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3 years ago

Graph the function y = |8 - 2x| + 3. Which is a point on the function? (6.2, 7.4) (7.8, 11.2) (8.6, 6.8) (9.6, 7.3)

Mathematics

1 answer:

Fiesta28 [93]3 years ago

8 0

For this case we have the following function:
$y = | 8 - 2x | + 3
$
The first thing you should do is graph the function to see the behavior.
When observing the graph (in the attached image) we observe that the following point belongs to the graph:
$(6.2, 7.4)
$
To prove it, let's evaluate the point in the function:
$7.4 = l 8 - 2 (6.2) l + 3

7.4 = l 8 - 12.4 l + 3

7.4 = l -4.4 l + 3

7.4 = 7.4$
The equation is fulfilled and therefore the point belongs to the graph.
Answer:
(6.2, 7.4)
See attached image

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3 years ago

Graph the line with slope 2 5 and y -intercept − 7 .

tia_tia [17]

Answer:

See attachment

Step-by-step explanation:

We want to graph the line with slope

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$b = - 7$

The equation of this line is

$y = \frac{2}{5}x - 7$

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3 years ago

Use the discriminant to determine the number of solutions to the quadratic equation 3x^2+5x=-1

kari74 [83]

Answer:

Two real distinct solutions

Step-by-step explanation:

Hi there!

Background of the Discriminant

The discriminant $b^2-4ac$ applies to quadratic equations when they are organised in standard form: $ax^2+bx+c=0$ .

All quadratic equations can be solved with the quadratic formula: $x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}$ .

When $b^2-4ac$ is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

Solving the Problem

$3x^2+5x=-1$

We're given the above equation. It hasn't been organised completely in $ax^2+bx+c=0$ , but we can change that by adding 1 to both sides to make the right side equal to 0:

$3x^2+5x+1=0$

Now that we can identify the values of a, b and c, we can plug them into the discriminant:

$D=b^2-4ac\\D=(5)^2-4(3)(1)\\D=25-4(3)(1)\\D=25-12\\D=13$

Therefore, because the discriminant is positive, the equation has two real, distinct solutions.

I hope this helps!

4 0

3 years ago

Write a proportion to find how many points x a student needs to score on a test worth 50 points to get a test score of 78%.

olganol [36]

The answer is: "39 points" .
_______________________________________________________
Explanation:
_______________________________________________________
" x/ 50 = 78/100 " ; in which "x" equals the number of points needed.

_______________________________________________________

To solve for "x" ;
_______________________________________________________

Look at the denominators: 50 * (what value?) = 100.

→ "100 ÷ 50 = 2" .

→ So; "50 * 2 = 100" ;

So, let us look at the numerators:

x * 2 = 78 ;

↔ 2x = 72 ;

Divide each side of the equation by "2" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
_____________________________________________
→ 78 ÷ 2 = 39 ;

The answer is: "39 points" .
_____________________________________________

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3 years ago