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Soloha48 [4]
3 years ago
9

The width of a rectangle is s. Its length is 3s. How long is a diagonal of the rectangle? Express your answer in simplified radi

cal form.
Mathematics
1 answer:
Valentin [98]3 years ago
3 0
By the pythagorean theorem:

h^2=x^2+y^2, h is the diagonal, and x and y are the sides so...

d^2=s^2+(3s)^2

d^2=s^2+9s^2

d^2=10s^2

d=s√10  (since 10=2*5 neither of which is a square so √10 cannot be simplified any further)

The diagonal is s√10 units
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Fred has 30 minutes to do a three-problem quiz. He spent 10 7/10 minutes on question a and 5 2/5 minutes on question b. How much
tatiyna

Answer:Fred has 13 9/10 minutes left for question C

Step-by-step explanation:

The total time that Fred has to do the three-problem quiz is 30 minutes.

He spent 10 7/10 minutes on question A. Converting 10 7/10 minutes to improper fraction, it becomes 107/10 minutes.

He spent 5 2/5 minutes on question B. Converting 5 2/5 minutes to improper fraction, it becomes 27/5 minutes.

Total time that Fred spent on question A and question B is

107/10 + 27/5 = (107 + 54)/10

= 161/10 minutes.

The amount of time that he has left for question C would be

30 - 161/10 = (300 - 161)/10 = 139/10

= 13 9/10 minutes

3 0
3 years ago
Please help me!!
ipn [44]

{\color{chartreuse}{Measure\:of\: ∠\:on\: one\: side\:of\:line\:=\:180°}}

∠ Given are (x + 18)° , x° , 4x° and one Angle is 90° as per diagram

Let ,

1st∠ = (x + 18)°

2nd∠ = x°

3rd∠ = 4x°

so ,

⟶\:(x \:+\: 18)°\:+\:x°\:+\: 4x°\:+\:90°\:=\:180°

⟶\:6x°\:+ \:18°\:+\:90°\:=\:180°

⟶\:6x°\:+ \:108°\:=\:180°

⟶\:6x°\:=\:180°\:-\:108°

⟶\:6x\:=\:72°

⟶\:x\:=\:\frac{72}{6} \\

⟶\:x\:=\:12°

substituting x = 12 at the place of x .

= x° + 18°

= 12° + 18 °

1st∠ = 30°

__________________________________

= x°

2nd∠ = 12°

__________________________________

= 4x°

= 4(12)°

3rd∠ = 48°

7 0
2 years ago
The area of the shaded segment is 100cm^2. Calculate the value of r.
Reil [10]
Hello, 

The formula for finding the area of a circular region is: A=  \frac{ \alpha *r^{2} }{2}

then:
A_{1} = \frac{80*r^{2} }{2}

With the two radius it is formed an isosceles triangle, so, we must obtain its area, but first we obtain the height and the base.

cos(40)= \frac{h}{r}  \\  \\ h= r*cos(40)\\ \\ \\ sen(40)= \frac{b}{r} \\ \\ b=r*sen(40)

Now we can find its area:
A_{2}=2* \frac{b*h}{2}  \\  \\ A_{2}= [r*sen(40)][r*cos(40)]\\  \\A_{2}= r^{2}*sen(40)*cos(40)

The subtraction of the two areas is 100cm^2, then:

A_{1}-A_{2}=100cm^{2} \\ (40*r^{2})-(r^{2}*sen(40)*cos(40) )=100cm^{2} \\ 39.51r^{2}=100cm^{2} \\ r^{2}=2.53cm^{2} \\ r=1.59cm

Answer: r= 1.59cm
7 0
2 years ago
Read 2 more answers
a small business averages 5,500$ per month in online revenue plus another 300$ per salesperson per month. which graph shows all
SOVA2 [1]

Answer:

C

Step-by-step explanation:

considering you need at least 6 people, you would either need 6 or more, so 6 or greater, so C

7 0
3 years ago
A2=b2=c2 solve for a
Over [174]

Step-by-step explanation:

A²+B²=C²

A²+4²=5²

A²+16=25

    -16 -16

A²=9

√A=√9

  A=3

3 0
2 years ago
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