Find the perimeter and area of the following triangle.

Step-by-step explanation:

we have to solve 2 right-angled triangles via Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle).

one triangle is 37, 12 and the longer part of the long diagonal.

the second triangle is 13, 12 and the shorter part of the long diagonal.

the whole diagonal is then the sum of both parts.

37² = 12² + longer part²

1369 = 144 + longer part²

longer part² = 1225

longer part = 35

13² = 12² + short part²

169 = 144 + short part²

25 = short part²

short part = 5

so, the total diagonal is 35 + 5 = 40 units.

The length of the longer diagonal obtained using Pythagorean theorem is 40 units

The Pythagorean theorem is a fundamental geometric relationship that states that the square of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the other two sides (the legs). Mathematically, we get

c² = a² + b²

Where a and b are the lengths of the legs  and c is the length of the hypotenuse side of the right triangle.

The diagonals of a kite are perpendicular to each other

The diagonal that is bisected in a kite is the shorter diagonal

The lengths from the left point to the middle and the distance from the right point to the middle are both 12, which indicates that the diagonal from left to right of the kite is bisected, which is the shorter diagonal. Therefore;

The length of the shorter diagonal is; 12 + 12 = 24

Therefore, the longer diagonal forms two right triangles to the left and two right triangles to the right

The hypotenuse length of the right triangles are 37 and 13, while the leg common to both right triangles on each side is half the length of the shorter diagonal, or 12

The Pythagorean theorem indicates that we get;

Length of the longer diagonal = √(13² - 12²) + √(37² - 12²) = 40

The length of the longer diagonal is 40 units

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Answer:

F = mg

Step-by-step explanation:

g is the constant of proportionality and force is the product of mass and the acceleration due to gravity

f is directly proportional to m, therefore, f = mg

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

Simple Interest is calculated using the following formula: SI = P × R × T/100, where P = Principal , T is time and r is interest rate.

So , by the values given

Principal :-rs 4000

Time :-2

rate of interest :- 10%

[tex] \frac{p \times r \times t}{100} [/tex]

[tex] \frac{4000 \times 10 \times 2}{100} [/tex]

[tex] = 800 \: rs[/tex]

Answer:

144√3 square feet

Step-by-step explanation:

There is a 30°-60°-90° triangle. In this triangle, the longer leg, which is the height of this parallelogram, is √3 times the length of the shorter leg (8 feet). Multiplying base times height, we have

18 * 8√3, which is 144√3 square feet.

Answer:

En la Imagen adjunta

Step-by-step explanation:

Toca Para Abrir Imagen

Espero haberte ayudado si es así dame Corona

Answer: x = 5

Step-by-step explanation:

    If you need to solve for x,

Given:

-1 (1 + 7x) - 6(-7 -x) = 36

Distribute:

-1 - 7x + 42 + 6x = 36

Combine like terms:

- x + 41 = 36

Subtract 41 from both sides of the equation:

- x = -5

Divide both sides by -1:

x = 5

Answer:

85cm^3

Step-by-step explanation:

Volume = Base Area * Height

17*5=85

Answer:

(i)  [tex]64+192 x^2+240 x^4+160x^6[/tex]

(ii) 1072

Step-by-step explanation:

Part (i)

Using Binomial series formula:

[tex](2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3[/tex]

              [tex]=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6[/tex]

              [tex]=64+192 x^2+240 x^4+160x^6[/tex]

Part (ii)

[tex](1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})[/tex]

               [tex]=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}[/tex]

[tex](2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)[/tex]

[tex]=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...[/tex]

There is no need to keep expanding since the remaining will include the variable.

Therefore, the term independent of x = 64 - 1152 + 2160 = 1072

Answer:

gh1

Step-by-step explanation:

19 is prime and 29 is not divisible by 19 therefore 1g is the highest. 5 and 3 are both prime so again, 1h and finally, 5 is a prime number so gh1 is the greatest factor

Answer: Fragment.

Step-by-step explanation:

A Fragment phrase can be defined as a sentence that resembles a sentence but lacks delivering a complete idea. This sentence serves as a dependent clause in a sentence.

The given sentence is an example of a fragment phrase or sentence. Though the phrase appears to be a sentence but it lacks complete idea because we don't know about which 'people' is it talking about.

