Between every pair of distinct points, there is a positive unique number called the ??? , which can be determined as the ??? of the corresponding real numbers of the two points.

Combining the like-terms, the result of the addition of polynomials f(x) and g(x) is given by:

[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]

We add polynomials combining the like-terms, that is, adding terms with the same exponent.

In this problem, the polynomials are:

Combining the like terms, the addition is given by:

[tex]f(x) + g(x) = \left(3 - \frac{7}{4}\right)x^{\frac{1}{2}} + (7 + 12)x^{-\frac{1}{4}} + 8x^{-4} + 21x^3[/tex]

[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]

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Answer:

Graphs Attached Below

Step-by-step explanation:

Hello!

Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]

From our Equation:

There are several values that are needed to drawing a parabola:

Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]

The y-intercept is the "c" value. Given that our equation has a "c" value of 0, the y -intercept is 0.

A parabola is always symmetrical vertically. The line in which the fold happens is the Axis of Symmetry.

To calculate the AOS, we use the formula [tex]AOS = \frac{-b}{2a}[/tex], from the values of the equation.

Calculate

The Axis of Symmetry is a vertical line, so the AOS is the line x = 2.

The vertex is the highest or lowest point on the graph of a parabola. It resides on the AOS of the graph.

To calculate the vertex, we simply have to find the y-value, given that we have the x-value from the AOS. We can find the y-value by plugging in the AOS for x in the original equation.

Calculate

The y-value is -2. The vertex is (2, -2).

The x-intercepts are the points where the graph intersects the x-axis (y = 0).

Solve by Factoring

The roots are (0,0) and (4,0).

Now we just draw the y-intercept, vertex, AOS, and the x-intercepts, and draw a curved line between them.

Image Attached

The Domain (x-values) are being restricted to all x-values that are greater than or equal to -2 and less than 4.

That means we remove the parts of the line that don't belong in that domain.

Image Attached

Answer: Peyton

Step-by-step explanation:

Michelle: Greatest common factor is 1

Naomi: Greatest common factor is abc

Olivia: Greatest common factor is 2ab

Peyton: Greatest common factor is ab

Answer: Options 1 and 2

Step-by-step explanation:

To model exponential decay, the base of the exponential has to be less than 1.

Model exponential decay equation are

y = 0.34(0.98)^x

y = 8 (0.28)^x

Model exponential decay equation

Option C and D have the base value greater than 1. So it can't be model exponential decay equation.

Hence, the model exponential decay equation are

y = 0.34(0.98)^x

y = 8 (0.28)^x

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The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation h(x) = -1/2(x -3)² + 4

The given graph is a quadratic graph. Given the function of the blue parabola expressed as:

f(x) = -1/2x²

The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation

h(x) = -1/2(x -3)² + 4

Note that the upward translation will be positive while the horizontal shift to the right will be negative

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Answer:

They are not similar because corresponding sides are not proportional.

Condition for similarity of two triangles -

The ratio of corresponding sides should be equal.

Condition for congruence of two triangle -

Any of the following -

Side side side

side angle side

angle angle

angle side angle

The area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

It is defined as the four-sided polygon in geometry having four edges and four corners. It has one pair of opposite congruent angles and the diagonals of a kite are perpendicular.

We have a quadrilateral shown in the picture.

The diagonal divides the quadrilateral into two triangles

The area of the quadrilateral = area of the triangle ADC + area of the

                                                   triangle ADB

= (1/2)3.42×4.39 + (1/2)5.44×3.42

= 7.5069 + 9.3024

= 16.80 square units

Thus, the area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

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Substituting into the formula d=m/v,

[tex]7.98=\frac{m}{60}\\\\m=\boxed{478.8 \text{ gm}}[/tex]

Answer:

Domain: [1, infinity)

Range: All real numbers or (- infinity, + infinity)

Step-by-step explanation:

Hope this helps

Answer: [tex]4.5 \text{ cm}^{2}[/tex]

Step-by-step explanation:

[tex]A=\frac{1}{2} bh\\\\A=\frac{1}{2}(3)(3)\\\\\boxed{A=4.5 \text{ cm}^{2}}[/tex]

The area of the triangle will be equal to 4.5 square centimeters.

The space occupied by any two-dimensional figure in a plane is called the area. The space covered by the triangle in the two-dimension is called an area of the triangle.

