one day, duncan and his friends had lunch while sitting at tables of 6. another day, they had lunch at tables of 5. what is the smallest number of people that could be in the group?

Answer:

A. (5, 13)

Step-by-step explanation:

The function f(x) = (x - 4) + 5 is the translation of the function f(x) 4 units right and 5 units up and the rule is:

(x, y) → (x + 4, y + 5)

Apply the rule to the given point to get:

(1, 8) → (1 + 4, 8 + 5) = ( 5, 13)

Correct choice is A

Answer:

-5x + 1

Step-by-step explanation:

Hello!

We can find the quotient by factoring the numerator, and cancelling common factors.

The quotient is (-5x + 1).

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{\dfrac{15x^2 - 3x}{-3x}}[/tex]

[tex]\huge\textbf{Simplify the current equation:}[/tex]

[tex]\mathbf{= \dfrac{-3x(-5x + 1)}{-3x}}[/tex]

[tex]\huge\textbf{Cancel out \boxed{\bf -3x} \& simplify it:}[/tex]

[tex]\mathbf{= \dfrac{-15x + 3}{3}}[/tex]

[tex]\huge\textbf{Simplify that above:}[/tex]

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

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{-5x + 1 }}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

Find the slope of the line that passes through the pair of points.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

In this problem we have two points given to us, which are...

... and we should find the slope.

[tex]\bf{We\;will\;use\;the\;Slope-Equation:}\\m=\dfrac{y2-y1}{x2-x1}[/tex]

[tex]\bf{\dfrac{0-6}{7-2}=\dfrac{-6}{5} =-\dfrac{6}{5}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Slope:}[/tex]

                                [tex]\bf{=-\dfrac{6}{5}}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Answer:

7)  y⁹

9)  a⁸

Step-by-step explanation:

when we multiply two exponents (of the same base), we can add them

so, a² · a³ = a² ⁺ ³ = a⁵

let's test it out!

(a = 2 in our example)

2² · 2³ = 2⁵

4 · 8  = 32   (2⁵ = 32)

32 = 32

because this is true, we know that we can add exponents of the same base when multiplying them together

now, let's try out the question at hand:

y³ · y⁶

well, we know that 3 + 6 = 9, so y³ · y⁶ can be simplified to y⁹

--

now, we're going to be working with division. We know that division is the inverse of multiplication, so we logically know that instead of adding exponents, we subtract them when dividing

here,

a³ ÷ a² would equal a¹    (3 - 2 = 1)

let's put a = 2 again:

a³ ÷ a² = a³ ⁻ ² = a¹ = a

2³ ÷  2² =   2¹

8  ÷   4   =  2

2   =  2

once again, we have proven this shortcut to be true

now, to the problem at hand!

first, we can multiply a³ · a⁹

a³  ·  a⁹   =  a³ ⁺ ⁹  =  a¹²

so, let's rewrite the problem:

a¹² /  a⁴

because we're dividing with exponents, we can subtract 12 - 4

a¹² / a⁴

a¹² ÷  a⁴

a¹² ⁻ ⁴

a⁸

so, our simplified answer is a⁸

(note: they must be the same base, [the thing that the exponent is attached to] for this to apply)

hope this helps (and makes sense)! have a lovely day :)

The required simplification is   [tex]y^{9}[/tex]  and  [tex]a^{8}[/tex] .

To simplify the following 1 )  [tex]y^3* y^6[/tex]  2 ) [tex]\frac{a^3*a^9}{a^4}[/tex].

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

1 )  [tex]y^3* y^6[/tex]
= [tex]y^3* y^6[/tex]
since the base of the exponents is the same so the powers of y get added
[tex]=y^{3+6}[/tex]
[tex]=y^{9}[/tex]

2 ) [tex]\frac{a^3*a^9}{a^4}[/tex]
[tex]=\frac{a^3*a^9}{a^4}[/tex]
since the base of the exponents is the same so the powers of a get added in the numerator.
[tex]=\frac{a^{3+9}}{a^4}[/tex]
[tex]=\frac{a^{12}}{a^4}[/tex]
Now, the power of the numerator will get decreased by the power of the denominator because the base is common i.e. a
[tex]=a^{12-4}[/tex]
[tex]=a^{8}[/tex]

Thus the required simplification is   [tex]y^{9}[/tex]  and  [tex]a^{8}[/tex] .

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Answer:

A

Step-by-step explanation:

So whenever you're finding the difference between two numbers you generally use the equation: |a-b| since a-b may or may not be negative, but |a-b| will always equal |b-a|. Since the only thing that differs is the sign. So when you have: [tex]|-\frac{2}{3}-\frac{5}{3}|[/tex], in this case a=-2/3 and b=5/3 (b is positive since you're subtracting b, so if b appeared positive in the equation, it's actually negative, since the negative sign in |a-b|, which would make the two negatives cancel out). This means A is the correct answer. You could also calculate what the value is. Calculating gives you: [tex]|-\frac{7}{3}| = \frac{7}{3}[/tex]. And as you can see the top one, has two numbers separated by 7 one thirds.

