What is the vertex form of the function: f(x) = -12x - 6x^2- 13?

Answer:

113 + 22 = 135

113.5 + 22.41 = 135.91

The answer would be 135.91

Step-by-step explanation:

Answer:

you got the answer right there

Step-by-step explanation:

Answer:

-14/25

Step-by-step explanation:

7x +2 / 2 - 5x = -2 / 5

First you can cross multiply (shown in the picture):

Next, expand the brackets:

5(7x + 2) = -2(2 - 5x) → 35x + 10 = -4 + 10x

Now, simplify:

35x + 10 = -4 + 10x → 35x - 10x = -4 - 10 → 25x = -14 → x = -14/25

Hope this helps!

Answer:

6*10^-4 has a greater value.

Step-by-step explanation:

7*10^-9=   0.000000007

6*10^-4=   0.0006

Answer:

320

Step-by-step explanation:

2 times 64 plus 4 times 48 equals 320

Answer:

RMT or TMR

Step-by-step explanation:

The angle between the sides is just the angle at which they meet. Since MR and TM meet at M, the resulting angle must include M as well as the ends of the angle, T and R.

Answer:

H(-3)= -0.5

H(0)= 7

H(1)= 9.5

Step-by-step explanation:

For H(-3)

Substitute all of the x into -3

H(-3)=2.5(-3)+7

2.5 times -3 is -7.5

-7.5+7 is -0.5

So the answer for H(-3) is -0.3

For H(0)

Substitute all of the x into 0

H(0)=2.5(0)+7

2.5 times 0 is 0

0+7 is 7

So the answer for H(0) is 7

For H(1)

Substitute all of the x into 1

2.5(1)+7

2.5 times 1 is 2.5

2.5+7 is 9.5

So the answer for H(1) is 9.5

Hope this helps!

Answer:

8.25 feet

Step-by-step explanation:

3 2/3 times 2 1/4 equals 8.25

Answer:

34 hours

Step-by-step explanation:

Lets call M the number of hours that Maddie volunteered. Ryan volunteered 1 + 3×M hours, and altogether they volunteered 45 hours, so:

1 + 3×M + M = 45

1 + 4M = 45 Subtract 1 in both sides

4M = 44 Divide both sides by 4

M = 11 hours

So Maddie volunteered 11 hours, and Ryan volunteered

1 + 3×11 = 34 hours

Answer:

uhh I'm pretty sure it's (9,1) went from quadrant 3 to 2 which is all positives

Answer:

D

Step-by-step explanation:

First, we will move the variable to the left-hand side and change its sign: 5x + 3 - 10x = -17

Next, we need to collect like terms: -5x = -20

Finally, we will divide both sides of the equation by -5 to give us the answer of x = 4.

55°

Step-by-step explanation:

110+15+x =180

x = 180 - 125

x = 55°

Answer:

Step-by-step explanation:

D.

I am so sorry if it is wrong

Answer:

Translation

Step-by-step explanation:

Answer:

7 for your x axis and -3 for Y

So your are going from G to H, thats important.

You go to the right seven times and down (hence -3) three times

Answer:

3 is -15/2 and 4 is -3/2

Step-by-step explanation:

If im not mistaken these are the awansers

The length of the ladder that makes an angle of 75 degrees and lies against the wall of a house that's 23 feet tall is approximately 25.88 feet.

The ladder forms a right triangle as it lies against the wall as shown in the image below.

Thus:

x = length of the ladder (hypothenuse)

Reference angle [tex](\theta) = 75^{\circ}[/tex]

25 ft = Opposite

Apply SOH:

Thus,

[tex]sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

[tex]sin(75) = \frac{25}{x}\\\\x = \frac{25}{sin(75)} \\\\\mathbf{x = 25.88}[/tex]

Therefore, the length of the ladder that makes an angle of 75 degrees and lies against the wall of a house that's 23 feet tall is approximately 25.88 feet.

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Answer:

x=32.09 feet long

Step-by-step explanation:

Answer:

4(2x+1)(x−1)

Step-by-step explanation:

8x2−4x−4

8x2−4x−4

=4(2x+1)(x−1)

Answer:

Volume, Mass

Step-by-step explanation:

Mass is how much stuff something is made of. Volume is how much space an object takes up. 1.

Answer:

A, B, C

Step-by-step explanation:

Assuming the choices are:

A. [tex](x-2)(x^{4}+3)[/tex]

B. [tex]x^{2} -1[/tex]

C. A+[tex]x^{4} +16[/tex]

D. [tex]\frac{1}{x} +2[/tex]

Put simply, a polynomial in this case will be a function that has at least one variable raised to a power greater than 1.

Choice A already has a variable raised to a power greater than 1 ([tex]x^{4}[/tex]), so no additional manipulation is needed.

Choice B also has a term that is already raised to a power greater than 1 ([tex]x^{2}[/tex]). It is the same for choice C ([tex]x^{4}[/tex]).

Choice D does not have an obvious variable raised to a power greater than 1. When the equation is manipulated it becomes [tex]x^{-1} +2[/tex]. Since -1 is less than 1, choice D is not a polynomial.

Answer:

Option D

Step-by-step explanation:

[tex]\\ \sf\longmapsto \dfrac{1}{x}+2[/tex]

Simplify

[tex]\\ \sf\longmapsto x^{-1}+2[/tex]

Degree is less than 1 .It's not a polynomial

i would say y + 2/5y is the equivalent expression of 7/5y and y - 2/5y is the quivalent expression of 3/5y but im not sure

Answer:

434 sweatshirts were sold

Step-by-step explanation:

$2,170/$5 = 434

Answer:

Fraction  3 out of 3 /4

Step-by-step explanation:

[tex]y = -2x^2 + 8x + 3[/tex]

The equation of a quadratic function of vertex (h,k) is given by:

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

The vertex is the maximum point, which is (2,11), hence [tex]h = 2, k = 11[/tex]. Then:

[tex]y = a(x - 2)^2 + 11[/tex]

The initial height is of 3 feet, then when [tex]x = 0, y = 3[/tex], and this is used to find a.

