Equivalent fractions for 1 3/4 and 1 4/5 using 20 as the common denominator

Elimination is a method used to solve systems of linear equations with two or more variables. One possible method to solve a equation with 3 variables using elimination is solving algebraically.

To use elimination to solve a system of equations with three variables, you can follow these steps:

1. Write the system of equations. For example, if you have the equations:

3x + 2y - z = 5

2x - 4y + 2z = 6

5x - 2y + 3z = 10

2. Multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say y in two of the equations.

3. Next, you can multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say x in two of the equations.

4. Now substitute this value of z in the first or the second equation to solve for x

5. Now substitute this value of x and z in the second equation or any other equation to solve for y

This is one possible way to use elimination to solve a system of equations with three variables. Depending on the specific problem, there may be different ways to eliminate variables, but the general idea is to use scalar multiplication and addition or subtraction to create a new equation with one variable having the same coefficient but with opposite signs. One can also use Gaussian elimination or matrix inversion method.

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The solution of the system of equations is:

x = 5t - 4

y = -5t + 1

z = t

Option B is the correct answer.

A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.

We have,

From the row-echelon form of the augmented matrix of a system of equations, we get,

x + 0y -5z = -4

x - 5z = -4

x = 5z - 4

0x + y + 5z = 1

y + 5z = 1

y = -5z + 1

0x + 0y + 0z = 0

Now,

Put z = t (any real number)

We get,

x = 5t - 4

y = -5t + 1

Thus,

The solutions are:

x = 5t - 4

y = -5t + 1

z = t

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The true equations are - 15·0 = 015·0, 1.4 + 2.7 = 4.1, and 4(2/3) = 5-(1/3).

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first equation is -

5 + 0 = 0

This equation is false, as if 0 is added to any number, the result is the same number itself, and not 0.

The second equation is -

15·0 = 015·0

Any number multiplied by 0, gives the result as 0.

In the above equation LHS = RHS = 0.

Hence, this equation is true.

The third equation is -

1.4 + 2.7 = 4.1

Solving LHS -

= 1.4 + 2.7

= 4.1

So, LHS = RHS and hence, this equation is true.

The fourth equation is -

(2/3) · (5/9) = 7/12

Solving LHS -

= (2/3) × (5/9)

= 10/27

Here, LHS ≠ RHS.

Hence, this equation is false.

The fifth equation is -

4(2/3) = 5-(1/3)

Solving LHS -

4(2/3) = 14/3

Solving RHS -

= 5 - 1/3

= (15 - 1)/3

= 14/3

Therefore, LHS = RHS and hence, this equation is true.

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Answer:

Isosceles triangle

Step-by-step explanation:

Thorough explanation: Through the angles in the triangle ABC.

First, observe that angle ACD = 50 degrees (given)

Since lines AB and DE are parallel to each other,

angle BAC = angle ACD = 50 degrees (by the property of alternate angles)

It is also given that angle ABC = 80 degrees.

Since ABC is a triangle, the sum of the three angles must add up to 180 degrees.

Angle BAC + Angle ABC + Angle ACB = 180 degrees

50 + 80 + Angle ACB = 180

Angle ACB = 180 - 50 - 80

                   = 50 degrees

Since two of the angles, angles ACB and BAC are the same at 50 degrees, triangle ABC is an isosceles triangle. (With sides AB and BC equal)

Answer:

01?

Step-by-step explanation:

I didn't see a picture so maybe just one

Answer:

"equivalent"

Step-by-step explanation:

Right!!

The solution to this system of linear equations is x = 3, y = 2.

2x - 3y = 3

2x = 3 + 3y

2x = 3y + 3

x = (3y + 3) / 2

x = 3/2 + 3/2y

x = 3, y = 2

This system of linear equations features two unknown variables, x and y. The equation 2x - 3y = 3 can be rearranged into 2x = 3y + 3. This equation can then be solved for x by dividing both sides by 2, resulting in x = 3y + 3/2. Since 3y + 3/2 must equal 3, this means that y must equal 2. Substituting 2 for y in the original equation yields 2x = 3 + 3(2), or 2x = 9. Dividing both sides by 2 yields x = 9/2, or x = 3. Therefore, the solution to this system of linear equations is x = 3 and y = 2.

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The solution to the system of linear equations 2x + 3y = 3 is x = 1 and y = -1/3.

1. Rewrite the equation in standard form is

2x + 3y = 3

2. Subtract 2x from both sides of the equation:

3y = 3 - 2x

3. Divide both sides by 3:

y = (3 - 2x)/3

4. Solve for x by substituting y in the original equation:

2x + 3(3 - 2x)/3 = 3

5. Simplify and solve for x:

2x + 3 - 2x = 3

x = 1

6. Substitute x into the equation y = (3 - 2x)/3

y = (3 - 2(1))/3

y = -1/3

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Answer: To solve a division problem of the form a ÷ b = c, you need to find the value of c that makes the equation true. This means that if you multiply b by c, the result should be equal to a.

a) In the problem 3.2 ÷ 0.8 = ?, we are looking for the value of c that makes the equation true.

