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3 years ago

Help me ASAP i always give brainliests, and thanks i need u!

Mathematics

2 answers:

pychu [463]3 years ago

7 0

Answer:

Answer is (4) -11.333

Step-by-step explanation:

multiply : 2x /12-4/3= 4x /15 -1/5

bring variable on one side :

2x/12 -4x/15= 4/3 - 1/5

common denominator : -6x/60=17/15

simplify : -x/10= 17/15

x= - 170/15= -11.3333

andrew11 [14]3 years ago

6 0

Answer:

4. $11.333...$

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GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

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Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

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Consider an experiment with sample space S 5 50, 1, 2, 3, 4, 5, 6, 7, 8, 96 and the events A 5 {0, 2, 4, 6, 8} B 5 {1, 3, 5, 7,

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Answer with Step-by-step explanation:

S={0,1,2,3,4,5,6,7,8,9}

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C={0,1,2,3,4}

D={5,6,7,8,9}

a.A'=S-A

A'={0,1,2,3,4,5,6,7,8,9}-{0,2,4,6,8}

A'={1,3,5,7,9}

b.C'=S-C

C'={0,1,2,3,4,5,6,7,8,9}-{0,1,2,3,4}

C'={5,6,7,8,9}

c.D'=S-D

D'={0,1,2,3,4,5,6,7,8,9}-{5,6,7,8,9}

D'={0,1,2,3,4}

d. $A\cup B=$ {0,2,4,6,8} $\cup$ {1,3,5,7,9}

$A\cup B=$ {0,1,2,3,4,5,6,7,8,9}=S

e. $A\cup C$ ={0,2,4,6,8} $\cup$ {0,1,2,3,4}

$A\cup C$ ={0,1,2,3,4,6,8}

f. $A\cup D$ ={0,2,4,6,8} $\cup$ {5,6,7,8,9}

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