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3 years ago

How do you construct a 112.5 degree angle? (step by step) Please help =)

Mathematics

1 answer:

KATRIN_1 [288]3 years ago

5 0

First you take a protractor and a pencil
next, you draw a horizontal line (red)
then find the value of the angle, and draw a line with the matched value (green)
please look at the image

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3y-y+8-2=20<br> combine like terms and solve

Flauer [41]

3y - y + 8 - 2 = 20
3y - y = 2y
8 - 2 = 6
2y + 6 = 20
2y = 20 - 6
y = 10 - 3
the answer is: y = 7

4 0

3 years ago

Rewrite each problem so that x appears on only one side

Vlad1618 [11]

Answer:

x = -5/21

Step-by-step explanation:

Step 1: Write equation

2(12x - 1) = (21x - 49)/7

Step 2: Solve for <em>x</em>

Multiply both sides by 7: 14(12x - 1) = 21x - 49
Distribute 14: 168x - 14 = 21x - 49
Subtract 21x on both sides: 147x - 14 = -49
Add 14 to both sides: 147x = -35
Divide both sides by 147: x = -5/21

5 0

2 years ago

The sum of the diagonals of a rhombus is 5√2.

Alex

Greetings!
Let ABCD be a rhombus
AC + BD = 5√2 cm

Area of ABCD = Ar△ABD + Ar △BCD
$= \frac{1}{2} \times BD \times AO + \frac{1}{2} \times BD \times OC$
$= \frac{1}{2} BD (AO + OC)$
$\frac{1}{2} BD \times AC$

$So, \frac{ BD \times AC}{2} = 4 \: cm {}^{2}$
$BD \times AC = 8$
$Now, AC + \: BD = 5 \sqrt{2}$

Squaring both sides, we get
$AC {}^{2} + BD {}^{2} + 2 AC.BD =50$
$AC {}^{2} + BD {}^{2} + 2 \times 8 = 50$
$AC {}^{2} + BD {}^{2} = 50 - 16$
$AC {}^{2} + BD {}^{2} = 34$

In △AOB, we have
$OA {}^{2} + OB {}^{2} =AB {}^{2}$
$( \frac{ AC }{2} ) {}^{2} + ( \frac{ BD}{2} ) {}^{2} = AB {}^{2}$
$\frac{ AC {}^{2} } {4} + \frac{ BD {}^{2} }{4} = AB {}^{2}$
$AC {}^{2} + BD {}^{2} = 4 AB {}^{2}$
$34 = 4 AB {}^{2}$

Square rooting both sides
$\sqrt{34} = 2 AB$
$Perimeter = 4 \: AB \\ = 2 \times 2 \: AB \\ = 2 \: \times \sqrt{34 } \\ = 2 \sqrt{34 \: } units$ .

Hope it helps!

7 0

3 years ago

Order of operations (41-3^2)-(4+4)

ladessa [460]

Order is operation is PEMDAS which means Parentheses, Exponents Mulitiplication,division,Addition and Subtraction so you follow the order whether they exist or not.

So (41-3^2)-(4+4)=

41-9-8 = 32-8 = 24

8 0

2 years ago

A radioactive substance decays exponentially: The mass at time t is m(t) = m(0)ekt, where m(0) is the initial mass and k is a ne

velikii [3]

Answer:

M = 1/0.000121 = 8264.5 years

Step-by-step explanation:

M = − k ∫∞₀ teᵏᵗdt

To obtain this mean life, we'll use integration by parts to integrate the function ∫ teᵏᵗdt

∫udv = uv - ∫ vdu

u = t

du/dt = 1

du = dt

∫ dv = ∫ eᵏᵗdt

v = eᵏᵗ/k

∫udv = ∫ teᵏᵗdt

uv = teᵏᵗ/k

∫ vdu = eᵏᵗ/k

∫ teᵏᵗdt = (teᵏᵗ/k) - ∫eᵏᵗ/k

But, ∫eᵏᵗ/k = (1/k) ∫eᵏᵗ = (1/k²) eᵏᵗ = eᵏᵗ/k²

∫ teᵏᵗdt = (teᵏᵗ/k) - eᵏᵗ/k²

The rest of the calculation is done on paper in the image attached to this question

3 0

3 years ago