Express the terms of the following geometric sequence by giving an explicit formula. 8 , -32 , 128 , -512 , 2,048 , ...

Answer:

x=6, x= -5

Step-by-step explanation:

Factor the equation

x^2 - x - 30 = 0 ----> (x-6)(x+5)=0

Next find the solution by setting those in the paranthesis equal to zero.

x-6=0 ----> x= 6

x+5=0 ----> x= -5

Step-by-step explanation:

[tex] {x}^{2} - x - 30 = 0[/tex]

➡️ [tex] {x}^{2} + 5x - 6x - 30 = 0[/tex]

➡️ [tex]x \times (x + 5) - 6(x + 5) = 0[/tex]

➡️ [tex](x + 5) \times (x - 6) = 0[/tex]

➡️ [tex]x + 5 = 0[/tex]

➡️ [tex]x - 6 = 0[/tex]

➡️ [tex]x = - 5[/tex]

➡️ [tex]x = 6[/tex]

➡️ [tex] x_{1} = - 5. \: x_{2} = 6[/tex]

Answer:

The inverse of the function is

[tex]{ \underline{f {}^{ - 1}(x) = \sqrt{ \frac{x + 4}{2} } }}[/tex]

Step-by-step explanation:

let the inverse of f(x) be m:

[tex]m = {2x}^{2} - 4 [/tex]

take 4 to the left hand side ( changes sign to positive ):

[tex]m + 4 = {2x}^{2} \\ \frac{m + 4}{2} = {x}^{2} [/tex]

take a square root on all sides:

[tex] \sqrt{ \frac{m + 4}{2} } = \sqrt{ {x}^{2} } \\ \\ x = \sqrt{ \frac{m + 4}{2} } [/tex]

substitute x in place of m:

[tex] {f}^{ - 1} (x) = \sqrt{ \frac{x + 4}{2} } [/tex]

Answer:

95

Step-by-step explanation:

you can watch answer in photo. by the way where r u from?

Answer:

I hope it helped U

stay safe stay happy ❤️❤️

Answer:

tea

Step-by-step explanation:

just cuz lol

Answer:

Gin

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

4/3 cup for 3 dozen.

how many cups for 18 dozen ?

what factor do I need to use to turn 3 into 18 ?

3×x = 18

x = 18/3 = 6

so, I need 6 units of flour (1 unit is 4/3 cup) to make 6 units of cookies (1 unit is 3 dozen).

therefore, we need

4/3 × 6 = 6×4/3 = 2×4 = 8 cups of flour.

Answer:

Step-by-step explanation:

The unknown number is reflected as n.

The sum of 5 and four times a number is 32:

Four less than the square of a number is 12:

The product of 3 and four more than a number is 20:

Answer:

x = 4

y = 36

Step-by-step explanation:

use substitution

y=3x+24

y=9x

therefore . 9x=3x+24

x = 4

sub 4 in for x and solve for y

y = 9(4) = 36

Answer:

8/3 or 2.6667

Step-by-step explanation:

when you divide fractions you use a technique called KCF

K = keep

C = change

F = flip

You write the equation [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{4}[/tex]

you keep [tex]\frac{2}{3}[/tex]

you change the symbol, so from ÷ you change it to x

and flip the last fraction, so you would have  [tex]\frac{4}{1}[/tex]

then you solve it

[tex]\frac{2}{3}[/tex] x  [tex]\frac{4}{1}[/tex] = [tex]\frac{8}{3}[/tex]

The result of 2/3 divided by 1/4 in simplest form is 8/3 .

Division: It is one of the four basic mathematical operation, the other three being addition, subtraction, multiplication.

Given, division of [tex]\frac{2}{3}[/tex] by [tex]\frac{1}{4}[/tex].

Division of fractional terms:

[tex]=\dfrac{\frac{a}{b}}{\frac{c}{d}}\\= (a)\times(d)/(b)\times(c)[/tex]

Apply, division process of fractional terms.

[tex]=\dfrac{\frac{2}{4}}{\frac{1}{3}}\\ = (2)\times(4)/(1)\times(3)[/tex]

[tex]= \frac{8}{3}[/tex]

Know more about division,

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Answer:

157.5

Step-by-step explanation:

14×180/16

= 315/2

= 157.5

Answer:

Step-by-step explanation:

16 sides  

n-2=14

14x 180 = 2250

2250/16 =157.5 = 158

Answer:

Option B is correct

Step-by-step explanation:

Let the number be x

Second number = x + 1

Sum = 85

x + x + 1 = 85

2x + 1 = 85

2x = 85 - 1

2x = 84

x = 84/2 = 42

Numbers are 42 and 43

Answer:

B) x+(x+1)=85

Step-by-step explanation:

Consecutive means in a row

Let x be the first integer

x+1 is the next integer

x+x+1 = 85

Answer:

The correct answer is D

Take D

Answer:

The last step is to simplify the result if it can be done. To simplify a fraction, you have to find the greatest common factor (GCF) of both the numerator and the denominator. The GCF is the largest number that can be evenly divided into both numbers. In the case of 12 and 96, 12 happens to evenly divide into 96.

Answer:

x=12

Step-by-step explanation:

2x-15 + 2x-6 = 15

4x = 36

x = 9

2 x 9 - 6 = 12

Answer:0.50

Step-by-step explanation:

Range= Highest number - lowest number

=1.50 -1.00= 0.50

[tex]2 {m}^{8} - 6 {m}^{2} [/tex]

Step-by-step explanation:

[tex](12 {m}^{7} - 36m) \div 6m[/tex]

➡️ [tex] \frac{1 {2m}^{7} - 36m }{6} \times m[/tex]

➡️ [tex] \frac{6(2 {m}^{7} - 6m)}{6} \times m[/tex]

➡️ [tex](2 {m}^{7} - 6m)m[/tex]

➡️ [tex]2 {m}^{8} - 6 {m}^{2} [/tex]

Answer:

Step-by-step explanation:

Hi :)

Radius is half the diameter

4.6 mm (2) = 9.2 mm

The diameter of the circle is 9.2 mm.

Answer: 2 pens and 4 pencils.

Step-by-step explanation:

If you buy 2 pens it is equal to $2.

If you buy 4 pencils it is also equal to $2.

2+2=4

and 2 pens and 4 pencils is equal to 6 in total.

Answer

[tex]2[/tex] pens and [tex]4[/tex] pencils were bought for [tex]\$4[/tex] such that [tex]6[/tex] pens and pencils are bought for [tex]\$4[/tex] and each pen costs [tex]\$1[/tex] and each pencil costs [tex]\$0.50[/tex].

The equation whose variables' highest power is one is known as linear equation.

To find the unknown quantities, always assume it to be a variable and then form the equation based on the conditions given in the question.

Let the number of pens bought be [tex]x[/tex].

and the number of pencils bought be [tex]y[/tex].

The total number of pens and pencils [tex]=6[/tex].

So, the first equation is,

[tex]x+y=6[/tex]

[tex]x=6-y[/tex] ... (i)

And the costs per pen and pencil is [tex]\$1[/tex] and [tex]\$0.50[/tex] respectively.

So, the second equation is,

[tex]x+0.5y=4[/tex] ... (ii)

Now, solve the pair of linear equations.

Put the value of [tex]x[/tex] in the equation (ii),

[tex]6-y+0.5y=4\\-0.5y=-2\\y=4[/tex]

So,

[tex]x=6-4\\x=2[/tex]

Thus, [tex]2[/tex] pens and [tex]4[/tex] pencils were bought for [tex]\$4[/tex].

