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2 years ago

PLEASE HELP ASAP!! WILL GIVE BRAINIEST + 30 POINTS!!

Mathematics

1 answer:

Goryan [66]2 years ago

6 0

Given rectangle RUTS, the missing reasons that justifies the five statements in the two-column proof are:

Given
Definition of rectangle.
Definition of rectangle.
By SAS Congruence Theorem.
By CPCTC.

<h3>What is a Rectangle?</h3>

A rectangle is a quadrilateral.
All four angles in a rectangle are right angles.
The opposite sides of a rectangle are parallel and congruent to each other.

Therefore, based on what we are given and the definition of a rectangle, we can establish that △URS ≅ △STU by SAS.

Since △URS ≅ △STU, therefore ∠USR = ∠SUT by CPCTC.

In conclusion, given rectangle RUTS, the missing reasons that justifies the five statements in the two-column proof are:

Given
Definition of rectangle.
Definition of rectangle.
By SAS Congruence Theorem.
By CPCTC.

Learn more about properties of rectangle on:

brainly.com/question/2835318

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Elis [28]

Answer: 151 books

Step-by-step explanation: 243-65-59+32=151

4 0

2 years ago

Read 2 more answers

Sheila has 12 1/2 pounds of potato salad. She wants to divide the potato salad into containers, each of which holds 2 1/4 pounds

NeX [460]

Answer:

6 containers needed

Step-by-step explanation:

Given

$Total = 12\frac{1}{2}\ lb$ ----- Size

$Container = 2\frac{1}{4}\ lb$ ----- Size

Required

Determine the number of containers needed

This question illustrates the knowledge of fraction and division.

To get the number of containers needed, we simply divide the total size by the size of the container as follows;

$Number = Total/Container$

$Number = 12\frac{1}{2}/2\frac{1}{4}$

Convert to improper fractions

$Number = \frac{25}{2}/\frac{9}{4}$

$Number = \frac{25}{2}*\frac{4}{9}$

$Number = \frac{100}{18}$

$Number = 5.5555556$

$Number = 6$ --- Approximated

4 0

3 years ago

Given the function f(x) = 3x + 1, evaluate f(a + 1). <br> A. 3a + 1 <br> B. a + 2<br> C. 3a + 4

Aleks [24]

Answer:

Given the function f(x) = 3x + 1, evaluation of f(a + 1) gives:

C. 3a + 4

Step-by-step explanation:

Given function:

f(x) = 3x + 1

We have to find f(a+1).

For this purpose, we will take x = a+1 and

substitute it in the function f(x) = 3x+1:

f(x) = 3x + 1

f(a+1) = 3(a+1) +1

f(a+1) = 3(a) + 3(1) +1

f(a+1) = 3a+3+1

f(a+1) = 3a + 4

So the function f(a+1) is equal to option C. 3a + 4.

5 0

2 years ago

can someone pls help me? i have no idea what to do. pls show the work steps for the questions. i will mark u as

tiny-mole [99]

Ok, so the question is based on geometric progression. Remember, the formula for calculating the nth-term of a geometric progression is: $a*r^{n-1}$ . The a in the expression stands for the 1st term of the sequence, and r is the common ratio of the elements of the sequence. Now let's take a look at the problem.

"A ping pong ball has a 75% rebound ration". We can infer that our common ratio, r, is 75% which is 0.75.

"When you drop it from a height of k feet...", this means the first height you drop it from, a.k.a, the first term.

Now going back to the expression, the nth-term = $a*r^{n-1}$ , we can substitute our common ration, 0.75 with r, and our 1st term, k, with a. This becomes: $k * 0.75^{n-1}$ . This becomes our expression.

a. The highest height achieved by the ball after six bounces. Our nth-term here is 6, so let's use our expression to find the 6th term. $n_{6} = 235 * 0.75^{6-1} = 235*0.75^{5} = 235*0.2373 = 55.7655ft$

b. The total distance travelled by the ball when it strikes the ground for the 12th time. This involves the use of the sum of elements in the geometric progression. The formula for that is $\frac{a(1 - r^{n})}{1-r}$ , provided that r is less than 1, which it is in this case, since 0.75 is less than one. Our nth-term here is 12, so we substitute.