graph f(x)= x if x < 2, 2 if x ≥ 2

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:

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

Answer: $183,731

Step-by-step explanation:

After 30 years, the interest is $183,731

Answer:

[tex]f(x) = 9x^2+9x - 18/3x + 6\\= 9(x^2 + x - 2)/3(x+2)\\= 3(x^2+x-2)/x+2\\= 3(x+2)(x-1)/x+2\\= 3x - 3[/tex]

so y = 3x - 3

since 3x + 6 is on the bottom,

[tex]3x + 6\neq 0\\3x\neq -6\\x\neq -2[/tex]

so this means it should be the graph of y = 3x - 3, but with a hole at (-2, -9)

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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Answer:

Domain: [1, infinity)

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

Step-by-step explanation:

Hope this helps

The area of the rectangular garden given the length and width is 16 1/2 square feet

Area of a rectangular garden = length × width

= 5 1/2 feet × 3 feet

= 11/2 × 3

= 33/2

= 16 1/2 square feet

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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

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]

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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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!

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: [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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Substituting into the formula d=m/v,

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

Answer:

110

Step-by-step explanation:

Suppose lines EH and BD are parallel:

Angle <GFE and angle <ABC are supplementary so their sum is equal to 180

2x + 10 + x  + 20 = 180 add like terms

3x + 30 = 180 subtract 30 from both sides

3x = 150 divide both sides by 3

x = 50

We are asked the value of <ACD

<ABD and <ACD are also supplementary so we can find the value od <ACD:

x + 20 + <ACD = 180 we know x = 50 so we can replace x with that

50 + 20 + <ACD = 180

70 + <ACD = 180 subtract 79 from both sides

<ACD = 110

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:

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

Answer: C - (-1, 2)

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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Answer: y = 4x + 5/4

Step-by-step explanation: Plug in the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y-intercept, and such that m, b ≠ 0.

Answer:

40 divided by 10

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

dvdywuwhfuwi eurue wuid

Answer:

12x^18

Step-by-step explanation:

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]

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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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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