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rewona [7]
3 years ago
12

If G (x) = 1/x were shifted 2 untold to the left and 2 united up, what would the new equation be?

Mathematics
1 answer:
klemol [59]3 years ago
6 0

Horizontal translation are obtained by the following transformation:

f(x)\mapsto f(x+k)

In particular, you translate k units to the left if k>0, k units to the right if k<0.

Similarly, vertical translation are obtained by the following transformation:

f(x)\mapsto f(x)+k

In particular, you translate k units up if k>0, k units down if k<0.

So, you proceed like this: start with

G(x)=\dfrac{1}{x}

Translate 2 units to the left:

G(x+2) = \dfrac{1}{x+2}

Translate 2 units up:

G(x+2)+2 = \dfrac{1}{x+2}+2

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a 400 g of a liquid of density 1.6g/cm3 is made from mixing liquids of density 1.2g/cm3 and 1.8g/cm3 find the mass of the liquid
gogolik [260]

Answer:

133.33g

Step-by-step explanation:

Let the:

Mass of 1.2g/cm³ of liquid = x

Mass of 1.8g/cm³ of liquid = y

From our Question above, our system of equations is given as:

x + y = 400........ Equation 1

x = 400 - y

1.2 × x + 1.8 × y = 1.6 × 400

1.2x + 1.8y = 640..... Equation 2

We substitute, 400 - y for x in Equation 2

1.2(400 - y) + 1.8y = 640

480 - 1.2y + 1.8y = 640

- 1.2y + 1.8y = 640 - 480

0.6y = 160

y = 160/0.6y

y = 266.67 g

Solving for x

x = 400 - y

x = 400 - 266.67g

x = 133.33g

Therefore, the mass of the liquid of density 1.2g/cm³ is 133.33g

7 0
2 years ago
the line containing the altitude to the hypotenuse of a right triangle whose vertices are p(-1, 1), q(3, 5), and r(5, -5).
finlep [7]

The equation of the straight line is given by 5y-x=6

An equation can be used to describe a straight line drawn on the Cartesian Plane. These equations have a generic structure and can change based on the slope and where the line intersects the axes.

We will greatly simplify this issue by utilizing the fact that this triangle is specified as a right triangle. We would have had to establish the presence of a right angle if it had been presented as a general triangle.

The segment QR is the hypotenuse of the triangle.

Any side's altitude is located along a line that is perpendicular to that side. We are aware that the slopes of perpendicular lines are negative reciprocals, or:

Slope of line joining  Q(3, 5) and R(5, -5)

m=\frac{y_2-y_1}{x_2-x_1}

Hence slope is= -10/2= -5

Now we know that for two perpendicular line the slope of one line is the negative reciprocal of the other.

Slope of line perpendicular to QR=1/5

This line passes through P(-1,1)

Equation of the straight line that passes through (1,-1) and with a slope of 1/5 is given by:

(y-y_1)=m(x-x_1)\\

Substituting the values we get:

y-1=1/5(x+1)

or,5y-5=x+1

or,5y-x=6

Hence the equation of the required line is : 5y-x=6

To learn more about straight lines visit:

brainly.com/question/17757770

#SPJ4

8 0
2 years ago
Find the GCF of -10c2d and 15 ca2
jonny [76]

Answer:

5c

Step-by-step explanation:

5c is the only value you can take out of both factors

4 0
3 years ago
1. the sum of two rational numbers is always always a (irrational number / rational number)
Blizzard [7]

One

The sum of two rational numbers is always rational. sqrt(9) + sqrt(25) = 3 + 5 which is rational. sqrt(16/100) = 4/10 = 2/5 is also rational. 3/28 is rational as well.

Two

Those are irrational. sqrt(10) + pi = ???? You cannot reduce this to any kind of fraction. Two irrationals always give a rational.

Three

The irrational number controls the answer. 10 + sqrt(5) is irrational. The 10 is OK. It is raional, but sqrt(5) is not a rational number.

8 0
3 years ago
Solve for x.<br><br> X = ____?
I am Lyosha [343]
Set up a proportion
EA / EB = ED/ EC
16 / (5x + 2 + 16) = 12 / (12 + 24)
16/(5x + 18) = 12 / 36 Cross multiply
16 * 36 = (4x + 18)*12 Remove the brackets
576 = 48x + 216 Subtract 216 from both sides.
360 = 48x Divide by 48
360/48 = x
7.5 = x

8 0
3 years ago
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