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3 years ago

Between which two ordered pairs does the graph of f(x) = x2 + x – 9 cross the negative x-axis? Quadratic formula: x =

Mathematics

2 answers:

katrin2010 [14]3 years ago

8 0

(-6,0) and (-5,0) I got it right

madreJ [45]3 years ago

5 0

Answer: It must be between two ordered pair i.e. (-4,0) and (-3,0).

Step-by-step explanation:

Since we have given that

Quadratic equation : $x^2+x-9$

First we use the quadratic formula to get the value of x:

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-1\pm\sqrt{1+36}}{2\times 1}\\\\x=\dfrac{-1\pm\sqrt{37}}{2}\\\\x=\dfrac{-1+\sqrt{37}}{2}\ or\ \dfrac{-1-\sqrt{37}}{2}\\\\x=2.54\ or\ -3.5$

Since the negative root of x is -3.5.

So, it must be between two ordered pair as follows :

(-4,0) and (-3,0).

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Let T: P2 → P3 be the transformation that maps a polynomial p(t) into the polynomial (t-2)p(t).

lutik1710 [3]

(a) Applying T to p(t) = 2 - t + t ² gives

T ( p(t) ) = (t - 2) (2 - t + t ²) = -4 + 4t - 3t ² + t ³

(b) T is a linear transformation if for any p(t) and q(t) in P₂ and complex scalars a and b, the image of any linear combination of p and q is equal to the linear combination of the images of p and q. In other words,

T ( a p(t) + b q(t) ) = a T ( p(t) ) + b T ( q(t) )

Let

p(t) = α₀ + α₁ t + α₂ t ²

q(t) = β₀ + β₁ t + β₂ t ²

Compute the images of p and q :

T ( p(t) ) = (t - 2) (α₀ + α₁ t + α₂ t ²)

… = -2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + α₂ t ³

Similarly,

T ( q(t) ) = -2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + β₂ t ³

Then

a T ( p(t) ) + b T ( q(t) ) = a (-2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + α₂ t ³) + b (-2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + β₂ t ³)

… = c₀ + c₁ t + c₂ t ² + c₃ t ³

where

c₀ = -2 (a α₀ + b β₀)

c₁ = a (α₀ - 2α₁) + b (β₀ - 2β₁)

c₂ = a (α₁ - 2α₂) + b (β₁ - 2β₂)

c₃ = a α₂ + b β₂

Computing the image of a p(t) + b q(t) would give the same result; just multiply it by t - 2 and expand. This establishes that T is indeed linear.

(c) Find the image of each vector in the basis for P₂ :

T (1) = (t - 2) × 1 = t - 2

T (t ) = (t - 2) t = t ² - 2t

T (t ²) = (t - 2) t ² = t ³ - 2t ²

Then

$T=\begin{bmatrix}-2&0&0\\1&-2&0\\0&1&-2\\0&0&1\end{bmatrix}$

4 0

3 years ago

Assume the table gives data on field goal shooting for two members of the Benedict College 2014-2020 men's basketball team. Seth

Contact [7]

Answer:

(a) What percent of all field goal attempts did Seth Fitzgerald make? (Enter your answers rounded to two decimal places.)

Seth Fitzgerald's overall field goal percentage:__59.69%_____

What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.)

Roberto Mantovani's overall field goal percentage: ______40.31%________.

(b) Find the percent of all two-point field goals and all three-point field goals that both Seth and Roberto made. (Enter your answers rounded to two decimal places.)

Seth Fitzgerald's two-pointers: _____58.57%_________%

Roberto Mantovani's two-pointers:_____41.43%______ %

Seth Fitzgerald's three-pointers:_____64.58%_______

Roberto Mantovani's three-pointers:_____35.42%_____

(c) Roberto had a lower percent than Seth for both types of field goals, but had a better overall percent. That sounds impossible, select the correct statement concerning the situation.

i) This is an example of Simpson's paradox. The comparison that holds for both field goal groups is reversed when the groups are combined into one group

Step-by-step explanation:

a) Data and Calculations:

Benedict College 2014-2020 men's basketball team:

Seth Fitzgerald Roberto Mantovani Total

Made Missed Made Missed Made Missed

Two-pointers 123 118 87 84 210 205

Three-pointers 31 6 17 2 48 8

Total 154 124 104 86 258 210

a) All field goal attempts = 258 (154 + 104)

Field goal attempts by Seth Fitzgerald = 154/258 * 100 = 59.69%

Goal 154 - 124 = 30/258 * 100 = 11.63%

Roberto Mantovani = 104/258*100 = 40.31%

Goal 104 - 86 = 18/258 *100 = 6.98%

Percent of all two-point field goals and all three-point field goals that both Seth and Roberto made:

Goals by both = 48 (30 + 18) = 48/258*100 = 18.61 (11.63 + 6.98)

Seth Fitzgerald's two-pointers = 123/210*100 = 58.57%

Roberto Mantovani's two-pointers = 87/210*100 = 41.43%

Seth Fitzgerald's three-pointers = 31/48*100 = 64.58%

Roberto Mantovani's three-pointers = 17/48*100 = 35.42%

b) Simpson's paradox, also called Yule-Simpson effect, says that when we combine all of the groups together (e.g. two-pointer and three-pointer games played by Seth and Roberto respectively) and look at the data in total form, the correlation that we noticed before may reverse itself. The cause of this reversion is lurking variables or numerical values of the data.

4 0

3 years ago

A cola container is in the shape of a right circular cylinder. The radius of the base is 4 centimeters, and the height is 10 cen

noname [10]

Answer:

$V=160\pi$

Step-by-step explanation:

$V=h\pi r^{2}$

$V=10*\pi 4^{2}$

$V=160\pi$

5 0

3 years ago

Two parallel lines are cut by a transversal, as shown below. What is the solution when solved for x?

elixir [45]

Answer:

Step-by-step explanation:

128° and 2x° are Co interior angles since the two parallel lines is cut by a transversal

so, 128+2x = 180(since sum of co interior angles always add to 180)

so, 2x = (180-128)

or, x = 52/2

or, x = 26

3 0

3 years ago

What rule describes the translation 5 units left and 10 units up?

Whitepunk [10]

The rule (x, y) (x-5, y+10) would describe the translation 5 units to the left (because when you go to the left the numbers on the x axis become smaller) and 10 units up (because when you go up the numbers on the y axis increase).

3 0

3 years ago