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hjlf
3 years ago
11

How does changing the function from f(x) = −4 cos 3x to g(x) = −4 cos 3x − 6 affect the range of the function?

Mathematics
2 answers:
ASHA 777 [7]3 years ago
5 0
The function shifts down 6 units so the range will change from (-4, 4) to (-10,-2)
Option # 3
ArbitrLikvidat [17]3 years ago
5 0

Answer:

The function shifts down 6 units, so the range changes from −4 to 4 in f(x) to −10 to −2 in g(x).

Step-by-step explanation:

Given  : f(x) = −4 cos 3x  and  g(x) = −4 cos 3x − 6.

To find  :    How does changing the function affect the range of the function?

Solution : We have given that  

Function change from  f(x) = −4 cos 3x  to   g(x) = −4 cos 3x − 6.

By the transformation rule : f(x) →→→f(x) -k it mean function shifted down k unit .

Then Function would shift down 6 unit .

For  f(x) = −4 cos 3x  

Range:  [ -4,4]

For  g(x) = −4 cos 3x − 6.

Range : [-10 ,-2]

Therefore, The function shifts down 6 units, so the range changes from −4 to 4 in f(x) to −10 to −2 in g(x).

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Given triangle abc with vertices A(2,-1), B(5,6), C(-1,4) as shown. Find the number of square units in the area of triangle abs
Roman55 [17]

Answer:

The area of the triangle is 18 square units.

Step-by-step explanation:

First, we determine the lengths of segments AB, BC and AC by Pythagorean Theorem:

AB

AB = \sqrt{(5-2)^{2}+[6-(-1)]^{2}}

AB \approx 7.616

BC

BC = \sqrt{(-1-5)^{2}+(4-6)^{2}}

BC \approx 6.325

AC

AC = \sqrt{(-1-2)^{2}+[4-(-1)]^{2}}

AC \approx 5.831

Now we determine the area of the triangle by Heron's formula:

A = \sqrt{s\cdot (s-AB)\cdot (s-BC)\cdot (s-AC)} (1)

s = \frac{AB+BC + AC}{2} (2)

Where:

A - Area of the triangle.

s - Semiparameter.

If we know that AB \approx 7.616, BC \approx 6.325 and AC \approx 5.831, then the area of the triangle is:

s \approx 9.886

A = 18

The area of the triangle is 18 square units.

7 0
2 years ago
How many quarter pound burgers can george make out of 3 1/2 pounds of ground beef ?
lana [24]
Assuming that there is no wastage of beef. 

Note that 3 1/2 = 7/2 = 14/4 = 14 * 1/4 
This means that we can have 14 sets of quarter pound beef. 

This in turn means that George can make 14 quarter pound burgers.
6 0
3 years ago
Read 2 more answers
What is 9× >270 using inequalities
swat32

Answer:

x > 30

Step-by-step explanation:

divide both sides by 9

this gets the x on one side by itself.

270/9 = 30

don't let the inequality mess with you

treat it like an equal sign and leave it the way it is.

move things around it.

5 0
3 years ago
Can you please help me answer this question what's a+3
Inessa [10]

Answer:

a+3

Step-by-step explanation:

You cannot go any further in answering this question.  These two terms are not like terms so they cannot be combined.  Therefore, the answer is just a+3 itself.

7 0
3 years ago
What is the solution to the system of equations below? -4x+6y=-18 and y=-2x+21
Verdich [7]

Answer:

x=9 and y=3

Step-by-step explanation:

Let's solve your system by substitution.

−4x+6y=−18 and y=−2x+21

Rewrite equations:

y=−2x+21;−4x+6y=−18

Step: Solve  y=−2x+21for y:

y=−2x+21

Step: Substitute−2x+21foryin−4x+6y=−18:

−4x+6y=−18

−4x+6(−2x+21)=−18

−16x+126=−18(Simplify both sides of the equation)

−16x+126+−126=−18+−126(Add -126 to both sides)

−16x=−144

−16x

−16

=

−144

−16

(Divide both sides by -16)

x=9

Step: Substitute9forxiny=−2x+21:

y=−2x+21

y=(−2)(9)+21

y=3(Simplify both sides of the equation)

Answer:

x=9 and y=3

3 0
3 years ago
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