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MissTica
4 years ago
10

Write the equation shown by the

Mathematics
1 answer:
VashaNatasha [74]4 years ago
3 0

Answer:

Part 1) y=3x-5

Part 2) The graph in the attached figure

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

take the points

(2,1) and (3,4)

substitute

m=\frac{4-1}{3-2}

m=\frac{3}{1}

m=3

step 2

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=3

point\ (2,1)

substitute

y-1=3(x-2)

step 3

Convert to slope intercept form

Isolate the variable y

y-1=3x-6\\y=3x-6+1\\y=3x-5

step 4

Plot the given points to graph the line

see the attached figure

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The graph of a function is a parabola that has a minimum at the point (-3,9). Which equation could represent the function?
Scilla [17]

Answer:

g(x)=2(x+3)^2+9, which corresponds to answer D.

Step-by-step explanation:

Recall that the maximum or minimum of a parabola is always located at its vertex. Notice that all quadratic functions listed are given in what is called "vertex" form, since they explicitly show the vertex coordinates in their formulation:

f(x)=a(x-x_v)^2+y_v where x_v, and  y_v stand for the x and y coordinates respectively of the vertex.

Examining all four options, we notice that in all four cases listed, the y_v is correct (equal to positive 9), so we proceed to examine what the (x-x_v)^2 expression should look like for  x_v=-3:

Notice that when replace  x_v with "-3", we end up with a sign change:

(x-x_v)^2\\(x-(-3))^2=(x+3)^2

Therefore we find that the last two options can be candidates. Then we recall that the question also states that this should be a minimum. Then, for a parabola to have a minimum, its branches must go upwards, and this corresponds to a case in which the factor a (leading coefficient) multiplying (x-x_v)^2 is positive. So in looking for such condition, we find that the very last option is the only one that verifies such.

Then, g(x)=2(x+3)^2+9 is the option we select.

4 0
4 years ago
For which value of x does f(x) = g(x)
Natali5045456 [20]

Answer:

x=-3 and x=0

Step-by-step explanation:

The values where f(x) = g(x) is where the graphs intersect

One point is at (-3,0) and the other point is at (0,6)

We have two points of intersection since one is a parabola and the other is a line

8 0
3 years ago
Eight less a number is less than or equal to 17​
Karolina [17]

Step-by-step explanation:

n-8≤17

add 8 on both sides to isolate the variable.

n is less than or equal to 25

6 0
3 years ago
What two numbers multiply by 25 but adds up to 6
Natalka [10]
No two <em>intergers</em> can solve this problem. If you're not in Algebra II yet, the answer is probably "none."

Just look at the factor pairs of 25:
1 × 25
-1 × 25
5 × 5
-5 × -5
Clearly none of those can add up to 6.

If you want the more complex answer, I'll show you how here. If you don't understand why it doesn't work, that's okay. I just want you to see that  there's not an actual answer to the problem.

a+b = 6
a = 6-b
ab = 25
(6-b)b = 25
6b -b² = 25
-b² + 6b = 25
b² -6b = -25
Factor by splitting the middle.
Half of -6 is -3, (-3)² = 9. Add this to each side.
b² -6b + 9 = -16
Factor the perfect square trinomial.
(b-3)² = -16
Take the square root of each side.
b-3 = 4i
b = 3+4i
a+b = 6
a+3+4i = 6
a= 3-4i
<em>(The "i" stands for an imaginary number, specifically, the square root of -1.)</em>
8 0
3 years ago
Evan says that the value of the numerical expression 0.2+ 12 ÷ (1.5×4) is 32.04 . do you agree ?
12345 [234]

Answer:

NO! The correct answer is 2.03 (where 3 is repeating)

Step-by-step explanation:

0.2 + 12 / (1.5*4) does not equal 32.04

Parenthesis first! 1.5 times 4 equals 6.

0.2 + 12 = 12.2

12.2/6

12.2/6= 2.0333... but it should be rounded to 2, because


3 0
3 years ago
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