write the equation of the line in fully simplified slope-intercept form

Step-by-step explanation:

as we see in the sequence, each term is twice of the previous term.

we mark the Nth as a(N), then:

a(N)=2a(N-1)

Answer:

[tex]a_{n}[/tex] = 5[tex](2)^{n-1}[/tex]

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

10 ÷ 5 = 20 ÷ 10 = 40 ÷ 20 = 80 ÷ 40 = 2

this indicates the sequence is geometric with explicit formula

[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 5 and r = 2 , then

[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]

The value of expression is -(x- 4y/3 + 5z/3)

A fraction represents a part of a whole or, more generally, any number of equal parts.

Given:

1/3 · (-3x + 4y - 5z)

= 1/3(-3x) + 1/3 *4y + 1/3* (-5z)

= -x +4/3*y -5/3 *z

=-(x- 4y/3 + 5z/3)

Hence, 1/3 · (-3x + 4y - 5z)= -(x- 4y/3 + 5z/3)

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If the given differential equation is

[tex]\cos^2(x) \sin(x) \dfrac{dy}{dx} + \cos^3(x) y = 1[/tex]

then multiply both sides by [tex]\frac1{\cos^2(x)}[/tex] :

[tex]\sin(x) \dfrac{dy}{dx} + \cos(x) y = \sec^2(x)[/tex]

The left side is the derivative of a product,

[tex]\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)[/tex]

Integrate both sides with respect to [tex]x[/tex], recalling that [tex]\frac{d}{dx}\tan(x) = \sec^2(x)[/tex] :

[tex]\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx[/tex]

[tex]\sin(x) y = \tan(x) + C[/tex]

Solve for [tex]y[/tex] :

[tex]\boxed{y = \sec(x) + C \csc(x)}

which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}[/tex].

A function assigns the values. The input value that produces the same output value for the two functions is 1.

A function assigns the value of each element of one set to the other specific element of another set.

For the given tables the x is the input while f(x) and g(x) are the outputs of the respective functions. Therefore, the input for which the two given functions will return the same output is 1.

Hence, the input value that produces the same output value for the two functions is 1.

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Answer:

9 and 27

Step-by-step explanation:

let me know if you want an explanation

After calculating the value, l & w could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].

The inquiry relates to the laws of indices

where, [tex]x^{a} * x^{b}=x^{a+b}[/tex]

Provided the query, A= [tex]24x^{6}y^{15}[/tex]

[tex]2* 12[/tex] might be used to calculate the length and width of 24.

Hence,

[tex]x^{6}=x^{5} * x^{1} =x^{5+1}[/tex]

& [tex]y^{15}= y^{8} * y^{7} =y^{8+7}[/tex]

So, it can be written as,

A=l * w

⇒ [tex]24x^{6}y^{15}[/tex] = [tex]2x^{5}y^{8}[/tex] * [tex]12xy^{7}[/tex]

Therefore, it is concluded that the dimensions of the rectangle could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].

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Step-by-step explanation:

[-5, 4] because it is an empty circle, meaning less than

Let's see

[tex]\boxed{\sf log_aa=1}[/tex]

Now

[tex]\\ \rm\Rrightarrow log_{10}0.0001)[/tex]

[tex]\\ \rm\Rrightarrow log_{10}10^{-4}[/tex]

[tex]\\ \rm\Rrightarrow -4log_{10}10[/tex]

[tex]\\ \rm\Rrightarrow -4[/tex]

Answer:

This has already been answered correctly, but I'll add an additional perspective.  The log of (0.0001 to the base 10 is -4.

Step-by-step explanation:

log(base 10) says give us an exponent, x, that would be required to make [tex]10^{x}[/tex] equal to a specified number, in this case 0.0001.

[tex]10^{0}[/tex] = 1

[tex]10^{1}[/tex] = 10

[tex]10^{-1}[/tex] = 0.1

[tex]10^{-2}[/tex] = 0.01

[tex]10^{-4}[/tex] = 0.0001

The log of (0.0001) to the base 10 is -4.

[tex]14-a=19-12\\14-a=7\\a=14-7\\a=7[/tex]

Answer:

7

Step-by-step explanation:

14-a=19-12

14-a=7

14-7=a

7=a

Combine like terms

Answer:

The rectangular table

Step-by-step explanation:

Square table: 36*36=1296

Rectangular table: 20*42=1460 [tex]in^{2}[/tex]

Circular table: [tex]\pi * 21^{2}[/tex]≅1384

Answer:

1.3 or 1.333333

Step-by-step explanation:

Just do it!

