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eduard
3 years ago
13

When a transversal is perpendicular to two parallel lines, all the angles formed measure 90°. Explain why.

Mathematics
1 answer:
kotykmax [81]3 years ago
5 0
When two parallel lines are cut by a transversal, due to the natures of the different relationships among the angles, all of them will be either equal to the measure of the first angle or equal to that angle subtracted from 180.  If the transversal is perpendicular to the parallel lines, forms a right angle, then both the angle given and the angle subtracted from 180 will be 90.  This means all of the angles will be 90.
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Which line has a slope of 2 and please tell me how to figure it out on my own
Yakvenalex [24]
Lines b and c
they both go up 2 and over 1 (rise over run is slope)
3 0
3 years ago
Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B a
evablogger [386]

Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1=\frac{1}{2} *PQ*RM

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2=\frac{1}{2} *SR*PN

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1=\frac{1}{2}*PQ*h

S2=\frac{1}{2}*SR*h

Adding them together, we get the area of the whole trapezoid:

S=S1+S2=\frac{1}{2} (PQ+SR)h,

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}

Simplifying, we have

=>A= \frac{ah+2b_{1+C} }{2}

Factoring we have,

=> A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2}  \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}

 But, a+ b_{1} + c  is equal to b_{2}, the longer base of our trapezoid.

Hence, A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}

We have discussed two ways by which we can derive area of a trapezoid.

Read to know more about Trapezoid

brainly.com/question/4758162?referrer=searchResults

#SPJ10

5 0
1 year ago
How can you use the measures of center and the range to compare two populations?
DochEvi [55]

The measure of center and range to be used to compare the population is the median and the inter quartile range.

<u>Explanation:</u>

You utilize the median and the interquartile range (IQR) to portray skewed distributions of information. To look at two populaces, utilize the mean and the MAD when the two populations are symmetric. Utilize the middle and the IQR when possibly one or the two circulations are slanted.

In statistics and probability theory, the median is the worth isolating the higher half from the lower half of an information test, a populace or a likelihood circulation. For an informational collection, it might be thought of as the "center" esteem.

8 0
3 years ago
Constance wants to purchase an school jacket. She saw the same jacket at a few stores. Store A had the jacket for 15% off the or
soldi70 [24.7K]

Store A will be the better buy.

The price will be $53.70 after sales tax at store A.

Step-by-step explanation:

Price of Jacket at store A = $59.60

Discount = 15%

Discount Amount = \frac{15}{100}*59.60\\

Discount Amount = 0.15*59.60=\$8.94

Price after discount = Original price - Discount amount

Price after discount = 59.60 - 8.94 = $50.66

Price of Jacket at store B = $50.99

The price at store A becomes less than store B after discount, therefore, buying from store A is better.

Sales tax = 6%

Sales tax amount = \frac{6}{100}*50.66

Sales tax amount = 0.06*50.66=\$3.0396

Price after sales tax = Discount price at store A + Sales tax amount

Price after sales tax = 50.66 + 3.0396 = $53.6996

Rounding off to nearest hundredth;

Price after sales tax = $53.70

The price will be $53.70 after sales tax at store A.

Keywords: percentage, addition

Learn more about percentages at:

  • brainly.com/question/10557938
  • brainly.com/question/10600222

#LearnwithBrainly

8 0
2 years ago
7. Use the​ compound-interest formula to find the account balance A with the given​ conditions, where P=​principal, r=interest ​
Artist 52 [7]

Answer:

<u>$173,954.01</u>

Step-by-step explanation:

Finding compound interest :

  • A = (150,000)(1 + 0.025)⁶
  • A = (150,000)(1.025)⁶
  • A = (150,000)(1.15969342)
  • A = <u>$173,954.01</u>
4 0
2 years ago
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