the function f(x)= 3x squared+12x+11 can be written in vertex form as A. f(x)=(3x+6) squared-25 B. f(x)=3(x+6) squared-25 C. f(x)= 3(x+2) squared-1 D. f(x)= 3(x+2) squared+7) explain and show your work ​and what is vertex form

tan(theta)=tan(pi+theta)

So your answer would be 5pi/3

Answer:

The angle measure [tex]\frac{5\pi}{3}[/tex] has the same value as [tex]\frac{2\pi}{3}[/tex]

Step-by-step explanation:

[tex]tan(\theta)=tan(\pi+\theta)[/tex]

[tex]tan(\theta)=tan(\pi+\theta)[/tex]

so, here [tex]\theta=\frac{2\pi}{3}[/tex]

[tex]tan(\frac{2\pi}{3})=tan(\pi+\frac{2\pi}{3})[/tex]

[tex]tan(\frac{2\pi}{3})=tan(\frac{5\pi}{3})[/tex]

Hence, The angle measure [tex]\frac{5\pi}{3}[/tex] has the same value as [tex]\frac{2\pi}{3}[/tex]

ANSWER

A. [-3,4]

EXPLANATION

We want to determine from the graph the interval on which

[tex]f(x) \geqslant 0[/tex]

This refers to the interval on which the the graph lies on or above the x-axis.

This interval is from x=-3 to x= 4

The correct choice is A. [-3,4]

Answer:

x = classic

x + 2342 = contemporary

3500 = x + (x +2342)

3500= 2x + 2342

and then you would just solve the equation, but it does not ask for a solution

Step-by-step explanation:

x = classic

x + 2342 = contemporary

3500 = x + (x +2342)

3500= 2x + 2342

Answer: Jared has a total of 3500 dvds of two types, contemporarys and classics.

we also know that Jared has 2342 more contemporary dvds than classics.

Now, how we write this as system of equations?

if x is the number of classics, and y the number of contemporarys, then:

1) x + y = 3500

and

2) y - x = 2342

this is the system of equations, but just for fun we can solve it!

in the second equation we can leave y alone in the right side ande get: y = 2342 + x, and then replace it in the first equation.

x + y = 3500

x + (2342 + x) = 3500

2*x = 3500 - 2342 =1158

x = 1158/2 = 579

So Jared has 579 classic titles.

then:

y + x =3500

y + 579 = 3500

y = 3500 - 579 = 2921

And Jared has 2921 contemporary titles.

the answer is x = -28

ANSWER

[tex]P(4)'= \frac{1}{3} [/tex]

EXPLANATION

The sample space of rolling a 6-sided die is

{1,2,3,4,5,6}

The even numbers apart from 4, are

{2,6}

The probability of rolling an even number that is not 4 is

[tex]P(4)'= \frac{2}{6} = \frac{1}{3} [/tex]

Answer:

The answer would be eight.

Step-by-step explanation:

The range is the difference between the largest and smallest number you need to make sure you have them in order or it won’t work.

Answer:

the answer is eight

Step-by-step explanation:

Answer:

the answer is 77

Step-by-step explanation:

46.20 divided by 60 cents = 77

tan <B is 16/30 which is 8/15

Answer:

Step-by-step explanation: It’s gotta be b or c.

Answer:

H

Step-by-step explanation:

The parallel line BC divides the sides AD and AE in proportion, that is

[tex]\frac{AB}{BD}[/tex] = [tex]\frac{AC}{CE}[/tex], that is

[tex]\frac{2}{3}[/tex] = [tex]\frac{AC}{4}[/tex] ( cross- multiply )

3AC = 8 ( divide both sides by 3 )

AC = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex], hence

AE = AC + CE

     = 2 [tex]\frac{2}{3}[/tex] + 4 = 6 [tex]\frac{2}{3}[/tex] → H

Answer:

Step-by-step explanation:

The given expression is x- [tex]\frac{15}{x}[/tex] = 2

and we have to solve this for the value of x,

( x- [tex]\frac{15}{x}[/tex]) = (2)

[tex]\frac{x^{2}-15 }{x} =2[/tex]

x² - 15 = 2x

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

x ( x-5 ) + 3(x - 5) = 0

( x+3 )( x-5 ) = 0

( x+3) = 0

x = -3

or ( x- 5 ) = 0

x = 5

Therefore, x = -3 and 5 will be the solution.

Option E is the answer.

at 10:30 there will be 64 bacteria

Answer:

At 10:20 a.m., there will be 16 cells in the bottle.

At 10:30 a.m. there will be 64 cells in the bottle .

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

Kumar needs only $80 to buy bicycle.

Subtraction is mathematic operation. Which is used to remove terms or objects in expression.

Given, bicycle costs $375.25.

