MATHEMATICS
HIGH SCHOOL

Answer: Answer: " y = x + 3 " .

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Explanation:

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Consider the equation of a line, in "slope-intercept form" ;

which is: " y = mx + b" ;

in which: "m" refers to the "slope of the line", which is the coefficient of "x".

"b" refers to the "y-intercept" of the line", which is given as "3" ; which is the coordinate of "x" of the point at which "y = 0".

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So, we can plug in our given values for "m" and "b" into the equation, and write the equation:

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y = 1x + 3 .

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By convention, we can write the "1x" as simply "x" ; since there is an "implied coefficient" of "1" ; and an ["implied"] slope, "m", of "1" ; since any value, multiplied by "1", results in that exact same number. So we can write the equation as:

________________________________________

" y = x + 3 " .

________________________________________

___________________________

Explanation:

___________________________

Consider the equation of a line, in "slope-intercept form" ;

which is: " y = mx + b" ;

in which: "m" refers to the "slope of the line", which is the coefficient of "x".

"b" refers to the "y-intercept" of the line", which is given as "3" ; which is the coordinate of "x" of the point at which "y = 0".

_________________________________________________

So, we can plug in our given values for "m" and "b" into the equation, and write the equation:

_________________________________________________

y = 1x + 3 .

_________________________________________________

By convention, we can write the "1x" as simply "x" ; since there is an "implied coefficient" of "1" ; and an ["implied"] slope, "m", of "1" ; since any value, multiplied by "1", results in that exact same number. So we can write the equation as:

________________________________________

" y = x + 3 " .

________________________________________

Answer:

Answer:

y=x+3

Step-by-step explanation:

HIGH SCHOOL

Can someone check my answer please HELP! Sonji paid $25.00 for two scarves, which were different prices. When she got home she could not find the receipt. She remembered that one scarf cost $3 more than the other. What was the price of the more expensive scarf?

i believe i got 14 for the most expensive scarf am i correct?

Let price of one scarf be $x

Price of the other is 3 more than $x

Therefore price of the other scarf =$x +3

The total price she paid = $25.00

That is, x+x+3=25

2x+3=25

2x=25-3

2x=22

x=22/2

x=11

The price of one scarf is $11 and the price of the other is 11+3=$14

The price of the expensive scarf =$14.

Price of the other is 3 more than $x

Therefore price of the other scarf =$x +3

The total price she paid = $25.00

That is, x+x+3=25

2x+3=25

2x=25-3

2x=22

x=22/2

x=11

The price of one scarf is $11 and the price of the other is 11+3=$14

The price of the expensive scarf =$14.

HIGH SCHOOL

Given the perimeter of a rectangle and either the length or width, find the unknown measurement using the appropriate formula. The perimeter is 76 cm and the length is 20 cm.

What is the width of the rectangle? Show all your work

The width is 18.

step by step:

1. 2 lengths are 20 which is 20+20 that's 40.

2. 76-40= 36

3. Two widths are 36 cm.

4. so do 36÷2 and that equals 18

step by step:

1. 2 lengths are 20 which is 20+20 that's 40.

2. 76-40= 36

3. Two widths are 36 cm.

4. so do 36÷2 and that equals 18

The formula of a perimeter of a rectangle:

P = 2(w + l)

We have P = 76 cm and l = 20 cm.

Substitute:

2(w + 20) = 76 use distributive property

(2)(w) + (2)(20) = 76

2w + 40 = 76 subtract 40 from both sides

2w = 36 divide both sies by 2

w = 18

Answer: the width = 18 cm
MIDDLE SCHOOL

Darla is creating a family tree. SHe starts by writing down the names of her two parents. For each of her parents, she writes down the names of their two parents, and so on. After six generations how many names has she written down, not including herself? Write and evaluate an expression using an exponent to find out

Let the number of generation be x.

Number of names =

When x = 6,

Answer: There will be 64 names written down.

Number of names =

When x = 6,

Answer: There will be 64 names written down.

MIDDLE SCHOOL

What is the decimal equivalent of four over nine ?

Answer: 0.44444444444....

Step-by-step explanation: 4/9 is the same as 4 ÷ 9. 9 does not divide into 4, so we add a 0 and bring down a 0 to get 9 divided by 40. 9 can be multiplied by 4 to get 36, 40 - 36 = 4, bring down another 0, 9 can be multiplied by 4 to get 36, 40 - 36 = 4.... this is a never ending decimal.

MIDDLE SCHOOL

How to make average ?

add all numbers and divide by the count of numbers.

HIGH SCHOOL

A student and a professor each choose a number between 1 and 8 (1 and 8 are both possible choices). what is the probability that the two choose the same number

Method 1: The student chooses a number x. The professor has 8 possible numbers to choose from, but only one choice is the number x. Therefore, the probability that they both choose the same number is 1/8. Method 2: There are 8*8 = 64 possible pairs of choices that the student and professor can make. Eight of these choices are the same number for the student and the professor, namely (1,1), (2,2),...(8,8). Therefore the probability that they both choose the same number is 8/64 = 1/8.

HIGH SCHOOL

Prove that tan60+tan70-tan50+tan10=2sqrt3?

{tan(60) + tan(10)}/{1 - tan(60)*tan(10)} - {tan(60) - tan(10)}/{1 + tan(10)*tan(60)}

ii) Taking LCM & simplifying with applying tan(60) = √3, the above simplifies to:

= 8*tan(10)/{1 - 3*tan²(10)}

iii) So tan(70) - tan(50) + tan(10) = 8*tan(10)/{1 - 3*tan²(10)} + tan(10)

= [8*tan(10) + tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}

= [9*tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}

= 3 [3*tan(10) - tan³(10)]/{1 - 3*tan²(10)}

= 3*tan(30) = 3*(1/√3) = √3 [Proved]

[Since tan(3A) = {3*tan(A) - tan³(A)}/{1 - 3*tan²(A)},

{3*tan(10) - tan³(10)}/{1 - 3*tan²(10)} = tan(3*10) = tan(30)]

ii) Taking LCM & simplifying with applying tan(60) = √3, the above simplifies to:

= 8*tan(10)/{1 - 3*tan²(10)}

iii) So tan(70) - tan(50) + tan(10) = 8*tan(10)/{1 - 3*tan²(10)} + tan(10)

= [8*tan(10) + tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}

= [9*tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}

= 3 [3*tan(10) - tan³(10)]/{1 - 3*tan²(10)}

= 3*tan(30) = 3*(1/√3) = √3 [Proved]

[Since tan(3A) = {3*tan(A) - tan³(A)}/{1 - 3*tan²(A)},

{3*tan(10) - tan³(10)}/{1 - 3*tan²(10)} = tan(3*10) = tan(30)]

MIDDLE SCHOOL

Some hot dogs come in packages of 8 why would a baker of hot dog buns package 7 hot dog buns to a package

Answer:

( I will just think this is a math question) 56

Step-by-step explanation:

8 x 7 = 56

7 hot dog is each package

MIDDLE SCHOOL

Wich is longer? A cabinet that is 3/4s foot or a shingle that is 2/3s foot? How much longer?

Answer:

The cabinet is longer by 1/12 foot.

Step-by-step explanation:

3/4 x 3/3 = 9/12

2/3 x 4/4 = 8/12