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Answer:

(a)

sin²A×cos²A+sin⁴A

we will take sin²A as an common factor

so it become

sin²A×(cos²A+sin²A)

sin²A+cos²A=1

sin²A×1=sin²A

(c)

sinA×cotA

cotA= cosA/sinA

sinA×cosA/sinA=cosA

(e)

(1+sinA)²-(1-sinA)²

(a+b)²=a²+b²+2×a×b

(a-b)²=a²+b²-2×a×b

1²+sin²A+2×1×sinA-(1²+sin²A-2×1×sinA)

1+sin²A+2sinA-1-sin²A+2sinA=4sinA

(g)

(cosec²A-1)/cosec²A

cosecA=1/sinA

1/sin²A-1/1/sin²A

(1/sin²A-1)×sin²A

1-sin²A

1=sin²A+cos²A

sin²A+cos²A-sin²A=cos²A

(i)

sqrt(1+tan²A)×sqrt(1-cos²A)

1+tan²A=

1+sin²A/cos²A=

sin²A+cos²A/cos²A

sin²A+cos²A=1

=1/cos²A

1-cos²A

1=sin²A+cos²A

sin²A+cos²A-cos²=sin²A

sqrt(1/cos²A)×sqrt(sin²A)

1/cosA×sinA=sinA/cosA=tanA

have a great day

Answer:

range is the y part and domain is the x so the range is the y coordinates

-6,-3,-2,-2,1,4

Step-by-step explanation:

Answer:

Here is your answer . Hope this is helpful to you.

Answer: 7

Step-by-step explanation:

1. multiply both sides by -6 so the -6 on the right side could cancel out and the left side would be -6:  1= a-13/-6 ==> -6=a-13

2. add both sides by 13 so -13 on the right side could cancel out and the left side would be -6+13: -6=a-13 ==> -6+13=a-13+13

3. you know -6+13 equals 7 right? so the answer is a=7

Hey there! I'm happy to help!

We want to get the a all by itself. For me, I always like to have the variable on the left side, so first, let's just flip this around.

[tex]\frac{a-13}{-6} =1[/tex]

What we want to do is get all of the constants (numbers without variables) on the right side. This will leave a all on its own.

We see that the quantity a-13 is being divided by -6. To undo this, we will just multiply both sides by -6. This will cancel out that -6 and get us closer to having the a isolated.

[tex]\frac{a-13}{-6} *-6=1*-6\\\frac{a-13}{1}=-6\\a-13=-6[/tex]

Now we add 13 to both sides to undo the -13 on the left side.

[tex]a-13+13=-6+13[/tex]

[tex]a+0=7\\a=7[/tex]

Have a wonderful day and keep on learning! :D

Answer:

(x+y+5)(x-y+1)

Step-by-step explanation:

factor by grouping

x^2+6x+5-4y-y^2

x^2+6x+9 - (y^2+4t+4) + 5-9+4

(x+3)^2 - (y+2)^2

(x+3+(y+2))(x+3-(y+2))

(x+y+5)(x-y+1)

Answer:

x = 3

13 miles between Madison and Jamie's house.

Step-by-step explanation:

If we add the distance between Anoa's and Madison's house with the distance between Jamie's and Madison's house, then we get the total distance between Anoa's and Jamie's house.

(3x + 2) + (3x + 4) = 9x - 3

Let's add up the terms first

3x + 2 + 3x + 4 = 9x - 3

6x + 6 = 9x - 3

Let's move the variables to the right side by subtract 6x from both sides

6x + 6 = 9x - 3

-6x         -6x

6 = 3x - 3

Add 3 to both sides

6 = 3x - 3

+3        +3

9 = 3x

Isolate the variable, x, by dividing both sides by the coefficient, 3.

9/3 = 3x/3

x = 3

Now we need to find the distance between Madison's and Jamie's house.

3x + 4

Plug in 3 in place of the x

3(3) + 4

9 + 4 = 13

Answer:

Step-by-step explanation:

If we add the distance between Anoa's and Madison's house with the distance between Jamie's and Madison's house,then we get the total distance between anoa's and Jamie's house.