Hometown Buffet has tables that can seat 6 people and booths that can seat 4 people. The restaurant has 38 seating units for seating a total of 188 people. How many tables and booths are at the restaurant?

The area of the rhombus is a rational number, specifically 5/12, which can be expressed as a fraction. Therefore, we can conclude that when d1 is a terminating decimal and d2 is a repeating decimal, the area of the rhombus can be expressed as a rational number.

When d1 is a terminating decimal and d2 is a repeating decimal, we can conclude that the area of the rhombus can be expressed as a rational number.

To see why, consider the formula for the area of a rhombus: A = (1/2)d1d2. If d1 is a terminating decimal, it can be expressed as a finite fraction.

For example, if d1 = 1.25, then d1 can be expressed as 5/4. If d2 is a repeating decimal, it can be expressed as an infinite series of the form:

d2 = a + b/10 + c/100 + ...

where a, b, c, etc. are digits. We can express this as a fraction by multiplying both sides by a power of 10 which eliminates the repeating decimal. For example, if d2 = 0.666..., we can multiply both sides by 100 to get:

100d2 = 66.666...

Subtracting d2 from both sides, we get:

99d2 = 66

So, d2 = 66/99, which can be simplified to 2/3.

Substituting these values into the formula for the area of the rhombus, we get:

[tex]A = (1/2)(5/4)(2/3)\\= 5/12[/tex]

So, the area of the rhombus is a rational number, specifically 5/12, which can be expressed as a fraction. Therefore, we can conclude that when d1 is a terminating decimal and d2 is a repeating decimal, the area of the rhombus can be expressed as a rational number.

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Answer:

The point is (-2, -3)

Step-by-step explanation:

Given function:

[tex]f(x)= (x+2)^2-3[/tex]

For: [tex]f(x)=y[/tex] and [tex]x=-2[/tex]

[tex]f(-2)= (-2+2)^2-3\\f(-2)= (0)^2-3\\f(-2)= -3\\[/tex]

∴[tex]y=-3; x=-2[/tex]

Answer:

n = 18

Step-by-step explanation:

2n - 5 = 31

Add 5 to each side

2n - 5+5 = 31+5

2n = 36

Divide each side by 2

2n/2 = 36/2

n = 18

Answer:

x = -1, x = 3  (B)

Step-by-step explanation:

25ˣ=5ˣ²⁻³

Can be simplified to:

5²ˣ=5ˣ²⁻³

2x=x²-3

x²-2x-3=0

(x-3)(x+1)

x = -1, x = 3

Plz mark my answer as brainiest

Answer:

B  x=-1   x=3

Step-by-step explanation:

25^x = 5 ^ (x^2 -3)

Replace 25 by 5^2

5^2^x = 5 ^ (x^2 -3)

We know that a^b^c = =a^(b*c)

5^(2x) = 5 ^ (x^2 -3)

The bases are the same so the exponents must be the same

2x = x^2 -3

Subtract 2x from each side

2x-2x = x^2 -3 -2x

0 = x^2 -2x-3

Factor

0 =(x-3) (x+1)

Using the zero product property

x-3 =0       x+1 =0

x=3             x=-1

A)

Number of Gallons drained per hour; Number of hours (Independent Variables)

Number of Gallons in the pool (Dependent Variable)

B) -25 (It's the negative value of how many gallons are drained in an hour)

C)13000 (It means how many gallons were in the pool to begin with)

D)3000 (It's the corresponding value for 40 as the x-value)

Answer:

This is the completed table:[tex]\left[\begin{array}{ccccccccccc}trapezoids&1&2&3&4&5&6&10&18&n\\perimeter&10&16&22&28&34&40&64&112&6n+4\end{array}\right][/tex]

for the words and graph please see below and the attached image.

Step-by-step explanation:

Notice that every time you add a trapezoid in the given fashion (attached to the right of the previous figure) yo are adding a net of 6 units (2+4) to the total perimeter (which started in the first figure as 2+2+2+4 = 10).

We can then write the following values to complete the given table:

1 trapezoid , gives perimeter = 1*4 + 3*2 = 10

2 trapezoids, give perimeter = 2*4 + 4*2 = 16

3 trapezoids, give perimeter = 3*4 + 5*2 = 22

4 trapezoids, give perimeter = 4*4 + 6*2 = 28

5 trapezoids, give perimeter = 5*4 + 7*2 = 34

6 trapezoids, give perimeter = 6*4 + 8*2 = 40

10 trapezoids, give perimeter = 10*4 + 12*2 = 64

n trapezoids, give perimeter = n*4 + (n+2)*2 = 4n + 2n + 4 = 6n + 4

Now, given this general relationship for "n" trapezoids, one can find the number of trapezoids that render a perimeter = 112, as required in the table:

6n + 4 = 112

then 6n = 112 - 4 = 108

then n= 108/6 = 18

so 18 trapezoids give a perimeter of 112 (to complete that missing value in the table).

