All categories

2 years ago

Solve the system y = -x + 7 and y = -0.5(x - 3)^2 + 8.

Mathematics

1 answer:

AlladinOne [14]2 years ago

8 0

Answer:

(1,6) & (7,0)

Step-by-step explanation:

y = -x + 7

y = -0.5(x - 3)² + 8

To solve the system, solve these two equations simultaneously

-x + 7 = -0.5(x - 3)² + 8

-x + 7 = -0.5(x² - 6x + 9) + 8

-x + 7 = -0.5x² + 3x - 4.5 + 8

0.5x² - 4x + 3.5 = 0

x² - 8x + 7 = 0

x² - 7x - x + 7 = 0

x(x - 7) - (x - 7) = 0

(x - 1)(x - 7) = 0

x = 1, 7

y = -1 + 7 = 6

y = -7 + 7 = 0

(1,6) (7,0)

Since the system has two distinct solutions, the line and the curve meet at two distinct poibts9: (1,6) & (7,0)

You might be interested in

Graph the area bounded by y =12, x>=0 and x<=12

BlackZzzverrR [31]

Answer:

Graph.

y=12

x>=0

x<=12

3 0

2 years ago

Cabe nur

JulsSmile [24]

Answer:

22, 25, 28, 31

Step-by-step explanation:

The question is mixed up. The only clear question is:

Given:

4, 7, 10, 13, 16, 19

Required

Write the next 4

Notice that the rule of the above sequence is to "add 3". So, the next 4 numbers is gotten by adding 3 to the previous number on the sequence.

The next 4 are:

$19 + 3 = 22$

$22 + 3 = 25$

$25 +3 = 28$

$28 + 3= 31$

4 0

2 years ago

Which of the following statements is not true about the function shown above?

Studentka2010 [4]

Answer A would the one that's false

8 0

2 years ago

Determine whether the number is a perfect square 47

Ghella [55]

Perfect squares are n² where n is a whole number
whole numbers are like 0,1,2,3,4,5,6, etc
no decimal or fractions

we can do that be looking at the perfect squares we know
2²=4
3²=9
4²=16
5²=25
6²=36
7²=49
8²=64
etc

so we see 47 is between 6² and 7²
therefor, for n²=47, n is between 6 and 7 and is therfore not a whole number
that makes 47 not a perfect square

7 0

3 years ago

Read 2 more answers

Simplify 3x^2y^4 x 2x^6y

Feliz [49]

Answer:

6x^8y^5

Step-by-step explanation:

(3)(2)= 6

add the exponents for the variables

8 0

2 years ago