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weeeeeb [17]
3 years ago
7

Triangle XYZ is an isosceles Triangle with legs XY and ZY. Segments QR and QS are perpendicular bisectors of triangle XYZ. Find

the length of segment QR if QS = 1/2x + 2 and QS = x - 10.

Mathematics
1 answer:
Oduvanchick [21]3 years ago
3 0

we know XYZ is an isosceles, thus XY = YZ, the perpendicular segment bisectors of QR and QS are also equal to each other in length, because they both are segment bisectors and thus YR=RX=YS=SZ, so any perpendicular line stemming from the same length on each side will meet its counterpart right on the middle of the triangle.

\bf \stackrel{QR}{\cfrac{x}{2}+2}~~=~~\stackrel{QS}{x - 10}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( \cfrac{x}{2}+2 \right)=2(x-10)}\implies x+4=2x-20 \\\\\\ 4=x-20\implies 24=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{QR}{\cfrac{24}{2}+2}\implies 12+2\implies 14

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List 5 fractions that are between 1/3 and 4/5
koban [17]

9514 1404 393

Answer:

  2/5, 7/15, 8/15, 3/5, 2/3

Step-by-step explanation:

If these fractions are expressed with a common denominator, that would be 3×5 = 15. Then the given fractions are 1/3 = 5/15, and 4/5 = 12/15. The numerators 5 and 12 differ by 7, so we can easily choose 5 fractions in that range:

  6/15 = 2/5

  7/15

  8/15

  9/15 = 3/5

  10/15 = 2/3

_____

<em>Alternate solutions</em>

There is no requirement for the fractions to be written any particular way or with any particular spacing. The limits in decimal are 1/3 = 0.3333...(repeating) and 4/5 = 0.8. We could choose the decimal fractions ...

  0.34, 0.40, 0.50, 0.60, 0.70

or

  0.41, 0.52, 0.63, 0.74, 0.79

7 0
3 years ago
3. In class today, 1/4 of the students wore shorts and
Mkey [24]

Answer:

A. \frac{1}{4} = \frac{3}{12}

Step-by-step explanation:

\frac{1}{4} of the students wore shorts.

\frac{3}{12} of the students wore jeans.

Converting the fractions of the students who wore shorts and jeans respectively;

\frac{1}{4} = 0.25

\frac{3}{12} = 0.25

This means that the ratio of students who wore shorts is the same as that of students who wore jeans.

i.e \frac{1}{4} = \frac{3}{12}

4 0
3 years ago
Read 2 more answers
5/8 - 3/10 <br> A. 13/40 <br> B. 1/20 <br> C. 1/4<br> D. 1/5
densk [106]

5/8 - 3/10

Find the common denominator:

Multiples of 8:  8, 16, 24, 32, 40 (8 x 5 = 40)

Multiples of 10: 10, 20, 30, 40  (10 x 4 = 40)


5/8 = 5*5 / 8*5 = 25/40

3/10 = 3*4 / 10 *4 = 12/40


Now you have 25/40 - 12/40

25 -12 = 13

Answer = 13/40


The answer is A.

7 0
2 years ago
Read 2 more answers
What is the y intercept of the line? X=24,36,48 and y= -8, 1, 10
goldenfox [79]

Answer:

y intercept = - 40

Step-by-step explanation:

x 24 36 48

y -8 1 10

y = ax + b

a is the gradient (or slope).

b = y intercept.

a = (48-36) / (10-1) = 12/9

Rewrite to solve for b, which means it starts with b = ...

b = y - 12/9 * x

Substitute one point ( 24 , -8 )

b = -8 - (12/9 * 24)

b = y intercept = - 40

4 0
3 years ago
A skate ramp is 4.2 meters long. It rises up 1.7 meters. What’s is the angle of elevation to the nearest tenth of a degree?
Kipish [7]
Θ
=
arcsin
(
.7
4.2
)
≈
10
∘
Explanation:
We view the ramp as a right triangle. The hypotenuse is 4.2 and the vertical side .7, which is opposite the angle
θ
we seek.
sin
θ
=
.7
4.2
=
1
6
I'm going to finish the problem but I'll note if we were actually building the ramp we don't need to know the angle; this sine is sufficient.
θ
=
arcsin
(
1
6
)
θ
≈
10
∘
which I think is a pretty steep ramp for a wheelchair.
There will be another inverse sine that is the supplementary angle, around
170
∘
, but we can rule that out as a value for a ramp wedge angle.
4 0
3 years ago
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