Now, we can plot a general function of similar form of that we got for a collection of n trapezoids but using "x" instead of "n" and having clear in our mind that the values we want to use are only positive integers greater than zero to represent the number of trapezoids:

f(x) = 6x +4

See attached image were the actual valid points are marked as blue dots.

Answer:

25 and 30

Step-by-step explanation:

because one angle measures 280 and the other 25 you add it.

280 + 25 = 305

Since there is 360 degrees in a quadrilateral you subtract

360 - 305 = 55

the other 2 measures are in the ratio of 5:6

So add those to ratios 5 + 6 = 11

55/11 = 5

multiply it by the ratio

5 * 5 = 25

5 * 6 = 30

Answer:

The solved problem is in the photo. Hope it helps.

The value of a, b, and c is 25, -20, and 4 respectively. Then the value of the expression will be 41.

Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.

If (5x - 2)² = ax² - bx + c.

Then the value of the expression will be a + c²

Open the bracket, then we have

(5x - 2)² = 25x² - 20x + 4

Then the value of the a, b, and c will be

a = 25, b = -20, c = 4

Then the value of the expression a + c² will be

→ 25 +4²

→ 41

More about the Algebra link is given below.

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Answer: 24

Step-by-step explanation:

Lowest common multiple means the lowest number that can be divisible by 8,12,3

Looking at this, let's pick 8&3 first

8×3=24

12×3=36

12×8=96

Looking at this value,24 seems to be the lowest,

Therefore the lowest common multiple is 24

Answer:

3/7

Step-by-step explanation:

Answer:

11:45 AM

Step-by-step explanation:

We have that in one hour the body temperature decreased

went down in

81.7 - 80.2 = 1.2

i.e. 1.2 degrees.

Normal body temperature is 98.6 degrees.

The difference between normal and 11 pm is 98.6-81.7 = 16.9

i.e. 16.9 degrees

now to know how much it decreases every hour:

16.9/ 1.5 = 11.26, that is 11 hours and 15 minutes (1/4 of an hour)

If that was 11:00 PM - 11:15 minutes, the murder was at 11:45 AM

Final answer:

To determine the time of death using body temperature changes from normal to discovered levels, applying physics principles is essential.

Explanation:

The time of death for the old man can be determined by calculating the rate at which body temperature decreases from the normal level to the discovered level. In this case, we have a normal body temperature of 37°C, a discovered temperature of 28°C, and subsequent temperatures of 24°C and 0°C. Using the information provided, the time of death for the old man was approximately 10:00 PM.

This calculation is based on the rate of body temperature decrease from the point of discovery to the hospital, considering the normal body temperature, room temperature, and the temperatures recorded during the investigation. This scenario demonstrates the application of physics principles in forensic investigations to determine the time of death based on body temperature changes.

The net change of Franklin's account is 10.

Subtraction is a fundamental arithmetic operation that involves finding the difference between two numbers. It is denoted by the minus sign (-). To subtract one number from another, align the digits according to place value and subtract each column, starting from the rightmost column

To find the net change of Franklin's account, we need to evaluate the expression |35| - |-25|.

The absolute value of 35 is 35, and the absolute value of -25 is 25.

Subtracting these values, we have 35 - 25 = 10.

Therefore, the net change of Franklin's account is 10.

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Answer:

62.8

Step-by-step explanation:

d=10

10x3.14

31.4

31.4x2

62.8 is the perimeter

The compound interest on 2000 is 60.

Step-by-step explanation:

Given,

Principal (P) = 2000

Rate of interest (r) = 3%

Time (T) = 1 years

To find the interest calculated compound in 1 year.

Formula

Amount = P[tex](1+\frac{r}{100} )^{T}[/tex]

Putting the given values we get,

Amount = 2000[tex](1+\frac{3}{100} )^{1}[/tex]

= 2060

So,

The interest = 2060-2000 = 60

Answer:

d

Step-by-step explanation:

i got it right

Answer:

the median, because it decreases the influence of outliers

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

B because an admission is a constant.

Answer:

C=1.50x+12

Step-by-step explanation:

1 ride with admission is $13.50

2 rides with admission is $15.00

3 rides with admission is $16.50

4 rides with admission is $18.00

It's $1.50(x) difference between each total cost(c) letting us know that is the cost for 1 ticket meaning it cost $12.00 for admission.

Answer:

The first one is c.

The second one is a.

third is 272.83 and -272.83

fourth is a

Step-by-step explanation:

your welcome

Answer:

8 = 104 - 3x

Step-by-step explanation:

Answer:

A U C = {2,3,5,6,7,9,11}

Step-by-step explanation:

A = {2,3,5,6,7,9,11}

C = {3,5,6,7}

The union of two sets is a set that has every element that belongs to one or the other set.

A U C = {2,3,5,6,7,9,11}

The volume of a sphere with a radius of 5 inches is 523.6 cubic inches.

To find the volume of a sphere, you can use the formula V = (4/3)πr³, where V represents the volume and r represents the radius.

In this case, the radius is given as 5 inches. So we substitute 5 into the formula:

V = (4/3)π(5)³

Simplifying the expression:

V = (4/3)π(125)

Finally, we calculate the volume:

V = 523.6 cubic inches

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Answer:

64 pi

Step-by-step explanation:

lmk if you need an explanation

Answer:

[tex]64\pi[/tex]

Step-by-step explanation:

The area of a circle can be found using:

[tex]a=\pi r^{2}[/tex]

We have the circumference, but we need the radius. Circumference can be found using:

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

We know the circumference is 16[tex]\pi[/tex], so we can substitute that in for c

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

We need to solve for r, or the radius. To do this, divide both sides by 2[tex]\pi[/tex]. This will get r by itself.

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

8=r

Now we know the radius, and can substitute it into the area formula

[tex]a=\pi r^2[/tex]

Substitute 8 in for r

[tex]a=\pi 8^2[/tex]

[tex]a=64\pi[/tex]

This answer is expressed in terms of pi, since it includes pi in the answer. Therefore, the area, in terms of pi is [tex]64\pi[/tex]

Answer:

495760

Step-by-step explanation:

Answer:

495760

Step-by-step explanation:

add 2 to 8

Answer:

A. -8, infinity

Step-by-step explanation:

2020 edg

Using quadratic function concepts, it is found that the function is decreasing over the interval (-8, infinity).

The equation of a quadratic function, of vertex (h,k), is given by:

[tex]y = a(x - h)^2 + k[/tex]

In which a is the leading coefficient, determining the behavior of the function as follows.

In this problem, the equation is given by:

[tex]f(x) = -(x + 8)^2 - 1[/tex]

Hence the coefficients are a = -1 < 0, h = -8, k = 1, meaning that the function is decreasing over the interval (-8, infinity).

More can be learned about quadratic function concepts at https://brainly.com/question/24737967

Answer: x = 5

Step-by-step explanation:

[tex]-2x+6x-8=12\\4x-8=12\\4x=20\\x=\frac{20}{4}\\ x=5[/tex]

Answer:

c.

Step-by-step explanation:

All of the things are correct with this one.

Hope this will help u....

Answer:

0

Step-by-step explanation:

2x+4

x= -4/2

x= -2

2(-2)+4

-4+4

= 0

We can see here that the area of the sidewalk surrounding the circular garden is approximately 216.66 ft².

To find the area of the sidewalk surrounding the circular garden, we need to calculate the difference between the area of the larger circle and the area of the smaller circle.

The radius of the circular garden is given as 10 ft. The radius of the garden plus the sidewalk is equal to the sum of the radius of the garden and the width of the sidewalk. Since the width of the sidewalk is 3 ft, the radius of the larger circle (including the sidewalk) is 10 + 3 = 13 ft.

Now, let's calculate the area of the larger circle using the formula A = πr², where A represents the area and r represents the radius. Substituting the values, we have A = 3.14 × (13)² = 3.14 × 169 = 530.66 sq ft.

Next, we calculate the area of the smaller circle (just the garden) using the same formula. A = 3.14 × (10)² = 3.14 × 100 = 314 sq ft.

Finally, we subtract the area of the smaller circle from the area of the larger circle to find the area of the sidewalk. 530.66 - 314 = 216.66 sq ft.

Therefore, the area of the sidewalk surrounding the circular garden is approximately 216.66 square feet.

The complete question is:

A sidewalk that is 3 ft wide surrounds a circular garden with a radius of 10 ft. What is the area of the side walk? use pi=3.14

Answer:

$80

Step-by-step explanation:

25% is 1/4 of a whole with 75% of the cost left over, so $60 is 1/3 of the price. divide 60 by 3=$20, $20 discounted, original price $80