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2 years ago

6

A line passes through ( - 1, 1) and (3,9).

1 answer:

Ivan2 years ago

4 0

Answer:

y=2x+3

Step-by-step explanation:

The slope-intercept form of the equation of a line is y = mx + b,where m = slope.

Hope this helps...

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In rhombus MNPQ, diagonals MP and NQ intersect at point K. If m_MQP = 56', then which of the

Murrr4er [49]

the answer is 90 degrees

3 0

2 years ago

A box with a rectangular base and open top must have a volume of 128 f t 3 . The length of the base is twice the width of base.

noname [10]

Answer:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

Step-by-step explanation:

Given

$Volume = 128ft^3$

$L = 2W$

$Base\ Cost = \$9/ft^2$

$Sides\ Cost = \$6/ft^2$

Required

The dimension that minimizes the cost

The volume is:

$Volume = LWH$

This gives:

$128 = LWH$

Substitute $L = 2W$

$128 = 2W * WH$

$128 = 2W^2H$

Make H the subject

$H = \frac{128}{2W^2}$

$H = \frac{64}{W^2}$

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

$A = LW + 2(WH + LH)$

The cost is:

$Cost = 9 * LW + 6 * 2(WH + LH)$

$Cost = 9 * LW + 12(WH + LH)$

$Cost = 9 * LW + 12H(W + L)$

Substitute: $H = \frac{64}{W^2}$ and $L = 2W$

$Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)$

$Cost =18W^2 + \frac{768}{W^2}*3W$

$Cost =18W^2 + \frac{2304}{W}$

To minimize the cost, we differentiate

$C' =2*18W + -1 * 2304W^{-2}$

Then set to 0

$2*18W + -1 * 2304W^{-2} =0$

$36W - 2304W^{-2} =0$

Rewrite as:

$36W = 2304W^{-2}$

Divide both sides by W

$36 = 2304W^{-3}$

Rewrite as:

$36 = \frac{2304}{W^3}$

Solve for $W^3$

$W^3 = \frac{2304}{36}$

$W^3 = 64$

Take cube roots

$W = 4$

Recall that:

$L = 2W$

$L = 2 * 4$

$L = 8$

$H = \frac{64}{W^2}$

$H = \frac{64}{4^2}$

$H = \frac{64}{16}$

$H = 4$

Hence, the dimension that minimizes the cost is:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

8 0

2 years ago

PLEASE HELP!!! 30 POINTS!!!!

nirvana33 [79]

Answer:

no.3

Step-by-step explanation:

an = 2n + 10

7 0

1 year ago

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PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! <br><br> Simplify.

scZoUnD [109]

The answer is B, I attached a picture of the steps.

7 0

3 years ago

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What is the value of x in the product of powers below? 6^9 6^x=6^2 -11 -7 11 7

Elodia [21]

Answer:

x = - 7

Step-by-step explanation:

Using the rule of exponents

$a^{m}$ × $a^{n}$ = $a^{(m+n)}$

Given

$6^{9}$ × $6^{x}$ = 6², then

$6^{(9+x)}$ = 6²

Since the bases on both sides are equal then equate the exponents

9 + x = 2 ( subtract 9 from both sides )

x = - 7

8 0

3 years ago

Read 2 more answers