Gertrude is deciding which cell phone plan is the best deal for her to buy. Super Cell charges a monthly

fee of $10 and also charges $0.15 per call. She makes a note that the equation is M = $0.15C + $10.

where M is the monthly charge, in dollars, and C is the number of calls placed. Global Cellular has a plan

with no monthly fee but charges $0.25 per call. She makes a note that the equation is M = $0.25C, where

M is the monthly charge, in dollars, and C is the number of calls placed. Both companies offer unlimited

text messages.

Type your answer to c - which cell phone plan is a better buy for Gertrude? Be specific.

Answers

Answer 1

Answer:

It is dependent on the number of calls she plans to make per month

Step-by-step explanation:

Please refer to the attached image for explanations

Gertrude Is Deciding Which Cell Phone Plan Is The Best Deal For Her To Buy. Super Cell Charges A Monthlyfee

Related Questions


Thomas's room is 11.4 feet long. He wants to put up
a poster that takes up 0.25 of the length of a wall.
How long should his poster be?

Answers

Answer:

2.85 ft

Step-by-step explanation:

To find the length of the poster, take the length of the wall and multiply the the decimal length

11.4* .25

2.85

26)
Which expression demonstrates the distributive property applied to the expression 4(3 + 7)?
4 (7 + 3)
4 x 3 +7
4* (7 * 3)
4x3+4x7

Answers

Answer:

The answer is D.

Step-by-step explanation:

Distributive Property

4x3=12

4x7=28

28+12=40

I think the answer is d

Does a dilation produce a congruent figure

Answers

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation that creates a larger image is called an enlargement. ... If the scale factor is 1, the figure and the image are congruent. The word "dilate" is often heard in relation to the human eye.

After dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.

Recall:

When two figures are congruent, it means they have the same shape and size, whereby, all pairs of corresponding angles and sides of both figures are congruent or equal in measure.The image attached below shows a dilated figure.

Dilation is a transformation that enlarges a figure or reduces the figure.

After dilation, the new figure maintains the same shape of the original figure.

However, after dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.

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Olivia works 3-hour shifts at the
library. She is paid $45 per shift.
What equation can be used to
represent the amount of money
Olivia earns, m, for working a
total of h hours?

Answers

Answer:

14 hours

antonio es gay

Step-by-step explanation:

Olivia’s pay: 3x45=135 = m for her shift

Write the numbers in order from greatest to least.
-2, 1 1⁄2, -2 3⁄4, 3⁄10

Answers

Answer:

11/2, 3/10 , -2, -2 3/4

Step-by-step explanation:

negatives are definitely on the least side. And 11/2 is 5 1/2 which is way greater 3/10. -2 3/4 means it is 3/4 more away from 0 than -2 is. So here!

The order from greatest to least is:

1 1/2  3/10  -2  -2 3/4

-2: This is a negative number, which means it is less than zero.

1 1/2 (or 1.5): A positive number greater than zero.

-2 3/4 (or -2.75): This is also a negative number and is less than -2.

3/10 (or 0.3): This is another positive number, but less than 1.

Negative numbers always rank lower than positive numbers.

Among the negative numbers, -2 is greater than -2.75.

Comparing the positive numbers:  

1.5 is greater than 0.3.

WILL MARK BRAINLIEST!!!!!!! NEED HELP FAST!!!!

Answers

Answer:

Darcy and Joe

Step-by-step explanation:

Hi there! Hopefully this helps!

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

The answer is D; Darcy and Joe.

Everyone's area's:

Tess = 21.

Darcy = 24.

Meg = 25.

Joe = 24.

If john had 9 apples and pickles gave him ten more how much apples does John have?
(9+10)

Answers

Answer:

21

but if ur serius then 19

Step-by-step explanation:

Answer:

19 Apples

Step-by-step explanation:

If john originally had 9 apples and then added ten more to his pile, then John would have 19 apples in all.

Mary spent a total of $320.91 for a party. She spent $200.39 on food, plus an additional $30.13 for
each hour of the party. How long was the party?
A.. 3 hours
B.. 4 hours
C.. 5 hours
D.. 6 hours

Answers

Answer:

The party was 4 hours long.

Step-by-step explanation:

Subtract the total by the amount already known was spent directly.

320.91-200.39= 120.52

Now, in order to figure out how many hours the part was, take how much each hour and divide it by the remainder of money.

Thus, 120.52/30.13 = 4

All things put into consideration, The party was 4 hours long.

I hope this helped!!

~ Penny

It’s 3 because I don’t know but I’m just kinda confused tho

A construction company charges $50, per square feet for building floors. How much will it cost to build a floor with radius 10 ft. use the dollars sign in your answer. Use π = 3.14

Answers

Answer:

$15700

Step-by-step explanation:

To find the cost, you multiply $50 by the area of the floor.  The floor must be a circle ("radius"), so to find the area of a circle, use the formula[tex]A=\pi r^2 \\ A=\pi(10)^2 \\ A=(3.14)(100)=314\text{ square feet}[/tex]

Multiply 314 sq. ft. by the cost per sq. ft.

314 x 50 = 15700

Answer:

69

Step-by-step explanation:for the boys

Daniel has read 60​% of a book. He has 28 more pages to finish. How many pages are there in the​ book? There are nothing pages in the book.

Answers

The total number of pages in Daniel's book is 70 pages.

Given that Daniel has read 60% of it and that he has 28 pages left to finish it. The remaining 28 pages represent the

40% of the book that Daniel has not read yet.

We can set up the equation where 40% of the total page number (represented as x) equals 28 pages.

0.40x = 28

x = 28 / 0.40

x = 70

There are 70 pages in the book.

To find the total number of pages in the book, we'll start by setting up an equation based on the information provided. Let's denote the total number of pages in the book as x.

Daniel has read 60% of the book, leaving 40% unread. Given that he has 28 more pages to finish, we can express this information in an equation:

0.40x = 28

This equation represents the 40% of the book that Daniel has yet to read, which equals the 28 pages remaining.

To find the total number of pages ( x ), we divide both sides of the equation by 0.40:

[tex]\[ x = \frac{28}{0.40} \][/tex]

x = 70

So, there are 70 pages in the book. This solution implies that there are 70 pages, considering that "nothing" is simply a placeholder value and doesn't affect the calculation.

I need help on this math problem

Answers

Answer:IS C

Step-by-step explanation:

what is perpendicular to -96/17

Answers

Answer:

[tex]\frac{17}{96}[/tex]

Step-by-step explanation:

Given  m = - [tex]\frac{96}{17}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{96}{17} }[/tex] = [tex]\frac{17}{96}[/tex]

Please help me...

1A cashier earns $8 per hour.


2.tomatoes cost $0.70 per pound

Please help me I would really appreciate it ty

Answers

Answer:

1) 2/16 |  4/32 | 5/40 | 9/72

2) 2/1.4 | 3/2.1 | 6/4.2 | 8/5.3

Step-by-step explanation:

4*8 is 32

40/8 is 5

72/8 is 9

2.1/.7 is 3

6*.7 is 4.2

8*.7 is 5.6

With the first chart all it is doing is going up by 8. So, take the time and multiply it by 8. An if you noticed the time is counting up by 2. So for the missing time just count up by 2.

For the second chart it is a little harder. The second box for the weight seems to be 3 and all you have to do for the price is take the top number and multiply it by 0.70 and you should get your answer!

Thank you for asking you question i enjoyed helping!

-MajorJax3

One letter weights 12 ounces.The mail carrier is allowed to carry 30 pounds.How many letters can he carry?

Answers

Answer:

The mail carrier can carry 40 letters.

Step-by-step explanation:

The first step is to put ounces into pounds.

1 lb = 16 oz  This is the unit rate

0.75 lbs = 12 oz

Now put the 30 lbs into ounces

30 lbs = 480 oz

Divide 480 oz by 12 oz to find how many letters equal 480 oz.

480/12 = 40 letters

If this answer is correct, please make me Brainliest!

Answer:

Hi! I am late but its 40 oz

Step-by-step explanation:

A pole 6m high has a shadow 10 m long when the shadow of a nearby building is 220 m long. How tall is the building?

Which ratio is equal to the ratio of the height of the building to its shadow?



Answers

Final answer:

By using the similar triangles principle, the height of the building is found to be 132 meters. We find this by setting up a proportion between the known ratios of the pole's height to its shadow and solving for the building's height.

Explanation:

We can solve the problem using similar triangles. The ratio of the height of the pole to its shadow is the same as the ratio of the height of the building to its shadow. Since the height of the pole is 6m and its shadow is 10m, we have the ratio of the height to the shadow for the pole as 6/10 or 3/5.