[tex]y = a(x - 2)^2 + 11[/tex]

[tex]3 = 4a + 11[/tex]

[tex]4a = -8[/tex]

[tex]a = -\frac{8}{4}[/tex]

[tex]a = -2[/tex]

Then:

[tex]y = -2(x - 2)^2 + 11[/tex]

In standard format, the model is:

[tex]y = -2x^2 + 8x - 8 + 11[/tex]

[tex]y = -2x^2 + 8x + 3[/tex]

It hits the ground when [tex]y = 0[/tex], so:

[tex]-2x^2 + 8x + 3 = 0[/tex]

[tex]2x^2 - 8x - 3 = 0[/tex]

Which has coefficients [tex]a = 2, b = -8, c = -3[/tex]. So

[tex]\Delta = b^2 - 4ac = (-8)^2 - 4(2)(-3) = 88[/tex]

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{8 + sqrt{88}}{4} = 4.35[/tex]

[tex]x_1 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{8 - sqrt{88}}{4} = -0.35[/tex]

Time is positive, so it lands on the ground after 4.35 seconds.

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Answer:

C, move (translate) 5 units left

Step-by-step explanation:

Sliding or moving is called translating, and MATH is to the right of M'A'T'H' (prime), so translate 5 units left.

Answer:

1. x=6

2. x = -4

3. x³ = 0

Step-by-step explanation:

Step 1: Equation at the end of step 1

((x⁵) - ( 2 · (x⁴)))-(2³· 3x³) = 0

Step 2:

Equation at the end of step 2:

((x⁵)-2x⁴)-(2³ · 3x³) = 0

Step 3: X

Step 4: Pulling out like terms

Pull out like factors :

x⁵ - 2x⁴ -24x³ = x³· (x² - 2x -24)

Trying to factor by splitting the middle term

Factoring  x² -2x - 24

The first term is, x² ts coefficient is  1 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  -24  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -24 = -24  

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -2 .

     -24    +    1    =    -23  

     -12    +    2    =    -10  

     -8    +    3    =    -5  

     -6    +    4    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  4

 x2 - 6x + 4x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-6)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x-6)

            Which is the desired factorization

Equation at the end of step

4

:

 x3 • (x + 4) • (x - 6)  = 0  

STEP

5

:

Theory - Roots of a product

5.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

5.2      Solve  :    x3 = 0  

 Solution is  x3 = 0

Solving a Single Variable Equation:

5.3      Solve  :    x+4 = 0  

Subtract  4  from both sides of the equation :  

                     x = -4

Solving a Single Variable Equation:

5.4      Solve  :    x-6 = 0  

Add  6  to both sides of the equation :  

                     x = 6

Supplement : Solving Quadratic Equation Directly

Solving    x2-2x-24  = 0   directly  

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

6.1      Find the Vertex of   y = x2-2x-24

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).  

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.  

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.  

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   1.0000  

Plugging into the parabola formula   1.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 1.00 * 1.00 - 2.0 * 1.00 - 24.0

or   y = -25.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-2x-24

Axis of Symmetry (dashed)  {x}={ 1.00}  

Vertex at  {x,y} = { 1.00,-25.00}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-4.00, 0.00}  

Root 2 at  {x,y} = { 6.00, 0.00}  

Solve Quadratic Equation by Completing The Square

6.2     Solving   x2-2x-24 = 0 by Completing The Square .

Add  24  to both side of the equation :

  x2-2x = 24

Now the clever bit: Take the coefficient of  x , which is  2 , divide by two, giving  1 , and finally square it giving  1  

Add  1  to both sides of the equation :

 On the right hand side we have :

  24  +  1    or,  (24/1)+(1/1)  

 The common denominator of the two fractions is  1   Adding  (24/1)+(1/1)  gives  25/1  

 So adding to both sides we finally get :

  x2-2x+1 = 25

Adding  1  has completed the left hand side into a perfect square :

  x2-2x+1  =

  (x-1) • (x-1)  =

 (x-1)2

Things which are equal to the same thing are also equal to one another. Since

  x2-2x+1 = 25 and

  x2-2x+1 = (x-1)2

then, according to the law of transitivity,

  (x-1)2 = 25

We'll refer to this Equation as  Eq. #6.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-1)2   is

  (x-1)2/2 =

 (x-1)1 =

  x-1

Now, applying the Square Root Principle to  Eq. #6.2.1  we get:

  x-1 = √ 25

Add  1  to both sides to obtain:

  x = 1 + √ 25

Three solutions were found :

x = 6

x = -4

x3 = 0

The average amount earned based on the information given is $5.31 per product.

Number of farm products = 293

Total amount earned = $1557

Therefore, the average amount will be gotten by dividing the total amount by the number of farm products and this will be:

= $1557/293

= $5.31

In conclusion, the average will be $5.31.

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Answer:

4^10

subtract 15-5 and leave the 14 be

Answer:

14 to the tenth power

Step-by-step explanation:

fifteen - fifth = ten. When you are working on exponential problems like this, remember to add or subtract the powers.

Answer:

x° = 35°

Step-by-step explanation:

at 125° to get the opposite angle

180° - 125° = 55°

then,

x° + 90° + 55° = 180°

x° = 180° - 145°

x° = 35°

Answer:

quadrant 4 i think

Step-by-step explanation:

Answer:

Actually the correct answer is 2

Step-by-step explanation: