5. An airplane 30,000 feet above the ground begins to descend at a
rate of 2,000 feet per minute. Choose an equation to model this
situation.
A y = 30,000 – 2,000x
B
y = 30,000x - 2,000
Cy= 30,000 + 2,000x
D y = 30,000x + 2,000

Step-by-step explanation:

the total surface area is the sum of the 5 individual areas in the surface :

2 triangle sides (left and right).

1 back rectangle side

1 rectangle floor

1 inclined rectangle front side

to get the length of the baseline (Hypotenuse) of the right-angled triangles on the side. we use Pythagoras

c² = a² + b²

where c is the Hypotenuse (the side opposite of the 90° angle).

c² = 3² + 4² = 9 + 16 = 25

c = 5

so, now, we have everything we need.

the area of a triangle side (since it is right-angled) :

4×3/2 = 6

2 sides, that makes 12

the area of the back side

6×3 = 18

the area of the floor

6×4 = 24

the area of the inclined front side

6×5 = 30

so, the total surface area is

12+18+24+30 = 84

The equation shows that the value of x will be 6.

It should be noted that an equation is simply used to illustrate the relationship that exists between two variables. 

0. 16 + 0.08 x = 0.64

0.08 x = 0.64 - 0.16

0.08 x = 0.48

x = 0.48 / 0.08x = 6

The value of x is 6.

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Answer:

x=6

Step-by-step explanation:

The amount of soil needed to fill the garden box is given as follows:

1728 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

V = 19 x 12 x 6 + 10 x 3 x 12

V = 1728 ft³.

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The new surface area is (1/4)S, which is equivalent to (1/4) times the original surface area.

Let the original surface area of the figure be S.

If the new surface area is 1/4 of the original, then the new surface area is (1/4)S.

Since the surface area is proportional to the square of the dimensions, we know that the ratio of the new dimensions to the original dimensions must be √(1/4) = 1/2.

Therefore, if the original dimensions were x, y, and z, then the new dimensions must be (1/2)x, (1/2)y, and (1/2)z.

The new surface area can be calculated using the formula for the surface area of the figure with the new dimensions:

New surface area = 2((1/2)xy + (1/2)xz + (1/2)yz)

                  = xy + xz + yz

But we know that the new surface area is (1/4)S, so we have:

xy + xz + yz = (1/4)S

Multiplying both sides by 4 gives:

4xy + 4xz + 4yz = S

Factor out 4:

4(x+y+z)² - 4x² - 4y² - 4z² = S

Substituting the expressions for the new dimensions:

4((1/2)(x+y+z))² - 4((1/2)x)² - 4((1/2)y)² - 4((1/2)z)² = S

Simplifying:

(1/4)(x+y+z)² - (1/4)x² - (1/4)y² - (1/4)z² = (1/4)S

Multiplying both sides by 4 again:

x² + 2xy + y² + 2xz + 2yz + z² - x² - y² - z² = S

Simplifying:

2xy + 2xz + 2yz = S

Substituting (1/2)x, (1/2)y, and (1/2)z for x, y, and z:

2(1/2)(1/2)xy + 2(1/2)(1/2)xz + 2(1/2)(1/2)yz = (1/4)S

Simplifying:

(1/4)xy + (1/4)xz + (1/4)yz = (1/4)S

Therefore, the new surface area is (1/4)S, which is equivalent to (1/4) times the original surface area.

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To compute the angle between successive azimuths, you can use the following formula:

Angle between successive azimuths = (360° / Number of azimuths)

For example, if you have 4 azimuths, the angle between each successive azimuth would be:

Angle between successive azimuths = (360° / 4) = 90°

So, the angle between each successive azimuth would be 90 degrees.

Here are the steps to compute the angle between successive azimuths:

1. Determine the number of azimuths you have.
2. Plug the number of azimuths into the formula: Angle between successive azimuths = (360° / Number of azimuths)
3. Solve the equation to find the angle between successive azimuths.

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Answer: 2 and 19/56

Step-by-step explanation:

x = (16/7 + 2 11/28)/2

x = (64/28 + 67/28)/2

x = (131/28)/2

x = 131/56 or 2 19/56

Answer:

Step-by-step explanation:

The standard form of linear function y = - (1 / 2) · x + 6 is (1 / 12) · x + (1 / 6) · y = 1.

In this question we find a linear function in slope-intercept form:

y = m · x + b

Where:

From which we must obtain the linear function in standard form:

a · x + b · y = c

Where:

We can derive the standard form of the linear equation by algebra properties:

y = m · x + b

(1 / b) · y = (m / b) · x + 1

- (m / b) · x + (1 / b) · y = 1

If we know that m = - 1 / 2 and b = 6, then the equation of the line in standard form is:

- [(- 1 / 2) / 6] · x + (1 / 6) · y = 1

(1 / 12) · x + (1 / 6) · y = 1

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Hope you Understand :)

Answer:

f (x) = 2(3x) + 4

Step-by-step explanation:

Answer:

67.5

Step-by-step explanation:

Answer:

$13,511

Step-by-step explanation:

Year 1: $22,000×.85=$18,700

Year 2: $18,700×.85=$15,895

Year 3: $15,895×.85=$13,510.75

($13,511 to nearest dollar)

Answer:

-------------------

Given three interior angle measures of a triangle:

Use the triangle sum theorem to find the missing angle:

So the missing angle is 67°.

The environment changed in such a way that, "guppies with small spots had a better chance of survival and reproduction, leading to an increase in their population and a decrease in the population of guppies with large spots".

Over many generations, guppies with small spots had a survival advantage in the river because the rocks on the river bottom became smaller. This made guppies with small spots harder for larger fish to see and catch, increasing their chances of survival and reproduction.

As a result, more guppies with the small spot gene passed it on to their offspring, leading to an increase in the population of guppies with small spots. At the same time, the population of guppies with large spots decreased as they were more visible to predators and had a lower chance of survival. This process of natural selection led to a change in the frequency of different traits within the population of guppies.

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Answer: x^2-4x-12

Step-by-step explanation:

(x-6)(x+2)

-Use the FOIL Method (First Outer Inner Last)

x(x)=x^2

x(2)=2x

x(-6)=-6x

(-6)(2)=-12

-6x+2x=-4x

x^2-4x-12

Answer:a z score corresponding to an area located entirely in the left side of the curve

Step-by-step explanation:

The Surface area of the pyramid  is 68 square cm

The total surface area is the area of all the triangles

Area of a triangle = 0.5bh

b is the base

h is the height

Given te followin

b = 6cm

h = 5.2cm

Surface area of the pyramid = 5(0.5 * 6 * 5.2)

Surface area of the pyramid = 78 square cm

Hence the Surface area of the pyramid  is 68 square cm

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Answer:That’s um tuff

Step-by-step explanation:

Answer:

2.08 this is answer

Answer: look up alaskan pipeline

Step-by-step explanation:

Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

Answer:

50 degrees

Step-by-step explanation:

Alternate interior angles are equal

Answer:

the answer is 50 dg I took the test lol my explanation is that the line is going obtuse

Given the inverse demand function p = 100 - 20q for toasters and a price of $35, we can find the consumer surplus.

First, we'll find the quantity demanded at the given price:

35 = 100 - 20q
20q = 100 - 35
q = (100 - 35) / 20
q = 65 / 20
q = 3.25

Now, to find the consumer surplus, we'll use the formula:

Consumer Surplus = (1/2) × Base × Height

The base represents the quantity (q = 3.25) and the height is the difference between the maximum willingness to pay (p = 100) and the actual price (p = 35).

Consumer Surplus = (1/2) × 3.25 × (100 - 35)
Consumer Surplus = 0.5 × 3.25 × 65
Consumer Surplus = 105.625

So, the consumer surplus is $105.63 when rounded to two decimal places.