The equivalent expression to [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex] is given by [tex]=\mathbf{\frac{n^{10}}{16m^6}}[/tex].

From the principle of indices we get,

Addition of exponent, [tex]a^{m+n}=a^m.a^n[/tex]

Subtraction, [tex]a^{m-n}=\frac{a^m}{a^n}[/tex]

Multiplication, [tex]a^{mn}=(a^m)^n[/tex]

negative exponent, [tex]a^{-m}=\frac{1}{a^m}[/tex]

Here in the problem given expression is [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

Calculating we get,

[tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

[tex]=\left(4m^{1-(-2)}n^{1-6}\right)^{-2}[/tex], using addition and subtraction of indices formulae

[tex]=\left(4m^3n^{-5}\right)^{-2}[/tex]

[tex]=16^{-1}m^{-6}n^{10}[/tex], using multiplication of indices

[tex]=\frac{n^{10}}{16m^6}[/tex], using negative exponent formula

Hence the equivalent required expression is [tex]=\frac{n^{10}}{16m^6}[/tex].

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Answer:

b

Step-by-step explanation:

edge 23

Firstly, let’s assume the the whole capacity the work requires is 1.

Then, let’s see how 1 man can do in 50 days: 1/5.

Further, let’s see how 1 man can do in 1 day : 1/(5×50) = 1/250.

Similarly, let’s see how 1 woman can do in 1 day: 1/(10×50) = 1/500.

Now, we have 8 men, and they can do 8*1/250 in 1 day, which is 4/125.

Besides, we have 4 women, and they can do 4×1/500 in 1 day, which is 1/125.

Therefore, all people we have can do 4/125 + 1/125 of the work in 1 day, which is 1/25.

As a result, the work takes 1/(1/25)= 25 days.

Answer:

Step-by-step explanation:

If two ratios make a proportion then it can be shown as:

Let's verify the answer choices with this method

A. 1/4 and 5/25

B. 1/4 and 7/24

C. 1/4 and 10/48

D. 1/4 and 9/36

We conclude that after the discount and the coupon, Will paid $36 for the skateboard.

We know that the original price was $60, and two discounts were applied. One of 20% and other of 25%.

Then the amount that he paid is given by:

P = $60*(1 - 20%/100%)*(1 - 25%/100%)

P = $60*(0.8)*(0.75)  = $36

We conclude that after the discount and the coupon, Will paid $36 for the skateboard.

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The cross-section parallel to the base of a cone is a circle

The cross-section parallel to the base of a cylinder is a circle

The cross-section perpendicular to the base of a cone is a triangle

The cross-section perpendicular to the base of a cylinder is a rectangle

The solution to the equation is x = 7 , -2 , Option C and D is the right answer.

An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.

It is given that the equation is

[tex]\rm 3 +\sqrt{3x - 5}= x[/tex]

Taking square on both sides

3x-5 = (x-3)²

3x-5 = x² +9 -6x

x² -9x -14 = 0

x² -7x +2x -14 = 0

x(x-7) +2(x-7) = 0

(x-7)(x+2) = 0

x =7 , x = -2

Therefore the solution to the equation is x = 7 , -2 , Option C and D is the right answer.

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Answer:

shown below

Step-by-step explanation:

a) V = h(pi)r²

let x = height

and c = the constant radius

V1 = 2x(pi)c²

V2 = x(pi)c²

let c = random number, such as 2

let x = 3

2x(pi)4

x(pi)4

pi(4) = 12.57

3 x 12.57 = 37.7

6 x 12.57 = 75.4

We can compare these ans realise that the cylinder with double the height will also have double the volume.

b) SA = h(pi)2c

SA1 = 2x(pi)2c

SA2 = x(pi)2c

let c = 2

let x = 3

2(3)(pi)(2(2))

6(pi)4

24(pi)

3(pi)(2)(2)

3(pi)(4)

12(pi)

I don't need to finish the calulation to see that this is also halved. So the surface area of the one with the double length is twice the surface area of the one with a smaller height.

Comparatively, both the volume and surface area are doubled when the height is doubled.

QED.

Answer:

broken line

Step-by-step explanation:

for the graph of an inequality with < or >  use a broken line

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

for the graph of an inequality with ≤ or ≥ use a solid line

Answer:

the answer is 4 units im pretty sure

Step-by-step explanation:

The height of the prism is 6 units.

The correct option is C.