This ratio will be equal to the ratio of the height of the building (which we'll call h) to the shadow of the building (220 m), so we can write the proportion as:

3/5 = h/220

Now we solve for h:

3/220 = h/5

h = (3/5) × 220

h = (3 × 44)

h = 132m

So the height of the building is 132m.

The explicit formula for the geometric sequence -1/9, 1/3, -1, 3, -9, ... is -1/9(-3)^x-1 . What is the common ratio and recursive formula for this sequence

Answers

Answer:

r=3[tex]\left\{\begin{array}{ccc}a_1=-\frac{1}{9}\\a_n=-3a_{n-1}\end{array}\right[/tex]

Step-by-step explanation:

Given the sequence

[tex]-1/9, 1/3, -1, 3, -9, ...[/tex]

The common ratio is determined by the division of term by the previous term.

Common Ratio, [tex]r=\frac{1/3}{-1/9} =\frac{-1}{1/3} =\frac{3}{-1}=-3[/tex]

A recursive formula is a formula that defines each term of a sequence using preceding term(s).

For the given sequence, the recursive formula is:

[tex]\left\{\begin{array}{ccc}a_1=-\frac{1}{9}\\a_n=-3a_{n-1}\end{array}\right[/tex]

Answer:

−3; f(x + 1) = −3(f(x))

The answer is B.

Step-by-step explanation:

HELP PLEASE PLEASE :’(

The path of a shotput thrown is represented by the following parametric equations. Distance is measured in feet and time in seconds. Rewrite the parametric equations by eliminating the time parameter.
x(t)=23t
y(t)=5+19.3t-16t^2

a. y=5+444x-10,210x^2, x>or equal to 0
b. y=5+0.84x-0.70x^2, x>or equal to 0
c. y=5+444x-16x^2, x>or equal to 0
d. y=5+0.84x-0.03x^2, x>or equal to 0


Water is dripping out of a gutter onto a splash guard that follows the path represented by the parametric equations. Rewrite the parametric equations by eliminating the parameter.
x(t)=e^t
y(t)=2e^-t

a. y= 2/x, x>or equal to 0
b. y= 2/x, x>0
c. y= 2/(x^2), x>or equal to 0
d. y= 2/(x^2), x>0

Thanks!!!!!!

Answers

Practice:

1. A.

2. D. y=5+0.84x-0.03x^2, x>=0

3. B. y=2/x, x>0

Quiz:

1. A C E. (-4,4) (0,0) (6,9)

2. A. y=-1/3x+19/3

3. D. x=2y^2-1, y>=0

4. B. y=3/x^2, x>0

For the first parametric functions the cartisian function is y = 5+ 0.84x - 0.7x², and for the second parametric function the cartisian function is y = 2/x where x>0

What are parametric equations?

A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.

For the first parametric functions:

[tex]\rm x(t)=23t \\\\y(t)=5+19.3t-16t^2[/tex]

[tex]\rm t = \dfrac{x}{23}[/tex]

Put this value in the y(t)

[tex]\rm y=5+19.3(\dfrac{x}{23})-16(\dfrac{x}{23})^2[/tex]

y = 5+ 0.84x - 0.7x²

For the second parametric functions

[tex]\rm x(t)=e^t .....(1)\\\\y(t)=2e^-^t[/tex]

Taking ln in equation (1)

lnx = t

Put this value in equation (2)

[tex]\rm y=2e^{-lnx}[/tex]

y = 2/x,   x>0

Thus, for the first parametric functions the cartisian function is y = 5+ 0.84x - 0.7x², and for the second parametric function the cartisian function is y = 2/x where x>0

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How can you use the Pythagorean Theorem to solve real-world problems?
You can use the Pythagorean Theorem to find missing ________ (angles or lengths) in objects that are_________. ( squares, right triangles, or equilateral Triangles)

Answers

1st answer is lengths and 2nd answer is right triangles

You can use the Pythagorean Theorem to find missing lengths in objects that are right triangles.

What is Pythagorean Theorem?

The Pythagorean Theorem is a mathematical principle that relates to right triangles. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

You can use the Pythagorean Theorem to find missing lengths in objects that are right triangles.

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

By rearranging the formula, you can solve for the missing length when given the lengths of the other two sides.

This can be applied to real-world problems involving measurements of objects or distances, such as determining the length of a ladder needed to reach a certain height on a wall or calculating the distance between two points on a map.

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Rewrite the radical expression as an expression with a rational exponent.
The answer choices are in the picture!

Answers

Answer:

first one is the right answer

Answer:

[tex] = {x}^{ \frac{5}{4} } [/tex]

Step-by-step explanation:

[tex] \sqrt[4]{ {5}^{5} } \\ {5}^{(5) \times \frac{1}{4} } \\ = {5}^{ \frac{5}{4} } [/tex]

A rectangle with a length of 2 w and width of w. An equilateral triangle with side lengths of w + 8. The perimeters of a rectangle and an equilateral triangle are equal. What is the equation for this scenario? rectangle’s perimeter: equilateral triangle’s perimeter: scenario’s equation:

Answers

Answer:

rectangles perimeter: 6w

equilateral triangles perimeter: 3w+24

scenario’s equation: 6w=3w+24

Step-by-step explanation:

w=8

rectangles perimeter= 48

EQUTRI perimeter= 48

Answer:

1st part: 3rd option

2nd part: 4th option

3rd part: 4th option

Step-by-step explanation:

Which expression represents the rectangle’s perimeter?

2(2w-6)+2(w)

Which expression represents the triangle’s perimeter?

3(w+8)

What is the perimeter of both polygons?

60 units

Without drawing the graphs, find the points of intersection of the lines:

11x–6y=2 and –8x+5y=3


PLZZZZZZZ HELP!

Answers

The point of intersection of the lines given by the equations [tex]\( 11x - 6y = 2 \) and \( -8x + 5y = 3 \) is \( (4, 7) \).[/tex]

To find the points of intersection of the given lines, we need to solve the system of linear equations simultaneously.

 The given equations are:

[tex]\[ 11x - 6y = 2 \quad \text{(Equation 1)} \][/tex]

[tex]\[ -8x + 5y = 3 \quad \text{(Equation 2)} \][/tex]

 We can solve this system using the method of substitution or elimination. Let's use the elimination method to find the values of [tex]\( x \)[/tex]and [tex]\( y \).[/tex]

 First, we will make the coefficients of [tex]\( y \)[/tex] the same in both equations by multiplying Equation 1 by 5 and Equation 2 by 6:

 [tex]\[ 5(11x - 6y) = 5(2) \][/tex]

[tex]\[ 6(-8x + 5y) = 6(3) \][/tex]

 This gives us:

[tex]\[ 55x - 30y = 10 \quad \text{(Equation 3)} \][/tex]

[tex]\[ -48x + 30y = 18 \quad \text{(Equation 4)} \][/tex]

 Now, we add Equation 3 and Equation 4 to eliminate [tex]\( y \):[/tex]

[tex]\[ (55x - 30y) + (-48x + 30y) = 10 + 18 \][/tex]

[tex]\[ 7x = 28 \][/tex]

 Dividing both sides by 7, we get:

[tex]\[ x = 4 \][/tex]

 Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into either Equation 1 or Equation 2 to find the value of [tex]\( y \)[/tex]. Let's use Equation 1:

[tex]\[ 11(4) - 6y = 2 \][/tex]

[tex]\[ 44 - 6y = 2 \][/tex]

 Subtracting 44 from both sides, we get:

[tex]\[ -6y = -42 \][/tex]  Dividing both sides by -6, we get:

[tex]\[ y = 7 \][/tex].

PLEASE HELP ME!!!
Select the statement that correctly completes the sentence. When using more than one adjective, ________.

A. size comes after color
B. size comes after shape
C.size comes before color
D. size comes before opinion

Answers

Answer:

more comfortable

Step-by-step explanation:

Final answer:

When using more than one adjective, 'size comes before color', which is option C. Adjectives in English typically follow an established order, with the size adjective placed before the color adjective.

Explanation:

The correct statement that completes the sentence when using more than one adjective is C. size comes before color. In English, adjectives follow a specific order in which they appear before a noun. This order is generally: opinion, size, shape, age, color, origin, material, and purpose. Therefore, size should be placed before color when describing a noun with multiple adjectives.

For example, when arranging adjectives in a sentence, the phrase would be 'a small green book' rather than 'a green small book'. The adjective 'small' represents the size and 'green' represents the color, and according to the correct adjective order, size should come before color.

The volume of one prism is known, along with the height For the two prisms to be congruent, what must the area
of another prism. The values are shown below.
of the base be, given that the triangular bases are
congruent?
3 in 2
6 in?
12 in 2
15 in 2
15 in.
V = 90 in 3

Answers

Answer:

6in2

Step-by-step explanation:

i`m doing the assignment.

