Which pairs of quadrilaterals can be shown to be congruent using rigid motions? Select Congruent or Not Congruent for each pair

Answer:

The correct statements are;

1) ΔBCD is similar to ΔBSR

2) BR/RD = BS/SC

3) (BR)(SC) = (RD)(BS)

Step-by-step explanation:

1) Since RS is parallel to DC, we conclude that;

∠BDC = ∠BRS (Angles formed on the same side of the transversal)

Furthermore;

∠BCD = ∠BSR (Angles formed on the same side of the transversal)

∠CBD = ∠CBD (Reflexive property)

Thus;

ΔBCD ~ ΔBSR by the Angle-Angle-Angle (AAA) similarity criterion.

2) Given that  ΔBCD ~ ΔBSR, we obtain;

BC/BS = BD/BR → (BS + SC)/BS = (BR + RD)/BR = 1 + SC/BS = RD/BR + 1

1 + SC/BS = 1 + RD/BR thus, SC/BS = 1 + BR/RD - 1

SC/BS = RD/BR

By inverting both sides we find;

BR/RD = BS/SC

3) From BR/RD = BS/SC, we apply cross multiplication;

BR/RD = BS/SC leads to;

BR × SC = RD × BS → (BR)(SC) = (RD)(BS).

The ratio of women to men is 34 to 382. To find the total sales, we compute 382 multiplied by 2.50, resulting in $955. For women, the calculation is 34 multiplied by 1.25, which equals $42.50. Therefore, summing these amounts gives us $955 + $42.50 = $997.50.

Response:

Monomial

Trinomial

Monomial

Trinomial

Binomial

Explanation in detail:

A monomial consists of one distinct term

A binomial consists of two distinct terms

A trinomial consists of three distinct terms

In the first example, the -x^2 and +x^2 cancel each other, and since 2x and 4x are similar terms, combining gives you 6x, which is a monomial.

In the second example, after adding +3 and -2, you get three distinct terms that can't be combined, thus it's a trinomial

In the third example, all variables cancel out, resulting in just one term, 3, making it a monomial

In the fourth one, after combining like terms, you end up with:

x^3 + 3x^2 + 7x

This makes it a trinomial

In the last example, the 6x and -6x cancel, leaving two terms, qualifying it as a binomial.

Answer: CI = (0, 8)

Step-by-step explanation: The confidence interval for the difference in means is given as

Lower limit

= (x1 - x2) + margin of error

Upper limit

= (x1 - x2) - margin of error

Where x1 - x2 = 8 and the margin of error = 8

For the lower limit,

= 8 - 8 = 0

For the upper limit

= 8 + 8 = 16

Thus, CI = (0, 8)