A restaurant has a sign by the front door that says, "Maximum occupancy: 75 people."

What percentage of its capacity is 84 people?

Answer:

3

Step-by-step explanation:

x x6=18

x=3

Answer:

(18=6 times x)  you would divide both sides by 6 since inverse operations and to leave the x by itself. 18/6 is 3 so 3=x

Given:

In triangle ABC, m∠A=(8x-2)°, m∠B=(2x-8)° and m∠C=(94-4x)°.

To find:

The sides of the triangle ABC in order from shortest to  longest.

Solution:

In triangle ABC,

[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]              (Angle sum property)

[tex](8x-2)^\circ+(2x-8)^\circ+(94-4x)^\circ=180^\circ[/tex]

[tex](6x+84)^\circ=180^\circ[/tex]

[tex]6x+84=180[/tex]

[tex]6x=180-84[/tex]

[tex]6x=96[/tex]

Divide both sides by 6.

[tex]x=\dfrac{96}{6}[/tex]

[tex]x=16[/tex]

Now,

[tex]m\angle A=(8(16)-2)^\circ[/tex]

[tex]m\angle A=(128-2)^\circ[/tex]

[tex]m\angle A=126^\circ[/tex]

Similarly,

[tex]m\angle B=(2(16)-8)^\circ[/tex]

[tex]m\angle B=(32-8)^\circ[/tex]

[tex]m\angle B=24^\circ[/tex]

And,

[tex]m\angle C=(94-4(16))^\circ[/tex]

[tex]m\angle C=(94-64)^\circ[/tex]

[tex]m\angle C=30^\circ[/tex]

In a triangle the smaller angle has shorter opposite side and larger angle has longer opposite side.

[tex]24^\circ<30^\circ<126^\circ[/tex]

[tex]m\angle B<m\angle C<m\angle A[/tex]

[tex]AC<AB<BC[/tex]

List the sides of triangle ABC in order from shortest to  longest is AC:AB:BC.

Therefore, the correct option is A.

Answer:

f(-7)= 21

Step-by-step explanation:

-(-7)^2-10(-7)

-7^2-10×-7

-49-10×-7

-49-(-70)

-49+70

21

Answer:

sm[tex]prism M and Cylinder P\\[/tex][tex]Plato[/tex]

Step-by-step explanation:

Answer:

the second is better deal

the unit rate for the better deal is $4.07

Answer:

The interval of converges of a power series is the interval of input values for which the series converges.

Step-by-step explanation:

Answer:

3i

Step-by-step explanation:

3i x 3i = -9

-3i x -3i = -9

Therefore the square root of -9 is 3i or -3i

The simplified radical expression ±√(-9) is ±3i

The expression ±√(-9) involves finding the square root of a negative number. In the real number system, this is not possible, as no real number multiplied by itself will result in a negative value. To overcome this limitation, mathematicians introduced the concept of imaginary numbers. The imaginary unit, denoted by 'i,' is defined as √(-1).

Now, let's simplify the expression ±√(-9) step by step:

Step 1: Begin by recognizing that √(-9) is the square root of -9.

Step 2: Since √(-1) is 'i,' we can rewrite √(-9) as √(9) * √(-1).

Step 3: The square root of 9 (√9) is 3.

Step 4: Replace √(-1) with 'i.'

Step 5: The final result is 3i.

Therefore, the simplified form of ±√(-9) is ±3i.

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Answer:

A- Brady multiplied the first equation by 5 and the second equation by 3.

B- He can use elimination for his next step. 15y and -15y will cancel each other out, 20x-18x is 2x...50-48 is 2 so 2x=2 divide and x is 1

C- x=1 y=2

Step-by-step explanation:

Answer:

I am not sure about this question but u guess its c

Answer:

6

Step-by-step explanation:

3 - 5 = -2

4 - (-2) = 6

When subtracting a negative from a positive number you add them together to get you sum or difference.

Answer:

1250 m²

Step-by-step explanation:

Let x and y denote the sides of the rectangular research plot.

Thus, area is;

A = xy

Now, we are told that end of the plot already has an erected wall. This means we are left with 3 sides to work with.

Thus, if y is the erected wall, and we are using 100m wire for the remaining sides, it means;

2x + y = 100

Thus, y = 100 - 2x

Since A = xy

We have; A = x(100 - 2x)

A = 100x - 2x²

At maximum area, dA/dx = 0.thus;

dA/dx = 100 - 4x

-4x + 100 = 0

4x = 100

x = 100/4

x = 25

Let's confirm if it is maximum from d²A/dx²

d²A/dx² = -4. This is less than 0 and thus it's maximum.

