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3 years ago

Which lists these numbers in order from least to greatest?

1 answer:

6 0

B. because the negative numbers are the smallest so they have to come first and -14.6 is smaller than -1.295. a.07 is smaller than 24.6 and 159 is the largest number listed.

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Consider the linear expression 3x -15

Jobisdone [24]

Answer:

In linear expresiion 3 is the coefficient

X will be the variable and -15 will be the constant term.

5 0

3 years ago

Please prove this........

Crazy boy [7]

Answer: see proof below

<u>Step-by-step explanation:</u>

Given: A + B + C = π → C = π - (A + B)

→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))

→ sin C = sin (A + B) cos C = - cos(A + B)

Use the following Sum to Product Identity:

sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]

cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]

Use the following Double Angle Identity:

sin 2A = 2 sin A · cos A

<u>Proof LHS → RHS</u>

LHS: (sin 2A + sin 2B) + sin 2C

$\text{Sum to Product:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-\sin 2C$

$\text{Double Angle:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-2\sin C\cdot \cos C$

$\text{Simplify:}\qquad \qquad 2\sin (A + B)\cdot \cos (A - B)-2\sin C\cdot \cos C$

$\text{Given:}\qquad \qquad \quad 2\sin C\cdot \cos (A - B)+2\sin C\cdot \cos (A+B)$

$\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]$

$\text{Sum to Product:}\qquad 2\sin C\cdot 2\cos A\cdot \cos B$

$\text{Simplify:}\qquad \qquad 4\cos A\cdot \cos B \cdot \sin C$

LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C $\checkmark$

7 0

3 years ago

A father and his daughter together weigh seven times the daughter's weight x. The father weighs 180 lbs. Which equation can be u

bezimeni [28]

Father and daguther together
father=180
father and daughter is 7 times daught
father+x=7x
180+x=7x
D is answer
and daughter=30lb

3 0

3 years ago

Read 2 more answers

Henry is making a corn grits recipe that calls for 1/4 cup of corn grits for every 1/2 cup of water. How much water will he need

Archy [21]

Method 1:

$\begin{array}{ccc}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}\\\\1\dfrac{1}{2}=\dfrac{3}{2}\ \text{cup of corn}&-&x\ \text{cup of water}\end{array}\qquad\text{cross multiply}\\\\\\\dfrac{1}{4}\cdot x=\dfrac{3}{2}\cdot\dfrac{1}{2}\\\\\dfrac{1}{4}x=\dfrac{3}{4}\qquad\text{multiply both sides by 4}\\\\\boxed{x=3}$

<h3>Answer: Henry will need 3 cups of water.</h3>

Method 2:

$\begin{matrix}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}&|\text{multiply both sides by 2}\\\\\dfrac{1}{2}\ \text{cup of corn}&-&1\ \text{cup of water}&|\text{multiply both sides by 2}\\\\1\ \text{cup of corn}&-&2\ \text{cup of water}&|\end{matrix}$

$\begin{matrix}\left(\dfrac{1}{2}+1\right)\ \text{cups of corn}&-&(1+2)\ \text{cups of water}\\\\1\dfrac{1}{2}\ \text{cups of corn}&-&3\ \text{cups of water}\end{matrix}$

<h3>Answer: Henry will need 3 cups of water.</h3>

5 0

3 years ago

Read 2 more answers

K/75 + 57.1 = 40.8<br> k = ?

Ronch [10]

K/75 + 57.1 = 40.8

k/75 = 40.8 - 57.1

k/75 = -16.3

k = -16.3 • 75

k = -1222.5 or -1222 1/2

Hope it helps!

5 0

3 years ago