two kinds of tickets to an outdoor concert were sold: lawn tickets and seat tickets. fewer than 400 tickets in total were sold.

solve:

a. write an inequality to describe the constraints. specify what each variable represents.

b. use graphing technology to graph the inequality. sketch the region on the coordinate plane.

c. name one solution to the inequality and explain what it represents in that situation.

d. answer the question about the situation: if you know that exactly 100 lawn tickets were sold, what can you say about the number of seat tickets?

Answer:

[tex]x=\frac{1}{4}[/tex]

Step-by-step explanation:

We can use some logarithmic rules to solve this easily.

Note: Ln means [tex]Log_e[/tex]

Now, lets start with the equation:

[tex]ln(2x) + ln(2) = 0\\ln(2x) = -ln(2)[/tex]

Writing left side with logarithmic base e, we have:

[tex]Log_{e}(2x) = -ln(2)[/tex]

We can now use the property shown below to make this into exponential form:

[tex]Log_{a}b=x\\means\\a^x=b[/tex]

So, we write:

[tex]Log_{e}(2x) = -ln(2)\\e^{-ln(2)}=2x[/tex]

We recognize another property of exponentials:

[tex]a^{bc}=(a^{b})^{c}[/tex]

So, we write:

[tex]e^{-ln(2)}=2x\\(e^{ln(2)})^{-1}=2x[/tex]

Also, another property of natural logarithms is:

[tex]e^{(ln(a))}=a[/tex]

Now, we simplify:

[tex](e^{ln(2)})^{-1}=2x\\(2)^{-1}=2x\\\frac{1}{2}=2x\\x=\frac{\frac{1}{2}}{2}\\x=\frac{1}{4}[/tex]

This is the answer.

Answer:

x=0, exactly one solution.

Step-by-step explanation:

y=3x+3

y=-2x+3

-----------

3x+3=-2x+3

3x-(-2x)+3=3

3x+2x+3=3

5x+3=3

5x=3-3

5x=0

x=0/5

x=0

Answer:

Asha's present age is 27 years and Nisha's present age is 5 years.

Step-by-step explanation:

Let the present age of Nisha be [tex]x[/tex] years.

As per question, Asha's present age is 2 more than the square of Nisha's age.

[tex]\therefore[/tex] Asha's present age = [tex]x^2+2[/tex]

Now, Nisha will reach her mother's age after [tex]x^2+2-x[/tex] years.

Therefore, age of Asha after [tex]x^2+2-x[/tex] years will be = [tex]x^2+2+x^2+2-x=2x^2-x+4[/tex]

Now, as per question,

[tex]2x^2-x+4=10x-1\\2x^2-x-10x+4+1=0\\2x^2-11x+5=0\\2x^2-x-10x+5=0\\x(2x-1)-5(2x-1)=0\\(2x-1)(x-5)=0\\x=\frac{1}{2}\ or\ x=5[/tex]

As age can't be in fraction, we consider the present age of Nisha as 5 years. So, Asha's present age is [tex]x^2+2=5^2+2=25+2=27[/tex] years.

Therefore, Asha's present age is 27 years and Nisha's present age is 5 years.

Answer:

Your answer is 15/2 i hoped i helped

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

3×5/2

15/2

The remainder is 1

Answer:

$5.24

Step-by-step explanation:

If Mom bought 4, she bought [tex]$1.19*4=$4.76[/tex] worth of pie filling. Since she paid $10, she needs [tex]$10-$4.76=$5.24[/tex] change

Answer:

i believe you answer would be B. 3

Step-by-step explanation:

Answer:

OPTION C - Distributive Property

Step-by-step explanation:

Given: [tex]$ \frac{6x + 9}{3} $[/tex]

This is equal to: [tex]$ \frac{6x}{3} + \frac{9}{3} $[/tex]

⇒ [tex]$ 2x + 3 $[/tex]

Here, [tex]$ 3 $[/tex] is distributed over each term. Hence, distributive property is used.

Answer:

C. Distributive property

Step-by-step explanation:

From the question,

      [tex]\frac{6x+ 9}{3}[/tex] =  [tex]\frac{6x}{3} + \frac{9}{3}[/tex]     (distributive property of the denominator)

             = 2x + 3

The denominator in the question is distributive over the two terms in the numerator.

Answer:

D

Step-by-step explanation:

D contains terms x, y, and z. All three are different.

Answer:

1.

Step-by-step explanation:

The perimeter is a length - degree 1.

The degree of the expression that represents the perimeter of this triangle is 2

The formula for calculating the perimeter of a triangle is expressed as;

P = a + b + c

Such that the parameters are denoted as;

From the diagram shown, we have that;

Perimeter = 2x²+ 2x ² + 4x + 5

collect the like terms, we get;

Perimeter = 4x²+ 4x + 5

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Answer:

4 tens + 5 tenths

Step-by-step explanation:

40+5\10= 40+1/2=40.5

The other leg is 12cm long.