Let's plug in 25 for x in the area equation;

A_max = 25(100 - 2(25))

A_max = 1250 m²

my name is jeff   Step-by-step explanation:

The answer is b bbbbbbbbbbbbbbb

Answer:

The answer is B

Step-by-step explanation:

I hope this helps! :D

Answer:

g(3a – 6) = a - 4

Step-by-step explanation:

g(x) = 1/3x - 2

g(3a – 6) = 1/3(3a – 6) - 2

= a - 2 - 2

= a - 4

Answer:

g(3a - 6) = a - 4

Step-by-step explanation:

If you start with g(x) = 1/3 x - 2

Then whatever x = on the left, must take on the value on the right.

g(3a - 6) = 1/3 (3a - 6) - 2     Notice the x is gone and 3a - 6 has taken it's place.

Now you must distribute the 1/3 for both 2a and 6

g(3a - 6) = 1/3 * 3a - 1/3 * 6 - 2

g(3a - 6) = a - 2 - 2

g(3a - 6) = a - 4

Answer:

180º

Step-by-step explanation:

All the interior angles add up to 180º degrees.

Answer:

180 degrees

Step-by-step explanation:

In a Euclidean space, the sum of angles of a triangle equals the straight angle

Answer:

Claire has 16 stamps

Step-by-step explanation:

Proportions

If two variables are proportional, their ratio is constant. For example, the distance traveled by car is proportional to the time it travels at a constant speed. We write it as d:t=constant.

It's known the number of Claire's stamps to the number of John's stamps is 2:3 and John has 24 stamps.

This means the following relation must stand:

[tex]\displaystyle \frac{C}{J}=\frac{2}{3}[/tex]

Where C is the number of stamps of Claire and J is the number of stamps of John. We know J=24, thus:

[tex]\displaystyle \frac{C}{24}=\frac{2}{3}[/tex]

Solving for C:

[tex]\displaystyle C=24\cdot\frac{2}{3}[/tex]

C = 16

Claire has 16 stamps

Answer:

Simplifying then comparing both terms

−5 and −3, −5 is less than −3, which means that the first term is less than the second term.  −5 < −3

Step-by-step explanation:

Hope this helps have a good day^^

Answer:

The greatest y-intercept c = 6

Step-by-step explanation:

we know that

        slope-intercept form y = mx +c

a) Given that  f(x) = [tex]6x + \frac{1}{6}[/tex]

                       [tex]y = 6x + \frac{1}{6}[/tex]

   comparing    y = mx +c

  slope of the line m = 6 and Y - intercept c= 1/6

b)    Given that  f(x) = [tex]6x -6[/tex]

                        y = 6x -6

   comparing    y = mx +c

  slope of the line m = 6 and Y - intercept c= -6

c)

    Given that  f(x) = [tex]\frac{1}{6} x +6[/tex]

                        y =  [tex]\frac{1}{6} x +6[/tex]

   comparing    y = mx +c

  slope of the line m =  [tex]\frac{1}{6}[/tex]  and Y - intercept c= 6 ( greatest intercept)

d)

 Given that  6 k(x) = x

                     k(x) = [tex]\frac{1}{6} x[/tex]

                        y = [tex]\frac{1}{6} x[/tex]

   comparing    y = m x +c

 The slope of the line m =[tex]\frac{1}{6}[/tex]  and Y-intercept c=0

Final answer:-

The greatest y-intercept c = 6

Answer:

C. h(x)=1/6x+6

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

5 = 3x - 4

9 = 3x

x = 3

Answer:

They're both the same

Answer:

70.24 is less then 70.240

Step-by-step explanation:

please follow me

-2x + 6 + 6x = 6 (2x - 3) this is the equation

-2x + 6 + 6x = 12x - 18 distributive property has been applied

4x + 6 = 12x - 18 like terms have been added

6 = 8x -18 4x has been subtracted from both sides

24 = 8x -18 has been added to both sides

3 = x 8 has been divided from both sides

I hope this helps! Let me know if I need to explain more or if I got something wrong. Have a nice day!

Answer:

[tex]\frac{dr}{dh} =-\frac{r}{2h}[/tex]

Step-by-step explanation:

The volume of a cylinder is given by the formula:

V = πr²h,

Where V is the volume, r is the radius of the cylinder and h is the height of the cylinder.