The area of the triangle ABD will be calculated as:-

Area = [tex]\dfrac{1}{2}[/tex] x Base x height

Area = [tex]\dfrac{1}{2}[/tex] x 3 x 3

Area = 4.5 cm.

Therefore the area of the triangle will be equal to 4.5 square centimeters.

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Answer:

1/2(6-8), 1/2(-3+7)=-1,2

Answer: C - (-1, 2)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

dvdywuwhfuwi eurue wuid

The function will be given as C(x) = 25 + 0.2(x) here x is in minutes.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

Given that:-

The cost of the 250 minutes is $25 and if the time extends from 250 minutes then the function will be expressed in the form of.

C(x) = 25 + 0.2 (x)

Here C(x) is the total cost and the x is in minutes.

Hence the function will be given as C(x) = 25 + 0.2(x) here x is in minutes.

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Part 1

[tex]D \cup E[/tex] denotes the union of the two sets (in other words, all the elements in both sets).

This means it is [tex](-\infty, 4) \cup [7, \infty)[/tex]

Part 2

[tex]D \cap E[/tex] denotes the elements shared between both sets.

This means the answer is [tex](4, 7][/tex]

Question 1

The complement of set B is all the elements in S but that are not in B, which is [tex]\{2, 4, 5, 9, 10, 11, 12, 13, 14, 17, 19\}[/tex].

We want to find the intersection of set A and the complement of set B, which is the set of all elements that both sets contain.

This is {2, 9, 10, 12}, meaning there are 4 elements.

Question 2

Following a similar logic as the last problem, the complement of set A is [tex]\{1,3,4,5,6,7,11,13,14,15,17,18,19\}[/tex].

Therefore, the desired set is [tex]\{1,3,6,7,15,18\}[/tex], and thus there are 6 elements.

Answer: -24

Step-by-step explanation:

I am assuming you want the value of (f × g)(-2)

[tex]f(-2)=(-2)^2+4\\f(-2) = 4+4\\f(-2)=8[/tex]

[tex]g(-2)=2(-2)+1\\g(-2)=-4+1\\g(-2)=-3[/tex]

8 × -3 = -24

Answer: $183,731

Step-by-step explanation:

After 30 years, the interest is $183,731

Answer:

No

Step-by-step explanation:

no because just muiltiplying 7.00 * 8 is 56 not inculuding the 99 cents it is already over 50. The answer is 63.92 so a reasonable estimate would be around $60

Answer:

12x^18

Step-by-step explanation:

Probability helps us to know the chances of an event occurring. The probability of winning the bet is 0.125.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given the odds on a bet are 7:1, therefore, there are a total of 8 cases out of which only one case is of winning. Thus, the probability of winning the bet will be,

Probability = 1/8 = 0.125

Hence, the probability of winning the bet is 0.125.

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O is parallel to q

let's take the angle opposite to angle 4 is alpha

angle 4 = angle alpha ( vertically opposite angles)

angle alpha = angle 3 ( as angle 4 = angle 3).

hence o is parallel to q as both the angles are equal

The part of the trinomial that will equal the product of p and q is the constant part

The expression is given as:

(x + p)(x + q)

From the expression, p and q are both constants.

When a constant is multiplied to another, the result is a constant

This means that:

pq = constant

Hence, the part of the trinomial that will equal the product of p and q is the constant part

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Answer:

x= 0, y= -1

Step-by-step explanation:

To obtain the values of x and y from a system of equations, start by labelling the given equations.

8x +5y= -5 -----(1)

7x -3y= 3 -----(2)

Let's solve by elimination.

Here, I will be working to eliminate the y term. This is done by ensuring both equations have the same numerical value in the coefficient of y.

(1) ×3:

24x +15y= -15 -----(3)

(2) ×5:

35x -15y= 15 -----(4)

Add the two equations together since the coefficient of y has opposite signs.

(3) +(4):

24x +15y +35x -15y= -15 +15

59x= 0

Divide both sides by 59:

x= 0

Now, substitute the value of x into any equations to find the value of y.

Substitute x= 0 into (1):

8(0) +5y= -5

5y= -5

Divide both sides by 5:

y= -5 ÷5

y= -1

Additional:

For similar questions on system of equations, do check out the following!

Answer: -15625

Step-by-step explanation:

The explicit formula for the sequence is

[tex]a_{n}=-1(5)^{n-1}\\\\\implies a_{7}=-1(5)^{7-1}=\boxed{-15625}[/tex]