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Vika [28.1K]
3 years ago
8

Which system of inequalities is represented by the graph? A) A B) B C) C D) D

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
5 0

Answer:

C

Step-by-step explanation:

It is not A or B because the line is not dotted.

It is not B or D because y should be greater than x

So it is C

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Complete the table using the equation y = 9x + 8.
Volgvan

Answer:

Y  =  (  -1) | 8 | 17 | 26 | 35|

Step-by-step explanation:

y = 9x + 8  \\ \\  \\ x = ( - 1) \\ y = 9( - 1) + 8 \\ y =  - 9 + 8 =  - 1 \\  \\ x = 0 \\ y = 9(0) + 8 \\ y = 0 + 8 = 8 \\  \\ x = 1 \\ y = 9(1) + 8 \\ y = 9 + 8 = 17 \\  \\ x = 2 \\ y = 9(2) + 8 \\ y = 18 + 8 = 26 \\  \\ x = 3 \\ y = 9(3) + 8 \\ y = 27 + 8 = 35 \\  \\  \\  Y  =  (  - 1) | 8 | 17 | 26 | 35|

7 0
3 years ago
The outside temperature decreases by 7F in 3 1 2hours. Part A How would you represent the temperature change as a unit rate? Exp
Evgesh-ka [11]

Answer:

A)  2f / hour

B) 10 f

Step-by-step explanation:

outside temperature decreases by ; 7 F in 3 1/2 hours

a ) represent temperature change as a unit rate

To do this you will need to represent the temperature change per hour

7 f / 3.5 hours

= 7 f / 3.5 = 2 therefore the temperature change as a unit rate = 2f / hour

b) Temperature change after 5 hours

Δ temperature  in 5 hours = temperature change per hour * 5

                             = 2 F * 5 =  10 F

6 0
3 years ago
Which ones are true?​
Aleks [24]

Answer:

The first, third and last one are true

7 0
2 years ago
-y-x=0<br> Write in y=Mx+b
Ymorist [56]

Answer:

y = (-1)x

Step-by-step explanation:

What you are to do here is to "rewrite -y - x = 0 in the slope-intercept form y = mx + b."

Start by solving -y - x = 0 for y:  -y = x or y = -x.

Rewrite this by inserting the coefficient 1 and representing b by 0:

y = (-1)x + 0

which is equivalent to y = (-1)x

6 0
3 years ago
Triangle ABC has vertices A(-5, -2), B(7, -5), and C(3, 1). Find the coordinates of the intersection of the three altitudes
Darina [25.2K]

Answer:

Orthocentre (intersection of altitudes) is at (37/10, 19/5)

Step-by-step explanation:

Given three vertices of a triangle

A(-5, -2)

B(7, -5)

C(3, 1)

Solution A by geometry

Slope AB = (yb-ya) / (xb-xa) = (-5-(-2)) / (7-(-5)) = -3/12 = -1/4

Slope of line normal to AB, nab = -1/(-1/4) = 4

Altitude of AB = line through C normal to AB

(y-yc) = nab(x-xc)

y-1 = (4)(x-3)

y = 4x-11           .........................(1)

Slope BC = (yc-yb) / (xc-yb) = (1-(-5) / (3-7)= 6 / (-4) = -3/2

Slope of line normal to BC, nbc = -1 / (-3/2) = 2/3

Altitude of BC

(y-ya) = nbc(x-xa)

y-(-2) = (2/3)(x-(-5)

y = 2x/3 + 10/3 - 2

y = (2/3)(x+2)    ........................(2)

Orthocentre is at the intersection of (1) & (2)

Equate right-hand sides

4x-11 = (2/3)(x+2)

Cross multiply and simplify

12x-33 = 2x+4

10x = 37

x = 37/10  ...................(3)

substitute (3) in (2)

y = (2/3)(37/10+2)

y=(2/3)(57/10)

y = 19/5  ......................(4)

Therefore the orthocentre is at (37/10, 19/5)

Alternative Solution B using vectors

Let the position vectors of the vertices represented by

a = <-5, -2>

b = <7, -5>

c = <3, 1>

and the position vector of the orthocentre, to be found

d = <x,y>

the line perpendicular to BC through A

(a-d).(b-c) = 0                          "." is the dot product

expanding

<-5-x,-2-y>.<4,-6> = 0

simplifying

6y-4x-8 = 0 ...................(5)

Similarly, line perpendicular to CA through B

<b-d>.<c-a> = 0

<7-x,-5-y>.<8,3> = 0

Expand and simplify

-3y-8x+41 = 0 ..............(6)

Solve for x, (5) + 2(6)

-20x + 74 = 0

x = 37/10  .............(7)

Substitute (7) in (6)

-3y - 8(37/10) + 41 =0

3y = 114/10

y = 19/5  .............(8)

So orthocentre is at (37/10, 19/5)  as in part A.

8 0
3 years ago
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