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creativ13 [48]
2 years ago
13

smiddle" class="latex-formula">
solve the equation using any method you prefer. Give imaginary roots.
Mathematics
1 answer:
Mrrafil [7]2 years ago
3 0
5=x^2+2x\\
x^2+2x-5=0\\
x^2+2x+1-6=0\\
(x+1)^2=6\\
x+1=\sqrt6 \vee x+1=-\sqrt6\\
x=-1+\sqrt6 \vee x=-1-\sqrt6
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Amanda's sewing a flag for a competition. The dimensions of her flag are shown below. Approximately, how many square yards of bl
DedPeter [7]

To calculate the area of the black material on the flag, we need the shape and the dimensions of the black material itself.

<em>Since the question is incomplete, as the dimension of the flag and the dimension of the black material are not given, I will provide a general explanation</em>

<em />

Assume the shape of the black material is a rectangle.

The area will be calculated as:

Area = Length * Width

Take for instance;

Length = 4yd;\ Width = 5yd

The area is:

Area  = 4yd * 5yd

Area  = 20yd^2

Assume the shape of the black material is a square.

The area will be calculated as:

Area =Length^2

Take for instance;

Length = 4yd

The area is:

Area = (4yd)^2

Area = 16yd^2

Assume the shape of the black material is a triangle

The area will be calculated as:

Area = 0.5 * Base * Height

Take for instance;

Base = 4yd;\ Height = 5yd

The area is:

Area = 0.5 * 4yd * 5yd

Area =10yd^2

So, in general.

You need to first get the shape of the black segment on the flag, then calculate the area using the appropriate formula.

Related link:

brainly.com/question/24251781

5 0
3 years ago
Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?
Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

sec^4 x + sec^2 x tan^2 x - 2 tan^4 x

Required

Simplify

(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2

Represent sec^2x with a

Represent tan^2x with b

The expression becomes

a^2 + ab- 2 b^2

Factorize

a^2 + 2ab -ab- 2 b^2

a(a + 2b) -b(a+ 2 b)

(a -b) (a+ 2 b)

Recall that

a = sec^2x

b = tan^2x

The expression (a -b) (a+ 2 b) becomes

(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)

..............................................................................................................................

In trigonometry

sec^2x =1  +tan^2x

Subtract tan^2x from both sides

sec^2x - tan^2x =1  +tan^2x - tan^2x

sec^2x - tan^2x =1

..............................................................................................................................

Substitute 1 for sec^2x - tan^2x in (sec^2x -tan^2x) (sec^2x+ 2 tan^2x)

(1) (sec^2x+ 2 tan^2x)

Open Bracket

sec^2x+ 2 tan^2x ------------------This is an equivalence

(secx)^2+ 2 (tanx)^2

Solving further;

................................................................................................................................

In trigonometry

secx = \frac{1}{cosx}

tanx = \frac{sinx}{cosx}

Substitute the expressions for secx and tanx

................................................................................................................................

(secx)^2+ 2 (tanx)^2 becomes

(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2

Open bracket

\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})

\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}

Add Fraction

\frac{1 + 2sin^2x}{cos^2x} ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

sin^2x + cos^2x= 1

Make sin^2x the subject of formula

sin^2x= 1  - cos^2x

................................................................................................................................

Substitute the expressions for 1  - cos^2x for sin^2x

\frac{1 + 2(1  - cos^2x)}{cos^2x}

Open bracket

\frac{1 + 2  - 2cos^2x}{cos^2x}

\frac{3  - 2cos^2x}{cos^2x} ---------------------- This is another equivalence

8 0
3 years ago
An automobile manufacturer claims that its van has a 44.3 miles/gallon (MPG) rating. An independent testing firm has been contra
natulia [17]

Step-by-step explanation:

H0: u = 44.3

Hi : u# 44.3

Z1-0.05/2

Z1-0.025

Z0.975 = 1.96

Z = x-u/s.d/√n

Z= 44.4 -44.3/2.6/√130

Z = (0.1×11.4018)/2.6

Z=0.44

Since the calcalculated value is less than the table value and does not fall in the rejection region we fail to reject the null hypothesis

7 0
3 years ago
A circle has a radius of 4 ft. What is the area of the sector formed by a central angle that measures 5 Π radians? Use 3.14 for
makkiz [27]
Sorry I don’t know,but maybe 37.4
5 0
2 years ago
What is 30% of 7.99 ?!?
stiks02 [169]
<span>2.397 is the answer.
</span>
4 0
3 years ago
Read 2 more answers
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