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3 years ago

7

Kello has $17 savings.she receives a $11 weekly allowance.write and solve an inequality to find the least amount of weeks it wil

l take her to save $72

1 answer:

IceJOKER [234]3 years ago

3 0

Let, the number of weeks = x
It would be: 17 + 11x ≥ 72
Subtract 17 from both sides,
11x ≥ 55
Divide by 11,
x ≥ 5

So, at-least he needs 5 weeks for that

Hope this helps!

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The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal siz

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Answer:

$(a)\ Area = 3765.32$

$(b)\ Area = 4773$

Step-by-step explanation:

Given

$A_1 = 169in^2$ --- area of each square

$Shade = 4in$

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

$L^2 = A_1$

$L^2 = 169$

$L = \sqrt{169$

$L=13$

The length of two squares make up the radius of the semicircle.

So:

$r = 2 * L$

$r = 2*13$

$r = 26$

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

$A_2 = 16 * 169$

$A_2 = 2704$

The area of the semicircle is:

$A_3 = \frac{\pi r^2}{2}$

$A_3 = \frac{3.14 * 26^2}{2}$

$A_3 = 1061.32$

So, the area of the window is:

$Area = A_2 + A_3$

$Area = 2704 + 1061.32$

$Area = 3765.32$

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

$Length = 4 * 13 + 8$

$Length = 60$

$Height = 4*13 + 4$

$Height = 56$

The area is:

$A_1 = 60 * 56 = 3360$

The radius of the semicircle becomes initial radius + 4

$r = 26 + 4 = 30$

The area is:

$A_2 = \frac{3.14 * 30^2}{2} = 1413$

The area of the shade is:

$Area = A_1 + A_2$

$Area = 3360 + 1413$

$Area = 4773$

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hodyreva [135]

Answer:

$q = 16 \sqrt{2}$ and $r = 16$

Step-by-step explanation:

We know that

$\sin( \alpha ) = \frac{side \: opposite \: to \: \alpha }{hypotenuse \: of \: triangle}$
$\cos( \alpha ) = \frac{side \: adjacent \: to \: \alpha }{hypotenuse \: of \: traingle}$
$\tan( \alpha ) = \frac{side \: opposite \: to \: \alpha }{side \: adjacent \: to \: \alpha }$

where $\alpha$ is an angle of a triangle.

In the triangle given above , $\alpha = 45°$ . So,

1) $\sin( 45) = \frac{16}{q}$

$= > \frac{1}{ \sqrt{2} } = \frac{16}{q}$

$= > q = 16 \sqrt{2}$

2) $\tan(45) = \frac{16}{r}$

$= > 1 = \frac{16}{r}$

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Step-by-step explanation:

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3 years ago

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motikmotik

Answer:

The value of $4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}$ is $4^{\dfrac{8}{15}}$ .

Step-by-step explanation:

We need to simplify the numeric expression using property. The expression is as follows :

$4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}$

The property to be used is : $x^a{\cdot} x^b=x^{a+b}$

This property is valid if the base is same. Here, base is x.

In this given problem, x = 4, a = 1/3 and b = 1/5

So,

$4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}$

So, the value of $4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}$ is $4^{\dfrac{8}{15}}$ .

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