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2 years ago

What is the remainder when P(x) is divided by (x-2) will mark brainliest if answer is correct

Mathematics

1 answer:

docker41 [41]2 years ago

8 0

Answer:

pls make it even more clear

Step-by-step explanation:

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A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude

I am Lyosha [343]

Answer:

Area of given triangle is 939.15cm² and smallest altitude is 30.8cm

<h3>Solution:</h3>

We are given three sides of a triangle, Let the sides be :

( a ) = 35 cm

( b ) = 54 cm

( c ) = 61 cm

We can find the area of the triangle with its three sides using Heron's Formula

<u>Heron's </u><u>Formula</u>

Heron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:

$\sf{ \pmb { \longrightarrow \: \sqrt{s(s - a)(s - b)(s - c)} }}$

where ( s ) :

$\sf \longrightarrow s = \dfrac{a + b + c}{2}$

Therefore, for the given triangle first we will calculate ( s )

$\begin {aligned}\quad & \quad \longmapsto \sf s = \dfrac{a + b + c}{2} \\ & \quad \longmapsto \sf s = \dfrac{35 + 54 + 61}{2} \\ & \quad \longmapsto \sf s = \dfrac{150}{2} \\ & \quad \longmapsto \sf s = 75cm \end{aligned}$

Now, Area of triangle will be:

$\begin{aligned}&:\implies \sf\quad \sf \: A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \: A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\&:\implies \sf\quad \sf \: A = \sqrt{75 \times 40 \times 21 \times 14} \\ &:\implies \sf\quad \sf \: A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5} \\ &:\implies \sf\quad \sf \: A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5} \\ &:\implies \sf\quad \sf \: A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf A =939.15 {cm}^{2} }} \end{aligned}$

Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,

$\begin{aligned}&:\implies \sf\quad \sf \: Area =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times b \times h =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times 61 \times h = 939.15 \\&:\implies \sf\quad \sf \: h =939.15 \times \dfrac{2}{61} \\&:\implies \sf\quad \sf \: h = \dfrac{1818.3}{61} \\ &:\implies \sf\quad \boxed{ \pmb{\sf \: h =30.79 \: (approx)}} \end{aligned}$

3 0

1 year ago

Read 2 more answers

Triangle ABC is congruent to triangle DEF. If DE = 41, EF = 23, DF = 36, and AB = 8x − 7, what is x? Round to the nearest tenth.

Nadya [2.5K]

The side AB is equal to the side DE. Then the value of x is 6.

<h3>What is the triangle?</h3>

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

Triangle ABC is congruent to triangle DEF.

If DE = 41, EF = 23, DF = 36, and AB = 8x − 7.

Then the side AB is equal to the side DE.

AB = DE

8x - 7 = 41

8x = 48

x = 6

Then the value of x is 6.

More about the triangle link is given below.

brainly.com/question/25813512

#SPJ1

5 0

2 years ago

Read 2 more answers

An airplane is flying from New York City to Los Angeles the distance it travels in Miles D is related to the time in seconds T b

tatiyna

Answer:

It takes 85 seconds to go 12.75 miles

Step-by-step explanation:

We are given

An airplane is flying from New York City to Los Angeles

the distance it travels in Miles D is related to the time in seconds T by the equation

$d=0.15T$

we are given to find time when distance is 12.75 miles

so, we can set d=12.75

and then we can solve for T

$12.75=0.15T$

We can divide both sides by 0.15

$T=\frac{12.75}{0.15}$

$T=85$

So,

It takes 85 seconds to go 12.75 miles

6 0

2 years ago

HELP ME PLS!!!

atroni [7]

Answer:

A. This conclusion was drawn using the law of detachment

Step-by-step explanation:

Definition:

Law of Detachment

If p equals q and p is also true. Then q is true.

if a number is a whole number, then it is an integer.

3 is a whole number (true statement) , so it 3 is an integer. (must be true)

8 0

2 years ago

2. Ms. Groves has trays of paints for students in her

olga55 [171]

Answer:

Each tray has 5 colours and one of the colour on the tray is purple. Hence 1/5 of the colours on the tray is purple and thus 1/5 of the colours on the 20 trays is purple. The fraction of colours on the trays will not change. If written out logically, 20 purples out of 100 colours in total on the trays will also given the fraction 1/5.

4 0

3 years ago