On Monday you sent x number of text messages. On Tuesday you sent twice as many. On Wednesday you sent 12 more texts than you sent on Tuesday. On Thursday you sent half as many as you sent on Wednesday. Which expression represents the number of text messages you sent on Tuesday? Which expression represents the number of text messages you sent on Wednesday? Which expression represents the number of text messages you sent on Thursday?

Answer:

16 years, 13 years

Step-by-step explanation:

Let their ages be x, 29-x

Equation formed:-

(x - 7) + 4 = 29 - x

→ 2x = 29 + 3

→ x = 16 years

Answer: 16 years, 13 years

Answer:

answer is b

Step-by-step explanation:

The preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of the new long-distance aircraft is approximately $700 million.

To estimate the cost of building a 600-MW fossil-fuel plant, we can use the cost capacity exponent factor and the cost index.

First, let's calculate the cost capacity ratio (CCR) for the 600-MW plant compared to the 200-MW plant:

CCR = (600/200)^0.79

Next, we need to adjust the cost of the 200-MW plant for inflation using the cost index. The cost index ratio (CIR) is given by:

CIR = (current cost index / base cost index)

Using the given information, the base cost index is 400 and the current cost index is 1200. Therefore:

CIR = 1200 / 400 = 3

Now, we can estimate the cost of the 600-MW plant:

Cost of 600-MW plant = Cost of 200-MW plant * CCR * CIR

Using the information provided, the cost of the 200-MW plant is $100 million. Plugging in the values, we have:

Cost of 600-MW plant = $100 million * CCR * CIR

Calculating CCR:

CCR = (600/200)^0.79 ≈ 2.3367

Calculating the cost of the 600-MW plant:

Cost of 600-MW plant = $100 million * 2.3367 * 3

Cost of 600-MW plant ≈ $700 million

Your question is incomplete but most probably your full question was

Suppose that an aircraft manufacturer desires to make a preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of its new long- distance aircraft. It is known that a 200-MW plant cost $100 million 20 years ago when the approximate cost index was 400, and that cost index is now 1,200. The cost capacity exponent factor for a fossil-fuel power plant is 0.79. What is he preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of the new long-distance aircraft?

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(1) To solve this linear programming problem, we need to graph the constraints and find the feasible region. Starting with the first constraint, x + y ≤ 7, we can plot the line x + y = 7 and shade the region below it (since we want x and y to be greater than or equal to 0).

Next, the constraint 2x + y ≤ 12 corresponds to the line 2x + y = 12, and we shade the region below this line as well.
Finally, the constraint y ≤ 4 corresponds to the horizontal line y = 4, which we shade everything below.
The feasible region is the overlapping shaded region of these three constraints.
To maximize f = 2x + 4y within this feasible region, we need to find the corner point with the highest value of f.
Checking the corner points of the feasible region, we have (0,4), (3,4), and (5,2).

Plugging each of these into the objective function f = 2x + 4y, we get:
- (0,4): f = 2(0) + 4(4) = 16
- (3,4): f = 2(3) + 4(4) = 22
- (5,2): f = 2(5) + 4(2) = 18
Therefore, the maximum value of f = 22 occurs at the point (3,4).
(x,y) = (3,4)
f = 22 .

2) Again, we need to graph the constraints to find the feasible region.Starting with the first constraint, x + y ≤ 7, we plot the line x + y = 7 and shade the region below it.The second constraint, 2x + y ≤ 12, corresponds to the line 2x + y = 12, which we shade the region below as well. Finally, the third constraint, x + 3y ≤ 15, corresponds to the line x + 3y = 15, which we shade the region below.

The feasible region is the overlapping shaded region of these three constraints. To maximize f = 2x + 8y within this feasible region, we need to find the corner point with the highest value of f. Checking the corner points of the feasible region, we have (0,0), (0,5), (3,4), and (7,0).

Plugging each of these into the objective function f = 2x + 8y, we get:- (0,0): f = 2(0) + 8(0) = 0
- (0,5): f = 2(0) + 8(5) = 40
- (3,4): f = 2(3) + 8(4) = 34
- (7,0): f = 2(7) + 8(0) = 14, Therefore, the maximum value of f = 40 occurs at the point (0,5). , (x,y) = (0,5)
f = 40.

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The value of limit when x approaches -1 is -4.

To find the limit as x approaches -1 of the expression x(x-1)², we substitute -1 for x:

lim x(x-1)²

Plug in x value as -1.

= (-1)(-1-1)²

Let us evaluate the value with in the parenthesis.

-1-1=-2

= (-1)(-2)²

Now square the -2 which results 4.

= (-1)(4)

When minus one is multiplied with four we get minus four.

'= -4

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Find the limit by substitution.

lim x(x-1)²

X→-1

Answer: D¢(-3, 10), E¢(0, -1), F¢(-5, 8)

Step-by-step explanation:

Answer: J. A = 12 (4⋅6).

Step-by-step explanation:

Answer: J. A = 12 (4⋅6).

