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2 years ago

Resolve into factors (4a+b)(4a-b)

Mathematics

2 answers:

aliya0001 [1]2 years ago

4 0

Answer : $16^a - b^2$

$(4a + b) (4a - b )$

$= (4a + b) (4a - b )$

$= (4a) (4a) + ( 4a) (-b) + (b)(4a) + (b) (-b)$

$= 16^a - 4ab + 4ab - b^2$

$= 16^a - b^2$

Ray Of Light [21]2 years ago

4 0

The answer would be 16^a-b^2

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A restaurant operator in Accra has found out that during the partial lockdown, if she sells a plate of her food for GH¢20 each,

Lilit [14]

Answer:

Step-by-step explanation:

First, note this parameters from the question.

We let x = number of $5 increases and number of 10 decreases in plates sold.

Our Revenue equation is:

R(x) = (300-10x)(10+5x)

We expand the above equation into a quadratic equation by multiplying each bracket:

R(x) = 3000 + 1500x - 3000x - 1500x^2

R(x) = -1500x^2 - 1500x + 3000 (collect like terms)

Next we simplify, by dividing through by -1500

= 1500x^2/1500 - 1500x/1500 + 3000/1500

= X^2 - x + 2

X^2 - x + 2 = 0

Next, we find the axis of symmetry using the formula x = -b/(2*a) where b = 1, a = 1

X = - (-1)/2*1

X = 1/2

Number of $5 increases = $5x1/2 = $2.5

=$2.5 + $20 = $22.5 ticket price gives max revenue.

7 0

3 years ago

A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the

Vedmedyk [2.9K]

(a) Using Newton's Law of Cooling, $\dfrac{dT}{dt} = k(T - T_s)$ , we have $\dfrac{dT}{dt} = k(T - 75)$ where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get $\dfrac{dT}{T - 75} = k dt$ . Integrate both sides to get $\ln|T - 75| = kt + C$ .

Since $T(0) = 185$ , we solve for C:
$|185 - 75| = k(0) + C\ \Rightarrow\ C = \ln 110$
So we get $\ln|T - 75| = kt + \ln 110$ . Use T(30) = 150 to solve for k:
$\ln| 150 - 75 | = 30k + \ln 110\ \Rightarrow\ \ln 75 - \ln 110= 30k \Rightarrow \\ k= \frac{1}{30}\ln (75/110) = \frac{1}{30}\ln(15/22)$

So

$\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t} \Rightarrow \\
T = 75 \pm110e^{(1/30)\ln(15/22)t}$

But choose Positive because T > 75. Temp of turkey can't go under.

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
T(45) = 75 + 110e^{(1/30)\ln(15/22)(45)} = 136.929 \approx 137{}^{\circ}F$

(b)

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} = 75 + 110(15/22)^{t/30} \\
100 = 75 + 110(15/22)^{t/30} \\
25 = 110(15/22)^{t/30} 
\frac{25}{110} = (15/22)^{t/30} \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22) \approx 116\ \mathrm{min}$

Dogs of the AMS.

4 0

3 years ago

Vivenne, John and nassim ran for 6th grade class president. Vivenne got four votes for every 3 votes that John got. Nassim got t

liq [111]

Answer:

John received 10% of the overall votes.

Step-by-step explanation:

Let us assume that the number of votes John got = m

So, the number of votes Vivienne received = 3 times (John's share )

= 3 times m = 3 m

Also, The number of Votes Nassim received = 2 times ( Vivienne's share)

2 x (3 m) = 6 m

Total Votes in the grade 6

= Votes received by { John + Vivienne + Nassim}

= m + (3 m) + (6 m) = 10 m

Hence, the total number of students who voted in grade 6 = 10 m

$\textrm{The percentage of John's Votes } = \frac{\textrm{Number of votes John received}}{\textrm{Total number of votes }} \times 100$

= $\frac{m}{10m} \times 100 = 10$

or, The percentage of John's Votes = 10%

Hence, John received 10% of the overall votes.

3 0

3 years ago

-4-(-1) answer the question

Sholpan [36]

Answer:

-3

Step-by-step explanation:

Since you are subtracting a negative, it turns positive so it will be.

-4+1

-3

4 0

3 years ago

Read 2 more answers

A salesman is paid a salary of $2500 per month and a commission of 10% on all sales above $7000. Calculate his gross salary if h

Verizon [17]

Answer:

$4150

Step-by-step explanation:

Given data

Salary= $2500

Commission= 10%

Sales= $16500

Let us find the amount of the commission made

=10/100*16500

=0.1*16500

=$1650

Hence the total amount made for the month is

=commission + salary

=1650+2500

=$4150

3 0

3 years ago

Resolve into factors (4a+b)(4a-b)​

Resolve into factors (4a+b)(4a-b)