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lidiya [134]
3 years ago
12

The sum of a number and its square is 2. find the number(s)

Mathematics
1 answer:
just olya [345]3 years ago
4 0
X+x^2=2
x^2+x-2=0
(x+2)(x-1)=0
So x=-2, 1
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Write a quadratic function in vertex form whose graph has the vertex
ELEN [110]

Answer:

y = \frac{1}{2}(x - 5)² - 2

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (5, - 2), thus

y = a(x - 5)² - 2

To find a substitute (7, 0) into the equation

0 = a(7 - 5)² - 2

0 = 4a - 2 ( add 2 to both sides )

2 = 4a ( divide both sides by 4 )

a = \frac{2}{4} = \frac{1}{2}

y = \frac{1}{2} (x - 5)² - 2 ← in vertex form

4 0
2 years ago
The sum of two consecutive integers is 139, find the integers.
Ad libitum [116K]
They would be 69 and 70.

Your equation would be x + (x + 1) = 139

X would be the first integer and x + 1 would be the second

You would then solve the equation to get x as 69

X + 1 would then be 70
7 0
3 years ago
David hikes 2 ¼ miles in ½ an hour at this rate, how long will it take him to walk 18 miles?
8090 [49]
So in 30 min will hike 2 1/4 miles =9 of those 1/4 miles therefore in 10 min will hike 9/3 =3 of those 1/4 miles = 3/4 of a mile

3/4 mile in 10 min;
(3/4)• 4 = 3 miles in 40 min;
6 miles in 80 min;
9 miles in 120 min;
12 miles in 160 min;
15 miles in 200 min;
18 miles in 240 min or 4 hours

5 0
3 years ago
What is 1/6x=4 in solving equations with rational coefficients
Debora [2.8K]
To solve an equation with a rational (fraction) coefficient you need to multiply both sides of the equation by the reciprocal (invert the fraction - flip it).

\frac{1}{6}x =4 The reciprocal of 1/6 is 6/1 or 6
6( \frac{1}{6} x)= 6(4)  The product of reciprocals equals 1 
1x = 24
x = 24


7 0
3 years ago
Which sequence could be described by the explicit definition: t_n=2^n+1t n = 2 n + 1
yuradex [85]

Answer:

2. 27

3. Option C. 3, 5, 9, 17, 33, ...

Step-by-step explanation:

2. The sequence is defined by the explicit function t_{n} = 2^{n}  - n

Therefore, the 5th term i.e. t_{5} of the sequence.

t_{5} = 2^{5}  - 5 = 32 - 5 = 27 (Answer)

3. The explicit definition is t_{n} = 2^{n}  + 1

Hence, t_{1} = 2^{1}  + 1 = 3

t_{2} = 2^{2}  + 1 = 5

t_{3} = 2^{3}  + 1 = 9

t_{4} = 2^{4}  + 1 = 17

Therefore, the option C is the right sequence. (Answer)

4 0
3 years ago
Read 2 more answers
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