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Greeley [361]
3 years ago
5

The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)?

Mathematics
2 answers:
Inga [223]3 years ago
8 0
For this case , the parent function is given by [tex f (x) =x^2
[\tex]
We apply the following transformations
Vertical translations :
Suppose that k > 0
To graph y=f(x)+k, move the graph of k units upwards
For k=9
We have
[tex]h(x)=x^2+9
[\tex]
Horizontal translation
Suppose that h>0
To graph y=f(x-h) , move the graph of h units to the right
For h=4 we have :
[tex ] g (x) =(x-4) ^ 2+9
[\tex]
Answer :
The function g(x) is given by
G(x) =(x-4)2 +9
Y_Kistochka [10]3 years ago
6 0
If it’s horizontally translated, the x value/ input is altered, meaning that the value is added or subtracted from x. In this case, you move 4 units to the right, so you’d have (x-4)^2. Then vertical change is shown by changes to the y value, so it would be outside the parentheses. So you get +9 out of the parentheses.

g(x)=(x-4)^2+9
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Discuss the different kinds of real numbers. In your answer
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Answer:

Real numbers are mainly classified into rational and irrational numbers. Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.

Step-by-step explanation:

5 0
3 years ago
1. There are two differnt maps of Ohio. The scale on the first map is 1 cm to 10 km. The distance from Cleveland to Cincinnati i
xeze [42]

Answer:

1.  0.8 cm

2.  1.6 cm

Step-by-step explanation:

1.

The scale for 2nd map is 1 cm to 50 km, that means "1 cm on map" is "50 km in real life".

We already know distance from Cleveland to Cincinnati is 40 km, which is less than 50, so we know the distance on map would be less than 1 cm.

So we set up ratio and figure out (let x be distance on map from Cleveland to Cincinnati):

\frac{1}{50}=\frac{x}{40}\\50x=40\\x=\frac{40}{50}\\x=0.8

Hene, 0.8 centimeters would be the distance in 2nd map

2.

A scale of 1:50 means 1 cm equal 50 cm

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2 years ago
Please help me for this question
rosijanka [135]

The volume of the given trapezoidal prism is 312 cubic units.

Step-by-step explanation:

Step 1:

To find the volume of a trapezoidal prism, we multiply the area of the trapezoidal surface with the height of the prism.

The area of a trapezoidal surface, A = \frac{a+b}{2} (h).

a and b are the lengths of the upper and lower bases and h is the height of the trapezoid.

For the given trapezoid, a is 5 units long and b is 8 units long while height, h is 4 units.

The area of the trapezoidal surface, A =  \frac{5+8}{2} (4) = 6.5(4) = 26.

So the area of the trapezoidal surface is 26 square units.

Step 2:

To determine the volume of the prism, we multiply the area of the trapezoidal surface with the height of the prism.

The area is 26 square units and the height of the prism is 12 units.

The volume of the prism, V= 26(12) = 312.

The volume of the given trapezoidal prism is 312 cubic units.

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Answer:

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Step-by-step explanation:

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