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1 year ago

If points (7,a), (-5,2) and (3,6) are collinear, find a.

Mathematics

1 answer:

uysha [10]1 year ago

7 0

Answer:

The value of a is 8

Step-by-step explanation:

If the three lines are collinear, they all lie on the same line

So let us have the equation of a line that passes through the known ends

the slope will be;

m = (6-2)/(3 + 5) = 4/8 = 1/2

The general form is;

y = mx + b

so, we have

y = 1/2x + b

To get b, we use any of the two known points

6 = 3/2 + b

b = 6-3/2

b = (12-3)/2 = 9/2

So the equation of the line is;

y = 1/2x + 9/2

Multiply through by 2

2y = x + 9

So for the point , to get a , we have that

2(a) = 7 + 9

2a = 16

a = 16/2

a = 8

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Expression is equivalent question

kiruha [24]

Answer:

-40+44i

Step-by-step explanation:

4(-10+11i) = -40+44i

hope its clear

7 0

2 years ago

The measure of one a cite angle of a right triangle is 6 less than twice the measure of the other acute angle find the measure o

jeka57 [31]

Answer:

32°, 58°

Step-by-step explanation:

Let one acute angle measure x.

The other acute angle measures 2x - 6.

The sum of the measures of the acute angles of a right triangle is 90.

x + 2x - 6 = 90

3x - 6 = 90

3x = 96

x = 32

2x - 6 = 2(32) - 6 = 58

Answer: 32°, 58°

8 0

1 year ago

Sara is building a triangular pen for her pet rabbit. If two of the sides measure 8 feet and 15 feet, the length of the third si

Nesterboy [21]

Answer:

1) 13 ft

Step-by-step explanation:

1) 13+8=21 which is greater than 15. Would be a triangle.

2) 7+8=15 This would be a single line, not a triangle.

3) 3+8<15 This would be a single line, not a triangle.

2) 15+8=23 This would be a single line, not a triangle.

3 0

2 years ago

Read 2 more answers

A new security system needs to be evaluated in the airport. The probability of a person being a security hazard is 4%. At the ch

ivolga24 [154]

Answer:

(a) 0.9412

(b) 0.9996 ≈ 1

Step-by-step explanation:

Denote the events a follows:

$P$ = a person passes the security system

$H$ = a person is a security hazard

Given:

$P (H) = 0.04,\ P(P^{c}|H^{c})=0.02\ and\ P(P|H)=0.01$

Then,

$P(H^{c})=1-P(H)=1-0.04=0.96\\P(P|H^{c})=1-P(P|H)=1-0.02=0.98\\$

(a)

Compute the probability that a person passes the security system using the total probability rule as follows:

The total probability rule states that: $P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})$

The value of P (P) is:

$P(P)=P(P|H)P(H)+P(P|H^{c})P(H^{c})\\=(0.01\times0.04)+(0.98\times0.96)\\=0.9412$

Thus, the probability that a person passes the security system is 0.9412.

(b)

Compute the probability that a person who passes through the system is without any security problems as follows:

$P(H^{c}|P)=\frac{P(P|H^{c})P(H^{c})}{P(P)} \\=\frac{0.98\times0.96}{0.9412} \\=0.9996\\\approx1$

Thus, the probability that a person who passes through the system is without any security problems is approximately 1.

7 0

2 years ago

Give 20 points<br> 3×+1=2×+4+×

Nezavi [6.7K]

3x+1=2x+4+x
3x
3x+1=3x+4
-1 -1
3x=3x+3
-3x
x=3

i think that would be your anser

8 0

3 years ago

Read 2 more answers