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marta [7]
3 years ago
15

Form the union for the following sets. R = {10, 15, 20} S = {20, 25} R ∪ S =

Mathematics
1 answer:
Alja [10]3 years ago
3 0
R = {10; 15; 20}

S = {20; 25}
R U S = {10;15; 20; 25;
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sergey [27]
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3 years ago
Reduce to the lowest terms by canceling -14/9 times -3/7
maksim [4K]

Answer:

2/3

Explanation:

Given the below;

\frac{-14}{9}\times\frac{(-3)}{7}

We can see from the above that 9 is divisible by 3 and that 14 is divisible by 7, let's go ahead and reduce to the lowest term as shown below;

\frac{-14}{9}\times\frac{(-3)}{7}=\frac{-2}{3}\times\frac{(-1)}{1}=\frac{2}{3}

5 0
1 year ago
Find the volume and area for the objects shown and answer Question
klio [65]

Step-by-step explanation:

You must write formulas regarding the volume and surface area of ​​the given solids.

\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2

\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\

\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}

\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}

SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}

6 0
3 years ago
While playing a trivia game Adam answer eight questions correct in the first half and two questions correct in the second half i
ratelena [41]

Answer:

80 points

Step-by-step explanation:

First Half:                                    Second Half:                        Total Right Answers

8 questions right            +          2 questions right        =       10 questions right

10*8 points a piece = 80 points

3 0
3 years ago
What does Fish equal?<br> A Nothing <br> B 2+2<br> C More Fish
zhuklara [117]

Answer:

A nothing

Step-by-step explanation:

5 0
3 years ago
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