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2 years ago

Write 5(6x+4)-2(5x-2) in the form a(bx+c) where a,b and c integers and a>1

Mathematics

1 answer:

Tamiku [17]2 years ago

6 0

Answer:

Step-by-step explanation:

$5(6x+4)-2(5x-2)\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\=(5)(6x)+(5)(4)+(-2)(5x)+(-2)(-2)\\\\=30x+20-10x+4\qquad\text{combine like terms}\\\\=(30x-10x)+(20+4)\\\\=20x+24$

$20x=4\cdot5x\\\\24=4\cdot6\\\\20x+24=4(5x+6)$

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Convert 444 yards to meters. Use 1 yard = 0.9144 meters

Nitella [24]

Answer:

405.9936 meters

Step-by-step explanation:

We know that

1 yard = 0.9144 meters

We are converting 444 yds to meters

444 yds * .9144 meters/ 1 yds = 405.9936 meters

4 0

3 years ago

Please someone help me answer this

atroni [7]

Answer:

x = 7

Step-by-step explanation:

( x +16)° = (4x - 5)°

x + 16 = 4x - x

16 + 5 = 4x - x

21 = 3x

7= x

hence, x =7

4 0

2 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

Made this question if you can able to make

Vilka [71]

Answer:Serkan teacher regularly buys 75 TL of gasoline in his car every week.

At the end of the 13th week, how much is the total gasoline expenditure made by the serkan teacher?

A)390 B)420 C)900 D)975

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Please please help

777dan777 [17]

Step-by-step explanation:

Statement. Reason

→ 9(x-6)+41 = 75. Transposing the like terms.

→ 9(x-6) = 75 - 41 Performing subtraction of the term in RHS

→ 9(x-6) = 34 Performing multiplication in LHS.

→ 9x - 54 = 34 Distributive property

→ 9x = 34 + 54 Performing addition of the term in RHS.

→ 9x = 88. Now, transpose 9 from LHS to RHS , it's arthmetic operator will get changed.

→ x = 88/9

6 0

2 years ago