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2 years ago

Given the number x=78 and y=-13 which statement is true

Mathematics

2 answers:

Phoenix [80]2 years ago

5 0

Answer:

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Step-by-step explanation:

rjkz [21]2 years ago

4 0

|x| = |78| = 78

so x = 78

and

|y| = |-13| = 13

so y = 13

Answer is C. |x| = 78 and |y| = 13

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Ramona's backyard is fenced and represented by parallelogram YARD with measures in meters. She installed a 12-meters fence to se

Alisiya [41]

The fencing line x is the height of a rectangle triangle of base = y, hypothenuse of 9 m, so we use Pythagoras theorem to solve:

hyp^2 = height^2 + base^2
9^2 = x^2 + y^2
x^2 = 81 - y^2

we can see that x is also the height of another rectangle triangle of base = 15 - y, hypothenuse of 12 m, so we use Pythagoras theorem to solve:
hyp^2 = height^2 + base^2
12^2 = x^2 + (15 - y)^2

lets expand:
144 = x^2 + 225 - 30y + y^2

substitute x^2 from the first equation in the last:
144 = 81 - y^2 + 225 - 30y + y^2
144 = 81 + 225 - 30y
30y = -144 + 81 + 225
y = 5.4 m

substitute in the fence equation:
x^2 = 81 - y^2
x^2 = 81 - 5.4^2
x = 7.2 m that is the length of the fence

3 0

2 years ago

Find the length of side AB Give answer to 3 significant figures

Rina8888 [55]

Answer:

AB = 8.857 cm

Step-by-step explanation:

Here, we are given a right angle $\triangle ABC$ in which we have the following things:

$\angle A = 90 ^\circ\\\angle C = 41 ^\circ\\\text{Side }BC = 13.5 cm$

Side BC is the hypotenuse here.

We have to find the side AB.

Trigonometric functions can be helpful to find the value of Side AB here.

Calculating $\angle B$ :

Sum of all the angles in $\triangle ABC$ is $180^\circ$ .

$\Rightarrow \angle A + \angle B + \angle C = 180^\circ\\\Rightarrow 90^\circ + \angle B + 41^\circ = 180^\circ\\\Rightarrow \angle B = 49^\circ$

We know that cosine of an angle is:

$cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\Rightarrow cos B = \dfrac{AB}{BC}\\\Rightarrow cos 49^\circ = \dfrac{AB}{13.5}\\\Rightarrow AB = 13.5 \times 0.656\\\Rightarrow AB = 8.857 cm$

So, side AB = 8.857 cm .

6 0

2 years ago

What is the difference between 4Σn=1, 2n+1 and 4Σi=1, (2i+1)?

alina1380 [7]

Answer:

Step-by-step explanation:

Each expression is a way to write the sum ...

3 + 5 + 7 + 9

That sum in each case is 24, so the difference is 24-24 = 0.

6 0

2 years ago

Jason bought 10 of the 30 raffle tickets for a drawing. What is the probability that Jason will win all 3 of the prizes if once

svet-max [94.6K]

Given:

Total of raffle tickets = 30

Number of tickets Jason bought = 10

Number of prizes = 3

To find:

The probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away.

Solution:

Total of raffle tickets = 30

Number of prizes = 3

So, number of total outcomes is

$n(S)=^{30}C_3$

Number of tickets Jason bought = 10

So, number of favorable outcomes is

$n(A)=^{10}C_3$

Now,

$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$\text{Probability}=\dfrac{n(A)}{n(S)}$

$\text{Probability}=\dfrac{^{10}C_3}{^{30}C_3}$

$\text{Probability}=\dfrac{\dfrac{10!}{(10-3)!3!}}{\dfrac{30!}{(30-3)!3!}}$

$\text{Probability}=\dfrac{10\times 9\times 8\times 7!}{7!3!}\times\dfrac{27!3!}{30\times 29\times 28\times 27!}$

$\text{Probability}=\dfrac{10\times 9\times 8}{30\times 29\times 28}$

$\text{Probability}=\dfrac{6}{203}$

Therefore, the correct option is A.

7 0

2 years ago

Read 2 more answers

The mean sat verbal score is 486, with a standard deviation of 95. use the empirical rule to determine what percent of the score

Pavel [41]

Find the z-scores for the two scores in the given interval.

$z=\frac{x-\mu}{\sigma}$

For the score x =391, $z=\frac{391-486}{95}=\frac{-95}{95}=-1$ .

For the score x = 486, $z=\frac{486-486}{95}=0$

Now you want the area (proportion of data) under the normal distribution from z = -1 to z = 0. The Empirical Rule says that 68% of the data falls between z = -1 to z = 1. But the curve is symmetrical around the vertical axis at z = 0, so the answer you want is HALF of 68%.

8 0

2 years ago