To solve this problem, we can multiply 0.8 by c to find the value of c that makes the equation true:

0.8 * c = 3.2

Dividing both sides of the equation by 0.8, we get:

c = 4

Therefore, the value of c that makes the equation 3.2 ÷ 0.8 = ? true is 4.

b) In the problem 7.5 ÷ 0.5 = ?, we are looking for the value of c that makes the equation true.

To solve this problem, we can multiply 0.5 by c to find the value of c that makes the equation true:

0.5 * c = 7.5

Dividing both sides of the equation by 0.5, we get:

c = 15

Therefore, the value of c that makes the equation 7.5 ÷ 0.5 = ? true is 15.

P.S. I don't need a brainliest, i am just happy that I am helping someone

Step-by-step explanation:

Answer:

0.04 < 0.1 < 1/6

Step-by-step explanation:

Answer:

25.6 grams of the second ingredient (25% protein) to make 28 grams of the mixture that is 30% protein.

Step-by-step explanation:

To make 28 grams of a substance that is 30% protein, Becky will need to mix together different ingredients to get the desired amount of protein.

Let's call the amount of the first ingredient (50% protein) "x" and the amount of the second ingredient (25% protein) "y".

We know that:

The total amount of the mixture is 28 grams

The mixture is 30% protein

The first ingredient is 50% protein

The second ingredient is 25% protein

We can set up the following equations to represent the problem:

x + y = 28 (the total amount of the mixture is 28 grams)

(0.50)x + (0.25)y = 0.30(28) (the mixture is 30% protein)

Now we can use the first equation to solve for one variable in terms of the other. If we solve for y, we get:

y = 28 - x

We can substitute this into the second equation:

(0.50)x + (0.25)(28-x) = 0.30(28)

Which gives us:

0.50x + 7 - 0.25x = 8.4

And further simplifying

0.25x = 0.6

x = 2.4

Now we know that the first ingredient, which is 50% protein, makes up 2.4 grams of the mixture. We can use this information to find the amount of the second ingredient:

y = 28 - x = 28 - 2.4 = 25.6 grams

So, Becky needs to use 2.4 grams of the first ingredient (50% protein) and 25.6 grams of the second ingredient (25% protein) to make 28 grams of the mixture that is 30% protein.

A unit rate I found at the grocery store was 10 bananas/ $5 this describe the price for 10 bananas but can also be used to identify the price for 1 banana.

In mathematics, a unit rate can be defined as a mathematical expression that includes two units to show the rate of a specific activity. For example, the expression 50 kilometers/2 hours shows a car covers a distance of 50 kilometers in two hours, which can be simplied as 25 kilometers per hour.

A unit rate I could observe last weekend while buying fruits and vegetables was 10 bananas/ $5. This unit rate is mainly used to inform buyers about the price of 10 bananas. However, this can also be simplified as $0.5 per banana and this would inform the buyers about the price per unit.

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Answer:

3 minutes

Step-by-step explanation:

30÷1.5=20

1h=60mins

60÷20=3minutes

To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.

What is function ?

A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.

Have given ,

f of G in a pair of functions ,

Let a example that f(x) = [tex]x^{2}[/tex] and g(x) = √x + 2

To find f(g(x)), we take f(x) and everywhere there's an x, we replace it with g(x).

f(x) = x2

f(g(x)) = g(x)2

= (√x + 2)2

= x + 2√x + 4

To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.

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Let S be the amount of money the salesperson needs to sell in a week to earn the same amount with the two options. The salesperson earns 40 * $18 = $<<40*18=720>>720 with Option A.

We can set up the following equation to represent the amount of money the salesperson earns with Option B:

0.04S = $720

Solving for S, we find that the salesperson needs to sell $720 / 0.04 = $<<720/0.04=18000>>18,000 to earn the same amount with Option B.

Answer:

Step-by-step explanation:

Solve for x: -24 = 6x

-24 = 6x

x = -24 : 6

x = -4

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

check

-24 = 6(-4)

-24 = -24

Edna's phone can operate for up to 12 more hours without running out of battery. ​

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

fully charged

T = 18Hr

It has been 6 hours since Edna's phone was fully charged.

remaining battery =18- 6= 12Hr

x=12Hr

6 + x < 18

6 +x > 18

neither nor.

both equations are wrong.

6 +x = 18

Edna's phone can operate for up to 12 more hours without running out of battery. ​

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Answer:

81.54

Step-by-step explanation:

% of a # = (% * #)/100

% = 108
# = 75.5

(108 * 75.5)/100

8,154/100

81.54

OR

% of a # = (%/100) * #

% = 108
# = 75.5

(108/100) * 75.5 = 1.08 * 75.5

81.54

It is both of the pair of intersecting lines and degenerate hyperbola.

A conic section, conic or quadratic curve is a curve formed by the surface of a cone crossing a plane. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, however it was frequently referred to as a fourth type. Parabolas, ellipses, circles, and hyperbolas are the four main forms of conics. Examine the diagrams below to discover how a conic is defined geometrically. The plane does not travel through the vertex of a non-degenerate conic.

