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Answer:

y = - [tex]\frac{5}{2}[/tex] x + [tex]\frac{31}{2}[/tex]

Step-by-step explanation:

Calculate the slope m of BC using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = B (7, 5 ) and (x₂, y₂ ) = C (2, 3 )

[tex]m_{BC}[/tex] = [tex]\frac{3-5}{2-7}[/tex] = [tex]\frac{-2}{-5}[/tex] = [tex]\frac{2}{5}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{5} }[/tex] = - [tex]\frac{5}{2}[/tex] , then

y = - [tex]\frac{5}{2}[/tex] x + c ← is the partial equation

To find c substitute A (3, 8 ) into the partial equation

8 = - [tex]\frac{15}{2}[/tex] + c ⇒ c = 8 + [tex]\frac{15}{2}[/tex] = [tex]\frac{16}{2}[/tex] +[tex]\frac{15}{2}[/tex] = [tex]\frac{31}{2}[/tex]

y = - [tex]\frac{5}{2}[/tex] x + [tex]\frac{31}{2}[/tex] ← equation of perpendicular line

The equation for a line passing through point A and perpendicular to BC is 2y = -5x +31 or y = -2.5x +15.5.

The equation of the straight line is represented by

y = mx+c

where m is the slope , and c is the intercept on y axis.

The equation of the line BC for points B(7,5), and C(2,3) is

y- y' = m(x-x')

m = 2/5

and c =

y-5 = (2/5)x - (14/5)

y = (2/5)x+(11/5)

The slope of the line perpendicular rot this line is given by

as the product of two perpendicular lines should be -1

m = -5/2

y = (-5/2)x +c

8 = (-15/2) + c

8 +(15/2) = 0

31/2 = c

Therefore the equation for a line passing through point A and perpendicular to BC is

2y = -5x +31

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Answer:

2hr 48 minutes

Step-by-step explanation:

65t + 85t = 420

150t = 420

t = 2 120/150 = 2 4/5 = 2hr 48 minutes

Time taken by two trains to cover 420 miles is 2hr 48 minutes.

Given, that two trains are travelling towards each other.

Relation between speed, time and distance:

Distance = Speed × Time

When the two trains are travelling towards each other the speeds of two trains are added.

When the two trains are moving in same direction then the relative speed is difference of the two.

So, here the trains are moving towards each other.

65t + 85t = 420

150t = 420

t = 420/150

t = 42/15

t = 2hr 48 minutes

Therefore total time required by two trains to meet is  2hr 48 minutes.

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Answer:

x = 0.428571 repeating

Step-by-step explanation:

Answer:

-0.428571 repeating

Step-by-step explanation:

add 4.6 both sides

1.5 = -3.5x

divide -3.5 both sides

-0.428571 repeating

Answer:

S, S, S

Step-by-step explanation:

Given the graph and the table of functions, f(x) and g(x), the following evaluated:

a. f(0) = 9

b. g(2) = -3

c. f(-1) = 5

Given the functions, f(x) and g(x), the following can be evaluated:

a. Find f(0):

Using the table given, what we need to determine is the of the output, f(0) that an input value, x = 0, will give.

Therefore,

f(0) = 9

b. Find g(2):

From the graph, find the corresponding value of g(x) that corresponds with x = 2.

Therefore,

g(2) = -3

c. Find f(-1):

From the table, find the corresponding value of f(x) that corresponds with x = -1.

Therefore,

f(-1) = 5

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I made an f in math last year

Answer:

a) 1.8

b) 11.8

c) 23.6

Step-by-step explanation:

1) 2.4+1.6+3.2+0.3+1.5=9

you divide 9 by 5 because that is the number of elements in the data.

9/5=1.8

2) the total would be 50 more because 5*10=50.

50+9=59

59/5=11.8

3) i think this question is referencing the previous question.

59*2=118

118/5=23.6

Answer:

Zahid had/has 31480 cards

7350 + 520= 7870

7870 times 4 = 31480

Step-by-step explanation:

Hope this helps

can i get braineist

Answer:

Step-by-step explanation:

Zahid and nasir had game cards= 7350

Zahid gave cards =520

Total cards left= 7350 - 520= 6830

Let

Zahid =x

Nasir = 4x

x+4x=6830

5x=6830

x=6830/5=1366

Zahid=1366

Nasir=4x=4(1366)=5464

Check

Zahid=1366+520=1886

Nasir=5464

Zahid+Nasir=1886+5464=7350

Answer: 3

Step-by-step explanation:

Answer:23

Step-by-step explanation:10 people make up 30 percent so we have 33 people . 33 - 10 = 23

Answer:

C.

Step-by-step explanation:

After the given, you need another pair of congruent angles to prove the triangles congruent by AAS. Those angles you need are vertical angles, so they are congruent.

