I really need help with this. Please and thank you.

If the length of the hypotenuse of a right triangle is 39 millimeters and the length of one leg is 15 millimeters what is the le

Genrish500 [490]

Answer:

36 millimeters

Step-by-step explanation:

From Pythagoras theorem, the square of the hypotenuse is equal to the sum of the square of the two other legs

In mathematical terms;

a^2 = b^2 + c^2

Let a represent the hypotenuse = 39 mm and the length of one leg, say c, is 15 mm

Slotting in the values of a and b

39^2 = b^2 + 15^2

1521 = b^2 + 225

collect like terms

1521 - 225 = b^2

1296 = b^2

Take the square root of both sides

36 = b

Therefore b = 36 mm

6 0

3 years ago

What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0

1 year ago

5. Given: BCDF is a parallelogram; line AB is congruent to line BF

solong [7]

A and E are corresponding angles so A=E

3 0

2 years ago

Help me please I’m begging you:(

alex41 [277]

Answer:

Chips = 14

Pretzel = 14

Cookie = 8

Popcorn = 13

Question Mark = 222

Step-by-step explanation:

First Equation:

Chips + Pretzel + Chips = 42

Third Equation: Chips = Pretzel.

This means that

Pretzel + Pretzel + Pretzel = 42

Pretzel = $\frac{42}{3} =14$

Chips = Pretzel

Chips = $14$

Second Equation:

Cookie + Chips + Cookie = 30

We know that Chips = 14.

Cookie + 14 + Cookie = 30

Subtract 14 on both sides:

Cookie + Cookie = 16

Cookie = $16\div 2 =8$ .

Fourth Equation:

Cookie + Cookie + Popcorn = 29

We know that Cookie = 8.

8 + 8 + Popcorn = 29

16 + Popcorn = 29

Subtract 16 on both sides:

Popcorn = 13.

Question Mark:

(Popcorn + Popcorn) $\times$ Cookie + Chips = (13 + 13) $\times$ 8 + 14 = 26 $\times$ 8 + 14 = $208+14=222$

6 0

3 years ago

Read 2 more answers

Please help with this math problem for trig. A 6 m ladder is leaning against a wall. The base of the ladder is 1.5 m from the wa

VladimirAG [237]

Answer:

a = 5.81 m

Step-by-step explanation:

We can use the Pythagorean theorem

a^2 + b^2 = c^2

where b= 1.5 and c= 6

a^2 +1.5^2 = 6^2

a^2 +2.25 = 36

Subtract 2.25 from each side

a^2 +2.25-2.25 = 36-2.25

a^2 = 33.75

Take the square root of each side

sqrt(a^2) = sqrt(33.75)

a = 5.809475019

We only take the positive root because length must be positive

4 0

3 years ago