#10: A Caterer’s total cost for a party includes a fixed cost, in addition the caterer also charges a certain amount for. Each guest
$300 to serve 25 guests
$420 to serve 40 guests
Find the fixed cost and the cost per guest

According to the solving the length of the road in real life will be = 8 km.

The relationship (or ratio) between the distance on a map and the comparable distance on the ground is referred to as map scale. For example, on a 1:100000 scale map, 1cm on the map represents 1km on the ground.

You've probably seen maps with just a scale bar representing equal sections, each marked with kilometres or miles. These divisions have been used to calculate ground distance on a map. In other words, a map scale specifies the relationship between the map and indeed the entire or a portion of the earth's surface depicted on it.

scale on a map is 1 : 200,000.

= 1 : (200,000/(100*1000))

= 1:2

= 2km

So,

length of a road on the map is 4 cm.

= 4*2

= 8km

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Answer:

x = [tex]\frac{15-3y}{5}[/tex]

Step-by-step explanation:

5x + 3y = 15 ( isolate the term in x by subtracting 3y from both sides )

5x = 15 - 3y ( isolate x by dividing both sides by 5 )

x = [tex]\frac{15-3y}{5}[/tex]

Answer:

Step-by-step explanation:

25 divide 77 = 0.32467532 x 100 = 32 (Leave off the rest, there is no such thing as a fraction of a person in this)

Simplified: (25/77)*100 = 32

To check our answer we would do 32 x 77%(.77) = 24.64 round-up and you get 25!

If you are still confused please do tell :)

Answer:

A and C

Step-by-step explanation:

Factors are numbers that can multiplied with another number to create a product. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

The answer to this question is (gof)(x)=2x+7

According to question:

Given: f(x)=4 x, g(x)=1/2 x+7,h(x)=-2 x+4

We always simplify everything in brackets first using BODMAS. Therefore, in order to compute f(g(x)), g(x) must first be calculated and then substituted within f(x). Similar to this, in order to determine g(f(x)), f(x) must first be computed and then substituted in g(x). In other words, the sequence is important when locating the composite functions. It implies that g(f(x)) and f(g(x)) may not be equal. The following procedures are used to obtain the composite function f(g(a)) for any two functions f(x) and g(x).

By changing x = a in g, find g(a) (x).

Put x = g(a) into f to find f(g(a)) (x)

∴(gof)(x)=2x+7

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The value of the expression log₃54 is 3.6.

Given that the expression is log₃54.

We are required to find the value of the expression by using the change of base formula.

The change of base formula is the formula that will give us the answer of a log with a different base by using only log calculations with a base of 10.

The expression is log₃54.

log₃54= log (54)/log (3)          

(We know that [tex]log_{a}b[/tex]=log b/ log a)

Now we have to use the values of logarithms in the above expression to find its value.

=1.73/0.48

=3.6

Hence the value of the expression log₃54 is 3.6.

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Answer:

x= -6/5

Step-by-step explanation:

-2x=3x +6

collect like terms

-6=3x+2x

-6=5x

x= -6/5

Answer: x= -6/5 make that a fraction

decimal form: x= -1.2

mixed number form: x= - 1 1/5, 1 is the whole number

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

It is false that 2x + 7 = 3x + 1

The equations are given as

2x + 7 = 27

3x + 1 = 28

The above equations have different values

This means that

It is false that 2x + 7 = 3x + 1

The above statement is true because 27 does not equal 28

Hence, it is false that 2x + 7 = 3x + 1

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Answer:

Step-by-step explanation:

Volume of the cube = 2*4*6 = 48 cm^3.

Its density is 24 g / cm^3

The density of water is 1g /cm^3 so it will sink in water.

The sum of numbers from 1 to 100 is 50 × 101.

Carl Friedrich Gauss is a renowned mathematician. He has contributed many theories to the fields of mathematics and physics.

The sum of the first hundred numbers is calculated by making pairs of two numbers. The sum of these pairs is 101.

And there is a total of 50 pairs.

So, the sum of all these numbers is,

101 ×50

= 5050

Therefore, the sum of numbers from 1 to 100 is 5050.

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Answer:a

Step-by-step explanation:a cult

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The amount they will expect to have in there account at the end of the investment is 44,440.71 dollars.

He grand parents wanted to invest in a bank.

They have $35,000 they are willing to invest for 6 years.

The interest rate is 4% and compounded quarterly.

The amount they will have in there account after 6 years can be calculated as follows:

using compound interest formula,

A = p(1 + r/n)ⁿᵇ

Where

Therefore,

p = 35000

r = 4% = 0.04

n = 4

b = 6

Amount = 35,000(1 + 0.04 / 4)⁴ˣ⁶

Amount = 35,000(1.01)²⁴

Amount = 35,000 × 1.26973464853

Amount = 44440.7126986

Amount = 44440.71 dollars

Therefore, the amount they will expect to have in there account at the end of the investment is 44,440.71 dollars.

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The composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.

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The values of x and measures of angles are:

1. x = 12; m<PQS = 71°; m<PQT = 142°; m<TQR = 41°

2. x = 8; m<GDH = 126°; m<FDH = 200°; m<FDE = 137°

1. Since QS bisects angle PQT, therefore:

measure of angle PQS = measure of angle SQT

Given:

m<SQT = 8x - 25

m<PQT = 9x + 34

m<SQR = 112°

Thus:

m<PQT = 2(m<SQT)

Substitute

9x + 34 = 2(8x - 25)

9x + 34 = 16x - 50

9x - 16x = -34 - 50

-7x = -84

x = 12

m<PQS = m<SQT = 8x - 25

Plug in the value of x

m<PQS = 8x - 25 = 8(12) - 25

m<PQS = 71°

m<PQT = 9x + 34 = 9(12) + 34

m<PQT = 142°

m<TQR = m<SQR - m<SQT [angle addition theorem]

m<TQR = 112 - 71

m<TQR = 41°

2. Given:

m<GDE = 8x - 1

m<EDH = 6x + 15

m<CDF = 43

m<GDE = m<EDH [reason: DE bisects GDH]

Substitute

8x - 1 = 6x + 15

8x - 6x = 1 + 15

2x = 16

2x/2 = 16/2

x = 8

m<GDH = 2(m<GDE)

m<GDH = 2(8x - 1)

m<GDH = 16x - 2 = 16(8) - 2

m<GDH = 126°

m<FDG = 180 - m<CDF - m<GDE

m<FDG = 180 - 43 - (8x - 1)

m<FDG = 180 - 43 - (8(8) - 1)

m<FDG = 180 - 43 - 63

m<FDG = 74°

m<FDH = m<FDG + m<GDH

m<FDH = 74 + 126

m<FDH = 200°

m<FDE = m<FDG + m<GDE

m<FDE = 74 + 63

m<FDE = 137°

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Answer:

x≥2

Step-by-step explanation:

-16≥ -8x

x≥2

Answer:

A

Step-by-step explanation:

70-271=20

Answer: it's 7/10

Step-by-step explanation:

the 49 simplifies to 7, and the 100 simplifies to 10

Answer:

9x³y²

Step-by-step explanation:

To simplify, factorize 81 in powers of 2 ;  x⁶ in powers of 2 and y² in powers of 2.

[tex]\sf \sqrt{81x^6y^2}=\sqrt{9^2 * x^{3*2}*y^2}[/tex]

             [tex]\sf = \sqrt{9^2* (x^3)^2)* y^2}\\\\ = 9 * x^3*y^2\\\\=9x^3y^2[/tex]

The answer is 9cmsquare +5cmsquare equal to =106cm

The slope intercept form of a line is y=mx+c, where m is slope.slope of a line perpendicular to 6x+y=8 is 1/6

The slope intercept form of a line is y=mx+c, where m is slope.

The equation of a line is 6x+y=8.

We need to convert to slope intercept form

y=8-6x

y=-6x+8

where m=-6 is slope of a line.

Two lines are said to be perpendicular when m1m2=-1

m1 is slope of given line and m2 is slope of other line which we have to find.

-6.m2=-1

m2=1/6.

Therefore slope of a line perpendicular to 6x+y=8 is 1/6.

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The solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

It follows from the task content that the solution to the equation is to be determined and expressed in its simplest form.

Given;

-1/2 -1/2(4/5x+1) = -2 -3x

By distributing the coefficients: we have;

-1/2 - 2/5x - 1/2 = -2 -3x

Hence, by collecting like terms; we have;

-1/2 - 1/2 + 2 = -3x + (2/5)x

1 = -13x/5

Therefore; by cross-multiplication; we have;

5 = -13x

Divide both sides by; -13.

x = -5/13.

Ultimately, the solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

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After solving the equation the value of r in 4 r²=3 is [tex]\sqrt{3/4}[/tex].