Answer: C.

I think it is B

It makes the most sense to me to do that

Answer:

48

Step-by-step explanation:

6 + 14 ÷ 7

= 8

= 8 _ 2× 3

= 8_ 6

=8×6

=48

Answer:

9p+8

Step-by-step explanation:

p+8p= 9p

6+2= 8

9p+8

Answer:

Step-by-step explanation:

(p+6) + (8p+2)

(p+8p) + (6+2)

9p + 8

Testing the conditions, we get that [tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.

For each person sampled, there are only two possible outcomes. Either they believe in Hell, or they do not. The probability of a person believing in hell is independent of any other person, which means that the binomial distribution is used to solve this question.

Binomial distribution:

Probability of x successes on n trials, with p probability.

If [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex], it can be approximated to the normal distribution.

In this problem:

Then

[tex]np = 100(0.58) = 58 \geq 10[/tex]

[tex]n(1 - p) = 100(0.42) = 42 \geq 10[/tex]

[tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.

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9514 1404 393

Answer:

  400 minutes

Step-by-step explanation:

The cost of the first plan is ...

  A = 14 + 0.15m . . . . . . . . where m is the number of minutes used

The cost of the second plan is ...

  B = 30 + 0.11m

The costs will be equal when ...

  14 +0.15m = 30 +0.11m

  0.04m = 16 . . . . . . . . . . . . . subtract 14+0.11m from both sides

  m = 400 . . . . . . . . . . . . . . . divide by 0.04

The plans will have the same cost for 400 minutes of calls.

Answer:

0.6

Step-by-step explanation:

Lets plug these points in:

[tex]\frac{((-6)-0)}{(0-10)} =\frac{-6}{-10} =0.6[/tex]

__________

[tex] \: [/tex]

f(x) = -3x - 1

g(x) = 2x + 2

Soo :

f(2) = -3(2) - 1

f(2) = -6 - 1

f(2) = -7✔

.

g(-2) = 2(-2) + 2

g(-2) = -4 + 2

g(-2) = -2✔

Answer:

80 m High and 157 m away

Step-by-step explanation:

Cos(27)=x/176

x= 156.8 m

Sin(27) = y/176

y = 80

Answer:

metric po

Step-by-step explanation:

measurements and metric units of measure

Answer:

Click on the 2

Step-by-step explanation:

In this problem, first we find the sample mean and the standard deviation, and then, we use the normal distribution. Then, we get that:

a) The mean is of 199.69 and the standard deviation is of 25.02.

b) 0.2148 = 21.48% probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares.

c) 0.1131 = 11.31% probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

The mean is the sum of all observations divided by the number of observations, thus:

[tex]\mu = \frac{214 + 163 + 265 + 194 + 180 + 202 + 198 + 212 + 201 + 174 + 171 + 211 + 211}{13} = 199.69[/tex]

The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of values. Thus:

[tex]\sigma = \sqrt{\frac{(214-199.69)^2 + (163-199.69)^2 + (265-199.69)^2 + (194-199.69)^2 + ... + (211-199.69)^2}{13}} = 25.02[/tex]

The mean is of 199.69 and the standard deviation is of 25.02.

Item b:

This probability is the p-value of Z when X = 180, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{180 - 199.69}{25.02}[/tex]

[tex]Z = -0.79[/tex]

[tex]Z = -0.79[/tex] has a p-value of 0.2148.

0.2148 = 21.48% probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares.

Item c:

This probability is 1 subtracted by the p-value of Z when X = 230, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{230 - 199.69}{25.02}[/tex]

[tex]Z = 1.21[/tex]

[tex]Z = 1.21[/tex] has a p-value of 0.8869.

1 - 0.8869 = 0.1131

0.1131 = 11.31% probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares.

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Answer:

1.1

Step-by-step explanation:

slope = (-4-7)/(-6-4)= -11/-10 = 1.1

Answer:

1.25 or 1 1/4

Step-by-step explanation:

1 ounce is 0.0625 pounds

therefore 20 oz = 1.25 or 1 1/4

9514 1404 393

Answer:

  27

Step-by-step explanation:

You want to find x when c = 120.

  120 = x^2 -24x +39

  x^2 -24x -81 = 0 . . . . . . subtract 120 to put in standard form

  (x -27)(x +3) = 0 . . . . .  .factor it

Solutions are ...

  x = 27, x = -3 . . . . . values of x that make the factors zero

The number of flags manufactured for a cost of $120 is 27 flags.

Answer:

12

Step-by-step explanation:

2 ( - 2x + 6 )

= 2 ( - 2x ) + 2 ( 6 )

= - 4x + 12