Answer:
see explanation
Step-by-step explanation:
given the 2 equations
y = x² - 2x - 19 → (1)
y + 4x = 5 → (2)
substitute y = x² - 2x - 19 into (2)
x² - 2x - 19 + 4x = 5 ( subtract 5 from both sides )
x² + 2x - 24 = 0 ← in standard form
(x + 6)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 4 = 0 ⇒ x = 4
substitute each value of x into (1) for corresponding y- coordinate
x = - 6 : y = (- 6)² - 2(- 6) - 19 = 36 + 12 - 19 = 29 ⇒ (- 6, 29)
x = 4 : y = 4² - 2(4) - 19 = 16 - 8 - 19 = - 11 ⇒ (4, - 11)
the solutions are (- 6, 29), (4, - 11)
I hope this helps you
4r=p-3t
r=p-3t/4
Step-by-step explanation:
ABC is an isoceles triangle (both legs are equally long). and AB is its baseline.
OC is now a median for ABC splitting the angle at C and AB in half.
so, we have 2 right-angled triangles : OAC and OBC.
the half-angles at C are 42/2 = 21°.
the angles at A and B are 90°.
and the half-angles at O are 180 - 90 - 21 = 69°.
remember that the sum of all angles in a triangle must always be 180°.
AB are the heights of both of these triangles.
the single height is sin(69)×7 = 6.535062985... cm
and so,
AB = 2× height = 13.07012597... cm.
So 16=heads
18=tails
after you add some tails
18+x
ratio of heads to tails is 1:1.5
heads=16, didn't change
tails=18+x
so
1:1.5=16:18+x
fractionify
1/1.5=16/(18+x)
1/1.5=2/3
2/3=16/(18+x)
mutiply both sides by (3)(18+x)
2(18+x)=3(16)
36+2x=48
subtract 36 from both sides
2x=12
divide 2
x=6
6 tails added
total=heads+tails
heads=16
tails=18+6=24
total=16+24
total=40
6 tails added
40 total coins
Convert the fractions to decimals:
3/5=0.6
4/5=0.8
You have to find 2 fractions between these 2 numbers. You could pick anything.
7/10= 0.7 = less than 0.8 but greater than 0.6
75/100=0.75 = less than 0.8 but greater than 0.6
Hope this helps
