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3 years ago

Solve for x if 2(5x + 2)^2 = 48

Mathematics

2 answers:

Artyom0805 [142]3 years ago

6 0

Answer:

Step-by-step explanation:

First divide both sides by 2

then apply (a+b)^2 = a^2+b^2+2ab formula

solve quadratic equation

then apply discriminant formula

Hope you get it dear ☺️

blagie [28]3 years ago

6 0

C is correct I’ve done this one before

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Chelsea took out three loans for a total of $ 78 comma 000 78,000 to start an organic orchard. Her business-equipment loan was

lianna [129]

Answer:

Business-equipment loan, A=$15000

Small-business loan, B=$24000

home-equity loan, C= $39000

Step-by-step explanation:

Let the Business-equipment loan at an interest rate of 11%=A

Let the small-business loan was at an interest rate of 5% =B

Let her home-equity loan was at an interest rate of 4.5%.=C

Since her total Loan=$78000

A+B+C=78000....(I)

Simple Interest = (P X R X T)/100

Since the Time, T=1 year

Interest on A = 0.11A

Interest on B = 0.05B

Interest on C = 0.045C

The total simple interest due on the loans in one year was $4605.

0.11A+0.05B+0.045C=4605....(II)

The annual simple interest on the home-equity loan was $105 more than the interest on the business-equipment loan.

0.045C = 0.11A +105...(III)

We proceed to solve the simultaneous equations.

A+B+C=78000....(I)

0.11A+0.05B+0.045C=4605....(II)

0.045C = 0.11A +105...(III)

From (III), 0.045C = 0.11A +105

Substitute 0.045C = 0.11A +105 into (II).

0.11A+0.05B+0.11A +105=4605

0.22A+0.05B=4500

From (III),

$C=\frac{22A}{9}+\frac{7000}{3}$

Substitute into (I)

$A+B+\frac{22A}{9}+\frac{7000}{3}=78000$

$\frac{31A}{9}+B=78000-\frac{7000}{3}$

$\frac{31A}{9}+B=\frac{227000}{3}$

$\frac{31A+9B}{9}=\frac{227000}{3}$

3(31A+9B)=9 X 227000

31A+9B=681000

0.22A+0.05B=4500 (Multiply by 9)

31A+9B=681000 (Multiply by 0.05)

1.98A+0.45B=40500

1.55A+0.45B=34050

Subtracting

0.43A=6450

A=$15000

From (III)

$C=\frac{22A}{9}+\frac{7000}{3}$

$C=\frac{22X15000}{9}+\frac{7000}{3} =39000$

C=$39000

from (I)

A+B+C=78000

15000+B+39000=78000

B=$24000

8 0

3 years ago

If a card is drawn at random from a standard deck of cards, what is the probability that it will be a 10 or a spade?

natita [175]

Answer:1 out of 52

Step-by-step explanation:

Will there is only one 10 out shades and there are 52 cards I a standard desk of cards so for that it would be one out of fifty-two

7 0

3 years ago

Help please thanksssssssssss

sattari [20]

Answer:

what is your from my from is province philippines

7 0

2 years ago

A new DVD is available for sale in a store one week after its release. The cumulative revenue,

ratelena [41]

Answer:

f(2) = $180.22

f'(2) = $130.00/week

f'(2)/f(2) = 72.13%

Two weeks after the DVD was released, the revenue from sales is $180.22 and is increasing at a rate of $130 per week, or 72.13% per week.

Step-by-step explanation:

The revenue from sales, in dollars, as a function of time, in weeks, is given by:

$f(t)=260ln(t)$

After two weeks (t=2), the revenue from sales is:

$f(2)=260ln(2)\\f(2) = \$180.22$

The rate of change, which is given by the derivate of the revenue function, at t = 2 weeks is:

$f'(t)=\frac{d}{dt} 260ln(t)\\f'(t) = \frac{260}{t}\\f'(2) = \frac{260}{2}=\$130.00/week$

The relative rate of change is:

$\frac{f'(2)}{f(2)}=\frac{130}{180.22}=0.7213=72.13\%$

Therefore, Two weeks after the DVD was released, the revenue from sales is $180.22 and is increasing at a rate of $130 per week, or 72.13% per week.

5 0

3 years ago

F(x)=-1/2(x-2)^2-4 <br> Graph the function

telo118 [61]

Answer:

see below

Step-by-step explanation:

The function is written in vertex form. It has a negative vertical scale factor, so you know ...

the vertex is (2, -4)
the vertical scale factor is 1/2
the parabola opens downward

Vertex form is ...

f(x) = a(x -h)^2 +k . . . . . . . . . . vertical scale factor "a", vertex (h, k)

Since you know the vertex and scale factor, you can plot some points on the graph. I find it convenient to think in terms of units either side of the vertex. These are values of x that would make (x-2)^2 be 1^2, 2^2, 3^2, 4^2 and so on. The vertical scale factor of -1/2 tells you that the y-differences for these points will be -1/2, -4/2, -9/2, -16/2 from the vertex. Then we have ...

vertex: (2, -4)

1 unit either side of the vertex: (1, -4.5), (3, -4.5)

2 units either side of the vertex: (0, -6), (4, -6)

3 units either side of the vertex: (-1, -8.5), (5, -8.5)

4 units either side of the vertex: (-2, -12), (6, -12)

You can plot these points and draw a smooth curve through them. Or, you can let a graphing calculator do it. The result will be similar to that shown below.

6 0

3 years ago