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3 years ago

The function f(x) is shown in the graph. What is the equation for f(x)? f(x)=____

Mathematics

2 answers:

Oksanka [162]3 years ago

8 0

Answer:

$f(x)=\frac{3x}{7} -5$

Step-by-step explanation:

Hello

you can look for two points in the graph and find the slope

p1(0,-5) and p2(7,-2)

$m=\frac{y2-y1}{x2-x1} \\m=\frac{-2+5}{7-0} \\m=\frac{3}{7} \\m=\frac{3}{7}$

then , with the slope- point equation you are able to find f(x) ,let´s use p1(0,-5)

$y-y_{0} =m(x-x_{0} )\\\\$

$y-(-5)=\frac{3}{7} (x-0)\\y=\frac{3x}{7} -5\\\\f(x)=\frac{3x}{7} -5$

Have a great day

Illusion [34]3 years ago

7 0

I think it's f(x)=7/3x–5

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Morgarella [4.7K]

Answer:

$=5x+1$ or $=5x-1$

Step-by-step explanation:

One is given the following equation:

$5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}$

The problem asks one to simplify the expression, the first step in solving this equation is to factor the equation. Rewrite the numerator and denominator of the fraction as the product of two expressions. Remember the factoring patterns:

$(a-b)^2=a^2-2ab+b^2$

$=5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}$

$=5x-\frac{\sqrt{(3x-1)^2}}{-(3x-1)}$

Now simplify the numerator. Remember, taking the square root of a squared value is the same as taking the absolute value of the expression,

$=5x-\frac{\sqrt{(3x-1)^2}}{1-3x}$

$=5x-\frac{|3x-1|}{-(3x-1)}$

Rewrite the expression without the absolute value sign in the numerator. Remember the general rule for removing the absolute value sign:

$|a-b|\\=a -b$ or $(-a-b) = b-a$

$=5x-\frac{|3x-1|}{-(3x-1)}$

$=5x-\frac{3x-1}{-(3x-1)}$ or $=5x-\frac{-(3x-1)}{-(3x-1)}$

Simplify both expressions, reduce by canceling out common terms in both the numerator and the denominator,

$=5x-\frac{3x-1}{-(3x-1)}$ or $=5x-\frac{-(3x-1)}{-(3x-1)}$

$=5x-(-1)$ or $=5x-(1)$

Simplify further by rewriting the expression without the parenthesis, remember to distribute the sign outside the parenthesis by the terms inside of the parenthesis; note that negative times negative equals positive.

$=5x-(-1)$ or $=5x-(1)$

$=5x+1$ or $=5x-1$

6 0

3 years ago

Simplify: -14cd-2c^2d^2+15cd+9c^2d^2-15cd

MaRussiya [10]

7c^2d^2-14cd

Hope this helps a bunch!!!!!!!!!!!!

7 0

4 years ago

What is the volume of a square pyramids

frozen [14]

Answer:

$\large\boxed{V=75\ in^3}$

Step-by-step explanation:

The formula ogf a volume of a pyramid:

$V=\dfrac{1}{3}BH$

B - area of a base

H - height

We have a base length a = 5 in and a height H = 9 in.

In the base we have a square. The formula of an area of a square is:

$B=a^2$

Substitute:

$B=5^2=25\ in^2$

Calculate the volume:

$V=\dfrac{1}{3}(25)(9)=(25)(3)=75\ in^3$

7 0

3 years ago

Avery can run at 10 uph. The bank of a river is represented by the line 4x + 3y = 12, and Avery is at (7, 5). How much time does

Reil [10]

The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)

4x+3y=12

3y=-4x+12

y=-4x/3+12/3

So a line perpendicular to the bank will be:

y=3x/4+b, and we need it to pass through (7,5) so

5=3(7)/4+b

5=21/4+b

20/4-21/4=b

-1/4=b so the perpendicular line is:

y=3x/4-1/4

So now we want to know the point where this perpendicular line meets with the river bank. When it does y=y so we can say:

(3x-1)/4=(-4x+12)/3 cross multiply

3(3x-1)=4(-4x+12)

9x-3=-16x+48

25x=51

x=51/25

x=2.04

y=(3x-1)/4

y=(3*2.04-1)/4

y=1.28

So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(7-2.04)^2+(5-1.28)^2

d^2=38.44

d=√38.44

d=6.2 units

Since he can run at 10 uph...

t=d/v

t=6.2/10

t=0.62 hours (37 min 12 sec)

So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.

8 0

3 years ago

2(1/3x-5)=5/3x-11<br> can somebody help me ASAP

maw [93]

Answer: x=1 my friend

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers