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Pepsi [2]
3 years ago
13

Prove that the angles at the base of an isosceles triangle are acute

Mathematics
1 answer:
garik1379 [7]3 years ago
7 0
1. Since it is an isosceles triangle, we know that the two length sides have to be the same. Therefore, the angles across from the sides are the same. They cannot be 90 degrees or above because 90+90+0 would mean we would have all the interior angles at 180 but the thing is the third angle cannot be zero. Therefore, the other two angles cannot be 90 or more. They must be acute.



Also, if it had two right angles (90 degrees) or more, it could not close to be a triangle.


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GuDViN [60]

Answer:

(-2, 11) and (2, 3)

Step-by-step explanation:

<u>Given system of equations:</u>

1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3

2) f(x) = -2x + 7 ⇒ y = -2x + 7

Solve Using the Substitution Method:

<u>Step 1:</u> Substitute the the first equation into the second.

⇒ x² - 2x + 3 = -2x + 7

<u>Step 2:</u> Solve for x.

x² - 2x + 3 = -2x + 7 [ Add 2x to both sides. ]

x² - 2x + 2x + 3 = -2x + 2x + 7

⇒ x² + 3 = 7 [ Subtract 3 from both sides. ]

x² + 3 - 3 = 7 - 3

⇒ x² = 4 [ Take the square root of both sides. ]

√x² = √4

x = ± 2

⇒ x = -2, x = 2

<u>Step 3:</u> Solve for y.

<em>Substitute the found x-values into one of the given equations.</em>

y = -2x + 7 ⇒ y = -2(-2) + 7 ⇒ y = 4 + 7 ⇒ y = 11

y = -2x + 7 ⇒ y = -2(2) + 7 ⇒ y = -4 + 7 ⇒ y = 3

The solutions to the system of equations are: (-2, 11) and (2, 3).

Learn more about system of equations here:

brainly.com/question/26094713

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3 years ago
Jamal is making two paintings using canvases that are similar rectangles. The length of the smaller canvas is 3 ft and the width
Alex787 [66]
Let's start with what we know:

Smaller canvas:
Length (L_{1}) = 3ft
Width (W_{1}) = 5ft

Larger canvas:
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Width (W_{2}) = 10ft

Since these are similar rectangles, we can cross-multiply to calculate the missing length. Here's that formula:

\frac{ L_{1} }{ L_{2} } =  \frac{ W_{1} }{ W_{2} }
So let's plug it all in from above:

\frac{ 3 }{ L_{2} } = \frac{ 5 }{ 10 }
Now we cross multiply by multiplying the top-left by the bottom-right and vice versa:

(3)(10) = (5)(L_{2})
30 = 5L_{2}
Now divide each side by 5 to isolate L_{2}

\frac{30}{5} =  \frac{ 5L_{2}}{5}
The 5s on the right cancel out, leaving us with:

6 =  L_{2}

So the length of the larger canvas is 6 ft
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3 years ago
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