The function f is given in three equivalent forms.
Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
f(x) = 1/2(x-5)^2-2
f(x)= 1/2(x -3) (x -7)
f(x) = 1/2x^2-5x+21/2
Write one of the zeros

Here is one way to show that the left side is identical to the right side.

[tex]\sec(x)-\tan(x)\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin(x)}{\cos(x)}\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{1-\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{\cos^2(x)}{\cos(x)} = \cos(x)\\\\\\\cos(x)=\cos(x)\\\\\\[/tex]

Throughout the entire process, the right hand side stayed the same. When working on identities, it's important to keep one side the same while you transform the other side.

Despite the two sides being identical when simplified, there is the issue of cos(x) being zero in the denominator on the left hand side. Be sure to account for this when forming the domain. No such issue occurs on the right hand side. For instance, the value x = pi/2 leads to a division by zero error when in radian mode. So if I was your teacher, I would revise the "for any value of x" and replace it with something along the lines of "for any x value in the domain".

Answer:

Infinitely many solutions

Step-by-step explanation:

[tex]4(x+6)=2(2x+12)[/tex]

[tex]4(x+6)=2(2(x+6))[/tex]

[tex]4(x+6)=4(x+6)[/tex]

Infinitely many solutions

Answer:

Hiya There....!!!

______________________

Any value of  x  makes the equation true.  Always true

Interval Notation:

( − ∞ , ∞ )

_______________________

“Most things are forgotten over time. Even the war itself, the life-and-death struggle people went through is now like something from the distant past. We’re so caught up in our everyday lives that events of the past are no longer in orbit around our minds. There are just too many things we have to think about everyday, too many new things we have to learn. But still, no matter how much time passes, no matter what takes place in the interim, there are some things we can never assign to oblivion, memories we can never rub away. They remain with us forever, like a touchstone.”

__________________________

Think of life as a mytery because well it sort of is! You don't know what may happen may be good or bad but be a little curious and get ready for whatever comes your way!!  ~Ashlynn

Answer:

Step-by-step explanation

Area of a triangle

      A = ½bh

dA/dt = ½(b(dh/dt) + h(db/dt)

dA/dt = ½(4(9) + 12(-5))

dA/dt = ½(36 - 60)

dA/dt = ½(-24)

dA/dt = -12 cm²/s

The rate of change of the area of the triangle is [tex]-12 cm^2/s[/tex].

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to an area of an open surface or even the boundary of a three-dimensional object, whereas the area of a plane region as well as plane area refers to a area of a shape or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of a curve's length.

A shape's area can be calculated by contrasting it with squares of a known size.

[tex]\frac{\mathrm{d} b(t)}{\mathrm{d} t}=-5cm/s[/tex]

[tex]\frac{\mathrm{d} h(t)}{\mathrm{d} t}=9 cm/s[/tex]

[tex]\frac{\mathrm{d}A }{\mathrm{d} t}=\frac{1}{2}\left (b\frac{\mathrm{d} h}{\mathrm{d} t} +h\frac{\mathrm{d} b}{\mathrm{d} t}\right )[/tex]

[tex]\frac{\mathrm{d} A}{\mathrm{d} t}=-12 cm^{2}/s[/tex]

Hence, The rate of change of the area of the triangle is [tex]-12 cm^2/s[/tex].

Learn more about area from link

https://brainly.com/question/25292087

#SPJ2

5x - 8 = 3x + 12

- 3x -3x

You have to subtract them both.

2x - 8 = 12

Answer:7 + (-5)= 2

Step-by-step explanation:

7 + (-5)= 2 i hope its right'

..................✨✨✨✨✨✨✨✨✨✨✨✨✨✨

Answer:

Step-by-step explanation:

Given expression:

Simplify considering like terms:

The simplified expression is:

Answer:

110

Step-by-step explanation:

We know that 5/8 of 176 so the answer is 110.

110 bottles class collect.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A sixth grade class collects 176 items.

Now,  three out of every eight items are cans

= (8- 3)

= 5

So, number of bottles class collect

= 176 x 5 / 8

= 22 x 5

= 110

Hence, 110 bottles class collect.

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ2

Answer:

I think the answer is 21.

Step-by-step explanation:

So, there are 5 spins for 3 levels + 2 spins for another 3 levels. This would be 5(3)+2(3)

15+6

21

Answer:

3 feet on each side

Step-by-step explanation:

11 - 5 = 6

6/2 = 3

Answer:

0, 10, and 20 only

Step-by-step explanation:

    −15x + 3 ≤ 7

−15x + 3 - 3 ≤ 7 - 3

          −15x ≤ 4

  −15x / -15 ≥ 4 /- 15   multiplying by a negative number reverses the sign.

               x ≥ -4 / 15

probably quicker to just plug the numbers in. Any negative input will immediately create a false statement.

Answer:

one solution.

Step-by-step explanation:

using elimination, u can get one solution

Answer:

1a. 195x

1b. 195

Step-by-step explanation:

1a. To determine the expression, we know that we need to get x amount of dogs and we need to pay $80+$65+$50 for each dog so we would be $195x.

1b. The coefficient of an expression is where a constant is multiplied by a variable and the integer is the coefficient. The integer that is being multiplied by the variable is 195 so 195 is the coefficient

hope this helps!

Mark me as brainiest if you can

The content of the mixture, which are the colour, developer, and

conditioner, are in a fixed proportion to each other.

