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2 years ago

14

At a movie theater, the cost of admission to matinee is $5.25. If this price represents a 30% discount from the evening price, f

ind the evening price to the nearest cent

2 answers:

mojhsa [17]2 years ago

6 0

Let y be the original price
Yx.70= 5.25
.70 =5.25
Y= 5.25/.70
Y= $7.50

AysviL [449]2 years ago

5 0

The price of the evening Will be $3.74

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3 years ago

What simple interest rate would allow $6000 to grow to an amount of $14550 in 10 years?

Harman [31]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{ \: 14.25 \: \% \: }}}}}$

Step-by-step explanation:

Given,

Principal ( P ) = $ 6000

Amount ( A ) = $ 14550

Time ( T ) = 10 years

Rate ( R ) = ?

<u>Finding </u><u>the </u><u>Interest</u>

The sum of principal and interest is called an amount.

From the definition,

$\boxed{ \sf{Amount = \: Principal + Interest}}$

plug the values

⇒ $\sf{14550 = 6000 + Interest}$

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⇒ $\sf{6000 + Interest = 14550}$

Move 6000 to right hand side and change its sign

⇒ $\sf{Interest = 14550 - 6000}$

Subtract 6000 from 14550

⇒ $\sf{Interest = \: 8550 \: }$

Interest = $ 8550

<u>Finding </u><u>the </u><u>rate </u>

${ \boxed{ \sf{Rate = \frac{Interest \times 100}{Principal \times Time}}}}$

plug the values

⇒ $\sf{ Rate = \frac{8550 \times 100}{6000 \times 10} }$

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⇒ $\sf{Rate = \frac{855000}{60000} }$

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3 years ago

15. Work out the<br> area of a<br> rectangle with<br> sides 3.4cm and<br> 4.5cm

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2 years ago

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LuckyWell [14K]

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3 years ago

Y=x^2-6x-16 in vertex form

satela [25.4K]

Answer:

$y=(x-3)^{2} -25$

Step-by-step explanation:

The standard form of a quadratic equation is $y=ax^{2} +bx+c$

The vertex form of a quadratic equation is $y=a(x-h)^{2} +k$

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

$h=\frac{-b}{2a}$

In this case, our quadratic equation is $y=x^{2} -6x-16$ . Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

$h=\frac{-b}{2a}$ ⇒ $h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3$

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is $y=x^{2} -6x-16$

$y=x^{2} -6x-16$ ⇒ $y=(3)^{2} -6(3)-16$ ⇒ $y=9-18-16$ ⇒ $y=-25$

This y-value that we just found is our k-value.

Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: $y=a(x-h)^{2} +k$

a: 1

h: 3

k: -25

$y=(x-3)^{2} -25$

Hope this helps!

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3 years ago