In which step was the addition property of equality applied?

a) The function is continuous in it's entire domain.

b) The increasing and decreasing intervals for the function are given as follows:

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

In this problem, we have a piece-wise function which has the definition changing at x = 2, hence the continuity must be studied at x = 2.

The lateral limits for the function in this problem are defined as follows:

The second limit is also equals to the numeric value at x = 2, due to the equal sign in the definition, hence the function is continuous at x = 2 and for all other values in the domain.

The intervals of increase and decrease are given as follows:

The function for this problem is the piece-wise function A(x).

Item a asks if the function is continuous.

Item b asks when the function is increasing and when it is decreasing.

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Answer:

A

Step-by-step explanation:

The segment from the vertex to the base , bisects the base at right angles

Then there are 2 right triangles with legs x and 4 and hypotenuse [tex]\sqrt{52}[/tex]

Using Pythagoras' identity in either of the 2 right angles

x² + 4² = ([tex]\sqrt{52}[/tex] )²

x² + 16= 52 ( subtract 16 from both sides )

x² = 36 ( take the square root of both sides )

x = [tex]\sqrt{36}[/tex] = 6 → A

Answer:

45ft is the missing length j.

Answer:

yes

Step-by-step explanation:

Answer:

412 (pls add the unit cuz i dont learn yd thx)

Step-by-step explanation:

13*12/2*4 + 10*10

= 312 + 100

= 412

9514 1404 393

Answer:

  AB = 10

  BC ≈ 11.40

Step-by-step explanation:

The distance formula is useful for finding distances between points.

  d = √((x2 -x1)² +(y2 -y1)²)

  AB = √((18 -10)² +(4 -10)²) = √(8² +(-6)²) = √100

  AB = 10

__

  BC = √((25 -18)² +(-5-4)²) = √(7² +(-9)²) = √130

  BC ≈ 11.40

_____

A sketch tool can be useful for finding or checking the answer.

Answer:

B

Step-by-step explanation:

N=4x0+12=12

Answer:

12

Step-by-step explanation:

N = 4m + 12 =

N = (4 x 0) + 12

N = 0 + 12 =

N = 12

Answer:

the value of FJ would end up being 10

Answer:

10

Step-by-step explanation:

Answer:

No   g(x) = x/6     for (60, 10) to be a possible solution

by this function 60 people would have to donate 1/6th of a garment each to achieve 10 full garments

Step-by-step explanation:

g(x)   number of items

   x   number of people  

the data point (60, 10) make sense as a possilbe solution     NO

g(x) = number of items       x = 60   g(x) = 10

g(60) = x/6 = 10              

         = 60/10            

by this function 60 people would have to donate 1/6th of a garment each to achieve 10 full garments

Answer: 65

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=(x+4)+3

Answer:

y = x + 7

Step-by-step explanation:

Since y = x is a linear function, it may be confusing when using the translation tips you learned from class to solve it. However, there is an easy way to go about it.

1. Remember that when a function moves left, we use + inside of the parenthesis.

4 units left:

y = (x + 4)

2. Remember that when a function moves up, we use + outside of the parenthesis.

3 units up:

y = (x + 4) + 3

3. Add 'em up

y = x + 7

Since the function is linear, it may be confusing to see whether the graph moved up or left. However, by following the origin (0,0) of y = x and moving 4 units left and 3 units up, you will see that the origin has moved from (0,0) to (-4, 3), representing 4 units to the left and 3 units up on a graph.

Hope this helps :)

Answer:

The area of AEBC is 36 cm²

hope it is helpful to you

Given:

Two cards are drawn from a standard deck of cards without replacement.

To find:

The probability of drawing a heart and a club in that order.

