All categories

3 years ago

I really need help with this! Thank you!!

Mathematics

1 answer:

photoshop1234 [79]3 years ago

7 0

<h3>Answer:</h3>

x = 13; NP = 2 18/23 ≈ 2.8; NL = 5 5/23 ≈ 5.2
D. x = 17, y = 5

<h3>Step-by-step explanation:</h3>

1. In order for this problem to be workable, we need to assume PQ ║ ML. Then ΔPNQ ~ ΔLNM and ∠L = ∠P = 60°.

... ∠L = 60°

... (3x+21)° = 60°

... 3x = 39 . . . . . . . divide by °, subtract 21

... x = 13 . . . . . . . . .divide by 3

The side lengths of similar triangles are proportional, so we have ...

... (3.2 cm)/y = (6 cm)/(8-y)

Multiplying by the product of the denominators, and dividing by (cm), we have ...

... 3.2(8 -y) = 6y

... 3.2×8 = 9.2y . . . . . add 3.2y

... y = 3.2×8/9.2 = 64/23 = 2 18/23 ≈ 2.78 = NP

Then ...

... 8-y = NL ≈ 5.22

In summary: x = 13; NP ≈ 2.8; NL ≈ 5.2

_____

2. If we assume figures ABCD and PSRQ are similar, we can find the values of the variables. We assume ∠C ≅ ∠R, so ...

... 4x +27° = 95°

... 4x = 68° . . . . . subtract 27°

... x = 17° . . . . . . . divide by 4

___

AB/AD = PS/PQ . . . . . corresponding sides of similar figures are proportional

... 4y/(3y-5) = 10/5 . . . . . units of ft cancel

... 5×4y = 10(3y -5) . . . . . multiply by 5(3y-5)

... 20y = 30y -50 . . . . . . simplify

... 50 = 10y . . . . . . . . . . . add 50-20y

... 5 = y . . . . . . . . . . . . . . divide by 10

Using this value of y, we have ...

AB = 4y ft = 20 ft; AD = (3y-5) ft = 10 ft. Both these values are double the corresponding lengths on PSRQ.

In summary, x = 17°, y = 5. . . . . . (note that the ° symbol is appropriate for x)

_____

You should have your teacher show you how to work these problems <em>using only the given information</em>.

In the second problem, you cannot start with the assumption that the figures are similar, as that is what you're being asked to prove. Please note, too, that two sides and one angle of a quadrilateral are insufficient to show similarity.

You might be interested in

find the equation of a circle which passes through the point (2,-2) and (3,4) and whose centre lies on the line x+y=2

Nadusha1986 [10]

Answer:

Equation of the circle

(x - 0.7)² + (y - 1.3)² = 12.58

Step-by-step explanation:

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle.

a) We are told in the question that the equation of the circle passes through point(2, -2)

Hence,

Substituting 2 for x and -2 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(2 - a)² +(-2 - b)² = r²

Expanding the bracket

(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²

4 - 2a - 2a +a² +4 +2b +2b +b² = r²

4 - 4a + a² + 4 + 4b + b² = r²

a² + b² -4a + 4b + 4 + 4 = r²

a² + b² -4a + 4b + 8 = r²............Equation 1

We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y

Hence,

Substituting 3 for x and 4 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(3 - a)² +(4 - b)² = r²

Expanding the bracket

(3 - a) (3 - a) + (4 - b)(4- b) = r²

9 - 3a - 3a +a² +16 -4b -4b +b² = r²

9 -6a + a² + 16 -8b + b² = r²

a² + b² -6a -8b + 9 + 16 = r²

a² + b² -6a -8b + 25 = r²..........Equation 2

The next step would be to subtract Equation 1 from Equation 2

a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²

a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²

Collecting like terms

a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0

2a + 12b -17 = 0

2a + 12b = 17...........Equation 3

Step 2

We are going to have to find the values of a and b in other to get our equation of the circle.

Since the center of the circle(a, b) lies on x + y = 2

Therefore, we have

a + b = 2

a = 2 - b

2a + 12b = 17 ..........Equation 3

Substituting 2 - b for a in

2(2 - b) + 12b = 17

4 - 2b + 12b = 17

4 + 10b = 17

10b = 17 - 4

10b = 13

b = 13/10

b = 1.3

Substituting 1.3 for b in

a + b = 2

a + 1.3 = 2

a = 2 - 1.3

a = 0.7

hence, a = 0.7, b = 1.3

Step 3

We have to find the value of r using points (2, -2)

(x - a)² + (y - b)² = r²

Where x = 2 and y = -2

(-2 - 0.7)² + (-2 - 1.3)² = r²

(-2.7)² + (-3.3)² = r²

1.69 + 10.89 = r²

r² = 12.58

r = √12.58 = 3.55

Step 4

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle

a = 0.7

b = 1.3

r² = 12.58

Equation of the circle =

(x - 0.7)² + (y - 1.3)² = 12.58

7 0

3 years ago

Anelle subtracts –4 from a number. The result is 2. What is the number?<br> –6<br> –2<br> 2<br> 6

Lynna [10]

Answer:

the answer is 2. so it is 2

Step-by-step explanation:

2 ➕ 2 is 4

8 0

3 years ago

Read 2 more answers

Which function represents a reflection of f(x) =

liubo4ka [24]

If your original equation was $f(x) = 3(2)^x$ , then a reflection over the x-axis means you need all the y-values to switch sign. This means you need to multiply that function by -1.

$g(x) = -1\cdot 3(2)^x$ or $g(x) = -3(2)^x$

8 0

2 years ago

Of the people who fished at Clearwater Park today, 48 had a fishing license, 32and did not. Of the people who fished at Mountain

horrorfan [7]

Answer:

The probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

Step-by-step explanation:

Denote the events as follows:

<em>X</em> = a fisher at Clearwater Park had a fishing license

<em>Y</em> = a fisher at Mountain View Park had a fishing license

The two events are independent.

The information provided is:

n (X) = 48

n (X') = 32

n (Y) = 72

n (Y') = 18

Then,

N (X) = n (X) + n (X')

= 48 + 32

= 80

N (Y) = n (Y) + n (Y')

= 72 + 18

= 90

Compute the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license as follows:

$P(X'\cap Y)=P(X')\times P(Y)$

$=\frac{n(X')}{N(X)}\times \frac{n(Y)}{N(Y)} \\\\=\frac{32}{80}\times\frac{72}{90}\\\\=0.32$

Thus, the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

7 0

3 years ago

There are 3 blouse and 2 pieces cloths for sale in the market. how many possible sets are there?

Andrew [12]

Answer:

Each item could be included in a set or not included. That gives 2^5 = 32 ways to choose sets, including 1 set with no items, 5 sets of 1 item, 10 sets of 2 items, 10 sets of 3 items, 5 sets of 4 items, and 1 set of 5 items.

7 0

3 years ago