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2 years ago

Write the sum in sigma notation. $ \noindent 1 - x + x^2 - x^3 + \cdot\cdot\cdot + {(-1)}^n x^n $

Mathematics

1 answer:

Neko [114]2 years ago

3 0

$1-x+x^2-x^3...+(-1)^nx^n=\sum\limits_{n=0}^{\infty}(-1)^nx^n=\sum\limits_{n=1}^{\infty}(-1)^{n-1}x^{n-1}$

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a local charity held a crafts fair selling donated,handmade items. Total proceeds from the sale were $1,875. A total of 95 items

Lana71 [14]

15x+25y=1875
Let
y=95-x
15x+25 (95-x)=1875
Solve for x
15x+2375-25x=1875
15x-25x=1875-2375
-10x=-500
X=500/10
X=50 the number of $15 items

Y=95-50=45 the number of $25 items

5 0

2 years ago

Greatest common factor of 88 and 48

kupik [55]

GFC is 8. Use a tree of 88 and 48. 88= 2^3 x 11 or 2 x 2 x 2 x 11

48=2^4 x 3 or 2 x 2 x 2 x 2 x 3 see how many groups count as the number once and multiply and bam GFC. Hope I helped! (:

4 0

2 years ago

Triangle XYZ with vertices X(0, 0), Y(0, –2), and Z(–2, –2) is rotated to create the image triangle X'(0, 0), Y'(2, 0), and Z'(2

Marina86 [1]

Answer: The correct options are

(A) Rotation 90° anticlockwise.

(D) (x, y) → (–y, x).

Step-by-step explanation: Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.

Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.

The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).

And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).

Option (A) Rotation 90°:

We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.

So, rotation of 90° anticlockwise is a correct option.

Option (B) Rotation 180°:

If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.

So, rotation of 180° is NOT a correct option.

Option (C) Rotation 270°:

If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.

So, rotation of 270° clockwise is also a correct option.

Option (D) (x, y) → (–y, x):

We see that the co-ordinates of both the triangle follow the transformation

X(0, 0) ⇒ X'(0, 0)

Y(0, -2) ⇒ Y'(2, 0)

Z(-2, -2) ⇒ Z'(2, -2).

So, the transformation is (x, y) ⇒ (-y, x).

Therefore, the transformation (x, y) → (–y, x) is a correct option.

Option (E) (x, y) → (y, -x):

We see that the co-ordinates of both the triangle does NOT follow this transformation

For example, suppose this transformation is correct. Then, we have

Y(0, -2) ⇒ (-2, 0), which are not the co-ordinates of Y'.

Therefore, the transformation (x, y) → (–y, x) is NOT a correct option.

Thus, the correct options are:

(A) Rotation 90° anticlockwise.

(D) (x, y) → (–y, x).

9 0

2 years ago

Read 2 more answers

Un globo busca aterrizar en medio de dos ciudades A y B, cuya distancia entre si es de 200 km. Si se mide el ángulo de elevación

scoundrel [369]

Answer:

$h \approx 59.898\,km$

Step-by-step explanation:

El diagrama trigonométrico que representa el enunciado es incluido abajo como adjunto. Las siguientes relaciones trigonométricas describen la localización del globo. (The trigonometric diagram representing the statement is included below as attachment. The following trigonometric relations describes the location of the balloon):

$\tan 27^{\circ} = \frac{h}{x}$