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3 years ago

5

ryan has a collection of 140 books to donate to the neighborhood library 20% of the books are childrens books 25% are non-fictio

n and the rest are fiction how many books in ryan's collection are fiction

1 answer:

Lyrx [107]3 years ago

3 0

Answer:

77

Step-by-step explanation:

Percentage of Fiction books

= 100% - 20% - 25%

= 55%

Number of Fiction books

= 55/100 × 140

= <u>7</u><u>7</u>

There are <u>7</u><u>7</u><u> </u><u>F</u><u>i</u><u>c</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>B</u><u>o</u><u>o</u><u>k</u><u>s</u>

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WILL GIVE BRAINLIEST

galina1969 [7]

Answer:

x= 3 inches

Step-by-step explanation:

-The volume of a box is given by the formula:

$V=lwh\\\\l-length\\w-width\\h-height$

-We are given the dimensions h=x+2, l=2x+5 and w=4x-1.

We substitute this values in the formula and equate to the volume value.

$V=lwh\\\\605=(x+2)(2x+5)(4x-1)\\\\605=8x^3+34x^2+31x-10$

#We take the values to the same side and equate to zero;

$8x^3+34x^2+31x-615=0\\\\\\\#Factor\\\\\\(x-3)(8x^2+58x+205)=0$

#Applying the zero factor principal to obtain the different values of x:

$(x-3)=0\\\\\therefore x=3\ \ \ \ \ \ ...i\\\\(8x^2+58x+205)=0$

#We use the quadratic formula to solve the two other values of x:

$(8x^2+58x+205)=0\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\=\frac{-58\pm\sqrt{58^2-4\times 8\times 205}}{2\times 8}\\\\x=-3.625+3.533i \ and \ x=-3.625-3.533i$

The two other values are negatives. Ignore them since length cannot be a negative.

The only reasonable value of x is x=3

#We substitute in the formula to validate:

$V=lwh\\\\=(x+2)(2x+5)(4x-1)\\\\=(3+2)(2*3+5)(4*3-1)\\\\=605$

Hence, the value of x is 3 inches

7 0

3 years ago

Consider the function f(x) = x3 − 4x2 + 2. Calculate the limit of the difference quotient at x0 = 3 for f(x).

m_a_m_a [10]

<h2>Part 1.</h2>

Answer: $\boxed{f'(x)=3x^2-8x}$

The limit of the difference quotient is simply the derivative, so we can express this as follows:

$f'(x)=\underset{\Delta x\rightarrow0}{lim}\frac{\triangle y}{\Delta x}=\frac{f(x+\Delta x)-f(x)}{\Delta x}$

So our function is:

$f(x)=x^3-4x^2+2$

Taking the derivative, we have:

$f'(x)=3x^2-8x$

So the correct option is:

$\boxed{f'(x)=3x^2-8x}$

<h2>Part 2.</h2>

Answer: $\boxed{y=3x-16}$

The equation of the line that passes through the same point can be found as:

$y-y_{0}=m(x-x_{0})$

Where $x_{0}=3$ , so we need to find $y_{0}$ . Plug in that x-value in the function we have:

$y_{0}=f(3)=(3)^3-4(3)^2+2 \\ \\ y_{0}=-7 \\ \\ \\ So \ the \ point \ is: \\ \\ P(x_{0},y_{0})=(3,-7)$

And the slope is:

$m=f'(3)=3(3)^2-8(3) \\ \\ m=3$

Then, the equation of the line is:

$y-(-7)=3(x-3) \\ \\ \therefore y+7=3x-9 \\ \\ \boxed{y=3x-16}$

<h2 /><h2>Part 3.</h2>

Answer: Shown below

As you can see below, the graph of the function of $f$ is continuous. This is so because we have plotted a polynomial function whose domain is the set of all real numbers. So the function is defined at the point $P(3,-7)$ , so the derivative exists at this point, hence we can calculate a tangent line there. In conclusion, we get the graph shown below. The blue line is the tangent line while the red curve is the graph of $f$

3 0

3 years ago

I need help I don’t understand how to do it

Kazeer [188]

Answer:

7.2 inches

Step-by-step explanation:

area of a rhombus = base x height

to find the base (length) of the rhombus you rearrange this equation so that it becomes

base = area / height

base = 21.6in² / 3

base (length) = 7.2in

hope this helps :)

4 0

3 years ago

Help please thank you

Sergeeva-Olga [200]

Answer:

0.25

Step-by-step explanation:

4 0

3 years ago

A quadrilateral has vertices A(11, -7), B(9, -4), C(11, -1), and D(13, -4). Quadrilateral ABCD is a . If the vertex C(11, -1) we

rosijanka [135]

Answer:

Quadrilateral A(11, -7), B(9, -4), C(11, -1), and D(13, -4) forms a rhombus.

Quadrilateral A(11, -7), B(9, -4), C'(11,1), and D(13, -4) forms a kite.

Step-by-step explanation:

Rhombus is a quadrilateral whose all sides have equal length.

Kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides which are adjacent to each other.

The quadrilateral formed by the vertices A(11, -7), B(9, -4), C(11, -1), and D(13, -4) would result in a rhombus (see figure below) because it had four equal sides.

If C(11,-1) is shifted to the point C'(11,1), it would become a kite (see figure below) because it has two pairs of equal sides.

5 0

4 years ago