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2 years ago

Find the midpoint of the line segment with the given endpoints: (-1, -6) and (-6, 5).

Mathematics

1 answer:

Vikentia [17]2 years ago

8 0

Answer:

Step-by-step explanation:

First, we will find the midpoint for the x - coordinate first.

Midpoint (x) = $\frac{-1+(-6)}{2} \\=\frac{-1-6}{2} \\=\frac{-7}{2} \\=-3.5$

Now we will find the midpoint for the y - coordinate.

Midpoint (y) = $\frac{-6+5}{2} \\=\frac{-1}{2} \\=-0.5$

Therefore from these 2 values we know that the midpoint of this 2 points is (-3.5,-0.5)

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What is the slope of a line perpendicular to the line of y=-1/4x-1

harina [27]

Answer: 4

The given line has a slope of -1/4 as this is the number in front of the x. The general equation y = mx+b has m as the slope. So m = -1/4 is given

Flip the sign to get -1/4 turn into +1/4 or just 1/4

Then flip the fraction (aka reciprocal) to go from 1/4 to 4/1 and that simplifies to 4.

Multiplying the original slope (-1/4) and the perpendicular slope (4) will result in -1.

5 0

3 years ago

A 35 foot rope is cut into two pieces with one section 6 times as long as the other section, how is the shorter piece?

guajiro [1.7K]

-------------------------------------------
Define x:
-------------------------------------------
Let the shorter piece be x.
Shorter piece = x
Longer piece = 6x

-------------------------------------------
Construct equation:
-------------------------------------------
x +6x =35
7x = 35
x =5

-------------------------------------------
Find the length:
-------------------------------------------
Shorter length = x = 5 feet
Larger length = 6x = 6(5) = 30 feet

-------------------------------------------
Answer: The shorter piece is 5 feet.
-------------------------------------------

4 0

3 years ago

The mass of a bacteria culture doubles every four days. If the initial sample is 5mg: a) how much will you have after one week (

maks197457 [2]

Answer:

a) 16.82 mg

b) 24 days

Step-by-step explanation:

Formula for exponential growth is given as:

$A=A_0b^{\frac{t}{c}}$

Where A is the final population

$A_0$ is the initial population

b is the growth factor

c is the time taken for the growth 'b'

t is the amount of time

Here, We are given the following:

$A_0$ = 5 mg

b = 2 (Given because it doubles)

c = 4 days

a) A = ?

Using the formula:

$A=5 \times 2^{\frac{7}{4}}\\\Rightarrow A=5 \times 2^{1.75} \\\Rightarrow A = \bold{16.82\ mg}$

b) Given

A = 320 mg

t = ?

Using the above formula again:

$320 = 5 \times 2^{\frac{t}{4}}\\\Rightarrow \dfrac{320} 5= 2^{\frac{t}{4}}\\\Rightarrow 2^{\frac{t}{4}} = 64\\\Rightarrow 2^{\frac{t}{4}} = 2^6\\\Rightarrow \dfrac{t}{4} = 6\\\Rightarrow t = 6 \times 4\\\Rightarrow \bold{t = 24\ days}$

So, the answers are:

a) 16.82 mg

b) 24 days

6 0

3 years ago

Solve 5x^2 + 16 = 10 by using the quadratic formula<br><br>ax^2 + bx + c = 0

bagirrra123 [75]

2 Imaginary Solutions

5 0

3 years ago

I WILL DO ANYTHING YOU NAME IT BUT PLz SOLVE THIS

vekshin1

Answer: AD = 9cm

Step-by-step explanation: This is a 30-60-90 triangle, so the hypotenuse is equal to twice the length of the short side of the right angle.

BC is the short side of the large triangle, so AB, the hypotenuse of the large triangle is 2×6, 12 cm

BC is also the hypotenuse of the small triangle, ΔBCD, so it is twice the length of BD, to that makes BD = 6/2= 3

Subtract BD from AB.

That's 12 - 3 = 9 the length of AD

6 0

3 years ago