This equation can be used to find the area of the triangle in the diagram because it uses the formula for the area of a triangle, which is A = 1/2 * b * h, where b is the base and h is the height. Since the triangle in the diagram has a base of 4 and a height of 6, the equation A = 12 (4⋅6) can be used to find the area.

Answer:

The diagram is not provided, so it's difficult to determine the exact dimensions of the triangle and parallelogram. However, we can make some general observations to determine which equation can be used to find the area of the triangle.

First, we know that the area of a triangle is given by the formula:

A = 1/2 * base * height

We also know that the area of a parallelogram is given by the formula:

A = base * height

In the diagram, the triangle can be formed into a parallelogram by taking one of its sides and using it as the base of the parallelogram. The height of the parallelogram is the same as the height of the triangle.

Based on these observations, we can conclude that the equation that can be used to find the area of the triangle is:

A = 1/2 * base * height

where the base is one of the sides of the triangle, and the height is the height of the parallelogram (which is the same as the height of the triangle).

None of the answer choices provided match this equation, so the correct answer is not given.

Answer:

I think its m=3/2

Step-by-step explanation:

If it right can I please have brainliest :)

Answer:

here is how to figure this out

Step-by-step explanation:

point 1 = (9,8)  =  (x1,y1)

point 2 =(7,5)  = (x2,y2)

slope= y2-y1 / x2-x1

slope = 5-8 / 7-9

slope = -3 / -2

slope = 3/2  :)

Answer:

the answer is 13

Step-by-step explanation:

x < 13 that's what the answer is

Answer: (-♾️ 13)

Step-by-step explanation:

3x+11<50

3x<50-11

3x<39

X<13

The solution will be (-♾️ 13)

Answer: 24 ft

Step-by-step explanation:

We use Pythagoras' Theorem.

So, Hypotenuse^2 = Side A^2 + Side B ^2

=> 30^2 = 18^2 + b^2

=> b^2 = 30^2 - 18^2

=> \(\sqrt{b^{2} }\) = \(\sqrt{30^{2} - 18^{2} }\)

=> b = \(\sqrt{576}\)

=> b = 24 ft

Answer:

f(10)=sqrt(14)

Step-by-step explanation:

f(10) = sqrt(2x-6)

f(10)= sqrt(20-6)

f(10)=sqrt(14) - simplest form, no way to factor it.

We will solve as follows:

*We will have that the following function models the perimeter of the rectangle:

Here l is the length and w is the width. Now, we replace l and solve for w:

So, the width is 14 ft.

The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

here, we have,

Given data:

{1 ,2, 3 ,4, 5}

Formula for combinations is used since the order does not matter and repetition is allowed.

nCr = (n + r -1) /(r! * (n-1)!)

where n is the total number of items and r is the items to be picked

now, we get,

5C3 = (5 + 3 - 1)! /(3! * (5 -1)!

5C3 = 7!/(3! *4!) Simplifying the factorials)

5C3 = 5040/(6*24)

5C3 =5040/144

5C3 = 35

Hence, The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.

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let   −5x+2y=14   be [1]

&        y=3x+2    be [2]  

Finding the value of x

By substituting y in [2] for y in [1]

⇒  −5x + 2(3x+2) = 14         [expand the bracket]

⇒     -5x + 6x + 4 = 14         [subract 4 from both sides and simplify]

⇒                       x = 10

Finding the value of y

Since x =10, we can substitute value of x into [2]

⇒     y = 3(10) + 2

⇒     y = 32

The vertex of the parabola is V(2, 0). The focus is F(5, 0). The directrix is x = -1. The axis of symmetry is the vertical line x = 2.

The given equation of the parabola is y^2 = 12(x - 2). We can rewrite this equation in the standard form of a parabola, which is (x - h)^2 = 4p(y - k), where (h, k) represents the vertex.

Comparing the given equation with the standard form, we can determine the values of h and k:

h = 2

k = 0

So, the vertex of the parabola is V(2, 0).

To find the focus and the directrix, we need to determine the value of p. In the standard form of a parabola, the value of p represents the distance between the vertex and the focus (or the vertex and the directrix).

From the equation (x - h)^2 = 4p(y - k), we can see that p = 3. Since the coefficient of (y - k) is positive, the parabola opens to the right.

The focus is located at a distance of p = 3 to the right of the vertex. Therefore, the x-coordinate of the focus is 2 + 3 = 5. Since the vertex has a y-coordinate of 0, the y-coordinate of the focus remains the same. Hence, the focus is F(5, 0).

The directrix is a vertical line located at a distance of p = 3 to the left of the vertex. Therefore, the x-coordinate of the directrix is 2 - 3 = -1. As the parabola opens to the right, the directrix is a vertical line given by the equation x = -1.

Finally, the axis of symmetry is a vertical line passing through the vertex. Since the vertex is V(2, 0), the equation of the axis of symmetry is x = 2.

In summary, for the parabola with the equation y^2 = 12(x - 2):

- The vertex is V(2, 0).

