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Rudik [331]
3 years ago
5

Jackson loves to take day trips during weekends. Last weekend, he drove 80 miles to Crabclaw Beach. He used 4 gallons of gas to

get there. This weekend, he will drive 100 miles to get to Mount Highmore. If he uses gas at the same rate, how many gallons of gas will Jackson use to get to Mount Highmore?
Mathematics
1 answer:
ra1l [238]3 years ago
4 0

Answer:

5 gallons of gas

Step-by-step explanation:

From the above question:

If:

80 miles = 4 gallons of gas

100 miles = x gallons of gas

Cross Multiply

80 × x = 100 × 4

x = 100 × 4/80

x = 5 gallons of gas

Therefore, Jackson would use 5 gallons of gas to get to Mount Highmore.

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2x^2=9-3x <br> Find the factors
d1i1m1o1n [39]

Answer:

x = -3, $ \frac{3}{2} $

Step-by-step explanation:

The given quadratic equation is: $ 2x^2 = 9 - 3x $

This can be written as: $ 2x^2 + 3x - 9 = 0 $

To solve a quadratic equation of the form $ ax^2 + bx + c = 0 $ we use the formula:

           $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

Here, a = 2; b = 3; c = - 9

Therefore, the roots of the equation are:

$ x = \frac{- 3 \pm \sqrt{9 - 4(2)(-9)}}{2(2)} $

$ \implies x = \frac{-3 \pm \sqrt{81}}{4} $

$ \implies x = \frac{-3 \pm 9}{4} $

We get two values of 'x', viz.,

x = $ \frac{-3 + 9}{4} $ and $ \frac{- 3 - 9}{4} $

$ \implies x = \frac{6}{4} \hspace{5mm} \& \hspace{5mm} \frac{-12}{4} $

⇒ x = -3, 3/2

Since the factors of the quadratic equation is asked, we write it as:

(x + 3)(x - $ \frac{3}{2} $) = 0

because, if (x - a)(x - b) are the factors of a quadratic equation, then 'a' and 'b' are its roots.

Multiply (x + 3) and (x - $ \frac{3}{2} $ to see that this indeed is the given quadratic equation.

5 0
3 years ago
Explain the difference between deductive and inductive arguments in your own words.
lyudmila [28]

Answer: The difference is as follows:

Step-by-step explanation:

  • Deductive Arguments: A deductive argument is an argument wherein it is felt that the premises give an assurance of reality of the end. In a deductive arguments, the premises are planned to offer help for the conclusion that is so strong to an extent that, if the premises are valid, it would be impossible for the conclusion to be false.

  • Inductive Arguments: An inductive arguments is an arguments where it is believed that the premises provide reasons supporting the likely truth of the conclusion. In an inductive arguments, the premises are proposed distinctly to be strong to an extent that, on the off chance that they are valid, at that point it is impossible that the conclusion is false.

The contrast between the two originates from the kind of connection the author or explainer of the argument takes there to be between the premises and the conclusion. In the event that the author of the argument accepts that reality of the premises certainly sets up reality of the conclusion because of definition, l<igical entailment or scientific need, at that point the argument is deductive. In the event that the author of the argument does not feel that reality of the premises certainly sets up reality of the conclusion, however in any case accepts that their fact gives valid justification to accept the conclusion genuine, at that point the argument is inductive.

5 0
3 years ago
Hannah travels 6 times as many minutes to work as Raoul does. Together, they travel for 63 minutes. How many minutes does Hannah
Anna71 [15]
The equation would be 6x+x=63. Not sure how the models play out, but good luck
7 0
3 years ago
If someone could please help me I’m confused thanks:)
Sedbober [7]
<h3>Answer:  x = 45</h3>

Work Shown:

x+x+90 = 180 .... all three angles of a triangle add to 180

2x+90 = 180

2x = 180-90

2x = 90

x = 90/2

x = 45

This is a 45-45-90 right triangle. We also consider it an isosceles right triangle because the base angles (45) are equal.

3 0
2 years ago
Carol Ann buys a TV at 70% off the original price. If she pays $120, what was the original price of the TV?
Keith_Richards [23]
If the TV is 70% off, then that means she paid 30% of the original cost.  If 30% of the original cost  is $120, then...

30% * x = 120
.30x = 120
x = 120/.30
x = 400

The original cost was $400
5 0
3 years ago
Read 2 more answers
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