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3 years ago

What is the value of x? Show your work. (The JKL and MNP picture)

Mathematics

2 answers:

azamat3 years ago

4 0

Answer:

$x=7$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

Triangles JKL and MNP are similar by AA Similarity Theorem

Remember that

If two figures are similar then the ratio of its corresponding sides is proportional

$\frac{JK}{MN}=\frac{JL}{MP}$

substitute the given values

$\frac{25}{30}=\frac{20}{4x-4}$

solve for x

Simplify

$4x-4=\frac{30}{25}(20)$

$4x-4=24$

$4x=24+4$

$4x=28$

$x=7$

Trava [24]3 years ago

3 0

In this case the answer would be the last option

because it is shrunk by 2/3 on just the x side

D is the only one who has that first transformation

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oksian1 [2.3K]

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3 years ago

Write 4 feet to 15 inches as a ratio. Compare in inches. Write the ratio in lowest terms.

Alja [10]

1 ft = 12 inches....so 4 ft = (4 * 12) = 48 inches

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3 years ago

F(x) = x + 4 G(x) = x^2 + 4 Find (fog) (3)

Anika [276]

Answer: 17

Steps:

1. Plug in (3) into “x” of the g(x) equation:
g(3) = (3)^2 + 4
g(3) = 9 +4
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5 0

3 years ago

The hypotenuse of a right triangle is 7 feet long. One leg is 4 feet longer than the other. Find the lengths of the legs, Round

Andrews [41]

Answer:

Shorter leg = 2.5 ft.

Longer leg = 6.5 ft.

Step-by-step explanation:

a^2 + b^2 = c^2

Because the hypotenuse = 7 ft, a^2 + b^2 = 49

To represent the two legs, we can use x and x+4.

x^2 + (x+4)^2 = 49

Simplifying this equation using FOIL gives us 2x^2 + 8x - 33 = 0.

Then, using the quadratic formula, we find that x = 2.5.

Thus, the shorter leg is 2.5 ft. and, when 4 is added, the longer leg is 6.5 ft.

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2 years ago

EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 11z on the curve of intersection of the plane x − y + z =

Taya2010 [7]

Answer:

$\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}$

Maximum value of f=2.41

Step-by-step explanation:

Lagrange Multipliers

It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.

$\bigtriangledown f=\lambda \bigtriangledown g$

for some scalar $\lambda$ called the Lagrange multiplier.

For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is

$\bigtriangledown f=\lambda \bigtriangledown g+\mu \bigtriangledown h$

The gradient of f is

$\bigtriangledown f=$

Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in $x,y,z,\lambda,\mu$ .