Explain the Golden Rule for solving equations using an example. NEED HELP QUICK

Answer:

f (1) = 1/ 2(1) + 3

= 1/2 + 3

= 1/5

Answer:

360

Step-by-step explanation:

First, we need to solve the numbers in the parentheses.

(14-2)^2 = (14 - 2)(14 - 2) = 196 -56 +4 = 144 (Use FOIL)

Then, we multiply that by 5.

144 * 5 = 720

Finally, we divide by two to get our answer.

720 ÷ 2 = 360

Answer:

360.

Step-by-step explanation:

Step 1:

Combine and Determine sums of certain numbers: 12 = 22•3

(12)2 = (22•3)2 = 24 • 32 =

--5 • (24•32) /2

Step 2:

Simplify: 24•32) /2 =

--5 • 72

Step 3:

Multiply: 360

We know that the area of a circle in terms of π will be πr². However the area with respect to the diameter will be a different story. The first step here is to find a function relating the area and diameter of any circle --- ( 1 )

For any circle the diameter is 2 times the radius,

d = 2r

Therefore r = d / 2, which gives us the following formula through substitution.

A = π(d / 2)² = πd² / 4

Hence the area of a circle as the function of it's diameter is A = πd² / 4. You can also say f(d) = πd² / 4.

Now we can substitute " d " as 4, solving for the area ( A ) or f(4) --- ( 2 )

f(4) = π(4)² / 4 = 16π / 4 = 4π - This makes the area of circle present with a diameter of 4 inches, 4π.

Answer:

To cover the remaining ten kilometres and average 40 km/hr, the autonomous car must drive at infinite speed (light speed)

Step-by-step explanation:

The average speed = (The total distance)/(The total time taken)

The given parameters are;

The required average speed of the autonomous car = 40 km/hr

The average speed of the car during the first 20 km = 40 km/hr

The  average speed of the car during the next 10 km = 20 km/hr

Therefore, we have;

The time taken = Distance/Speed

The time taken by the car during the first 20 km = 20 km/40 km/hr = 0.5 hour

The time taken by the car during the next 10 km = 10 km/20 km/hr = 0.5 hour

Therefore, the amount of time elapsed = 0.5 hour + 0.5 hour = 1 hour

The distance covered = 30 km

Which gives;

To drive the remaining distance of 10 km the car has 0 hour left,

The speed of the remaining 10 km must therefore be 10/0 =  Infinite (speed).

To cover the remaining ten kilometres and average 40 km/hr, the autonomous car must drive at infinite speed.

Answer:

It will take 19 days from Sunday.

Step-by-step explanation:

You can use the equation 172 + 6d = 1 + 15d for this equation. 172 and 1 are how many items Jose and Biruk started with. 6d and 15d represent how many items they get a day. Here's how you can solve the equation:

172 + 6d = 1 + 15d

       -6d         -6d

        172 = 1 + 9d

           -1   -1

         171 = 9d

          ÷9    ÷9

          19 = d   (write it as d = 19)

(When you type the answer, be sure to always put the letter first.)

Answer:

The maximum height of the particle is 484 m.

Step-by-step explanation:

Given that,

A particle is moving along a projectile path at an initial height of 160 feet with an initial speed of 144 feet per second. This can be represented by the function :

[tex]H(t) = -16t^2 + 144t + 160[/tex] ....(1)

We need to find the maximum height of the particle. For maximum height put [tex]\dfrac{dH}{dt}=0[/tex]

So,

[tex]\dfrac{d(-16t^2+144t+160)}{dt}=0\\\\-32t+144=0\\\\t=4.5\ s[/tex]

Put t = 4.5 s in equation (1) as :

[tex]H(t) = -16(4.5)^2 + 144(4.5)+ 160\\\\H(t)=484\ m[/tex]

So, the maximum height of the particle is 484 m.

Answer:

484 feet

Step-by-step explanation:

First, look at H(t) = −16t^2 + 144t + 160 as ax^2 + bx + c

Second, write out a=, b=, c=, which are a=-16, b=144, c=160

Third, plug a, b, & c into the equation for vertex which is t= -b/(2a) or t=-144/[2*(-16)], t=4.5.

Fourth, plug t=4.5 into the original equation H(t) = −16t^2 + 144t + 160, so H(4.5)=−16((4.5)^2) + 144(4.5) + 160 = -324 + 648 +160 = 484 feet

Answer:

They will win 70 games

Step-by-step explanation:

if for 39 games they won 35 of them,

for 78 they will win X

39*X= 78* 35

39X= 2730

X= 70

Answer:

11

Step-by-step explanation:

The midpoint of AB is half the distance from A to B.  Here that distance is 22.  Thus, the midpoint of AB is 11.

Answer:

Hey there!

The answer is 11. We can use the midpoint formula, but since this is a number line, we can easily see that 11 is half of 22.

