Perform the operation. (10x2 – 10x

What is an equation of the line that passes through the points (5,5) and (-5,-7)?

tatyana61 [14]

Answer:

y=6/5x-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-7-5)/(-5-5)

m=-12/-10

simplify

m=6/5

y-y1=m(x-x1)

y-5=6/5(x-5)

y=6/5x-30/5+5

y=6/5x-6+5

y=6/5x-1

7 0

4 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

What is the volume of this sphere?

JulsSmile [24]

<h3>Answer: 24416.64</h3>

Work Shown:

$V = (4/3)*\pi*r^3\\\\V \approx (4/3)*3.14*18^3\\\\V \approx 24416.64\\\\$

6 0

2 years ago

Express the value of each tangent ratio to the nearest tenth or as a fraction

Alex73 [517]

9514 1404 393

Answer:

1) 5/12

2) 4/3

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the tangent ratio is ...

Tan = Opposite/Adjacent

__

1) For angle Z, the ratio is ...

tan(Z) = XY/YZ = 10/25 = 5/12

__

2) For angle C, the ratio is ...

tan(C) = AB/BC = 20/15 = 4/3

7 0

3 years ago

I have attached 3 different problems, please could you help. Thank you

nydimaria [60]

Answer:

1a) 210

1b) 0.18

2) 17.7 will fit (> 17)

3) 515 cm^2

Step-by-step explanation:

1a) The sample of 25 is exactly 1/30 of the population of 750, so the number of orange cakes in the population will be 30 times the number in the sample.

The total number of orange cakes made on Monday is 30·7 = 210.

__

1b) The lowest number that will round to 5 is 4.5. The lowest probability that a cake is an orange cake is ...

4.5/25 = 18/100 = 0.18

The lower bound on the probability that the cake is orange is 0.18.

____

2) The working shown is partly correct.

The possible error in the box dimension is 1/2 cm, so the box may be as short as 28 -1/2 cm = 27.5 cm.

The possible error in the disc case dimension is 1/2 mm = 0.05 cm, so the case may be as thick as 1.5 +.05 = 1.55 cm.

The minimum number discs that will fit in the case is (27.5 cm)/(1.55 cm) = 17.7. Thus, 17 cases will definitely fit in the box.

____

3) The shaded area will be the largest when the outside rectangle is the largest and the inside rectangle is the smallest. Errors in dimensions can be as much as 1/2 cm, so the Outside rectangle can be 42.5 cm by 21.5 cm. The inside rectangle can be as small as 27.5 cm by 14.5 cm.

Then the shaded area can be as large as ...

(42.5)(21.5) -(27.5)(14.5) = 515 . . . . cm^2

3 0

4 years ago

Perform the operation. (10x2 – 10x – 6) + (x+6)