Sara is moving into a new apartment. The Resort complex charges a $600 security
deposit and costs $950 a month for rent. The Uptown Suites Duplex charges a $300
security deposit and costs $1100 a month for rent. After how many months would the
apartments cost the same amount? Which apartment would you recommend Sara move
to if she plans on staying for 6 months? Please show work.

Answers

Answer 1

Answer:

The rent is the same when 2 months have passed.

If she'd live in them for 6 months, I'd recommend the resort complex, since it'd be cheaper.

Step-by-step explanation:

Sara has two options, the resort complex and the uptown suites duplex, which can be represented by functions where "c" is the cost and "t" is the number of months Sara lives on each apartment.

The Resort complex:

[tex]c_{resort}(t) = 600 + 950*t[/tex]

The Uptown Suites Duplex:

[tex]c_{uptown}(t) = 300 + 1100*t[/tex]

To find the number of months she has to live in them in a way that they have the same cost, we need to find the value of t that makes both equations equal, this is done below:

[tex]600 + 950*t = 300 + 1100*t\\1100t - 950t = 600 - 300\\150t = 300\\t = \frac{300}{150} = 2\\[/tex]

The rent is the same when 2 months have passed.

If she intends to live in them for 6 months, the cost of each are:

[tex]c_{resort}(t) = 600 + 950*6 = 6300[/tex]

[tex]c_{uptown}(t) = 300 + 1100*6 = 6900[/tex]

If she'd live in them for 6 months, I'd recommend the resort complex, since it'd be cheaper.


Related Questions

Can someone please help me answer this question?

Answers

Answer:

132.5 inches

Step-by-step explanation:

The area of a triangle is 1/2 base height. the area of a rectangle is base height. Applying those principles gives us two equations: 8.5 x 10 / 2, and 9 x 10

then we have 42.5 and 90. in order to find the entire figure, they must be added so 42.5 plus 90 is 132.5. make sure to add the unit!

Answer:

Step-by-step explanation:

Triangle area

A=h_b*b/2

=8.5*10/2

=42.5in^2

Rectangle area

A=lw

=9*10

=90

Add all together

42.5+90

=132.5in^2

A cake recipe calls for 40 milliliters of water for every 20 milliliters of cooking
oil. How many milliliters of water are needed if 50 milliliters of cooking oil
were used?
O A) 25 ml
OB) 100 ml
O C) 200 ml
OD 1,000 ml

Answers

Answer:

B

Step-by-step explanation:

20x2 is 40, so 50x2 is 100

Answer:

BBBBBBBBBBBBBBBB

Step-by-step explanation:

The equation y = 65.89x + 22.17 fits the scatterplot of the values for stock
ABC over the past month with an r-value of 0.9948. How much do you think
ABC will be worth at x = 34 days?
A. $2343.31
B. $22.17
C. $2262.43
D. $65.89

Answers

The answer is C. $2262.43!

The amount of ABC will be at x = 34 days is, $2245.46.

What is an expression?

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 equation y = 65.89x + 22.17 fits the scatterplot of the values for stock ABC over the past month with an r-value of 0.9948.

Now, we can calculate the value of ABC by substituting x = 34 into the equation as;

y = 65.89(34) + 22.17

y = 2245.46

Therefore, the value of ABC at x = 34 days is approximately $2245.46.

Learn more about the mathematical expression visit:

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#SPJ5

the vertex of this parabola is at (3,-2). When the x-vaue is 4, the y-value is 3. What is the coefficient of the squared expression in the parabola equation?

Answers

Answer:   5

=========================================================

Explanation:

Vertex form is

y = a(x-h)^2 + k

We are told the vertex is (3,-2), so we know (h,k) = (3,-2)

y = a(x-h)^2 + k will update to y = a(x-3)^2 - 2

--------

Then we also know that (x,y) = (4,3) is a point on the parabola. Plug those x and y values into the equation and solve for 'a'

y = a(x-3)^2 - 2

3 = a(4-3)^2 - 2

3 = a(1)^2 - 2

3 = a - 2

3+2 = a

5 = a

a = 5

This is the coefficient of the x^2 term since the standard form is y = ax^2+bx+c.

i need help please....

Answers

Answer:

34

Step-by-step explanation:

area = (1/2)base * height.

area= half of 17 times 4

a=8.5 x 4

a=34

Answer: C

Step-by-step explanation:

Area = 1/2 bh

Area = 1/2 x 4 x 17

= 34 sq inches

NEED ANSWER ASAP. WILL MARK THE BRAINLIEST!

Answers

A(t)=4000(1+5.5/100)^4 choice 4955.30

Answer: C) 4955.30

Step-by-step explanation:

Where: A = P(1 + r/n)nt

A= 4000 (1+0.055/1)1*4

A= 4000 x (1.055)^4

A= 4955.30

Solve & Share
Evaluate the expression 3+ (6 – 2) X 4.
Solve this problem using the order of operations.
3 + (6 – 2) X 4

Answers

Answer:

[tex]19[/tex]

Step-by-step explanation:

[tex]3 + (6 -2) \times 4[/tex]

[tex]3 + (4) \times 4[/tex]

[tex]3 + 16[/tex]

[tex]=19[/tex]

Answer:

19

Step-by-step explanation:

use the other of operations

Find two consecutive whole numbers that square root 2 lies between.

Answers

Answer:

1 can be written as √1 and 2 can be written as √4 and because 1 < 2 < 4, our answer is 1 and 2.

There are some parallelograms that are not rectangles

Answers

Answer:

true

Step-by-step explanation:

This is a true statement

To be a rectangle it must have 4 right angles and 2 pairs of parallel sides

A rhombus has 2 pairs of parallel sides so it is a parallelogram, but does not have to have 90 degree angles.    (Rhombuses with 90 degree angles are squares)

_________________________________

Yes,it is true.

There are some parallelograms that are not rectangles.

Rectangle are just the special case of parallelogram where the angles are all 90 degree.All rectangles have 90 degree angles and with parallelogram that does not always have to be the case. Some parallelograms are squares,rhombus and many more.A parallelogram is a quadrilateral with 2 pairs of opposite,equal and parallel sides.

Hope it helps..

Good luck on your assignment

______________________________


ANSWER ASAP IM GIVING BRAINLIEST!
The trapezoid is composed of a rectangle and two triangles. What is the area of the rectangle? What is the total area of the triangles? What is the area of the trapezoid?

A) 13 cm2; 15 cm2; 28 cm 2
B) 26 cm2; 15 cm2; 41 cm 2
C) 40 cm2; 15 cm2; 55 cm 2
D) 40 cm2; 7.5 cm2; 47.5 cm 2

Answers

Step-by-step explanation:

is there any diagram included about this question

The recipe calls for 5 cups of strawberries for every 3 cups of whipped cream. Write this comparison as a ratio. A. 5:3 B. 3:5 C. 5>3 D.

Answers

Answer: the answer is A 5:3

Step-by-step explanation:

let z - 2 be an odd integer, is z+1 odd or even? explain

Answers

Answer:

Even

Step-by-step explanation:

If z-2 is an odd integer, that means z itself is an odd integer because very other integer is odd. Next, an odd integer + 1 is always an even integer. Therefore, z + 1 is an even integer.

Jayne polled 50 students about their preferred after-school sport and then recorded the data in the table below. Which sport is more popular? *

A. 7th
B. 8th
C. Baseball
D. Soccer

Answers

Answer:

Baseball

Step-by-step explanation:

You look at the table and find that 38/50 students play baseball, while the other 12 play soccer.

For both 7th and 8th grade, baseball is the most popular sport. Baseball has 11 votes for 7th grade and 27 votes for 8th grade.

whats a quadrilateral with two sides going in the same direction

Answers

Answer:

Trapezoid.

Step-by-step explanation:

That is a trapezoid ( in the UK a trapezium).

There is a pair of parallel sides.

x-y+z for x= 1,y=6,z=1

Answers

Answer:

-4

Step-by-step explanation:

1-6+1=-4

Answer:

The answer is (2, -1, 3)

Step-by-step explanation:

Hope this helped.

Two similar cylinders have radii of 28 inches and 32 inches. What is the ratio of their volumes?

Answers

Answer: A or B

Step-by-step explanation:

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5x2+3=0. find a=, b=, c=. thank you:)​

Answers

Answer:

a=5 b=0 c=3

Step-by-step explanation:

The quadratic equation is written as

ax^2 + bx+c =0

5x^2 +3 =0

5x^2 +0x  +3 =0

a=5 b=0 c=3

Verify sin^4 x - sin^2 x = cos^4 x - cos^2 x is an identity

Answers

Answer:

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

sin(x)^4 - sin(x)^2 = cos(x)^4 - cos(x)^2

sin(x)^2 = 1 - cos(x)^2:

sin(x)^4 - 1 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2

-(1 - cos(x)^2) = cos(x)^2 - 1:

cos(x)^2 - 1 + sin(x)^4 = ^?cos(x)^4 - cos(x)^2

sin(x)^4 = (sin(x)^2)^2 = (1 - cos(x)^2)^2:

-1 + cos(x)^2 + (1 - cos(x)^2)^2 = ^?cos(x)^4 - cos(x)^2

(1 - cos(x)^2)^2 = 1 - 2 cos(x)^2 + cos(x)^4:

-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = ^?cos(x)^4 - cos(x)^2

-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = cos(x)^4 - cos(x)^2:

cos(x)^4 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2

The left hand side and right hand side are identical:

Answer:  (identity has been verified)

Will Give Brainilest If Correct:

True or False:
0 is neither positive or negative.

Answers

Answer:

true

Step-by-step explanation:

0 is one of the many things in life that make no sense.

// have a great day //

Answer:

True

Step-by-step explanation:

0 is like the barrier between positive and negative numbers.

So the answer is true.

Diana and marie went out for lunch. Their Food and beverages cost $26.00 and there is an 8% meals tax. How much do they pay in total? Show your work.

Answers

$26.00 x %0.08 = 2.08
$26.00 + $2.08
= $28.08

Fabiola’s dog is 5 pounds heavier than one-third of the weight of Luisa’s dog. Fabiola’s dog weighs 23 pounds. Use the diagram to write an equation to represent the dogs’ weights. Let f represent the weight of Luisa’s dog. A long rectangle is the top section. 2 smaller rectangles are the bottom section. The top section represents . The bottom section represents . The equation is . ASAP PLEASE MARKING BRAINLIEST

Answers

Answer:

[tex]\frac{1}{3}[/tex]f + 5 = 23

Step-by-step explanation:

Let's put this statement into words: Fabiola’s dog is 5 pounds heavier than one-third of the weight of Luisa’s dog. Fabiola’s dog weighs 23 pounds.

This is an equation representing the weight of Fabiola's dog:

[tex]\frac{1}{3}[/tex]f + 5 = 23

I honestly have no idea what the diagram is supposed to mean, it'd be great if you could provide a picture :), then I'll edit my answer.

Answer:

The top section represents...........23 pounds

The bottom section represents..........5 + 1/3f

The equation is.........23 = 1/3f + 5

Step-by-step explanation:

I need help on my algebra. :)

Answers

Answer:

Option B

Step-by-step explanation:

Consider the steps below;

[tex]3x - 4y = 25,\\3x + 2y = 1\\\\3x - 4y = 25,\\+ ( - 3x - 2y = - 1 )\\\\- 6y = 24,\\y = - 4\\\\3x - 4y = 25,\\3x - 4 * ( - 4 ) = 25,\\3x + 16 = 25,\\3x = 9,\\x = 3\\\\Solution, x = 3, y = - 4[/tex]

To solve this system of equations, I applied process of elimination, which I thought was most convenient. Multiplying the bottom equation by - 1, I added both equations to cancel out the x's and solved for the value of y. Substituting this value of y into the top equation, I solved for the value of x;

Solution ⇒ Option B

The solution is option B

Prove that the following statements are false provide counter examples to disprove them: (1) If two angles have common vertex and their bisectors create one line, then these angles are vertical. (2) If the angle bisectors of two equal angles belong to the same line, then these angles are vertical.

Answers

Answer:

Examples to disprove them are as follows;

1) Angles of two different inscribed regular polygon in contact at their vertices

2) Angles on the opposite corners of a regular even sided polygon

Step-by-step explanation:

The statement to be disproved can be presented as follows;

1) ∠A and ∠B share a common vertex

2) The bisectors of ∠A and ∠B create one line then

∠A and ∠B are vertical, that is ∠A and ∠B are on the opposite sides of the point where two lines cross or ∠A = ∠B

Given that ∠A = Interior angle of a inscribed square = 90°

∠B = Interior angle of an inscribed equilateral triangle = 60°

Therefore the two circles can be arranged such that the line connecting the centers of both circles, are the bisectors of ∠A and ∠B

However, ∠A ≠ ∠B hence the two angles are not vertical QED

(2) The angles ∠A and ∠B where ∠A = ∠B are on the opposite corners of an even sided regular polygon are equal and their bisectors belong to the same line, however, it can be shown that ∠A and ∠B  are not vertical.