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The total number of ways an ice-cream can be selected is 27.

A combination is "an arrangement of objects where the order of the constituents is immaterial," according to the definition. In situations where the order of the elements is immaterial, combining these two terms means "Selection of things." Combinations are a subset of permutations in which the order of the choices is ignored.

As per the given data:

A table is given, in which information regarding the ice cream menu is shown.

We have to find the total number of different choices of ice cream that can be made.

Number of sizes = 3

Number of flavors = 3

Number of toppings = 3

ways for selecting one ice cream = \(^3C_{1} \times ^3C_{1} \times ^3C_{1}\) = 3 × 3 × 3 = 27

The total number of ways an ice-cream can be selected is 27.

Hence, The total number of ways an ice-cream can be selected is 27.

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The compound inequality represented by the graph shown in the image below is 5 < x < 9

An equation is an expression that shows the relationship between two or more variables and numbers.

The image shown represents a compound inequality. It represents:

x > 5 and x < 9

The compound inequality represented by the graph shown in the image below is 5 < x < 9

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Answer:

3rd option

Step-by-step explanation:

The equation of a line in point slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Given

y - 4 = \(\frac{1}{4}\) (x - 8)

with m = \(\frac{1}{4}\) and (a, b) = (8, 4 )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then

y = \(\frac{1}{4}\) x + c ← is the partial equation

To find c substitute (8, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = \(\frac{1}{4}\) x + 2 ← equation in slope- intercept form

Answer:

I think it is A or D not sure

Where the above is given, the required angle m∠BAC = 45°.

In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

According to conditions angle b = 90°

The sum of angles of a triangle= 180°

That is a + b + c = 180

Therefore, c = a

       a = (180 - b)/2

          = (180 - 90) / 2

          = 90 / 2

          = 45°

Hence, the required angle m∠BAC = 45°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?

Therefore, our initial assumption that a and n are not relatively prime must be false, and we can conclude that a and n are indeed relatively prime numbers.

To prove that both a and b are relatively prime to n given that ab ≡ 1 (mod n), we will use contradiction. Assume that a and n are not relatively prime, meaning they have a common factor greater than 1. Then, we can write a = kx and n = ky, where k > 1 and x and y are relatively prime.

Substituting a = kx into ab ≡ 1 (mod n), we get kxb ≡ 1 (mod ky). Multiplying both sides by x, we get kxab ≡ x (mod ky). Since k > 1 and x are relatively prime, kx and ky are also relatively prime. Therefore, we can cancel out kx from both sides of the congruence, leaving b ≡ x (mod y). Now, suppose that b and n are not relatively prime, meaning they have a common factor greater than 1. Then, we can write b = jy and n = jm, where j > 1 and y and m are relatively prime.

Substituting b = jy into ab ≡ 1 (mod n), we get ajy ≡ 1 (mod jm). Multiplying both sides by y, we get ajym ≡ y (mod jm). Since j > 1 and y are relatively prime, jy and jm are also relatively prime. Therefore, we can cancel out jy from both sides of the congruence, leaving am ≡ 1 (mod j). But since k and j are both greater than 1, and n = ky = jm, we have k and j as common factors of n, which contradicts the assumption that x, y, and m are relatively prime.

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Margo is raising money for her club by selling boxes of nuts. She discovers that cashews are sold in three out of every seven cartons of nuts. The ratio, y=3/7, is the proportion of cashew boxes sold to all boxes sold.

Describe ratio:

A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other. A ratio between two quantities, let's say 'a' and 'b,' is typically expressed as a: b.

Three out of every seven boxes of nuts, according to Margo, are cashews. These steps can be used to determine the ratio of two quantities: Before we can calculate the ratio, we must first figure out the values for both instances. There are three cashews and seven boxes present in this scenario. As a fraction, write it as a/b. Therefore, we express it as y= 3/7. As a result, the ratio of the number of cashew boxes to the total number of boxes sold is given as y=3/7.

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