And so for he has saved $295.25

To find the rest of money, we subtract the total cost to a saved money.

required money = $375.25 - $295.25 = $80

Therefore, he needs only $80 to buy a bicycle.

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Answer:

(2,-1)

Step-by-step explanation:

The solution of the system of equations 2x + 3y = 1 and 5x + 2y = 8 is x = 2 and y = -1.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.

And simultaneous equation is the system of equation.

Given:

System of equations,

2x + 3y = 1,  {equation 1}

And 5x + 2y = 8.    {equation 2}

To find the solution:

Multiply 5 to the equation 1 and multiply 2 to the equation 2.

And then subtract the equation 2 to the equation 1.

We get,

11y = -11

y = -1

And 2x = 4

x = 2

Therefore, the solution is x = 2 and y = -1.

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Answer: OPTION C

Step-by-step explanation:

Complete the square:

Having the equation in the form [tex]ax^2+bx=c[/tex], you need to add [tex](\frac{b}{2})^2[/tex] to both sides of the equation:

You can identify that "b" in the equation [tex]x^2+6x=5[/tex] is:

[tex]b=6[/tex]

Then:

[tex](\frac{6}{2})^2=3^2[/tex]

Add this to both sides:

[tex]x^2+6x+3^2=5+3^2[/tex]

Rewriting, you get:

[tex](x+3)^2=14[/tex]

Solve for "x":

 [tex]x+3=\±\sqrt{14}\\\\x+3=\±\sqrt{14}\\\\x=\±\sqrt{14}-3[/tex]

Then, the solutions are:

[tex]x=-3+\sqrt{14}\ or\ x=-3-\sqrt{14}[/tex]

I think 5x represents 90 degrees.

5x = 90

x = 90/5

x = 18

ANSWER

[tex]x = 18 \degree[/tex]

EXPLANATION

A semicircle subtends an angle of 90° at the circumference.

From the diagram, the semicircle subtends an angle of (5x)° at the circumference.

We equate this angle to 90° and solve for x.

This implies that,

[tex]5x = 90 \degree[/tex]

Divide both sides by 5.

[tex]x = \frac{90}{5} [/tex]

[tex]x = 18 \degree[/tex]

Answer:

Yes, the following equation is a quadratic function in vertex form

Step-by-step explanation:

we know that

The quadratic function of the vertical parabola into vertex form is equal to

[tex]y=a(x-h)^{2} +k[/tex]

where

(h,k) is the vertex of the parabola

If the coefficient a is > 0 ----> the parabola open upward (vertex is a minimum)

If the coefficient a is < 0 ----> the parabola open downward (vertex is a maximum)

in this problem we have

[tex]y=4(x-2)^{2} +6[/tex]

The squared term contain the x-coordinate of the vertex

[tex]h=2[/tex]

The constant term is the y-coordinate of the vertex

[tex]k=6[/tex]

The vertex is the point (2,6)

The coefficient is equal to

[tex]a=4[/tex] ----> open upward (vertex is a minimum)

Down

The formula for a quadratic equation is y = ax^2 + bx + c. In this case, a = -4, b = 8, and c = 12. The direction of the parabola can be determined by a. If a is positive, the parabola opens upwards, and if a is negative, the parabola will open downwards.

c = 2x + 3. The third side of the triangle is 2x + 3.

The key to solve this problem is using the perimeter of a triangle equation which is P = a + b + c, where a, b, and c are the sides of the triangle.

We know that the perimeter P = 3x² + 7x, let's suppose a = 6x - 7, b = 3x² - x + 4, and c is the unknow.

Clearing c from the equation:

c = P - (a + b)

c = 3x² + 7x - (6x - 7 + 3x² - x + 4)

c = 3x² + 7x - 6x + 7 - 3x² +x - 4

Grouping the equal terms:

c = 3x² - 3x² + 7x + x - 6x + 7 - 4

c = 0 + 8x - 6x + 3

c = 2x + 3

Answer:

[tex]\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]

Step-by-step explanation:

The given logarithmic expression;

[tex]3\log_2x-(\log_23-\log_2(x+4))[/tex]

Expand the parenthesis:

[tex]3\log_2x-\log_23+\log_2(x+4)[/tex]

Use the product rule on the last two terms;

[tex]\log_aM+\log_aN=\log_aMN[/tex]

[tex]3\log_2x-\log_23(x+4)[/tex]

[tex]3\log_2x-\log_23(x+4)[/tex]

Apply the power rule:

[tex]\log_2x^3-\log_23(x+4))[/tex]

We now apply the quotient rule of logarithms:

[tex]\log_aM+\log_aN=\log_a(\frac{M}{N})[/tex]

[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{x^3}{3(x+4)})[/tex]

Or

[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]

Answer:

5 : 4

Step-by-step explanation:

To simplify the ratio , find the greatest common factor of 60 and 48, then divide both parts of the ratio by it

the greatest common factor of 60 and 48 is 12, hence

60 ÷ 12 : 48 : 12 = 5 : 4 ← in simplest form

30:24 = 10:8 = 5:4

Step-by-step explanation:

First divide them by 2

then divide the answer (30:24) with 3

then divide the answer with 2

And the answer comes as 5:4

Answer:

9?