Answer:

Choice C.

An isosceles triangle always has two sides of the same length.

Answer:

1- manners

2-respect

3-behaviour

4-avoid

Answer:

1- manners

2- respect

3- behavior

4- avoid

Answer:

Triangle C

Step-by-step explanation:

Triangle C contains a 90° angle.

Answer:

Triangle C

Step-by-step explanation:

The right triangle has one side that is 90° the other two sides have to add up to 90° (45 + 45= 90)

The rectangular equation which represents the parametric equations x =t^(1/2) and y = 2t is; y=2x².

According to the task content;

It follows that the parametric equations given are; x =t^(1/2) and y = 2t.

Since x =t^(1/2), then it follows that; x² = t.

Therefore, by substituting x² for t in y= 2t, then we have; y = 2x².

Read more on Parametric equations;

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Answer:

B on edg!

Step-by-step explanation:

just did the assingment

Answer:

24 degrees

Step-by-step explanation:

24 degrees because

angle a is 24 degrees

and since its the middles and main angle

24 degrees is the answer

Answer:

2 and 6

Step-by-step explanation:

Answer:

=x^3/4

Step-by-step explanation:

(x^1/2)(x^1/4)

same base

1/2+1/4

=3/4

=x^3/4

well, from birth to your twentieth birthday that'll just be 20 years, so

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=7000\left(1+\frac{0.08}{4}\right)^{4\cdot 20}\implies A=7000(1.02)^{80}\implies A\approx 34128.07[/tex]

Answer:

t = 55

Step-by-step explanation:

The figure is a  straight line and the sum of angles that make a straight line is 180 degrees

90 + t+ 35 = 180

125+t = 180

Subtract 125 from each side

125 +t-125 = 180-125

t = 180-125

t = 55

Answer 19.35 km

Step-by-step explanation:

We are looking for the Distance that Apostle Paul walked in 4.5 Hours!

I will be using the formula Distance=rate*time 1)

We DONT know the distance so I'll leave it as variable "D".

We know his rate of walking is 4.3 km/h, and we know he walked for a total of 4.5 hours.

Set up the following equation. D=4.3*4.5 2)

Simplify the equation above: D=19.35

Answer:

that is a Trapezoid

Step-by-step explanation:

it has two lines that are parallel and two lines that are not. crd. MathGeek99

Answer:

I believe it is a Quadrilateral

Step-by-step explanation:

It's a quadrilateral because of how many sides it has and other stuff

Answer: 3 11/12

Step-by-step explanation:

1 1/3 * 2 = 2 2/3

5/8 * 2 = 1 1/4

2 2/3 + 1 1/4 = 3 11/12

Answer: B) 24

Step-by-step explanation:

      All of these are multiples of 2 since they are all even numbers, so we will look to see which is a multiple of four.

Multiples of four are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, etc.

      I bolded and underlined 24 because it is in the list of options. B) 24 is a common multiple of 2 and 4.

24 / 2 = 12

24 / 4 = 6

Answer:

Step-by-step explanation:

The inequality that represent the number of students in the class is x ≤ 24. They could be 20 students

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Let x represent the number of students in the class, hence:

x ≤ 6(4)

x ≤ 24

If each team has at least 2 students:

x ≥ 6(2)

x ≥ 12 and x ≤ 24

The inequality that represent the number of students in the class is x ≤ 24. They could be 20 students

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Answer:

-2x + y

Step-by-step explanation:

This is distributive property, so multiply the terms inside the parentheses by 1/2.

1/2 (-4x) = -2x

1/2(2y) = y

-2x + y

Answer:

1st answer: 61000+(X-1) x 700

2nd answer: 64500

Step-by-step explanation:

Since it says the population increases linearly, which means by the same amount, it is an arithmetic progression. So the formula to find a term in arithmetic progression is [tex]T_{n}[/tex]=a + ( n - 1 ) x d , where a is the first term, n is number of terms, and d is common difference. So now just put the values in the equation, where 61000 is a, x is n and d is 700. To find second answer put 6 in place of n as it says from 2003 to 2009 which is 6 years later.

Answer:

it's true because the x=0 and that why it must be true FX may be the some I would say it's true