The difference between two numbers is 8. if 2 is added to the bigger number the result will be three times the smaller number. Find the numbers.

[tex]\text{Given that,}\\\\\sin \theta = -\dfrac{12}{13}\\\\\implies \sin^2 \theta = \dfrac{144}{169}\\\\\implies 1- \cos^2 \theta = \dfrac{144}{169}\\\\\implies \cos^2 \theta = 1- \dfrac{144}{169}\\\\\implies \cos^2 \theta = \dfrac{25}{169}\\\\\implies \cos \theta = \pm \sqrt{\dfrac{25}{169}} = \pm \dfrac 5{13}\\\\\\\text{Since,}~ \tan \theta >0,\\\\\cos \theta =- \dfrac{5}{13}[/tex]

The solution to the limit expression [tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} [/tex] is 6

The limit expression is given as:

[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5}[/tex]

Express 25 as 5^2

[tex] \lim_{x \to 1} \frac{x^2 - 5^2}{x - 5}[/tex]

Express the numerator as the difference of two squares

[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} \frac{(x - 5)(x +5)}{x - 5}[/tex]

Evaluate the quotient

[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} (x +5)[/tex]

Remove bracket

[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} x +5\\ [/tex]

Substitute 1 for x

[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 1 +5[/tex]

[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 6[/tex]

Hence, the solution to the limit expression [tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} [/tex] is 6

Read more about calculus at:

https://brainly.com/question/15182568

Answer:

18 minutes and 45 seconds

Step-by-step explanation:

[tex]\frac{1}{50}[/tex] + [tex]\frac{1}{30}[/tex] = [tex]\frac{3+5}{150}[/tex] = [tex]\frac{4}{75}[/tex]

1 ÷ [tex]\frac{4}{75}[/tex] = [tex]\frac{75}{4}[/tex] = 18' 45''

Answer:

18.75 minutes If A and B work together

Answer:

c = 5b ±sqrt(-10(b+a)+2)

Step-by-step explanation:

By using the Pythagoras theorem,

c² = a² + b²

a = b-5

b = a+5

c² = (b-5)² + (a+5)²

c² = b²-10b+25 + a²+10a+25

c² = b²-10b-10a+50

c² = b²-10(b+a)+50

c = 5b ±sqrt(-10(b+a)+2)

Answer:

Step-by-step explanation:

(2x-5y)^2

(2x-5y)(2x-5y)

4x^2-10xy-10xy+25y^2

4x^2-20xy+25y^2

------------------------------

(11a+2)(11a-2)

121a^2+22a-22a-4

121a^2-4

------------------------------

(7m+3)(7m+3)

49m^2+21m+21m+9

49m^2+42m+9

Answer:

0.18 i think

Step-by-step explanation:

Answer:

6x sec2 (x2+5) the number to are in the top of x a c.

Answer:d

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

y-3=6(x-8)

Step-by-step explanation:

given that the slope is 6 and the line passes through (8,3), we can use the formula y-y1=m(x-x1), where (x1, y1) is the ordered pair and m is the slope. we can plug the given values in from there. m=6, x1=8, and y1=3. hope this helps!

Answer:

It is an example of a nonlinear function.

Step-by-step explanation:

Use a graphing calculator or graph the points and try to make a line, as it will not work

Answer:

[tex]\frac{KL}{JL}[/tex] = [tex]\frac{6.4}{7.7}[/tex] = 0.83

Step-by-step explanation:

The key understanding here is that ΔJKL is similar to triangle 3 based on the AA criterion (they both have a right angle and a 40° angle).

We can find [tex]\frac{KL}{JL}[/tex] by setting up a proportion statement that includes KL, JL, and the lengths of their corresponding sides in triangle 3.

We can use this proportion:

[tex]\frac{KL}{6.4}[/tex] = [tex]\frac{JL}{7.7}[/tex]

[tex]\frac{KL}{6.4}[/tex] ⇒ opposite to 40° angle

KL, JL ⇒ ΔJKL

[tex]\frac{JL}{7.7}[/tex] ⇒ adjacent to 40° angle

6.4, 7.7 ⇒ triangle 3

[Now see the attachment]

Now we can rewrite the equation to show the ratios of the side lengths within each triangle.

