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3 years ago

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The 7th-grade class took a survey on their favorite ice cream. 58 people said they prefer vanilla, while 28 people said they pre

fer chocolate. Write a ratio comparing chocolate to vanilla. (Write it in a :b form)

1 answer:

MA_775_DIABLO [31]3 years ago

6 0

Since 58 for vanilla and 28 for chocolate
The ratio would be 28:58
You can simplify it even further
to 14:29

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The function f(x)=(x-5)^2 +2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the in

Anon25 [30]

We have been given a quadratic function $f(x)=(x-5)^{2} +2$ and we need to restrict the domain such that it becomes a one to one function.

We know that vertex of this quadratic function occurs at (5,2).

Further, we know that range of this function is $[2,\infty)$ .

If we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

Let us know find its inverse.

$y=(x-5)^{2}+2$

Upon interchanging x and y, we get:

$x=(y-5)^{2}+2$

Let us now solve this function for y.

$(y-5)^{2}=x-2\\
y-5=\pm \sqrt{x-2}\\
y=5\pm \sqrt{x-2}\\$

Hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .

8 0

3 years ago

considering the leading term of the polynomial function. what is the end behavior of the graph? describe the end behavior and pr

mario62 [17]

The leading term of polynomial function is the the term contain highest degree so here in the given question leading term is $-3x^5$

and leading coefficient is the coefficient of the term with greatest exponent -3

RULES for End behaviour

we have following four cases

CASE1: Even degree and positive leading coefficient

$x\rightarrow -\infty$ $f(x)\rightarrow \infty$

$x\rightarrow \infty$ $f(x)\rightarrow \infty$

CASE2: Even degree and negative leading coefficient

$x\rightarrow -\infty$ $f(x)\rightarrow -\infty$

$x\rightarrow \infty$ $f(x)\rightarrow -\infty$

CASE3: Odd degree and positive leading coefficient

$x\rightarrow -\infty$ $f(x)\rightarrow -\infty$

$x\rightarrow \infty$ $f(x)\rightarrow \infty$

CASE4: Odd degree and negative leading coefficient

$x\rightarrow -\infty$ $x\rightarrow \infty$

$x\rightarrow \infty$ $f(x)\rightarrow -\infty$

Here in the given case we have odd degree and negative leading coefficient

$x\rightarrow -\infty$ $x\rightarrow -\infty$

$x\rightarrow \infty$ $f(x)\rightarrow -\infty$

3 0

3 years ago

What is the distance around a triangle that has sides measuring 2 1/8, 3 1/2, and 2 1/2 feet?

Mashcka [7]

Perimeter = 2 1/8 + 3 1/2 + 2 1/2 = 7 (1 + 4 + 4)/8 = 7 9/8 = 8 1/8

3 0

3 years ago

An angelfish was 1 1/2 inches long when it was bought. Now it is 2 1/3 inches long.

____ [38]

A)

Earlier, The length of the angelfish = $1 \frac{1}{2}$ inches

Now, the length of angelfish = $2 \frac{1}{3}$ inches

We have to determine the grown length of angelfish

= $2 \frac{1}{3}$ - $1 \frac{1}{2}$

= $\frac{7}{3}- \frac{3}{2}$

LCM of '2' and '3' is '6',

= $\frac{14-9}{6}$

= $\frac{5}{6}$ inch

Therefore, the angelfish has grown by $\frac{5}{6}$ inch.

B)

We have to determine the increased length of angelfish in feet.

Since $1 inch = \frac{1}{12}$ foot

So, $\frac{5}{6} inch = \frac{5}{6} \times \frac{1}{12} = \frac{5}{72}$

= 0.069 foot.

7 0

3 years ago

Read 2 more answers

HELP PLEASE I NEED ANSWER ASAP!

mixas84 [53]

Answer:

86+18 $\sqrt{2}$

Step-by-step explanation:

Use the properties of 45-45-90 triangles to get a side length of 18 for the 2 legs of the isosceles triangle. Then add 43+18, which is the shorter length of the rectangle, +25, which is the longer edge, +18 $\sqrt{2}$ . The answer is now 86+18 $\sqrt{2}$ .

3 0

2 years ago

Read 2 more answers