(h) Three meals per day are provided by the hotel. The hotel will charge a total of $9,240 for all meals for the entire group. What is the cost of meals for each person?

After completing the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we find that the possible result is [tex]\((x + 6)^2 = 49\)[/tex].

To complete the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we follow these steps:

1. Take half of the coefficient of the [tex]x[/tex] term, which is [tex]\(12/2 = 6\)[/tex].

2. Square this result, [tex]\(6^2 = 36\)[/tex].

3. Add this value, 36, to both sides of the equation to maintain balance:

[tex]\[x^2 + 12x + 36 - 85 = 36 - 85.\][/tex]

4. Simplify both sides of the equation by combining like terms:

  [tex]\[(x + 6)^2 - 49 = 0.\][/tex]

5. Rearrange the equation to isolate the perfect square term:

 [tex]\[(x + 6)^2 = 49.\][/tex]

From this process, we can conclude that the equation [tex]\((x + 6)^2 = 49\)[/tex] could be the result of completing the square for the given equation [tex]\(x^2 + 12x - 85\)[/tex]. This equation represents a perfect square trinomial with a perfect square term, and it allows us to solve for the value of [tex]x[/tex] by taking the square root of both sides.

It's important to note that completing the square allows us to rewrite quadratic equations in a form that reveals key properties and facilitates solving for unknowns.

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Answer:

Step-by-step explanation:

PEMDAS (order in which to do operations)

P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction

there are no parentheses so skip that

5^2 is an exponent so do that first

3x10 + 3x5^2 + 3 -->    3 x 10 + 3 x 25 + 3

Next, do multiplication/division operations from left to right

3 x 10 + 3 x 25 + 3 -->    30 + 75 + 3

Finally, do the addition operations

30 + 75 + 3 = 108

final answer: 108

Answer: attached in image, look at both

Step-by-step explanation:

The amount Sam needs to pay in each installment is $141.1

From the question, we have the following parameters that can be used in our computation:

Cost of refrigerator = 1058

Down payment = 211.40

Number of equal installments = 6

Using the above as a guide, we have the following:

Each installment = (Cost of refrigerator - Down payment)/Number of equal installments

substitute the known values in the above equation, so, we have the following representation

Each installment = (1058 - 211.40)/6

Evaluate

Each installment = 141.1

Hence, the amount in each installment is $141.1

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The value of the limit of the function f(x) = x² - 2 is 7.

The value of the limit of the function f(x) = -3x + 15 is -6.

We have,

To evaluate the limit as x approaches 3, we need to find the limit of function f(x) as x approaches 3 from both sides of 3.

First, let's evaluate the limit from the left side of 3:

lim x → 3⁻ f(x) = lim x → 3⁻ (x^2 - 2)

Substituting x = 3 - h (where h approaches zero) gives:

lim h → 0⁺ [(3 - h)^2 - 2]

= lim h → 0⁺ [9 - 6h + h^2 - 2]

= lim h → 0⁺ [h^2 - 6h + 7]

= 7

(since the limit of a quadratic function as h approaches zero is the constant term)

Next, let's evaluate the limit from the right side of 3:

lim x → 3⁺ f(x)

= lim x → 3⁺ (-3x + 15)

= -6

Since the limit from the left side is not equal to the limit from the right side, the limit of f(x) as x approaches 3 does not exist.

Thus,

The value of the limit of the function f(x) = x² - 2 is 7.

The value of the limit of the function f(x) = -3x + 15 is -6.

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The remaining credit after 91 minutes of calls is $16.76.

We are given that;

(24, 22.12) and (63, 17.44)

Now,

To find the slope and the y-intercept of the function. You can write your solution as:

Slope = (y2 - y1) / (x2 - x1) = (17.44 - 22.12) / (63 - 24) = -0.08 y-intercept = y - mx = 22.12 - (-0.08)(24) = 24.04 Equation: y = -0.08x + 24.04

To find the remaining credit after 91 minutes of calls, you need to substitute x = 91 in the equation and simplify. You can write your answer as:

y = -0.08(91) + 24.04 y = -7.28 + 24.04 y = 16.76

Therefore, by the intercept the answer will be $16.76.

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Measure of one exterior angle = 30 degree

Measure of one interior angle = 150 degree

In the given regular pentagon

Number of terms = 12

We know that,

Sum of all exterior angles = 360 degree

To find one exterior angle,

Divide the complete angle by number of terms

Therefore,

One exterior angle = 360/12  =  30 degree

Since,

Sum of all interior angles = 180 degree

And To find one interior angle,

subtract the interior  angle by one exterior angle

Therefore,

One exterior angle = 180 - 30  =  150 degree

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The height of the kite off the ground is approximately 17.87 feet rounded to two decimal places.