A prism is a polyhedron in three dimensions with two identical ends.

To find the height of the prism, we need to use the formula for the volume of a prism, which is:

Volume = Base area x Height

Since the prism has two congruent hexagonal bases, we can find the base area by adding the areas of the two congruent isosceles trapezoids.

The area of an isosceles trapezoid is given by the formula:

Area = ((b1 + b2) / 2) x h

where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.

In this case, the two parallel bases have lengths of 5 and 8, and the height of each trapezoid is 3, so the area of one trapezoid is:

Area = ((5 + 8) / 2) x 3 = 19.5 square units

The base area of the prism is then:

Base area = 2 x 19.5 = 39 square units

We are given that the volume of the prism is 234 cubic units, so we can use the formula for the volume of a prism to find the height:

Volume = Base area x Height

234 = 39 x Height

Height = 6 units

Therefore, the height of the prism is 6 units.

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Answer:

450 N

Step-by-step explanation:

Since you have the VOLUME and the HEIGHT of the prism, you can calculate the AREA of the prism base :

 18 m^3 / 3 m =   6 m^2    area

Now you are given  pressure = force / area

                                      75 n/m^2 =  force / 6 m^2

        6 *75 = force = 450 N

Answer:

450 newtons

Step-by-step explanation:

To solve for the force, we first need to find the area. (Force = Pressure × Area)

[tex]Area = \frac{volume}{height} = \frac{18m^{3} }{3m} = 6m^{2}[/tex]

Now we just substitute this number into [tex]Force = Pressure * Area[/tex] and get that [tex]Force = 75newtons/m^{2} * 6m^{2} = 450 newtons[/tex]

(p.s. Units are very important! This question doesn't require any unit

conversions, but others might.)

The unit rate at which Martin paints in walls per gallon is 1 7/25 walls per gallon

Unit rate of paint per gallon = Quantity of wall / gallon of paint

= 4/5 ÷ 5/8

= 4/5 × 8/5

= (4 × 8) / (5 × 5)

= 32/25

= 1 7/25 walls per gallon

Complete question:

Martin uses 5/8 of a gallon of paint to cover4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon

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Answer:

m=3

b=(0,5)

Step-by-step explanation:

Answer: 90 degrees

Step-by-step explanation:

The hypotenuse is opposite the right angle, which is created by the two shortest sides.

Step-by-step explanation:

im sorry but im not sure about this question

Answer:

334.488 miles

Step-by-step explanation:

You don't have a specific request on what I should answer, if it was distance then here's your answer

Answer:

[tex]3^x=5[/tex]

Step-by-step explanation:

Given:

[tex]9^x=25[/tex]

Rewrite 9 as 3²:

[tex]\implies (3^2)^x=25[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{2x}=25[/tex]

Apply the same exponent rule:

[tex]\implies (3^x)^2=25[/tex]

Square root both sides:

[tex]\implies \sqrt{(3^x)^2}=\sqrt{25}[/tex]

[tex]\implies 3^x=5[/tex]

Answer:

Laurel has to cover this area with 2.64 ounces of seeds.

Step-by-step explanation:

Given

Base of Parallelogram = 30ft

Height of Parallelogram = 22ft

Area of Parallelogram = 1/2*base*height

Therefore, Area of Parallelogram =  1/2*30*22

                                                        = 330sq. ft

Given

One ounce of seed covers 125 sq. ft

Hence, No. of ounces needed to cover 330 sq. ft= 330/125

                                                                                  = 2.64

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Answer:

18, 36, 54

Step-by-step explanation:

Find the least common multiple of 6 and 9:

Multiples of 6: 6, 12, 18, ......

Multiples of 9: 9, 18, 27, ......

We see that 18 is the least common multiple of 6 and 9.

Additional multiples of 18 are 36 and 54.

If an integer is divisible by 6 and by 9 , then the integer must be divisible by 54.

Consider the statement as a contradiction.

The assertion exists that any natural number divisible by 6 and 9 exists also divisible by 54.

Let us consider divisible to mean that the outcome of the division of the number and 54 provides another natural number. We can take the prime factors of 6 and 9 which are {2,3} and {3,3}. We can consider that the product [tex]$2 \times 3 \times 3=18$[/tex] exists a number that exists divisible by 6 and 9 but exists not divisible by 54. Another instance exists the product of [tex]$2 \times 2 \times 3 \times 3=36$[/tex] which exists also not divisible by 54.

Therefore, the correct answer is option e) 54.

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