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Goshia [24]
3 years ago
10

Find the value of a.

Mathematics
1 answer:
Elena-2011 [213]3 years ago
6 0

Answer: 14

Step-by-step explanation: The perimeter is all of the side added together. When finding the perimeter of a rectangle the opposing sides have the same value. So the equation would be 2(12) + 2(a) = 52. 12 x 2 is 24. 52- 24 is 28 and youre left with 28 = 2(a). You divide each side by 2 and get 14 = a

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Triangle ABC has vertices A(- 3, - 4), B(16, - 2) and C(13, - 10) . Show algebraically that ABC is a right angled triangle.​
8_murik_8 [283]

Given:

The vertices of a triangle ABC are A(-3,-4), B(16,-2) and C(13,-10).

To show:

That the triangle ABC is a right angled triangle.​

Solution:

Distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The vertices of a triangle ABC are A(-3,-4), B(16,-2) and C(13,-10).

Using the distance formula, we get

AB=\sqrt{(16-(-3))^2+(-2-(-4))^2}

AB=\sqrt{(19)^2+(2)^2}

AB=\sqrt{361+4}

AB=\sqrt{365}

Similarly,

BC=\sqrt{\left(13-16\right)^2+\left(-10-\left(-2\right)\right)^2}

BC=\sqrt{73}

And,

AC=\sqrt{\left(13-\left(-3\right)\right)^2+\left(-10-\left(-4\right)\right)^2}

AC=\sqrt{292}

Now, add the square of two smaller sides.

BC^2+AC^2=(\sqrt{73})^2+(\sqrt{292})^2

BC^2+AC^2=73+292

BC^2+AC^2=365

BC^2+AC^2=(AB)^2

Since the sum of the square of two smaller sides is equal to the square of the largest side, therefore the given triangle is a right angle triangle by using Pythagoras theorem.

Hence proved.

7 0
3 years ago
A- CE=CD <br> B- CE = CA <br> C- BF=DF <br> D- DF=EF<br><br> please help!!
Oksana_A [137]

The perpendicular bisector theorem gives the statements that ensures

that \overleftrightarrow{FG} and \overleftrightarrow{AB} are perpendicular.

The two statements if true that guarantee  \overleftrightarrow{FG} is perpendicular to line \overleftrightarrow{AB} are;

  • \overline{CE} = \overline{CD}
  • \overline{DF} = \overline{EF}

Reasons:

The given diagram is the construction of the line \mathbf{\overleftrightarrow{FG}} perpendicular to line \mathbf{\overleftrightarrow{AB}}.

Required:

The two statements that guarantee that  \overleftrightarrow{FG} is perpendicular to line \overleftrightarrow{AB}.

Solution:

From the point <em>C</em> arcs <em>E</em> and <em>D</em> are drawn to cross line \overleftrightarrow{AB}, therefore;

\overline{CE} = \mathbf{\overline{CD}} arcs drawn from the same radius.

\overleftrightarrow{FG} is perpendicular to line \overleftrightarrow{AB}, given.

Therefore;

\overline{DF} = \overline{EF}  by perpendicular bisector theorem.

Learn more about the perpendicular bisector theorem here:

brainly.com/question/11357763

7 0
3 years ago
Subtract. 82.6 - 27.9​
Tamiku [17]

Answer:

the answer is 54.7

Step-by-step explanation:

82.6 - 27.9 = 54 7

5 0
3 years ago
What is the equation of line d and c? What is the slope of line d and line c?​
amm1812

Answer:

Step-by-step explanation:

I understand why this was kind tough

the slope of line d is infinite  and the slope of line c is zero

so line c 's  equation looks like  y = 3  ... it's kinda  confusing but  the line is always 3  so you could pick any x value and y = 3 still.  the equation y=3 doesn't rely on x at all to answer it.    But x is part of the "frame work" that is implied.    

line d  is  x = 3   , again , y is part of the "frame work" and implied that y doesn't matter in this equations, you always have x = 3 .. or a vertical line , btw. line d does NOT pass the vertical line test , and therefore isn't a function,  so the question is wrong, that d will have an equation,  b/c there is an implication that d is a function when you say "what is the equation to line d" that is must be a function. But in this case it's not.   hm :/  food for thought

5 0
3 years ago
There are 40 marbles in a bag if 14 if the marbles are red what percent of the marbles in the bag are red
Neporo4naja [7]
\frac{14}{40} \times 100\%=\frac{7 \times 2}{20 \times 2} \times 100\%=\frac{7}{20} \times 100\%=7 \times \frac{100}{20} \%=7 \times 5\%=35\%

35% of the marbles are red.
4 0
3 years ago
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