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3 years ago

Given: AR ⊥ RS , TS ⊥ RS AT=26, RS=24 AR=12 Find: TS Answer: TS =

Mathematics

2 answers:

Olenka [21]3 years ago

6 0

Answer:

Solution -

Drawing a perpendicular from AQ to TS, we get a right angle triangle AQT

Using Pythagoras Theorem,

AT² = AQ² + QT²

⇒26² = 24² + QT² (∵ Due to symmetry AQ = RS)

⇒QT² = 676-576 = 100

⇒QT = 10

As TS = QT + QS = 12 + 10 = 22 ( ∵ Due to symmetry AR = QS )

∴ TS = 22 (ans)

kogti [31]3 years ago

4 0

Solution -

Drawing a perpendicular from AQ to TS, we get a right angle triangle AQT

Using Pythagoras Theorem,

AT² = AQ² + QT²

⇒26² = 24² + QT² (∵ Due to symmetry AQ = RS)

⇒QT² = 676-576 = 100

⇒QT = 10

As TS = QT + QS = 12 + 10 = 22 ( ∵ Due to symmetry AR = QS )

∴ TS = 22 (ans)

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Show your work to find X

Kamila [148]

Answer:

x = 20

Step-by-step explanation:

(2 + 3x) and 62° are vertically opposite angles and are congruent, so

3x + 2 = 62 ( subtract 2 from both sides )

3x = 60 ( divide both sides by 3 )

x = 20

3 0

3 years ago

Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a law

NARA [144]

Answer:

Slope of this line is given by:

Aaron’s rate for mowing lawns is 0.5 acres per hour

Step-by-step explanation:

It is given that time is tracked by Aaron related to x coordinate.

and the area of land mowed in acres is related to y coordinate.

Two of his points are given as:

(3, 1.5) and (5,2.5)

We know that the coordinates are represented in the form of (x,y)

i.e. first coordinate represents x coordinate and

second coordinate represents y coordinate.

So, it can be observed that:

$x_1=3, y_1=1.5\\x_2=5, y_2=2.5$

Change in x coordinate = $x_2-x_1=5-3 = 2$

i.e. total time taken is 2 hours.

Change in y coordinate = $y_2-y_1=2.5-1.5 = 1$

i.e. total land mowed taken is 1 acre.

In other words, it takes 2 hours for Aaron to mow 1 acre of land.

So, "option 1) It takes Aaron about 1 hour to mow 2 acres." is incorrect.

Rate of mowing lawn is the land mowed by Aaron in 1 hour.

Land mowed in 2 hours = 1 acre

Land mowed in 1 hours = $\frac{1}{2}$ acre i.e. 0.5 acre

Also, slope of a line is given as:

$m = \dfrac{y_2-y_1}{x_2-x_1}$

Here $y_2 - y_1 = 1$

$x_2 - x_1 = 2$

As per formula:

$m = \dfrac{1}{2} = 0.5$

So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.

6 0

3 years ago

Read 2 more answers

An atom of chlorine has several valence electrons in its

Vitek1552 [10]

Chlorine atom has 7 electrons in their valence shell

5 0

3 years ago

Harvard University accepts 6 students for every 100 applicants. How many students will be accepted if 850 applicants apply for a

patriot [66]

Answer:

51 accepted

Step-by-step explanation:

Well, if 6 are accepted out of 100, that's 6% or 0.06. To find how many are accepted out of 850, multiply 850 by 0.06.

4 0

3 years ago

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the length of a rectangle is 9 cm and the diagonal of the rectangle is 11 cm. Find the width of the rectangle

ss7ja [257]

Answer: The width is the square root of 40 or 6.32

Step-by-step explanation:

9^2 + b^2 = 11^2 where b squared is the width

81 + b^2 = 121

-81 -81

b^2 = 40

b= 6.32

7 0

3 years ago