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Lemur [1.5K]
3 years ago
8

Dana has n quarters. Ivan has 2 fewer than 3 times the number of quarters Dana has. The expression n + 3 n−2 gives the number of

quarters they have altogether. Which is another way to write this expression?
Mathematics
1 answer:
Nesterboy [21]3 years ago
3 0
You can "collect terms" and write it as
  4n -2
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The figure, polygon ABCD is dilated by a factor of 2 to produce A B C D with the origin as the center of dilation
cestrela7 [59]

In the polygon ABCD, the production of point A' and point D' is (-2,-2)  and (4,-2) respectively.

<h3>What is the transformation rule?</h3>

In coordinate planes, the rule of transformation involves interchanging the x and y values on the plane such that:

\mathbf{(x,y) \to  (k_x, k_y)}

where;

  • k = scale factor

From the given information:

  • The scale factor = 2
  • the origin as a center of dilation for image vertices = (0, 0)

Now, using the coordinate vertices:

  • A = (-1, -1)
  • D = (2, -1)

The corresponding coordinate of the image vertices is as follows:

A(-1,-1) → A'(2 × (-1), 2 × (-1))

A' = (-2,-2)

D(2,-1) → A'(2 × (2), 2 × (-1))

D' = (4,-2)

Learn more about the transformation rule in coordinate planes here:

brainly.com/question/4251601

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7 0
2 years ago
Daryl has a total of 160 National Football League (NFL) trading cards from both the American Football Conference (AFC) and the N
Svet_ta [14]

Answer:

B

Step-by-step explanation:

Since A represents the number of AFC cars and N represents the number of NFC cards, and that Daryl has 160 total cards, then A+N = 160, the total number of cards. Furthermore, the number of AFC cards Daryl has is 8 more than 3 times the number of NFC cards, so A would be equal to 8 + 3N, or A = 3N + 8. The only system of equations with both of these correct equations is B.

4 0
3 years ago
use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos^4
Firdavs [7]

The expression cos⁴ θ in terms of the first power of cosine is <u>[ 3 + 2cos 2θ + cos 4θ]/8.</u>

The power-reducing formula, for cosine, is,

cos² θ = (1/2)[1 + cos 2θ].

In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.

We can do it as follows:

cos⁴ θ

= (cos² θ)²

= {(1/2)[1 + cos 2θ]}²

= (1/4)[1 + cos 2θ]²

= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}

= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)

= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]

= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8

= 3/8 + cos 2θ/4 + cos 4θ/8

= [ 3 + 2cos 2θ + cos 4θ]/8.

Thus, the expression cos⁴ θ in terms of the first power of cosine is <u>[ 3 + 2cos 2θ + cos 4θ]/8</u>.

Learn more about reducing trigonometric powers at

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5 0
2 years ago
Select all equations that match the tape diagram.
patriot [66]

Answer:

6x+8=35

35=8+6x

Step-by-step explanation:

id.k about 35=8+x+X+X+x+X+x

5 0
2 years ago
ABCD is a rectangle. AD = 15, AC = 25, and DC = 20. Find BD.
agasfer [191]

Answer:

20

Step-by-step explanation:

it is the same length as DC just going diagonal.

(i am not good at explaining in case you could not tell)

6 0
3 years ago
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