

For the given equation, m = 1 and n = 2 so we use option 3 --> y = 0

Zeros: Set the equation equal to zero and solve for x.

[tex]0=\dfrac{5x}{x^2-25}[/tex]

Multiply both sides by x²- 25   -->    0 = 5x

Divide both sides by 5       -->          0 = x

Using function concepts, it is found that:

The function is given by:

[tex]f(x) = \frac{5x}{x^2 - 25}[/tex]

Applying the subtraction of perfect squares, the function will be given by:

[tex]f(x) = \frac{5x}{(x - 5)(x + 5)}[/tex]

The zero is the value of x for which:

[tex]f(x) = 0[/tex]

In a fraction, it is when the numerator is zero, thus:

[tex]5x = 0[/tex]

[tex]x = \frac{0}{5}[/tex]

[tex]x = 0[/tex]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, thus:

[tex](x - 5)(x + 5) = 0[/tex]

[tex]x = \pm 5[/tex]

The horizontal asymptote is:

[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]

Hence:

[tex]y = \lim_{x \rightarrow \infty} \frac{5x}{x^2 - 25} = y = \lim_{x \rightarrow \infty} \frac{5x}{x^2} = y = \lim_{x \rightarrow \infty} \frac{5}{x} = 0[/tex]

A similar problem is given at https://brainly.com/question/23690889

Answer:

40%=45

So, 100%=45*100/40

=112.2

Answer:

The answer would be C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

[tex]\sqrt{\dfrac{36}{25}}=\sqrt{\dfrac{6^2}{5^2}}=\dfrac{6}{5}[/tex]

Therefore, the correct answer is choice C. Hope this helps!

Answer:

The answer would be, 36 sq m

Answer:

-74

Step-by-step explanation:

Answer: -74

Step-by-step explanation: