Anna is trying to find the height of a radio antenna on the roof of a local building. Shestands at a horizontal distance of 19 meters from the building. The angle of elevationfrom her eyes to the roof (point A) is 34°, and the angle of elevation from her eyes tothe top of the antenna (point B) is 41°. If her eyes are 1.5 meters from the ground,find the height of the antenna (the distance from point A to point B). Round youranswer to the nearest tenth of a meter if necessary.

Answer: 4k

Step-by-step explanation:

The additional acres that the parks occupy will be 33.75 acres.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the additional acres that the parks occupy will be:

= (12.5 × 3) - 3.75

= 33.75 acres.

Note that the information is incomplete and the complete information is given below.

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A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres

The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?

The cone that has the greatest volume is cone C

The given parameters in the question are

Cone A

Height = 10 cm

Diameter = 4 cm

Cone B

Height = 20 cm

Diameter = 4 cm

Cone C

Height = 10 cm

Diameter = 8 cm

The volume of a cone can be calculated using the following volume equation

Volume of a cone = 1/3π(d/2)²h

Where

h = height of the cone

r = radius of the cone

d = diameter of the cone

Using the above equations, we have the following computations

Volume of a cone A = 1/3π * (4/2)² * 10

Volume of a cone A = 40/3π

Volume of a cone B = 1/3π * (4/2)² * 20

Volume of a cone B = 80/3π

Volume of a cone C = 1/3π * (8/2)² * 10

Volume of a cone C = 160/3π

We can see that 160/3π is greater than 40/3π and 80/3π

Hence, cone C has the highest volume

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Answer:

5^a= 1/5^3

5^a= 5^-3

a=-3

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

It's true

Answer:

False ur welcome

Step-by-step explanation:

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Step-by-step explanation:

5(x - 3) = 3 + 5x + 3x

5x - 15 = 3 + 8x

5x - 8x = 3 + 15

-3x = 18

x = 18/-3

x = -6

The number in the given word problem is -6.

Thus:

unknown number = x

Therefore:

\(5 \times (x - 3) = 3 + (5x + 3x)\)

\(5x - 15 = 3 + 8x\)

\(5x - 8x= 3 + 15\\\\-3x = 18\\\\\)

\(x = -6\)

Therefore, the value of the number is -6.

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Answer:

its the second expression

Step-by-step explanation:

Answer:

B. 6w^2  Second option

Step-by-step explanation:

You are multiplying, therefore when a digit is next to a letter in a math expression. It means to multiply

Find the actual Dimensions of the triangle.

Multiply the size of the triangle on paper by 1.5 feet per inch:

Width = 5 x 1.5 = 7.5 feet.

Height= 7 x 1.5 =10.5 feet

Area of a triangle is 1/2 x base x height:

Area = 1/2 x 7.5 x 10.5 = 39.375 square feet.

Answer: 39.375 square feet.

The area of the actual banner is 39.375 feet²

Scaling is used to increase or decrease the size of a figure so as to create an image.

Given that 1 inch on the drawing Is equivalent to 1.5 feet on the actual banner, hence:

Base = 5 in * 1.5 feet per in = 7.5 feet

Height = 7 in * 1.5 feet per in = 10.5 feet

Area of the actual banner = (1/2) * 7.5 * 10.5 = 39.375 feet²

The area of the actual banner is 39.375 feet²

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Answer:

9 16-ounce packages

Step-by-step explanation:

144oz. ÷ 16 = 9 Packages

Answer:

The speed of the plane in the still air is 420 miles/hour

The speed of the wind 60 miles/hour

Step-by-step explanation:

Let the speed of the plane with the wind be v

Let the speed of the plane against the wind be u

Now, speed = distance/time

With the wind,

v = (1440 miles)/(3 hours) = 480 miles/hour

v = 480 miles/hour

Against the wind,

u = (1440 miles)/(4 hours) = 360 miles/hour

u = 360 miles/hour

Now, let the speed of plane be p, and speed of wind be w,

Now, with the wind, the speed is 480 mph,

so,

speed of plane + speed of wind = 480 mph

p + w = 480  (i)

and against the wind, the speed is 360 mph,

so,

speed of plane - speed of wind = 360mph

p-w = 360 (ii)

adding equations (i) and (ii), we get,

p+w + p-w = 480 + 360

2p = 840

p = 840/2

p = 420 miles/hour

Then, the speed of the wind will be,

p + w = 480,

420 + w = 480

w = 480 - 420

w = 60 miles/hour

The speed of the plane in still air is calculated to be 420 mph, and the speed of the wind is calculated to be 60 mph by solving the two simultaneous equations obtained from the time, rate, and distance relationship.

This problem is about the rate, time, and distance relationships. The rate at which the airplane travels in still air is r (unaffected by wind), and the speed of the wind is w. When the plane flies with the wind, it is 'assisted' and therefore travels faster - at a speed of (r + w); against the wind, it travels slower - at a speed of (r - w).

From the problem, we know that:

By solving these two equations, we get the following:

Adding these two gives 2r = 840 => r = 420 mph (the speed of the plane in still air), and subtracting gives 2w = 120 => w = 60 mph (the speed of the wind).

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Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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Answer:

7x+10

Step-by-step explanation:

2x(3x)+1x(x+10)

6x+1x+10

7x+10

For the function f(x) = 7/8x² - 14, the x-intercepts are x = -4 and x = 4.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the x-intercepts of the function f(x), we need to solve the equation f(x) = 0.

f(x) = 7/8x² - 14

Substitute f(x) with 0 -

0 = 7/8x² - 14

Add 14 to both sides -

7/8x² = 14

Multiply both sides by 8/7 -

x² = 16

Take the square root of both sides -

x = ±4

Therefore, the x-intercepts of the function f(x) are x = -4 and x = 4.

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Answer: If Jamie is selling bags of carrots for $5 each and already has $30 what would he use to calculate how much money he made.

Answer:

C=6.6666666666666666666666666

Answer:

\(D.\frac{2}{6}\)

Step-by-step explanation:

√15 = 3.87298334621

11/25 = 11 ÷ 25 = 0.44

3/20 = 3 ÷ 20 = 0.15

2/6 = 2 ÷ 6 = 0.33333333333

Answer:

carbon dioxide emissions from human activity carbon dioxide emissions from activities in nature global sea level global rates of photosynthesis changes in Earth's orbital path acidity of ocean water Affects the Temperature Predictions

Does Not Affect the Temperature Predictions

The  function of the model  for Average Global temperature can be  expressed as

\(T (x,y,z,p,q) \\where \; x, y,z, p,q\; are \; the \; variables\)

The variables are sorted as follows

Rank          Variable

1                 x = Carbon dioxide emissions from human activity

2                y = Carbon dioxide emissions from activities in nature

3                z= Global sea level

4                p= Global rates of photosynthesis changes in Earth's orbital path                

5                q = Acidity of ocean water

Given ,

Scientists are developing  computer model to predict the change in average global temperatures over the next 100 years.

Let \(T\) be the average global temperature

According to the given question

\(T\) is a function of many variables

\(T (x,y,z,p,q) \\where \; x, y,z, p,q\; are \; the \; variables\)

These variables are given below

let

x = Carbon dioxide emissions from human activity

y = Carbon dioxide emissions from activities in nature

z= Global sea level

p= Global rates of photosynthesis changes in Earth's orbital path

q = Acidity of ocean water

We have to Sort the variables according to whether they likely would affect the temperatures that the model predicts.

Human activities have increased the amount of   \(CO_2\) in atmosphere.

\(CO_2\) is major green house gas which causes global warming and also glaciers are melting due to rise in average global temperature.

The Time interval is sufficiently  large to have a greater impact due to Global sea level.

The Ranks of different variables are given as follows.

