What is the equation in standard form of the line which passes through (-2, 6) and has a slope of -1?

Answer:

9.42 feet

Step-by-step explanation:

The distance around the edge of a circle is called the circumference.  The formula for circumference is C = dπ   where d is the diameter.  We are given

d = 3, so we have C = 3π.  We are told to use 3.14 for pi, so we have

C = 3(3.14) = 9.42

The pipes can fill the pool individually in 16 and 20 hours respectively, by solving the simultaneous equations: 1/x + 1/y = 1/5 and 1/2x + 1/2y = 18.

Let's assume one pipe can fill the pool in x hours, while the other pipe can fill it in y hours. When the two pipes work together, they complete one job in 5 hours, which can be expressed as 1/x + 1/y = 1/5.

When each pipe fills half the pool, it takes 18 hours. Since each of them is doing half the work, this can be represented as 1/2x + 1/2y = 18.

To solve these simultaneous equations, it is best to use the substitutive method. We can set the two equations equal to each other to get x = 36 - y. Plugging this into the first equation and solving for y, we find y = 20. Substituting y back into the equation x = 36 - y, we find x = 16.

So, one pipe could fill the pool alone in 16 hours, while the other could do it in 20 hours.

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The first pipe would take approximately 6.92 hours to fill the pool if it were working alone, and the second pipe would take 18 hours to fill the pool if it were working alone.

Let's assume that the first pipe can fill the pool in x hours, and the second pipe can fill the pool in y hours.

When the two pipes fill the pool together, they can complete the job in 5 hours. So, their combined rate of work is 1/5 of the pool per hour.

When the first pipe fills half the pool, it takes over for the second pipe, which then finishes filling the pool. This entire process takes 18 hours. So, the first pipe fills half the pool in 18 hours, which means that its rate of work is 1/18 of the pool per hour.

Using the concept of work done, we can set up the following equation:

1/x + 1/y = 1/5 (equation 1)

1/y = 1/18 (equation 2)

Solving the equations simultaneously, we can find the values of x and y:

From equation 2, y = 18 hours.

Substituting the value of y in equation 1, we get:

1/x = 1/5 - 1/18 = (18 - 5)/90 = 13/90.

Therefore, x = 90/13 hours.

So, the first pipe would take approximately 6.92 hours to fill the pool if it were working alone, and the second pipe would take 18 hours to fill the pool if it were working alone.

Answer:

CE = 12

Step-by-step explanation:

ΔCDB and ΔEAB are similar, hence the ratios of corresponding sides are equal

We require to find the length of BC to complete CE

[tex]\frac{BC}{BE}[/tex] = [tex]\frac{DB}{AB}[/tex], substitute values

[tex]\frac{BC}{8}[/tex] = [tex]\frac{5}{10}[/tex] ( cross- multiply )

10BC = 40 ( divide both sides by 10 )

BC = 4

CE = CB + BE =4 + 8 = 12

Answer:

csc^2(theta)

Step-by-step explanation:

1 / cot^2(theta) = tan^2(theta)

=============

sec(theta) = cos(theta)

therefore sec(theta)*cos(theta) = 1/cos(theta) * cos(theta) = 1

==========

tan^2(theta) + 1 = y

One of the fundamental theorems of trigonometry is

tan^2(theta) + 1 = csc^2(theta)

Answer:

[tex]\large\boxed{803.8\ cm^2}[/tex]

Step-by-step explanation:

The formula of a surface area of a sphere:

[tex]S.A.=4\pi R^2[/tex]

R - radius

We have R = 8 cm. Substitute:

[tex]S.A.=4\pi(8^2)=4\pi(64)=256\pi\ cm^2[/tex]

[tex]\pi\approx3.14[/tex]

Substitute:

[tex]S.A.\approx256(3.14)=803.84\ cm^2[/tex]

Answer:

a=[tex]2\frac{3}{16}[/tex]

Step-by-step explanation:

formulas:

a= b x h x [tex]\frac{1}{2}[/tex]

or           (both equations get the same answers)

a= b x h ÷ 2

imma stick with the second one kuz i usually use that one but ur preference.

so,

base(b) = [tex]2\frac{1}{2}[/tex] = [tex]\frac{5}{2}[/tex]

height(h) = [tex]1\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]

now fill it in to the equation:

a=b x h x [tex]\frac{1}{2}[/tex]                        a= b x h ÷ 2

a=[tex]\frac{5}{2}[/tex] x [tex]\frac{7}{4}[/tex] x [tex]\frac{1}{2}[/tex]                         a=[tex]\frac{5}{2}[/tex] x [tex]\frac{7}{4}[/tex] ÷ 2

a=[tex]\frac{35}{16}[/tex]                                   a=[tex]\frac{35}{16}[/tex] ÷ 2

a=[tex]2\frac{3}{16}[/tex]                                   a=[tex]\frac{35}{8}[/tex] ÷ 2

                                          a=[tex]\frac{35}{16}[/tex]  

                                           a=[tex]2\frac{3}{16}[/tex]

o well i did both lol

now you ca compare the two equations now  :]

plz give brainliesttttt

Final answer:

The area of a triangular poster with a base of 2 1/2 feet and a height of 1 3/4 feet is calculated using the formula A = 1/2 × base × height, resulting in an area of 2.1875 square feet.

