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antoniya [11.8K]
2 years ago
7

50 POINTS (SUPER IMPORTANT PLEASE HELP)

Mathematics
1 answer:
sergeinik [125]2 years ago
5 0
The answer would be you can’t simplify the first one but the second would be 15 square root 5

Hope this helps

Have a great day/night

Feel free to ask any questions
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Please answer question three and four if you can :)<br> Show full working out ty;)
nikklg [1K]

Step-by-step explanation:

3

Let D be the mid point of side BC, [B(2, - 1), C(5, 2)].

Therefore, by mid-point formula:

D = ( \frac{2 + 5}{2},  \:  \:  \frac{ - 1 + 2}{2} ) = ( \frac{7}{2}, \:  \:  \frac{ 1}{2} ) \\ \therefore D= (3.5, \:  \: 0.5) \\  \& \: A=(-1,\:\:4)...(given) \\\\  now \: by \: distance \: formula \\  \\ Length  \: of \:  segment  \: AD \\  =  \sqrt{( - 1 - 3.5)^{2}  +  {(4 - 0.5)}^{2} }  \\ =  \sqrt{(4.5)^{2}  +  {(3.5)}^{2} }  \\ =  \sqrt{20.25 + 12.25 }  \\  =  \sqrt{32.5}  \\    \red{ \boxed{\therefore Length  \: of \:  segment  \: AD  = 5.7 \: units}}

4 (a)

Equation of line AB[A(2, 1), B(-2, - 11)] in two point form is given as:

\frac{y-y_1}{y_1-y_2} =\frac{x-x_1}{x_1 - x_2} \\\\\therefore \frac{y-1}{1-(-11)} =\frac{x-2}{2 - (-2) } \\\\\therefore \frac{y-1}{1+11} =\frac{x-2}{2 +2} \\\\\therefore \frac{y-1}{12} =\frac{x-2}{4} \\\\\therefore \frac{y-1}{3} =\frac{x-2}{1} \\\\\therefore y-1= 3(x - 2)\\\\\therefore y= 3x - 6+1\\\\\therefore y= 3x - 5\\\\ \huge \purple {\boxed {\therefore 3x - y-5=0}} \\

is the equation of line AB.

Now we have to check whether C(4, 7) lie on line AB or not.

Let us substitute x = 4 & y = 7 on the Left hand side of equation of line AB and if it gives us 0, then C lies on the line.

LHS = 3x - y-5\\=3\times 4-7-5\\= 12-12\\=0\\= RHS

Hence, point C (4, 7) lie on the straight line AB.

4(b)

Like we did in 4(a), first find the equation of line AB and then substitute the coordinates of point C in equation and if they satisfy the equation, then all the three points lie on the straight line.

4 0
3 years ago
Add. Write fractions in simplest form.<br> 4-12 EVENS
Virty [35]
4. 1/3   6.-0.9 or -9/10    8. 2 1/3  10. -3.45   12.4.54 or 4 27/50
7 0
3 years ago
15PTS PLEASE HELP ASAP!<br> (dont write random answers pls!)
Tcecarenko [31]

Answer:

52

Step-by-step explanation:

.................................

4 0
3 years ago
Read 2 more answers
How do I solve -(x+7)-5=4(x+3)-6x
sasho [114]

Answer:

x = 24

Step-by-step explanation:

I checked and made sure the answer was correct.

Hope this helps!

Please Mark Brainliest!

4 0
3 years ago
A gate is made up of a rectangle and a semicircle, as shown. Find the area of the gate. Use 3.14 for .Round your answer to the n
allochka39001 [22]

Answer:

<em>797.0ft²</em>

Step-by-step explanation:

<u>Find a related diagram attached</u>

Area of the gate = Area of the semicircle + Area of the Rectangle

Area of the semicircle = πr²/2

r is the radius

From the diagram, radius r = 20/2 = 10ft

Area of the semicircle = 3.14(10)²/2

Area of the semicircle = 3.14(100)/2

Area of the semicircle = 314/2

Area of the semicircle = 157ft²

Area of the rectangle = Length * Width

Area of the rectangle = 20*32

Area of the rectangle = 640ft²

Area of the gate = 157 + 640

Area of the gate = 797ft²

<em>Hence the area of the gate is 797.0ft²</em>

7 0
3 years ago
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