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3 years ago

Which statement proves that PQRS is a parallelogram?

Mathematics

2 answers:

hoa [83]3 years ago

7 0

Answer:

A .The slopes of SP and RQ are both –2 and SP = RQ

Step-by-step explanation:

edg2020

Vesnalui [34]3 years ago

4 0

Answer: The slope of two parallel lines are same. Since one pair of opposite sides are equal and parallel, therefore the another set of opposite sides is also parallel and equal. The opposite sides are prallel and equation, so the quadrilateral PQRS is a parallelogram.

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Need to find volume, step by step explanation pls

worty [1.4K]

Given:

A figure of combination of hemisphere, cylinder and cone.

Radius of hemisphere, cylinder and cone = 6 units.

Height of cylinder = 12 units

Slant height of cone = 10 units.

To find:

The volume of the given figure.

Solution:

Volume of hemisphere is:

$V_1=\dfrac{2}{3}\pi r^3$

Where, r is the radius of the hemisphere.

$V_1=\dfrac{2}{3}(3.14)(6)^3$

$V_1=\dfrac{6.28}{3}(216)$

$V_1=452.16$

Volume of cylinder is:

$V_2=\pi r^2h$

Where, r is the radius of the cylinder and h is the height of the cylinder.

$V_2=(3.14)(6)^2(12)$

$V_2=(3.14)(36)(12)$

$V_2=1356.48$

We know that,

$l^2=r^2+h^2$ [Pythagoras theorem]

Where, l is length, r is the radius and h is the height of the cone.

$(10)^2=(6)^2+h^2$

$100-36=h^2$

$\sqrt{64}=h$

$8=h$

Volume of cone is:

$V_3=\dfrac{1}{3}\pi r^2h$

Where, r is the radius of the cone and h is the height of the cone.

$V_3=\dfrac{1}{3}(3.14)(6)^2(8)$

$V_3=\dfrac{25.12}{3}(36)$

$V_3=301.44$

Now, the volume of the combined figure is:

$V=V_1+V_2+V_3$

$V=452.16+1356.48+301.44$

$V=2110.08$

Therefore, the volume of the given figure is 2110.08 cubic units.

7 0

2 years ago

This is really confusing me: Simplify so that your answers contain only positive exponents.

xxTIMURxx [149]

Answer:

see below

Step-by-step explanation:

For simplifying expressions of this sort, there are four rules of exponents that come into play;

$a^ba^c=a^{b+c}\\\\(ab)^c=a^cb^c\\\\(a^b)^c=a^{bc}\\\\\dfrac{1}{a^b}=a^{-b}\ \quad\text{which means}\quad a^b=\dfrac{1}{a^{-b}}$

I find it convenient to eliminate the fractions by adding the exponents, then rewrite any negative exponents as denominator factors.

$23. \quad\dfrac{1}{x^{-2}}=x^2\\\\24. \quad\dfrac{mn}{m^2n^3}=m^{1-2}n^{1-3}=m^{-1}n^{-2}=\dfrac{1}{mn^2}\\\\25. \quad\dfrac{k^{-2}}{k^{-3}}=k^{-2-(-3)}=k\\\\26. \quad\left(\dfrac{m^2}{n^3}\right)^3=\dfrac{m^{2\cdot 3}}{n^{3\cdot 3}}=\dfrac{m^6}{n^9}\\\\27. \quad\dfrac{x^2y^3z^4}{x^{-3}y^{-4}z^{-5}}=x^{2-(-3)}y^{3-(-4)}z^{4-(-5)}=x^5y^7z^9$

3 0

3 years ago

Circumference - Item 2838 Question 4 of 7

nevsk [136]

First, the formula of the circumference.

There are two formulas:
1. C = π*d
[Note: d = diameter]
2. C = 2*π*r
[Note: r = radius]
[Note: This symbol * means to multiply.]

Since we are given the diameter, it’s easier to use the first formula, π*d. Let’s not be too hard on ourselves.

Okay, so let’s state our decided formula:
C = π*d
Then replace d with the car tire’s diameter:
C = π*(32)
Afterwards, find a calculator and multiply π with 32. You will get 100.5309649 as result.

If where to round is stated in your question, round to that. If not, it’s best to round by two decimal places. In this case, we’ll round 100.5309649 to 100.53.

Please add your units as well. In this case, the final answer will be: 100.53 inches.

Since this is a word problem, don’t forget your final statement!

“The approximate circumference of the tire is 100.53 inches.”

7 0

3 years ago

Write the equation of the line with the given slope through the given point Slope = 6; (1, 2).

xz_007 [3.2K]

Answer:

Y=6x-4

Step-by-step explanation:

Y=mx+b

in this cace we have m- the slope

Y=6x+b

now we can plug in the coordinates to solve for b- the y intercept

(1,2) 1 being the x value, and 2 being the y value

2= 1·6+b

2=6+b

-4=b

now we take our previous equation, and add to it

Y=6x-4

4 0

3 years ago

A square wall is 30 ft ^2. What is the length of one wall?

Serggg [28]

√30 = 5.47722557505

so 5.5ft × 5.5ft ≈ 30ft²

I hope I helped

ΩΩΩΩΩΩΩΩΩΩ

8 0

2 years ago