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Solve the binomial.
(1/2y - 50)(3/5y + 10)

Answer:

The length of the hypotenuse side is (9 + 2·√7) cm

Step-by-step explanation:

The given parameters of the triangle are;

The type f triangle = Right triangle

The length of the sides 2 cm and 7 cm shorter than the hypotenuse

Let 'h' represent the length of the hypotenuse side of the triangle, in centimeters we have;

The length of one side of the right triangle = (h - 2) cm

The length of the other side of the right triangle = (h - 7) cm

By Pythagoras's theorem, we have;

h² = (h - 2)² + (h - 7)²

Using search function on the internet, we have;

h² = (h - 2)² + (h - 7)² = 2·h² - 18·h + 53

∴ h² = 2·h² - 18·h + 53

∴ 2·h² - 18·h + 53 = h²

h² - 18·h + 53 = 0

53 is a prime number, therefore, by the quadratic formula, we have;

h = (18 ± √((-18)² - 4×1×53))/(2 × 1)

h = 9 + 2·√7 cm ≈ 14.29 cm or h = 9 - 2·√7 ≈ 3.71

However, given that one of the side is 7 cm shorter than the hypotenuse, for all the sides to remain positive, we have h = 9 + 2·√7 cm ≈ 14.29 cm , because for h ≈ 3.71 cm, we have;

The length of the other side = (h - 7) cm ≈ (3.71 - 7) cm ≈ -3.29 cm which is not possible for a real triangle

Therefore, the length of the hypotenuse side, h = 9 + 2·√7 cm ≈ 14.29 cm.

Answer:

2p should be the correct answer!

Answer:

2p is the answer

Step-by-step explanation:

I took the answer edg2021

Answer:

9

Step-by-step explanation:

because the FIM and LAK are similar, then

FI/LA=IM/AK=MF/KL

MF/KL=2/3

Answer:

should be a hope it helps

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

90/1=90

140/2=70

190/3=63.3333333

240/4=60

so the first hour cost more than the others, hope this helps!

Answer:

[tex]1) \frac{1}{13} \\ 2) \frac{12}{13} [/tex]

Step-by-step explanation:

according to the question

according to the question

Answer:

no of 7=4

total no of card =52

total not no.7=52-4=48

Step-by-step explanation:

probability of getting 7=4/52=1/13

probability of not getting 7=48/52=12/13

Answer:

$1.95

Step-by-step explanation:

Answer:

Both sides that are parallel ( 6 inches I believe ) would be 12 in total for both sides. Then the top and bottom would be 3 inches ( I believe ) which would be 6. I think you need to do 6 times 12 until you get 360 and then see how many times you multiplied it and that is your answer. But I am not FULLY sure. Hope this helps somehow!

Step-by-step explanation:

Answer:

a) X - Y = 10

and,

X - 5 = 10

or, X = 10 + 5

or, X = 15

And i don't get the other two questions

Hope this helped

Hope this helped ALL THE BEST !!

Answer:

you have to do that we don't know k sorry bro

Answer:

a

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Do 400 divided by 16 to convert to pounds

400/16=25

Hope this helped :)

Answer:

25 pounds

Step-by-step explanation:

1 Pound=16 ounces

? Pounds=400 ounces

400 divided by 16=25

25 pounds=400 ounces

Answer:

I think no. Because degree is the sum all variables in first equation degree. Is14 but second equation degree not 14.

Answer:

C=50.24

Step-by-step explanation:

Formula for circumference with radius: 2[tex]\pi[/tex]r

r= radius

C=circumference

Now subsitute the variables with the values given.

Formula:  2[tex]\pi[/tex]r  -> 2(3.14)(8)

C=50.24

Answer:

answer:250 pieces

1 metre=100cm so

10metres =100*10 =1000cm

each piece is 4 CM long, so.,

no. of pieces=1000/4

by dividing by 2....

=500/4

again by dividing by2...

=250/1=250 pieces

so 250 pieces of ribbon can be cuttted from 10 metre long ribbon.

Answer:

1 135

2 80

3 145

4 45

Step-by-step explanation:

Thats the answer

.

.

.

Answer: When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection. Here, lines P and Q intersect at point O, which is the point of intersection.

I think this the answer‍♀️

Answer:

A is a concave polygon,....,.

Answer:

the answer will be A.

Step-by-step explanation:

Answer:

3/8!! hope i helped :))

Answer:

hi

Step-by-step explanation:

Option 4th is correct

The solution of the system of equations is, (9, 3)

Step-by-step explanation:

Given the system of equations:

⇒                .....[1]

⇒                 .....[2]

Add equation [1] and [2] we have;

Divide both sides by 2 we have;

Substitute x = 9 in [1] we have;

Subtract 9 from both sides we have;

2y = 6

Divide both sides by 2, we have;

y = 3

Therefore, the solution of the system of equations is, (9, 3)

Answer:

Me too

Step-by-step explanation:

Answer: hello

your answer will be C

Step-by-step explanation:

What is the answer?

here is the image

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image.