Explanation:

To find the area of a triangle, we use the formula A = ½ × base × height. Given that the base of the triangle is 2 1/2 feet (which is 2.5 feet when converted to a decimal) and the height is 1 3/4 feet (which is 1.75 feet in decimal), we can calculate the area as follows:

A = ½ × base × height

A = ½ × 2.5 ft × 1.75 ft

A = ½ × 4.375 ft²

A = 2.1875 ft²

Therefore, the area of the poster is 2.1875 square feet.

Answer:

A will appear to the left of B.  The answer is B) hope this helps

Step-by-step explanation:

If A < B, A will appear to the left of B on the number line.

A number line is a linear line on which points are marked equidistant from each other and used to represent the position of a certain linear number on it.

Let us take an example where A = 2 and B = 3. Here 2 < 3.

We know that 2 is to the left of 3 on the number line.

Now let us take an example of negative numbers. A = -3 and B = -2.

Here, -3 < -2. - 3 is also to the left of - 2.

Therefore we can say that A is always to the left of B.

Therefore, if A < B, A will appear to the left of B on the number line.

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ANSWER

y-intercept:

(0,-13)

x-intercept:

[tex](4 \frac{1}{3} ,0)[/tex]

EXPLANATION

The given line has equation

[tex]y + 1 = 3(x - 4)[/tex]

At y-intercept , x=0.

This implies that;

[tex]y + 1 = 3(0 - 4)[/tex]

[tex]y = - 12 - 1[/tex]

[tex]y = - 13[/tex]

The y-intercept is

(0,-13).

At x-intercept y=0,

This implies that;

[tex]0+ 1 = 3(x - 4)[/tex]

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

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

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

The x-intercept is

[tex](4 \frac{1}{3} ,0)[/tex]

Answer:

x-intercept = [tex]\frac{13}{3}[/tex]

y-intercept = [tex]-13[/tex]

Step-by-step explanation:

We are given the following equation of a line and we are to find the x and y intercepts for it:

[tex] y + 1 = 3 ( x - 4 ) [/tex]

In order to find the x-intercept, we will substitute 0 in place of y to get:

[tex] 0 + 1 = 3 ( x - 4 ) \\\\ 1 = 3 x - 12 \\\\ 3 x = 1 + 12 \\\\ x = \frac { 13 } { 3 } [/tex]

And to find the y-intercept, we need to substitute 0 in place of x:

[tex] y + 1 = 3 ( 0 - 4 ) \\\\ y + 1 = -124 \\\\ y = - 12 - 1 \\\\ y = - 13 [/tex]

So the x-intercept is [tex]\frac{13}{3}[/tex] while the y-intercept is [tex]-13[/tex].

Answer:

[tex]\boxed{\bold{2(3a + 4) = 6a + 8}}[/tex]

Step-by-step explanation:

Distributive Property: [tex]\bold{a(b+c) \ = \ (a*b)+(a*c)}[/tex]

2(3a + 4)

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

(2 * 3a) + (2 * 4)

(2 * 3a) = 6a

(2 * 4) = 8

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

6a + 8

El resultado es 0.0166666667

The answer is the 4th option.

Equivalent inequalities are inequalities with the same solutions. They're also the most likely paired together.

Answer:

it is equivalent to the number that you want to find it out

Step-by-step explanation:

Inequalety

Answer:

9220

Step-by-step explanation:10^3 = 1000 then times it by 9.22 and you should have 9220

Answer:

9220

Step-by-step explanation:

9.22 x 10^4 would be 92200

9.22 x 10^3 would be 9220

9.22 x 10^2 would be 922

9.22 x 10^1 would be 9.22

Can you work out the pattern?. Also you can work this out on your calculator by pressing the standard form button in the bottom middle of your calculator.

