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Katarina [22]
2 years ago
15

Need ASAP. What is the measure of angle T??​

Mathematics
1 answer:
Vesna [10]2 years ago
5 0

Answer:

B. 52

Step-by-step explanation:

T and S are the same

2x + 2 + 2x + 2 + 3x + 1 = 180

2x + 2x + 3x + 2 + 2 + 1 = 180

7x + 5 = 180

7x = 180 - 5

7x = 175

7x/7 = 175/7

x = 25

2x + 2

2(25) + 2

50 + 2

53

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Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4), and the coordinates of Mare M(3,-2). Find the slopes of sid
lozanna [386]
L(1, -4)=(xL, yL)→xL=1, yL=-4
M(3, -2)=(xM, yM)→xM=3, yM=-2

Slope of side LM: m LM = (yM-yL) / (xM-xL)
m LM = ( -2 - (-4) ) / (3-1)
m LM = ( -2+4) / (2)
m LM = (2) / (2)
m LM = 1

The quadrilateral is the rectangle KLMN
The oposite sides are: LM with NK, and KL with NK
In a rectangle the opposite sides are parallel, and parallel lines have the same slope, then:
Slope of side LM = m LM = 1 = m NK = Slope of side NK
Slope of side NK = m NK = 1

Slope of side KL = m KL = m MN = Slope of side MN

The sides KL and LM (consecutive sides) are perpendicular (form an angle of 90°), then the product of their slopes is equal to -1:
(m KL) (m LM) = -1
Replacing m LM = 1
(m KL) (1) = -1
m KL = -1 = m MN

Answer:
Slope of side LM =1
Slope of side NK =1
Slope of side KL = -1
Slope of side MN = -1 
3 0
3 years ago
Roberto rowed 20 miles downstream in 2.5 hours. The trip back, however, took him 5 hours. Find the rate that Roberto rows in sti
almond37 [142]

Answer:

<em>Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour</em>

Step-by-step explanation:

<u>Relative Speed</u>

When a body is moving at a constant speed v, the distance traveled in a time t is:

d=v.t

When Roberto rows downstream, his speed in still water is added to the speed of the water, making it easier to travel the required distance.

When Roberto rows upstream, his speed in still water is affected by the speed of the water, both are subtracted and the required distance is covered in more time.

Let's call

x = Roberto's rowing speed in still water

y = Speed of the river current

The speed when rowing downstream is x+y, thus the distance traveled is

d=(x+y).t_1

Where t1=2.5 hours. Substituting values:

20=(x+y)*2.5

Rearranging, we find the downstream equation:

2.5x+2.5y=20\qquad[1]

The speed when rowing upstream is x-y, and the distance traveled is

d=(x-y).t_2

Where t2=5 hours. Substituting values:

20=(x-y)*5

Rearranging, we find the upstream equation:

5x-5y=20\qquad[2]

Multiplying [1] by 2:

5x+5y=40

Adding this equation to [2]:

10x=60

Solving:

x=60/10=6

Dividing [2] by 5:

x-y=4

Solving for y

y=x-4=6-4=2

Thus, Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour

3 0
3 years ago
Hi guys, can someone pls explain how to divide fractions? pls and thank u
irina [24]

when dividing two fractions ex:

(1/3) / (1/6)

we take the reciprocal (we switch the bottom and top numbers) of the second fraction and then change the division into multiplication

(1/3) x (6/1)

multiply across to get

6/3

which is 2

hope this helps

5 0
3 years ago
Read 2 more answers
Derek collects quarters that have the names of the 50 U.S. states on them. He has collected 12
Lelechka [254]

Time taken to collect 12 different state quarters is 2.5 months.

Now , we need to find time taken to collect all 50 state quarters.

Let , time required is x.

So,

\dfrac{x}{50}=\dfrac{2.5}{12}\\\\x=\dfrac{2.5}{12}\times 50\\\\x=10.4

Therefore, time required is 10.7 months.

Hence, this is the required solution.

3 0
2 years ago
​a) What percent of all applicants were​ Asian? The percent of all applicants who were Asian is nothing​%. ​(Round to one decima
Likurg_2 [28]

Answer:

Follows are the solution to this question:

Step-by-step explanation:

The missing data is defined in the attached file please find it.

Given:

                                            Admission Status

\left\begin{array}{ccccc}Ethnography &Acceptable \ Approval &Waitlisted & Turned \ Away & Total\\\\ Hispanic/ Black & 51  &206&143 & 400 \\Asia &57&289&100&446\\White&                62&222&145&429\\ Total & 170& 717& 388& 1275\end{array}\right \\\\\\

In point A:

The overall percent of applicants, which is Asia:

= \frac{446}{1275} \\\\ = 0.3498039 \approx 34.98 \%

In point B:

The overall percent of the students, who admitted to Asia:

P(accepted\  Asian) = P( \frac{Placcepted \ Asian}{Asian})

                              =  \frac{\frac{57}{1275}}{\frac{446}{1275}} \\\\=  \frac{57}{1275} \times \frac{1275}{446} \\\\=  \frac{57}{446} \\\\= 0.1278027\approx 12.78 \%

In point C:

The Asian percentage approved:  

P(Asian/accepted) =\frac{P(accepted, Asian)}{P(accepted)}\\

                                =\frac{\frac{57}{1275}}{\frac{170}{1275}} \\\\= \frac{57}{1275} \times \frac{1275}{170} \\\\= \frac{57}{170} \\\\= 0.3352941\approx 33.52%

In point D:

The number of all students admitted:

=\frac{170}{1275}\\\\= 0.13333 \\\\= 13.33%

8 0
3 years ago
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