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3 years ago

Can someone answer this, please? I need a bit of help on this

Mathematics

1 answer:

Aneli [31]3 years ago

8 0

Answer:

x=0 or f square root of 3f/9 or -f square root of 3f/9

Step-by-step explanation:

the steps are very long but I'm pretty sure it's correct

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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

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

2 years ago

Which is f(5) for the function -2x2 + 2x - 3?

Schach [20]

The value of f(5) is -37

Solution:

Given function is:

$f(x) = -2x^2+2x+3$

We have to find the value of f(5)

To find the value of f(5), we have to substitute x is equal to 5 in given function

Plug in x = 5 in f(x)

$f(x) = -2x^2+2x+3\\\\f(5) = -2(5)^2+2(5) + 3\\\\\text{Simplify the above expression }\\\\f(5) = -2(25) + 10 + 3\\\\\text{Solve the above expression }\\\\f(5) = -50 + 10 + 3\\\\f(5) = -40 + 3 = -37$

Thus value of f(5) is -37

6 0

3 years ago

What is the smallest degree of rotation that will map a regular 18 gon on to itself

natali 33 [55]

Answer:

20°

Step-by-step explanation:

Rotating the figure through an angle equal to the central angle of one "sector" will do the required mapping. That is 360°/18 = 20°.

5 0

3 years ago

1/2x + 6= 3x - 4 Solve the system of equations

shepuryov [24]

1.Combine multiplied terms into a single fraction

2. Multiply by 1

3. Subtract 6 from both sides of the equation

4.Simplify

5.Subtract 3x from both sides of the equation

6.Simplify

7.Multiply all terms by the same value to eliminate fraction denominators

8.Simplify

9.Divide both sides of the equation by the same term

10.Simplify

Solution:x=4

5 0

2 years ago

A plane can fly 7 miles per minute. The plane will fly 8 trips, and each trip is 810 miles. How many hours will the plane fly? S

ELEN [110]

7*60 = 420

810/420 = 1.9285

93- 100 = 53-60

subtract 40 from 93.

1.53*8 = 12.24

Answer: 12 hours and 24 Minutes

If this helps give a brainliest :)

4 0

3 years ago