_____ > -2°C select one -3,0,-2.5,-5

If the circumference of a circle is increased by 50%, then its area will be increased by (a) 100% (b) 125% (c) 150% (d) 75%

Svetradugi [14.3K]

Answer:

Hi, There!

Option B 125% Is the Most Accurate Answer

Step-by-step explanation:

Circumference is the distance around a plane shape. So, it also measures length.

Length and area of two similar shapes are related by the formula

$\frac{A_{1} }{A_{2} } =(_{} \frac{I_{1} }{I_{2\\ ^{~2~} }}$

Where the A in both cases represents area and the L represents length. But here the Ls will represent circumference.

Since the circumference of the circle increased by 50%, then the new circumference becomes

$l_{2} = l_{1} + 0.5l_{1} =1.5l_{1}$

Now subtracting from the original area then

$2.25 - 1=1.25$

This means that the area was increased by 1.25, which means 125%

Hence option B is the correct answer

7 0

3 years ago

6. A pizza maker has a 64-ounce package of whole wheat pizza

d1i1m1o1n [39]

Answer:

D

Step-by-step explanation:

16 ounces, she can use all the dough and still make evenly sized pizzas 80 / 16 = 5, 64 / 16 = 4.

5 0

3 years ago

Rogers steps include a scale holding five bricks of equal weight. The scale reads 300 pounds. Write an equation relating Rogers

natta225 [31]

Answer:

R + 5b = 300

Step-by-step explanation:

Rogers steps include a scale holding five bricks of equal weight and the scale reads 300 pounds.

We want to write an equation relating Rogers weight and the weight of the bricks to the total weight of the bricks to the total weight shown on the scale.

We have been told to use R for Rogers weight and b for the weight of a single brick.

Since Rogers is holding 5 bricks, the weight of 5 bricks will be 5b.

The sum of Rogers weight and the five bricks is equal to 300 pounds.

Therefore, the equation relating them is:

R + 5b = 300

3 0

3 years ago

Calculate the area of triangle ABC with altitude CD, given A (6,0) B(1,5) C (2,0) and D (4,2)

Elina [12.6K]

So hmm check the picture below

the height or altitude is CD
and the base is AB

how long are those? well $\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ 6}}\quad ,&{{ 0}})\quad 
% (c,d)
B&({{ 1}}\quad ,&{{ 5}})\\\\
C&({{ 2}}\quad ,&{{ 0}})\quad 
% (c,d)
D&({{ 4}}\quad ,&{{ 2}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
AB=\sqrt{(1-6)^2+(5-0)^2}\qquad \qquad CD=\sqrt{(4-2)^2+(2-0)^2}$

7 0

4 years ago

Read 2 more answers

Which is the following is the set of real zeros of the function f(x) = (x3 + 1000)(x4 - 160,000)?

marusya05 [52]

Answer:

A. { -20, -10, 20 }

Step-by-step explanation:

Given:

The function is given as:

$f(x)=(x^3+1000)(x^4-160000)$

Let us simplify the function.

First, we use the identity $a^3+b^3=(a+b)(a^2-ab+b^2)$

$x^2+1000= x^3+10^3=(x+10)(x^2-10x+10^2)\\x^3+1000=(x+10)(x^2-10x+100)$

Next, we use the identity $a^4-b^4=(a-b)(a+b)(a^2+b^2)$

$x^4-160000=x^4-20^4=(x-20)(x+20)(x^2+20^2)=(x-20)(x+20)(x^2+400)$

Now, the function can be rewritten as:

$f(x)=(x+10)(x^2-10x+100)(x-20)(x+20)(x^2+400)$

Now, the zeros are those values of $x$ for which $f(x)=0$

Now, for $f(x)=0$ , we must have either of the factors 0.

$x+10=0\\x=-10$

$x-20=0\\x=20\\\\x+20=0\\x=-20$

The factors $x^2-10x+100$ and $x^2+400$ can have no zeros as the first one has imaginary roots and second one is always greater than 0 irrespective of the $x$ values.

So, the possible set of zeros are { -20, 10, 20 }.

6 0

4 years ago