A triangle has sides measuring 15 15 and 15sqrt2 what are the angle measures of the triangle

Answers

Answer 1

Answer: We observe that we are in the presence of a rectangular triangle.
Therefore, we have:
An angle of 90 degrees.
An angle that is given by:
sine (x) = (15 / (15 * root (2)))
sine (x) = (1 / root (2))
x = asine (1 / root (2))
x = 45 degrees
And an angle that is given by:
180-90-45 = 45 degrees
Answer:
The angle measures of the triangle are:
90-45-45 degrees

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Solve the inequality 2x - 3 < x + 2 ≤ 3x + 5.

Answers

Hello,

1) 2x-3<x+2 ==>x<5

2) x+2<=3x+5==>-2x<=3==>x>=-3/2

Thus : -3/2<=x<3

Which is true about the polynomial –3xy2 + 5x2y?It is a binomial with a degree of 2.
It is a binomial with a degree of 3.
It is a trinomial with a degree of 2.
It is a trinomial with a degree of 3.

Answers

Answer: B. it is a binomial with a degree of 3

Step-by-step explanation:

3xy² + 5x²y

There are two terms so it is a BINOMIAL

xy² has a degree of 1 + 2 = 3

x²y has a degree of 2 + 1 = 3

The largest sum of exponents in a term is three so DEGREE is 3

The true statement about the polynomial is (a) It is a binomial with a degree of 2.

What are polynomials?

Polynomials are algebraic expressions that are represented by terms and factors

The polynomial is given as:

$-3xy^2 + 5x^2y$

The above polynomial has two terms; so it is a binomial

The highest power of the polynomial is 2; so it has a degree of 2

Hence, the true statement about the polynomial is (a) It is a binomial with a degree of 2.

Answers

First you must add the same numbers together, for instance, you wouldn't add 4y with 4 you have to add it with another number that is just like it, for instance 4y and 9y they are the same, so you can add them. So let's get to the problem now: 5y(2y-3)=(2y-3) 5y*2y=10y (10y-3)=(2y-3) You can do nothing to the other side because there are no numbers, that are the same.

Solve the equation for x
3/10x-1/5=1

Answers

Answer:

x=4

Step-by-step explanation:

$(3)/(10)x-(1)/(5)=1\n \n(3)/(10)x=(6)/(5) \n3x=12\nx=4$

Write a explicit formula for the sequence 10, 9.5, 9, 8.5, 8 then find ^a8

Answers

Answer:

Explicit formula for the sequence is $a_n=10.5-0.5n$ and $a_8=6$

Step-by-step explanation:

Given: Sequence = 10, 9.5 , 9 , 8.5 , 8

To find: Explicit Formula for the sequence and 8th term of sequence

1st term of sequence = 10

2nd term of sequence = 9.5

3rd term of sequence = 9

4th term of sequence = 8.5

5th term of sequence = 8

Difference between 2nd and 1st term = 9.5 - 10 = -0.5

Difference between 3rd and 2nd term = 9 - 9.5 = -0.5

Since, Difference is same in both cases

⇒ It is Arthematic Progression

⇒ First term, a = 10 and Common term, d = -0.5

using formula of AP for nth term we get,

$a_n=a+(n-1)d$

$a_n=10+(n-1)(-0.5)$

$a_n=10-0.5n+0.5$

$a_n=10.5-0.5n$

⇒ 8th Term of AP, $a_8=10.5-0.5*8=10-4=6$

Therefore, Explicit formula for the sequence is $a_n=10.5-0.5n$ and $a_8=6$

Answer:

The term number eight is 6.5

$a_(8)=6.5$

Step-by-step explanation:

The given sequence is an arithmetic sequence, because each term can be found by applying a difference.

In this case, you can observe that such difference is -0.5, because each term is going down by 0.5 units.

The formula that describes an arithmetic sequence is

$a_(n)=a_(1)+(n-1)d$

Where $a_(n)$ is the last term, $a_(1)$ is the first term, $n$ is the position of the last term and $d$ is the difference.

Each variable is

$a_(1) =10\nd=-0.5\nn=8\n$

Where we are gonna find $a_(8)$ the term number eight. So, replacing values, we have

$a_(n)=a_(1)+(n-1)d\na_(8)=10+(8-1)(-0.5)\na_(8)=10+7(-0.5)=10-3.5\na_(8)=6.5$

Therefore, the term number eight is 6.5.

How much will you save if you buy an item listed at $75.50 at a 25% discount?

Answers

Answer:

Amount of money saved = $18.87

Step-by-step explanation:

List Price of the item which is bought = $75.50

Now, This item is on discount.

Discount rate offered by the seller on the item = 25%

Discounted Price of the Item = List Price - 25% of List price

⇒ Discounted Price = 75.50 - 25% of 75.50

⇒ Discounted Price = 75.50 - 0.25 × 75.50

⇒ Discounted Price = 75.50 - 18.875

⇒ Discounted Price = $56.63

Now, Amount of money saved = List price - Discounted price

⇒ Amount saved = 75.50 - 56.63

Hence, Amount of money saved = $18.87

From the information we have been given, the original sale price is 75.50 and the discount is 25% of this price.

We need to calculate what value 25% stands for, so:

25 % of 75.50 → (25/100) ×100 → 0.25 ×75.50 = 18. 88

Therefore value of 25% of original price is 18.88 dollars

Rounded off 18.88 = 18.90 dollars.

You will save $ 18.90

The item will be sold to you at:

75.50 - 18.90 = 56. 60 dollars.

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