Solve by substitution
3x-y=12
Y=4x-14

Taking into account the definition of a system of linear equations, the weight of meteorite A and meteorite B is 126 tons and 18 tons respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

[tex]\left \{ {{A=7B} \atop {A+B=144}} \right.[/tex]

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the first equation in the second one you get:

7B + B= 144

Solving:

8B= 144

B= 144÷8

B= 18 tons

Remembering that A= 7B, the value of A is calculated as:

A= 7×18

A= 126 tons

Finally, the weight of meteorite A and meteorite B is 126 tons and 18 tons respectively.

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Answer:

454

Step-by-step explanation:

Answer: The Answer is 454.

Answer:

x = 6

Step-by-step explanation:

The 'ZERO" of the function is the 'x' value(s) where it crosses the x-axis (and

'y' = ZERO)

Answer:

x = 6

Step-by-step explanation:

the zero of the function is the value of x on the x- axis where the graph crosses.

the graph crosses the x- axis at 6

then the zero is x = 6

Answer: 176cm

Step-by-step explanation:  To find the circumference of the circle, we will use the circumference formula: 2πr = 2 × 22/7 × 28

We get the equation in logarithmic form as log₁₀ 1000 = 3.

A “logarithmic equation” is an equation which involves the “logarithm” of any expression which is containing a variable.

Now, we have been given an equation:

10 ³ = 1000

We need to write it in the logarithm form.

We know that, it will be written as:

log₁₀ 1000 = 3

Since the power goes after the equal sign, so 3 is placed after the equal sign.

The actual value is taken after log, so 1000 is placed there and the base number is taken as the base for the log, so 10 is taken as the base for the log.

Therefore, we get the equation in logarithmic form as log₁₀ 1000 = 3.

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The inequalities which shows the closest whole number range for :

a) y = √74 is 8 < y < 9.

b)  z = ∛74  is 4 < z < 5.

What is an mathematical expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

it is given that for x = √28 the value of x ranges between 5 and 6 that is 5 < x < 6  because square root of 28 is approximately 5.29 which  is less than 6 and greater than 5.

a)  Now, for y = √74 :

the square root of 74 is approximately 8.6 which  is less than 9 and greater than 8 that is the value of y ranges between 8 and 9 that is :

8 < y < 9.

b) Now, for z = ∛74 :

the cube root of 74 is approximately 4.19 which  is less than 5 and greater than 4 that is the value of z ranges between 4 and 5 that is :

4 < z < 5.

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The line parallel to line  y = 7x - 6 and passing through points  (5, 8)  is

Given data

y = 7x - 6

(5, 8) and is parallel

From the line,  y = 7x - 6, the slope is 7. Since slope of parallel lines are equal, the new line will have same slope and pass through points  (5, 8).

y - 8 = 7 ( x - 5 )

y - 8 = 7x - 35

y = 7x - 35 + 8

y = 7x - 27

Hence we can say that the line parallel to line  y = 7x - 6 and passing through points  (5, 8)  is y = 7x - 27

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The equation of the line parallel to y = 7x - 6 passing through (5, 8) is y = 7x - 27

The equation of the line is parallel to the equation y = 7x - 6.

Parallel line have the same slope.

Therefore, let's represent the equation as follows:

y = mx + b

where

Therefore, the slope of the graph y = 7x - 6 is 7.

The equation of the line that contains (5, 8) and parallel to the graph can be computed as follows

y = 7x + b

let's find the y-intercept

8 = 7(5) + b

8 - 35 = b

b = - 27

Therefore, the equation of the line parallel to y = 7x - 6 passing through (5, 8) is y = 7x - 27

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Answer:

18213

Step-by-step explanation:

Given equation,

→ 467 × 39

Let's solve the problem,

→ 467 × 39

→ 18213

Thus, the answer is 18213.

The function that is the inverse of f is C. The function g because the graphs of f and g are symmetrical about the line y = x

The inverse of a function is a function that can reverse into another function.

If we have function f and g, and f f(x) = y, then g is the inverse of f if and only if g(y) = x

To determine which graph is an inverse of f, it has to satisfy the following condition

So, looking at the graph, we see that the only the graphs of f and g are symmetic about the line y = x.

Thus function g is the inverse of f.

So, the function that is the inverse of f is C. The function g because the graphs of f and g are symmetrical about the line y = x

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The median of a data set is 9.5

Mean is the ratio of sum of the observations to the total number of observations.

Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong same number of observations.

The median of a data set is the middle number when all of the data points are ordered from smallest to largest. For the data set, the first thing you want to do is put them in order from smallest to largest gives you:

6 6 7 7 7 9 10 10 10 10 11 12

Then we will find the middle of the data set. Since there is an even number of twelve data points; it will be between the sixth and seventh point:

6 6 7 7 7 9 ^ 10 10 10 10 11 12

Now the average of those two in the middle to get the median:

9.5

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Answer:

y equals negative one-sixth times x plus 5

This is correct, it's not plus 3, it's plus 5!

Answer: I hope this helps.

Step-by-step explanation:

Answer:

The correct answer is -2+1.

So yeah

Answer:

b = 10

Step-by-step explanation:

You take the decimal, divide it by the addend and then you take the fraction and subtract that by the sum and then multiply your answer by 5.

Answer:

The answer to the given equation is 1

Logarithmic scale: A measurement scale in which the position is marked using the logarithm of a value rather than the actual value.

A logarithmic equation includes a logarithm in the variable x.

An exponential equation is one in which the variable is represented by an exponent. A logarithmic equation is one in which the logarithm of a variable-containing expression is used.

For logarithmic equations, log b (x) = y is equivalent to b^y = x such that x > 0, b > 0 and b is not equal to 1.

In the given problem b = 4, x = 1 and y = 0

b = 4

x = 1

y = 0

Substituting the values of b, x and y into the equation b^y = x;

4^(0) = 1

Therefore, the value of the given equation log₄1=0 is 1

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Answer:

18/36×100%

The answer will be 50

Step-by-step explanation:

Hope it helps you

Decimal should the digital scale show is 0.2

The grocery store asked me to buy 3 [tex]\frac{1}{5}[/tex] pounds of ham. You will be asked to find the number of decimal places displayed by the digital scale.

3 [tex]\frac{1}{5\\}[/tex] lbs = 3 lbs + [tex]\frac{1}{5}[/tex] lbs

[tex]\frac{1}{5}[/tex] = 0.2

3 [tex]\frac{1}{5}[/tex] = 3.2

Therefore, the digital scale is displayed in decimal.

Real numbers, natural numbers, whole numbers, rational numbers, and other sorts of numbers can all be categorized in mathematics. There are decimal numerals among them. Integer and non-integer numbers are represented using this format as a standard.

One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

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The Inverse of given function F(x) = 1 / 4x is F⁻¹(x) = 1 / 4 x

F(x) = 1 / 4x is a function of x.

Changing F(x) to the variable y

This means that F(x) = 1/4x becomes y = 1/4x.

Changing the variables x and y in the previously obtained equation

This means that we can deduce x = 1 / 4y from the equation y = 1 / 4x.

Solving the newly discovered equation for y

This means that we must simplify the equation by rearranging the terms in order to obtain the equation in terms of the variable x.

x =  1 / 4y

=> 4 y = 1 / x

=> y = 1 / 4 x

As a result, we obtain the required equation.

Switching the variable y with F⁻¹(x)

This assumes, y = 1 / 4 x becomes F⁻¹(x) = 1 / 4 x

Hence, the value of the given function F⁻¹(x) = 1 / 4 x

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The Simplest form of the expression = [tex]2^{-16} x^{-1} y^{-4}[/tex]

We need to express as:

[tex]a^{m}[/tex]/[tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]

As the expression is given :

[tex](16 x^{1/4}y^{3/3} ) ^{-4}[/tex]

= 1/ [tex](16 x^{1/4} y^{3/3}) ^{4}[/tex]

= 1/[tex](2^{4} x^{1/4} y^{3/3}) ^{4}[/tex]

= 1/[tex](2^{16} x^{1} y^{4} )[/tex]

= [tex]2^{-16} x^{-1}y^{-4}[/tex]    (Simplest form of the equation)

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Answer:

Step-by-step explanation:

Let n represent the unknown number-

[tex]\frac{3}{4}n-3=-9\\ \\ \frac{3}{4} n-3+3=-9+3\\ \\ \frac{3}{4} n=-6\\\\ \frac{4}{3}(\frac{3}{4}n)=\frac{4}{3}(-6)\\ \\ n=-8[/tex]

Unknown number = -8

Saying it in digits = [tex]\frac{3}{4}n-3=9[/tex]

Solution of exponential equation 27³x=81 is , [tex]x = \frac{1}{243}[/tex]

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the exponential function can be written as   .

   [tex]a^n = x[/tex]

where, a = the base of function

            x = main expression

            n = exponential

Mathematically, if  [tex]log_ax = n[/tex] is an logarithmic function then, this can be converted to exponential function as    [tex]a^n = x[/tex] .

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

According to given statement,

27³ x = 81

divide both side by 27³ , the equation becomes :

[tex]= > x = \frac{81}{27^3} \\\\= > x = \frac{3^4}{(3^3)^3}\\\\= > x = \frac{3^4}{3^9}\\\\= > x = \frac{1}{3^5} = \frac{1}{243}[/tex]

Thus solution for this equation is  [tex]x = \frac{1}{243}[/tex]  

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Answer:

your equation is Y = 6

Step-by-step explanation:

Use Midpoint Formula to find the slope M first

Name the coordinates of both points x1 = -2, y1 = -6, x2 = 4,  y2 = 6

Plug them in the formula

M = y2 - y1/ x2 - x1

M =( 6 - 6)/( 4 - (-2))

M = 0/6

M = 0

Then use point slope formula

Plugin the slope M = 0 in the formula and pick one of the points above. Name the coordinates of  the point X1 = 4 and y1 = 6

y - y1 = m(x - x1)

y - 6 = 0(x - 4)

y - 6 = 0

y = 6

your equation is Y = 0x  + 6 but keep in this form y = b

This is a horizontal Line

Answer:

98

Step-by-step explanation:

(49)2

= 49 • 2

= 98

Therefore, (49)2 = 98

..............

Height of entertainment center will be 32 inches .

Given : Depth of entertainment center = x

Length of entertainment center = x

Height of entertainment center = 2 * depth = 2 * x = 2 x

To find : height of entertainment center .

Volume of entertainment center = depth * height * length

Substituting values in formula above :

8192 = x * x * 2 x

Solving for x ,

[tex]x^{3}[/tex] = 4096

x = 16

Hence , height of entertainment center = 2 x = 2 * 16 = 32 inches .

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