28. Ashton is hosting a banquet. He plans to spend $400, plus/minus $50, at a
cost of $25 per guest,
a. Find the maximum and minimum number of guests.
b. If there can be up to 7 guests per table, what is the minimum number of
tables Ashton should reserve so everyone has a seat?

Answer:

Just study and pay attention in class and take good notes. I would say that you should pay more attention when they teach you the trigonometry unit.

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

AB is not a ray. It has two endpoints.

"It is a part of a line that has a fixed starting point but no end point."

For given example,

We have been given a part of a line AB.

The starting point is A and the end point is B.

We know, one of the end of the ray is denoted by arrow.

Since both the ends of given figure are fixed, it is not ray.

AB is called as line segment.

Therefore, AB is not a ray. It has two endpoints.

Learn more about ray here:

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Answer:

Step-by-step explanation:

1) 7/10 × 2/21

1/15

2) 9/16 × 10/21

90/336

15/56

3) 11/12 × 26/55

13/30

4) 2/6 × 18/12 × 2/3

72/216

1/3

5) ⅚ × 9/10

45/60

3/4

Answer:

Step-by-step explanation:

Let the greater part = x

Smaller part = 105 - x

2*(greater part) = (3*smaller part) - 15

2*x = 3*(105 -x) - 15

Use distributive property

2x = 3*105 - 3*x - 15    

2x = 315 - 3x - 15

2x =  300 - 3x

Add 3x to both sides

2x +3x = 300

5x = 300

Divide both sides by 5

x = 300/5

x =60

Smaller part = 105 - 60  = 45

Greater part = Rs. 60

Smaller part = Rs. 45

Answer:

7/8

Step-by-step explanation:

1/4 + 5/8 = 2/8 + 5/8 = 7/8

= amount used for pepper and tomatoes

2 1/2 - 3/4 = 5/2-3/4 = 10/4 -3/4 = 7/4

= total amount used

so

7/4 - 7/8 = 14/8 - 7/8 = 7/8 for lettuce

If 101 is given in base b, then in base 10 you have

[tex]101_b = 1\times b^2 + 0\times b^1 + 1\times b^0 = b^2 + 1[/tex]

For instance, if b = 2, then

101₂ = 2² + 1 = 5₁₀

If b = 3, then

101₃ = 3² + 1 = 9₁₀

If b = 4, then

101₄ = 4² + 1 = 17₁₀

The answer depends entirely on the base of the given number.

I HOPE IT WILL HELP YOU.

Have a great day ahead.

Answer:

9.14 miles an hour

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

since it can be expressed as a fraction, it is rational

komhnyrtgfdedavfbfsfb

Answer:

any file to have a reference?

Answer:

vsddddddddddddddddddddddddddddddddddddddddddddddddddddddbgtresxvzjdhdf;lsjb

Step-by-step explanation:

Answer:

(-3,-4)

Step-by-step explanation:

Answer:

slope = - 6, y- intercept = 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

0 = 2x - [tex]\frac{5}{3}[/tex] + [tex]\frac{1}{3}[/tex] y ( multiply through by 3 to clear the fractions )

0 = 6x - 5 + y ( subtract 6x - 5 from both sides )

- 6x + 5 = y , that is

y = - 6x + 5 ← in slope- intercept form

with slope m = - 6 and y- intercept c = 5

Answer: A

Step-by-step explanation:

Answer:

-6 < x < 6

Step-by-step explanation:

Domain refers to the list of all x-values included in the function. In this instance, the list of x-values in this function is between -6 and 6.

Answer:

Hope it helped

Step-by-step explanation:

The restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function  would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

An inverse function or an anti function is defined as a function, which can reverse into another function.

Now the given quadtratic function is,

f(x) = x² + 2

Now vertex of the given quadratic function is (0,2)

Thus the range of the function is [2,∞)

If we restrict the domain of this function to either (-∞,0} or [0.∞), it will become one to one function.

Now the inverse function is given as,

y = x² + 2

Upon interchanging x and y, we get:

x = y² + 2

⇒ y² = x - 2

or, y = ±[tex]\sqrt{x-2}[/tex]

Hence, the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

Thus, the restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function  would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

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Answer:

Reflection is shown in the graph.