Answer:

soda = 35mg

coffee = 81mg

energy = 83mg

Step-by-step explanation:

coffee + energy + soda = 199

coffee = 11 + (2 * soda)

energy = (soda + coffee) - 33

(11 + (2 * soda)) + ((soda + (11 + (2 * soda))) - 33) + soda = 199

11 + 2s + s + 11 + 2s - 33 + s = 199

22 + 6s - 33 = 199

-11 + 6s = 199

6s = 210

s = 35

soda = 35mg

c  = 11 + 2s

c = 11 + 2(35)

c = 11 + 70

c = 81

coffee = 81mg

e = s + c - 33

e = (35) + (81) - 33

e = 116 - 33

e = 83

energy = 83mg

Final answer:

One serving of soda contains 35 mg of caffeine, one serving of coffee contains 81 mg of caffeine, and one serving of energy drink contains 83 mg of caffeine.

Explanation:

Let's solve this problem step by step:

To find the value of x, we can set up an equation:

Simplifying the equation:

Combine like terms:

Add 11 to both sides:

Divide both sides by 6:

Therefore, one serving of soda contains 35 mg of caffeine. Substituting this value into the previous equations:

Answer: -87

Step-by-step explanation: −27−42−18

Answer:

[tex]\large\boxed{f(-3)=3.6}[/tex]

Step-by-step explanation:

[tex]f(x)=0.6(3-x)\\\\f(-3)\to\text{Put x = -3 to the equation of a function:}\\\\f(-3)=0.6(3-(-3))=0.6(3+3)=0.6(6)=3.6[/tex]

we just have to locate these coordinates on graph and see which one lies on line .

you will find option 4 lies on line so it's the one of the solution of line

Answer:

(--3,2)

The only (x,y) that is on the line is (-3,2)

the rest don't fit on the line.

Answer:

see explanation

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(5)

x² + (y - 4)² = 25 ← is in standard form

with centre = (h, k) = (0, 4) → A

(6)

here (h, k) = ( 9, - 5) and r = 1, hence

(x - 9)² + (y - (- 5))² = 1², that is

(x - 9)² + (y + 5)² = 1 ← equation of circle

Answer:

The perimeter of rectangle is [tex]18\ cm[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

[tex]x=y+5[/tex] ----> equation A

[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)

substitute the equation A in equation B

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}[/tex]

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]

using a graphing calculator -----> solve the quadratic equation

The solution is

[tex]y=2\ cm[/tex]

Find the value of x

[tex]x=y+5 ----> x=2+5=7\ cm[/tex]

Find the perimeter of rectangle

[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]

Answer:

It is true. It is a number value therefore it is true.

A term can be having a positive or negative value. Therefore -8 is also a term. Hence the given statement is true.

A term or phrase that is used to describe something or to express a thought, particularly in a certain language or field of study.

A term's value might be either positive or negative. Consequently, -8 is also a term.

As a result, the statement is accurate.

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Answer:

-1050

Step-by-step explanation:

I know the answer because descending means going down so 2100 is the big number and its negative to if you do -2100 divided by 2 then you will get -1050.

The equation to represent the submarine's elevation and time is elevation = 2100 - (rate of descent × 2).

To represent the submarine's elevation and time, we can use the equation:

elevation = starting altitude - (rate of descent ×  time)

Where:

In this case, the equation would be:

elevation = 2100 - (rate of descent × 2)

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ANSWER

[tex]y = 5x + 5[/tex]

EXPLANATION

Using any two ordered pairs we can find the equation.

Let us use

(2,15) and (5,30).

The slope is

[tex] = \frac{30 - 15}{5 - 2} = \frac{15}{3} = 5[/tex]

The equation is given by:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-15=5(x-2)[/tex]

This implies that,

[tex]y = 5x - 10 + 15[/tex]

The required equation is

[tex]y = 5x + 5[/tex]

Answer:

The one on the bottom CANNOT be represented by the equation.

Step-by-step explanation:

For the equation in the problem there has to be a 4x, meaning the cost per case multiplied times the about of them (x). Then there has to be a +7 somewhere in the equation for shipping. The two on the top fit both of those descriptions.

Mark Brainliest plz!

y = -2x - 4 would be the answer

Answer: OPTION B

Step-by-step explanation:

Let's call:

c: the number of cars.

m: the number of motorcycles.

Based on the given information, you can set up the following system of equations:

[tex]\left \{ {{c+m=38} \atop {4c+2m=104}} \right.[/tex]

You can solve it by the Elimination method:

- Multiply the first equation by -4.

- Add both equations to cancel out the variable "c".

- Solve for "m":

[tex]\left \{ {(-4)(c+m)=38(-4)} \atop {4c+2m=104}} \right.\\\\\left \{ {-4c-4m=-152} \atop {4c+2m=104}} \right.\\-------\\-2m=-48\\m=24[/tex]

(24 motorcycles)

 - Substitute m=24 into any of the original equations ans solve for "c". Then:

[tex]c+24=38\\c=38-24\\c=14[/tex]

(14 cars)

The answer is:

Option B.

[tex]Cars=14\\Motorcycles=24[/tex]

We know that the total of tires of all the vehicles was 104, and there were 38 vehicles with 4 tires and motorcyles with 2 tires, so, we can calculate how many cars and motorcyles participated in the ride using the following equation:

Let x be the cars and y be the motorcyles, so:

[tex]x+y=38[/tex]

and,

[tex]4x+2y=104[/tex]

So, isolating x in terms of y from the first equation, we have:

[tex]x=38-y[/tex]

Then, substituting "x" into the second equation we have:

[tex]4(38-y)+2y=104\\152-4y+2y=104\\152-2y=104\\2y=152-104\\2y=48\\y=\frac{48}{2}=24[/tex]

Now, substituting "y" into the first equation, we have:

[tex]x+24=38[/tex]

[tex]x=38-24=14[/tex]

So, there were a total of 14 cars and 24 motorcycles in the ride.

Have a nice day!

Answer:

Step-by-step explanation:

The area of a triangle is base*height/2

So one triangle is 2*4/2=4

Multiplied by 4 sides, 4*4=16

Finally the base is a square, so 2*2=4

Therefore the entire shape is 16+4=20 square feet

The amount of paper it will take to make each tree, including the bottom is 20 ft²

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.

Surface area of paper tree = sum of areas of those 4 slant standing triangles + area of base

Area of each of those 4 triangles are same (assuming they're symmetric).

Each triangle has height of 4 ft and base of 2 ft. (the base is a square of side length 2 ft).

Thus, we get:

Area of 4 triangles = 4(area of each tree ) = [tex]4\left (\dfrac{1}{2} \times \text{base} \times \text{height}\right) = 4\left (\dfrac{1}{2} \times 2 \times 4\right) = 16 \: \rm ft^2[/tex]

Area of square base = [tex]\text{side}^2 = 2^2 = 4 \: \rm ft^2[/tex]

Thus, we get:

Surface area of paper tree = 16 + 4 = 20 ft²

Thus, the amount of paper it will take to make each tree, including the bottom is  20 ft²

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Answer:

256 Coins

Step-by-step explanation:

On the first day, Jada starts with one coin, so all you have to do here is multiply it by 2.

Day 1: 2 coins

Day 2: 2 x 2 = 4 coins

Day 3: 4 x 2 = 8 coins

Day 4: 8 x 2 = 16 coins

Day 5: 16 x 2 = 32 coins

Day 6: 32 x 2 = 64 coins

Day 7: 64 x 2 = 128 coins

Day 8: 128 x 2 = 256 coins

Hope this helps! Just message me if you have more questions or need more help! :)

The number of coins that Jada will have after 8 days is; 256 coins

We are told that on the first day, Jada starts with one coin and that the number of coins doubles each day. Thus;

Day 1: She has 2 coins

Day 2: She has 2 * 2 = 4 coins

This follows a geometric pattern 2ⁿ

where n is number of days

Thus, for 8 days, she will have; 2⁸ coins = 256 coins

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Answer:

8*x > 72

x > 72/8

x > 9

The number is any number greater than 9.

It could be 9.5, 10, 11, 12,....

Step-by-step explanation:

The mathematical expression representing the verbal expression given is 8n < 72

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, a verbal expression. eight times a number n less than 72,

We need to convert it in mathematical expression

So, the expression will be

8n < 72

Now, solving for n,

8n < 72

n < 9

Therefore, values of n below 9 is the solution of the inequality.

Hence, the mathematical expression representing the verbal expression given is 8n < 72

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Answer:

x=16, x=8

Step-by-step explanation:

since x in |x-12| can be both negative and positive, we have to find two numbers for each senario. if x-12 is negative, we flip them so it becomes 12-x. so 12-x=4 is easily solved and the answer would be 8. if it is positive, we would keep it and x-12 would be 4. we also solve this to get 16. we can check our work by putting them in to get 16-12 is 4 and |8-12| is 4

Answer:

Step-by-step explanation:

[tex]Use\\\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{b^n}=\left(\dfrac{a}{b}\right)^n\\=================\\A.\ 3^{x+1}=3^x\cdot 3\neq3^x\\\\B.\ 3\cdot3^{x-1}=3\cdot3^x\cdot3^{-1}=(3^1\cdot3^{-1})\cdot3^x=3^{1+(-1)}\cdot3^x=3^0\cdot3^x=1\cdot3^x=3^x\\\\C.\ \dfrac{18^x}{3}\neq3^x\\\\D.\ \left(\dfrac{18}{6}\right)^x=(3)^x=3^x\\\\E.\ x^3\neq3^x\\\\F.\ \dfrac{18^x}{6^x}=\left(\dfrac{18}{6}\right)^x=(3)^x=3^x[/tex]