7.(08.03)
Consider the following pair of equations:
y = x + 4
y = - 2x - 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form. (20 points!)

Answer:

1.870828693387

Step-by-step explanation:

Standard Deviation, σ: 1.870828693387

Count, N:4

Sum, Σx: 12

Mean, μ: 3

Variance, σ2:  3.5

Steps

σ2 = Σ(xi - μ)2

N  =   (6 - 3)2 + ... + (1 - 3)2

4 = 14

4  = 3.5

σ = √3.5

= 1.870828693387

Answer:

377 feet

Step-by-step explanation:

Find the circumference on the circle, using the formula C = 2[tex]\pi[/tex]r

Plug in 12 as r, the radius, then solve:

C = 2[tex]\pi[/tex]r

C = 2[tex]\pi[/tex](12)

C = 24[tex]\pi[/tex]

Multiply this by 5, since the kids ran around it 5 times:

24[tex]\pi[/tex](5)

= 120[tex]\pi[/tex]

To the nearest foot, this is 377.

So, the kids ran round 377 feet

it's b because the graph of two lines that intersect at the point one it's like

Answer:

[tex] \huge{x = \frac{7}{2} }[/tex]

Step-by-step explanation:

5(x - 9) + 3(x + 4) = 2(x - 6)

First expand the terms in the bracket

That's

5x - 45 + 3x + 12 = 2x - 12

Simplify

8x - 33 = 2x - 12

8x - 2x = 33 - 12

6x = 21

Divide both sides by 6

[tex] \frac{6x}{6} = \frac{21}{6} \\ x = \frac{21}{6} [/tex]

Simplify

We have the final answer as

[tex]x = \frac{7}{2} \\ [/tex]

Hope this helps you

Answer:

x=3.5

Step-by-step explanation:

5(x-9)+3(x+4)=2(x-6)

5x-45+3x+12=2x-12

8x-33=2x-12

8x-2x=-12+33

6x=21

x=21÷6

=3.5

Hope it helps!!!

Answer:

2.93 but rounding because he must purchase whole tubes: 3.

Step-by-step explanation:

So, to figure this out, we must recall the formula for sufrace area of a rectangle:

2*L*H+2*L*W+2*W*H

This is a bit long, so lets break it up into 3 seperate segments, and plug in values:

2*L*H

Plug in the values:

2*20*10

=

400

2*L*W

Plug in the values:

2*20*8

=

320

2*W*H

Plug in the values:

2*8*10

=

160

Now that we have solved for each segment, lets add them together to get our total surface area:

400+320+160

=

880

So this is the surface area.

Now, we know that a tube of paint covers 300 of the 880 surface area.

To find the exact amount, lets divide the 880 by the 300:

[tex]\frac{880}{300}[/tex]

Simply:

[tex]\frac{44}{15}[/tex]

This is sligthly less than 3, and doing it out, you actually get 2.93 with the 3 repeating.

Now we need to think about something. Lets say you are going to the grocery store, and you need 1.895893 lettuce. Do you think you will find 1.89 lettuce? No, you could get 1 or 2, but not 1.89 lettuce, that just doesnt make sense.

It is the same thing here, we have to round up. Note that when doing problems such as these, you will never round down. If you need 1.253 tubes of paint, you arent going to get 1. You are going to need 2.  So note that you will always round up when you solving a problem like this.

So your answer is 3.

Hope this helps!

Answer:

bisector

Step-by-step explanation:

A bisector divides a segment or angle in half.

Answer:

bisector

Step-by-step explanation:

Answer:

{x,y} = {-5,-2}

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The size of each box in the grid is 1 unit by 1 unit.

From the image, we can see that the size of the base of the square pyramid is 4 units by 4 units, hence:

Area of the base = 4 units * 4 units = 16 unit²

Also, as shown in the image, all the triangular face of the square pyramid are of the same size. the distance from the middle of the triangle base to the top of the vertex of the triangle is considered to be the height of the triangle. Hence, the height of each triangular face = 2 units

Answer:

91,858

Step-by-step explanation:

This is the right answer

Answer: the answer is B hope it helps

Step-by-step explanation:

16,468 plus 75,390 = 91858

Answer:

6.9 in²

Step-by-step explanation:

(4×8)-(2×3.14×2²)

= 32 - 25.12

= 6.9

Answer:

Both 4x^2 and 64 are perfect squares

Step-by-step explanation:

If you are looking for the difference of squares, the two terms both have to be squares. We know that 64 is a square because it is 8 x 8. Also, we can say 4x^2 is a square because it can also be written as (2x)^2. We are basically looking for an option that tells us that they are square. This is option 1.

The second option is invalid because being an even number does not mean the number is a square.

The third option does not help the case much either. Just because there is a common perfect square factor, does not mean the numbers themselves are perfects squares.

Answer:

Because if two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar

Step-by-step explanation:

Answer: they look similar

Step-by-step explanation: to try to figure it out rotate one triangle to make it look identical :)

Answer:

my school

Step-by-step explanation:

block me from sieng the image

Answer:

answer: Hi = 15

Step-by-step explanation:

the larger shape is the same as the smaller shape just flipped over and bigger of course so to find this out you have to take 2 simular angles and find out what multiplied by the small angle will get the big angle so I see angles gh and ba are simular I try 4.5 ÷ 1.5 = 3 so 3 is how much the shape is being multiplied by so bc is simular to hi so I do 5 x 3 = 15 and theres are answer 15 is the length of hi hope this helps you!

The answer would be 46 gal.

9514 1404 393

Answer:

  y = 0

Step-by-step explanation:

Subtracting the right side gives ...

  [tex]\dfrac{y}{P-9}-\dfrac{y}{P+9}=0\\\\y\left(\dfrac{(P+9)-(P-9)}{P^2-81}\right)=0\\\\y\left(\dfrac{18}{P^2-81}\right)=0\\\\\boxed{y=0}[/tex]

The factor multiplying y cannot be zero, so y must be zero.

Answer:

9y^2 - 25

Step-by-step explanation:

This is the product of the sum and difference of two squares:

(a - b)(a + b) = a^2 - b^2 (a formula well worth memorizing)

Therefore, (3y - 5)(3y + 5) = 9y^2 - 25, which is in standard form.

==========================================================

Explanation:

Let's solve 6x = 3y + 5 for y

6x = 3y + 5

6x-5 = 3y

3y = 6x-5

y = (6x-5)/3

y = (6x)/3 - (5/3)

y = 2x - (5/3)

This final equation is in the form y = mx+b with m = 2 as the slope and b = -5/3 as the y intercept.

With the equation y = 2x, aka y = 2x+0, the m and b values are m = 2 and b = 0 respectively.

We see that both equations have the same slope (m = 2), but different y intercepts. Therefore, the two lines are parallel. If both y intercepts were the same as well, then we'd be talking about the same identical line.

If the slopes multiplied to -1, then the lines are perpendicular. In any other case, the two lines are neither parallel nor perpendicular.

Answer: It’s 6 meters

Step-by-step explanation:

if we know the area and the length we need to divide the two to get the width.

78 divided by 13. = 6

Answer:

f(x) = x(x-1)

Step-by-step explanation:

The easy way to do this is to look at it graphically. an inverse function is reflected across the line y=x. f(x)=x(x-1) is an upward opening parabola when reflected, there are two y-values for all positive values of x. A function can only have one y for every x.

Answer:

2nd to the left

Step-by-step explanation:

9514 1404 393

Answer:

  (a)  Interest = Principal x Rate x Time

Step-by-step explanation:

The letters in the simple interest formula ...

  I = Prt

stand for ...

  Interest = Principal x Rate x Time

Answer:

62.8

Step-by-step explanation:

3.14 times 2 times 10

I hope this helps!

Answer:

C)

Step-by-step explanation:

Answer:

[tex]18th=44032[/tex]

Step-by-step explanation:

From the question we are told that:

9th term [tex]a9=\frac{43}{256}[/tex]

14th term [tex]a14=172[/tex]

Generally the equation for Geometric sequence is mathematically given by

 [tex]a_n=a_1r^{n-1}[/tex]

For 9th term

 [tex]\frac{43}{256}=a_1r^{8}[/tex]

For 14th term

 [tex]172=a_1r^{13} \\a_1=\frac{172}{r^13}[/tex]

Substitute in 9th term

 [tex]\frac{43}{256}=\frac{172}{r^13}*r^{8}[/tex]

 [tex]\frac{43}{256*172}=r^{-5}[/tex]

 [tex]r=^5sqrt{\frac{44032}{43}}[/tex]

 [tex]r=4[/tex]

Therefore First term a is given as

 [tex]a_1=\frac{172}{4^13}[/tex]

 [tex]a_1=2.563*10^{-6}[/tex]

Generally the equation for the 18th term is mathematically given by

 [tex]18th=a_1r^{17}[/tex]

 [tex]18th=2.563*10^{-6}*4^{17}[/tex]

 [tex]18th=44032[/tex]

Answer:

16.5 feet is the height of the house.

Answer:

the value of the independent variable is 6

Answer:

6

Step-by-step explanation:

they are pretty much telling you to find the x-coordinate.

it is independent because the days do not depend on what the mass is, but the mass depends on what day it is.

sorry if this is confusing, have a good day!

Answer:

50 litres

Step-by-step explanation:

If you think of it as a ratio, there are 20 litres to every 160 km. There are __ litres to every 400 km. To get to 400, 160 is multiplied by 2.5

So multiply 20 by the same number and you get the number of litres for 400 km.

20 * 2.5 = 50

Answer:

y=1/3x+2

Step-by-step explanation: