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3 years ago

Which expressions are equal to 7(53)? Select all that apply.

Mathematics

1 answer:

skad [1K]3 years ago

3 0

Answer:

7(50 + 3)

7(50) + 7(3)

371

Step-by-step explanation:

7(53)

50 can be written as (50 + 3)

∴7(53) = 7(50 + 3)

Proceeding with the above expression we get;

7(53) = 7(50 + 3)

= 7(50) + 7(3)

Completing the above expression we get;

7(53) = 7(50) + 7(3)

= 350 + 21

= 371

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Rewrite in Polar Form.... x^(2)+y^(2)-6y-8=0

skad [1K]

$\bf x^2+y^2-6y-8=0\qquad 
\begin{cases}
x^2+y^2=r^2\\\\
y=rsin(\theta)
\end{cases}\implies r^2-6rsin(\theta)=8
\\\\\\
\textit{now, we do some grouping}\implies [r^2-6rsin(\theta)]=8
\\\\\\\
[r^2-6rsin(\theta)+\boxed{?}^2]=8\impliedby 
\begin{array}{llll}
\textit{so we need a value there to make}\\
\textit{a perfect square trinomial}
\end{array}$

$\bf 6rsin(\theta)\iff 2\cdot r\cdot \boxed{3\cdot sin(\theta)}\impliedby \textit{so there}
\\\\\\
\textit{now, bear in mind we're just borrowing from zero, 0}
\\\\
\textit{so if we add, \underline{whatever}, we also have to subtract \underline{whatever}}$

$\bf [r^2-6rsin(\theta)\underline{+[3sin(\theta)]^2}]\quad \underline{-[3sin(\theta)]^2}=8\\\\
\left. \qquad \right.\uparrow \\
\textit{so-called "completing the square"}
\\\\\\\
[r-3sin(\theta)]^2=8+[3sin(\theta)]^2\implies [r-3sin(\theta)]^2=8+9sin^2(\theta)
\\\\\\
r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}\implies r=\sqrt{8+9sin^2(\theta)}+3sin(\theta)$

3 0

2 years ago

Select the correct volume.

Bond [772]

Answer:

i think it is 8/125

Step-by-step explanation:

slect B

6 0

3 years ago

The lines below are perpendicular if the slope of the solid line is 4 what is the slope of the dashed line

const2013 [10]

Answer:

The slope of the dashed line is $-\frac{1}{4}$

Step-by-step explanation:

Perpendicular lines and slopes:

If two lines are perpendicular, the multiplication of their slopes is -1.

What is the slope of the dashed line

Perpendicular to a line with slope 4, so:

$4m = -1$

$m = -\frac{1}{4}$

The slope of the dashed line is $-\frac{1}{4}$

8 0

2 years ago

Name the edges of an hexagonal pyramid

aleksandrvk [35]

Given:

Hexagonal pyramid

To find:

The edges of an hexagonal pyramid.

Solution:

Edges means lines which connecting to vertices.

Edges in the base of the pyramid:

AB, BC, CD, DE, EF, FA

Edges in the triangular shape of the pyramid:

AG, BG, CG, DG, EG, FG

Therefore edges of an hexagonal pyramid are:

AB, BC, CD, DE, EF, FA, AG, BG, CG, DG, EG, FG

4 0

3 years ago

Two more than the square of a number is 123 what is the number? Can someone please explain to me how to do this

max2010maxim [7]

Give the number a label. That can be anything you want. A lot of people will use 'x' every single time they do a math problem,but there's no reason to do that and it's boring. Let's call our number ' M ' for 'Mystery number'. OK ?

The number . . . M
The square of the number . . . M²
Two more than the square of the number . . . M² + 2

You said that this is equal to 123, so we can write  M² + 2 = 123

That's the equation we have to take and solve for ' M '.

Subtract 2 from each side of the equation, and you have M² = 121 .

Take the square root of each side: M = √121 .

The Mystery number is the square root of 121.

If you don't happen to know what that is, then you can use your pocket
calculator, or the calculator that comes with your computer (if you know
how to find it). They will all tell you that the square root of 121 is 11 .

That's a fine and wonderful answer, but technically, it's only half of the
answer. Any equation that has something squared in it almost always
has two solutions, and this one does.

The square root of 121 is a number that gives you 121 when you
multiply it by itself. ' 11 ' does that: (11 x 11) = 121 . Is there another
number that does the same thing ?

How about ' -11 ' ? Look at this: ( -11 x -11 ) = 121 . (Remember that
if both numbers being multiplied have the same sign, then their product
is positive.)

The bottom line is: The mystery number is +11 and also -11 .
Either one does what you want . . . When you square it and then
add 2 more, you get 123 either way.

6 0

3 years ago