Here,

It consists of a pair of intersecting lines as well as a degenerate hyperbola.

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Answer: y = 2/5x + 4

Step-by-step explanation:

       We will write a point-slope form equation for this line, then simplify it into a slope-intercept form equation.

Given point-slope form:

➜ m is the slope

➜ (x1, y1) is the point given

       y - y1  = m(x - x1)

Substitute values in:

       y - (4)  = (2/5)(x - (0))

Distribute 2/5:

       y - 4  = 2/5x - 0

Add 4 to both sides of the equation:

       y = 2/5x + 4

Step-by-step explanation:

since we have the slope and a point, we can start with the point-slope form

y - y1 = a(x - x1)

a is the slope, (x1, y1) is the given point.

y - 4 = (2/5)(x - 0) = 2x/5

y = 2x/5 + 4

or

y = (2/5)x + 4

Answer:

  b)  250,000

Step-by-step explanation:

You want to estimate the product of 5,398 and 47 by rounding to the nearest thousand and ten.

Rounding 5,398 to the nearest thousand gives 5000.

Rounding 47 to the nearest ten gives 50.

The product of these is the estimate you want:

  5000·50 = 250,000

Step-by-step explanation:

12 holes / 6 minutes = 2 holes / 1 minute

the simplified ratio is 2/1 = 2.

so, for 25 minutes we need to keep the same ratio :

x holes / 25 minutes = x/25 = 2

x = 2×25 = 50

it drills 50 holes in 25 minutes.

Monomial, binomial, and trinomial expressions are all categorized by the number of terms they include.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a binomial. An algebraic expression having three terms is called a trinomial.

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Answer:

y =x+3

y =-x²+[?]

Find the gradient;

What is the formula for the gradient of a graph?

Finding the gradient of a straight-line graph

X2 = 2

Y2 = 7

ΔX = 4

ΔY = 3

θ = 36.869897645844°

Equation of the line:

y = 0.75x + 5.5

When x=0, y = 5.5

When y=0, x = -7.3333333333333

OR

X2 = -6

Y2 = 1

ΔX = -4

ΔY = -3

θ = 216.86989764584°

Equation of the line:

y = 0.75x + 5.5

When x=0, y = 5.5

When y=0, x = -7.3333333333333

Answer:

In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line.

Step-by-step explanation:

In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line. A linear function is defined as a function of the form y = mx + b, where m and b are constants. The graph of a linear function is a straight line with a constant slope, and so any graph that is not a straight line is not a linear function.

Without the actual graph it's hard to say for sure, but based on the provided information, "The graph does not contain the point (20, –8)" indicates that the graph does not pass through this point (20, -8), and it could be indicating that it's not a straight line, So, The graph does not represent a linear function.

The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.

(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.

Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.

Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian

W(t) = e-2t, to derive the specific integral related to f(t) = e-t.

Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y

Obtain yp = (1/2)(t2)e-t for the given situation.

As a result, the general integral is provided by

y = C1e-t + C2te-t + (1/2)(t2)e-t.

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''By taking log'' on both side Mike solve this equation.

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

Given that;

The expression is,

⇒ 37ˣ = 12

Now,

Since, The expression is,

⇒ 37ˣ = 12

Solve this expression as;

⇒ 37ˣ = 12

Taking log both side, we get;

⇒ log 37ˣ = log 12

⇒ x log 37 = log 12

⇒ x = log 12 / log 37

⇒ x = 1.08 / 1.57

⇒ x = 0.69

Thus, The value of x = 0.69

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Solving for W in the equation 4 = (2 + W) / 2 gives W = 6

Using the equation 4 = (2 + W) / 2, W is solved by making it the subject of the formula and this is means placing W alone at the left hand side of the equation'

This is achieved by the following procedure

clearing the fraction

4 = (2 + W) / 2,

8 = 2 + W

rearranging the equation

W + 2 = 8

subtracting 2 from both sides of the equation

W + 2 - 2 = 8 - 2

since 2 - 2 = 0 we have

W = 6

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The number of acres that can be planted per pound of seed is 0.16.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

32 pounds = 5-acre field

Divide 32 into both sides.

1 pound = 5/32 acre field

1 pound = 0.16 acre field

Thus,

0.16-acre field can be planted per pound of seed.

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No, isosceles triangles are not always 180 degrees. The sum of the interior angles of an isosceles triangle is 180 degrees, but the individual angles can be different.

Isosceles triangles do not necessarily have a 180-degree angle. Any triangle with two equal sides is said to be isosceles. Any triangle's internal angles add up to 180 degrees. An isosceles triangle's individual angles can change depending on how long its sides are, though. An isosceles triangle, for instance, might have a third side that is longer or shorter than the other two sides if the first two sides are equal. The size of the inner angles will be impacted by this. As a result, an isosceles triangle need not have angles that are 180 degrees. An isosceles triangle has interior angles that add up to 180 degrees, but the individual angles might vary.

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