Answer:

165/14

Step-by-step explanation:

(7-4) + 17 / -14 + 2 x 5

3 + 17/-14 + 2 x 5

3 - 17/14 + 2 x 5

3 - 17/14 + 10

165/14

Answer:

320/420 = 4/3

Step-by-step explanation:

4/7= x /560

Cross multiply

7x = 2240

Divide by 7:

x=320

The school has 320 boys and 240 girls

I hope this helps u:)

Answer:

Problem(1):     [tex]21[/tex]

Problem(2):     Side length = [tex]\frac{1}{4}[/tex]    Area = [tex]\frac{1}{16}[/tex]

Problem(3):     Boys = [tex]320[/tex]     Girls = [tex]240[/tex]

Step-by-step explanation:

(Notes steps are cut from this answer so that it isn't too long)

1. Problem (1)

One is given the following information:

The most logical first step is to solve for the value of (x). One can solve for the numerical value of (x) with the first equation.

[tex]x+\frac{1}{x}=5[/tex]

Multiply the entire equation by (x),

[tex]x^2+1=5x[/tex]

Inverse operations put the equation in the general format of a quadratic equation. The general format of a quadratic equation is as follows,

[tex]ax^2+bx+c=0[/tex]

Put the given equation in this format,

[tex]x^2-5x+1=0[/tex]

Now use the quadratic formula to solve for the value of (x). The quadratic formula uses the coefficients of the terms in a quadratic equation to find the roots of the equation. The quadratic formula is as follows,

[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]

Use the coefficients of the terms in the given quadratic equation in the formal, then simplify to solve for solutions of the given equation,

[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]

Simplify,

[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]

[tex]\frac{5(+-)\sqrt{21}}{2}[/tex]

Now substitute these values into the equation and simplify, even though there are two values of (x), there will only be one solution,

[tex]((\frac{5+\sqrt{21}}{2}-\frac{1}{\frac{5+\sqrt{21}}{2}})^2[/tex]                                      [tex]((\frac{5-\sqrt{21}}{2}-\frac{1}{\frac{5-\sqrt{21}}{2}})^2[/tex]  

[tex](\frac{5+\sqrt{21}}{2}-\frac{2}{5+\sqrt{21}})^2[/tex]                                      [tex](\frac{5-\sqrt{21}}{2}-\frac{2}{5-\sqrt{21}})^2[/tex]

Convert to a common denominator,

[tex](\frac{5+\sqrt{21}}{2}*\frac{5+\sqrt{21}}{5+\sqrt{21}}-\frac{2}{5+\sqrt{21}}*\frac{2}{2})^2[/tex]                   [tex](\frac{5-\sqrt{21}}{2}*\frac{5-\sqrt{21}}{5-\sqrt{21}}-\frac{2}{5-\sqrt{21}}*\frac{2}{2})^2[/tex]

[tex](\frac{(5+\sqrt{21})^2-4}{2(5+\sqrt{21})})^2[/tex]                                           [tex](\frac{(5-\sqrt{21})^2-4}{2(5-\sqrt{21})})^2[/tex]

Simplify,

[tex](\frac{25+10\sqrt{21}+21-4}{10+2\sqrt{21}})^2[/tex]                                     [tex](\frac{25-10\sqrt{21}+21-4}{10-2\sqrt{21}})^2[/tex]

[tex](\frac{42+10\sqrt{21}}{10+2\sqrt{21}})^2[/tex]                                              [tex](\frac{42-10\sqrt{21}}{10-2\sqrt{21}})^2[/tex]

[tex]\frac{1764+840\sqrt{21}+2100}{100+40\sqrt{21}+84}[/tex]                                      [tex]\frac{1764-840\sqrt{21}+2100}{100-40\sqrt{21}+84}[/tex]

[tex]\frac{3864+840\sqrt{21}}{184+40\sqrt{21}}[/tex]                                               [tex]\frac{3864-840\sqrt{21}}{184-40\sqrt{21}}[/tex]

[tex]21[/tex]                                                            

