1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Damm [24]
3 years ago
15

Laura is designing a rectangular porch for her house. On her scale drawing, the vertices of the rectangle are (2, 7), (8, 7), an

d (2, 9). What are the coordinates of the fourth vertex?

Mathematics
2 answers:
mote1985 [20]3 years ago
7 0

Answer:

Coordinates of fourth vertex are (8,9)  

Step-by-step explanation:

Given that Laura is designing a rectangular porch for her house. On her scale drawing, the vertices of the rectangle are (2, 7), (8, 7), and (2, 9).

we have to find the coordinates of the fourth vertex.

As diagonals of rectangle bisect each other and are congruent then the coordinates of E is the mid-point of AC as well as BD.

By mid-point formula if (a,b) and (c,d) are the coordinates of line segment then the coordinates of mid point are

(\frac{a+c}{2},\frac{b+d}{2})      

Mid-point of AC= mid point of BD

(\frac{a+2}{2},\frac{b+7}{2})=(\frac{8+2}{2},\frac{7+9}{2})

(\frac{a+2}{2},\frac{b+7}{2})=(5,8)

Comparing both sides , we get

\frac{a+2}{2}=5 and \frac{b+7}{2}=8

a+2=10 and b+7=16

a=8 and b=9

Hence, coordinates of fourth vertex are (8,9)    

Semenov [28]3 years ago
4 0
It has to be (8, 9) because that would put the 4th corner above (8, 7) and right of (2, 9).
You might be interested in
Omg please help idek ​
Nataly [62]
I believe The exact form is 2/45, while the decimal form would be 0.4 continuous
7 0
2 years ago
Evaluate -6-(-6) +7+(-4) + (-1).​
frutty [35]

<em>solution</em><em> </em><em>:</em><em>-</em><em>-</em>

  • = -6 + 6 + 7 - 4 - 1

  • = 6 + 7 - 6 - 4 - 1

  • = 13 - 11

  • = 2
3 0
3 years ago
Clark and Lana take a 30-year home mortgage of $128,000 at 7.8%, compounded monthly. They make their regular monthly payments fo
svp [43]

Answer:

Step-by-step explanation:

From the given information:

The present value of the house = 128000

interest rate compounded monthly r = 7.8% = 0.078

number of months in a year n= 12

duration of time t = 30 years

To find their regular monthly payment, we have:

PV = P \begin {bmatrix}  \dfrac{1 - (1 + \dfrac{r}{n})^{-nt}}{\dfrac{r}{n}}    \end {bmatrix}

128000 = P \begin {bmatrix}  \dfrac{1 - (1 + \dfrac{0.078}{12})^{- 12*30}}{\dfrac{0.078}{12}}    \end {bmatrix}

128000 = 138.914 P

P = 128000/138.914

P = $921.433

∴ Their regular monthly payment P = $921.433

To find the unpaid balance when they begin paying the $1400.

when they begin the payment ,

t = 30 year - 5years

t= 25 years

PV= 921.433 \begin {bmatrix}  \dfrac{1 - (1 - \dfrac{0.078}{12})^{25*30}}{\dfrac{0.078}{12}}    \end {bmatrix}

PV = $121718.2714

C) In order to estimate how many payments of $1400  it will take to pay off the loan, we have:

121718.2714 =  \begin {bmatrix}  \dfrac{1300  (1 - \dfrac{12.078}{12}))^{-nt}}{\dfrac{0.078}{12}}    \end {bmatrix}

121718.2714 = 200000  \begin {bmatrix}  (1 - \dfrac{12.078}{12}))^{-nt}   \end {bmatrix}

\dfrac{121718.2714}{200000 } =  \begin {bmatrix}  (1 - \dfrac{12.078}{12}))^{-nt}   \end {bmatrix}

0.60859 =  \begin {bmatrix}  (1 - \dfrac{12}{12.078}))^{nt}   \end {bmatrix}

0.60859 = (0.006458)^{nt}

nt = \dfrac{0.60859}{0.006458}

nt = 94.238 payments is required to pay off the loan.

How much interest will they save by paying the loan using the number of payments from part (c)?

The total amount of interest payed on $921.433 = 921.433 × 30(12) years

= 331715.88

The total amount paid using 921.433 and 1300 = (921.433 × 60 )+( 1300 + 94.238)

= 177795.38

The amount of interest saved = 331715.88  - 177795.38

The amount of interest saved = $153920.5

6 0
3 years ago
——————- more than 123 is 223.
Vinil7 [7]

Answer:

x=100

Step-by-step explanation:

x+123=223

x=223-123

x=100

3 0
3 years ago
Explain the areas in which you will find integration to be significant in your day to day work as an EHT.
andrey2020 [161]

Answer:

Step-by-step explanation:

An EHT is an Environmental Health Technician. Integration (Integral Calculus, if that's what you mean) will be applied to an Environmental Health Technician's job in the following way:

1. In the analysis or examination of samples from an environment, such as soil sample, water sample, domestic waste sample, septic waste sample, etc.

Essentially, Integral Calculus (and other forms of Maths) must be studied, before a person is able to be an Environmental Health Technician.

Degrees in any of the following fields are a necessary criterion;

- Applied Science

- Public Health

- Environmental Science

- Biochemistry

- Health Data Analysis

7 0
3 years ago
Other questions:
  • what is the volume of this right cone with a radius of 12 CM a height of 15 cm and a slant of 19.2 cm​
    5·2 answers
  • Jeff trip will cost $9.00 if he has 2 attendees at the conference of there are 36 attendees how much will the trip cost
    9·1 answer
  • Find the vertex of the function<br> h(x) = -x^2 + 14
    14·1 answer
  • What is a 3D shape that has 3 rectangular sides and 2 triangular sides ?
    15·2 answers
  • Consider the table of values for functions f and g below.
    14·1 answer
  • 15/16 - 7/32 Also find the sum or difference <br> A.13/32 <br> B.23/32<br> C 3/4
    12·1 answer
  • 1.25 x 8 - 1.5<br><br> please help me
    7·2 answers
  • What it the common ratio for 17, 51, 153, 459,.....
    7·2 answers
  • Please help me I’ll give you brainless it’s due in 20 minutes
    13·1 answer
  • #
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!