Answer:

A

Step-by-step explanation:

It is absolute value and when it is absolute value, it is positive.

Using linear functions, it is found that the temperatures would be equal after 8 hours.

A linear function is modeled by:

y = mx + b

In which:

Two functions are equal when they intersect. In this problem, both lines pass through point (8,70), that is, they have the same temperature(of 70 degrees) after 8 hours.

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Answer:

The answer in decimal form is 33.6.

The answer in fraction form is [tex]33\frac{3}{5}[/tex].

Step-by-step explanation:

To find 40% of 84, multiply 84 and 0.4.

84 × 0.4 = 33.6

The answer in decimal form is 33.6.

The answer in fraction form is [tex]33\frac{3}{5}[/tex].

Hope this helps!

The true statement about the graph's slope is (c) Its slope is zero.

From the question, we have:

A horizontal line is at y = 2.5.

The horizontal line implies that the cost of lunch do not change

Horizontal lines have a slope of 0

Hence, the true statement about the graph's slope is (c) Its slope is zero.

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Answer: 1010

Step-by-step explanation:

[tex]V=\frac{1}{3}(\pi)(8^{2})(15) \approx \boxed{\text{ } 1010 \text{ cm}^{3}}[/tex]

Answer: 1

Step-by-step explanation:

When [tex]x=0[/tex], [tex]y=\boxed{1}[/tex]

is that 2.11 I think so

Step-by-step explanation:

I don't know explain it to you and

Answer:

Step-by-step explanation:

The ratio of Anne's height: Ben's height is 7:9.

Anne's height is 1.4m.

Find Ben's height.

we can solve with an equation

7 : 9 = 1.4 : x

x = 9 * 1.4 : 7

x = 1.8 m

[tex](x - a)(x - b)(x - c) \\ (x {}^{2} - bx - ax + ab)(x - c) \\ x {}^{3} - bx {}^{2} - ax {}^{2} + abx - cx {}^{2} + cbx + cax - abc[/tex]

[tex]x {}^{3} + ( - a - b - c)x {}^{2} + (ab + cb + ca)x - abc [/tex]

[tex] - a - b - c = - 7 \\ ab + ac + bc = 16 \\ - abc = - 12 \: \: \: \: \: abc = 12[/tex]

The rate of change of the the given table is: 3/4soda per dollar.

Rate of change = change in total cost / change in number of sodas.

Using (24, 18) and (28, 21), we would have:

Rate of change = (21 - 18)/(28 - 24)

Rate of change = 3/4

Therefore, the rate of change is 3/4soda per dollar.

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The parabola equation in the factored and standard form are f(x) = (x + 2)(x - 5), and f(x) = (x - 3/2)² - 49/4 respectivly.

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have:
Parabola with zeros at (-2, 0) and (5, 0) and passes through the point (-1, -4)

In factored forms:

f(x) = (x + 2)(x - 5)

Because zeros at (-2, 0) and (5, 0)

In the standard form:

f(x) = x² - 3x - 10 or

f(x) = (x - 3/2)² - 49/4

Thus, the parabola equation in the factored and standard form are f(x) = (x + 2)(x - 5), and f(x) = (x - 3/2)² - 49/4 respectivly.

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The value of (g-f)(X) is 2x - 6x³ +6.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x)= 6x³-4, g(x)= 2x+2

Now,

(g-f)(x)= g(x)-f(x)

= 2x+2-( 6x³-4)

=2x+2- 6x³+4

=2x - 6x³ +6

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The numeric values for the expressions are given as follows:

The numeric value of an expression is found replacing the letters by their numeric values.

The values of the letters are given as follows: A = 5, B = 4.4, C = 4.25.

Hence the values of the expressions are:

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The final loss percent is 0.25%.

The gap between the cost price and the selling price is what is referred to as a loss. And the loss percent is the loss as a percentage of the actual cost.

Total CP=Rs. 400

Let the CP of the first watch be Rs. x

So, CP of the second watch=Rs.(400-x)

For the first watch,

Gain Percent=5%

SP = [tex](1+\frac{5}{100})*x[/tex]

SP=105x/100

For the second watch,

Loss Percent=5%

SP=[tex](1-\frac{5}{100})(400-x)[/tex]

SP=95(400-x)/100

As the SP of both the watches is the same.

