All categories

2 years ago

Consider isosceles ΔXYZ.

Mathematics

2 answers:

kompoz [17]2 years ago

8 0

The value of n : 3 . ( 9x3+12 = 39 ) so leg XY equals 39
( 15x3-6 = 39 ) so that makes leg XZ equal 39 as well.

julia-pushkina [17]2 years ago

5 0

1) An Isosceles triangle has three sides, in which two sides are of the same length and the third has a different length. It has two angles of the same value and a third angle with a different value, as well.

In the figure is shown that angles Y and Z are the same, then the sides of this angles must be of the same length. This means that:

XY=XZ

(9n+12)ft=(15n-6)ft

From this equation we have to find n:

9n-15n=-6-12

-6n=-18

$n=\frac{-18}{-6}$

n=3

2) The measure of the leg XY in ft

XY=(9n+12)ft

Substitute the value of n calculated in the first question:

XY=(9(3)+12)ft

XY=39 ft

3) The measure of the leg XZ in ft

XZ=(15n-6)ft

Substitute the value of n calculated in the first question:

XZ=(15(3)-6)ft

XZ=39ft

You might be interested in

Which term describes the seller's ability and desire to sell goods and services? A. supply B. demand C. equilibrium

Leya [2.2K]

Answer:

A. supply

Step-by-step explanation:

The term that best describes the seller's ability and desire to sell goods and services out of given options is supply.

Buyer's willingness to buy a certain good at a certain price is defined as demand by most economists.

where as the seller's willingness to provide a certain good or service at a certain price is defined as supply by most economists. Supply does not merely means amount of goods supplied rather, for economists supply is a relationship between set of assigned prices and the amount of goods assigned to be sold at those prices.

hence the term that best describes the seller's ability and desire to sell goods and services out of given options is supply !

8 0

2 years ago

PLEASE HELP ASAP Prove that x+a is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5

Brums [2.3K]

$P(x)=(x+a)^5 + (x+c)^5 + (a-c)^5$

If $x+a$ is a factor of $P(x)$ , then $-a$ is a root of $P(x)$ .

Therefore

$(-a+a)^5+(-a+c)^5+(a-c)^5=0\\\\0^5+(-1(a-c))^5+(a-c)^5=0\\\\(-1)^5(a-c)^5+(a-c)^5=0\\\\-(a-c)^5+(a-c)^5=0\\\\0=0$

6 0

2 years ago

The function f describes the value of a sculpture after t years. The function g describes the value of a painting by the same ar

Anna11 [10]

H(t) = f(t) - g(t)
= 500(1.2)^t - 380(1.15)^t
Taking out the greatest common factor, which is 20:
= 20[(25)(1.2)^t - (19)(1.15)^t]
This is the third choice.

Note that you cannot subtract the bases of the exponents, for example (1.2^t - 1.15^t) cannot be simplified into something like 0.05^t.

6 0

2 years ago

Read 2 more answers

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form? Y = 3 (x minus seven-halves) squared minus StartFraction 27

densk [106]

Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

$y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

Step-by-step explanation:

Vertex form of equation : $f (x) = a(x - h)^2 + k,$ where (h, k) is the vertex of the parabola.

$y=3(x-2)^2-(x-5)^2\\\\=3(x^2+4-4x)-(x^2+25-10x)\\\\=3x^2+12-12x-x^2-25+10x\\\\=2x^2-2x-13\\\\=2(x^2-x-\dfrac{13}{2})\\\\=2(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{13}{2})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{1+26}{4})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{27}{4})=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

Hence, the vertex form of the equation is $y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

8 0

2 years ago

Read 2 more answers

Paulina is remodeling her bathroom. the tile she has chosen are squares and trapezoids. the side length of each square inthe til

NemiM [27]

Check the picture below.

is not very specific above, but sounds like it's asking for an equation for the trapezoid only, mind you, there are square tiles too.

but let's do the trapezoid area then,

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-------------------------------\\\\$

$\bf A=\cfrac{h(a+b)}{2}\quad 
\begin{cases}
A=At\\
a=x\\
h=x\\
b=2x
\end{cases}\implies At=\cfrac{x(x+2x)}{2}
\\\\\\
At=\cfrac{x(3x)}{2}\implies At=\cfrac{3x^2}{2}\impliedby \textit{now, solving for \underline{x}}
\\\\\\
2At=3x^2\implies \cfrac{2At}{3}=x^2\implies \sqrt{\cfrac{2At}{3}}=x\implies \left( \frac{2At}{3} \right)^{\frac{1}{2}}=x$

8 0

2 years ago