2. Problem (2)

All four sides of a square are congruent (have the same measure), thus dividing the perimeter of a square by (4) will yield the side length of the square,

[tex]Perimeter\ of\ the\ square: 4\\Side\ length: \frac{1}{4}[/tex]

The area is the two-dimensional space that a figure takes up, in the case of a square, the area is the side length times itself:

[tex]A=(\frac{1}{4})^2=\frac{1}{16}[/tex]

3. Problem (3)

Let (x) represent the amount by which the ratio of boys to girls was scaled down. Assuming that these are the only two genders in the school, one can state that the sum ratio coefficients times the scaling value for both boys and girls, will equal the total number of people in the school. Thus, one can form the following equation and solve it with inverse operations and simplification,

[tex]boys + girl = total\ students\\4x + 3x = 560\\7x = 560\\x = 80[/tex]

Now substitute this into the expression for the two genders in this scenario, respectively, to solve for the actual number of students of that gender,

Boys,                         Girls,

[tex]4(x)[/tex]                             [tex]3(x)[/tex]

[tex]4(80)[/tex]                           [tex]3(80)[/tex]

[tex]320[/tex]                              [tex]240[/tex]

Answer:

A

Step-by-step explanation:

-2x-4>8

-2x>12

-x>6

x<-6

Answer:

[tex]x < - 6[/tex] (first option)

Step-by-step explanation:

[tex] - 2x - 4 > 8[/tex]

[tex] - 2x > 8 + 4[/tex]

[tex] - 2x > 12[/tex]

[tex] = x < - 6[/tex]

Answer:

k + 8 = y

9x - 17

4(x²-8)

The volume of a rectangular prism is the product of the prism's dimension (i.e. length, width and height). The dimension of the rectangular prism are:

[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]

Given that:

[tex]Volume = (18x^4 + 15x^3 - 12x^2)[/tex]

First, we factor out [tex]3x^2[/tex]

[tex]Volume = 3x^2 \times (6x^2 + 5x - 4)[/tex]

Expand

[tex]Volume = 3x^2 \times (6x^2 + 8x-3x - 4)[/tex]

Factorize

[tex]Volume = 3x^2 \times (2x(3x + 4) -1(3x + 4))[/tex]

Factor out [tex]3x + 4[/tex]

[tex]Volume = 3x^2 \times ((2x -1) (3x + 4))[/tex]

Rewrite as:

[tex]Volume = 3x^2 \times (2x -1) \times (3x + 4)[/tex]

The volume of a rectangular prism is:

[tex]Volume = Length \times Width \times Height[/tex]

So; by comparison:

[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]

Read more about polynomials and volumes at:

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y= 3x –4

3x + y = –4

3x + (3x –4) = –4

3x+3x – 4 = – 4

6x = – 4 +4

6x=0 —> x= 0/6 —> x=0

y = 3x – 4 —> y = 3(0) – 4 = – 4

I hope I helped you^_^

Answer:

(0,-4)

Step-by-step explanation:

3x + y = -4

3x + (3x - 4) = -4

3x + 3x - 4 = -4

6x = 0

x = 0

y = 3(0) - 4

y = -4

Answer:

Step-by-step explanation:

Solve the equation for n:

The number is 80

Answer:

Number is 40

Step-by-step explanation:

Let the number be n

(n - 20)/2 = 30

(n - 20) = 2 × 30

n = (2 × 30) + 20

n = 60 + 20

n = 80

Answer:

408

Step-by-step explanation:

Surface area formula is A=2(wl+hl+hw)

Substituting these values into the formula you would get

2·(3·8+4·8+4·3)=136

136 accounts for one rectangular prism.

Since you have 3 multiply 136 by 3 which would leave you with 408

Answer:

280 in²

Step-by-step explanation:

The opposite faces are congruent , then surface area (SA ) is

SA = top/ base + front/ back + 2 sides

note for the front/ back and 2 sides we have 3 + 3 + 3 = 9 in

   SA  = 2(8 × 4) + 2(8 × 9) + 2(4 × 9)

         = 2 × 32 + 2 × 72 + 2 × 36

        = 64 + 144 + 72

      = 280 in²