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jarptica [38.1K]
2 years ago
5

The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 90 cm

Mathematics
1 answer:
svet-max [94.6K]2 years ago
7 0
The sides of the triangle are 3x, 4x and 5x

3x + 4x + 5x = 90
12x = 90
x = 90/12
x = 7.5

first side = 3x = 3 * 7.5 = 22.5 cm
second side = 4x = 4 * 7.5 = 30 cm
third side = 5x = 5*7.5 = 37.5 cm
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On your math quiz, you earn 5 points for each question that you answer correctly. In the equation below, x represents the number
belka [17]

Answer:

Dependent variable: y because you get the points by doing the quiz.

Independent variable: x because you don’t know how many questions you answered correctly.

Total points you score: Unknown until you know how many you got right also the same as y.

Number of questions you answer correctly: Unknown until you get your paper back, also the same as x.

7 0
3 years ago
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The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let x represent t
Galina-37 [17]

Answer:

x = 1, y = 60

Step-by-step explanation:

Value of new-releases (x) = $20 each

Value of classic (y) = $8 each

Total budget = $500

Equation : 20x + 8y = 500

The librarian wants to purchase maximum DVDs. She can get more DVDs of classic movies for $8 as they are less costly.

Lets assume the librarian buys at least one new-release DVD.

x=1

20x + 8y = 500

8y + 20(1) = 500

y = 60

<em>Therefore, in a budget of $500, the librarian can purchase 60 classic movies and 1 new-release.</em>

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8 0
3 years ago
Drag the expressions into the boxes to correctly complete the table.
lora16 [44]

Answer:

SUMMARY:

x^4+\frac{5}{x^3}-\sqrt{x}+8                               →    Not a Polynomial

-x^5+7x-\frac{1}{2}x^2+9                           →    A Polynomial

x^4+x^3\sqrt{7}+2x^2-\frac{\sqrt{3}}{2}x+\pi              →    A Polynomial

\left|x\right|^2+4\sqrt{x}-2                                   →    Not a Polynomial

x^3-4x-3                                        →    A Polynomial

\frac{4}{x^2-4x+3}                                              →    Not a Polynomial

Step-by-step explanation:

The algebraic expressions are said to be the polynomials in one variable which consist of terms in the form ax^n.

Here:

n = non-negative integer

a = is a real number (also the the coefficient of the term).

Lets check whether the Algebraic Expression are polynomials or not.

Given the expression

x^4+\frac{5}{x^3}-\sqrt{x}+8

If an algebraic expression contains a radical in it then it isn’t a polynomial. In the given algebraic expression contains \sqrt{x}, so it is not a polynomial.

Also it contains the term \frac{5}{x^3} which can be written as 5x^{-3}, meaning this algebraic expression really has a negative exponent in it which is not allowed. Therefore, the expression x^4+\frac{5}{x^3}-\sqrt{x}+8 is not a polynomial.

Given the expression

-x^5+7x-\frac{1}{2}x^2+9

This algebraic expression is a polynomial. The degree of a polynomial in one variable is considered to be the largest power in the polynomial. Therefore, the algebraic expression is a polynomial is a polynomial with degree 5.

Given the expression

x^4+x^3\sqrt{7}+2x^2-\frac{\sqrt{3}}{2}x+\pi

in a polynomial with a degree 4. Notice, the coefficient of the term can be in radical. No issue!

Given the expression

\left|x\right|^2+4\sqrt{x}-2

is not a polynomial because algebraic expression contains a radical in it.

Given the expression

x^3-4x-3

a polynomial with a degree 3. As it does not violate any condition as mentioned above.

Given the expression

\frac{4}{x^2-4x+3}

\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}

Therefore, is not a polynomial because algebraic expression really has a negative exponent in it which is not allowed.

SUMMARY:

x^4+\frac{5}{x^3}-\sqrt{x}+8                               →    Not a Polynomial

-x^5+7x-\frac{1}{2}x^2+9                           →    A Polynomial

x^4+x^3\sqrt{7}+2x^2-\frac{\sqrt{3}}{2}x+\pi              →    A Polynomial

\left|x\right|^2+4\sqrt{x}-2                                   →    Not a Polynomial

x^3-4x-3                                        →    A Polynomial

\frac{4}{x^2-4x+3}                                              →    Not a Polynomial

3 0
3 years ago
A cube has a volume of 64 cubic units. What is its surface area
Alona [7]
The volume of a cube is length x width x depth. In a cube all would be equal therefore. 

<span>x^3= 64 </span>
<span>x =4 </span>
<span>The area in square feet of one side would then be length x width </span>

<span>There are 6 sides so the surface area of the cube would be </span>

<span>(4)(4)(6) = 96 square feet</span>
7 0
3 years ago
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Overview Park has a picnic area and a playground, as shown in the diagram below. What is the area of the playground, in square f
laiz [17]

Answer:

Hi,

Step-by-step explanation:

The playground 's area is the difference of 2 squares:

20²-10²=(20+10)*(20-10)=30*10=300 (ft²)

7 0
1 year ago
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