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2 years ago

Can u help me in this problem. i don't know how to do it

Mathematics

1 answer:

Readme [11.4K]2 years ago

5 0

Answer:

x=11

Step-by-step explanation:

The angles directly opposite 80 and 60 are also 80 and 60 respectively, because they are vertical angles
Now the triangle we see there, on the bottom left corner the angle is 80 degrees and the bottom right the angle is 60 degrees
Theorem states that the sum of angles in a triangle is 180 degrees
So 80 degrees plus 60 degrees plus the angle (x+51) is equal to 180
$80+60+(x+51)=180\\x+80+60+51=180\\x+191=180\\x+191-(191)=180-(191)\\x=11$

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If you multiply two prime numbers, will the result be prime or composite?

ki77a [65]

Answer:

It can never be a prime number.

Step-by-step explanation:

This is because the product of the two prime numbers are divisible by those two numbers, therefore going against the definition of a prime number. For example 3 and 5 are prime numbers and their product is 15. 15 can be divided by 3 and 5 so it is not a prime number.

Hope this helps.

4 0

2 years ago

On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter

andrezito [222]

Answer:

1) The common ratio = 1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio = 1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

3 0

2 years ago

The diameter of a circle is 3.2 meters. Which is the circumference of the circle rounded to the nearest hundredth of a meter?

Paraphin [41]

Answer:

10.05 meters

Step-by-step explanation:

If the diameter is 3.2 meters, then the radius is 1.6 meters.

Use the circumference formula, C = 2 $\pi$ r, and solve for C

C = 2 $\pi$ r

C = 2 $\pi$ (1.6)

C = 3.2 $\pi$

C = 10.05

So, to the nearest hundredth of a meter, the circumference is 10.05 meters

4 0

2 years ago

What is true about equivalent fraction

lisabon 2012 [21]

Numerators will be equal after the multiplication.

5 0

2 years ago

Solve x^2+2x+7=0 using the quadratic formula.

Aneli [31]

Answer:

$x=-1\pm \sqrt{6}i$

Step-by-step explanation:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(2)\pm\sqrt{2^2-4(1)(7)}}{2(1)}$

$x=\frac{-2\pm\sqrt{4-28}}{2}$

$x=\frac{-2\pm\sqrt{-24}}{2}$

$x=\frac{-2\pm\sqrt{-1*24}}{2}$

$x=\frac{-2\pm\sqrt{-1}\sqrt{24}}{2}$

$x=\frac{-2\pm i\sqrt{4*6}}{2}$

$x=\frac{-2\pm i\sqrt{4}\sqrt{6}}{2}$

$x=\frac{-2\pm2i\sqrt{6}}{2}$

$x=-1\pm \sqrt{6}i$

5 0

2 years ago

Can u help me in this problem. i don't know how to do it​

Can u help me in this problem. i don't know how to do it