work out the number of students at the school

I'll do part (a) to get you started. Part (b) will follow the same sort of steps.

In part (a), we have these two points

You can call the points any letters you want. Let's find the slope of line AB

m = (y2-y1)/(x2-x1)

m = (8-2)/(3-(-3))

m = (8-2)/(3+3)

m = 6/6

m = 1

The slope of line AB is 1.

The mirror line will have the negative reciprocal of this slope, so the slope of the mirror line is -1. In other words, the mirror line slope is perpendicular to line AB. We'll use this perpendicular slope later.

-------------------------------------------

Next, we find the midpoint of segment AB

Average the x coordinates to get (x1+x2)/2 = (-3+3)/2 = 0/2 = 0

Repeat for the y coordinates:  (y1+y2)/2 = (2+8)/2 = 10/2 = 5

The midpoint of AB is (0,5)

-------------------------------------------

The mirror line will have two defining traits

So,

y = mx+b

y = -1x+b ... plugging in that perpendicular slope

5 = -1*0+b .... plugging in (x,y) = (0,5)

5 = 0+b

b = 5

The equation of the mirror line is y = -x+5 as shown in the diagram below. The mirror line is shown in green. Point D isn't important as it's just used to help set up the 90 degree angle.

This wraps up part (a) and I'll let you handle part (b). If you're stuck, then feel free to ask.

Answer:

1 = -x

Step-by-step explanation:

group like terms together so

this 5 + 4x - 7 = 4x -3 - x

becomes this 5 - 7 + 3 = 4x -4x -x

then simplify     1 = - x  

Answer:

31

Step-by-step explanation:

Substitute the values for the variables.

[tex]2(5)+7(3)\\10+21\\31[/tex]

hello,

substitute in the numbers

2(5) + 7(3)

10 + 21

= 31

Answer:

Perpendicular

Step-by-step explanation:

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Answer:

w=x÷a-b

Step-by-step explanation:

w=a-b/x

or, wx= a-b

or, x= a-b/w

Answer:

1B, 2E, 3D, 4C, 5A

Step-by-step explanation:

integers are whole numbers and their opposites. ex. -1, 1, 0, 2, -2

natural numbers are 1 to infinity.

whole numbers are 0 to infinity

rational numbers are fractions and decimals

irrational numbers are square roots

Answer:

what topic???????????????????

If you add 8x and 14x it will give you 22x

If you subtract 11-1 you have 10.

so the answer is 22x -10

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

Given, K is the midpoint of JL. So, JK = KL.

________

JL = JK + KL (given that K is the midpoint of JL)

JL = (8x + 11) + (14x - 1)

________

[tex] \large \boxed{\mathfrak{Steps} \downarrow}[/tex]

[tex] \sf( 8 x + 11 ) + ( 14 x - 1 )[/tex]

Combine 8x and 14x to get 22x.

[tex] \sf \: 22x+11-1 [/tex]

Subtract 1 from 11 to get 10.

[tex] \boxed{ \boxed{ \bf22x+10 }}[/tex]

________

Also given that, JK = KL.

So, (8x + 11) = (14x - 1)

⇨ (8x + 11) = (14x - 1)

⇨ 8x + 11 = 14x - 1

⇨ 11 + 1 = 14x - 8x

⇨ 12 = 6x

⇨ x = 12 / 6

⇨ [tex] \boxed{ \boxed{ \bf \: x= 2 }}[/tex]

________

Now, value of JL will be,

JL = 22x + 10

Substitute the value of x.

JL = 22(2) + 10

JL = 44 + 10

[tex] \boxed{ \boxed{ \bf\: JL = 50 }}[/tex]

⇨ So, the value of JL will be 50 units.

Answer:

ANSWER IS BELOW

Step-by-step explanation:

Find the properties of the given parabola.

Tap for more steps...

Direction: Opens Up

Vertex:

(

0

,

0

)

(0,0)

Focus:

(

0

,

3

4

)

(0,34)

Axis of Symmetry:

x

=

0

x=0

Directrix:

y

=

−

3

4

y=-34

Select a few

x

x

values, and plug them into the equation to find the corresponding

y

y

values. The

x

x

values should be selected around the vertex.

Tap for more steps...

x

y

−

2

4

3

−

1

1

3

0

0

1

1

3

3

3

xy-243-1130011333

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex:

(

0

,

0

)

(0,0)

Focus:

(

0

,

3

4

)

(0,34)

Axis of Symmetry:

x

=

0

x=0

Directrix:

y

=

−

3

4

y=-34

x

y

−

2

4

3

−

1

1

3

0

0

1

1

3

3

3

xy-243-1130011333

Answer:

13. Bestie literally 9+4

Answer:When solving a question like "What number is 4 less than 9?", take a close look at what it is really asking.

You have the number 9 and you are looking for a number that is 4 less than 9. In other words, if you have 9 and take away 4, then how many do you have?

You guessed it! This is a subtraction problem. 9 is the minuend and 4 is subtrahend and the answer we are looking for is the difference.

