MATHEMATICS HIGH SCHOOL

Let f(x)=8x and g(x)=8x+5+1.Which transformations are needed to transform the graph of f(x to the graph of g(x)?

Select each correct answer.

horizontal translation 1 unit left

vertical translation 1 unit down

vertical translation 5 units up

vertical translation 1 unit up

horizontal translation 5 units right

horizontal translation 5 units left

Answers

Answer 1

Answer:

Transformation involves changing the form of a function

The transformations are:

vertical translation 1 unit up .
horizontal translation 5 units left.

The functions are given as:

$\mathbf{f(x) = 8x}$

$\mathbf{g(x) = 8(x + 5) + 1}$

Considering f(x), we have:

$\mathbf{f(x) = 8x}$

Start by translating the function 5 units left.

The rule of this translation is:

$\mathbf{f'(x) = f(x + 5)}$

So, we have:

$\mathbf{f'(x) = 8(x + 5)}$

Next, translate the function 1 unit up

The rule of this translation is:

$\mathbf{f''(x) = f'(x) + 1}$

So, we have:

$\mathbf{f''(x) = 8(x + 5) + 1}$

Rewrite as:

$\mathbf{g(x) = 8(x + 5) + 1}$

Hence, the transformations are: vertical translation 1 unit up and horizontal translation 5 units left

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A. Find x. The figure is not drawn to scale.b. Is the triangle equilateral, isosceles, or scalene? Explain

Answers

Based on the given figure above, we can conclude that the triangle is an isosceles triangle. By definition, an isosceles triangle is a triangle that has at least two equal sides. Since this is an isosceles triangle, 8x-10 =6x. Now we can solve for x. So,
8x-10 =6x
8x-6x = 10
2x =10
x= 5.
Therefore, the value of x in the figure is 5. Hope this is the answer that you are looking for.

6. You deposit $1500 in an account that pays 5% interest yearly.a. Write an exponential equation describing this situation.

b. How much money do you have after 6 years?

Answers

The answer to B is $1950 because the 5% equal 75 dollars and 75 times 6 equals 450 so 1500 plus 450 equal 1950

Suppose a triangle has sides 3, 4, and 6. Which of the following must be true? A. The triangle in question is a right triangle. B. The triangle in question is not a right triangle. C. The triangle in question may or may not be a right triangle.

Answers

We can use the Pythagorean theorem:
c² = a² + b²
In this case:
6² = 3² + 4²
36 = 9 + 16
36 = 25 ( not correct )
This is not a right triangle.
Answer:
B ) The triangle in questionis not a right triangle.

Answer:

not a right triangle

Step-by-step explanation:

Given that a - b = 3 and ab=5, find, without the use of a calculator,
the value of a +b?

Answers

Answer:

√29

Step-by-step explanation:

We are here given that ,

a - b = 3
ab = 5 .

Now square the first equation ,

⇒ a - b = 3

⇒ ( a - b)² = 3²

⇒ a² + b² - 2ab = 9

⇒ a² + b² - 2(5) = 9

⇒ a² + b² -10 = 9

⇒ a² + b² = 9 + 10

⇒ a² + b² = 19

Adding 2ab both sides ,

⇒ a² + b² + 2ab = 19 + 2(5)

⇒ (a + b)² = 19 + 10

⇒ ( a + b)² = 29

⇒a+b=√29.

Why is it necessary to apply inverse operations on both sides of the equals l sign when solving an equations

Answers

Take this example (cause it's easy to explain)

10+5x=15x

To solve it we have to minus five on both side. We have to do this because we need to isolate the variable (in this case x) on the one side so we can divide and solve.

You would -5x (inverse from positive 5) from both sides on this because whatever you do to one side you have to do to the others to make it equal. In this case the answer would be x=1 (again cause it's easy lol.)

I hope this helps you!

The surface area of any shape is expressed in?a. feet and inches.
b. square units.
c. cubic units.
d. length and width.

Answers

the surface of any shape often is a result of multiple two dimension so it expressed in square units
the answer is B

b) square units is the answer

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