Let me know if this helps :)

Answer:

17/3  or  5 2/3  or 5.6 repeating

Step-by-step explanation:

z

Answer:

5(5/6)+(-1/6)+2(2/3)+(-2)(2/3)

(35/6)-(1/6)+(8/3)-(8/3)

find the least common multiple which is 3

therefore 70-3+16-16

the answer is 67

Answer:

He would need 3.3 gallons

Step-by-step explanation:

1 gallon = 128 ounces

35 * 5 = 420

420 / 128 = 3.28

Answer:

The Break Even point is the point at which the cost=revenue   14,980+20x=30x 14,980=10x 1,498=x   a. 1,498 units must be sold to break even. At $20 per unit, the dollar amount will be $29,960   b. The profit function is P(x)=R(x)-C(x) So P(x)=30x-(14,980+20x) If you want to solve for this equation just enter the value of x we found for the break even point to get the answer.

Hoped I helped

The profit for 90 downloads will be;

⇒ P = $223

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Your revenue for x downloads is given by,

⇒ f(x) = 3x

And, Your profit is $20 less than 90% of the revenue for x downloads create a function p to model the profit.

Now,

Since, Your revenue for x downloads is given by,

⇒ f(x) = 3x

And, Your profit is $20 less than 90% of the revenue for x downloads create a function p to model the profit.

Hence, We can formulate;

⇒ P = 90% of f (x) - 20

⇒ P = 90/100 × 3x - 20

⇒ P = 270x/100 - 20

⇒ P = 2.7x - 20

So, The profit for 90 downloads​ will be;

⇒ P = 2.7 × 90 - 20

⇒ P = $223

Thus, The profit for 90 downloads = $223

Learn more about the mathematical expression visit:

brainly.com/question/1859113

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Answer:

Brainliest!

Step-by-step explanation:

30+8

=38

16/2 = 8

Answer:

38

Step-by-step explanation:

16/2 = 8

30 + 8 = 38

Answer:

1/4

Step-by-step explanation:

you would have one fourth because you divide 3 and 12 by 4 and you get 1/4

3/3=1

12/3=4

Answer:

slope: 1/2

y-intercept: 4

11x - 55 - 5a + ax

11 (x - 5) - a ( 5 + x )

Answer:

11 (x - 5) - a ( 5 + x )

Answer:

The answer is option C

Step-by-step explanation:

Since the triangle is a right angled triangle we can use trigonometric ratios to find x and y

In order to find x we use tan

tan∅ = opposite/ adjacent

From the question

The opposite is 4

The adjacent is x

Substitute the values into the above formula

That's

We have the answer as

In order to find y we use sine

sin ∅ = opposite / hypotenuse

From the question

The opposite is 4

The hypotenuse is y

So we have

We have the answer as

Hope this helps you

Answer:

a,e,f

Step-by-step explanation:

a. 6p+6

b.12p

c.6p

d.5p+6

e.6p+6

f.6p+6

Answer:

£13

Step-by-step explanation:

Set up a system of equations where s represents the cost of one shirt and j represents the cost of one jumper:

2s + j = 29

s + j = 21

Multiply the bottom equation by -2 to solve by elimination by cancelling out the s variables:

2s + j = 29

-2s - 2j = -42

-j = -13

j = 13

One jumper will cost £13

Answer:     a) $481.62      b) $16,569.76

Step-by-step explanation:

The formula for compound interest is:    [tex]A = P(1 + r)^t[/tex]     where

Given: P = 3000, r = 1.15% (0.015), t = 10

[tex]A = 3000(1 + 0.015)^{10}\\\\\\A = 3000(1.015)^{10}\\\\\\A = 3,481.62[/tex]

Interest Earned = accrued amount - principle

                          = 3,481.62 - 3,000

                           =   481.62

******************************************************************************************

I couldn't remember the formula so I created a table:

[tex]\begin{array}{c||l|c||r}\underline{Jan\ 1}&\underline{Interest\ Earned}&\underline{Deposit}&\underline{Balance}\\2019&0&3000&3,000.00\\2120&3000(1.015)&1200&4,245.00\\2121&4245(1.015)&1200&5,508.68\\2122&5508.68(1.015)&1200&6,791.31\\2123&6791.31(1.015)&1200&8,093.17\\2124&8093.17(1.015)&1200&9,414.57\\2125&9414.57(1.015)&1200&10,755.79\\2126&10755.79(1.015)&1200&12,117.13\\2127&12117.13(1.015)&1200&13,498.88\\2128&13498.88(1.015)&1200&14,901.37\\2129&14901.37(1.015)&1200&16,324.89\\\end{array}[/tex]

2130  || 16324.89(1.015)  |       0      ||  16,569.76

Answer:

-5/4 0 6% 2/5 25% 6

Step-by-step explanation:

converting all to decimal -

.4, .06, 6, -1.25, 0, .25

Ok so we need to turn these all into the same type of number.

I'm going to turn it into decimals.

2/5 = 4/10 = 40/100 = 0.40

6%=0.06

6=6.00

-5/4 = -125/100 = -1.25

0 = 0.0

25% = 0.25

So now we order from least to greatest.

0.4, 0.06, 6, -1.25, 0, 0.25

Since -1.25 is a negative number, it goes first.

All of them except for -1.25 and 0 are positive numbers so 0 goes next.

Now you could ignore the decimal point; 40, 6, 600, 25

From least to greatest it is; 6, 25, 40, 600

So the final order from least to greatest is; -1.25, 0, 0.06, 0.25, 0.4, 6

Or; -5/4, 0, 6%, 25%, 2/5, 6

♡ Hope this helped! ♡

❀ 0ranges ❀

Answer:

Ratio of triangle = 3 : 4

Step-by-step explanation:

Given:

Parallel sides = 9 cm , 12 cm

Find:

Ratio of triangle

Computation:

Assume height = h

Area of triangle = [1/2]bh

Area of triangle (1) = [1/2](9)h

Area of triangle (1) = 4.5 h

Area of triangle (2) = [1/2](12)h

Area of triangle (2) = 6 h

Ratio of triangle = 4.5 h / 6 h

Ratio of triangle = 3 : 4

Answer:

160 m

Step-by-step explanation:

you can approach this question with the thinking of simple math. First, you have the value of -85 rose by 30 means +30 and descending 105 means -105.

So, the calculation you will get is -85+30-105=-160. The negative means going down as the direction.

Answer:

The standard deviation of the critical path = 5

Step-by-step explanation:

The formula for the standard deviation of a critical path is given as:

Standard deviation of a path

=√(sum of variances of activities on path)

Variance = (Standard deviation)²

In the above question, we are given:

Standard deviation of 1, 2, 4 and 2 days

Standard deviation of a critical path

=√(sum of variances of activities on path)

= √1² + 2² + 4² + 2²

= √1 + 4 + 16 + 4

= √25

= 5

Answer:

-5x²+13x+6

Step-by-step explanation:

(x-3)*(2x-7x-2)

(x-3)*(-5x-2)

-5x²-2x+15x+6

-5x²+13x+6

Answer:

The correct option is;

W

Step-by-step explanation:

The number of points that defines a plane in a Euclidean space in all dimensions is either three points which are not on the same line, or two colinear points and a third point not on the line

The given points of the plane are UVX, which gives the plane as being diagonal to the cube and perpendicular to the side face of the cube.

The fourth point in plane UVX is therefore W.

Answer:

2a). Height = 2 cm

2b). Surface area = 395.84 cm²

Step-by-step explanation:

2a). Volume of the cylinder = 308 cm³

      Radius of the base of the cylinder = 7 cm

      Formula to get the volume of a cylinder = πr²h

     308 = π(7)²h

     h = [tex]\frac{308}{49\pi }[/tex]

     h = 2 cm

     Therefore, height of the cylinder will be 2 cm.

2b). Formula to calculate the surface area of the cylinder = [tex]2\pi r(r + h)[/tex]

      By substituting the values in the given formula,

      S.A. = 2π(7)(7 + 2)

              = 395.84 cm²

     Therefore, Surface area of the cylinder is 395.84 cm².

Answer:

12(3 + 1)

Step-by-step explanation:

if you distribute the 12:

12 x 3 = 36

12 x 1 = 12

= 36 + 12

Question: In the following questions, look at different ways to represent the relation given by the equation y = x2 - 1. The table below shows some values for the given equation. Find the values of a and b.

Answer:

a= 3

b= 0

The value of a and be will be three and zero respectively.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

We are given the quadratic equation as;

y = x² - 1

From the given table;

At x = -2, y =  (-2)² - 1 = 3

At x = -1, y = 0

At x = 0, y = -1

At x = 1, y = 0

Now, from the values above, we can say that the first graph is the correct one that shows some values for the given equation.

Therefore, values of a and be will be three and zero respectively.

The complete question is given below:-

In the following questions, look at different ways to represent the relation given by the

equation y = x2 - 1.

The table below shows some values for the given equation. Find the values of a and b.

a =

b =

The table is attached with the answer.

Read more about Quadratic Function Graphs at; brainly.com/question/1523847

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Answer:

40

Step-by-step explanation:

[tex]5. {2}^{3} = 5.8 = 40 \\ [/tex]

Answer:     Grater than jacks debt    -$50 , -$30

less that jacks debt:   $15 , -$10 , $30 , $5.

srry if its wrong but this is how i got it right

hopefully im right .......................... bye.  

∩⁽° ⁻  °⁾∩

Answer:

Grater than jacks debt -$50 , -$30

less that jacks debt: $15 , -$10 , $30 , $5.

srry if its wrong but this is how i got it right

hopefully im right .......................... bye.

Step-by-step explanation: