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sergij07 [2.7K]

3 years ago

13

Roberta needs 355 beads a large box holds 100 beads a medium box hold 10 a small box hold 1 Roberta already has 3 large boxes an

d 5 small boxes how many medium boxes of beads does she has

1 answer:

Phantasy [73]3 years ago

7 0

I think that she would need 5 medium boxes because

3 large = 300 beads
5 medium= 50 beads
5 small = 05 beads
that all = 355 beads in total

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Find the domain and range of f(x). Please explain your answer.<br> f(x) = √(x^2+5x+6)

timama [110]

Answer:

Domain:— [ x ≥ -2, x ≤ -3 ]

Range:— [ y ≥ 0 ]

Step-by-step explanation:

You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.

First, factor the quadratic expression in the surd:—

$\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}$

We can find the x-intercepts by letting f(x) = 0.

I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.

__________________________________________________________

Finding x-intercepts

Let f(x) = 0.

$\displaystyle \large{0=\sqrt{(x+3)(x+2)}}$

Solve for x, square both sides:—

$\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}$

Simply solve a quadratic equation:—

$\displaystyle \large{x=-3,-2}$

Therefore, x-intercepts are:—

$\displaystyle \large{\boxed{x=-3,-2}}$

__________________________________________________________

Finding y-intercept

Let x = 0.

$\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}$

Therefore, y-intercept is:—

$\displaystyle \large{\boxed{\sqrt{6}}}$

__________________________________________________________

However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.

For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.

See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.

Hence, the domain is:—

x ≥ -2, x ≤ -3

4 0

2 years ago

If f is the function given by f(x)= integral from (4 to 2x) of sqrt(t^2-t)dt then f'(2) =?

sammy [17]

Hello,

$f(x)= \int\limits^{2x}_4 {\sqrt{t^2-t} \, dt \\

 \dfrac{df(x)}{dx} = \dfrac{df(x)}{d(2x)} * \dfrac{d(2x)}{dx} =2* \sqrt{(2x)^2-2x} \\

f'(2)=2 * \sqrt{4^2-4} =2* \sqrt{12} =4 \sqrt{3}$

3 0

3 years ago

Read 2 more answers

If function g is defined by the equation y − 3x = -14, which equation represents the function in function notation? A. g(x) = 3x

N76 [4]

The following equation represents the function g in function notation,

g(x) = 3x - 14 [Option (A)]

Definition of a Function

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.

Given equation is,

y -3x = -14

⇒ y = -14 + 3x

or y = 3x - 14

Here, y stands for or represents the function g(x) which is a function of independent variable x.

Thus, the correct function notation is as follows,

g(x) = 3x - 14

Learn more about a function here:

brainly.com/question/12431044

#SPJ1

6 0

1 year ago

Find the surface area of a square pyramid with base edges of 8 feet. The height of each lateral face is 10 feet. Explain or show

Zina [86]

Answer:

224 im pretty sure

Step-by-step explanation:

area of a triangle= base x height / 2

if we plug the values from the problem into the equation, we get 8 x 10 / 2 which simplifies into 80 / 2, which is 40. because this is a square pyramid, we know it has 4 triangles, so we multiply 40 by 4, which is 160. now, we find the area of the square, which can be found with the equation length x width. since all sides of square are equal, the equation becomes 8 x 8, which is 64. finally, we add the area of the triangles to that of the square, and we get 224. hope this helps!

6 0

3 years ago

6w = 77 - 5w<br> What does w equal

Digiron [165]

Answer:

$w=7$

Step-by-step explanation:

$6w=77-5w$

Add $5w$ to both sides

$11w=77$

Divide both sides by 11

$w=7$

5 0

2 years ago