Answer:

6in^2

Step-by-step explanation:

The answer is 6in^2, I just did the assignment on Ed$ge$nuity and I got it right.

Find an equation equivalent to r = 5/1+cos(theta) in rectangular coordinates.
a. x^2=25-10y
b. y^2=10x-25
c. x^2=10y-25
d. y^2=25-10x

Please select the best answer from the choices provided

A
B
C
D

Answers

Final answer:

By applying polar to rectangular coordinates conversion formulas, the polar equation r = 5/(1+cos(θ)) is equivalent to the rectangular coordinate equation y² = 25 - 10x, which matches option D.

Explanation:

To convert the polar equation r = 5/(1+cos(θ)) to rectangular coordinates, we use the relationships between polar and rectangular coordinates: r = √x² + y² and cos(θ) = x/r. Substituting these into the given equation, we get:

r = √x² + y²;

cos(θ) = x/r;

r(1+cos(θ)) = 5;

r + r x/r = 5;

r + x = 5;

r = 5 - x;
Substitute back in for r, we get:

(√x² + y²) = 5 - x;
Squaring both sides gives us x² + y² = (5 - x)² which can be simplified to x² + y² = 25 - 10x + x². Canceling x² from both sides and reordering the terms gives us y² = 25 - 10x, which matches option D.

The scale of a map is 1 inch : 9.5 miles.

a) The actual distance between Joseph's house and the airport is 24 miles. How far apart are Joseph's house and the airport on the map?

b) Joseph traveled from his house to the airport. He then traveled another 16 miles past the airport to a restaurant. How many inches on the map represent this distance?

c) Upload your work to show how you got to the answer.

PLEASE HELP, REALLY URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

2.526 in4.211 in

Step-by-step explanation:

To find the number of inches, divide miles by 9.5.

__

a) 24 miles = (24 mi)×(1 in)/(9.5 mi) = (24/9.5) in ≈ 2.526 in

__

b) 24 miles + 16 miles = 40 miles = (40 mi)×(1 in)/(9.5 mi) = 40/9.5 in ≈ 4.211 in

_____

Comment on units conversion

I find it convenient to work units conversion problems by writing a fraction that is equal to 1 and multiplying by that to change units. My fraction has the "to" units in the numerator, and the "from" units in the denominator. That way, the unwanted units cancel when the multiplication is carried out.

The fraction is equal to 1 because the measurement in the numerator is equal to the measurement in the denominator.

__

Some folks prefer proportions. If you do it that way, be sure "like" is matched with "like".

  map inches/ground miles = 1/9.5 = x/24

  route inches/scale inches = route miles/scale miles = x/1 = 24/9.5

Find the volume of the pool shown. It consists of two prisms.





A.
1,765 feet cubed

C.
1,620 feet cubed

B.
1,234 feet cubed

D.
1,985 feet cubed

Answers

The volume of the pool is 1,620 ft cubed
The volume of the top rectangle is 1200 ft cubed and the bottom is 420 ft cubed. In all it is 1620 ft cubed.

This set of ordered pairs is a function (22, 4), (21, 1), (0, 0), (1, 1), and (2, 4).

Please explain like you were teaching how you can know this is a function.

Answers

Answer:

Step-by-step explanation:

You know these ordered pairs are considered a function, because the x intercepts do not repeat themselves. In other words, each input numbers are different. If these ordered pairs were not a function, the x intercept would be repeating. For example,  22 is already a x intercept, (22,4), if 22 was put in as another x intercept like,(22,1) these ordered pairs would not be a function.

Sam is baking cakes at her parent’s bakery. She gets paid 20 a week in addition to 5 for every cake she bakes. She made 50 this week. Write an equation to show how many cakes Sam baked this week

Answers

Answer:

i think it is 20 + 5x = 50    or  f(x)=2(3^x)

Step-by-step explanation:

equation to show how many cakes sam baked this week:

20 + 5x = 50

20 = 20 dollars

5 = 5 more dollars

x = number of cakes

therefore, sam earned $50 this week.

