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3 years ago

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Maria and Jason are saving gas money for their trip to Boston. Maria has saved $20 more than double what Jason has. Combined Mar

ia and Jason were able to achieve their goal of saving $200 dollars! How much did Jason save for this trip?

1 answer:

valentina_108 [34]3 years ago

3 0

Answer:

$60

Step-by-step explanation:

Jason saved gas money (x). Maria saved $20 more than double what Jason has (20 + 2x). Combined, they saved $200. Solve for x for Jason's amount.

(x) + (20 + 2x) = 200

x + 20 + 2x = 200

3x + 20 = 200

3x + 20 = 200

3x + 20 - 20 = 200 - 20

3x = 180

3x/3 = 180/3

x = 60

Jason saved $60 for this trip.

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Answer:

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Step-by-step explanation:

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2 years ago

The wheels of a bicycle have a diameter of 70cm. How many meters will the bicycle travel if each wheel makes 50 revolutions

slava [35]

Answer:

see explanation

Step-by-step explanation:

1 revolution is equivalent to the circumference of the wheel

1 revolution = πd ( d is the diameter )

= 70π cm

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3 years ago

Read 2 more answers

HELP PLEASE ANYONE STEP BY STEP TIMED

UNO [17]

Answer:

$\huge\boxed{\text{B) 4}}$

Step-by-step explanation:

We can use the properties of some of these circles to solve and find the value of x.

FIrst off - we know that to find the side of a right triangle we can use the Pythagorean Theorem, which states that $a^2 + b^2 = c^2$ (a and b being legs, c being the hypotenuse.)

<h2><u>Finding the hypotenuse</u></h2>

We also know that this triangle is in a circle. Part of the hypotenuse and the altitude of the triangle are in the circle.

Point W is the center of the circle. Therefore, any points stretching to the edge from it will be equal (since this is a circle).

With this knowledge - UW and WZ are equal.

Therefore, since UW is $x-1$ , WZ will be too.

We also know the length of VZ. We can add this to WZ to find the length of the whole hypotenuse.

$\displaystyle x-1+2 \\ x+1$

So the length of the hypotenuse, WV, is $x+1$ .

<h2><u>Finding the value of x</u></h2>

Now that we know the length of the hypotenuse, we can use the Pythagorean Theorem like we stated before to find the value of x.

We know the two legs are $x-1$ and $2x-4$ , while the hypotenuse is

$\displaystyle (x-1)^2 + (2x-4)^2 = (x+1)^2$
$(x^2 - 2x + 1) + (4x^2-16x+16) = (x^2 + 2x + 1)$ (use FOIL to find the value of each expression squared)
$5x^2 - 18x + 17 = x^2 + 2x + 1$ (simplify the left side)
$4x^2 -20x + 16 = 0$ (subtract both sides by $x^2 +2x + 1$ )
$x = \frac{{ -b \pm \sqrt {b^2 - 4ac} }}{{2a}}$ (Quadratic formula)
$\frac{{ -(-20) \pm \sqrt {(-20)^2 - 4 \cdot 4 \cdot 16} }}{{2 \cdot 4}}$ (plug in values from equation)
$\frac{{ 20 \pm \sqrt {400 - 256} }}{8}}$ (simplify)
$\frac{{ 20 \pm \sqrt {144} }}{8}}$ (simplify)
$\frac{{ 20 \pm 12 }}{8}}$ (simplify)
$\displaystyle x = \frac{20+12}{8} \ \text{and} \ \frac{20-12}{8}$ (use plus/minus to find two roots)
$\displaystyle x = \frac{32}{8} \ \text{and} \ \frac{8}{8}$ (simplify)
$\displaystyle x = 4 \ \text{and} \ 1$

1 can not be a possible answer because UW would end up being $(1-1) = 0$ units long! This isn't possible!

Therefore, the correct answer would be B) 4.

Hope this helped!

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2 years ago