Step-by-step explanation:

Given,

Hypotenuse = c = 15cm

One leg = a = 9cm

Other leg = b

As the triangle is right angled, therefore, using Pythagoras theorem;

[tex]a^2+b^2=c^2\\(9)^2+b^2=(15)^2\\81+b^2=225\\b^2=225-81\\b^2=144\\[/tex]

Taking square root on both sides;

[tex]\sqrt{b^2} =\sqrt{144} \\b=12\ cm[/tex]

The other leg is 12cm long.

Keywords: triangle, square root

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= 4 = x²

x = Answer: Length= 11 , Brteadth = 2

Step-by-step explanation: Let the breadth of the rectangle be x

length = 9 + x

area = 36 cm²

A.T.Q

36cm² = 9x*x

36 = 9x²

36/9 = 4 = x²

x = root of 4

x= 2

Therefore , breadth of rectangle is 3cm and length is 12 cm

verification:

l*b = 12*3 = 36cm²

To simplify the expression x² + 3x + 2 / X + 1, factor the numerator and denominator expressions separately. The simplified form of the expression is (x + 2) / 1.

To simplify the expression, x² + 3x + 2 / X + 1, we can use the factoring method. First, we factor the numerator expression. The expression x² + 3x + 2 can be factored as (x + 2)(x + 1). Then, we factor the denominator expression X + 1. So, the simplified form of the expression is (x + 2) / 1.

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28 to nine means it is 8:32 ( to get this you subtract 28 from 9.) ( its saying there are 28 minutes left until it is 9)

add 8 hours

= 8+ 8 = 16

well we arent talking about military time sooo 16-12 = 4

4 : 32 and you need to add the 59 so

32+ 59 = 91

91 - 60 = 31 (dont forget to add the extra 1 hour because we subtracted 60 minutes :). )

so the correct time will be 5: 31

Answer: 5:31

Step-by-step explanation:

28 minutes to 9 is 8:32

8 hours and 59 minutes later it would be 5:31

Answer:

it's already in it's simplest form

Step-by-step explanation:

Answer:

the answer would still be the same as the problem because if you use prime factorization it would still be the square root of 41  

Step-by-step explanation:

[tex]\sqrt{41\\[/tex]

Answer:

angle sum of a triangle’Formula

Step-by-step explanation:

N stands for the number of edges, - 2 is the result after finishing, 2 has no special significance. Because the sum of outer angles is a constant n-edge shape with 360 degrees, take n flat angles 180n = inner angle and + 360, so the sum of inner angles = 180n-360 = 180 (n-2)

That formula tells you what is the sum of the interior angles of a polygon with n sides.

So, for example, a triangle has n=3 sides, and in fact the sum of its interior angles is

[tex](3-2)\cdot 180=180[/tex]

As another example, the sum of the interior angles of a polygon with 15 sides is

[tex](15-2)\cdot 180=13\cdot 180=2340[/tex]

Answer:

y=-2x+7

Step-by-step explanation:

Memorize the formula y=mx+b where m=slope and b=y-intercept.

y=-2x+b passes through the point (1, 5)

5=-2(1)+b

5=-2+b

b=5-(-2)=5+2=7

So the y-intercept in this case is 7.

y=-2x+7

Answer:

x = 64

Step-by-step explanation:

The sum of the interior angles of a quadrilateral = 360°

Sum the given angles and equate to 360

x + 2x + 114 + x - 10 = 360, that is

4x + 104 = 360 ( subtract 104 from both sides )

4x = 256 ( divide both sides by 4 )

x = 64

Answer:600

Step-by-step explanation:

The 6 is in the hundreds place, so you in order to round it you would look at the 4. Since 4 is a a number less than 5 you round down. That would mean 600 instead of 700.

Answer: 600

Step-by-step explanation: To round 649 to the nearest hundred, we first find the digit in the rounding place which in this case is the 6 in the hundreds place.

To decide whether to round up or down, we look at the digit to the right of the 6 which is 4.

According to the rules of rounding, if the digit to the right of the rounding place is less than 5, we round down.

So in this problem, since 4 is less than 5, we round down.

This means that the 6 in the hundreds place stays the same and all digits to the right if 6 become 0.

So 649 rounded to the nearest hundred is 600.

Without Table 14, a specific answer can't be provided. But generally you would find the y value when x is 3 for f(3), or find the x value when y is 1 for f(x)=1.

This question pertains to the evaluation of f(3) and solving for f(x)=1 within the given function f that's represented in Table 14. Unfortunately, as the Table 14 isn't provided, I can't give a specific answer. However, generally, to evaluate f(3), find the pair where the x value is 3; the corresponding y (or f(x)) value is the result of f(3). To solve f(x)=1, look for the pair in the table where the f(x) (or y) value is 1; the corresponding x value is the solution for f(x)=1.