Answer:

20+5x=50

x will represent the number of cakes she baked

she gets paid $5 for every cake she bakes, this is where the 5x comes from

she makes $20 ("in addition" that's where the "+20" comes from) a week. However, in this case we're only talking about what she made in one week, hense why there is no variable attached to the 20

she makes a total of $50

20+5=50

she baked a total of 6 cakes. How?

subtract 20 from both sides so you have:

5x=30

divide both sides by 5 to get x by itself:

x=6

Let G be the number (in billions) of new green tea sales. Let I be the number in billions)
of new fruit juice sales. During a 20-year period, G and I can be modeled by the following
equation, where t is the time in years).
G = 674 + 3t – 2t² + 5t + 60
J = 314 - 31 + 512 - 5t + 45
Find a new model A for the total number of new green tea and fruit juice sales.

Answers

The new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 1574 + 3t - 2t².

What is a mathematical function, equation and expression?                function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is that during a 20-year period, G and I can be modeled by the following equation (where t is the time in years) :

G = 674 + 3t – 2t² + 5t + 60

I = 314 - 31 + 512 - 5t + 45

where {G} is the number (in billions) of new green tea sales and {I} be the number in billions of new fruit juice sales.

A new model {A} for the total number of new green tea and fruit juice sales can be written as -

{A} = {G} + {I}

{A} = 674 + 3t – 2t² + 5t + 60 + 314 - 31 + 512 - 5t + 45

{A} = (674 + 60 + 314 - 31 + 512 + 45) + (3t + 5t - 5t) - 2t²

{A} = 1574 + 3t - 2t²

Therefore, the new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 1574 + 3t - 2t².

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Final answer:

To create a new model for the total sales of green tea and fruit juice, the sales equations for both products are added together and simplified, resulting in the model A = 3t² + 1093, representing combined sales in billions as a function of time in years.

Explanation:

To find a new model A for the total number of new green tea and fruit juice sales, we need to combine the models given for G (green tea sales) and J (fruit juice sales). The models provided had some errors, but they should be:

G = 674 + 3t – 2t² + 5t + 60

and

J = 314 – 3t + 5t² – 5t + 45

Combining these models to form A (total sales), we add G and J together:

A = G + J

= (674 + 3t – 2t² + 5t + 60) + (314 – 3t + 5t² – 5t + 45)

Now, we simplify the equation by combining like terms:

A = (674 + 314) + (3t – 3t) + (5t – 5t) – 2t² + 5t² + (60 + 45)

A = 988 + 0t + 0t + 3t² + 105

A = 988 + 3t² + 105

A = 3t² + 1093

Therefore, the new model A for the total sales is A = 3t² + 1093. This model represents the combined sales of green tea and fruit juice in billions of dollars during the 20-year period as a function of time t in years.

Sarah’s stands on a ground and sights the top of a steep Clift at a 60 degree angle of elevation she then steps back 50 meters then sights the top of the steep cliff at a 30 degree angle if Sarah is 1.8 meters tall how tall is the cliff to the nearest meter ?

Answers

Answer:

Cliff is 45 m tall.

Step-by-step explanation:

Given:

Height of Sarah = 1.8 m

Angle of elevation = 60°

Angle of elevation 50 m back = 30°

As shown in the figure we have two right angled triangles SPQ and SPR.

Let the height of the cliff be [tex]h[/tex] meters and [tex]h= h_1+h_s[/tex].

Using trigonometric ratios:

tan (Ф) = opposite/adjacent

In ΔSPQ.                                        In ΔSPR.

[tex]tan(60) = \frac{h_1}{x}[/tex] ...equation (i)        [tex]tan (30)=\frac{h_1}{x+50}[/tex]  ...equation (ii)

Dividing equation (i) and (ii)

[tex]\frac{tan(60)}{tan(30)} = \frac{h_1}{x} \times \frac{x+50}{h_1}[/tex]

[tex]3 = \frac{x+50}{x}[/tex]

[tex]3x=x+50[/tex]

[tex]3x-x=50[/tex]

[tex]2x=50[/tex]

[tex]x=\frac{50}{2}[/tex]

[tex]x=25[/tex] meters

To find [tex]h_1[/tex] plugging [tex]x=25[/tex] in equation (i)

[tex]h_1=x\times tan(60)[/tex]

[tex]h_1=25\times 1.73[/tex]

[tex]h_1=43.25[/tex] meters

The height of the cliff from ground :

[tex]h= h_1+h_s[/tex]

[tex]h= 43.25+1.8[/tex]

[tex]h=45.05[/tex] meters

The cliff is 45 m tall to the nearest meter.

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