We are to express the rate of change of the radius of the clay with respect to the height of the clay in terms of height h and radius r.

That means we express dr / dh in terms of height h and radius r. To do this, we have to first differentiate the volume with respect to the height, i.e. find dV / dh:

V = πr²h

[tex]\frac{dV}{dh}= \frac{d}{dh} (\pi r^2h)\\\\\frac{dV}{dh}= \pi r^2 + 2\pi rh \frac{dr}{dh} \\\\The\ volume\ is\ constant\ hence\ \frac{dV}{dh}=0.\ We\ get\ that:\\\\0= \pi r^2 + 2\pi rh \frac{dr}{dh}\\\\- \pi r^2 =2\pi rh \frac{dr}{dh}\\\\ \frac{dr}{dh}=-\frac{\pi r^2}{2\pi rh}\\\\ \frac{dr}{dh}=-\frac{r}{2h}[/tex]:

Answer:

0.00175

Step-by-step explanation:

Answer:

a. 76 cm

b. 16 in.

c. 225 cm

Step-by-step explanation:

a. Converting 30 inches to centimetres:

When y(inches) = 30, x (centimetres) = 76

So, 30 in. = 76 cm

b. When x (cm) = 40, y (in.) = 16

So, 40 cm = 16 in.

c. Given that a fence is 7 ft 6 in. high, and 1 ft = 12 in., to find the height of the fence in cm, first convert the height to in.

Convert 7ft to inches:

If 1 ft = 12 in., then,

7 ft = 7*12 = 84 inches

The height of the fence in inches = 84 + 6 = 90 inches

Using the graph, find the unit rate using any point on the line, say (100, 40):

Unit rate = y/x = inches/centimeters =

Unit rate (m) = 40/100 = ⅖

Write an equation for the line:

To do this, substitute m = ⅖ into y = mx

Equation: y = ⅖x

Let's convert the height of the fence, 90 inches, to centimetres:

To convert to cm, substitute y = 90 into y = ⅖x

Thus:

90 = ⅖*x

5*90 = 2x

450 = 2x

Divide both sides by 2

450/2 = x

225 = x

Height of the fence in cm = 225 cm

Answer:

y=0x-1

Step-by-step explanation:

y=0(x)+c

-1=0(7)+c

-1=0+c

C=-1

Answer:

Let the amount of water at beginning be x

x-1.5-0.750-2.250=1

x=5.5 litre

Step-by-step explanation:

Therefore there was 5 litre 5 mililters of water in the pail.

Answer:5500 ml or 5.5 liters

Step-by-step explanation:

First, we should note that there are 1000 milliliters in 1 liter of liquid.

So, in milliliters, Peter filled three containers with 1500 ml, 750ml, and 2250 ml with 1000ml left over.

To find the total amount, we find the sum of all the milliliters:

1500 + 750 + 2250 + 1000 = 5500 ml

Again, we know that there are 1000 milliliters in 1 liter of liquid, so:

= 5.5 liters

Answer:

Radius, r = 26.57 cm and diameter = 53.14 cm

Step-by-step explanation:

Given that,

The circumference of a coin, C = 167 cm

We need to find the radius and the diameter of the coin.

The formula for the circumference of a circle is given by :

[tex]C=2\pi r[/tex]

Where

r is radius of coin

[tex]r=\dfrac{C}{2\pi}\\\\r=\dfrac{167}{2\pi}\\\\r=26.57\ cm[/tex]

Diameter, d = 2r

d = 2(26.57) cm

= 53.14 cm

Hence, this is the required solution.

Answer:

3 3/5 as an improper fraction = 18/5

Answer:

18/5

Step-by-step explanation:

To find the improper fraction change the whole number into a fraction:

3 *5/5 = 15/5 which is the same as 3

then add the remaining 3/5 to the fraction

15/5 + 3/5

= 18/5

Answer: B

Step-by-step explanation:

Fourth diagram represent the 14x²+21x in factored form is 7x(2x + 3)

A number system is defined as a system of writing to express numbers.

The given expression is 14x²+21x

Fourteen x square plus twenty one times of x.

x is the variable and plus is the operator.

14x²+21x

We need to take 7x as common from two terms.

When the quadratic expression is a product of two factors where each one is a linear expression, this is called the factored form.

Seven x is product of two times of x plus three.

7x(2x+3)

The fourth diagram represent the 14x²+21x in factored form is 7x(2x + 3)

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