Find the distance of point U(2, 3) from point V(5, 7).​

Answers

Answer:

5

Step-by-step explanation:

You can draw a point at (5,3) and call it point A.

Connect point A with V and U to get VA = 4 and UA = 3.

You get a right triangle and use pythagoream theroem. The answer is the root of 4^2 + 3^2 which equals to 5.

The answer is 5

Which of the following is the explicit rule for a geometric sequence defined by a recursive formula of an=5an-1 for which the first term is 23?

Answers

Answer:

D

Step-by-step explanation:

The explicit rule for a geometric sequence is

[tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 23 and from the recursive formula

[tex]a_{n}[/tex] = 5[tex]a_{n-1}[/tex] , then r = 5 , thus explicit formula is

[tex]a_{n}[/tex] = 23 × [tex]5^{n-1}[/tex] → D

The correct option is D.

The calculation is as follows:

The explicit rule for a geometric sequence is

[tex]an = ar^{n-1}[/tex]

Here

a represents the first term

r represents the common ratio

So,

[tex]a_n = 5a_{n-1}[/tex]

So,

[tex]a_n = 23\times 5^{n-1}[/tex]

Learn more: brainly.com/question/17429689

PLSS HELP !!!A data set has a standard deviation of 2.5. The element 16 is an element of a data set, with a z-score of 2.4. What is the mean of the data set?

Answers

Answer:

10

Step-by-step explanation:

Given the following parameters

standard deviation σ = 2.5

z-score Z = 2.4

observed value x = 16

Mean of the dataset μ = ?

Using the formula for calculating the z-score as shown to calculate the mean

[tex]Z = \frac{x - \mu}{\sigma}[/tex]

On substituting the values;

[tex]2.4 = \frac{16-\mu}{2.5} \\2.4 * 2.5 = 16-\mu\\6 = 16-\mu\\\mu = 16-6\\\mu = 10[/tex]

The mean of the dataset is 10

points
In the diagram, m B = m AED, AD = 8, AC = 22, and
BC = 11. Find ED.
с
E
A
D
B

Answers

I would have to see the diagram

The value of ED is 4 units in the diagram.

It is given that in the diagram m ∠B = m∠AED, AD = 8, AC = 22, and BC = 11.

It is required to find the ED.

What is the triangle?

The triangle can be defined as a three-sided polygon in geometry and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have m ∠B = m∠AED both angles are equal.

And the m ∠A in the ΔADE and m ΔABC are the same.

By using the angle-angle similarity theorem ( ∵∠A=∠A)

[tex]\rm \frac{ED}{BC} = \frac{AD}{AC} \\\\\rm \frac{ED}{11} = \frac{8}{22} \\\\\rm \frac{ED}{11} = \frac{8}{22} \\\\\rm ED = 4 \ unit[/tex]

Thus, the value of ED is 4 units in the diagram.

Learn more about the triangle here:

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please answer i need some help

Answers

Answer: - 1.10

Step-by-step explanation:

Point D is one space after -1 before -1.5.

Means it is at -1.10

Which function has a vertex at the origin?

A f(x) = (x + 4)2
B fx) = x(x - 4)
C f(x) = (x - 4)(x + 4)
D f(x)= x²

Answers

answer D

Step-by-step explanation:

Hello,

we can check the graph of the functions as attached or compute the vertex analytically

from the graph you can see that D is the correct answer

I think that it is answer D

In a bag there are 3 red marbles, 2 yellow marbles, and 1 blue marble. What is the likelihood of a yellow marble being selected on the first draw?

Answers

Answer:

1/3

Step-by-step explanation:

there's 6 total marbles and 2 are yellow so this can be expressed as 2/6 which can be simplified to 1/3.

hope it helps!

Answer:

1/3

Step-by-step explanation:

The total number of marbles

3 red marbles, 2 yellow marbles, and 1 blue marble = 6 marbles

P( yellow) = yellow / total

                 = 2/6

                 = 1/3

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