To solve the problem can use similar triangles.

Let's draw a diagram:

     A

      |\

      | \

   h |   \   x

      |      \

      |____\

       d   B

Point A represents the kite, point B represents the tip of the kite's shadow on the ground and point D represents the point directly below the spool of string on the ground.

The height of the kite represented by h.

The length of the string is 42.9 feet so the distance from point A to point D is also 42.9 feet.

The distance from point B to point D is 16.5 feet.

These two lengths to find the length of segment AB:

AB/AD = BD/AD

AB/42.9 = 16.5/42.9

AB = 16.5

So AB is 16.5 feet.

Now we can use the similar triangles to find h.

We have:

h/x = AB/AD

h/x = 16.5/42.9

h = x × 16.5/42.9

We need to find x.

The spool of string is 3.4 feet above the ground and we know that the kite is directly above the spool when it is at its highest point in the sky.

So the height of the kite above the ground is the same as the height of the spool above the ground plus the length of string that has been let out:

x = 3.4 + 42.9

= 46.3

Now we can substitute this value of x into the previous equation to find h:

h = 46.3 × 16.5/42.9

= 17.87

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volume: 2,160cm

please let me know if this was what you needed or if it was something else.

The break-even point would be when the cost is equal to 44 dollars.

Option B is the correct answer.

We have,

The break-even point represents the point at which the cost equals the revenue or the point where there is no profit or loss.

Now,

In this case, if the graph represents the cost (dollars) on the y-axis and units on the x-axis, the break-even point occurs when the cost is equal to the revenue or total sales.

Given that two lines intersect at (11, 44),

The break-even point would be when the cost is equal to 44 dollars.

Thus,

The break-even point would be when the cost is equal to 44 dollars.

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Answer:

2 forms

Step-by-step explanation:

hope this helps <3

[tex] \sf \longrightarrow \: \frac{8}{5} \div 6 \\ [/tex]

[tex] \sf \longrightarrow \: \frac{5}{8} \times 6 \\ [/tex]

[tex] \sf \longrightarrow \: \frac{5 \times 6}{8} \\ [/tex]

[tex] \sf \longrightarrow \: \frac{30}{8} \\ [/tex]

[tex] \sf \longrightarrow \: \frac{8}{30} \\ [/tex]

[tex] \sf \longrightarrow \: 0.26 \\ [/tex]

_____________________________

After analysing the given data we conclude that the probability that Dina will randomly choose that is not green and change it and again randomly choose a marble that is yellow is 17.5%.

The given  probability of Dina drawing a green marble is 30%. Then, the probability of her not drawing a green marble is 70%. It can be said that  probability of her drawing a yellow marble is 25%. Hence, the probability of her not drawing a yellow marble is 75%.
The probability of Dina drawing a marble that is not green and then replacing it is
70% × 100% = 70%.
The probability of her then drawing a yellow marble is 25%. Therefore, the probability of Dina randomly drawing a marble that is not green, replace it, then randomly draw a yellow marble is
70% × 25% = 1750
 1750× 100 = 17.5%.
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1. The product of MG is as follows;

[tex]\left[\begin{array}{ccc}1&k_1+9&4k_2+36 \\2t_1&k_1t_1-17&3k_2-19t_1-11\\t_2+1&k_1-4t_2+5&k_2t_2-8\end{array}\right][/tex]

2. The values are k₁ = -9, k₂ = -9, t₁ = 0 and t₂ = -1 given that G = M⁻¹

Matrix M and matrix G are given as

M = [1, 4, 5; t₁, 3, -1; 1, t₂, 1] and

G = [2, k₁, -19; 1, -4, k₂; -1, 5, 11]

MG becomes

1×2 + 4×1 + 5×-1         1k₁+4×-4+ 5×5       1×-19+4k₂+5×11

t₁×2+3×1+-1×-1             t₁k₁+3×-4+-1×5       t₁×-19+3k₂+-1×11

1×2+t₂×1+1×-1               1k₁+t₂×-4+-1×5        1×-19+t₂k₂+1×11

=

1             k₁+9         4k₂+36

2t₁          k₁t₁-17        3k₂-19t₁-11

t₂+1        k₁-4t₂+5      k₂t₂-8

To solve G = M⁻¹ we know it is an identity matrix

I = | 1 0 0 |

    | 0 1 0 |

    | 0 0 1 |

We can equate the elements of MG and I to find the values of t₁, t₂, k₁, and k₂:

1 = 1,         k₁+9 = 0,       4k₂+36 = 0

2t₁ = 0     k₁t₁-17 = 1        3k₂-19t₁-11 = 0

t₂+1 = 0     k₁-4t₂+5 = 0   k₂t₂-8 = 1

k₁+9 = 0           4k₂+36 = 0            2t₁ = 0          t₂+1 = 0

k₁ = -9                 k₂ = -9                   t₁ = 0           t₂ = -1

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a) The first mistake that Fatima made was in the first step.

b) She incorrectly changed the place value of 0.02 in the subtraction operation.

c) Based on the correct subtraction operation and place value in step one, Fatima has 0.395 kilograms of rose petals left.

