Evaluate 4(a2 + 2b)

Aubrey and Charlie are driving to a city that is 120 miles from their house. They have already traveled 20 miles, and they are d

mario62 [17]

Answer:

f(1.5) = _95_

The value indicates that after_1.5 hours_

hours of driving, Aubrey and Charlie will be_95_

miles from home.

Step-by-step explanation:

8 0

1 year ago

Drag each expression to show whether it is equivalent to (5⋅9x)+(5⋅1), 45x+15, or 15(3x−1).

JulijaS [17]

Part A: Option e: $5(9 x+1)$

Option f: $45 x+5$

Part B: Option c: $15(3 x+1)$

Option d: $(5 \cdot 9 x)+(5 \cdot 3)$

Part C: Option a: $(5 \cdot 9 x)-(5 \cdot 3)$

Option b: $45 x-15$

Explanation:

Part A: The equation is $(5 \cdot 9 x)+(5 \cdot 1)$

Simplifying, we have,

$45x+5$

Taking the term 5 common out, we have,

$5(9 x+1)$

Thus, the above two expressions are equivalent to the equation $(5 \cdot 9 x)+(5 \cdot 1)$ .

Hence, Option e and Option f are the correct answers.

Part B: The equation is $45 x+15$

Taking the term 15 common out, we have,

$15(3 x+1)$

Also, the equation can be rewritten as,

$(5 \cdot 9 x)+(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $45 x+15$

Hence, Option c and Option d are the correct answers.

Part C: The equation is $15(3 x-1)$

Multiplying, we have,

$45 x-15$

The above expression can be rewritten as,

$(5 \cdot 9 x)-(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $15(3 x-1)$

Hence, Option a and Option b are the correct answers.

3 0

1 year ago

The graph of f(x) = StartRoot x EndRoot is reflected across the x-axis and then across the y-axis to create the graph of functio

Anna35 [415]

Answer:

The only value that is in the domains of both functions is 0

The range of g(x) is all values less than or equal to 0

Step-by-step explanation:

As the original function is

$f(x) = \sqrt{x}$

Since, domain is the set of all possible input values that define the function, and range is the set of all possible output values for all possible domain values for which the function is defined.

The domain of $f(x) = \sqrt{x}$ will be [0, ∞)

The range of $f(x) = \sqrt{x}$ will be [0, ∞)

Please check the attached figure a for visualizing the graph of $f(x) = \sqrt{x}$ .

Impact of double transformation:

When the function $f(x) = \sqrt{x}$ is reflected across x-axis, the function becomes $y = -\sqrt{x}$ after first transformation

After the second transformation across y-axis, the function $y = -\sqrt{x}$ becomes $g(x) = -\sqrt{-x}$

For

$g(x) = -\sqrt{-x}$

$-x$ must be equal to or greater than zero for $g(x) = -\sqrt{-x}$ to be defined i.e. -x ≥ 0.

So,

-x ≥ 0 can be written as x≤ 0

So,

The domain of $g(x) = -\sqrt{-x}$ will be (∞, 0]
The range of $g(x) = -\sqrt{-x}$ will be (∞, 0]

Please check the attached figure a for visualizing the graph of $g(x) = -\sqrt{-x}$ .

So, from the above discussion, we can say that

0 is the only that is in the domain of both function.
The range of g(x) is all values less than or equal to 0

So,

Only two statements are true about the functions f(x) and g(x) are true which are:

The only value that is in the domains of both functions is 0

The range of g(x) is all values less than or equal to 0

Keywords: graph, function

Learn more about graph and function from brainly.com/question/11152594

#learnwithBrainly

8 0

1 year ago

Read 2 more answers

These two triangles are similar. What are a and b? Note: the two figures are not drawn to scale. Please help with this!!!

sesenic [268]

9514 1404 393

Answer:

a = 6
b = 22.5

Step-by-step explanation:

The ratio of smallest sides in the two triangles is ...

smaller / larger = 4/10

To find A and B, we write proportions involving corresponding side lengths.

__

Side A in the smaller triangle is ...

A/15 = 4/10

A = (4/10)(15) = 6

__

The ratio of larger to smaller is the inverse of the above ratio, so ...

B/9 = 10/4

B = (10/4)(9) = 22.5

6 0

1 year ago

Leela invests $500 at 4.5% interest according to the equation mc018-1.jpg, where Vl is the value of the account after t years. A

Karolina [17]

ΔThe Answer to your question is D).109.2%Δ

8 0

1 year ago

Evaluate 4(a2 + 2b) - 2b