Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.

The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.

Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?

Select each correct answer.



1. (4, 36)

2. (0, 33)

3. (4.8, 30.5)

4. (2, 22)

5. (9, 26)

The three numbers will be 24, 14 and 12 respectively.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is the sum of three numbers is 50 and first number is 10 more than the second number and it is also twice the third.

Assume that the three numbers are [x] , [y] and [z].

Then, we can write -

x + y + z = 50       ..[1]

x = y + 10        ..[2]

x = 2z           ..[3]

Equating Eq [2] and Eq [3], we get -

2z = y + 10

Rearranging the equation above -

y = 2z - 10

Now, for Eq [1], we can write -

2z + z + y = 50

3z + y = 50

3z + 2z - 10 = 50

5z = 60

z = 12

Then, the value of [y] will be -

y = 2 x 12 - 10

y = 24 - 10

y = 14

and

x = 2z = 2 x 12 = 24

Therefore, the three numbers will be 24, 14 and 12 respectively.

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Answer: (2,1) (4,2) (-2,-1)

Step-by-step explanation:

thats apex, my dude

Answer:

Option A, C, F are the correct options.

Step-by-step explanation:

The given equation of line is [tex]y=\frac{1}{2}x[/tex]

Now we will plug in the values of points and validate the equation.

Option A. (2, 1)

[tex]y=\frac{1}{2}x[/tex]

[tex]1=\frac{2}{2}=1[/tex]

So this points lies on the given equation of line.

Option B. (3, 15)

[tex]15\neq \frac{3}{2}[/tex]

So the point is not on the line.

Option C. (4, 2)

[tex]2=\frac{4}{2}=2[/tex]

Point lies on the line.

Option D. (3, 6)

[tex]6\neq \frac{3}{2}[/tex]

Therefore point is not on the line.

Option E. (-2, 1)

[tex]1\neq \frac{-2}{2}[/tex]

Point does not lie on the line.

Option F. (-2, -1)

[tex]-1=\frac{-2}{2}=-1[/tex]

So this point lies on the line.

There are three points (2, 1), (4, 2) and (-2, -1) are on the line.

we know that

The CPCTC states that corresponding parts of congruent triangles are congruent

so

△FEB≅△CNB

that means

[tex]FE=CN\\FB=CB\\EB=NB[/tex]

we have

[tex]FE=6.1\ units\\FB=4.8\ units\\EB=3.8\ units[/tex]

therefore

[tex]BN=3.8\ units[/tex]

the answer is

the length of BN is [tex]3.8\ units[/tex]

Answer:

y ≥ 0

Step-by-step explanation:

The real absolute value function is defined on the set of all real numbers, assigning each real number its respective absolute value. Formally, the absolute value of any real number x, is defined by:

[tex]|x|=x,\hspace{3}if\hspace{3}x\geq0\\|x|=-x,\hspace{3}if\hspace{3}x<0[/tex]

The domain of the function is all real numbers, and by definition, the absolute value of x will always be greater than or equal to zero and never negative. Hence:

[tex]Domain:\\x\in R\\Range:\\y\in R : y\geq0[/tex]

I attached you a picture of the graph.

To maximize the area of a rectangular garden with one side already fenced, Lindsey should allocate the 45 ft of fencing available to form the remaining three sides in a way that makes the two lengths and the width as equal as possible. While an exact numerical answer depends on additional constraints, the guiding principle is that a more square-like configuration will yield the largest area.

The question asks what lengths of fencing will produce the largest area for a rectangular garden, given that Lindsey has 45 ft of metal fencing and an existing tall wooden fence will serve as one side of the rectangle. To maximize the area enclosed by a given perimeter, which in this case is the length of the fencing available for three sides of the rectangle (since one side is already in place), it is beneficial to review a principle regarding geometric figures and their areas.

It is a well-established mathematical principle that of all rectangles with a given perimeter, the square has the largest area. However, since one side is already provided and Lindsey is forming only three sides of the rectangle, the problem slightly deviates from forming a perfect square. Nonetheless, the principle that more equidistant lengths result in larger areas can guide us to maximize the area Lindsey can enclose.

Lindsey has 45 ft of fencing to create three sides of a rectangle. For simplicity, let's denote the lengths of the two equal sides as L, and the length of the third side (parallel to the existing fence) as W. Since the total length of fencing is 45 ft, the equation we have is 2L + W = 45. To maximize the area (A = L*W), Lindsey should opt for dimensions where L and W are as close as possible to each other within the constraint of the given perimeter (or in this case, the total length of fencing available).

However, without additional constraints (like the length of the existing fence), a definitive numerical answer cannot be provided. The general advice for Lindsey is to distribute the length of the fencing as evenly as possible between the two lengths and the width she needs to create, thereby approximating a square's dimensions which tends to maximize the enclosed area.

x=1 f = 10(5.5)(1) = 55

x=2, f = 10(5.5)(2) = 110

110-55 = 55

2-1 =1

55/1 = 55

 average rate of change = 55

replace the numbers inside () for x

 f(4) = -4(4)-3 = -16 -3 = -19

G(-4) = 2(-4)^2 -3(-4) = 44

The cost of each begonia is $11 at a fundraiser.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's assume the cost of each begonia x.

Since Cameron bought four begonias, the total cost of the begonias was 4x.

The total cost of the plants was the cost of the begonias plus the cost of the fern, or 4x + 19.

As per the question, the total cost was $63, so we can set up the equation:

4x + 19 = 63

To solve for x, we need to get x by itself on one side of the equation. We can do this by subtracting 19 from both sides:

4x + 19 - 19 = 63 - 19

This simplifies to:

4x = 44

To solve for x, we need to divide both sides by 4:

4x / 4 = 44 / 4

This simplifies to:

x = 11

Therefore, each begonia cost $11.

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41 is the best estimate for the number of people in line at 9am

Two or more expressions with an Equal sign is called as Equation.

y equal to minus five point one three one x square plus Thirty one point eight two one x minus three point three three three.

y=-5.131x²+ 31.821x-3.333 approximates the number of people standing in line to catch commuter train x hours after 5am.

There is 4 hours in between 9 am and 5 am. so x=4

Substitute x=4 into the equation

y=-5.131(4)²+ 31.821(4)-3.333

y=-5.131(16)+127.284-3.333

y=-82.096+127.284-3.333

y=41.855

Hence 41 is the best estimate for the number of people in line at 9am

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fans bought 5/8 so there is 3/8 still left

45000 * 3/8 = 16,875 seats are left

the right answer is actually 30,60,90, I got the answer right on the test

The measures of the angles are 30°, 60°, and 90° for the given right triangle. The correct answer would be option (A).

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The right triangle is given in the figure, as shown.

According to the figure,  

perpendicular = 7√3

hypotenuse = 14√3

As per the question, we have

Since sin θ = perpendicular/hypotenuse

Substitute the values in the above formula, and we get

sin θ = 7√3/14√3

sin θ = 1/2

θ = 30°

This means the measures of the angles are 30°, 60°, and 90°.

Hence, the correct answer would be an option (A).

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The question seems to be incomplete, the missing part has been attached below.

Answer:  The correct description is (C). the product of a number and 45.

Step-by-step explanation:  We are given to select the correct description that matches the algebraic expression 45n.

Let, 'n' be a number.

Then, the sum of 'n' and 45 is written as (45 + n).

So, option (A) is incorrect.

The quotient of 'n' and 45 is given by [tex]\dfrac{n}{45}~\textup{or}~\dfrac{45}{n}.[/tex]

So, option (B) is incorrect.

The product of 'n' and 45 is

45 × n = 45n, which means 45 times of a number 'n' or n times of 45.

So, option (C) is correct.

The difference of 'n' and 45 is (n - 45) or (45 - n), according as 'n' is greater or 45 is greater.

So, option (D) is incorrect.

Thus, the correct option is (C).

Answer:

B. seven $1 bills and eight $5 bills.

Step-by-step explanation:

n = number of $1 bills

m = number of $5 bills

Given:

n + m = 15

n($1) + m($5) = $47

Just solve 2 equations in 2 unknowns n and m:

(i)  n + m = 15

(ii) n + 5m = 47

Subtract (i) from (ii) and get

4m = 32

m = 32/4 = 8

Then from (i) get

n = 15 - m = 15 - 8 = 7

There are 7 $1 bills and 8 $5 bills.