The place value shows the position of a digit in a number.

The right place values are essential for correct mathematical operations.

The quantity of rose petals that Fatima bought initially = 0.454 kilograms

The quantity of rose petals used for making rose water = 0.02 kilograms

The remaining quantity of rose petals = 0.434 (0.454 - 0.02)

The additional quantity of rose petals Fatima bought = 0.056

The quantity of rose petals used for making the second rose water = 0.095

The quantity of rose petals left = 0.395 (0.434 + 0.056 - 0.095)

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Answer: yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

What is the Formula for Calculating the Square Root of a Number? The square root of any number can be expressed using the formula: √y = y½. In other words, if a number has 1/2 as its exponent, it means we need to find the square root of the number.

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number.

The square root of a number "a" is denoted by the symbol "√a" or "a^(1/2)." For example, the square root of 9 is 3 because 3 * 3 = 9.

1) Note that the population mean is 153.

2) there are 36 possible random samples of size two that can be selected from a population of nine.

1) Population Mean = (172 + 148 + 156 + 170 + 161 + 138 + 142 + 156 + 134) / 9

= 1377 / 9

Population Mean = 153

2) To get the number of possible random samples, we must use Combination whose equation is given as

nCr = n! / (r! (n-r)!)

nC2 = 9! / (2!(9-2)!)

= 9! / (2! 7!)

= (9 x 8 x 7!) / (2!7!)

= (9 x 8) / 2

= 36

Thus, the number of random samples that can be selected form a population of 9 is 36.

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[tex]w^2 - 6w + 4[/tex] is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.

The profit earned by selling w pear trees is 2w + 10

To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:

[tex](w^2 - 4w + 14) - (2w + 10)[/tex]

Simplifying the expression:

[tex]w^2 - 6w + 4[/tex]

Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is [tex]w^2 - 6w + 4[/tex].

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The equation of the quadratic function C(t) is given as follows:

C(t) = t² + 3.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The vertex is the turning point of the function, where it changes from decreasing to increasing, or vice versa, hence:

(0,3).

Then:

y = at² + 3.

When x = 1, y = 4, hence the leading coefficient a is obtained as follows:

4 = a(1)² + 3

a = 1.

Hence the function is given as follows:

y = t² + 3.

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Answer:

7

Step-by-step explanation:

yw ;)

Step-by-step explanation:

"Range'' is the values of 'y' that a graph can have....there are no limits on this one

(-∞,+∞)

Answer:

The correct answer is D. 56x^2.

Answer:

16 in

Step-by-step explanation:

50 ft x 12 in/ft = 600 in

Scale factor:  2 : 600 = 1 : 300

x = length of island on the map

400 ft = 4800 in

1/300 = x/4800

x = 4800/300 = 16 in

Answer:

Step-by-step explanation:

In the figure, AB is a diameter, and AB⊥CD, If m AC = 54°, BD is 36°. Option A

In a circle, a diameter divides it into two equal parts and forms a straight line that measures 180°.

Given that AB is a diameter = 180°.

AB is perpendicular to CD, therefore m∠AC + m∠BD = 90°.

Substituting m∠AC =54°, we get m∠BD + 54°  = 90°.

Solving for m∠BD, we get 90° - 54° = 36°.

There BD is 36°.

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Answer: Centre: (-2,5)

Radius = 3

so

Diameter = 6

Domain: (-5,1)

Range: (2,8)

Answer:

center (-2,5)

radius =3

domain = -5< x <1

range 2 <y<8

Step-by-step explanation:

siiuu

Answer:

301.59289cm²

Step-by-step explanation:

An equation that can be used to find the value of x include the following: 110° + 7x = 180°.

In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are supplementary angles:

110 + 7x = 180°

7x = 180° - 110°

7x = 70°

x = 70°/7

x = 10°

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Step-by-step explanation:

She walks the entire CIRCUMFERENCE of the circle

circumference = pi X diameter

                       = pi X 14 ft = 43.98 ft  = ~ 44 ft (rounded)