Solving a percent mixture problem using a system of linear equations

The area of the shaded region is calculated as: 6.88 yd²

The area of the shaded region in the diagram = area of rectangle - area of semicircle.

Given the following:

Area of the semicircle = 1/2(πr²) = 1/2 × 3.14 × 4² = 25.12 yd²

Area of the rectangle = length × width = 8 × 4 = 32 yd²

The area of the shaded region = 32 - 25.12 = 6.88 yd²

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Answer:

Rate = 72 km per hour
Distance traveled in 2 hours = 144 km

Step-by-step explanation:

The car speed is given as 20 meters per second

There are 3600 seconds in an hour

So in 1 hour the car would travel 20 x 3600 = 72,000 meters. This is equivalent to 72,000 meters per hour

There are 1000 meters in a kilometer

So, in terms of kilometers, the car would travel 72,000/1000 = 72 km i one hour. This is equivalent to a speed of 72 km per hour

In 2 hours the car would travel 72 x 2 = 144 km

A function is defined as a relation between a set of inputs having one output each.

Say, there is an element x in the sets of input, now it can be paired with no more than one y in the sets of output. We should note that the same y can be paired with different x's, but not the reverse. All linear equations, with the exception of vertical and horizontal lines, are functions.

The function is generally written as "f(x)" where x is the input value.

let us take an example-

f(x) = x/2

here, f(x) is a function because each input "x" has a single output "x/2":

• f(2) = 1

• f(5) = 2.5

• f(−12) = −6

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Answer:

makes over a 90 digre angle

Step-by-step explanation:

Inequalities to support the questions

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Each factory operates for at most 12 hours each day.

let maximum profit by factory A be x and Factory B be y.

Then, Inequalities to support the questions

2x + y ≤ 12

and, 2x+ 3y ≤ 12

and, x ≥ 0, y ≥ 0

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An example of linear graph is y=2x+1

A linear equation is graphically represented by a linear graph.

For given real numbers A, B, and C, where A and B are not 0, a linear equation is one that can be expressed as Ax + By = C.It is a straight line graph.

Let's examine the graph.

A straight line is formed on the graph by the equation y=2x+1, which is a linear equation. When the value of x rises, the value of y eventually rises by the sum of the value of x plus two.

1). Determine the two changing quantities.

2).Let x and y be the first and second quantities, respectively.

3).Next, find out three ordered pairs (x, y) which satisfy the given equation.

4).Present these values in a tabular form.

5).Plot the points given in the graph.

6).Join the points.

This way we can form our graph

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Answer:

8%

Step-by-step explanation:

1. Subtract:

  55000 - 50600 = 4400

2. Divide:

   4400/55000 = 0.08

The value of x is 5

What are algebric expressions?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values.

The given expression is 20 - 3x = 5

We need to calculate the value of x

20 - 3x = 5

20 - 5 = 3x

15 = 3x

3x = 15

x = 5

Therefore, the value of x is in the algebric expression  is 5

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Answer: [tex]\frac{11+\sqrt{146}}{5}[/tex] seconds

Step-by-step explanation:

[tex]10=-5t^2 +22t+15\\\\5t^2 -22t-5=0\\\\t=\frac{22 \pm \sqrt{(-22)^2 -4(5)(-5)}}{2(5)}\\\\t=\frac{11+\sqrt{146}}{5} \text{ } (t > 0)[/tex]

For 1, the number of positive divisors or factors is only one i.e. 1 itself. So, number one is not a prime number.

What are prime numbers ?

Prime numbers are numbers greater than 1. They only have two factors, 1 and the number itself. This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.

Numbers that have more than 2 factors are known as composite numbers.

For a number to be called as a prime number, it must have only two positive factors. Now, for 1, the number of positive divisors or factors is only one i.e. 1 itself. So, number one is not a prime number.

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Answer: I hope this is helpful mark me brainlist if this apply to you

Step-by-step explanation:

The square meter, also called the meter squared, is the International System of Units (SI) unit of area. The symbol for square meters is m2. Less formally, square meter is sometimes abbreviated as sq m.A metre square is a square with sides one metre in length – it refers to the shape and the side length, not the area. By contrast, a square metre is an area and can be any shape.The basic unit of length is the meter and is denoted as. In geometry, can be used as a variable to denote a line and can be used to name a point. In algebra, denotes the slope of a line in the equation y = m x + c .

Answer:

this 1

Step-by-step explanation:

same doubt pease any help

The system of linear equations have variable unique solutions, infinitely many solutions and no solutions.

In algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."

A system of equations as discussed above is a set of equations that seek a common solution for the variables included.

1.

y = -2x + 3 ...eq(i)

y = 1/2x - 7 ...eq(ii)

The solutions to the linear equations (x,y) are (4, -5)

2.

y = 2x - 7 ...eq(i)

y = 5x + 5 ...eq(ii)

The solutions to the linear equations (x,y) are (-4, -15)

3.

3y = -12x + 6 ...eq(i)

y = -4x + 2 ...eq(ii)

The linear equations (x, y) have infinitely many solutions

4.

y = -2x + 3 ...eq(i)

y = 2x - 1 ...eq(ii)

The linear equations (x,y) have solutions of (1, 1)

5.

y = 5x + 4 ...eq(i)

y = 5x - 2 ...eq(ii)

The linear equations have no solutions

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The logarithmic form of the equation is log₅ 4 = 625.

Logarithmic form

In math, a way to write an exponential function in reverse is called as logarithmic functions.

Given,

Here we have to convert the given equation

615 = 5⁴

Now, we have to convert this into the logarithmic form .

The general form of the logarithmic form is written as,

f(x) = logₐ x

Where a refers the base and x refers the exponent.

Here the value of base is 5 and the value of exponent is 4.

And the value of f(x) = 25,

Therefore, the logarithmic form is written as,

=> log₅ 4 = 625.

I HAVE ANSWERED THE QUESTION IN GENERAL AS GIVEN QUESTION IS INCOMPLETE.

Complete Question:

Convert the equation into logarithmic form: 615 = 5⁴

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The points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

A triangle is a three-sided polygon.

The triangle's three points are known as vertices.

Several triangle-related points:

Thus, the points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

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The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.

In the given question we have to define which symbol is represent function.

The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.

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The answer to this Question is A we can use basic knowledge from linear equations to find the answer

What is Linear Equation?

Linear Equation is a equation in which degree of variables is 1 only

Yes the given case is possible only under some conditions that we can define as follows and as given in Linear Equations from Options

together cole and maggie have won 30 games and we are also given that  out of those 30 maggie has won 4 games

we should closely see at Linear Equations given in Options.

therefore cole has won 26 games which is more than 13

Hence the answer to the Question is Yes

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a) The function velocity of the particle is v(t) = 0.5 · t² + 6 · t + 7, b) The distance traveled by the particle is 467 feet.

In this problem we have the equation that represents the acceleration of a particle. The function velocity (v) is obtained by integrating the function acceleration (a) and the function position is obtained by integrating the function velocity. Now we present the definitions of each function:

Velocity

v(t) = ∫ a(t) + C

Position

s(t) = ∫ v(t) + C

Where C is the integration constant.

The distance traveled during the time interval is found means of definite integrals:

Δs = [tex]\int\limits^b_a {v(x)} \, dx[/tex]= s(b) - s(a)

a) First, determine the function velocity of the particle:

v(t) = ∫ (t + 6) dt + C

v(t) = 0.5 · t² + 6 · t + C

7 = C

v(t) = 0.5 · t² + 6 · t + 7

b) Second, determine the distance traveled in the given time interval:

Δs = s(10) - s(0)

Δs = 0.167 · 10³ + 3 · 10² + 7 - 0.167 · 0³ - 3 · 0² - 7

Δs = 467

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It is Growing Exponential function because the base is greater than 1 and the exponent has a positive sign.

What is exponential decay function?

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

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

It is a function called "Exponential function". The base determines the growth or decay of the function.

If  base > 1, then the function grows, otherwise if base is between 0 and 1, the function decays.

Here, the  base is positive and it's not 1 or 0.

If we have

[tex]y=5^{-x}[/tex]

this function can be rewritten in this way:

[tex]y=(1/5)^x[/tex]

Here, base between 0 and 1, the function decays

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Answer:___(-4x⁴+9)x⁶  

                    3

The expression that shows the number of boxes ordered is 8p.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since the school custodian ordered p rolls of paper towels and the paper towels are sold in boxes of eight.

The expression will be:

= Number of rolls × 8

= p × 8

= 8p

The expression is 8p.

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Answer:

m<8=1024

Step-by-step explanation:

Since they are asking for m<8, we do 128*8=1024.

The maximum value of the parabola is represented by y-vertex whose value is 9.

What is a Quadratic Function?

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that you should apply the discriminant in the formula:[tex]x=\frac{-b\pm\sqrt{\Delta} }{2a}[/tex] .

The question gives a quadratic equation and two points, but you do not know some coefficients. Then, you should find the unknown coefficients and after that, you should find the y-vertex of the parabola ([tex]y_v=\frac{-{\Delta} }{4a}[/tex]).

             y = a(x - 1)² + k  ->  points (2, 6.5) and (-1, -1), thus

            6.5=a(2-1)² + k (1)

            -1=a(-1-1)² + k   (2)

         Simplifying the equations

             6.5=a(1)² + k  ( 1 )

            -1=a(-2)² + k  (2)

            6.5=a+ k      ( 1 )

            -1=4a+ k      (2)

         Multiply equation 1 by -1

            -6.5=-a- k    ( 1 )

            -1=4a+ k      (2)

          Sum equations 1 and 2

           -7.5=3a

              a= -2.5

        If a= -2.5, from equation 1, you have

            -6.5=-a- k    

            -6.5=-(-2.5)- k  

            -6.5=2.5- k

            k=2.5+6.5

            k=9

Then , the parabola equation is y= -2.5 (x-1)² +9. You can rewrite it as:

y=-2.5(x²-2x+1)+9

y= -2.5x²+5x-2.5+9

y= -2.5x²+5x+6.5

[tex]y_v=\frac{-{\Delta} }{4a}=y_v=\frac{-{(b^2-4ac)} }{4a}=\frac{-{(5^2-4*(-2.5)*(6.5))} }{4*(-2.5)}=\frac{-90}{-10} =9[/tex]

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To match equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

In mathematics, equivalent fractions are those with the same denominator and differing numerators.

According to equivalent fractions, two or more fractions are considered to be equal if both provide the same fraction following simplification. Let's imagine that two fractions, a/b and c/d, were simplified to provide comparable fractions, e/f. In this case, the two fractions are equal to one another.

For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.

We have to find how do we match equivalent expression.

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Answer: 1.41 meters

Step-by-step explanation:

14.1 decimeters to meters
Decimeters are 10 times smaller than meters, so you divide the value by 10 to get meters
14.1/10 = 1.41
1.41 meters

The values of k that allow us to factor it as a product of linear binomials with integer coefficients are k ≥ -16√3

Linear binomials are mathematical expression that contain only two terms. Examples include x + 3.

A quadratic equation is an equation in which the highest power of unknown is 2.

Since we have the quadratic equation 23x² + kx - 5 + x² - 3, to determine the value of k which makes it a linear binomial, we simplify and find the discriminant.

The discriminant of a quadratic equation ax² + bx + c is D = b² - 4ac

Simplifying the quadratic equation, we have

23x² + kx - 5 + x² - 3 = 23x² + x² + kx - 5 - 3

= 24x² + kx - 8

Comparing the above quadratic equation with ax² + bx + c, we have that

So the discriminant, D =  b² - 4ac

= k² - 4 × 24 × 8

= k² - 768

The allowable values of k are gotten when the discriminant D ≥ 0

So, D ≥ 0

⇒ k² - 768 ≥ 0

⇒ k² ≥ 768

⇒ k ≥ ±√768

⇒ k ≥ ±√(256 × 3)

⇒ k ≥ ±16√3

⇒ k ≥ -16√3

So, the values of k are k ≥ -16√3

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Answer:

Step-by-step explanation:

its a

Answer:

0

Step-by-step explanation:

0 = 0×0.1+8×0

0 = 0+8×0

0= 8×0

0=0

Answer:19.26%

Step-by-step explanation: yeah

Answer:

19%

Step-by-step explanation:

There are only 5 steps here they are:

1. Divide 144.77 by 179.30

2. You get the answer 0.80741773...

3. You round it to 0.81.

4. You turn it into a percent by moving the dot(decimal) to the right four times.

5. And then you subtract it from 100 and you get 19% for the discount.

so therefore the answer is 19%

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The Incenter of triangle ABC is I =  (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c).

Given:

Let I be the incenter of triangle ABC.

Let A(x1,y1) ,B(x2,y2) and C(x3,y3) are vertices.

Let a,b and c are lengths of the sides AB,BC and AC.

we know that:

Incenter I = (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c)

we can find a, b and c values using the distance formula between the vertices.

AB = a =  [tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

BC = b = [tex]\sqrt{(x3-x2)^2 + (y3-y2)^2}[/tex]

AC = c = [tex]\sqrt{(x3-x1)^2 + (y3-y1)^2}[/tex]

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