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2 years ago

Use the drop-down menus to describe the key aspects of the function f(x) = –x2 – 2x – 1.

Mathematics

2 answers:

siniylev [52]2 years ago

5 0

The vertex is the maximum value

The function is increasing when x < -1

The function is decreasing when x > -1

The domain of the function is all real numbers

The range of the function is All numbers less than or equal to zero

Marina86 [1]2 years ago

5 0

Answer:

2, 1, 2, 1, 3

Step-by-step explanation:

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What is the length of the longer of the two chords shown? Length of longer chord= ? units

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The psychology club is having a self-proclaimed psychic come to their campus fund-raising event to demonstrate his abilities. He

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Points H and F lie on circle c What is the length of line segment GH?

Nina [5.8K]

Answer:

6 units

Step-by-step explanation:

Given: Points H and F lie on circle with center C. EG = 12, EC = 9 and ∠GEC = 90°.

To find: Length of GH.

Sol: EC = CH = 9 (Radius of the same circle are equal)

Now, GC = GH + CH

GC = GH + 9

Now In ΔEGC, using pythagoras theorem,

$(Hypotenuse)^{2} = (Base)^{2} +(Altitude)^{2}$ ......(ΔEGC is a right triangle)

$(GC)^{2} = (GE)^{2} +(EC)^{2}$

$(GH + 9)^{2} = (9)^{2} +(12)^{2}$

$(GH )^{2} + (9)^{2} + 18GH = 81 + 144$

$(GH )^{2} + 81 + 18GH = 81 + 144$

$(GH )^{2} + 18GH = 144$

Now, Let GH = x

$x^{2} +18x = 144$

On rearranging,

$x^{2} +18 x - 144 = 0$

$x^{2} - 6x +24x + 144 = 0$

$x (x-6) + 24 (x - 6) =0$

$(x - 6) (x + 24) = 0$

So x = 6 and x = - 24

∵ x cannot be - 24 as it will not satisfy the property of right triangle.

Therefore, the length of line segment GH = 6 units. so, Option (D) is the correct answer.

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2 years ago

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Manuel thinks the tens digit goes up by 1 in these numbers. Do you agree? Explain. 460,470,480, 490,500,510

laila [671]

Answer:

Manuel is correct, since adding 10 is the same as the tens digit going up by 1.

Step-by-step explanation:

It is important to know the concepts of units, tenths and cents.

For example

1 = 1 unit

10 = 1*10 + 0 = The tens digit is one the unit digit is 0

21 = 2*10 + 1 = The tens digit is two and the unit digit is 1.

120 = 1*100 + 2*10 + 0 = The cents digit is 1, the tens digit is two and the unit digit is 0.

Adding 1 is the same as the unit digit going up by 1.

Adding 10 is the same as the tens digit going up by 1.

Adding 100 is the same as the cents digit going up by 1.

In this problem, we have that:

460,470,480, 490,500,510

Each number is 10 added to the previous, that is, the tens digit going up by 1.

Manuel thinks the tens digit goes up by 1 in these numbers. Do you agree?

Manuel is correct, since adding 10 is the same as the tens digit going up by 1.

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2 years ago

Suppose T is the transformation from ℝ2 to ℝ2 that results from a reflection over the y-axis followed by a reflection over the x

LenKa [72]

Answer:

A = \begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix}

Step-by-step explanation:

Let, there be a point (x , y) in R2

After reflection on Y axis, it will be ( -x , y) and thereafter if we reflect the image over X -axis , it will be (-x , -y)

So,

we need to find out a matrix

[tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex]

such that,

(x , y) [tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex] = (-x. -y)

So, we have the following set of equations.

ax + cy = -x ------------(1)

bx + dy= -y-----------(2)

We can get the solution (by inspection) as,

[tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex]

= [tex]\begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix}[tex]

So, the matrix is,

A = \begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix} (answer)

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2 years ago