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guajiro [1.7K]
2 years ago
12

Fred jumped into a lake from a rock 7 feet above the surface of the water. He sank five feet into the water and continued to swi

m down two additional feet.
•Sophie stated that the total distance would be 0 because the heights were additive inverses of each other.
•Jake disagrees and thinks that Fred covered 14 feet. He found his answer using a number line.
Do you agree with Sophie or Jake?
Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
3 0

Answer:

Sophie

Step-by-step explanation:

Jake is wrong because when he jump he was out of the water and you're supposed to count what he swam in the water so Sophie is correct.

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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
A home is to be built on a 56 foot 9 inch wide lot. The house is 5 feet 5 inches from the side of the lot and is 34 feet 10 inch
daser333 [38]
<span>Total lot - house -other side
=(56 ft 9 in) - (34 ft 10 in) - (5 ft 5 in)
=(55 ft 21 in) - (34 ft 10 in) - (5 ft 5 in)
=16 ft 6 in
Convert to inches: </span>16 ft x 12 in/ft)+ 6 in= Total in inches<span>192 in + 6 in= Total in inches
198 in= Total in inches 
Check: One side + house + other side = Lot width
(5 ft 5 in)+(34 ft 10 in)+(16 ft 6 in)=Lot width
56 ft 9 in=Lot width, which equals the given.</span>
8 0
3 years ago
4/5(p+1)=1 wgat equals p​
jeka94

Answer:

p= 1/4 or 0.25

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Is the relation a function? Why or why not?<br><br> {(–3, –2), (–1, 0), (1, 0), (5, –2)}
tankabanditka [31]

Answer:

yes, the given relation is a function.

Step-by-step explanation:

The given relation is

{(–3, –2), (–1, 0), (1, 0), (5, –2)}

A relation is called function if each element of the domain is paired with exactly one element of the range.

It means for each value of x there exist a unique value of y.

In the given relation for each value of x there exist a unique value of y.

Therefore the required solution is yes and this relation is a function.

5 0
3 years ago
What is the domain of the function graphed below?
I am Lyosha [343]

Answer:

x < 7

Step-by-step explanation:

the domain is the number range or interval of x the function is defined for to generate a y-value.

the graph shows that the y-values continue with x-values to the right up to but not including 7 (the empty dot says "excluding"). and with x- values to the left to negative infinity.

x=-1 is not a problem, because while for the left part of the function it is not included, but for the right part it is.

so, it is fully defined for all x < 7.

4 0
3 years ago
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