Step-by-step explanation:

Answer:

(-1,6)

Step-by-step explanation:

P= 1A + 2B

AP + PB

= 1(-3,6) + 2(0,6)

3

= (-3,6) + (0,12)

3

= (-3 + 18)

3

= (-1,6)

Answer:

-x^2+21x+18/ x^3-x^3-16x-20

Step-by-step explanation:

-x^2+21x+18/ (x-5)(x^2+4x+4)

= -x^2+21x+18/ x^3+4x^2+4x-5x^2-20x-20

= -x^2+21x+18/ x^3-x^2-16x-20

Looking at the shape, you should be able to tell immediately that this will be an absolute value function. Noticing that it is both 1 over and 1 up, you will get the equation y = - | x + 1 | + 1

Answer:

y=-|x+1|+1

Step-by-step explanation:

Answer:

f(-3) = -5/2

f(-1) = 3/2

f(3) = 3/4

Step-by-step explanation:

To find the values, we just have to replace by the values given (-3, -1, 3).  Since there are different definitions of the function depending on the range of x, we just have to pick the right one before replacing x by its value.

x = -3

When x ≤ -1, the function is 7/2 + 2x

So, x = -3 is certainly  ≤ -1, so....

f(-3) = 7/2 + 2 (-3) = 7/2 - 6 = 7/2 - 12/2 = -5/2

x = -1

When x ≤ -1, the function is 7/2 + 2x

So, we do the same calculation:

f(-1) = 7/2 + 2 (-1) = 7/2 - 2 = 7/2 - 4/2 = 3/2

x = 3

When x ≥ 3, the function is defined as: (1/4)x or x/4.  So,

f(3) = 3/4

The output values of f(-3), f(-1), and f(3) in the piece-wise function are -5/2,  3/2, and 3/4 respectively.  

To determine the output value of f(-3), f(-1), and f(3) in the piece-wise function, we simply plug in the values of x in the piece that is within the domain.

To solve for f(-3), plug x = -3 into the piece with the domain of x ≤ -1:

f( x ) = 7/2 + 2x

Pug in x = -3:

f( -3 ) = 7/2 + 2(-3)

f( -3 ) = -5/2

To solve for f(-1), plug x = -1 into the piece with the domain of x ≤ -1:

f( x ) = 7/2 + 2x

Pug in x = -1:

f( -3 ) = 7/2 + 2(-1)

f( -3 ) = 7/2 - 2

f( -3 ) = 3/2

To solve for f(3), plug x = 3 into the piece with the domain of x ≥ 3:

f( x ) = (1/4)x

Pug in x = 3:

f( 3 ) = (1/4) × 3

f( 3 ) = 3/4

Therefore, the values for f(-3), f(-1), and f(3) are -5/2,  3/2, and 3/4 respectively.  

Answer:

-12

Step-by-step explanation:

Is it equal to the measure if angle C

In an isosceles triangle, the measure of the vertex angle (Angle B in this case) is equal to the measure of the other base angle. This is because in an isosceles triangle, the angles opposite the equal sides are also equal.

In an isosceles triangle ABC, Angle B, the angle between the two sides of equal length, is known as the vertex angle. The two base angles of an isosceles triangle are always equal. Therefore the measure of Angle B will be equal to the measure of Angle C. This property comes from the fundamental characteristics of an isosceles triangle, where two sides are of equal length and the angles opposite these equal sides are also equal.

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Answer:

length of segment AB is 13

OR

AB = 13

Step-by-step explanation:

Use the Pythagorean Theorem with c being the length of segment AB.

a^2 + b^2 = c^2

5^2 + 12^2 = c^2

169 = c ^2 (square root both sides to get c by itself)

13 = c

Answer

x = 20

Explanation

Multiply the entire equation by 2 to get rid of the fraction.

x/2 * 2 = x

-4 * 2 = -8

6 * 2 = 12

Now, we have:

x - 8 = 12

To complete, add 8 to both sides

x = 20

For this case we must find the value of "x" of the following equation:

[tex]\frac {x} {2} -4 = 6[/tex]

So:

We add 4 sides of the equation:

[tex]\frac {x} {2} = 6 + 4\\\frac {x} {2} = 10[/tex]

We multiply by 2 on both sides of the equation:

[tex]x = 20[/tex]

Thus, the value of the variable x is 20

Answer:

[tex]x = 20[/tex]