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A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function f(x) and g(x) can be plotted as shown in the below image.

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Answer:

d

Step-by-step explanation:

         There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.

[1] using the quadratic formula

     When the equation is in the form of ax² + bx + c = 0.

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

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[2] factoring

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[3] completing the square

     To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c

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Answer:

if I am awake then it is 9 am.

Step-by-step explanation:

if p then q the converse is if q then p.

Answer:

24/5

Step-by-step explanation:

x is 4.8, improper simplified is 24/5

The proposition given by definition of function "division" is false as [tex]\frac{f}{g} \ne {(1, 2)}[/tex] for the former function f = (9, 5) and the latter function g = (9, 0).

In this question we have a definition of division between two functions, consisting in dividing each component of the ordered pair of the former function (f) by the component of the ordered pair of the latter function (g) such that resulting ordered pair is (1, 2).

We must check if the proposition is true for every ordered pair. Let analyze each case:

Case I

[tex]\frac{f}{g} = \left(\frac{1}{1}, \frac{6}{3} \right) = (1, 2)[/tex]

Case II

[tex]\frac{f}{g} = \left(\frac{9}{9}, \frac{5}{0} \right) = (1, NaN)[/tex]

Thus, the proposition is false.

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The set of input of the function are {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }

The set of output of the function is a multiple of 40 from 200 to 640

The input of the function can be found as follows:

The camp can only run if we have at least 5 students.

The limits of student is 16.

Therefore, the input are  {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }

The output are the dependent variables or the range. They are gotten when we input the values of the input in the function.

Therefore,

R(n) = 40n

R(5) = 40(5) = 200

R(16) = 40(16) = 640

The output are multiple of 40 from 200 to 640

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The probability that the student was NOT a female that got a "C" is 15 / 32.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C =  15 / 32.

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Answer:

$2142.86

Step-by-step explanation:

The remaining part of her money, after spending 3/5 of it and depositing 1/8 of it is equal to $750.

===============================================================

Retracing the steps :

⇒ She put 1/8 of the remainder in the bank, which gives $750

⇒ R - R/8 = 750

⇒ 7R/8 = 750

⇒ R = 750/7 × 8

⇒ R = 107.142857 × 8

⇒ R = 857.142856

* Don't worry, we'll simplify at the end of the answer *

=============================================================

Now, this remainder is what was left after spending 3/5 of it.

⇒ T - 3/5T = 857.142856

⇒ 2/5T = 857.142856

⇒ T = 857.142856/2 × 5

⇒ T = 428.571428 × 5

⇒ T = $2142.86 (nearest cent)

Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

where:

Rewrite both equations into slope-intercept form:

a) 2x + 4y = 15

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

b) 6x + 12y = 45

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

New equations:

[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

No Solution: the same slope (both lines will be parallel)

One Solution: different slopes and different y-intercepts

Infinitely Many Solutions: the same slope and y-intercept

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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.

Equation #1

Subtract 2x from both sides

Divide both sides by 4

Equation #2

Subtract 6x from both sides

Divide both sides by 12

Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other.  Therefore, there are infinite solutions as they will always continue on top of each other.

Answer:

The answer is in Step.

Step-by-step explanation:

Domain: (- inf, + inf)

Range: (- inf, 3]
Increasing: (- inf , 0)

Decreasing: (0 , + inf)
Positive: (- 1 , 1 )
Negative: (- inf , -1) , (1 , + inf)

Maximum: (0,3) or just 3.

Minimum: None.
x-int: -1, 1
y-int: 3

The sum of squares of the lengths  of the triangle is 130 and the square of the length of the hypotenuse is 65

This is a triangle with 3 sides and one side is called the hypotenuse which faces one of the angles 90°

Analysis:

distance between two points = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

distance AB with coordinates A(-2,4) B(5,0) = [tex]\sqrt{(5 - -2)^{2} + (0 - 4)^{2} }[/tex] = [tex]\sqrt{65}[/tex]

distance AC with coordinates A ( -2,4) C(2,6) = [tex]\sqrt{(2--2)^{2} + (6-4)^{2} }[/tex] = [tex]\sqrt{20}[/tex]

distance BC with coordinates B(5,0)  C(2,6) = [tex]\sqrt{(2-5)^{2} + (6-0)^{2} }[/tex] = [tex]\sqrt{45}[/tex]

sum of squares of the lengths = [tex](\sqrt{45} )^{2}[/tex] + [tex](\sqrt{65}) ^{2}[/tex] + [tex](\sqrt{20}) ^{2}[/tex] = 65 + 45 + 20 = 130

the square of the length of the hypotenuse = 65

In conclusion, the sum of the squares of the three length is 130 and the square of the hypotenuse is 65

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Answer:

[tex]\frac{1}{102}[/tex]

Step-by-step explanation:

1) Negative Power Rule: [tex]x}^{-a}=\frac{1}{{x}^{a}}[/tex].

[tex]\frac{1}{3}\div 34[/tex]

2) Use this rule: [tex]a\div \frac{b}{c}=a\times \frac{c}{b}[/tex].

[tex]\frac{1}{3}\times \frac{1}{34}[/tex]

3)  Use this rule: [tex]\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}[/tex].

[tex]\frac{1\times 1}{3\times 34}[/tex]

4) Simplify [tex]1\times 1[/tex] to [tex]1[/tex].

[tex]\frac{1}{3\times 34}[/tex]

5) Simplify  [tex]3\times 34[/tex] to [tex]102[/tex] .

[tex]\frac{1}{102}[/tex]

Answer:

Step-by-step explanation:

Answer:

6.28 ft

Step-by-step explanation:

using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer

Answer:

-4

Step-by-step explanation:

[tex]~~~~~-24 = 6x\\\\\\\implies -\dfrac{24} 6 = \dfrac{6x}6\\\\\\\implies x = -4[/tex]

The total cost when 881 minutes is used is $477.50.

a + 480b = 277 equation 1

a + 990b = 532 equation 2

Where:

Subtract equation 1 from equation 2

510b = 255

b = 255 / 510

b = $0.50

In order to determine the flat fee, substitute for b in equation 1

a + 480(0.5) = 277

a + 240 = 277

a = 277 - 240

a = $37

Total cost = flat fee + (variable cost x number of minutes spoken)

$37 + (881 x 0.5) = $477.50

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Answer:x ≤ 3

Step-by-step explanation:

(14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
14.5x - 5x-10 ≤ 4 + 16 - 1/2x Get rid of the parenthesis

9.5x-10 ≤ 20-1/2x Combine like terms

10x - 10 ≤ 20

10x/10 ≤ 30/10

x ≤ 3

So

Hence

Option A

Answer:

Option A

Step-by-step explanation:

y=4x+10

So

Put x ax 12°C

Hence

y=4(12)+10

y=48+10

y=58

Answer:

22 meters

Step-by-step explanation:

Let x = width of the rectangle

Let y = length of the rectangle

Equation 1

If the length of the rectangle is 6 meters shorter than four times the width then:

⇒ y = 4x - 6

Equation 2

Perimeter of a rectangle = 2(width + length)

If the perimeter is 58 inches, then:

⇒ 58 = 2(x + y)

Solve by substitution

Substitute Equation 1 into Equation 2 and solve for x:

⇒ 58 = 2(x + 4x - 6)

⇒ 58 = 2(5x - 6)

⇒ 58 = 2 · 5x - 2 · 6

⇒ 58 = 10x - 12

⇒ 58 + 12 = 10x -12 + 12

⇒ 10x = 70

⇒ 10x ÷ 10 = 70 ÷ 10

⇒ x = 7

Substitute found value of x into Equation 1 and solve for y:

⇒ y = 4(7) - 6

⇒ y = 28 - 6

⇒ y = 22

Conclusion

The dimensions of the rectangle are:

Therefore, the length of the longer side is 22 meters

The length of the longer side is 22 meters.

Let, one side of the rectangle is x meters.

According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

In this case, the perimeter is 58 meters:

58 = 2 * (x + 4x - 6)

Now, let's solve for x:

58 = 2 * (5x - 6)

58 = 10x - 12

Add 12 to both sides:

58 + 12 = 10x

70 = 10x

Now, divide both sides by 10 to isolate x:

x = 70 / 10

x = 7

So, one side of the rectangle is 7 meters.

