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Arte-miy333 [17]
3 years ago
5

A curve with equation y = x^2 + 2x + 3 crosses a straight line with equation y = x+9 in two places. Find the coordinates of the

two points where the lines intersect.
GUYS PLEASE HELP ME WITH THIS QUESTION. PLEASE LEAVE STAGES
Mathematics
1 answer:
ira [324]3 years ago
6 0
Got you fam or whatever people say....


We have equation 1 and 2
1. y= x^{2} +2x+3
2. y=x+9

Because equation 2 is simple and isn't quadtratic, we will insert 2 into 1,

x+9= x^{2} +2x+3 
0= x^{2} +x-6 

Then factor
x² +x -6=0
(x+3)(x-2)=0
x= -3, 2

Then using the values of x insert into either equation 1 or 2 to find y. I'm doing 2 because I'm lazy

y= x+9

when x=-3
y=x+9
  = -3+9
  = 6

(-3,6)

when x =2
y=x+9
  = 2+9
  = 11

(2,11)

Hence the co-ordinates are (2,11) and (-3,6)



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lesya [120]

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Step-by-step explanation:

\overline{AB} \cong \overline{BC} (Triangle ABC is isosceles)

m\angle CAB=m\angle CBA=30^{\circ} (base angles of an isosceles triangle are congruent)

\angle MCB=90^{\circ} (In triangle CMB, angles in a triangle add to 180 degrees)

\angle ACM=30^{\circ} (triangle sum theorem)

MB=24 (30-60-90 triangle CMB)

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2 years ago
A manufacturing company with 450 employees begins a new product line and must increase their number of employees by 18%. How man
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You just multiply 450 by .18 and it'll give you the 18% you have to add to 450.
So the equation would look like:

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3 years ago
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Select the correct answer from each drop-down menu.
finlep [7]

Answer:

Coordinates of point B are (10,-4)

Coordinates of point D are (3.6,-0.4)

Step-by-step explanation:

1) Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are ____

Let the coordinates of B be (x_2,y_2)

Coordinates of A =(x_1,y_1)=(-6,5)

Coordinates of C=(x,y)=(3.6,-0.4)

We will use section formula over here

x=\frac{mx_2+nx_1}{m+n} , y = \frac{my_2+ny_1}{m+n}

m:n=3:2

3.6=\frac{3x_2+2(-6)}{3+2} , -0.4=\frac{3y_2+2(5)}{3+2}3.6 \times 5 = 3x_2-12, -0.4 \times 5 = 3y_2+10\\18+12=3x_2 , -2=3y_2+10\\30=3x_2 , -12=3y_2\\10=x_2, -4=y_2\\

Coordinates of B = (10,-4)

2)If point D divides in the ratio 4 : 5, the coordinates of point D are ____

(fraction)

Let the coordinates of D be (x,y)

Coordinates of A =(x_1,y_1)=(-6,5)

Coordinates of B=(x_2,y_2)=(10,-4)

We will use section formula over here

x=\frac{mx_2+nx_1}{m+n} , y = \frac{my_2+ny_1}{m+n}

m:n=3:2

x=\frac{3(10)+2(-6)}{3+2} , y=\frac{3(-4)+2(5)}{3+2}\\x=3.6,y=-0.4

Coordinates of point B are (10,-4)

Coordinates of point D are (3.6,-0.4)

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AleksAgata [21]
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It's 10.75,sorry im late
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