MATHEMATICS HIGH SCHOOL

Find the length of the third side. If necessary, write in simplest radical form.
√51
10
Find the length of the third side. If necessary, write - 1

Answers

Answer 1
Answer:

Answer:

7

Step-by-step explanation:

10² - root 51² = a²

100 - 51 = a²

49 = a²

a = 7

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A sequence is defined recursively by f(1)=16 and f(n)=f(n-1)+2n. Find f(4)

1) 32

2) 30

3) 28

4) 34

Answers

f(1)=16 \ \ \ and \ \ \ \ f(n)=f(n-1)+2n \n \nf(2)=f(1)+2\cdot2=16+4=20\n \nf(3)=f(2)+2\cdot3=20+6=26\n \nf(4)=f(3)+2\cdot4 =26+8=34

Ans.\ 4)

5) What is the value of n in the picture?3n
n 14
A) 19
B) 33
C) 57
D) 41.5

Answers

ok. because those two angles are sumplimentary, (they equal 180 degrees) we can set up an equations.
3n+n+14=180

then isolate the variable
4n+14=180 
     -14   -14
4n=166

then divide to undo the multiplication

4n=166
---   ----
4      4
 
n=41.5
that's super wrong .the answer cannot be 41.5 because if n=41.5 then 41.5 ×4 =166 +90 +14 =270 and that's wrong because in the diameter need have 180 not 270 so is 19×4+90+14=180 answer = 19

OlympiDuring the 1996 Summer Olympics in Atlanta, Georgia
the American athlete Michael Johnson set an
and world record in the men's 200-meter run. He finishe
the race in 19.32 seconds, breaking the previous Olympi
record of 19.75 seconds. By how much did Micha
Johnson break the previous Olympic record?

Answers

Answer: he broke the record by 0.43 seconds

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Answers

1. The first theorem used is that vertical angles are congruent.
2. The next theorem used is that adjacent angles in a parallelogram are supplementary. 
3. The definition of supplementary angles is then used for angle formed by intersecting  lines.
4. The theorem on vertical angles is used again.
5. Finally, the definition of the transitivity property is used to prove that alternate exterior angles are congruent.

Using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Recall:

  • Alternate exterior angles are angles that lie outside the two lines that is cut across by a transversal but on opposite sides along the transversal.
  • Examples of alternate exterior angles are <2 and <7; <4 and <5 as shown in the figure attached below.

If we are given that m \parallel n in the diagram attached below, the following are theorems and definitions we can use to prove that \angle 4 \cong \angle 5 (alternate exterior angles).

Statement 1: \angle 4 \cong \angle 8

Reason: Corresponding Angles Theorem

The corresponding angles theorem states that when two parallel lines (lines m and n) are intersected by a transversal line (line w), the two corresponding angles formed (e.g. <4 and <8) are congruent.

Statement 2: \angle 8 \cong \angle 5

Reason: Vertical Angles Theorem

The Vertical Angles Theorem states that the opposite vertical angles (e.g. <8 and <5) formed when two lines (lines n and w) intersect are congruent to each other.

Statement 3: \angle 4 \cong \angle 5

Reason: Transitive Property of Congruence

The Transitive Property of Congruence states that if a = b; and b = c; then a = c.

Therefore, using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Learn more here:

brainly.com/question/16182992

A carpenter added a diagonal brace to gate. The gate is 8ft. Wide and 10 ft. Tall. How long is the brace

Answers

Answer:

The brace is 2√(41) ft ≅ 12.806 ft long

Step-by-step explanation:

The length of the diagonal of a rectangle can be found using this rule

d=\sqrt{l^(2)+w^(2)} , where

  • l is its length
  • w is its width

∵ The gate has shaped a rectangle

∵ Its length = 10 ft

∵ Its width = 8 ft

∴ l = 10 and w = 8

∵ The brace is the diagonal

→ By using the rule above

∴ d=\sqrt{(10)^(2)+(8)^(2)}=√(100+64)=√(164)

∴ The length of the brace = 2√(41) ≅ 12.806 ft

∴ The brace is 2√(41) ≅12.806 ft long

Please help me with this math question?? :)The measure of each exterior angle of a regular octogon is _____ the measure of each exterior agle of a regular hexagon.

A. Greater than
B. Less than
C. Equal to

Answers

\bf \textit{exterior angle of a regular polygon}\n\n\n\theta=\cfrac{360}{n}\qquad \begin{cases}\theta=\textit{the angle in degrees}\nn=\textit{number of sides}\end{cases}

now, an OCTAgon, has OCTA=8, sides
an HEXAgon, has HEXA=6, sides

check what their external angles are, and compare :)
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