Rank          Variable

1                 x = Carbon dioxide emissions from human activity

2                y = Carbon dioxide emissions from activities in nature

3                z= Global sea level

4                p= Global rates of photosynthesis changes in Earth's orbital path                

5                q = Acidity of ocean water

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The range of the graph is,

⇒ Range = { y | - 1 < y < 3 }

The domain of the graph is,

⇒ Domain = { x | - 4 < x < 2 }

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph is shown in figure.

Now, We know that;

The range of the graph is the value of y where the function of graph is defined.

Hence, The range of the graph is,

⇒ Range = { y | - 1 < y < 3 }

And, The domain of the function is defined the value of y where the function of graph is defined.

Hence, The domain of graph is,

⇒ Domain = { x | - 4 < x < 2 }

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Answer:

\(120^{\circ}, 120^{\circ}, 60^{\circ}, 60^{\circ}\)

Step-by-step explanation:

The angles of a quadrilateral add to \(360^{\circ}\).

\(2h+2h+h+h=360 \\ \\ 6h=360 \\ \\ h=60 \implies 2h=120\)

Answer:

(9,16)

Step-by-step explanation:

We Know

The equation y = 3x - 2

Find the y coordinate (9, ?)

We just simply put 9 in for x and solve for y

y = 3(9) - 2

y = 18 - 2

y = 16

So, the coordinate are (9,16)

Answer:

3x + y = 17   --------(1)

2x + y = 12 ---------(2)

from (1) : y = 17 - 3x.

Substitute y in (2)

2x + (17 -3x) = 12

2x + 17 -3x = 12

-x = 12 - 17

-x = -5

x = 5

Substitute x in (1)

3(5) + y = 17

15 + y = 17

y = 17 -15

y = 2

Answer : x = 5, y = 2

Answer:

BC = 21 cm

Step-by-step explanation:

In similar triangles the corresponding sides are in same proportion.

Its given in the sum that AC = 12 cm; DF = 20 cm and EF = 35 cm.

      \(\sf \dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}\\\\\\\dfrac{AC}{DF}=\dfrac{BC}{EF}\\\\\dfrac{12}{20}=\dfrac{BC}{35}\)

     \(\sf \dfrac{12}{20}*35=BC\\\\\\\dfrac{12}{4}*7=BC\\\\\\3*7=BC\\\\ \boxed{BC = 21 cm}\)

Answer:

125 percent

Step-by-step explanation:

25 percent *500.00 =

(25:100)*500.00 =

(25*500.00):100 =

12500:100 = 125

Now we have: 25 percent of 500.00 = 125

Question: What is 25 percent of 500.00?

Percentage solution with steps:

Step 1: Our output value is 500.00.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$500.00=100\%$.

Step 4: Similarly, $x=25\%$.

Step 5: This results in a pair of simple equations:

$500.00=100\%(1)$.

$x=25\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{500.00}{x}=\frac{100\%}{25\%}$

Step 7: Again, the reciprocal of both sides gives

{x}/{500.00}={25}/{100}$

$Rightarrow x=125$

Therefore, $25\%$ of $500.00$ is $125$

Answer:

0.38888888888

Step-by-step explanation:

The world population will be 6 ​billion in 54.36 years

Given: the logistic growth model for world​ population f(x)= 12.57/1+4.11e−0.026x and f(x) = 6000,000,000 = 6 × 10⁹

We want the x years in which the population will be  6 ​billion. That means we will solve for x in the model:

f(x) = 12.57/1+4.11e^(−0.026x)

6 × 10⁹ = 12.57/1+4.11e^(−0.026x)

1+4.11e^(−0.026x) =  12.57/ 6 × 10⁹

4.11e^(−0.026x) =  [12.57/ 6 × 10⁹] - 1

e^(−0.026x) = ( [12.57/ 6 × 10⁹] - 1 ) / 4.11

Take the ln of both sides:

−0.026x = ln[  ( [12.57/ 6 × 10⁹] - 1 ) / 4.11 ]

- 0.026x = ln (0.2433090019)

x = ln (0.2433090019) / - 0.026

x = 54.36 years

Therefore,  the world population be 6 ​billion in 54.36 years

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