Can someone help me please?1. Refer to the triangle below. If a = 3 and b = 3,
A. Find the exact length of c in unsimplified radical form
B. Find the exact length of c in simplified radical form
C. Find c to the nearest hundredth
I put the pic down below

2. Consider the numbers 4/13 and 3/10 .
A. Compare the numbers.
B. Find a rational number between the two given numbers.

3. Use the Babylonian method to approximate √19 to the nearest hundredth.

Answers

Answer 1

Answer: For 1) Use the pythagorean theorem and the formula for it is a^2+b^2=c2
so that will be 3^2+3^2=c^2
9+9=c^2
18=c2
then
$√(18) which is √(9(2)) √(9) √(2) the finally 3 √(2) ---- is the unsimplified formsimplified form is$ ≈4.2426
and the nearest hundredth 4.24

Answer 2

Answer:

The correct answers are:

#1: A) c = √18

B) c = 3√2

C) c = 4.24

#2: A) 4/13 > 3/10

B) 79/260

#3: 4.36

Explanation:

#1: A) We use the Pythagorean Theorem to solve this:

a² + b² = c²

3² + 3² = c²

9 + 9 = c²

18 = c²

Taking the square root of each side:

√18 = √c²

√18 = c

B) To simplify √18, we first find the prime factorization of 18:

18 = 9*2

9 = 3*3

This gives us

18 = 3*3*2

When we take the square root, we are looking for pairs. We have a pair of 3's; this means we take a 3 out:

3√2

C) In the calculator, we see that 3√2 = 4.24.

#2: A) First, we find a common denominator. The first thing that both 13 and 10 will divide into is 130:

(4*10)/130; (3*13)/130

40/130; 39/130

Since 40 > 39, this means that 4/13 > 3/10.

B) There is not enough space between the two fractions to use 130 as the denominator; we will double that to 260:

(40*2)/260; (39*2)/260

80/260; 78/260

The fraction between these two would be 79/260.

#3: Using the Babylonian method, we first make a guess. Since 9 is nearly half of 19, we will start there.

Next, we divide 19 by our guess:

19/9 = 2.111

We average this quotient with our guess:

(9 + 2.111)/2 = 11.111/2 = 5.5555

This is our new guess. Now divide 19 by this guess:

19/5.5555 = 3.4200342

Average this with our guess:

(5.5555+3.4200342)/2 = 4.4877671

This is our new guess. Divide 19 by this guess:

19/4.4877671 = 4.233731291

Average this with our new guess:

(4.4877671+4.233731291)/2 = 4.360749196

This is our new guess. Divide 19 by this guess:

19/4.360749196 = 4.357049476

Average this with our new guess:

(4.360749196+4.357049476)/2 = 4.358899

Make this our new guess. Divide 19 by this guess:

19/4.358899 = 4.3588988

Average this with our guess:

(4.358899+4.3588988)/2 = 4.3588989

Since the hundredths place has been the same the last few lines, we round to that: 4.36.

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Rachel plays a game by rolling two number cubes with side's numbered 1 through 6. To win the game, the sum of the numbers facing up must be 11. What is the probability that Rachel will win the game

Answers

Answer:

The probability that Rachel will win the game p(E) = 1/18 =0.055

Step-by-step explanation:

Explanation:-

Let "E" be the event of getting sum 11 on the two cubes with sides numbered through 1 to 6 so the number of favorable cases to E = { (6,5), (5,6)}

n(E) =2

The total number of exhaustive cases n(s) = 6^2 =36

Probability P(E) = $(number of favorable cases)/(total number of exhaustive cases.)$

The probability that Rachel will win the game

$P(E) = (2)/(36) = (1)/(18) =0.055$

The probability that Rachel will loose the game

$P(E)^(-) = 1-P(E)$

= 1 - 0.055 = 0.945

Answer:

1/18

Step-by-step explanation:

Which of the following best represents the average rate at which a person can quickly walk?3 steps per hours

3 steps per second

30 steps per minute

30 steps per second

Answers

B. 3 steps per second

Answer:

B. 3 steps per second

Step-by-step explanation:

the area of a rectangular plot 30 feet long and 20 feet wide will be doubled by creating a border around the plot. what width should the border be to accomplish this?

Answers

Answer:

(2x + 20)(2x + 30) = 1200 Aplus

Step-by-step explanation:

the area of the plot is 600 (20x30) and it needs to be 1200 (600x2)
only the width is changed so you divide it by the length which is 30
1200 divided 30 is 40 so the answer is 40 (another way is to just multiply the width by 2 since it's the only thing changing)

hope this helps :)

Please help and show work

Answers

Answer:

Step-by-step explanation:

Given: $g(x) = x^2 + 3$ and $h(x) = x - 2$ .

To find the composition of the functions: $(g \circ h)(x) = g(h(x))$

Here, $g(h(x)) = g(x - 2)$

$\implies (x - 2)^2 + 3$

$\implies x^2 -4x + 4 + 3 = x^2 - 4x +7$

We are to find $g(h(7))$ . That is to substitute $7$ in the place of $x$ .

We get: $(7)^2 -4(7) + 7 = 49 - 28 + 7 = 28$

Write the expression. Then, complete the statements.The word "twice" means
twice the difference of a number and seven
The words "the difference of indicate
Key Words
Replace With
The expression is written as
twice
2x
the difference of
(
a number
n
seven
7

Answers

The answer is shown below:

2
-
2(n-7)

What is expression?

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it

A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Expression Definition in Math

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

The complete statement is

The word "twice" means ( 2* )

The words "the difference of indicate (-)

The expression is written as

2( n-7)

Learn more about expression here:

brainly.com/question/14083225

#SPJ2

Answer:

The word “twice” means

✔ multiplication by 2

The words “the difference of” indicate