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NeTakaya
3 years ago
11

What is the slope of the line that contains the points (4, –4) and (7, –6)?

Mathematics
1 answer:
labwork [276]3 years ago
6 0
The slope is m=-2/3 you are welcome




You might be interested in
Fine length of BC on the following photo.
MrMuchimi

Answer:

BC=4\sqrt{5}\ units

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

AC^2=AD^2+DC^2

substitute the given values

AC^2=16^2+8^2

AC^2=320

AC=\sqrt{320}\ units

simplify

AC=8\sqrt{5}\ units

step 2

In the right triangle ACD

Find the cosine of angle CAD

cos(\angle CAD)=\frac{AD}{AC}

substitute the given values

cos(\angle CAD)=\frac{16}{8\sqrt{5}}

cos(\angle CAD)=\frac{2}{\sqrt{5}} ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

cos(\angle BAC)=\frac{AC}{AB}

substitute the given values

cos(\angle BAC)=\frac{8\sqrt{5}}{16+x} ----> equation B

step 4

Find the value of x

In this problem

\angle CAD=\angle BAC ----> is the same angle

so

equate equation A and equation B

\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}

solve for x

Multiply in cross

(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units

DB=4\ units

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

BC^2=DC^2+DB^2

substitute the given values

BC^2=8^2+4^2

BC^2=80

BC=\sqrt{80}\ units

simplify

BC=4\sqrt{5}\ units

7 0
3 years ago
I will give brainlest answer
KonstantinChe [14]
4 units right and 4 units down
4 0
3 years ago
The deck of a bridge is suspended 275 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of
Ivenika [448]

Answer:

Our equation for the height is:

y(t) = 275 - 16*t^2.

a) To find the average velocity between two times, t1 and t2, (where t2 > t1) the equation is:

AV = \frac{y(t2) - y(t1)}{t2 - t1}

Then:

i) t1 = 4s, t2 = 4s + 0.1s = 4.1s

The average velocity is:

AV = \frac{(275 - 16*4.1^2) - (275 - 16*4^2)}{4.1 - 4} = \frac{16(4^2 - 4.1^2)}{0.1} = -129.6

And the units will be ft/s, so the average speed is:

-129.6 ft/s

The minus sign is because te pebble is falling down.

ii)  t1 = 4s, t2 = 4s + 0.05s = 4.05s

The average velocity is:

AV = \frac{(275 - 16*4.05^2) - (275 - 16*4^2)}{4.05 - 4} = \frac{16(4^2 - 4.05^2)}{0.05} = -128.8

So the average speed is -128.9 ft/s

iii)  t1 = 4s, t2 = 4s + 0.01s = 4.01s

The average speed is:

AV = \frac{(275 - 16*4.01^2) - (275 - 16*4^2)}{4.01 - 4} = \frac{16(4^2 - 4.01^2)}{0.01} = -128.16

The average speed is -128.16 ft/s.

b) The instantaneous velocity of the pebble after 4 seconds can be obtained by looking at the velocity equation, that is the derivative of the height equation.

v(t) = dy(t)/dt.

v(t) = -2*16*t + 0

Then the velocity at t = 4s is:

v(4s) = -32*4 = -128

The instantaneous velocity at t = 4s is -128 ft/s.

3 0
3 years ago
A person invested $6,000, some at 7% and the rest at 5%. The income from the 7% investment is equal to the income from the 5% in
8090 [49]

Answer:

The person invested $3500 at 7% and $2500 at 5%

Step-by-step explanation:

We can say that 0,07x+0,05x=6000 because the investment is equal both in one as in another, where x is the income from the investment.

Solving the equation we have:

0,12x=6000\\x=50000

Then to get the incomes:

At 7%: I=0.07*50000\\I=$3500

And at 5%: I=0.05*50000\\I=$2500

Finally we can demonstrate the answer because the  income at 7% + income at 5% are 3500+2500=$6000

6 0
3 years ago
2x+y=10x-4y i dont know
Basile [38]

Step-by-step explanation:

2x-10x= -4y-y

-8x= -5y

cancel (-) on both sides we get

8x=4y

7 0
3 years ago
Read 2 more answers
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