We have to find r in  4 r²=3

⇒ 4 r² = 3

⇒ r² = 3/4

⇒ r = [tex]\sqrt{3/4}[/tex]

So, r is equal to  [tex]\sqrt{3/4}[/tex]

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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x = 3 and x = 6 is extraneous solution.

√(x+7) +5=x

Subtracting 5 on both sides of the equation

√(x+7) + 5 - 5 = x - 5

√(x+7) = x - 5

Squaring both sides of the equation

(√(x+7))² = (x - 5)²

x + 7 = x² + 25 - 10x

x² - 9x + 18 = 0 ...(1)

By middle term splitting equation (1) can be written as

x² - 6x - 3x + 18 = 0

x(x - 6) -3(x - 6) = 0

(x - 3)(x - 6) = 0

x - 3 = 0 and x - 6 = 0

x = 3, 6

Check extraneous solution by putting the value of x in the original equation, we get

Let x = 3

√(3+7) +5 = 3

✓10 + 5 = 3

which is a contradiction, so, x = 3 is an extraneous solution.

Let x = 6

√(6+7) +5 = 3

✓13 + 5 = 3

which is a contradiction, so, x = 6 is an extraneous solution.

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The ratio of impressions to fans is a measure of fan acquisition.

Given is to find the ratio of impressions to fans.

The ratio of impressions to fans is a measure of fan acquisition. Social marketing campaigns begin with fan acquisition, which involves using any of a variety of means, from display ads to News Feed and page pop-ups, to attract people to your Web page.

Therefore, the ratio of impressions to fans is a measure of fan acquisition.

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-2 is the extraneous solution of the equation.

The equation is:

[tex](x + 3)^{1/2}[/tex] - 1 = x

To find the extraneous solution of the expression first we need to find the value of x.

[tex](x + 3)^{1/2}[/tex] = x + 1

Squaring both sides we have,

[tex](x+ 3)^{}[/tex] = [tex](x + 1)^{2}[/tex]

x + 3 = [tex]x^{2}[/tex] + 2x + 1

[tex]x^{2}[/tex] + x - 2 = 0

[tex]x^{2}[/tex] + 2x - x - 2 = 0

x ( x + 2 ) - 1 (x + 2) = 0

(x+2) (x-1)=0

x = -2, 1

Now we have to put the value of x in the equation:

x = -2

[tex](-2 +3)^{1/2}[/tex] - 1 = -2

1-1 =-2

0≠ -2

x = 1

[tex](1 + 3)^{1/2}[/tex] - 1= 1

2 - 1 = 1

1= 1

Therefore we get x = -2 is as extraneous solution of the equation and x= 1 is the solution of the equation.

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We have a vertical line, so we have an undefined slope.

The general linear equation in the slope-intercept form is given by:

y = m*x + k

Where we define k as the y-intercept and m as the slope.

If we know that the line passes through two points (a, b) and (c, d), then the slope is given by the formula:

m = (d - b)/(c - a)

In this case we have the points (6,-8) and (6,-3), then the slope will give:

m = (-3 + 8)/(6 - 6)

Notice that the denominator becomes zero, so we have a "slope of infinity", thing that happens for vertical lines

Basically, these lines have undefined slopes, so that is the correct answer.

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Answer is B                                                        

because i did it out i dont feel like explaning lol

Both Katie and Ismailia are both correct because 20 is a coefficient and factor of the expression 20xy.

A coefficient is a number multiplied by a variable.

In other word, a coefficient is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial.

A factor is a number that divides another number, leaving no remainder.

Therefore, the coefficient of the expression 20xy is 20.

The factor of the expression 20xy is also 20.

Therefore, Both Katie and Ismailia are both correct.

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Answer:

there both right

Step-by-step explanation:

✔✔✔‍♂️‍♂️‍♀️

Answer:

x=m/2+k , k≠-2

Step-by-step explanation:

2x+kx=m

Factor out x from the expression:

(2+k)x=m

Assume 2+k≠0 and divide both sides of the equation by 2+k:

x=m/2k , 2+k≠0

Rewrite the restriction:

x=m/2+k≠-2

Solution:

x=m/2+k , k≠-2

The value of x in the given expression is x = m / (k+2)

An expression is a mathematical statement containing variables, numerical, and they are related by at least one mathematical operation.

Given an expression, 2x + kx = m

We are asked to rearrange the values and find the value of x.

Therefore,

2x + kx = m

Since, two terms have same variable, therefore, taking x common from both,

x(2+k) = m

x(k+2) = m

Now, transpose (k+2) to right side, we get,

x = m / (k+2)

Hence, we get the value of x as, x = m / (k+2)

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