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2 years ago

Randy is building a fence at the side of his warehouse. He has 120 m of fencing and plans to use the

Mathematics

1 answer:

skad [1K]2 years ago

8 0

Answer:

The width (side perpedicular to the wall of the werehouse): <u>x = 30 m</u>

The lenght (side parallel to the wall of the werehouse): <u>y = 60 m</u>

Step-by-step explanation:

x - the width of the fenced area

Randy has 120 m of fencing so for the lenght remain (120-2x) m of fencing:

y = 120 - 2x

Area of the fencing: A = x•y

A(x) = x•(120 - 2x)

A(x) = -2x² + 120x ← quadratic function

The maximum value of quadratic function occurs at: $x=-\frac b{2a}$

a = -2 b = 120

$x=-\frac b{2a}=-\frac{120}{2\cdot(-2)}=-\frac{120}{-4}=30$

y = 120 - 2•30 = 60

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Find the sum (3.2+4x)+(18.25+6x)=

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Answer: -2.145

Step-by-step explanation:

(3.2+4x)+(18.25+6x)=

Simplifying

(3.2 + 4x) + (18.25 + 6x) = 0

Remove parenthesis around (3.2 + 4x)

3.2 + 4x + (18.25 + 6x) = 0

Remove parenthesis around (18.25 + 6x)

3.2 + 4x + 18.25 + 6x = 0

Reorder the terms:

3.2 + 18.25 + 4x + 6x = 0

Combine like terms: 3.2 + 18.25 = 21.45

21.45 + 4x + 6x = 0

Combine like terms: 4x + 6x = 10x

21.45 + 10x = 0

Solving

21.45 + 10x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-21.45' to each side of the equation.

21.45 + -21.45 + 10x = 0 + -21.45

Combine like terms: 21.45 + -21.45 = 0

0 + 10x = 0 + -21.45

10x = 0 + -21.45

Combine like terms: 0 + -21.45 = -21.45

10x = -21.45

Divide each side by '10'.

x = -2.145

Simplifying

x = -2.145

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2 years ago

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A bag contains 100 marbles which are red, green, and blue. Suppose a student randomly selects a marble without looking, records

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Answer:

35 red marbles

Step-by-step explanation:

So we can put the different color marbles in a ratio. So 7:2:11. If we add all of those up we get 20. We do 100/20 to get 5. Each number in the ratio is equivalent to 5 marbles. Then we do 7*5 to get 35. We can check our work by doing, (7*5) + (2*5) + (11*5) = 100. And it does equal 100 so the answer is correct.

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Answer:

$\frac{7}{8}$

Step-by-step explanation:

Given: $\frac{1}{8}-(\frac{-3}{4} )$

To find: number which represents the expression

Solution:

Integers refers to natural numbers, 0 together with negative of rational numbers.

A rational number is the number of the form $\frac{p}{q}$ where p and q are integers and $q\neq 0$ .

$\frac{1}{8}-(\frac{-3}{4} )=\frac{1}{8}+\frac{3}{4}\\ =\frac{1+6}{8}\\ =\frac{7}{8}$

So, $\frac{7}{8}$ represents $\frac{1}{8}-(\frac{-3}{4} )$

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During geometry class, students are told that ΔTSR ≅ ΔUSV. Marcus states that ΔTSR is mapped to ΔUSV by performing a rotation ab

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Answer: Both students are correct.

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So, when Sam mapped $\triangle USV$ by the reflection of $\triangle TSR$ then the measurement of the $\triangle USV$ did not change. And, he also got the congruent triangle.

Thus, we can say that, Both Marcus and Sam are right.

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