what is the sum of the rational expressions below? 2x-1/7x + x/x-2
a. 9x^2-5x+2/7x^2-2
b. 9x^2-5x+2/7x^2-14x
c. 3x-1/8x-2
d. 2x^2-5x+2/7x^2-14x

Final answer:

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent and can only be used after proving triangles are congruent. It helps in confirming that corresponding parts of congruent triangles are congruent.

Explanation:

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It can only be used after you prove triangles are congruent. When two triangles are proven congruent, CPCTC allows you to show that corresponding parts like angles and sides are congruent as well.

To find the number of batches of pasta, convert the amount of flour per batch to an improper fraction, create an equation based on the total flour used, and solve for the number of batches, which is 16.

To solve for b, the number of batches of pasta the chef makes during the week using a total of 86 pounds of flour:

First, convert the amounts of each flour from mixed numbers to improper fractions:

1 5/8 pounds = 13/8 pounds

Now add the two amounts together to get the total flour used per batch:

(15/4) + (13/8) = 30/8 + 13/8 = 43/8 pounds per batch

The equation to solve for b is:

(43/8) * b = 86

To find b:

b = 86 / (43/8)

Multiply both sides by the reciprocal of 43/8:

b = 86 * (8/43)

b = (86 * 8) / 43

Calculate the value of b:

b = 688 / 43

b = 16

Answer with explanation:

1.⇒ The given equation is

  5x-2y=3

For one solution ,you should write linear equation in such a way

ax+by=c, such that

  [tex]\frac{5}{a}\neq \frac{-2}{b}\neq \frac{3}{c}[/tex]

So, the linear equation will be

→3x+4y=8

You can write many more by yourself.

2.⇒Exactly two solutions

The two lines intersect at only one point.So,there are no such lines which has two point of Intersection.

3.⇒No solutions

It means the two lines will never intersect.

 For no solution ,you should write equation of line in such a way

ax+by=c, such that

  [tex]\frac{5}{a}=\frac{-2}{b}\neq \frac{3}{c}[/tex]

So, the linear equation will be

→10x -4y=15

You can write many more by yourself.

4.⇒Infinitely many solutions

For Infinite number of solution ,you should write linear equation in such a way

ax+by=c, such that

  [tex]\frac{5}{a}=\frac{-2}{b}=\frac{3}{c}[/tex]

→10x-4y=6

The change in the cube's surface area is -180 m^2/min when the edge length is 3 m. This is found by differentiating the surface area with respect to time and substituting the given values.

The subject of the question is related to rates of change in the context of the geometry of a cube. To address this problem, we use the formula for a cube's surface area, which is given by A = 6x^2, where x represents the length of an edge. If x changes with respect to time, we denote this change as dx/dt, which is given as -5m/min. You want to find how quickly the surface area, A, changes when x = 3.

First, let us differentiate the surface area A with respect to time t. By the chain rule of differentiation, dA/dt = dA/dx * dx/dt. Given A = 6x^2, dA/dx = 12x. substituting x=3 and dx/dt=-5, we find that dA/dt = 12*3*-5, which equals -180m^2/min.

Therefore, the change in the cube's surface area is -180 m^2/min when the edge length is 3 m.

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Answer:  the correct option is (C) x - 1.

Step-by-step explanation:  We are given to select the correct binomial that is a factor of the following trinomial :

[tex]T=4x^2+20x-24~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To select the factor, we need to factorize expression (i). To factorize, we need two integers with sum 20 and product -96.

From (i), we have

[tex]T\\\\=4x^2+20x-24\\\\=4x^2+24x-4x-24\\\\=4x(x+6)-4(x+6)\\\\=(x+6)(4x-4)\\\\=4(x+6)(x-1).[/tex]

So, the factors of the given trinomial are 4, (x + 6) and (x - 1).

Since 4 and ( x + 6) are not in the options, so (x - 1),  is the correct binomial.

