MATHEMATICS HIGH SCHOOL

Simplify the expression shown below.
(6a⁴bc)(7ab³c)=

Answers

Answer 1
Answer: (6a^4bc)(7ab^3c)= 6\cdot 7\cdot a^4\cdot a\cdot b \cdot b^3\cdot c\cdot c =\n \n =42\cdot a^(4+1)\cdot b^(1+3)\cdot c^(1+1)=42a^5b^4c^2

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Determine the value of k so that 2x^2+kx+5=0 has each type of solutions: 2 real solutions:
2complex,nonreal solutions:
Exactly 1 real solution:

Answers

2x^2+kx+5=0 \n \na=2 \n b=k \n c=5 \n \Delta=b^2-4ac=k^2-4 * 2 * 5=k^2-40

When the discriminant Δ is greater than 0, the equation has 2 real solutions:
k^2-40 > 0 \nk^2>40 \nk>√(40) \ \lor \ k<-√(40) \nk>2√(10) \ \lor \ k<-2√(10) \n\boxed{k \in (-\infty,-2√(10)) \cup (2√(10), +\infty)}

When the discriminant Δ is less than 0, the equation has 2 complex and no real solutions:
k^2-40<0 \nk^2<40 \nk<√(40) \ \land \ k>-√(40) \nk<2√(10) \ \land \ k>-2√(10) \n\boxed{k \in (-2√(10),2√(10))}

When the discriminant Δ is equal to 0, the equation has exactly 1 real solution:
k^2-40=0 \nk^2=40 \nk=√(40) \ \lor \ k=-√(40) \nk=2√(10) \ \lor \ k=-2√(10) \n\boxed{k \in \{ -2√(10), 2√(10) \} }

Existen tres órdenes de producción en proceso. Las ordenes A y B juntas tienen 150 unidades; B y C juntas, 100 unidades, y A y C juntas, 150 unidades. ¿Cuánto tiene cada orden?

Answers

orders are a, b, c, lets write equations to represent the problem's info:
a + b = 150
b + c = 100
a + c = 150
so we have 3 unknowns and 3 equations, so we can solve.
Use the first equation:
a + b = 150
a = 150 - b
and substitute in the 3rd:
a + c = 150
150 - b + c = 150
then
b = c
and we can substitute that in the original equation:
b + c = 100
2b = 100
b = 50
c = 50
and substitute in the first equation:
a + b = 150
a = 150 - b = 150 - 50
a = 100
then a = 100, b = c = 50

How do you find the graph of f(x)= 5x-1/x-3 ?

Answers

f(x)=(5x-1)/(x-3)=(5x-15+14)/(x-3)=(5x-15)/(x-3)+(14)/(x-3)=(14)/(x-3)+(5(x-3))/(x-3)=(14)/(x-3)+5\n\ny=(14)/(x)\n\n\Downarrow T_{\vec{a}=[3;\ 5]-translate\ 3\ units\ right\ and\ 5\ units\ up}\n\nf(x)=(14)/(x-3)+5


y=(14)/(x)\n\n\underline{x|-28|-14|-7|-2|\ -1\ |\ 1\ |\ 2\ |\ 7\ |14|28|}\ny|-(1)/(2)\ |\ -1\ |-2|-7|-14|14\ |\ 7\ |\ 2\ |\ 1|\ (1)/(2)\ |

Brian claims that he can eat a pie that is divided into six equal pieces In two minutes.If he can eat the whole pie in two minutes, how long does he have to eat each piece

Answers

Answer:

He have to eat each piece in  (1)/(3) \ minute.

Step-by-step explanation:

Given:

Brian claims that he can eat a pie that is divided into six equal pieces In two minutes.

If he can eat the whole pie in two minutes.

Now, to find the time he have to eat for each piece.

So, to solve by using unitary method:

If Brian can eat 6 pieces in = 2 minutes.

Then, he can eat 1 piece in = (2)/(6)=(1)/(3) \ minute.

Therefore, he have to eat each piece in (1)/(3) \ minute.

LaTeX: \frac{16}{24} 1624 in simplest form?

Answers

Answer:

Im so sorry, I dont know the answer and accidentally clicked on it. It wont let me get out of this... SO SORRY!

Step-by-step explanation:

none

The equations 6x + 5y = 300 and 3x + 7y = 285 represent themoney collected from selling gift baskets in a school fundraising
event. If x represents the cost for each snack gift basket and
y represents the cost for each chocolate gift basket, what is the cost
for each chocolate gift basket?
(1) $20 (3) $30
(2) $25 (4) $54

Answers

Answer:

$30

Step-by-step explanation:

Solving the equation given simultaneously to get the x and y variable;

6x + 5y = 300... (1) × 1

3x + 7y = 285... (2) × 2

Using elimination method, we will multiply equation 1 by 1 and equation 2 by 2 as shown above to have;

6x + 5y = 300... 3

6x + 14y = 570... 4

Subtracting equation 3 from 4, we have;

5y-14y = 300-570

-9y = -270

y = 270/9

y = 30

Since y represent the cost for each chocolate gift basket, the cost of each chocolate gift basket will be $30
(3) $30
Multiply the second equation by -2, then subtract it from the first equation. It should be
6x+5y=300
-6x-14y=-570
                  
-9y=-270
y=30
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