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3 years ago

26plz I kind of get it

Mathematics

1 answer:

Leno4ka [110]3 years ago

6 0

I think you do

5c=120

5c/5 120/5 =24

you need to get c by itself so divide 5 . When you divide 5 by one side do it to the other

120/5=24

3. Answer 24

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Find the perimeter of a square with side a. Are the perimeter of the square and the length of its side directly proportional qua

inna [77]

The perimeter of a square with side a = 7.2 cm is 28.8 cm. Yes there exists a direct proportional relationship between Side length and Perimeter of square

<h3>Solution:</h3>

Given that side of square "a" = 7.2 cm

We have to find the perimeter of square

The perimeter of square is given as:

Perimeter of square = 4a

Where "a" represents the length of side of square

Substituting the given value a = 7.2 cm in above formula, we get perimeter of square

Perimeter of square = 4(7.2) = 28.8 cm

Are the perimeter of the square and the length of its side directly proportional quantities?

$\begin{array}{l}{\text { perimeter of square }=4 a=4 \times \text { length of side }} \\\\ {\frac{\text { perimeter of square }}{\text { length of side }}=4}\end{array}$

The Perimeter is equal to a constant times the Side length, or the Perimeter divided by the Side length is equal to four. So this is definitely a proportional relationship between Side length and Perimeter.

Two values are said to be in direct proportion when an increase in one results in an increase in the other.

So when length of sides increases, perimeter also increases

Hence perimeter and length of side of square are directly propotional quantities

4 0

3 years ago

In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm

tangare [24]

Answer:

$AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm$

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

$AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm$

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

$\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD$

Consider right triangle CAH.By the Pythagorean theorem,

$CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8$

The length cannot be negative, so CD=8 cm and

$CA=\sqrt{3}CD=8\sqrt{3}\ cm$

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

$AB=2CA=16\sqrt{3}\ cm$

By the Pythagorean theorem,

$BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm$

3 0

2 years ago

Complete the proof for the following conjecture.

Ray Of Light [21]

Answer:

Statements Reasons

AC+CD=AD and AB+BD=AD Segment Addition Postulate

AC+CD=AB+BD Transitive/Substitution Property

AC=BD Given

BD+CD=AB+BD Substitution Property

CD=AB Subtraction Property

AB=CD Symmetric Property

Step-by-step explanation:

By segment addition postulate, we can say the following two equations:

AC+CD=AD and AB+BD=AD.

By either substitution/transitive property, you can say AC+CD=AB+BD.

You are given AC=BD, so we use substitution and write AC+CD=AB+AC.

After using subtraction property (subtracting both sides by AC), you obtain CD=AB.

By symmetric property, you may say AB=CD.

So let's write it into the 2 column-proof you have there:

Statements Reasons

AC+CD=AD and AB+BD=AD Segment Addition Postulate

AC+CD=AB+BD Transitive/Substitution Property

AC=BD Given

BD+CD=AB+BD Substitution Property

CD=AB Subtraction Property

AB=CD Symmetric Property

Properties/Postulates used:

Transitive property which says:

If a=b and b=c, then a=c.

Substitution property which says:

If a=b, then b can be substituted(replaced with) for a.

Subtraction property which says:

a=b implies a-c=b-c.

Segment Addition Postulate says:

If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.

3 0

3 years ago

90 is 1/10 of what number

jeyben [28]

The answer is 900
900/90=10. Therefore 90/900=1/10

5 0

3 years ago

Read 2 more answers

Pls help will give brainliest answer and 5star

Ipatiy [6.2K]

1. Which polygon or polygons are regular?

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

Therefore your answer is:

A. equilateral triangle

C. square

2. Which polygon is always irregular?

traingle - NOT (equilateral triangle)

trapezoid - YES

square - NOT

hexagon - NOT (regular hexagon)

6 0

3 years ago