Thus, (C) is the correct option.

Answer:

Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].

Step-by-step explanation:

Given  : f(x) = y = 100 - x²

To find : Find inverse.

Solution : We have given that :

f(x) = y = 100 - x²

Step1) : Replace every x with a y and replace every y with an x .

x = 100 - y².

Step 2): Solve for y

On subtracting 100 from both sides

x - 100 = -y²

On multiplying both side by -1

100 -x = y²

Taking square root both sides and switching sides

y = ± [tex]\sqrt{100-x}[/tex].

Step3 ) : Replace y with [tex]f^{-1}(x)[/tex].

[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].

Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].

Answer:

A on edge

Step-by-step explanation:

The answer is  y=14 and x= 10

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here:  One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218.

Then we have 5x+13y=232

                         12x+7y=218

Solving these two equations here we get y=14 and x= 10

Hence, The answer is  y=14 and x= 10

Learn more about linear equations here:

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We can see here that to guarantee that no two adjacent rooms are the same color, a minimum of four colors is generally needed.

To determine the minimum number of colors needed to paint each room in a way that no two adjacent rooms have the same color, we can use a coloring algorithm known as the "Four Color Theorem." According to this theorem, it is possible to color any map on a plane using at most four colors, ensuring that no two adjacent regions have the same color.

Applying this concept to the rooms, we can conclude that a minimum of four colors is needed to satisfy the given condition. By using these four colors, we can ensure that no two adjacent rooms share the same color.

​x² - 5x - 24 = 0

First, we have to solve the quadratic equation and find the two values of x that fit the equation.​

[tex]x = \frac{5+- \sqrt{5^{2} + 4*1*24 } }{2*1} = \frac{5+- \sqrt{25 + 96} }{2} = \frac{5+- \sqrt{121} }{2} = \frac{5+-11}{2} [/tex]​

There are two values of x that fit:​

x₁ = (5+11)/2 = 16/2 = 8​

x₂ = (5-11)/2 = -6/2 = -3​

Now I can restate the original equation in terms of a product of factors, with this product being equal to zero:​

(x - x₁) * (x - x₂) = 0​

ANSWER ​(x-8) * (x+3) = 0

Now I can solve each factor by setting each one equal to zero and solving the resulting linear equations:​

x - 8 = 0 or x + 3 = 0​

x = 8 or x = -3​

We can check that these two values are the solution to the original quadratic equation.​

x² - 5x - 24 = 0​

​First value

​8² -5*8 -24 = 0

64 - 40 -24 = 0​

0 = 0 ¡Checked!​

Second value​

(-3)² -5(-3) -24 = 0​

9 + 15 -24 = 0​

0 = 0 ¡Checked!​

​Hope this helps!

​[tex]\textit{\textbf{Spymore}}[/tex]​​​

Answer:

(x+3)(x-8)=0

Step-by-step explanation:

Answer:

Hence, the length of the radius of a circle with center at origin is 17 units.

Step-by-step explanation:

" We know that radius of  a circle is any line segment joining center to any point on the circle ".

We have to find the length of the radius of a circle with a center at the origin i.e. (0,0) and a point on the circle at 8 + 15i i.e. at (8,15).

( Since any complex number of the form z=x+iy has a point in the coordinate plane as:  (x,y) ).

Hence , we have to find the distance between the point (0,0) and (8,15).

The distance between two points (a,b) and (c,d) is given by:

[tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]

Here (a,b)=(0,0) and (c,d)=(8,15)

Hence distance between (0,0) and (8,15) is:

[tex]\sqrt{(0-8)^2+(0-15)^2\\} \\=\sqrt{(8)^2+(15)^2\\} \\=\sqrt{64+225}\\ \\=\sqrt{289}\\ \\=17[/tex]

Hence, the length of the radius of a circle with center at origin is 17 units.

Answer: 17

Step-by-step explanation: the length of the radius of a circle with center at origin is 17 units.