[tex]\frac{105}{100}x=\frac{95}{100}(400-x)[/tex]

105x=38000-95x

105x+95x=38000

200x=38000

x=38000/200

x=190

CP of the first watch=Rs. 190

CP of the second watch=Rs. (400-190)=Rs. 210

SP of first watch=[tex]\frac{105}{100}*190[/tex] =Rs. 199.50

SP of second watch=[tex]\frac{95}{100}*210[/tex]=Rs. 199.50

Total SP=Rs. 399

Final Loss=Total CP-Total SP

                =Rs.(400-399)

                =Rs. 1

Final Loss Percent=100/400

                              =0.25%

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Answer:

Second option 1.6x10^14

Step-by-step explanation:

The numbers which are the means of the proportion as given in the task content are in; Choice D; 3 and 20

It follows from the task content that the proportion whose mean is to be evaluated in the task content is; 2/3 = 20/30.

On this note, it follows that the numbers 2 and 30 are the lower and upper extremes of the property and hence, 3 and 20 are the mean of the proportion.

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Option A is correct answer; i.e. 102 homes were sold in 2017.

A pie chart is a type of graph that records data in a circular manner that is further divided into sectors for representing the data of that particular part out of the whole part.

Here,

Total Homes sold in 2017 = 850 homes.

Homes sold in Southwest region = 12 % of the total.

                                                      = 0.12 X 850

                                                      = 102.

Thus, option A is correct answer; i.e. 102 homes were sold in 2017.

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Answer:

x = 2 and y = -1

Step-by-step explanation:

that is the solution above

Answer:

x = 2

y == -1

Step-by-step explanation:

     x - 10y = 12 ----------------(I)

   10x + 10y = 10 --------------(II)

We can find the value of 'x' by eliminating 'y'. To eliminate 'y', add equations (I) & (II)

           (I)             x - 10y = 12

          (II)         10x + 10y = 10   {Now add the equations}

                         11x          = 22

                                     x = 22 /11

                                  [tex]\sf \boxed{\bf x = 2}[/tex]

Now, Plugin x = 2 in equation (1)

 10*2 + 10y = 10

   20  + 10y = 10

             10y = 10 - 20

             10y = -10

                 y = -10/10

                [tex]\sf \boxed{\bf y = -1}[/tex]

In order to draw a perpendicular bisector you must have ruler , compass and a pencil.

Given nothing and we have to show the steps to draw a perpendicular bisector.

Perpendicular bisector is the line which divides the line into two equal parts and makes 90° angle on other line.

If we want to make a perpendicular bisector on a line then we have to follow the following steps:

1) First draw a line with the help of ruler on which we want to make perpendicular bisector.

2) Now take a compass and a pencil.

3) Put the pencil in the compass and strech the compass equal to half or little more of the length of the line.

4) Now put the compass on one end of the line and draw an arc on the line or may be just upward.

5) Now repeat the step 4 from other end.

6) Now draw a line from the point where two arcs intersects on the line.

7) It is the perpendicular bisector of the line.

Hence to draw a perpendicular bisector we require compass, ruler and a pencil.

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The minimum sample size needed in the research of systolic blood pressure is 68.

Given standard deviation=25 mm Hg, confidence level=90%, Estimation =5 mm Hg.

We have to first find the level of alpha which is known as error.

α=(1-0.9)/2

=0.05

Now we have to find z in the z table as such z has a p value of 1-α,that is z with a p value of 1-0.05

=0.95 ,so Z=1.645.

now finding the margin of error, which is as under:

[tex]M=z st/\sqrt{n}[/tex]

in which st is standard deviation and the n is sample size of population.

By assuming the standard deviation of 25 mm Hg we get values as under:

n is sample size.

[tex]M=z* st/\sqrt{n}[/tex]

[tex]5=1.645*25/\sqrt{n}[/tex]

[tex]5\sqrt{n}=1.645*25\\[/tex]

dividing both sides by 5

[tex]\sqrt{n}=1.645*5[/tex]

squaring both sides we get

n=67.65.

Hence the sample size needed by the researcher is 68.

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The given question is incomplete as it should includes :

standard deviation= 25mm Hg

Confidence level=90%

Estimation 5 mm Hg of u.

Answer: A=48 squared centimeters

Step-by-step explanation: First you need to find the area of the whole rectangle. Area equals length times width (9*8), which is 72. Next you find the area of the white region: 4*6=24. Finally, you subtract the smaller region from the whole: 72-24=48. BOOM: you got the exact right answer :)

Answer: If she waits on 13 tables than she should expect to earn $220

Step-by-step explanation:

15*13=195

195+25=220

Answer:

k = 20

Step-by-step explanation:

1) Isolate the variable

k - 8 = 12

  +8    +8

2) Solve

k = 12+8

k = 20