MATHEMATICS MIDDLE SCHOOL

Find the distance from the point (6, 4) to the line y=x+4.

Answers

Answer 1
Answer:

Answer:

\large \boxed{3√(2)}

Step-by-step explanation:

1. Express the line in standard form.

ax + by + c = 0

\begin{array}{rcl}y & = & x + 4\n-x + y - 4 & = & 0\n\end{array}

2. Calculate the distance

The formula for the distance d from a point (x, y) and the line is:

d = \frac{|ax + by + c|}{\sqrt{a^(2) + b^(2)}}

Insert the values: a = -1; b = 1; c = -4; x = 6; y = 4

\begin{array}{rcl}d &= &\frac{|(-1)(6) + 1*4 + (-4)|}{\sqrt{(-1)^(2) + 1^(2)}}\n\n& = & (|-6 + 4 - 4|)/(√(1 + 1))\n\n& = & (|-6|)/(√(2))\n\n& = &(6)/(√(2))\n\n& = & (3*√(2)*√(2))/(√(2))\n\n& = & \mathbf{3{√(2)}}\end{array}\n\text{The distance from the point to the line is $\large \boxed{\mathbf{3√(2)}}$}
Answer 2
Answer:

Hey!

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First, we need to find the second coordinate.

\text{We know that the slope is 1 and the y-intercept is 4.}\n\text{We use}~(1 - 4)/(x - 6) = 1~\text{to solve for x.}\n\text{We can simplify this to}~(-3)/(x-6)\n\text{Now we know that whatever x subtracts to 6 we get -3 to get a slope of 1.}\n\text{After solving we can use 3 for x.}\n\text{We subsitute for x and end of getting}~(-3)/(-3)~\text{which equals 1.}\n\text{The second point is (3, 4)}

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Second, we need to find the distance between both points.

d = √((3 - 6)^2 + (1 - 4)^2) \nd = √((-3)^2 + (-3)^2) \nd = √(9+9) \nd = √(18) \n\text{We can simplify this using what we know about radicals.}\nd = 3√(2)

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Hence, the answer is 3√(2)!

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Hope This Helped! Good Luck!

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Which number is between 0.5 and 5/8 A.1/4 B.8/28 C.9/16 D.19/25

Answers

try doing a number line :

0.5____________________________0_________________________5/8 

so then you need to convert 0.5 into a fraction so it looks like this :

0.5 is equal to 5/10 then you simplify 5/10 :

5 can go into 5 once so that's   1 
and  
5 can go into 10 twice so that's 2 

so you just simplify 5/10 into 1/2 
so your number line should now look something like this:

5/8_________________________________________________________1/2 

then you can convert your fractions into percents 

A.1/4 is 25%
B.8/28 is 28.5%  (not sure)
C.9/16 is 56%     (not sure )
D. 19/25 is 76%

then you convert your numbers on your numbers line so that would be the fractions 5/8 and 1/2 

5/8 is 63%
1/2 is 50%

put them on a number line like this 

50%_______________________________________63% 

and your answers 
A.25%
B.28.5%
C.56%
D.76%

** Now you can easily scratch A. B. and D. because there either too high or too low  !!!

And the Answer is C. 56% or in the original question it would be C. 9/16 

Tony spent $60.54 and bought 3 packs of notebooks and a calculator. How much does a pack of notebooks cost if a calculator costs $45.87?

Answers

The amount of money Tony spent in buying a pack of notebooks is $4.89.

Given the following data:

  • Cost of calculator = $45.87.
  • Quantity of notebooks = 3 packs.
  • Quantity of calculator = 1.
  • Total cost = $60.54 .

To determine the amount of money Tony spent in buying a pack of notebooks:

How to solve a word problem.

In this exercise, you're required to determine the cost of a pack of notebooks. Thus, we would translate the word problem into an algebraic equation.

T = 3n + c\n\n60.54=3n +45.87\n\n3n=60.54-45.87\n\n3n=14.67\n\nn=(14.67)/(3)

n = $4.89.

Read more on word problems here: brainly.com/question/13170908
start with starting price which is 60.54 subtract it from what you already know which is the calculator 45.87 and that equals 14.67 thats the total cost of the notebooks that you bought but because you bought three you divide it by 3

PLEASE HELP!!!Which pair of rectangles is similar?

A. 1 rectangle is 3 and 8 2 rectangle is 2 and 6

B. 1 rectangle is 3 and 6 2 rectangle is 2 and 9

C. 1 rectangle is 3 and 8 2 rectangle is 2 and 5

D. 1 rectangle is 3 and 9 2 rectangle is 2 and 6

Answers

Let us use proportion:
a:b = c:d
where: 
ad = bc

A) 3:8 = 2:6 ⇒ 3*6 = 8*2 ⇒ 18 = 19 NOT

B) 3:6 = 2:9 ⇒ 3*9 = 6*2 ⇒ 27 = 12 NOT

C) 3:8 = 2:5 ⇒ 3*5 = 8*2 ⇒ 15 = 16 NOT

D) 3:9 = 2:6 ⇒ 3*6 = 9*2 ⇒ 18 = 18 YES!!!

A cylindrical jar has a diameter of 9 in. and a height of 12 in. The water surface is 2.5 in. from the top. About how much water is in the jar? Use 3.14 for π.A: 763 in3


B: 604 in3


C: 668 in3


D: 636 in3

Answers

Answer:

r=4.5, half of diameter

(4.5)^2 *pi * 9.5 inches=604.06 in^3.

Step-by-step explanation:

hope this helped your boi - johnny joestar

each of the 28 students in romi's class raised at least $25 during the jump-a-thon. what is the least amount of money the class raised?​

Answers

Answer:

$700

Step-by-step explanation:

25 the least amount of money earned by each student multiplied by 28 the number of students.

A shop recorded total sales of $2,000 on Monday. On Tuesday, its sales fell by 10%. On Wednesday, sales fell by another 20% compared with Tuesday. From Wednesday to Thursday, sales increased by an amount equal to 25% of Monday’s total sales. What is the net change in total sales from Monday to Thursday? The net change in total sales was .

Answers

Answer:

The net change in total sales was sale is decreases by 40.

Step-by-step explanation:

Sale of shop on Monday = $2,000

On Tuesday sales of shop fell by 10%

∴ Sales of shop on Tuesday = $2,000 × (100-10)% = $1,800

On Wednesday sales of shop fell by 20% of Tuesday's sale

∴ Sales of shop on Tuesday = $1,800 × (100-20)% = $1,440

On Thursday sales of shop increased by 25% of Monday's Total sale

∴ Sales of shop on Thursday = $1,440 + (25 × 2000)% = 1440 + 500 =  $1,940

The net change in total sales was sale is decreases by 40.
Mon: $2000Tue: 0.9*$2000 = $1800Wed: 0.8*$1800 = $1440Thu: $1440 + 0.25*$2000 = $1940Net change = $1940 - $2000 = -$60 (-3%)
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