What is 7 more than the sum of 6 and t please help

Which best explains whether a triangle with side links 5 cm 13 cm and 12 cm is a right triangle

Genrish500 [490]

Answer:

$5^{2} + 12^{2} = 13^{2}\\25+144=169$

Step-by-step explanation:

Squaring base and adjacent then adding them and finally getting the squareroot of the sum gives hypotenuse of a right angle triangle. In this case, squaring 5 and 12 then getting their square roots gives you 13, proving that it is a right angle

Here is the proof

$5^{2}=25\\12^{2}=144\\13^{2}=169\\25+144=169$

Therefore, the above dimensions are for a right angled triangle.

5 0

3 years ago

Sarah is a computer engineer and manager and works for a software company. She receives a

daser333 [38]

Answer:

a) Number of projects in the first year = 90

b) Earnings in the twelfth year = $116500

Total money earned in 12 years = $969000

Step-by-step explanation:

Given that:

Number of projects done in fourth year = 129

Number of projects done in tenth year = 207

There is a fixed increase every year.

a) To find:

Number of projects done in the first year.

This problem is nothing but a case of arithmetic progression.

Let the first term i.e. number of projects done in first year = $a$

Given that:

$a_4=129\\a_{10}=207$

Formula for $n^{th}$ term of an Arithmetic Progression is given as:

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

Where $d$ will represent the number of projects increased every year.

and $n$ is the year number.

$a_4=129=a+(4-1)d \\\Rightarrow 129=a+3d .....(1)\\a_{10}=207=a+(10-1)d \\\Rightarrow 207=a+9d .....(2)$

Subtracting (2) from (1):

$78 = 6d\\\Rightarrow d =13$

By equation (1):

$129 =a+3\times 13\\\Rightarrow a =129-39\\\Rightarrow a =90$

Number of projects in the first year = 90

b)

Number of projects in the twelfth year =

$a_{12} = a+11d\\\Rightarrow a_{12} = 90+11\times 13 =233$

Each project pays $500

Earnings in the twelfth year = 233 $\times$ 500 = $116500

Sum of an AP is given as:

$S_n=\dfrac{n}{2}(2a+(n-1)d)\\\Rightarrow S_{12}=\dfrac{12}{2}(2\times 90+(12-1)\times 13)\\\Rightarrow S_{12}=6\times 323\\\Rightarrow S_{12}=1938$

It gives us the total number of projects done in 12 years = 1938

Total money earned in 12 years = 500 $\times$ 1938 = $969000

8 0

2 years ago

Shane is measuring a shelf. It is 24 inches long. He measures again to find the number of feet. Will the length of the shelf be

Bond [772]

Answer:

Same length

24 ÷ 2=12

There is 12 inches in a foot

1 + 1= 2 ft

24 inches = 2 feet

5 0

3 years ago

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Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Tju [1.3M]

Answer:

-10 because you do parenthesis first

4 0

3 years ago

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Use the quadratic formula to solve for the roots of the following equation. x 2 – 4x + 13 = 0

Artyom0805 [142]

Quadratic Formula: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , with a = x^2 coefficient, b = x coefficient, and c = constant

With our equation, plug in the values:

$x=\frac{4\pm \sqrt{(-4)^2-4*1*13}}{2*1}$

Next, solve the exponent and multiplications:

$x=\frac{4\pm \sqrt{16-52}}{2}$

Next, solve the subtraction:

$x=\frac{4\pm \sqrt{-36}}{2}$

Next, factor out i (i = √-1):

$x=\frac{4\pm \sqrt{36}i}{2}$

Next, solve the square root:

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

Lastly, divide and your answer is:

$x=2\pm 3i$

5 0

3 years ago

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