- The focus is F(5, 0).

- The directrix is x = -1.

- The axis of symmetry is x = 2.



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Answer:

∠ 1 = 149°, ∠ 2 = 31°

Step-by-step explanation:

∠ 1 and 31° are same-side interior angles and are supplementary, thus

∠ 1 = 180° - 31° = 149°

∠ 2 and 31° are alternate angles and congruent, thus

∠ 2 = 31°

Answer:

Step-by-step explanation:

Area of rectangle= Length x Breadth

= 34x 52

= 1768

Answer:

I think u old number is 7 it is my luck number

Let y = 0

0 = 2x^2 + 7x + 3

Using the quadratic formula, we get x = -3 and x = -1/2.

Answer:

Answer and Work is in photo

Step-by-step explanation:

Answer:

A = 6

B = 10

Step-by-step explanation:

[] Let's look at the system again:

\(\left \{ {{Ax+By=38} \atop {2Ax-By=16}} \right.\)

[] They give us a set of x and y values, (3, 2) so we can plug them into the system.

\(\left \{ {{A(3)+B(2)=38} \atop {2A(3)-B(2)=16}} \right.\)

[] Now, we can solve this with a graphing calculator. Let A be x and B be y for the sake of graphing.

A = x

B = y

\(\left \{ {{x(3)+y(2)=38} \atop {2x(3)-y(2)=16}} \right.\)

-> See attached

[] We can see the lines intersect at (6, 10) so the answer is A = 6 and B = 10.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

For a factorable trinomial x² + bx + c, the absolute value of b can be less than, equal to, or greater than the absolute value of c, depending on the specific values of b and c.

The quadratic trinomial formula in one variable has the general form ax2 + bx + c, where a, b, and c are constant terms and none of them are zero.

For any factorable trinomial of the form x² + bx + c, the absolute value of b can sometimes be less than, equal to, or greater than the absolute value of c. The relationship between the absolute values of b and c depends on the specific values of b and c.

Let's consider a few cases:

1. If both b and c are positive or both negative: In this case, the absolute value of b can be less than, equal to, or greater than the absolute value of c. For example:

  - In the trinomial x² + 2x + 3, the absolute value of b (|2|) is less than the absolute value of c (|3|).

  - In the trinomial x² + 4x + 3, the absolute value of b (|4|) is greater than the absolute value of c (|3|).

  - In the trinomial x² + 3x + 3, the absolute value of b (|3|) is equal to the absolute value of c (|3|).

2. If b and c have opposite signs: In this case, the absolute value of b can also be less than, equal to, or greater than the absolute value of c. For example:

  - In the trinomial x² - 4x + 3, the absolute value of b (|4|) is greater than the absolute value of c (|3|).

  - In the trinomial x² - 2x + 3, the absolute value of b (|2|) is less than the absolute value of c (|3|).

  - In the trinomial x² - 3x + 3, the absolute value of b (|3|) is equal to the absolute value of c (|3|).

Therefore, for a factorable trinomial x² + bx + c, the absolute value of b can be less than, equal to, or greater than the absolute value of c, depending on the specific values of b and c.

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Answer and Explaination:
a. To calculate the required seating area for the restaurant, we need to consider the average number of customers per group, the number of groups, and the space required per table.

Given:

Average number of customers per group = 4

Number of groups = 16

Space required per table and surroundings = 5.3 square meters

To calculate the required seating area, we can use the following formula:

Seating area = Number of groups * (Average number of customers per group / 2) * Space required per table

Seating area = 16 * (4 / 2) * 5.3

Seating area = 16 * 2 * 5.3

Seating area = 169.6 square meters

Therefore, the required seating area for the restaurant is approximately 169.6 square meters.

b. To determine the number of stoves required for the restaurant, we need to consider the average cooking time per meal, the number of elements per stove, and the total number of meals.

Given:

Average cooking time per meal = 10 minutes

Number of elements per stove = 4

To calculate the number of stoves, we divide the total cooking time by the average cooking time per stove:

Number of stoves = (Total cooking time) / (Average cooking time per stove)

Total cooking time = Number of groups * (Number of meals per table) * (Average cooking time per meal)

Number of meals per table = 2

Total cooking time = 16 * 2 * 10

Total cooking time = 320 minutes

Number of stoves = 320 minutes / 10 minutes per stove

Number of stoves = 32

Therefore, the restaurant would require 32 stoves.

Answer:

a

Step-by-step explanation:

A which is add 40x to both sides wich is A

\( \: \: \: \: 15.5 \\ - 11.2 \)

ANSWER :-

4.3

The rectangular coordinate form of a complex number is represented by the formula z=a+bi. The real axis is the horizontal one, and the imaginary axis is the vertical one. In terms of r and, where r is the vector's length and is the angle it makes with the real axis, we determine the real and complex components.

Rectangular form;-

Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical components. In essence, the angled vector is taken to be the hypotenuse of a right triangle, described by the lengths of the adjacent and opposite sides.

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