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lidiya [134]
3 years ago
12

Explain how to write the rational number 3.21 in the form a/b.

Mathematics
1 answer:
barxatty [35]3 years ago
6 0

Answer:

3 21/100

just a fraction.

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A rectangles tabletop has a length of 4 3/4 feet and a area of 11 7/8 square feet what is the width of the tabletop
Natalija [7]
Area is length times width. Therefore, width is area divided by length. Convert 11 7/8 to the improper fraction 95/8 and convert 4 3/4 to 19/4. Then, you can fine 95/8 divided by 19/4 by flipping the second fraction and multiplying so that you have 95/8 times 4/19. 4 times 95 is 380 and 8 times 19 is 152. Therefore, the answer is 380/152. This is equivalent to 5/2 or 2.5. 
3 0
3 years ago
What is the standard form equation of the line shown below?
ch4aika [34]
(-1,1)(1,4)
slope = (4 - 1) / (1 - (-1) = 3/(1 + 1) = 3/2

y = mx + b
slope(m) = 3/2
use either of ur points....(1,4)...x = 1 and y = 4
now sub and find b, the y int
4 = 3/2(1) + b
4 = 3/2 + b
4 - 3/2 = b
8/2 - 3/2 = b
5/2 = b

equation is y = 3/2x + 5/2...but we need it in standard form

y = 3/2x + 5/2
-3/2x + y = 5/2.....multiply both sides by -2
3x - 2y = -5 <==== ur standard form equation
3 0
3 years ago
Let $f(x) = x^2$ and $g(x) = \sqrt{x}$. Find the area bounded by $f(x)$ and $g(x).$
Anna [14]

Answer:

\large\boxed{1\dfrac{1}{3}\ u^2}

Step-by-step explanation:

Let's sketch graphs of functions f(x) and g(x) on one coordinate system (attachment).

Let's calculate the common points:

x^2=\sqrt{x}\qquad\text{square of both sides}\\\\(x^2)^2=\left(\sqrt{x}\right)^2\\\\x^4=x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x^4-x=0\qquad\text{distribute}\\\\x(x^3-1)=0\iff x=0\ \vee\ x^3-1=0\\\\x^3-1=0\qquad\text{add 1 to both sides}\\\\x^3=1\to x=\sqrt[3]1\to x=1

The area to be calculated is the area in the interval [0, 1] bounded by the graph g(x) and the axis x minus the area bounded by the graph f(x) and the axis x.

We have integrals:

\int\limits_{0}^1(\sqrt{x})dx-\int\limits_{0}^1(x^2)dx=(*)\\\\\int(\sqrt{x})dx=\int\left(x^\frac{1}{2}\right)dx=\dfrac{2}{3}x^\frac{3}{2}=\dfrac{2x\sqrt{x}}{3}\\\\\int(x^2)dx=\dfrac{1}{3}x^3\\\\(*)=\left(\dfrac{2x\sqrt{x}}{2}\right]^1_0-\left(\dfrac{1}{3}x^3\right]^1_0=\dfrac{2(1)\sqrt{1}}{2}-\dfrac{2(0)\sqrt{0}}{2}-\left(\dfrac{1}{3}(1)^3-\dfrac{1}{3}(0)^3\right)\\\\=\dfrac{2(1)(1)}{2}-\dfrac{2(0)(0)}{2}-\dfrac{1}{3}(1)}+\dfrac{1}{3}(0)=2-0-\dfrac{1}{3}+0=1\dfrac{1}{3}

6 0
3 years ago
Where are the parallelograms in this picture?
inysia [295]

Answer:

here the line A and H are parallel

7 0
2 years ago
What is the value of a in the equation a = 2 + 3a + 8? (5 points)
Luba_88 [7]

Step-by-step explanation:

a = 2 + 3a + 8

a = 10 + 3a

a - 3a = 10

-2a = 10

a = -5

5 0
2 years ago
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