evaluate 8+w/4 when w=14

The vertex form of the function f(x) is [tex]\rm f(x)= 7 ( x + 3 )^2 - 63[/tex].

Function; [tex]\rm f(x) = 7x^2 + 42x[/tex]

The vertex of a parabola is the point at which the parabola passes through its axis of symmetry.

The standard equation which represents the vertex form of the function is;

[tex]\rm f(x) =(x-h)^2+k^2[/tex]

Where h and k are vertexes of the given parabola.

The function is in vertex form;

[tex]\rm f(x)= 7 x^2 + 42 x\\\\ f(x) = 7 ( x^2+ 6 x ) \\\\ f(x)= 7 ( ( x^2+ 6 x + 9 ) - 9 ) \\\\ f(x)= 7 ( x + 3 )^2 - 63[/tex]

Hence, the vertex form of the function f(x) is [tex]\rm f(x)= 7 ( x + 3 )^2 - 63[/tex].

To know more about the Vertex form lick the link given below.

https://brainly.com/question/9070346

Answer:

f(x)=7(x+3)^2-63

Step-by-step explanation:

Please add brainliest

Answer:

The correct statement is each successful toss is worth 3 points.

It is a branch of mathematics that deals with the occurrence of a random event.

Players earn points for successful tosses and lose points for missed tosses.

Results for two players are shown in the table.

Number of successful toss, number of missed toss and total number of points for Player 1 and Player 2 are given in the table.

Let's assume that:

Each successful toss = +x points

Each missed toss = -y points

From the given table:

4x - 3y = 6 ...(i)

5x - 5y = 5

x - y = 1

y = x - 1

Substituting y in eq(i)

4x - 3(x - 1) = 6

4x - 3x + 3 = 6

x = 3 and y = 2

Hence, the correct statement is each successful toss is worth 3 points.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ2

∠ABD and ∠EBC are complementary by the definition of complementary angles.

Given that in a figure, BD ⊥ BC ; ∠ABD ≅ ∠DBE.

We need to prove ∠ABD and ∠EBC are complementary.

BD ⊥ BC = given

∠DBC = 90° by the definition of perpendiculars.

∠ABD ≅ ∠DBE = given

∴ ∠ABD = ∠DBE by the definition of congruence.

Using the angles addition postulate,

∠EBC + ∠DBE = 90°

Now, replace ∠DBE by ∠ABD, we get,

∠EBC + ∠ABD = 90°

Hence ∠ABD and ∠EBC are complementary by the definition of complementary angles.

Learn more about complementary angles click;

https://brainly.com/question/15380971

#SPJ3

The complete question is given below.

Answer:

They don't form a proportion.

Answer:

14 %

Step-by-step explanation:

rate of commission

[tex]=\frac{378}{2700} \times100\\=14 ~\%[/tex]

Answer

80

Step-by-step explanation:

1/5 of 120 is 24

120 - 24 because you dropped 1 /5

gives you 96

then you give 1/6 of what you have left to your friend and that means giving 16 candies to your friend so 96-16

and that gives you 80 candies remaining

sin(kx) has period 2π/k

so, you want

2 + 5sin(16π/7 x)

[tex]hope \: its \: helpful \: to \: you[/tex]

Answer:

The correct answers is letter C

Step-by-step explanation:

= x(1/6 + 2/5 - 8/3) + 42 - 19

= - 21/10x + 42 -19

= -21/10 x + 23

Answer:

y= -9x+14

Step-by-step explanation:

the equation of a straight line is y=mx+c

m is the slope

And we are given a y and x term

So we substitute these into the equation:

5= -9(1) + c

rearragne to find c

14= c

so the full equation is:

y= -9x+14

Answer:

30

Step-by-step explanation:

30 can be divided by 5, 6, and 10

Answer:

A right-angled triangle has 2 legs and a hypotenuse.

In trigonometry, the 2 legs are labelled opposite and adjacent, and this labeling is interchangeable, depending on which interior angle we are working with.

the hypotenuse is always the side opposite to the 90° angle and is therefore always the longest side.  So for this triangle, the hypotenuse is line LM.

For example, If we look at angle L, the line KL is adjacent (next) to it, and line KM is opposite to it.  However, if we look at angle M, the line KM is adjacent to it, and the line KL is opposite it.  Remember, the hypotenuse doesn't change.

Therefore:

Angle adjacent to side KL = angle L

Angle adjacent to side KM = angle M

Side opposite to angle L = side KM

Side opposite to angle M = side KL

Hypotenuse = side LM

Step-by-step explanation:

Total = $14+$3+$4

Total = $21

Each friend owe = $21/3

So, each friend owe $7

Answer:

$7 each

Step-by-step explanation:

Let's determine the total cost first to see how the friends can divide the cost.

