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3 years ago

10. Error Analysis A student draws a triangle with a perimeter 36 cm. The

Mathematics

1 answer:

Tasya [4]3 years ago

4 0

Answer:

see the explanation

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

In this problem

If the perimeter of triangle is equal to 36 cm

The longest side can't be equal to 18 cm

The student is incorrect

Because if the longest side is equal to 18 cm, and the perimeter is equal to 36 cm, then the sum of the other two sides is equal to 18 cm

and

Applying the triangle inequality theorem

Let

c -----> the longest side

a and b the other two sides

we have that

if c=18 cm

a+b > c

a+b > 18 cm

therefore

If the longest side is 18 cm, the sum of the other two sides must be greater than 18 cm and the perimeter will be greater than 36 cm

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The function C(x) = 29x + 54.5 represents the cost (in dollars) of cable for x months, including $54.50 installation fee. How ma

Ratling [72]

Hey there!!

Given equation :

... c(x) = 29x + 54.5

In this equation $54.50 is installation fee and this would remain as a constant. ( This value wouldn't change ).

'x' is represented as the number of months.

The total cost or c(x) is given as $344.50

Getting this into equations :

... 344.50 = 29x + 54.5

Subtracting 54.5 on both sides :

... 29x = 290

Dividing by 29 on both sides :

... x = 10

Hence, the number of months is 10.

Hope my answer helps!!

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3 years ago

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2 years ago

A pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10 liters o

ladessa [460]

X = amount of the 18% solution

y = amount of the 40% solution

we know the 18% solution has only 18% of alcohol, the rest is maybe water or something, now, how many liters is 18%? well, 18% of anything is just (18/100) * anything, so, 18% of x is just (18/100) *x or 0.18x, and that's how many liters are there.

likewise, how many liters are there in the 40% solution? well, (40/100) * y, or 0.4y, that many.

we know the mixture has to yield 10 liters at 20% alcohol, how many liters of only alcohol is that? well, (20/100) * 10, or 2 liters.

$\bf \begin{array}{lccclll}
&\stackrel{liters}{amount}&\stackrel{alcohol~\%}{quantity}&\stackrel{liters}{alcohol}\\
&------&------&------\\
\textit{18\% solution}&x&0.18&0.18x\\
\textit{40\% solution}&y&0.40&0.4y\\
------&------&------&------\\
mixture&10&0.20&2
\end{array}$

$\bf \begin{cases}
x+y=10\implies \boxed{y}=10-x\\
0.18x+0.4y=2\\
----------\\
0.18x+0.4\left( \boxed{10-x} \right)=2
\end{cases}
\\\\\\
0.18x-0.4x+4=2\implies -0.22x=-2
\\\\\\
x=\cfrac{-2}{-0.22}\implies x=\cfrac{100}{11}\implies x=9\frac{1}{11}$

how much of the 40% solution? well y = 10 - x

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3 years ago

3x * -2y= -100 Solve for y and x.

Sedbober [7]

Answer:

x=50/3y

y=50/3x

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

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2 years ago

Please Help! Solve the equation for x.

SOVA2 [1]

Answer:

Step-by-step explanation:

Given

$\frac{1}{3}$ x - 8 = - 12 ( multiply through by 3 to clear the fraction )

x - 24 = - 36 ( add 24 to both sides )

x = - 12 → A

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3 years ago