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3 years ago

What is the Square root of 45? (Step by step working plz)

Mathematics

1 answer:

kifflom [539]3 years ago

5 0

if you simplify it you would have to find factors of 45 that are perfect squares, for example, the square root of 9 times the square root of 5 is the square root of 45 so if you want to simplify it you would need to take the square root of 9 which is 3

so if you put in simplest form you would get 3 root 5

$3\sqrt{5}$

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write an equation in slope intercept form of a line that passes through the point (14,8) and is (a) parallel (b) perpendicular t

LenKa [72]

Slope-intercept form:

y = mx + b "m" is the slope, "b" is the y-intercept (the y value when x = 0)

First find the slope of the line that passes through (4,9) and (-3,6).

Use the slope formula and plug in the two points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{6-9}{-3-4}$

$m=\frac{-3}{-7} =\frac{3}{7}$

A.) For lines to be parallel, their slopes have to be the same.

Since the given line's slope is 3/7, the parallel line's slope is also 3/7

y = 3/7x + b To find "b", plug in the point (14,8) into the equation

8 = 3/7(14) + b

8 = 42/7 + b

8 = 6 + b Subtract 6 on both sides

2 = b

$y=\frac{3}{7}x+2$

B.) For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)

For example:

slope is 3

perpendicular line's slope is -1/3

slope is -2/3

perpendicular line's slope is 3/2

Since the given line's slope is 3/7, the perpendicular line's slope is -7/3

y = -7/3x + b Plug in (14, 8) to find "b"

8 = -7/3(14) + b

8 = -98/3 + b Add 98/3 on both sides

8 + 98/3 = b Make the denominators the same

24/3 + 98/3 = b

122/3 = b

$y=-\frac{7}{3}x+\frac{122}{3}$

7 0

3 years ago

The Area of a square at right is 72 square units Find the value of X, Did I do this right?

Assoli18 [71]

Yes, your work is correct.

The diagram does illustrate x²+6x+9=72. This is also represented by

(x+3)² = 72

We can take the square root of both sides:
$\sqrt{(x+3)^2}=\sqrt{72}
\\
\\x+3=\pm 6 \sqrt2
\\
\\x+3-3=\pm 6 \sqrt{2} -3
\\
\\x=-3\pm 6\sqrt{2}$

When we evaluate this, the answers are x = -11.5 or x = 5.5.

5 0

2 years ago

What is the answer for number 8 and pls give step by step

Pie

Answer:

Trapezoid 1 (left side):

Base 1 = 2

Base 2 = 5

Trapezoid 2 (right side):

Base 1 = 6

Base 2 = 8

Step-by-step explanation:

1st trapezoid:

b_1 = x

b_2 = x + 3

h = 4

Hence, area (from formula) would be:

$A=\frac{h}{2}(b_1+b_2)\\A=\frac{4}{2}(x+x+3)\\A=2(2x+3)\\A=4x+6$

2nd trapezoid:

b_1 = 3x

b_2 = 4x

h = 2

Putting into formula, we get:

$A=\frac{h}{2}(b_1+b_2)\\A=\frac{2}{2}(3x+4x)\\A=1(7x)\\A=7x$

Let's equate both equations for area and find x first:

$4x+6=7x\\6=7x-4x\\6=3x\\x=\frac{6}{3}\\x=2$

We can plug in 2 into x and find length of each base of each trapezoid.

Trapezoid 1 (left side):

Base 1 = x = 2

Base 2 = x + 3 = 2 + 3 = 5

Trapezoid 2 (right side):

Base 1 = 3x = 3(2) = 6

Base 2 = 4x = 4(2) = 8

8 0

3 years ago

Consider the expressions 3x(x − 2) + 2 and 2x2 + 3x − 18.

Rzqust [24]

Answer:

See answer below

Step-by-step explanation:

For the first expression

3 x (x - 2) + 2 = 3 x^2 - 6 x + 2

evaluated at x= 4 we get: 26

and for x = 5 we get 47.

For the second expression

2 x^2 + 3 x - 18

we get the exact same values when doing the evaluation at these two points.

Based on those results, one may think the expressions may be equivalent, but they are not equivalent. Because at any other x-value, their results are different. See for example that for x = 0 the first one gives "2" while the second one gives -18.

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2 years ago

use the explicit formula an = a1 + (n - 1) * d to find the 500th term of the sequence below. 24,30,36,42,48,... A. 3018 B. 3042

marishachu [46]

Answer:

Option A.

Step-by-step explanation:

The given sequence is

24, 30, 36, 42, 48, ...

It is an AP. Here,

First term = 24

Common difference = 30-24 = 6