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3 years ago

15

You need 70 bookmarks for a craft fair you begin with 35 bookmarks and make 10 bookmarks each hour. Write an expression that rep

resents the number of bookmarks you have after h hours

1 answer:

professor190 [17]3 years ago

7 0

Answer:

70 = 10x + 35 is your equation (10x + 35 is your expression).

3 1/2 hr is the time needed.

Step-by-step explanation:

Let hours = x.

You need 70 bookmarks, you have 35 (constant number), and you make 10 bookmarks an hour (varys).

Set the equation:

70 = 10x + 35

Solve for x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First subtract, then divide.

Subtract 35 from both sides:

70 (-35) = 10x + 35 (-35)

70 - 35 = 10x

35 = 10x

Isolate the variable (x). Divide 10 from both sides:

(35)/10 = (10x)/10

x = 35/10

x = 3.5

3 1/2 hours is your answer.

~

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Given:

The given function is

$y = 200(1.06)^x$

To find whether the function is growth or decay and the growth of decay.

Formula:

The function $a(1+r )^x$ is said to be an exponential growth, if the value of a > 0 and r > 0

Again, the function $a(1-r )^x$ is said to be an exponential decay, if the value of a > 0 and 0 < r < 1.

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A square park measures 170 feet along each side. Two paved paths run from each corner to the opposite corner and extend 3 feet i

Cerrena [4.2K]

Answer:

The total area, in square feet, taken by the paths is 2,004

Step-by-step explanation:

see the attached figure with lines to better understand the problem

I can divide the figure into four right triangles, one small square and four rectangles

step 1

Find the area of the right triangle of each corner of the path

The area of the triangle is

$A=(1/2)(b)(h)$

substitute the given values

$A=(1/2)(3)(3)=4.5\ ft^2$

step 2

Find the hypotenuse of the right triangle

Applying Pythagoras Theorem

Let

d -----> hypotenuse of the right triangle

$d^{2}=3^{2}+3^{2}$

$d^{2}=18$

$d=\sqrt{18}\ ft$

simplify

$d=3\sqrt{2}\ ft$

The hypotenuse of the right triangle is equal to the width of the path

step 2

Find the area of the small square of the path

The area is

$A=b^{2}$

we have

$b=3\sqrt{2}\ ft$ ----> the width of the path

substitute

$A=(3\sqrt{2})^{2}$

$A=18\ ft^2$

step 3

Find the length of the diagonal of the square park

Applying Pythagoras Theorem

Let

D -----> diagonal of the square park

$D^{2}=170^{2}+170^{2}$

$D^{2}=57,800$

$D=\sqrt{57,800}\ ft$

simplify

$D=170\sqrt{2}\ ft$

step 4

Find the height of each right triangle on each corner

The height will be equal to the width of the path divided by two, because is a 45-90-45 right triangle

$h=1.5\sqrt{2}\ ft$

step 5

Find the area of each rectangle of the path

The area of rectangle is $A=LW$

we have

$W=3\sqrt{2}\ ft$ ----> width of the path

Find the length of each rectangle of the path

$L=(D-2h-d)/2$

where

D is the diagonal of the park

h is the height of the right triangle in the corner

d is the width of the path (length side of the small square of the path)

substitute the values

$L=(170\sqrt{2}-2(1.5\sqrt{2})-3\sqrt{2})/2$

$L=(170\sqrt{2}-3\sqrt{2}-3\sqrt{2})/2$

$L=(164\sqrt{2})/2$

$L=82\sqrt{2}\ ft$

Find the area of each rectangle of the path

$A=LW$

we have

$W=3\sqrt{2}\ ft$

$L=82\sqrt{2}\ ft$

substitute

$A=(82\sqrt{2})(3\sqrt{2})$

$A=492\ ft^2$

step 6

Find the area of the paths

Remember

The total area of the paths is equal to the area of four right triangles, one small square and four rectangles

so

substitute

$A=4(4.5)+18+4(492)=2,004\ ft^2$

therefore

The total area, in square feet, taken by the paths is 2,004

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