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dsp73
3 years ago
7

One serving of Mike’s crackers has 150 calories and a mass of 30 grams. How many calories are in 6 grams of the crackers?

Mathematics
1 answer:
Elodia [21]3 years ago
3 0
\bf \begin{array}{ccll}
calories&grams\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
150&30\\
c&6
\end{array}\implies \cfrac{150}{c}=\cfrac{30}{6}\implies \cfrac{150\cdot 6}{30}=c
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<span>5-2x=15

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6 0
3 years ago
Find an equation of the plane orthogonal to the line
jolli1 [7]

The given line is orthogonal to the plane you want to find, so the tangent vector of this line can be used as the normal vector for the plane.

The tangent vector for the line is

d/d<em>t</em> (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩<em>t </em>) = ⟨7, -7, -6⟩

Then the plane that passes through the origin with this as its normal vector has equation

⟨<em>x</em>, <em>y</em>, <em>z</em>⟩ • ⟨7, -7, -6⟩ = 0

We want the plane to pass through the point (9, 6, 0), so we just translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,

(⟨<em>x</em>, <em>y</em>, <em>z</em>⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0

Simplifying this expression and writing it standard form gives

⟨<em>x</em> - 9, <em>y</em> - 6, <em>z</em>⟩ • ⟨7, -7, -6⟩ = 0

7 (<em>x</em> - 9) - 7 (<em>y</em> - 6) - 6<em>z</em> = 0

7<em>x</em> - 63 - 7<em>y</em> + 42 - 6<em>z</em> = 0

7<em>x</em> - 7<em>y</em> - 6<em>z</em> = 21

so that

<em>a</em> = 7, <em>b</em> = -7, <em>c</em> = -6, and <em>d</em> = 21

4 0
3 years ago
A trapezoid has a height of 8 cm and bases with lengths of 14 cm and 8 cm. Tina says the area of the trapezoid is 176 cm2.
Sonbull [250]

Answer:

Step-by-step explanation:

Let's do this properly:

                                 

Area of trapezoid =  average length times height.

Here,

Area = (1/2)(8 cm + 14 cm)(8 cm), or

         = (11 cm)(8 cm) = 88 cm^2

It appears that Tina forgot to divide the sum of 14 cm and 8 cm by 2.  Thus, her answer is twice as large as it should be.

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Answer:

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lora16 [44]

Answer:

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Step-by-step explanation:

if f(x)= -3-5 and g(x)= 4x-2, find (f-g)(x)=3^x+6x+2

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