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3 years ago

Help me answer please.

Mathematics

1 answer:

kari74 [83]3 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

(a)

For the graph to display direct proportion it must pass through the origin.

The graph shown does not pass through the origin thus does not represent direct proportion.

(b)

Given that q is directly proportional to r then the equation relating them is

q = kr ← k is the constant of proportion

To find k use the condition q = 76 when r = 20, thus

76 = 20k ( divide both sides by 20 )

3.8 = k

q = 3.8r ← equation of proportion

When r = 45, then

q = 3.8 × 45 = 171

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A number y multiplied by —3 is less than

Aliun [14]

Answer:

-3y < -2/5

Step-by-step explanation:

Multiplied means times

-3y

is less than means <

-3y < -2/5

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3 years ago

David made a class banner out of a large rectangular piece of paper. He

spin [16.1K]

Given:

A triangular piece is cut out of a rectangular piece of paper to make the class banner.

To find:

The area of the class banner.

Solution:

The rectangular piece of paper is 14 inches long and $5+3=8$ inches wide.

From the given diagram, the triangle has a base length of the same 8 inches and has a height of $14-11=3$ inches long.

To determine the area of the banner, we subtract the area of the triangle from the area of the rectangle.

The area of a triangle $= \frac{1}{2} (b)(h).$

The area of the triangle $= \frac{1}{2} (8)(3) = 12$ square inches.

The area of a rectangle $= (l)(w).$

The area of the rectangle $= (14)(8)= 112$ square inches.

The area of the class banner $= 112-12=100$ square inches.

So the banner has an area of 100 square inches which is the first option.

7 0

3 years ago

Question 3 of 13 Which represents the explicit formula for the arithmetic sequence a n = 15 + 5 ( n − 1 ) a n = 15 + 5 n - 1 in

tatyana61 [14]

Answer:

$\textbf{Option C: \mathmode{\mathit{f(n) = 5n + 10}}}\\$

Step-by-step explanation:

$\textrm{There are two simple ways to solve the equation:}\\{\underline{\textbf{Method I:}}\hspace{3mm} \textup{\textrm{ Substitute \mathmode{n = 1} in the equation{\mathit{a} = 15 + 5(n - 1)}}}}\\\textup{\textrm{i.e., \mathrm{a = 15 + 5(0) = 15}}}\\\\$

$\textup{\textrm{In the options, again substitute \mathbf{n = 1}.}}\\\textup{\textrm{We can easily see that only Option \mathbf{C} satisfies the equation and renders 15. }}\\\textup{\textrm{Now for \textbf{\underline{Method II:}}\textup{\textrm{Simplify the given equation into \mathit{a = 15 + 5n - 5}}}}}\\\implies \textup{\textrm{a = 5n + 10}}\\$