The size of the bulletin board is 8.47m. The teacher wants to divide it into 7 sections. What will be the size of each section?

The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below

Aleonysh [2.5K]

Answer:

$g(x)=x-1$

Step-by-step explanation:

Any problem of this kind should first be approached by solving the initial function.

This question is based on curve translation on x-axis. But, there can be questions asked on translation in both axes, rotation of curve about origin, or both combined.

Initial function f(x) is a straight line from picture.

Common equation of straight line is

$y=mx+c$

m= slope of the line

c= y-intercept

Slope of the line:

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

Let those points on graph be A(3,0) and B(0,-6)

Therefore, slope of line AB, using formula is:

$m=\frac{0-(-6)}{3-0}$

m=2

And c=(-6)

And equation of line AB is:

$y=2x-6$

$f(x)=2x-6$

Now this line is translated backwards by 2 units, (x) becomes (x+2)

Let us consider a X, such that, $X=x+2$

$f(X)=2X-6$

$f(x+2)=2(x+2)-6$

$f(x+2)=2x+4-6$

$f(x+2)=2x-2$

Now, there is another function such that, $g(x)= \frac{1}{2} f(x+2)$

$g(x)= \frac{1}{2}(2x-2)$

$g(x)= x-1$ ; according to your question.

In the picture, they are asking for a function, $g(x)= \frac{-1}{2} f(x+2)$

Then, $g(x)= -x+1$ ; according to the picture.

Here, I have attached a file showing all the graphs for clear understanding.

3 0

4 years ago

Read 2 more answers

Based on the information given say whether or not △ABC∼△FED. Explain your reasoning.

GalinKa [24]

Answer:

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F = $x$

m∠D = $2x-20$ °.

Now, let m∠A = m∠B = $y$

So, m∠C = m∠A + 30° = $y+30$

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B + m∠C = 180

$y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50$

Therefore, m∠A = 50°, m∠B = 50° and m∠C = m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

$2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50$

Therefore, m∠F = 50°

m∠E = 50° and

m∠D = $2x-20=2(50)-20=100-20=80\°$

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.

5 0

3 years ago

Pls help me out!! lol

miskamm [114]

Answer:

the answer is D

Step-by-step explanation:

it is D because in normal y=mx+b form the given equasion is y= -1/2x + 3/2. for a line to be parallel to another line, they both must have the same slope, D is the only answer with the same slope as the slope from the given equasion

8 0

3 years ago

Fill in the other coordinate for the line y=7/2x +6 (-3

erik [133]

We have the following equation:
y = 7 / 2x +6
For this case, what we must do is replace the value of x = -3 in the given equation.
We have then:
y = (7/2) * (- 3) +6
y = -4.5
Therefore, the other coordinate is:
(-3, -4.5)
Answer:
(-3, -4.5)

3 0

4 years ago

PLEASE HELP ME GUYS :((

Veseljchak [2.6K]

Answer:

8 - $8\sqrt{3}$

Step-by-step explanation:

For this problem you have to use the 45-45-90 triangle theorem and 30-60-90 theorem.

For 45-45-90, the isosceles sides = 4, so the hypotenuse of the 30-60-90 triangle is 4 times 2, which is 8. If x is 8, then since y is the side across from the 60 angle, y is $8\sqrt{3$ . Since this really can't be simplified after y is subtracted from x, the final answer is just 8 - $8\sqrt{3}$ .

7 0

3 years ago