Solution:

We have,

Total number of cards = 52

Number of cards of each suit (Spade, club, diamond, heart) = 13

The probability of drawing a heart card is:

[tex]P(Heart)=\dfrac{\text{Number of heart cards}}{\text{Total number of cards}}[/tex]

[tex]P(Heart)=\dfrac{13}{52}[/tex]

[tex]P(Heart)=\dfrac{1}{4}[/tex]

Now, the number of remaining card is 51. So, the probability of drawing a club card is:

[tex]P(club)=\dfrac{\text{Number of club cards}}{\text{Total number of remaining cards}}[/tex]

[tex]P(club)=\dfrac{13}{51}[/tex]

Using these probabilities, the probability of drawing a heart and a club in that order is:

[tex]P(\text{Heart and club})=P(\text{Heart})\times P(\text{Club})[/tex]

[tex]P(\text{Heart and club})=\dfrac{1}{4}\times \dfrac{13}{51}[/tex]

[tex]P(\text{Heart and club})=\dfrac{13}{204}[/tex]

Therefore, the required probability is [tex]\dfrac{13}{204}[/tex].

Answer: a = -4

Step-by-step explanation:

Answer:

3000

Step-by-step explanation:

5430=1.81x

solving for x, we take 1, which is equal to 100%, and divide it by 1.81 to get 1/1.81 or 0.55248618

multiply 1/1.81 by 5430 to get 3000

Answer:

The percentage decrease is 25%.

Step-by-step explanation:

The difference in price is $2:

$8 - $6 = $2

Now to find the percentage decrease, we use the formula decrease in price divided by original price (or new/old) times 100:

2/8 * 100.

This equals 200/800 which is 25%.

Answer:

A ..

Step-by-step explanation:

In the graph of a quadratic function with vertex (2, -4) is shown in the figure, the Domain: -∞ < x < ∞ and Range: -4 ≤ x < ∞.

When a polynomial function has one or more variables and the highest exponent of any one of the variables is two, the function is said to be quadratic function.

A polynomial of degree 2 is referred to as such because the highest degree term in a quadratic function is of second degree. There must be at least one second-degree term in a quadratic function. This function is algebraic.

Domain for this quadratic function is all possible values of x where function is defined.

Thus, Domain: -∞ < x < ∞

Range is the set of value functions that correspond to the value 'x.'

Range: -4 ≤ x < ∞

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This system of equations have 2 real solution.

As a result, all of these numbers—rational and otherwise—as well as fractions are regarded as real numbers. Due to the decimal's ability to float within the numbers, real numbers with decimal points are known as floating point numbers. No whole number or integer can be a floating point number.

y = 3x + 1 is a solution to 3x - y + 1 = 0.

This line's y-intercept is represented by (0, 1). Plot this point inside the circle with radius 6 that was previously mentioned, and then draw a straight line through it with a slope of 3.

Two points where this line crosses the circle denote actual solutions.

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In response to the above problem, we may state that the triangle's - 5/13 measurements correspond to sin and cos.

The first six essential trigonometric functions are used in trigonometry. These functions are trigonometric ratios. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six basic trigonometric functions. The side ratio of a right-angled triangle is equivalent to the identities and functions of trigonometry. Trigonometric formulas are applied to the perpendicular side, hypotenuse, and base of a right triangle in order to calculate the sine, cosine, tangent, secant, and cotangent values.

as base/hypotenuse = cos x

and sin x = hypotenuse/perpendicular

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Answer:

D) 4b

Step-by-step explanation:

9514 1404 393

Answer:

  d.  13

Step-by-step explanation:

The smallest number is 3.

The largest number is 16.

The range is the difference between these values:

  16 -3 = 13 . . . range of the data

Answer:

24xy - 32y

Step-by-step explanation:

4y × 6x =24xy

4y × -8 = -32y

brainliest plz? i got 1000+ points deleted

Answer:

4y(6x-8)

[tex]4y \times (6x - 8)[/tex]

[tex]4y \times - 6x + 8[/tex]

[tex] - 24xy + 8[/tex]

[tex] - 32xy[/tex]

Answer

Answer:

the other side is 5 i think

The required solution for the inequality a + 5 > -7 is (-12, ∞).

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

a + 5 > -7

To find the solution for the inequality,

Simplify the inequality,

a + 5 > - 7

a > - 7 - 5

a > -12

The value of a is greater than -12, implies that,

The solution for the value of the given inequality is (-12, ∞).

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