The total cost is $21. 14 for a pizza, 3 for the soda, and 4 for the cake.

There are 3 friends and 21 goes evenly in 3. So 21 divided by 3 is $7 per person.

Answer:

C. Yes, because every x- and y-value is positive

Answer:

The answer is C

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the surface area, we need to find the area of all the squares and triangles available.

Solution:

Now, multiply the area of the triangle by 4.

Now, let's find the area of the square.

Now, add the area of the triangles and the squares.

Hence, the surface area of the pyramid is 63 cm².

Answer:

X -3 -2 -1 0 1 2 3. 4 5. 6

y -9 -8 -7 -6 -5 -4. -3 -2. -1 0

Answer:

Train A = 128

Train B = 68

Step-by-step explanation:

We can set up a system of equations for this problem

Let A = # of tons of Train A

Let B = # of tons of Train B

A + B = 196

A = B + 60

Now, we plug in A for the first equation, using substitution

(B+60) + B = 196

2B + 60 = 196

Subtract 60 from both sides

2B = 136

Divide both sides by 2

B = 68

Plug in 68 for B in the 2nd equation

A = 68 + 60

A = 128

Checking work: 128 + 68 = 196 :D hope this helped

Answer:

h = 2[tex]\sqrt{3}[/tex]

b = 3[tex]\sqrt{2}[/tex]

Step-by-step explanation:

to find 'h' we can use the ratio of sides in a 30-60-90° triangle which, respectively, is 1 : [tex]\sqrt{3}[/tex] : 2

so we can set up this proportion:

h/2 = 1/[tex]\sqrt{3}[/tex]

cross-multiply:

h = 2[tex]\sqrt{3}[/tex]

to find 'b' we can use the ratio of sides in a 45-45-90° triangle which, respectively, is 1 : 1 : [tex]\sqrt{2}[/tex]

we can set up this proportion:

3/b = 1/[tex]\sqrt{2}[/tex]

cross-multiply:

b = 3[tex]\sqrt{2}[/tex]

sinθ is equal to the division of the opposite side of the reference angle (θ) by the hypotenuse.

the cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse

tan30 = h/2

[tex]tan30 = \frac{1}{ \sqrt{3} } [/tex]

1/sqrt3 = h/2

[tex]h = \frac{2}{ \sqrt{3} } [/tex]

sin45 = 3/b

[tex]sin45 = \frac{1}{ \sqrt{2} } [/tex]

1/sqrt2 = 3/b

b/sqrt2 =3

[tex]b = 3 \sqrt{2} [/tex]

[tex]=\int\limit(\frac{1}{t^{2} }-\frac{2}{t^{3} }) dt \\\\=\int\limit\frac{1}{t^{2} }dt-2\int\limit\frac{1}{t^{3} }dt\\\\=-\frac{1}{t}-2 \int\limit\frac{1}{t^{3} }dt\\\\=\frac{1-t}{t^{2} }[/tex]

Step-by-step explanation:

[tex]\\ \tt\hookrightarrow {\displaystyle{\int}}\left(\dfrac{1}{t^2}-\dfrac{2}{t^3}\right)dt[/tex]

[tex]\\ \tt\hookrightarrow {\displaystyle{\int}}(t^{-2}-2t^{-3})dt[/tex]

[tex]\\ \tt\hookrightarrow {\displaystyle{\int}}t^{-2}-2{\displaystyle{\int}}t^{-3}dt[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{t^{-1}}{-1}-2\dfrac{t^{-2}}{-2}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{-1}{t}+\dfrac{1}{t^2}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{-2+1}{t^2}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{-1}{t^2}[/tex]

Answer:  0.1

Explanation:

Because y = rx, we can divide both sides by x to isolate r.

r = y/x

Then we'll plug in the values from the table

You only need to show your work for one row.

Answer:

unrepresentative

Step-by-step explanation:

pretty sure dont quote me

Answer:

It contains 3 pints of fruit juice.

Step-by-step explanation:

A pint is 16 ounces.

48 ounces divided by 16 ounces equals 3, giving us 3 pints.

I hope this helps.

Answer:

June, July, and August.

Step-by-step explanation:

1600<2570-125.5x<2000  subtract 2570 from all terms...

-970<-125.5x<-570  divide all terms by -125.5 (and reverse signs because of division by a negative!)

7.73>x>4.54  and x is months since January, and since months can only be integers...

x=[5,7]

So January + 5, 6, and 7 respectively are the three months that satisfy the equation...

June, July, and August.

Multiply amount she saves per month by 5 months:

35 x 5 = $175

$175 is less than the price of the player so she won’t have enough to buy it.

197.99 - 175 = $22.99

She needs $22.99.more