MATHEMATICS HIGH SCHOOL

The diagonals of rectangle NOPQ intersect at point R. If OR=3x-4 and NP=5x+20, solve for x.A.
2
B.
3
C.
12
D.
28

Answers

Answer 1
Answer:

Answer:

D. 28

Step-by-step explanation:

Please find the attachment.

We have been given that the diagonals of rectangle NOPQ intersect at point R. We are asked to find the value of x.

We will use diagonal property of rectangle, which states that diagonals of rectangle are equal and bisect each other.

Using diagonal property of rectangle, we can conclude that the segment NP is 2 times segment OR, so we can set an equation as:

2* OR=NP

Upon substituting the given expressions for both segments we will get,

2(3x-4)=5x+20

Using distributive property we will get,

6x-8=5x+20

Subtracting 5x from both sides we will get,

6x-5x-8=5x-5x+20

x-8=20

Now, we will add 8 on both sides

x-8+8=20+8    

x=28

Therefore, the value of x is 28 and option D is the correct choice.
Answer 2
Answer: D) 28 is the right answer
find the attachments for the details

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(3-i)+(1-2i) =
O 4 - 3i
O 4 +3i
O 4+i

Answers

Answer:

4+i

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Find the height of the pole if the shadow of a boy 6 ft. tall is 3 ft. and the shadow of the pole is 2 1/3 yards.

Answers

The height of the pole in yards would be 4 2/3yds, and it's height in feet would be 14ft.

hope this helped :)

A surveyor measures the angle of elevation to the top of a building to be 70 degrees. The surveyor then walks 50 ft farther from the base of the tower and measures the angle of elevation to be 50 degrees. The surveyor's angle-measuring device 5.5 ft from the ground. How tall is the building, to the nearest foot?

Answers

Answer:

height of building,H = 5.5 ft + 105.2 ft = 111 ft to the nearest ft.

Step-by-step explanation:

in this question we have given angle of elevation=70^o

when surveyor walks 50m farther from the base of the tower that time angle of elevation=50^o

As shown in figure in triangle ABD

Tan (70)= (h)/(x) .............(1)

or h=2.74x

and in triangle ABC

Tan (50)= (h)/(50+x) ...........(2)

put value of h in equation 2

we got,

1.19= (2.74x)/(50+x)

(50+x)1.19=2.74x\n50* 1.19+1.19x-2.74x=0\n59.5-1.55x=0\n59.5=1.55x\nx=38.39ft

therefore,

Height of the tower is,h=2.74\times 38.39ft

h=105.2ft

Therefore,

height of building,H = 5.5 ft + 105.2 ft = 111 ft to the nearest ft.
43.804 ft

Working;
Start by drawing the diagram as shown in the attached diagram;
Then use the following trigonometric relations;
Tan (50)= (h)/(50+x)
Tan (70)=(h)/(x)

You can then use the value of x to find the value of h. Then add 5.5 ft to h to get height of the building

Which is a point 6units to the left of 4

Answers

-2 i believe, have a great day :)

I NEED HELP ASAP (A new pizza shop opened up and started out$5,344.46 in the hole. Their first month being open they sold 61 pizzas ($3.06 profit each) and 89 sodas ($1.42 profit each). Thier bills for the first month were $1,208.01. How much money do they still need to make to break even?

Answers

Answer:

$894.97 is needed more to break even

Step-by-step explanation:

In this question, we want to know how much money the pizza shop need so that their profits will equal their expenses.

Let’s calculate their profit

This can be calculated from the pizza sales

That would be;

61(3.06) + 89(1.42) = $186.66 + $126.38 = $313.04

Now, given that their bills for the first month is $1,208.01, the amount still needed to break even would be the amount of their bills minus the profit made from selling soda and pizza

That would be 1,208.01 - 313.04 = $894.97

Jerome recently moved to a new city and bought a home. The assessment rate is 51%. The property tax rate is $53.26 per $1000. What is the effective tax rate? Show all work.

Answers

Given:
assessment rate = 51%
tax rate = 53.26 per 1,000

53.26 / 1000 = 0.05326
0.05326 x 100% = 5.326%

Effective tax rate = assessment rate * tax rate
ETR = 51% * 5.326%
ETR = 2.72%
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