Reasons:

The table of the amount of each product used in the mixture are;

[tex]\begin{tabular}{|c|c|c|c|}Product&Colour&Developer&Conditioner\\Amount&30 ml&60 ml&60 ml\end{array}\right][/tex]

The number of appointment per month = 50

The quantities used per month have a proportional relationship

Quantity used a month are;

Colour = 30 ml × 50 = 1,500 ml

Developer = 60 ml = × 50 = 3,000 ml

Conditioner = 60 ml × 50 = 3,000 ml

Quantity available are;

Colour = 3.5 liters

Developer = 0.5 liters

Conditioner = 2.2 liters

The quantity needed = Quantity used - Quantity available

Therefore;

Quantity needed are;

Colour = 1,500 ml - 3,500 ml = -2,000 ml

Developer = 3,000 ml - 500 ml = 2,500 ml

Conditioner = 3,000  ml = 2,200 ml = 800 ml

Therefore, Poppy has enough colour but she needs 2,500 ml of developer and 800 ml conditioner

Therefore, she should order;

3,000 ml = 3 liters of developer

1,000 ml = 1 liter of conditioner

Therefore;

Poppy is incorrect, she should order 3 liters of developer and 1 liter of conditioner.

Learn more about proportional relationships here:

https://brainly.com/question/25610267

https://brainly.com/question/14567016

Answer:

-2.4f or -8 1/3

Step-by-step explanation:

I am not sure what should be at the end of the equal sign but if it is to simplify it would be -2.4f-20

If you want to solve then you get -2.4f=20 so f=-20/2.4 which equal to -8 1/3

Answer:

Step-by-step explanation:

A = ½(b₁ + b₂)h

b₂ = 2A/h - b₁

b₂ = 2(58)/4 - 12

b₂ = 17 ft

Answer:

Calvin's number: 16 Sanjay's number: 6

Step-by-step explanation:

6 x 3 = 18, 18 - 2 = 16

16 / 2 = 8, 8 - 2 = 6

Check the picture below.

the assumption here is that both triangles are similar, if that's so, then we can use proportions to get the sides.

[tex]\stackrel{\textit{assuming both triangles are similar}}{\cfrac{x}{10}=\cfrac{15}{6x}\implies \cfrac{x}{10}=\cfrac{5}{2x}}\implies 2x^2=50 \\\\\\ x^2=\cfrac{50}{2}\implies x^2=25\implies x=\sqrt{25}\implies \boxed{x=5}[/tex]

The prime numbers after 167, 118, 82, 57, 41 are 37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2.

Prime numbers are numbers that are divisible by 1 and itself.

This are number greater than one with only two factors which are 1 and itself.

In other words, this number, when they are divided by another number other

than 1 or itself , one will get a remainder that is not zero.

Example of prime numbers are 2, 5, 7, 11, 13 etc.

The prime numbers after  167, 118, 82, 57, 41 are as follows:

37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2.

learn more about prime number here: https://brainly.com/question/26013414

Answer:

y=6x-15

Step-by-step explanation:

y-y1=m(x-x1)

y-3=6(x-3)

y-3=6x-18

y=6x-18+3

y=6x-15

Answer:

$1400

Step-by-step explanation:

The Fresh and Green Company has a savings plan for employees. If an employee makes an initial deposit of $1000, the company pays 8% interest compounded quarterly. If an employee withdraws the money after five years, how much is in the account?

First you need to make 8% into a decimal.

To do that you need to move the decimal point to spaces to the left.

8. ----- 0.8 ----- 0.08

The decimal is 0.08.

Now multiply $1000 by 0.08.

Which is $80.

Now do $80 times 5 years.

which is $400 interest.

Now add $400 to $1000.

Which is $1400.

Answer:

x = 55.6

Step-by-step explanation:

Recall the 3 main trig functions

Sin = opposite / hypotenuse

Cos = adjacent / hypotenuse

Tan = opposite / adjacent

Note that hypotenuse = longest side length

We want to find angle "x".

We are given its opposite side length ( 19 ) as well as the adjacent side length

When dealing with the opposite and adjacent we use tan

Tan = Opp / Adj

Opp = 19 and Adj = 13

Tan(x) = 19/13

* take the inverse tan of both sides *

x = 55.6

Answer:

  x = 1/3

Step-by-step explanation:

Both bases can be written as powers of 6.

  36^x = (1/6)^(x-1) . . . . . . given

  (6^2)^x = (6^-1)^(x -1) . . . . . bases as powers of 6

  6^(2x) = 6^(-x+1) . . . . . . . . . simplify exponents

  2x = -x +1 . . . . . . . . . . . . . . . .equate exponents of the same base

  3x = 1 . . . . . . . add x

  x = 1/3 . . . . . divide by 3

Answer:

the third one

zero should always come after the negatives, and a whole number should always end the set.

Answer:

Sample Response: Since the statement is true, there are an infinite number of solutions to the system. This statement also indicates that the lines are equivalent.

Answer:

-5

Step-by-step explanation:

Use the slope triangle I mentioned in a previous question

Step-by-step explanation:

you drew already the right things, you have everything.

so, what is the problem ?

the most common form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and solve for b.

so, for the 2 marked points you showed correctly the differences :

x changes by +8 (from -4 to 4).

y changes by -2 (from 3 to 1).

so the slope is -2/+8 = -1/4

the y-intercept we also see directly in the chart : +2.

Answer:

The 6-minute half-mile time is continuous data; the number of people trying out for the team is discrete data.

Step-by-step explanation: