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3 years ago

Michelle buys 13 bags of gravel for her fish aquarium. If each bag weighs 12 pounds,how many pounds of gravel did she buy?

Mathematics

2 answers:

dalvyx [7]3 years ago

4 0

13x12=156
156lbs of gravel.

yarga [219]3 years ago

3 0

13×12=156lbs of gravel

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An architect is designing square windows with an area of ( x 2 + 20x + 100) ft2 . The dimensions of the windows are of the form

umka21 [38]

A) The dimensions are (x+10) by (x+10).
B) The perimeter is given by 4x+40.
C) The perimeter when x is 4 is 56.

The quadratic can be factored by finding factors of c, the constant, that sum to b, the coefficient of x. Our c is 100 and our b is 20; we want factors of 100 that sum to 20. 10*10=100 and 10+10=20, so those are what we need. This gives us (x+10)(x+10 for the factored form.
Since the dimensions are all (x+10), and there are 4 sides, the perimeter is given by 4(x+10). Using the distributive property we have 4*x+4*10=4x+40.
To find the perimeter when x=4, substitute 4 into our perimeter expression:
4*4+40=16+40=56.

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4 years ago

At what point do these lines intersect? A -24x - 4y =-164 y=41 - 6x

SSSSS [86.1K]

Answer:

Infinite points

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Functions
Terms/Coefficients
Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

-24x - 4y = -164

y = 41 - 6x

Step 2: Solve for x

Substitute in y [1st Equation]: -24x - 4(41 - 6x) = -164
[Distributive Property] Distribute -4: -24x - 164 + 24x = -164
[Addition] Combine like terms: -164 = -164

Here we see that -164 does indeed equal -164.

∴ We have an infinite amount of solutions.

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Step-by-step explanation:

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Step-by-step explanation:

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2 years ago

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Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter

jolli1 [7]

Answer:

the answer is incomplete, below is the complete question

"Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 3ti + (1 - 4t)j + (1 + 2t)k r(t(s)) ="

answer

$r(t(s)) = \frac{3s}{\sqrt{29} } i + (1 -\frac{4s}{\sqrt{29} }t)j + (1 + \frac{2s}{\sqrt{29} })k$

Step-by-step explanation:

The step by step procedure is to first determine the differentiate the given vector function

r(t) = 3ti + (1 - 4t)j + (1 + 2t)k

$\frac{d(r(t) = 3ti + (1 - 4t)j + (1 + 2t)k)}{dt} \\r'(t)=3i-4j+2k\\$

since s(t) is the arc length for r(t), which is define as

$s(t)=\int\limits^t_0 {||r'(t)||} \, dt$

if we substitute the value of r'(t) we arrive at

$s(t)=\int\limits^t_0 {||r'(t)||} \, dt\\s(t)=\int\limits^t_0 {\sqrt{3^{2} +4^{2}+2^{2}} \, dt\\s(t)=\int\limits^t_ 0{\sqrt{29} } \, dx\\$

$s(t)=\int\limits^t_ 0{\sqrt{29} } \, dx\\\\s(t)=\sqrt{29} t\\hence \\t(s)=\frac{s}{\sqrt{29} }$

substituting the value of t in to the given vector equation we have

$r(t(s)) = \frac{3s}{\sqrt{29} } i + (1 -\frac{4s}{\sqrt{29} }t)j + (1 + \frac{2s}{\sqrt{29} })k$

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4 years ago