[tex]\frac{KL}{JL}[/tex] = [tex]\frac{6.4}{7.7}[/tex]

[tex]\frac{KL}{JL}[/tex] ⇒ ΔJKL

KL, 6.4 ⇒ adjacent to 40° angle

[tex]\frac{6.4}{7.7}[/tex] ⇒ triangle 3

JL, 7.7 ⇒ adjacent to 40° angle

Answer: it’s 0.82

Step-by-step explanation:

Answer:

I think there answer is 4.74

Step-by-step explanation:

so you divide

[tex]6 \div 28.44 \: and \: you \: get \: answer[/tex]

Answer:

[tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]

Step-by-step explanation:

Because x=1 and x=4 are the solutions to x-1=0 and x-4=0, then we have (x-1)(x-4) in the denominator.

Because (-1,0) and (-6,0) are the solutions to x+1=0 and x+6=0, then we have (x+1)(x+6) in the numerator.

Now we have [tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex] where we plug in (0,8) to solve for a:

[tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex]

[tex]8=\frac{a(0+1)(0+6)}{(0-1)(0-4)}[/tex]

[tex]8=\frac{6a}{4}[/tex]

[tex]32=6a[/tex]

[tex]\frac{32}{6}=a[/tex]

[tex]\frac{16}{3}=a[/tex]

Therefore, the equation for the rational function is [tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]

Answer:

the domains is

[tex] - 10 < x \leqslant 10[/tex]

Answer:

Question!! What is the relationship between A and B?

Step-by-step explanation:

Answer:

25.13ft

Step-by-step explanation:

The length of the fence will be the circumference.

[tex]C=2*pi*r=2*pi*8/2=8pi=25.13ft[/tex]

Answer:

Other factor is 70

Step-by-step explanation:

Let,

Other factor = x

Then,

x × 60 = 4200

x = 4200/60

x = 420/6

x = 70

∴Another factor is 70.

Answer:

Solution given

let two factor be a and b.

if one factor a=60, then b=?

we have

product of factor=4200

a*b=4200

60*b=4200

b=[tex]\frac{4200}{60}=70[/tex]

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Two triangles are congruent so we can use the similarity ratio to find the length of XZ

8x - 10 = 5x - 4 export like terms to the same side of equation

8x - 5x = 10 - 4

3x = 6 divide both sides by 3

x = 2 and so the length of XZ is 8*2 - 10 = 6

Answer:

(40*4)-(32*4)=32

160-128=32

Step-by-step explanation:

This would be C because 27 and 1 are the only factors that can be cubed (remember, when there is no number, 1 is represented)

Answer: C

Step-by-step explanation:

Answer:

The answer is A.15c+3

Step-by-step explanation:

Answer:

192

Step-by-step explanation:

The 7 part of the ratio relates to Taylor's 84 CDs

Divide the amount by 7 to find the value of one part of the ratio.

84 ÷ 7 = 12 ← value of 1 part of the ratio, then

9 parts = 9 × 12 = 108 ← number of CDs Dave has

Total CDs = 84 + 108 = 192

Answer:

LCD= x²- 81

Step-by-step explanation:

x²-81 is difference of two squares

a²-b²= (a+b)(a-b)

x²- 81= (x+9)(x-9)

denominators, (x-9) and (x+9)(x-9)

x-9 is common in both denominators

x-9|(x-9)|(x+9)(x-9)

x+9| 1 | x+9

| 1 | 1

therefore the LCD= (x-9)(x+9)

simplifying= x²- 81

Answer:

i think 4x+3y = -24 is answer

Answer:

Total earning Kanica wants to make is at least $750

The commission she gets is 7.5 % Therefore to find the sales she should make we use :

(Total earnings * 100% )/ Commission

= (100 * 750) / 7.5

=75000/7.5

= $ 10,000

The minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells is $10,000.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Kanica wants to earn at least $750 this week in commission.

Let x be the minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells.

The value of x can be found as follows:

x = 750/(7.5%)

x = (750/7.5)x100

x = $10,000

Thus, the minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells is $10,000.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ5

Answer:

4,-1

Step-by-step explanation:

Please like!♥

Answer:

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

plug 2 into x to see

A.

x^2 + 8

2^2 + 8

4 + 8 = 12

B.

3x^2 + 1

3(2)^2 + 1

3(4) + 1

12 + 1 = 13

C.

2x^3 + 5

2(2)^3 + 5

2(8) + 5

16 + 5 = 21

D.

x^2 + x

2^2 + 2

4 + 2 = 6

7/8= B. 42/48

#HOPE THIS HELP