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vovikov84 [41]
3 years ago
5

One leg of a right triangle is 7 inches longer than the smaller leg and the hypotenuse is 8 inches longer than the smaller leg.

Find the lengths ofl the side
of the triangle
Mathematics
1 answer:
Makovka662 [10]3 years ago
3 0
Smaller leg = x
longer leg = y
hypotenuse = z

y=x+7
z=x+8

due to
{z}^{2}  =  {x}^{2}  +  {y}^{2}  \\ (x + 8) ^{2}  =  {x}^{2}  + (x + 7) ^{2}  \\  {x}^{2}  + 16x + 64 =  {x}^{2}  +  {x}^{2}  + 14x + 49 \\  {x}^{2}  + 16x + 64 = 2 {x}^{2}  + 14x + 49 \\  {x}^{2}  - 2 {x}^{2}  + 16x - 14x + 64 - 49 = 0 \\  -  {x}^{2}  + 2x + 15 = 0 \\  {x}^{2}  - 2x - 15 = 0 \:  \: (multiplied \: by \:  - 1) \\ (x - 5)(x + 3) = 0 \\ then \:  \: x = 5 \:  \: or \:  \: x =  - 3
but x cannot be -3
so smaller leg is 5 inches

then longer leg = 5+7 = 12 inches
and hypotenuse = 5+8 = 13 inches
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Toni drives her car 99 mi on the highway on 3 gal of gas. At this rate how many miles can she drive on 11 gal of gas?
Helen [10]

Answer:

333.67 miles

Step-by-step explanation:

She drives her car 91 mi on 3 gal of gas

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How many miles can she drive on 11 gal of gas .

Let the mile she can drive by 11 gal of gas be A

At the same rate ,

91 mi = 3 gall

A mi = 11 gal

Cross multiply

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At the same rate she’ll drive 333.67 miles on 11 gal of gas

4 0
2 years ago
What is the slope-intercept form of the equation of the line perpendicular to y = -x + 10 and passing throught the point (-2,7)?
notka56 [123]

Answer:

The slope-intercept form equation of the line perpendicular to y =  -\frac{1}{2} x + 10 and passes through point (-2, 7) is y = 2x + 11 ⇒ Not in the choices

Step-by-step explanation:

The slope-intercept form of the linear equation is y = m x + b, where

  • m is the slope
  • b is the y-intercept

The product of the slopes of the perpendicular lines is -1, if the slope of one is m, then the slope of the other is -\frac{1}{m}

  • To find the slope of the perpendicular line to a given line reciprocal the slope of the given line and change its sign

∵ The equation of the given line is y = -\frac{1}{2} x + 10

→ Compare it with the form of the equation above

∴ m =  -\frac{1}{2}

→ Reciprocal it and change its sign to get the slope of the ⊥ line

∴ m⊥ = 2

→ Substitute in the form of the equation above

∴ y = 2x + b

→ To find b substitute x and y in the equation by the coordinates of

   a point on the line

∵ The line passes through the point (-2, 7)

∴ x = -2 and y = 7

∵ 7 = 2(-2) + b

∴ 7 = -4 + b

→ Add 4 to both sides to find b

∵ 7 + 4 = -4 + 4 + b

∴ 11 = b

→ Substitute it in the equation

∴ y = 2x + 11

The slope-intercept form equation of the line perpendicular to y =  -\frac{1}{2} x + 10 and passes through point (-2, 7) is y = 2x + 11

<u><em>Note:</em></u> The answer is not in the choices

6 0
2 years ago
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