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3 years ago

Consider the function f(x)= (x+4)(x-2) what is the equation of the axis of symmetry

Mathematics

1 answer:

almond37 [142]3 years ago

8 0

if we zero out f(x), namely make y = 0, we can get the roots or x-intercepts for this quadratic equation

$\bf 0 = (x+4)(x-2)\implies \begin{cases} 0=x+4\implies &-4=x\\ 0=x-2\implies &2=x \end{cases}$

now, the equation is in x-terms, meaning is a vertically opening parabola, so the axis of symmetry will be x = something, a vertical line.

well, we have two x-intercepts, one at -4 and another at 2, and the vertex is right half-way between those guys

-4------------(-1)------------2

so the vertex is at x=-1, namely the axis of symmetry is x = -1.

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Jimmy invests $2500 in an account with a 5% interest rate, making no other deposits or withdrawals. What will Jimmy’s account ba

Alik [6]

Answer:

We conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

Step-by-step explanation:

Given

Principle P = $2500

Interest rate r = 5% = 0.05

Time period t = 8 years

To determine

Accrue Amount A = ?

Using the compound interest equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

where:

A represents the Accrue Amount

P represents the Principal Amount

r represents the interest rate

t represents the time period in years

n represents the number of compounding periods per unit t

Important tip:

Given that the interest is compounded 6 times each year, therefore, the value of n = 6.

now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

$A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}$

$\:A=2500\left(1+\frac{0.05}{6}\right)^{48}$

$A=2500\times 1.48935$ ∵ $\left(1+\frac{0.05}{6}\right)^{48\:\:}=1.48935$

$A=\:3723.38$ $

Therefore, we conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

8 0

2 years ago

2.6.PS-

mojhsa [17]

Answer:

Step-by-step explanation:

5 bags= $12.50

1= ?

$12.50*1= 12.50

$12.50/5= $2.5

$2.5*5=$12.5

$2.5*3= $7.5

3 bags= $7.5

8 0

2 years ago

A tourist purchases a car in england and ships it home to the united states. the car sticker advertised that the car's fuel cons

Valentin [98]

<u>Solution-</u>

Fuel consumption rate = 40 miles per UK gallon (As the car is manufactured in UK)

1 UK gallon = 4.5459631 lit

1 US gallon = 3.7853060 lit

$\therefore \frac{1 \ UK \ gallon}{1 \ US \ gallon} = \frac{4.5459631}{3.7853060} = 1.2009499$

$\Rightarrow 1 \ UK \ gallon = 1.2009499 \ US \ gallon$

As the fuel consumption rate = 40 miles per gallon

⇒ You need 1 UK gallon of fuel to go 40 miles

⇒ You need 1.2009499 US gallon of fuel to go 40 miles

Or you can say that, to go 40 miles you need 1.2009499 US gallon of fuel

⇒ To go 1 mile you will need $\frac{1.2009499}{40} = 0.0300237$

⇒ To go 738 miles you will need 0.0300237×738 = 22.1574906 US gallon of fuel

∴ 22.1574906 gallon of fuel is actually required.

∴ But, what she thinks will require is $\frac{738}{40} = 18.45 gallons$ (As she calculated using UK gallons)

6 0

3 years ago

Question in picture. The first box is A, the second box is B, etc.

TiliK225 [7]

Answer:

4th box and 1st box

Step-by-step explanation:

I learned this 7th nd passed it so u should be chillin

4 0

3 years ago

Read 2 more answers

What is the gcf of 12 78 and 90

Anuta_ua [19.1K]

The greatest common factor of 12, 78, and 90 is 6.

Factors are the numbers, that when multiplied with another number, equal the product.

Factors of 12: 1, 2, 3, 4, 6, and 12.
Factors of 78: 1, 2, 3, 6, 13, 26, 39, and 78.
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 20, 45, and 90.

The Greatest Common Factor is the highest factor shared among the products. Thus proving 6 is the GCF.

I hope this helps!

7 0

3 years ago