Therefore, to solve "What number is 4 less than 9?", you subtract 4 from 9 like so:

9 - 4 = 5

Step-by-step explanation:

Answer:

96 inches

Step-by-step explanation:

Because we already have the perimeter, we have to solve the formula for L (length). To do this, simply subtract 2W (width) from both sides so that we're left with 2L by itself. The formula is now 2L= P-2W. When we plug in the numbers we get 2L= 20'-2(2'). All we have to do is solve for L.

2L= 20'-4'

2L=16'

[tex]\frac{2L}{2}[/tex]=[tex]\frac{16}{2}[/tex]

L=8'

We need the answer to be in inches, so multiply 8(12) to get 96''

Answer:

No

Step-by-step explanation:

note [tex]\frac{7}{5}[/tex] = 1.4

and  sinA is defined for - 1 ≤ sinA ≤ 1

Thus sinA ≠ [tex]\frac{7}{5}[/tex]

Answer:

l=×+5

w=×

p=2(×+5+×)

=2(2×+5)

26=4×+10

26-10=4×

16=4×

×=4

length=5+4=9

width=4

Answer:

-23

Step-by-step explanation:

MN = ML(LM) - LN

MN = 31 - 54 = -23

CMIIW

Answer: Number 4 is the Bottom Bubble

Number 5 is the 2nd bubble

Step-by-step explanation:

0.012, 0.12, 1.2, 12

9.68, 9.7, 9.71, 9.90

Step-by-step explanation:

1 - (0.012 , 0.12 , 1.2 ,12)

2- (9.68 , 9.7 , 9.71 , 9.90)

The domain and the range is correct, and this is function, as it passes the vertical line test.

Answer:

D. 2¹⁵/4¹⁰

Step-by-step explanation:

(2³/4²)⁵ = 1/64

A. 2⁸/4⁷ = 1/128

B. 2⁵/4⁴ = 1/16

C. 2⁶/4⁶= 1/128

D. 2¹⁵/4¹⁰= 1/64

SO (2³/4²)⁵ = 2¹⁵/4¹⁰

Answer: 3(19)^2 - 19 - 20

3(361)-39

1083-39

1044

The area is 1044 ft.^2

The area is 1044

Step-by-step explanation:

The slope of the line is 1

Answer:

..................

Step-by-step explanation:

The slope of the line is 1.

Answer:

The choose;

[tex]3 \frac{9}{10} [/tex]

Step-by-step explanation:

[tex]2 \frac{3}{5} \div \frac{2}{3} \\ \\ = \frac{13}{5} \div \frac{2}{3} \\ \\ =\frac{13}{5} \times \frac{3}{2} = \frac{39}{10} \\ \\ = 3 \frac{9}{10} [/tex]

I hope I helped you^_^

Answer:

Step-by-step explanation:

Answer:

NO

YES

NO

YES

Step-by-step explanation:

for example :

(4³)³ = 4^9

4³.4³ = 4^6

Answer:

0.9375 is rational

Explanation:

A rational number is any integer, fraction, or terminating decimal (which 0.9375 is)

The decimal number 0.9375 is a rational number.

Irrational numbers are all real numbers that are not rational numbers in mathematics. Irrational numbers, on the other hand, cannot be stated as the ratio of two integers. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.

A rational number is any integer, fraction, or terminating decimal (which 0.9375 is). The given number 0.9375 is a rational number because it can be written in the form of the fractions like p / q.

Therefore, the decimal number 0.9375 is a rational number.

To know more about a rational number follow

https://brainly.com/question/511377

#SPJ2

Answer:

[tex](f + g)(x) = ( \frac{x}{2} - 3) + (3 {x}^{2} + x - 6) \\ \\ = 3 {x}^{2} + (\frac{x + 2x}{2} ) - 9 \\ \\ = 3 {x }^{2} + \frac{3x}{2} - 9 \\ \\ [/tex]

I hope I helped you^_^

Step-by-step explanation:

[tex]2^5\cdot\sqrt4\cdot(2^3)^4[/tex]

[tex]=2^5\cdot4^\frac12\cdot(2^3)^4[/tex]

[tex]=2^5\cdot(2^2)^\frac12\cdot(2^3)^4[/tex]

[tex]=2^5\cdot2^{2\cdot\frac12}\cdot2^{3\cdot4}[/tex]

[tex]=2^5\cdot2^1\cdot2^{12}[/tex]

[tex]=2^{5+1+12}[/tex]

[tex]=2^{18}[/tex]

Answer:

b=a-c/d

Step-by-step explanation:

just switch the variables for b

Answer:

he have to travel 12 cm/km

Step-by-step explanation:

lets find x by transposing

3x = 2x + 2        (as M is the midpoint)

3x - 2x = 2

x = 2

now put 2 instead of x

3x + 2x +2 =  (distance from friends home to house)

3 (2) + 2 (2) +2

6 + 4 + 2

10 + 2

= 12