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3 years ago

How do I find the slope of: y = -5x -1

1 answer:

5 0

In a slope intercept equation in the form of y=mb+b,
m is the slope. m is the coefficient of x, meaning it is the number x is multiplied by. In this case, m happens to be
-5
which is your answer

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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

Heron's Formula

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

Please help me out with this :)

yan [13]

Answer:

y = x - 5

Step-by-step explanation:

Given the equation

y = x + ?

We are being asked what value is added to x to give y

Consider the table, that is

x = 1 → y = - 4

x = 2 → y = - 3

x = 3 → y = - 2

x = 4 → y = - 1

x = 5 → y = 0

x = 6 → y = 1

In each case 5 is being subtracted from x to obtain y, that is

y = x - 5 ← equation relating x and y

6 0

3 years ago

Read 2 more answers

11. In a sample of n=6, five individuals all have scores of X=10 and the sixth person has a score of x=16. What is the mean for

ahrayia [7]

Answer:

Step-by-step explanation:

Given that in a sample of n=6, five individuals all have scores of X=10 and the sixth person has a score of x=16

i.e. the data entries are

10,10,10,10,10,16

Sum = 66

No of items n = 6

Average = sum/no of entries

= $\frac{66}{6} \\=11$

Average is 11.

mean of this sample is 11

8 0

3 years ago

Solve the inequality and enter your solution as an inequality comparing the variable to the solution in the box below. 18 + x &g

storchak [24]

Hi there! :)

Answer:

x>24

*The answer must have a positive sign and greater than symbol sign.*

Step-by-step explanation:

First, you switch sides.

$x+18>42$

Then, you subtract by 18 from both sides of an equation.

$x+18-18>42-18$

Finally, you subtract by the numbers from left to right.

$42-18=24$

Final answer is x>24

I hope this helps you!

Have a nice day! :)

-Charlie

7 0

2 years ago

Find the value of the combination. From a committee consisting of 8 men and 5 women, a subcommittee is formed consisting of 4 me

Alex787 [66]

Out of 8 men, 4 can be selected and lined up in (8 x 7 x 6 x 5) = 1,680 ways.
But within that number, each group of 4 appears in (4 x 3 x 2) = 24 orders.
So there are (1,680 / 24) = 70 different groups of men.

Out of 5 women, 3 can be selected and lined up in (5 x 4 x 3) = 60 ways.
But within that number, each group of 3 appears in (3 x 2) = 6 orders.
So there are (60 / 6) = 10 different groups of women.

Each different group of 70 men can be joined by any of the 10 groups
of women. So the total number of possible subcommittees is (70 x 10) = 700 .

5 0

3 years ago