Now, we can find the length of the longer side:

Length of the longer side = 4x - 6

Length of the longer side = 4 * 7 - 6

Length of the longer side = 28 - 6

Length of the longer side = 22 meters

Therefore, the length of the longer side is 22 meters.

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The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

The equation is given as:

f(x) = 3x + 3

Express f(x) as y

y = 3x + 3

Swap the positions of y and x

x = 3y + 3

Make y the subject

3y = x - 3

Divide by 3

y = 1/3x - 1

Replace y with the inverse function

f-1(x) = 1/3x - 1

Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

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Answer:

2 hours

Step-by-step explanation:

Mike has a six hour head start so he is    6 x 2 = 12 miles ahead

 their 'closing speed' is  8-2 = 6 m/hr

    it will take Kim   12 / 6  = two hours to catch Mike

=================================================================

Explanation:

Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.

The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.

Multiply this floor area with the height of the room (22 m) to get the volume of the room.

volume = (floor area)*(height) = 84*22 = 1848 cubic meters

The simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have an expression:

[tex]= 8 \dfrac{3}{8} + 3 \dfrac{3}{8} + 2 \dfrac{3}{8} + \dfrac{3}{8}[/tex]

After simplification:

[tex]= \dfrac{67}{8} + \dfrac{27}{8} + \dfrac{19}{8} + \dfrac{3}{8}[/tex]

[tex]= \dfrac{67+27+19+3}{8}[/tex]

= 116/8

= 29/2

[tex]= 14\dfrac{1}{2}[/tex]

Thus, the simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.

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Answer:

i dont understand your question

Step-by-step explanation:

Answer:

31°

Step-by-step explanation:

As the opposing side and adjacent side of the angle x are given, we need to take the tan ratio of the angle.

=============================================================

Solving :

⇒ tan x° = 9/15

⇒ tan x° = 3/5

⇒ x = tan⁻¹ (0.6)

⇒ x = 31°

The size of the unknown angle "x"

We'll have to check which is the appropriate one from SOHCAHTOA.

In this question we'll have to use tan because opposite and adjacent is given.

[tex]\large\boxed{Formula: tan(A)= \frac{opp}{adj}}[/tex]

Substitute according to the formula.

[tex]tan \: x= \frac{9}{15}[/tex]

We'll have to use tan inverse.

[tex]x={tan}^{-1}(\frac{9}{15})[/tex]

[tex]x=30.96375653[/tex]

[tex]\large\boxed{x=31° }[/tex]

Hence, the size of the unknown angle "x" is 31°

The computation of the index shows that the value of 9 × 10² will be 900.

From the information given, we are told to calculate the value of 9 × 10². This will be calculated thus:

= 9 × 10²

Note that 10² simply means that you've to multiply 10 twice. This will be:

= 10 × 10 = 100

Therefore, 9 × 10² will be:

= 9 × 100

= 900

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Answer:

  B.  27 < AB < 81

Step-by-step explanation:

The triangle inequality requires that the length of any given side of a triangle be greater than the difference and less than the sum of the other two sides.

__

  54 -27 < AB < 54 +27

  27 < AB < 81

_____

Additional comment

Some versions of the triangle inequality allow the "or equal to" case.

  27 ≤ AB ≤ 81

Apparently, the one used here does not.

If the sum of the two short sides is equal to the long side, the "triangle" looks like a line segment. Its altitude and area are zero.

Answer:

O The value of f(2) is smaller than the value of f(1).

Step-by-step explanation:

First, let's solve for both. When the problem says f(1) or f(2), this just means that the x value is equal to that. So:
f(1) = -5(1)^2 + 2(1) + 9 = 6
f(2) = -5(2)^2 + 2(2) + 9 = -7
Since f(1) = 6 and f(2) = -7, we know that f(1) is greater than f(2). Therefore, the value of f(2) is smaller than the value of f(1)

The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.

Conversion means to convert the same thing into different units.

Convert the degree measure to the radian measure.

⇒ 75°

We know the conversion is given as

180° = π radian

   1° = π/180°

Then we have

75° = 75° x π/180° radian

75° = 1.30899 radian

75° ≅ 1.31 radian

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