All categories

3 years ago

100 POINTS FOR WHOEVER ANSWER THIS QUESTION FULLY!!!

Mathematics

1 answer:

natulia [17]3 years ago

7 0

Answer:

Yes, diagonals bisect each other

Step-by-step explanation:

See attached

Plot the points on the coordinate plane

Visually, it is seen that the diagonals bisect each other.

We can prove this by calculating midpoints of AC and BD

Midpoint of AC has coordinates of:

x = (1 - 1)/2 = 0
y = (4 - 4)/2 = 0

Midpoint of BD has coordinates of:

x = (4 - 4)/2 = 0
y = (-1 + 1)/2 = 0

As per calculations the origin is the bisector of the diagonals.

You might be interested in

Let f(x)=2x^2-x-1 and let g(x)=x-1 Which statement is true?

sergij07 [2.7K]

Answer:

B is true

Step-by-step explanation:

given f(x) = 2x² - x - 1 and g(x) = x - 1

If x = - 1 is a root then f(- 1) = 0

f(- 1) = 2(- 1)² - (- 1) - 1 = 2 + 1 - 1 = 2 ≠ 0 ← False

If (x - 1) is a factor then x = 1 is a root and f(1) = 0

f(1) = 2(1)² - 1 - 1 = 2 - 1 - 1 = 0

⇒ g(x) = x - 1 is a factor of f(x) ← True

If x = 2 is a root then f(2) = 0

f(2) = 2(2)² - 2 - 1 = 8 - 3 = 5 ≠ 0 ← False

$\frac{x2x^2-x-1}{x-1}$ = $\frac{(2x+1)(x-1)}{x-1}$

Cancel the factor (x - 1) on the numerator/ denominator, leaving

$\frac{f(x)}{g(x)}$ = 2x + 1 with remainder 0 ≠ 2 ← False

7 0

3 years ago

Calculate surface area of pyramids

joja [24]

A=138.53 in
Use the formula and replace the variables with the length, width, and height to get the answer

3 0

3 years ago

In 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to com

PtichkaEL [24]

Answer:

The probability that exactly 97 of them finished the marathon is 0.221.

Step-by-step explanation:

We are given that in 2019, approximately 97.4% of all the runners who started the Boston Marathon were able to complete the 42.2 km race.

100 runners are chosen at random.

The above situation can be represented through the binomial distribution;

$P(X = x) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x = 0,1,2,3,......$

where, n = number of trials(or samples) taken = 100 runners

r = number of success = exactly 97

p = probability of success which in our question is the probability

that runners finished the marathon, i.e; p = 0.974

So, X ~ Binom(n = 100, p = 0.974)

Now, the probability that exactly 97 of them finished the marathon is given by = P(X = 97)

P(X = 97) = $\binom{100}{97} \times 0.974^{97} \times (1-0.974)^{100-97}$

= $161700 \times 0.974^{97} \times 0.026^{3}$

= 0.221

Hence, the required probability is 0.221.

6 0

3 years ago

A canoe shop owner wants to order more life jackets, He records what size life jackets he sells on one particular day to determi

Serga [27]

Answer:A:30

Step-by-step explanation:

The number 30 occurs the most

5 0

3 years ago

A new Community Center is being built in Oak Valley. The perimeter of the rectangular playing field is 382 yards. The length of

vesna_86 [32]

Answer:

The width is 50 yards and the length is 141 yards.

Step-by-step explanation:

Let's call: L the length of the field and W the width of the field.

From the sentence, the perimeter of the rectangular playing field is 382 yards we can formulate the following equation:

2L + 2W = 382

Because the perimeter of a rectangle is the sum of two times the length with two times the width.

Then, from the sentence, the length of the field is 9 yards less than triple the width, we can formulate the following equation:

L = 3W - 9

So, replacing this last equation on the first one and solving for W, we get:

2L + 2W = 382

2(3W - 9) + 2W = 382

6W -18 +2W = 382

8W - 18 = 382

8W = 382 + 18

8W = 400

W = 400/8

W = 50

Replacing W by 50 on the following equation, we get:

L = 3W - 9

L = 3(50) - 9

L = 141

So, the width of the rectangular field is 50 yards and the length is 141 yards.

3 0

3 years ago