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anyanavicka [17]

3 years ago

9

Jane currently has $3,360. In her savings account.prior to get paid,she had $1,230 in her savings account.hiw much was James pay

check?

1 answer:

Virty [35]3 years ago

5 0

James paycheck was $2130

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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

2 years ago

Read 2 more answers

What is the spees of the boat in meters per

Dahasolnce [82]

Answer C. 2.00 Meters/second

1 kilometer = 1000 meter
1 hour = 3600 seconds

7.2 x 1000 = 7200
so 7200 meters an hour
or 7200 meters every 3600 seconds
7200/3600
we then want the 3600 to become one second to find meters per (1)second.
so 7200/3600 simplified = 2. 2 meters per second
answer C

5 0

3 years ago

In a right triangle, the side opposite a 33 degree angle is 17 units. What is the length of the side adjacent to that angle to t

AnnyKZ [126]

Answer:

The length of the side adjacent to that angle is 26 units

Step-by-step explanation:

We are given

In a right triangle, the side opposite a 33 degree angle is 17 units

Firstly, we will draw diagram

we can use trig

$cot(33)=\frac{x}{17}$

now, we can solve for x

$x=17\times cot(33)$

$x=26.177$

So,

The length of the side adjacent to that angle is 26 units

6 0

3 years ago

Explain why 6^3x7^3=42^3 is correct.

Orlov [11]

Answer:

${6}^{3} \times {7}^{3} = {(6 \times 7)}^{3} = {42}^{3}$

Step-by-step explanation:

When two or more quantities have the same exponents, their bases can be multiplied together.

4 0

3 years ago

Read 2 more answers

Solve the quadratic equation:<br> 3x^2+x-5=0

adell [148]

3x²+x-5=0

a = 3, b = 1, c= -5

-> ∆ ( delta ) = b²-4ac = 61 > 0

-> x1 =( -b+√∆ )÷ 2a =...

x2 = (-b-√∆)÷2a =...

p/s: do your teachers teach you how to use ∆ ( delta ) in maths calculation ? i live in europe and our teachers teach us that way. however, it is a rịght and fast way. you should learn it.

4 0

2 years ago