if cos θ - sin θ = √2 sin θ, then prove that cos θ + sin θ = √2 cos θ.

Answer:

25.) Slope of AB = 5

Slope of CD = -1/5

Perpendicular

26.) Slope of EF = -3/5

Slope of GH = -3/5

Parallel

Step-by-step explanation:

Use this formula to find slope. [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Parallel lines have the same slope

Perpendicular lines have the opposite reciprocal and sign

25.)

Plug in AB slope is 5

2 - 7/ 3 - 4 = -5/-1 = 5

Plug in for CD slope is -1/5

3 - 4/ 2 - -3 = -1/5 = -1/5

The lines AB and CD are perpendicular because they have opposite reciprocals and opposite signs.

26.)

Plug in EF slope is -3/5

1 - 4/ 3 - -2 = -3/5 = -3/5

Plug in GH slope is -3/5

-5 - -2/ 4 - -1 =  -3/5 = -3/5

The lines EF and GH are parallel lines because they have the same slopes.

Hope this helps ya!

Answer:

what the other person said

Step-by-step explanation:

you were already saved just give them brainliest now

Answer:

Number of students who do not know = 24

Step-by-step explanation:

Year II students = 240

15% of the students want to go to college.

Number of year II students who wants to go to college = 15% of 240

= 15/100 × 240

= 0.15 × 240

= 36

¾ of the students want to stay at school.

Number of students who wants to stay at the school = 3/4 × 240

= (3 × 240) / 4

= 720 / 4

= 180

Number of students who do not know = Total year II students - Number of year II students who wants to go to college - Number of students who wants to stay at the school

= 240 - 36 - 180

= 24

Number of students who do not know = 24

Answer:

1

Step-by-step explanation:

Answer:

April took out a loan of $600 and paid it back with simple interest of $60 after 5 years. The formula to calculate interest is  given the principal  and the time   and the interest rate  is . For this problem we have to find the interest rate   given  . To archive that , we can just solve the equation making the interest rate the subject of the formula as shown below,

I= Prt

=> r= I/Pt

=> r= 60/600x5 = 1/50

The interest rate is 1/50 or 0.02 as a decimal. The interest rate is 2% as a percentage.

Answer:

You add 12.5+12.5+3.02+3.02 which equals 31.04

Step-by-step explanation:

Answer:

x intercept: 10, y intercept: -8

Step-by-step explanation:

make into y = mx + b

4x = 5y + 40

4x - 40 = 5y

y = 4/5x - 8

plug in 0 for x, to find y intercept

y = -8

plug in 0 for y, to find x intercept

0 = 4/5x - 8, x = 10

Answer:

Ok

Step-by-step explanation:

Step-by-step explanation:

Letthenumberofpensbexand

numberofpencilsbey

then

x+y=16ory=16−x

andtheirvalue

8x+1.5y=50

8x+(

2

3

)(16−x)=50

8x+24−(

2

3

)x=50

8x−(

2

3

)x=50−24

(

2

13x

)=26∴x=4

theny=16−x=16−4=12

Answer:

74F

Step-by-step explanation:

If it is 89F on Monday and it went DOWN 15 degrees, you subtract. 89-15= 74. The temp on Monday is 74 degrees F

Answer:

i think 7

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

It's a parallel line so the equation is

100+19x+4=180

19x=180-100-4

19x=76

x=76/19

x=4

Answer: x = 4

Step-by-step explanation: The 2 angles are same-side interior angles, which are supplementary, and supplementary angles add up to 180, so we know that 19x + 4 = 80.

- 4. -4

19x = 76

/19. /19

X = 4

Answer:

D

Step-by-step explanation:

The product of the greatest common factor and a sum is 12 (2 + 3).

Option C is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

24 + 36

We have the following cases:

2 (12 + 18)

3 (8 + 12)

4 (6 + 9)

6 (4 + 6)

12 (2 + 3)

Now,

The greatest common factor.

12 x 2 = 24

12 x 3 = 36

Thus,

12(2 + 3) is the product of the greatest common factor and a sum of (2 + 3).

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Answer:

1920 and 768

Step-by-step explanation:

its 40% of the numbers

40% of 30000 = 12000

40% of 12000 = 4800

next numbers

40% of 4800 = 1920

40% of 1920 = 768

Answer:

r=0.2

r= -0.75

Step-by-step explanation:

if im wrong im sorry

Step-by-step explanation:

please see it, i work on paper worksheet

Answer:

2 1/2 miles

24 minutes per mile

Answer:

A S A

Step-by-step explanation:

In ΔACE & ΔBCD,

   ∠A ≅ ∠B      {Given}     Angle

  AC = BC           {Given}    Side

  ∠ACE = ∠BCD    { Reflexive property} Angle

ΔACE ≅ ΔBCD      ------>A S A Property

Answer:

It is B.

Step-by-step explanation:

Edge2021

[tex]w -z =\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]

"The number of the form a + ib where a, b are real numbers and [tex]i=\sqrt{-1}[/tex] "

"The polar form of complex number z = x + iy is [tex]z=r~(cos\theta+i~sin\theta)[/tex] where [tex]r=\sqrt{x^{2} +y^{2} }[/tex] and [tex]\theta=tan^{-1}(\frac{y}{x} )[/tex]"

For given question,

We have been given two complex numbers in polar form.

[tex]w=\sqrt{2}(cos(\frac{\pi}{4} )+i~sin(\frac{\pi}{4} ))[/tex] and [tex]z=2(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))[/tex]

We simplify above complex numbers.

[tex]w=\sqrt{2}(cos(\frac{\pi}{4} )+i~sin(\frac{\pi}{4} )) \\\\w=\sqrt{2}(\frac{1}{\sqrt{2} } +i~ \frac{1}{\sqrt{2} } ) \\\\w=1+i[/tex]

And the second complex number is,

[tex]z=2(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))\\\\z=2(0+i~1)\\\\z=0+2i[/tex]

Now if we find the value of w - z

⇒ w - z = (1 + i) - (0 + 2i)

⇒ w - z = 1 - i

Now we find the polar form of complex number.

[tex]r=\sqrt{1^{2} +(-1)^{2} } \\\\r=\sqrt{2}[/tex]

And the value of [tex]\theta[/tex] would be,

[tex]\theta=tan^{-1}(\frac{-1}{1} )\\\\\theta=tan^{-1}(-1)\\\\\theta=\frac{3\pi}{4}[/tex]

So, w - z in the polar form would be [tex]1+i=\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]

Therefore, [tex]w -z =\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]

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Answer:

i beleve 26 or 48

good luck

Answer:

Hiiiiiii

Step-by-step explanation:

So to get the answer you have to turn the 3/8 into a mixed number and divide  it by 111

353.25

a=(3.14*15^2)/2

a=706.5/2

a=353 sq in

i think it is c if its wrong i apologize.

Answer:

.00963

Step-by-step explanation:

Since its 10^-3, the decimal point moves to the left 3 times. hope this helped :)

Answer:

there are 10 girls in the club

Step-by-step explanation:

25*40% is equal to 10

Answer:

B. 68

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

I calculated

No because something proportional can't have a y-intercept, the 3 is the y intercept so your statement is not proportional.

Answer:

it could be C or a

Step-by-step explanation:

more likey c be sorry if it's wrong