All categories

3 years ago

Another geometry problem!

Mathematics

2 answers:

Ahat [919]3 years ago

8 0

The triangle is isosceles with vertex angle = 116
So m < E = (180 - 116) / 2 = 32 degrees

andriy [413]3 years ago

8 0

Comment

<em>Fact One</em>
You are given 1 angle which is enclosed by 2 equal sides. That means you have an isosceles triangle. The angles opposite the equal sides are equal.

<em>Fact Two</em>
Every triangle has 180°

Step One
Set up the equation using fact one above.
2 equal angles + 116 = 180
2x + 116 = 180

Step Two
Solve the equation
2x + 116 = 180 Subtract 116 from both sides.
2x = 180 - 116
2x = 64 Divide by 2
x = 64/2
x = 32

Conclusion
Each of the equal angles = 32°

E = 32° <<<<< answer

You might be interested in

Consider x^2 + (b/a)x = (-c/a). Which variable cannot have a value of zero? Justify your answer.

GREYUIT [131]

The answer is C because if something is divided by zero, it is undefined.

5 0

3 years ago

a rhombus has an area of 60 square centimeters. if the length of one diagonal is 12 cm, find the length of the other

AlekseyPX

Answer:

10 cm

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = $\frac{1}{2}$ × d₁ × d₂ ( d₁ and d₂ are the diagonals )

Here A = 60, d₁ = 12, thus

60 = 0.5 × 12 × d₂ = 6 d₂ ( divide both sides by 6 )

d₂ = 10

The other diagonal is 10 cm

3 0

3 years ago

Please help me factor this!! Thanks!

Goryan [66]

We need to find two numbers that multiply to 24 (last coefficient) and add to 10 (middle coefficient). Through trial and error, the two values are 6 and 4

6 + 4 = 10
6*4 = 24

So we can break up the 10ab into 6ab+4ab and then use factor by grouping

a^2 + 10ab + 24b^2
a^2 + 6ab + 4ab + 24b^2
(a^2+6ab) + (4ab+24b^2)
a(a+6b) + 4b(a+6b)
(a+4b)(a+6b)

Therefore, the original expression factors completely to (a+4b)(a+6b)

5 0

3 years ago

Determine whether the triangles are similar by AA, SSS, SAS, or not similar

Anton [14]

Answer:

Step-by-step explanation:

If Δ JKL ~ Δ JHG , then

$\frac{LJ}{GJ}$ = $\frac{KJ}{HJ}$

$\frac{95}{68}$ ≠ $\frac{87}{72}$ ⇒ triangles are not similar

7 0

3 years ago

Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.

skelet666 [1.2K]

Answer:

$y=\dfrac {60} {x}$ or $xy=60$ (depending on your teacher's format preference)

Step-by-step explanation:

<h3><u>Proportionality background</u></h3>

Proportionality is sometimes called "variation". (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

Direct
Inverse.

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

$y=kx$ y is directly proportional to x
$y=kx^2$ y is directly proportional to x squared
$y=kx^3$ y is directly proportional to x cubed
$y=k\sqrt{x}}$ y is directly proportional to the square root of x
$y=\dfrac {k} {x}$ y is inversely proportional to x
$y=\dfrac {k} {x^2}$ y is inversely proportional to x squared

From these examples, we see that two things:

things that are <u>directly proportional</u> -- the thing is <u>multipli</u>ed to the constant of proportionality "k"
things that are <u>inversely proportional</u> -- the thing is <u>divide</u>d from the constant of proportionality "k".

<h3><u>Looking at our question</u></h3>

In our question, y is inversely proportional to x, so the equation we're looking at is the following $y=\dfrac {k} {x}$ .

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it: "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

<h3><u>Solving for k, and finding the general equation</u></h3>

General Inverse variation equation...

$y=\dfrac {k} {x}$

Substituting known values...

$(12)=\dfrac {k} {(5)}$

Multiplying both sides by 5...

$(12)*5= \left ( \dfrac {k} {5} \right ) *5$

Simplifying/arithmetic...

$60=k$

So, for our situation, k=60. So the inverse proportionality relationship equation for this situation is $y=\dfrac {60} {x}$ .

The way your question is phrased, they may prefer the form: $xy=60$

7 0

2 years ago