From the diagram:

Scale factor = A'B' / AB = 6/3 = 2

Center = (6, -6)

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

Find out more on dilation at: https://brainly.com/question/10253650

Part (c)

We'll use this identity

[tex]\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\\\\[/tex]

to say

[tex]\sin(A+45) = \sin(A)\cos(45) + \cos(A)\sin(45)\\\\\sin(A+45) = \sin(A)\frac{\sqrt{2}}{2} + \cos(A)\frac{\sqrt{2}}{2}\\\\\sin(A+45) = \frac{\sqrt{2}}{2}(\sin(A)+\cos(A))\\\\[/tex]

Similarly,

[tex]\sin(A-45) = \sin(A + (-45))\\\\\sin(A-45) = \sin(A)\cos(-45) + \cos(A)\sin(-45)\\\\\sin(A-45) = \sin(A)\cos(45) - \cos(A)\sin(45)\\\\\sin(A-45) = \sin(A)\frac{\sqrt{2}}{2} - \cos(A)\frac{\sqrt{2}}{2}\\\\\sin(A-45) = \frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\[/tex]

-------------------------

The key takeaways here are that

[tex]\sin(A+45) = \frac{\sqrt{2}}{2}(\sin(A)+\cos(A))\\\\\sin(A-45) = \frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\[/tex]

Therefore,

[tex]2\sin(A+45)*\sin(A-45) = 2*\frac{\sqrt{2}}{2}(\sin(A)+\cos(A))*\frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\2\sin(A+45)*\sin(A-45) = 2*\left(\frac{\sqrt{2}}{2}\right)^2\left(\sin^2(A)-\cos^2(A)\right)\\\\2\sin(A+45)*\sin(A-45) = 2*\frac{2}{4}\left(\sin^2(A)-\cos^2(A)\right)\\\\2\sin(A+45)*\sin(A-45) = \sin^2(A)-\cos^2(A)\\\\[/tex]

The identity is confirmed.

==========================================================

Part (d)

[tex]\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\\\\\sin(45+A) = \sin(45)\cos(A) + \cos(45)\sin(A)\\\\\sin(45+A) = \frac{\sqrt{2}}{2}\cos(A) + \frac{\sqrt{2}}{2}\sin(A)\\\\\sin(45+A) = \frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\\\\[/tex]

Similarly,

[tex]\sin(45-A) = \sin(45 + (-A))\\\\\sin(45-A) = \sin(45)\cos(-A) + \cos(45)\sin(-A)\\\\\sin(45-A) = \sin(45)\cos(A) - \cos(45)\sin(A)\\\\\sin(45-A) = \frac{\sqrt{2}}{2}\cos(A) - \frac{\sqrt{2}}{2}\sin(A)\\\\\sin(45-A) = \frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\\\\[/tex]

-----------------

We'll square each equation

[tex]\sin(45+A) = \frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\\\\\sin^2(45+A) = \left(\frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\right)^2\\\\\sin^2(45+A) = \frac{1}{2}\left(\cos^2(A)+2\sin(A)\cos(A)+\sin^2(A)\right)\\\\\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\frac{1}{2}*2\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\[/tex]

and

[tex]\sin(45-A) = \frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\\\\\sin^2(45-A) = \left(\frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\right)^2\\\\\sin^2(45-A) = \frac{1}{2}\left(\cos^2(A)-2\sin(A)\cos(A)+\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\frac{1}{2}*2\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\[/tex]

--------------------

Let's compare the results we got.

[tex]\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\[/tex]

Now if we add the terms straight down, we end up with [tex]\sin^2(45+A)+\sin^2(45-A)[/tex] on the left side

As for the right side, the sin(A)cos(A) terms cancel out since they add to 0.

Also note how [tex]\frac{1}{2}\cos^2(A)+\frac{1}{2}\cos^2(A) = \cos^2(A)[/tex] and similarly for the sin^2 terms as well.

The right hand side becomes [tex]\cos^2(A)+\sin^2(A)[/tex] but that's always equal to 1 (pythagorean trig identity)

This confirms that [tex]\sin^2(45+A)+\sin^2(45-A) = 1[/tex] is an identity

Answer:

13,500.00 yearly is the raise + 90000.00 original salary= 103500.00 a year

Rs 103500

Sorry hazy little bit

Answer:

Step-by-step explanation:

Answer:

An = A + (n - 1) ×d

hope it helps

Answer:

-5

Step-by-step explanation:

y=-2/3-5x

Rewriting the equation in the form y = mx+b where m is the slope and b is the y intercept

y = -5x -2/3

The slope is -5 and the y intercept is -2/3

Answer:

c-a=b

Step-by-step explanation: