To solve 49^3x = 343^2x+1, write each side of the equation in terms of base ____

The solution is, the value of x is 7.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

(10x-20)=(6x+8)

We simplify the equation to the form, which is simple to understand

(10x-20)=(6x+8)

Remove unnecessary parentheses

10x-20=(6x+8)

Remove unnecessary parentheses

10x-20=6x+8

We move all terms containing x to the left and all other terms to the right.

+10x-6x=+8+20

We simplify left and right side of the equation.

+4x=+28

We divide both sides of the equation by 4 to get x.

x=7

Hence, The solution is, the value of x is 7.

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The machine lays cable at a rate of 25 meters per minute. This is calculated by dividing 125 meters by 5 minutes.

To determine how quickly the machine can lay underground cable, we need to calculate the rate of cable it places per minute. We start by noting that the machine can lay 125 meters of cable in 5 minutes.

We calculate the rate as follows:

This means the machine lays cable at a rate of 25 meters per minute.

Complete Question: A machine laying underground cable can place 125 meters of cable in 5 minutes. What is the rate per minute?

Answer:

Since, by the quadratic formula,

The solution of a quadratic equation [tex]ax^2+bx+c=0[/tex] is,

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here, the given quadratic equation,

[tex]5-10x-3x^2=0[/tex]

[tex]-3x^2-10x+5=0[/tex]

By the above formula,

[tex]x=\frac{-(-10)\pm \sqrt{(-10)^2-4\times -3\times 5}}{2\times -3}[/tex]

[tex]=\frac{10\pm \sqrt{100+60}}{-6}[/tex]

[tex]=\frac{10\pm \sqrt{160}}{-6}[/tex]

[tex]=\frac{5\pm 2\sqrt{10}}{-3}[/tex]

[tex]\implies x=-\frac{5+2\sqrt{10}}{3}\text{ or }x=-\frac{5-2\sqrt{10}}{3}[/tex]

Final answer:

To find the number of pizza combinations available using 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, one multiplies the number of topping choices by the number of cheese choices, giving 8 x 3 = 24 possible combinations.

Explanation:

Calculating Pizza Combinations

When calculating the number of possible pizza combinations with 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, we use basic counting principles. Each pizza can be thought of as a combination of one topping and one cheese. Since these choices are independent, we multiply the number of options for toppings by the number of options for cheeses to find the total combination possibilities. This results in 8 toppings multiplied by 3 cheeses, giving 24 possible combinations.

The formula used is straightforward: Number of combinations = Number of toppings × Number of cheeses.

Pizza Combination Calculation Example

For instance, if you were at a pizza parlor where you could choose from pepperoni, mushrooms, onions, and 5 other toppings, along with mozzarella, cheddar, and one other cheese, you could create 24 unique pizzas. Just pick one topping and one cheese, and that's your combination.

Answer:

(0, 139) and (139/35, 0)

Step-by-step explanation:

To graph a line, two points are needed. Taking x = 0 and replacing this value in the equation, we get:

y+1=−35(0−4)

y = 140 - 1

y = 139

Then, the point (0, 139) is on the line.

Taking y = 0 and replacing this value in the equation, we get:

0+1=−35(x−4)

1/(-35) = x -4

1/(-35) + 4 = x

139/35 = x

3.971 = x

Then, the point (139/35, 0) is on the line.

As modeled by the function below: t=0.007x^2+0.003x. The time it will  take the computer to sort 15 objects is 1.62sec

What is Time?

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Given:

t = 0.007x^2+0.003x

x = 15

Substituting the value in the equation we get,

t = 0.007(15)^2+0.003(15)

t = 0.007(225) + 0.045

t = 1.575 + 0.045

t = 1.62sec

Hence, It will take 1.65sec to sort 15 objects

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Option C)The sales tax will be $2.25.

Convert the sales tax rate from a percentage to a decimal,
7.5% becomes 0.075.

Multiply the decimal by the total cost of the shoes,

0.075 × 29.95
= 2.24625.

$2.25.

Therefore, the sales tax on the shoes will be $2.25,Option C

Answer:

Answer is 31,

Step-by-step explanation:

PLATO Confirmed

The given equation y = 4 - 2x is a linear equation, however, it is not in standard form. The standard form is 2x + y = 4.

The equation y = 4 - 2x is indeed a linear equation. A linear equation is an equation that represents a straight line when graphed. It generally has the form 'y = mx + b' where 'm' represents the slope of the line, and 'b' represents the y-intercept. Here, 'm' is -2 and 'b' is 4.

However, it is not currently in standard form. The standard form of a linear equation is 'Ax + By = C', where A, B, and C are integers, and A and B are not both zero. To write the equation in standard form, we can re-arrange it as 2x + y = 4.

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Final answer:

The constant of proportionality when y = 18 and x = 60 is calculated by dividing y by x, which results in a constant of 0.3.

Explanation:

To find the constant of proportionality when y = 18 and x = 60, we must assume that the relationship between y and x is directly proportional. This means that as x increases, y increases at a constant rate, and vice versa. If the relationship is directly proportional, we can write y = kx, where k is the constant of proportionality.

To calculate k, we simply divide y by x. So we have:

k = y / x
k = 18 / 60
k = 0.3

Therefore, the constant of proportionality is 0.3.

Answer:

A) -4 over 9

Step-by-step explanation:

We have the fraction [tex]\frac{4}{-9}[/tex] the equivalent of this fraction is [tex]\frac{-4}{9}[/tex]

[tex]\frac{4}{-9}= \frac{-4}{9} =-\frac{4}{9}[/tex]

Both fractions are the same and equivalent, the negative sign makes the whole fraction negative regardless of whether it is in the numerator or denominator.

To solve the given differential equation, variables need to be separated, followed by integration of both sides. Since the equation involves both exponential and inverse square terms, separation of variables and integration are key steps. A specific solution also requires substituting a given function of y into the found general solution to determine any integration constants.

The question involves solving a differential equation 3e^(3x)dy/dx = -9x/y^2. First, we need to recognize this as a separable differential equation, which can be solved by isolating all terms involving y on one side and all terms involving x on the other side. After separation, we integrate both sides with respect to their respective variables.

Step 1: Separate the variables. We get dy/y^2 = -3x e^(-3x) dx.

Step 2: Integrate both sides. The integration of dy/y^2 with respect to y is -1/y, and the integration of -3x e^(-3x) with respect to x requires integration by parts or a table of integrals.

Step 3: Upon integration, we would find an implicit solution involving y and x, combined with an integration constant that needs to be determined based on initial conditions or additional information. Since specific initial conditions are not provided in the initial question, we'd include a constant C in our final expression.

For a specific solution when y(x) = cos(3x), additional steps are required to substitute this y expression into our general solution and solve for the constant.

The correct answer should be +18

Answer:

The answer is only one piece of candy

Step-by-step explanation:

Firstly, we have to determine the total amount of pieces of candy:

There are three bags with 75 pieces in each one, so the total is:

[tex]75+75+75=225[/tex]

Then, in order to determine the amount of pieces of candy for every friend,

we have to divide the total amount by 7, where the remainder of the division is the answer.

[tex]\frac{225}{7}=32*7+1[/tex]

Remainder=1

Finally, every friend of Scott receive 32 pieces of candy evenly and Scott is left with only one piece of candy.