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marysya [2.9K]
2 years ago
6

you want to save up enough money to buy a new pair of shoes that cost $100. you decide that you will put $7 in your piggy bank e

very week from youre allowance to buy the shoes. if you currently have $45 in your bank account, how long will it take you to save enough money? complete a table.​
Mathematics
1 answer:
nexus9112 [7]2 years ago
5 0
Start - 45
week 1 - 52
week 2 - 59
week 3 - 66
week 4 - 73
week 5 - 80
week 6 - 87
week 7 - 94
week 8 - 101
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Let f be the function given by f(x)= (x-1)(x^2-4)/x^2-a. For what positive values of a is f continuous for all real numbers x?
9966 [12]

Answer:

a =1 and a=4.

Step-by-step explanation:

The function is

f(x)=\frac{(x-1)(x^2-4)}{x^2-a}

If we want f(x) to be continuous the denominator needs to be different to 0, otherwise f(x) will be indeterminate.

Now, for a a positive real we have that x=\sqrt{a} will annulate the denominator, i.e

(\sqrt{a})^2-a = a-a = 0. But, if a = 1 we have:

f(x)=\frac{(x-1)(x^2-4)}{x^2-1} = \frac{(x-1)(x^2-4)}{(x-1)(x+1)}=\frac{(x^2-4)}{x+1}

so, the value x=\sqrt{a} = \sqrt{1} = 1 won't annulate the denominator.

Now, for a = 4 we have:

f(x)=\frac{(x-1)(x^2-4)}{x^2-4} = x-1

so, the value x=\sqrt{a} = \sqrt{4} = 2 won't annulate the denominator.

In conclusion, for a=1 or a=1, the function will be continuos for all real numbers, since the denominator will never be 0.

4 0
3 years ago
Find the property of this : 5x*(4y+3x)=5x*(3+4y)
7nadin3 [17]
Simplifying
5x(4y + 3x) = 5x(3x + 4y)

Reorder the terms:
5x(3x + 4y) = 5x(3x + 4y)
(3x * 5x + 4y * 5x) = 5x(3x + 4y)

Reorder the terms:
(20xy + 15x2) = 5x(3x + 4y)
(20xy + 15x2) = 5x(3x + 4y)
20xy + 15x2 = (3x * 5x + 4y * 5x)

Reorder the terms:
20xy + 15x2 = (20xy + 15x2)
20xy + 15x2 = (20xy + 15x2)

Add '-20xy' to each side of the equation.
20xy + -20xy + 15x2 = 20xy + -20xy + 15x2

Combine like terms: 20xy + -20xy = 0
0 + 15x2 = 20xy + -20xy + 15x2
15x2 = 20xy + -20xy + 15x2

Combine like terms: 20xy + -20xy = 0
15x2 = 0 + 15x2
15x2 = 15x2

Add '-15x2' to each side of the equation.
15x2 + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
0 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.
4 0
3 years ago
Read 2 more answers
3x+6=30 what is the value of x​
Volgvan

Answer:

8

Step-by-step explanation:

4 0
3 years ago
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How do u solve an inequality??
Yakvenalex [24]
Add (or subtract) a number from both sides.
Multiply (or divide) both sides by a positive number.
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3 0
3 years ago
A ramp is used to load a snowmobile onto the back of a pickup truck. The truck bed is 1.3m above the ground. For safety, the ang
kiruha [24]

Answer:

2.02 m

or 2 m 2 cm

Step-by-step explanation:

Imagine a triangle containing the 40° angle and that this angle is at the left.  Then the height of the truck bed is 1.3 m and the "shortest possible length of the ramp" is the hypotenuse of this triangle.  We need to find the length of this ramp, that is, the length of the hypotenuse.  

The sine function relates this 40° angle and the 1.3 m height of the truck bed:

sin 40° = opp / hyp = 1.3 m / hyp

which can be solved for 'hyp' as follows:

              1.3 m

hyp = ----------------- = (1.3 m) / 0.6428)

             sin 40°

                                                                                  1.3 m

Thus, the length of the ramp must be less than -------------- or 2.02 m

                                                                                 0.6428

where this last result is to the nearest cm.

If the ramp is shorter the angle of the ramp will be smaller and the ramp angle considered safer.

3 0
3 years ago
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