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3 years ago

The area of a right triangle is 210 square inches. The height of the right triangle is 35 inches.

Mathematics

1 answer:

Semmy [17]3 years ago

7 0

Answer:

37 inch

Step-by-step explanation:

Area of ∆ = ½ height x base

210 = ½ x 35 x base

12 = base

Using Pythagoras theorem,

=> hypotenuse = √height² + base²

=> hypotenuse = √35² + 12² = 37

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Step-by-step explanation:

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2 years ago

Angie takes a ferry ride with her niece. The cost of a ticket for an adult (Angie) is three dollars more than the cost of the ti

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3 years ago

There are 60 teachers in the school. 40 of them are from Ireland. What fraction of teachers are from Ireland?

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3 years ago

100 points + Brainliest Please help! Please give steps!!

Mrac [35]

Answer:

$\textsf{A)}\quad \dfrac{5}{10}, \:\: -\dfrac{6}{11}, \:\: \dfrac{7}{12}, \:\: -\dfrac{8}{13}$

$\textsf{B)} \quad \text{f}\:\!(n)=\dfrac{n}{n+5}$

If n is odd then f(n) is positive.

If n is even then f(n) is negative.

C) positive

Step-by-step explanation:

Given sequence:

$\dfrac{1}{6},\:\: -\dfrac{2}{7},\:\: \dfrac{3}{8}, \:\:-\dfrac{4}{9},...$

From inspection of the sequence the pattern is:

Add 1 to the numerator of the previous term.
Add 1 to the denominator of the previous term.
Make every other term negative.

Therefore, assuming the pattern continues, the next four terms in the sequence will be:

$\dfrac{5}{10}, \:\: -\dfrac{6}{11}, \:\: \dfrac{7}{12}, \:\: -\dfrac{8}{13}$

An <u>explicit formula</u> for an arithmetic sequence allows you to find the nth term of the sequence.

$\textsf{First term}: \quad \text{f}(1)=\dfrac{1}{6}$

$\textsf{Second term}: \quad \text{f}(2)=-\dfrac{2}{7}$

From inspection of the sequence, we can see that the <u>numerator</u> is the position of the term (n) in the sequence. So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.

The denominator is 5 more than the position of the term in the sequence. So when n = 1 the denominator is 1 + 5 = 6, and when n = 2 the denominator is 2 + 5 = 7.

We can also observe that if the numerator (the value of n) is odd then the term is positive, and if the numerator (the value of n) is even then the term is negative.

Therefore, the rule for the nth term is:

$\text{f}\:\!(n)=\dfrac{n}{n+5}$

If n is odd then f(n) is positive.

If n is even then f(n) is negative.

53 is an odd number.

As the function f(n) is positive when n is odd, the sign of f(53) is positive.

6 0

2 years ago

Which expressions have a value of 16/81? Check all that apply.

SSSSS [86.1K]

$\huge\text{Hey there!}$

$\large\textsf{Which expressions have a value of }\mathsf{\dfrac{16}{81}?\ }\large\textsf{Check ALL that APPLY. }$

$\mathsf{(\dfrac{2}{3})^4}\\\\\mathsf{= \bf \dfrac{2}{3}\times\dfrac{2}{3}\times\dfrac{2}{3}\times \dfrac{2}{3}}\\\\\mathsf{= \bf \dfrac{2\times2\times2\times2}{3\times3\times3\times3}}\\\\\mathsf{2\times2\times2\times2}\\\mathsf{2\times2 = \bf 4}\\\mathsf{4\times4= \bf 16}\\\\\mathsf{\dfrac{\bf 16}{3\times3\times3\times3}}\\\\\mathsf{3\times3\times3\times3}\\\mathsf{3\times3 = 9}\\\mathef{9\times9 = \bf 81}\\\\\mathsf{\dfrac{16}{\bf 81}}\\\\\mathsf{= \bf \dfrac{16}{81}}$

$\large\text{Option A. could POSSIBLY be your ANSWER}$

$\mathsf{(\dfrac{16}{3})^4}\\\\\mathsf{= \dfrac{16}{3}\times\dfrac{16}{3}\times\dfrac{16}{3}\times\dfrac{16}{3}}\\\\\mathsf{= \dfrac{16\times16\times16\times16}{3\times3\times3\times3}}\\\\\mathsf{16\times16\times16\times16}\\\mathsf{16\times16= \bf 256}\\\mathsf{256\times256 = \bf 65,536}\\\\\mathsf{\dfrac{\bf 65,536}{3\times3\times3\times3}}\\\\\mathsf{3\times3\times3\times3}\\\mathsf{3\times3 = \bf 9}\\\mathsf{9\times9 = \bf 81}\\\\\\\mathsf{\dfrac{65,536}{\bf 81}}\\\\\mathsf{\bf = \dfrac{65,536}{81}}$

$\large\text{Option B. CANNOT be your POSSIBLE ANSWER}$

$\mathsf{(\dfrac{4}{81})^2}\\\\\mathsf{=\dfrac{4}{81}\times\dfrac{4}{81}}\\\\\mathsf{= \dfrac{4\times4}{81\times81}}\\\\\mathsf{4\times4= \bf 16}\\\\\mathsf{\dfrac{\bf 16}{81\times81}}\\\\\mathsf{81\times81=\bf 6,561}\\\\\mathsf{\dfrac{16}{\bf 6,561}}\\\\\mathsf{= \bf \dfrac{16}{6,561}}$

$\large\text{Option C. CANNOT be your POSSIBLE ANSWER}$

$\mathsf{(\dfrac{4}{9})^2}\\\\\mathsf{= \dfrac{4}{9}\times \dfrac{4}{9}}\\\\\mathsf{= \dfrac{4\times4}{9\times9}}\\\\\mathsf{4\times4 = \bf 16}\\\\\mathsf{\dfrac{\bf 16}{9\times9}}\\\\\mathsf{9\times9 = \bf 81}\\\\\\\mathsf{\dfrac{16}{\bf 81}}\\\\\\\mathsf{= \bf \dfrac{16}{81}}$