1. A pair of shoes went on sale 40% off the original price of $78.00. What

The longer leg of a right triangle is 7 ft longer than the shorter leg. The hypotenuse is 9ft longer than the shorter leg. Find

julia-pushkina [17]

Answer:

8, 15 and 17 feet respectively

Step-by-step explanation:

Let the shorter leg=l feet

The longer leg of a right triangle is 7 ft longer than the shorter leg, therefore Length of the longer leg=(l+7) feet

The hypotenuse is 9ft longer than the shorter leg. Therefore Length of the hypotenuse=(l+9) feet

Using Pythagoras Theorem

$Hyp^2=Opp^2+Adj^2\\(l+9)^2=l^2+(l+7)^2\\(l+9)(l+9)=l^2+(l+7)(l+7)\\l^2+9l+9l+81=l^2+l^2+7l+7l+49\\l^2+18l+81=2l^2+14l+49$

This results into:

$2l^2-l^2+14l-18l-81+49=0$

$l^2-4l-32=0\\l^2-8l+4l-32=0\\l(l-8)+4(l-8)=0\\(l-8)(l+4)=0$

l-8=0 or l+4=0

l=8 or -4

Since length cannot be negative, The length l=8 feet

The sides of the rectangle are therefore: 8, 15 and 17 feet respectively

5 0

2 years ago

Maxine types 294 words in 7 minutes. How many words does Maxine type in 11 minutes? 352 words

WINSTONCH [101]

Answer:

462 words

Step-by-step explanation:

Maxine types :

294 words ⇒ 7 minutes

Let the known number of words be x.

So,

294 words ⇒ 7 minutes

x words ⇒ 11 minutes

Therefore,

294 ⇒ 7

x ⇒ 11

Now use cross multiplication and find the value of x.

7x = 294 × 11

7x = 3234

Now divide both sides by 7.

x = 462 words.

Hope this helps you :-)

Let me know if you have any other questions :-)

8 0

2 years ago

Passing through (1,9),slope=2

Natalka [10]

Passes through (1, 9) with a slope of 2.

Assuming that we want this in slope intercept form, which is y=mx+b (m=slope, b=y-intercept) then we need to find the y-intercept! :)

To find the y-intercept (or b!!) you simply need to plug everything into slope intercept form using our given points.

y = mx + b

Plug everything in.

9 = 2(1) + b

Simplify.

9 = 2 + b

Subtract 2 from both sides.

9 - 2 = b

b = 7

Therefore, our y-intercept is 7! :)

Now that we have both the y-intercept and the slope, we can finally plug this into a new equation, using slope intercept form.

y = mx + b

y = 2x + 7

~Hope I helped!~

5 0

3 years ago

Read 2 more answers

Evaluate 8(6+5)/2²+6(2)

klemol [59]

Answer:

34

Step-by-step explanation:

1. Add 6 and 5 and that multiplies with 8 which would be 88

2. Then divide by 4, leaving you with 22.

3. Add that with 6(2), 12, and that gives you 34

7 0

2 years ago

Read 2 more answers

PLEASE HELP I WILL GIVE A LOT OF POINTS!

vazorg [7]

9514 1404 393

Answer:

(2.27, 0.96)

Step-by-step explanation:

The orthocenter is the point of intersection of altitudes of the triangle. The equation for an altitude is the equation of a line through a vertex that is perpendicular to the opposite side.

For example, the line perpendicular to side AC can be found as ...

(∆x, ∆y) = C-A = (3, -1) -(-4, 2) = (7, -3)

∆x(x -h) +∆y(y -k) = 0 . . . . perpendicular through point (h, k)

For side AC, we want the point to be B(4, 5), so the equation is ...

7(x -4) -3(y -5) = 0

7x -3y -13 = 0

Similarly, the altitude to side AB can be written as ...

(∆x, ∆y) = B -A = (4, 5) -(-4, 2) = (8, 3)

8(x -3) +3(y +1) = 0

8x +3y -21 = 0

__

By the "cross multiplication method", the solution to these equations is ...

x = (-3(-21) -(3(-13))/(7(3) -8(-3)) = (63+39)/(21+24) = 102/45 = 2 4/15 ≈ 2.27

y = (-13(8) -(-21)(7))/45 = 43/45 ≈ 0.96

The orthocenter is near (2.27, 0.96).

__

A graphing application confirms this result.

_____

Additional information about the cross multiplication method

For the general form equations ...

ax +by +c = 0
dx +ey +g = 0

The "cross multiplication method" has you write the array ...

$\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}$

and form the "cross products" in groups of four coefficients:

D = ae -db, X = bg -ec, Y = cd -ga

Then the solution to the set of equations is ...

1/D = x/X = y/Y ⇒ x = X/D, y = Y/D

__

Additional note

Videos of this method show you writing the array as bcab/egde and using the final equation x/X=y/Y=1/D. The above gets the same result in a more straightforward manner.

3 0

2 years ago