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Answer:

X=-4

Step-by-step explanation:

In the attached file

GCF of 38 and 48

First find the prime factorization of 38 and 48.

38=2*19

48=2*2*2*2*3

The two number share the factor 2 and only 2. The GCF = 2.

Final answer:

The greatest common factor (GCF) of the number 38 is technically 38 itself. However, in the context of two or more numbers, it's the largest factor they share in common. For the single number 38, its factors are 1, 2, 19, and 38.

Explanation:

Finding the Greatest Common Factor (GCF) of 38

The greatest common factor of a number is the largest number that divides it, other than the number itself. Since 38 is a composite number and not a prime number, its factors are 1 and 38. The number 38 can also be divided evenly by 2 and 19, because 38 = 2 × 19. So, the factors of 38 are 1, 2, 19, and 38 itself. However, when we refer to the greatest common factor, it is usually in the context of finding the GCF between two or more numbers. For the single number 38, the GCF can be considered as the largest factor, which is 38 itself. But typically, the term 'greatest common factor' is more relevant when comparing it with another number to see the largest factor they have in common.

Answer:

3.75

Step-by-step explanation:

You take your 15 feed and divide it by 4 for the four pieces she cuts the rope into giving you with each section of the cut rope being 3.75 in.

The length of each piece is 3.75 feet long.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Megan who has a rope that is 15 feet in length and she cuts the rope into 4 pieces.

Assume that the length of each piece is x ft. Then -

4x = 15

x = 15/4

x = 3.75 ft

Therefore, the length of each piece is 3.75 feet long.

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Answer:

x = 3

y = 2

Step-by-step explanation:

When 2 triangles are congruent, they will have exact same 3 sides length and exact same 3 angles measure.

So we can say:

-2x + 6y = 6

and

-7x + 8y = -5

Let's multiply first equation by 7 and 2nd equation by -2, to get:

7 [-2x + 6y = 6] = -14x +42y = 42

and

-2 [-7x + 8y = -5] = 14x - 16y = 10

Now adding these 2 new equations and solving for y:

-14x +42y = 42

14x - 16y = 10

----------------------

26y = 52

y = 52/26

y = 2

Now we put y = 2 into 1st equation (or any other) and solve for x:

-2x + 6y = 6

-2x + 6(2) = 6

-2x + 12 = 6

6 = 2x

x = 6/2

x = 3

There are 8046.75 meters in 5 miles

Step-by-step explanation:

Method 1:

First of all we have to calculate the unit conversion.

Assuming that 3 miles is equal to 4828.05 meters

We have to find that how many meters make one mile

So,

3 miles = 4828.05 meters

[tex]1\ mile=\frac{4828.05}{3}\\=1609.35\ meters[/tex]

Now we know that:

[tex]1\ mile=1609.35\ meters\\5\ miles=1609.35*5 = 8046.74\ meters[/tex]

Method 2:

We can also use ratios to find the number of meters in 5 miles as:

3:4828.05::5:x

where x is the number of meters in 5 miles

[tex]\frac{3}{4828.05}=\frac{5}{x}\\x=\fac{5*4828.05}{3}\\=8046.75\ meters[/tex]

Hence,

There are 8046.75 meters in 5 miles

Keywords: Conversions, Units

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Answer:

1/5

Step-by-step explanation:

First, put the equation into slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept.

5y=x+10, then divide both sides by 5;

y=1/5x+2

The slope is m, and m=1/5.

Answer:

[tex]\displaystyle 45[/tex]

Step-by-step explanation:

[tex]\displaystyle (6 + 3i)(6 - 3i) = 36 - 9i^2 = 36 - 9[-1] = 36 + 9 = 45[/tex]

Extended Information on the Complex Number System

[tex]\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\:[Any\:multiple\:of\:four][/tex]

I am joyous to assist you anytime.

Check the picture below.

the idea being that sides of 2.5 andd 8 are fixed, what's are the possible lengths of "x"?

well, if we open the fixed sides, we'll end up with a 3rd side of 2.5 + 8 = 10.5, however if "x" is ever 10.5, the figure will become a flat-line and we'd be losing the triangle.

and if we close the fixed sizes, the longest "x" could be is 8 - 2.5 = 5.5, but the same, it can't be 5.5 exactly otherwise the figure will turn to a flat-line.

5.5 < x < 10.5.

Answer:

5.5 < x < 10.5

Step-by-step explanation:

Khan

Answer:

LENGTH OF AC IS 6

Step-by-step explanation:

Given :

the side AC = x ;

we need to find x;

since ∠A = ∠C , It's an isosceles triangle . i.e ,

the sides opposite to the angles ( AB and CB ) are also equal.

thus ,

side

AB = x+4 ;

CB = 3x-8 ;

thus AB = CB or ,

x+4 = 3x-8 ,

2x = 12 ,

x = 6 ;

therefore the side AC is 6.

Answer:

He left $6 for the tip.

Step-by-step explanation:

20%=0.2

0.2*30=6