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3 years ago

1. y=3x+6 2. y=-2x+4 3. y=1/2x-6 4. y=2/3x 5. y=-4x+1/8

Mathematics

1 answer:

bekas [8.4K]3 years ago

3 0

Answer:

Here u go bro. You have to just replace y and x with zero and then draw the I think structure say say:')

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If 75% of a number is 108, what is the number? A. 32 B. 81 C. 113 D. 144

Misha Larkins [42]

108 x 100/75 = 108 x 1.25 = 144
108 is 75% of 144.
Hope this helps :)

5 0

3 years ago

What is the area of a square rug that measures 6 feet on a side? 3 square feet 24 square feet 12 square feet 36 square feet

QveST [7]

Well we know the area of a square is l*w, or s^2. So we can use s^2 where s=6 in your case. Now 6^2 is 6*6, which is 36.

So the area of a square rug that measures 6 feet is 36 feet

Answer= 36 feet

4 0

3 years ago

Read 2 more answers

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d

eduard

The Lagrangian is

$L(x_1,\ldots,x_n,\lambda_1,\ldots,\lambda_n)=x_1+\cdots+x_n+\lambda_1({x_1}^2+\cdots+{x_n}^2)+\cdots+\lambda_n({x_1}^2+\cdots+{x_n}^2)$

with partial derivatives (set equal to 0)

$\dfrac{\partial L}{\partial x_i}=1+2x_i(\lambda_1+\cdots+\lambda_n)=0$

$\dfrac{\partial L}{\partial\lambda_i}={x_1}^2+\cdots+{x_n}^2-36=0$

for each $1\le i\le n$ .

Let $\Lambda$ be the sum of all the multipliers $\lambda_i$ ,

$\Lambda=\displaystyle\sum_{k=1}^n\lambda_k=\lambda_1+\cdots+\lambda_n$

We notice that

$x_i\dfrac{\partial L}{\partial x_i}=x_i+2{x_i}^2\Lambda=0$

so that

$\displaystyle\sum_{i=1}^nx_i\dfrac{\partial L}{\partial x_i}=\sum_{i=1}^nx_i+2\Lambda\sum_{i=1}^n{x_i}^2=0$

We know that $\sum\limits_{i=1}^n{x_i}^2=36$ , so

$\displaystyle\sum_{i=1}^nx_i+2\Lambda\sum_{i=1}^n{x_i}^2=0\implies\sum_{i=1}^nx_i=-72\Lambda$

Solving the first $n$ equations for $x_i$ gives

$1+2\Lambda x_i=0\implies x_i=-\dfrac1{2\Lambda}$

and in particular

$\displaystyle\sum_{i=1}^nx_i=-\dfrac n{2\Lambda}$

It follows that

$-\dfrac n{2\Lambda}+72\Lambda=0\implies\Lambda^2=\dfrac n{144}\implies\Lambda=\pm\dfrac{\sqrt n}{12}$

which gives us

$x_i=-\dfrac1{2\left(\pm\frac{\sqrt n}{12}\right)}=\pm\dfrac6{\sqrt n}$

That is, we've found two critical points,

$\pm\left(\dfrac6{\sqrt n},\ldots,\dfrac6{\sqrt n}\right)$

At the critical point with positive signs, $f(x_1,\ldots,x_n)$ attains a maximum value of

$\displaystyle\sum_{i=1}^nx_i=\dfrac{6n}{\sqrt n}=6\sqrt n$

and at the other, a minimum value of

$\displaystyle\sum_{i=1}^nx_i=-\dfrac{6n}{\sqrt n}=-6\sqrt n$

4 0

4 years ago

What is m∠BAC.<br><br> ............

gizmo_the_mogwai [7]

Answer:

37 degrees

Step-by-step explanation:

1. m∠CBA = 71+45 = 116 degrees

2. m∠CBA = m∠CDA because of the quadrilateral property of opposite sides.

3. m∠CBA + m∠CDA = 2*116 = 232.

4. Total angle measure of a quadrilateral is 360 degrees, so m∠BAD + m∠BCD = 360-232 = 128 degrees.

5. m∠BAD = m∠BCD = 128/2 = 64 degrees

6. m∠BAC = m∠BAD - m∠CAD = 64 - 27 = 37 degrees

8 0

3 years ago

Write the equations bellow in slope-intercept form. Determine if the lines are parallel, perpendicular, or neither

dexar [7]

A parallel is the correct answer

6 0

3 years ago

1. y=3x+6 2. y=-2x+4 3. y=1/2x-6 4. y=2/3x 5. y=-4x+1/8​

1. y=3x+6 2. y=-2x+4 3. y=1/2x-6 4. y=2/3x 5. y=-4x+1/8