given the equation g(x)= – x2–5x + 12
find g(9)

Answer:

  (d)  y = 3x² +2x -6

Step-by-step explanation:

The equation of a parabola through thee points can be found different ways. One is to use a quadratic regression tool. Another is to write and solve linear equations in the coefficients. (3 equations in 3 unknowns).

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Here, we can eliminate answer choices that don't work to arrive at the correct answer choice.

The point (0, -6) is the y-intercept of the function. That means the value of the constant term in the quadratic is -6. (Eliminates A and C.)

The y-values of the other two points are both greater than -6, indicating the parabola opens upward. That means the leading coefficient is positive. (Eliminates B.)

The only reasonable choice is D:

  y = 3x² +2x -6

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Additional comment

You get the same answer if you use a regression tool.

Answer:

[tex]y = 3\, x^{2} + 2\, x - 6[/tex].

Step-by-step explanation:

In general, the equation of a parabola is in the form [tex]y = a\, x^{2} + b\, x + c[/tex] for some constants [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex], where [tex]a \ne 0[/tex].

Let [tex]y = a\, x^{2} + b\, x + c\![/tex] denote the equation of this parabola for some constants [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] where [tex]a \ne 0[/tex]. A point [tex](x_{0},\, y_{0})[/tex] is on this parabola if and only if the equation of this parabola holds after substituting in [tex]x = x_{0}[/tex] and [tex]y = y_{0}[/tex]:

[tex]y_{0} = a\, {x_{0}}^{2} + b\, x_{0} + c[/tex].

Thus, each of the three distinct points on this parabola would give a equation about [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex]:

Simplify the equations:

[tex]\left\lbrace\begin{aligned}& 9\, a - 3\, b + c = 15 \\ & c = 6 \\ & 4\, a + 2\, b + c = 10\end{aligned}\right.[/tex].

Solve this linear system of three equations and three unknowns for [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex]:

[tex]\left\lbrace \begin{aligned} & a = 3 \\ & b = 2 \\ & c = (-6) \end{aligned}\right.[/tex].

Therefore, the equation of this parabola would be:

[tex]y = 3\, x^{2} + 2\, x - 6[/tex].

Answer:

Can you take a full picture

Step-by-step explanation:

Answer:
Choice A:
Final price:-  $17.50
Saved amount :-7.50


Choice B:
Final price: $24.00

Saved amount: $8.00

Therefore the choice A is better deal.

Answer:

2.02

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Answer:

•100 + 10 + (10 - 5)²=135

#Let's Study

#I Hope It's Help

#Keep On Learning

#Carry On Learning

Question

100 + 10 + (10 - 5)²

Answer:

Step by step explanation:

=100 + 10 + (10 - 5)²

=100 + 10 +5²

=100 + 10 + 25

=110 + 25

=135

I hope this helps

Answer:

61

Step-by-step explanation:

1. let the unknown be x

2. using theorem of Pythagoras that states the hypotenuse will be equal to the sum of the other two sides we can determine that 75=14+X

3. this implies that X=75-14

4. therefore X= 61

Answer:

3/8 & 4/8

Step-by-step explanation:

1/2 - 1/8 = 4/8 - 1/8 = 3/8

x - 1/8 = 3/8

x = 4/8    

SOH CAH TOA

Opposite is 7

Y is the hypotenuse - longest side

So, x is the adjacent

Find y first, we've got opposite & hypotenuse

=> SOH or Sin

Sin(30) = o/h

Sin(30) = 7/h

x h

h x sin(30) = 7

÷ Sin(30)

H = 14

Pythagoras' Theorem: a^2 + b^2 = c^2

(which I've already rearranged, to find value of x)

Square root of 14^2 - 7^2 = 7 root 3.

Thus, the missing lengths should be 14 and 7 root 3.

The answer is:

y = 14

x = 7 root 3

(root => a square root)

Hope this helps!

Answer:

74,000 words he can type in 37 minutes

Answer:

[tex]1\frac{1}{6} or 1.167[/tex]

Step-by-step explanation:

[tex]\frac{1}{2} + \frac{2}{3}[/tex]                    (convert 0.5 to a fraction: [tex]\frac{1}{2}[/tex]

[tex]= (\frac{3}{3} )\frac{1}{2}+ \frac{2}{3}(\frac{2}{2} )[/tex]     (find common denominator)

[tex]=\frac{3}{6} +\frac{4}{6}[/tex]               (add the numerators together)

[tex]=\frac{7}{6}[/tex]                      (if [tex]\frac{6}{6}[/tex] is equal to 1, but we have one extra it becomes...)

[tex]=1\frac{1}{6}[/tex]                    (convert to a decimal if needed)

[tex]= 1.167[/tex]

Hope this helps!! Please mark Brainliest!!

Step-by-step explanation:

Let the triangles be ADC and BEC.

Point D has coordinates of (0, 154), point E has coordinates of (0, 110).

ΔADC

The slope of AC

ΔBEC

The slope of BC

As we can see the slopes are equal

The y-intercept or initial value is represented by the point C and has coordinates of (0, 66)

The line is:

The initial value is the depth of 66 m where the shark is.

The slope is the 44 m increase of the depth every minute.

Answer:

Step-by-step explanation:

There are two methods of doing this

one is in the pin and another:

3 2/7 =23/7

7 5/14= 103/14

23/7 + 103/14 = Lcm 14

23/7 *2= 46/14

46/14 + 103/14 =149/14

149/14 = 10 9/14

Answer: I pretty sure the answer is 92!

Step-by-step explanation:

75% of the test score would be 76 x 0.75 = 57

80-57 = 23

They need 23 more points to get an 80

The 23 is 25% of the final exam grade so they would need to score a 23 x 4 = 92 on the final exam

answer: 92

Answer:

a

Step-by-step explanation:

Sales tax: $206.25

■ Cost/Price before ST: $2,750.00

■ Total Cost/Price including ST: $2,956.25

Answer:

BC||AD

Step-by-step explanation:

A parallelogram is said to be parallelogram iff it's opposite pairs of sides are parallel to each other.

Since one pair is parallel (given)

then another pair needs to be parallel.

Hence BC||AD

Answer:

Step-by-step explanation:

Sum of interior angles in a triangle is 180degree.

<B + 15degree + 45degree = 180degree

<B = 180 - 45 - 15 = 120 degree

By sine rule,

sin<B / AC = sin<C / AB = sin <A / BC

sin120degree / 200 = sin15degree / AB = sin45degree / BC

AB = 200*sin15degree/sin120degree

= 59.77

BC = 200*sin45degree/sin120degree

= 163.30

Answer: A local swiming

Answer:

14 square meters

Step-by-step explanation:

the first part of this question can be to find the bases area

the base is 2 * 2 which is 4 square meters

then you find the area of the triangles

the length is 3 and the base is 2

then you multiply the amount of that by 1/2 and then by 4 because of the number of triangles there are

2 * 3 * 1/2 * 4 = 12

this is the area of the triangles added together

then you add 12 to 2 for the total

12 + 2 = 14 m^2

Answer:

  see table below

Step-by-step explanation:

The exact metric conversions for length, mass, and volume are ...

An inch is 2.54 cm.

A pound is 0.45359237 kg.

A pint is 0.473176473 liters.

The approximate conversions would be ...

 2 inches ≈ 5 cm

  5 pounds ≈ 2 kg

  8 pints ≈ 4 liters

Answer:

Step-by-step explanation:

Step-by-step explanation:

c.is correct your welcome

Answer:

There

Step-by-step explanation:

mark me brainliest!!

Answer:

1.836 acres

Step-by-step explanation:

Answer: 5 meters

Why?:

Let the width of the room be denoted by 'W'

Since the room is three times as long as its width, the length will be '3W'

remember perimeter of a rectangle is =  2(length + width) and is given in the question as 40 meters.

      Perimeter =  2 (length + width)

                 40 = 2 (3W + W)

                 40 = 2 (4W)

                 40 = 8W

(Dividing both sides by 8), gives

                 5 = W

Answer:

l = 15

w = 5

Step-by-step explanation:

l = 3w

40 = 2l + 2w

40 = 6w + 2w

40 = 8w

8w = 40

w = 40/8

w = 5

l = 15

Answer:

  g(x) = 3 + tan(πx/4)

Step-by-step explanation:

A tangent function has a period of π. In order to make it have a period of 4, it needs to be stretched horizontally by a factor of 4/π. A function is stretched horizontally by a factor of k by replacing x with x/k.

In order for the function to be shifted vertically up by 3 units, 3 must be added to the function value. That is, the transformed function becomes ...

  g(x) = tan(x/(4/π)) +3

  g(x) = tan(πx/4) +3

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

and to get it, we simply need two points off of the straight line, hmm let's use the ones in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}[/tex]

Answer:

No there are not any outliers

Answer:

y = x² + 8x + 16

Step-by-step explanation:

blue square = x × x = x²

green rectangle = 4 × x = 4x

yellow square = 4 × 4 = 16

Let y = total area of the square

⇒ y = blue square + green rectangle + green rectangle + yellow square

       = x² + 4x + 4x + 16

       = x² + 8x + 16

Area:-

Answer:

$140

Step-by-step explanation:

Rent alone = 400

Rent with roommate = (400 + 30%) / 2
= (400 + 120) / 2

= 520 / 2

Rent with roommate = 260

400 - 260 = 140