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3 years ago

The polygons in each pair are similar. find the missing side length

Mathematics

1 answer:

pochemuha3 years ago

6 0

If both are similar ratio of sides will be same

$\\ \sf\longmapsto \frac{x}{25} = \frac{7}{5} \\ \\ \sf\longmapsto 5x = 7 \times 25 \\ \\ \sf\longmapsto 5x = 175 \\ \\ \sf\longmapsto x = \frac{175}{5} \\ \\ \sf\longmapsto x = 35$

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What are the coordinates of the vertex of the parabola with the equation y = x + 2x - 3?

loris [4]

Answer:

The coordinates of the vertex are (-1,-4).

Step-by-step explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

$y-k=a(x-h)^2$

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

We are given the function:

$y=x^2+2x-3$

We must transform the equation above by completing squares:

The first two terms can be completed to be the square of a binomial. Recall the identity:

$x^2+2xy+y^2=(x+y)^2$

Thus if we add and subtract 1:

$y=(x^2+2x+1)-3-1$

Operating:

$y=(x^2+2x+1)-4$

The trinomial in parentheses is a perfect square:

$y=(x+1)^2-4$

Adding 4:

$y+4=(x+1)^2$

Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).

The coordinates of the vertex are (-1,-4).

4 0

3 years ago

4 1/5 divided by 6 3/4 = ?

trasher [3.6K]

Answer: 28/45

Step-by-step explanation:

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3 years ago

A college library has five copies of a certain text on reserve. Two copies (1 and 2) are first printings, and the other three (3

sleet_krkn [62]

Answer:

B) Outcomes in A = {3, 4, 5} .

C) Outcomes in B = {5, 15, 25, 125, 215} .

D) Outcomes in C = {3, 4, 5, 23, 24, 25} .

Step-by-step explanation:

We are given that a college library has five copies of a certain text on reserve. From which two copies (1 and 2) are of first printings, and the other three (3, 4, and 5) are of second printings.

Also, it is stated that a student will stop examining the books only when a second printing has been selected.

A) The outcomes in S are :

 Number of outcomes Selection of Outcomes

1 3

2 4

3 5

4 13

5 14

6 15

7 23

8 24

9 25

10 123

11 124

12 125

13 213

14 214

15 215

Here outcome 123 means 1st copy of first printing is examined then 2nd copy of first printing is examined and then 3rd copy of second printing is examined and then the student stops.

B) A denote the event that exactly one book must be examined.

So, the outcomes in A will be outcome number 1, 2 and 3 corresponding to selection 3, 4 and 5 of second printing because in these outcomes only one book is examined.

Hence, outcomes in A = {3, 4, 5} .

C) B be the event that book 5 is the one selected. It means all those outcomes in which book 5 was last examined. So, the outcomes in B will be outcome number 3, 6, 9, 12, 15 corresponding to selection 5, 15, 25, 125, 215

Hence, outcomes in B = {5, 15, 25, 125, 215} .

D) C be the event that book 1 is not examined which is outcome number 1, 2, 3, 7, 8, 9 corresponding to selection 3, 4, 5, 23, 24, 25 .

Hence, outcomes in C = {3, 4, 5, 23, 24, 25} .

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abruzzese [7]

Answer:

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Step-by-step explanation:

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