All categories

2 years ago

If DF=7x-3 and EG=5x+9, find the value of X

Mathematics

1 answer:

PilotLPTM [1.2K]2 years ago

3 0

Answer:

$x=6$

Step-by-step explanation:

Using the given measurements of the angles and the lengths of the sides, we can determine that this figure must be a rectangle.

Diagonals of a rectangle are always equivalent/congruent.

We can use this information to set up an equation:

$DF=EG\\7x-3=5x+9$

Add 3 to both sides:

$7x-3+3=5x+9+3\\7x=5x+12$

Subtract 5x from both sides:

$7x-5x=5x-5x+12\\2x=12$

Divide both sides by 2

$\frac{2x}{2}=\frac{12}{2}\\x=6$

You might be interested in

If the cube is divided into two equal parts by a plane parallel to the face defined by vertices 2, 3, 6, and 7, what will be the

notsponge [240]

The area of the cross-section is 169 sq. cm.

That is the correct answer to this problem

5 0

3 years ago

Solve 76+45+98+76-7=

Olin [163]

Answer:

288

Step-by-step explanation:

76+45=121

121+98=219

219+76=295

295-7=288

7 0

3 years ago

Read 2 more answers

the half-life of strontium-90 is approximately 29 years. how much of a 500 g sample of strontium-90 will remain after 58 years

Yuliya22 [10]

Answer: 125 g

Step-by-step explanation:

$A = P_o\cdot e^{kt}\\\\\text{First, use the given information to find k:}\\\\\bullet A=\dfrac{1}{2}P_o\\\\\bullet k = unknown\\\\\bullet t=29\text{ years}\\\\\dfrac{1}{2}P_o=P_o\cdot e^{k(29)}\\\\\\\dfrac{1}{2}=e^{k(29)}\qquad divided\ both\ sides\ by\ P_o\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=ln\bigg(e^{k(29)}\bigg)\qquad applied\ ln\ to\ both\ sides\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=29k\qquad simplified-ln\ and\ e\ cancel\ out\\\\\\\dfrac{ln\bigg(\dfrac{1}{2}\bigg)}{29}=k\qquad divided\ 29\ from\ both\ sides\\\\\\-0.0239=k$

$\text{Now, use the following in the equation to solve for A:}\\\\\bullet A=unknown\\\bullet P_o=500\\\bullet k=-0.0239\\\bullet t=58\text{ years}\\\\A=500\cdot e^{(-0.0239)(58)}\\\\.\quad=500\cdot e^{-1.386}\\\\.\quad=125$

8 0

3 years ago

Write an appropriate inverse variation equation if y = 9 when x = 3.

pav-90 [236]

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
y=9\\
x=3
\end{cases}\implies 9=k3\implies \cfrac{9}{3}=k\implies \boxed{3=k}
\\\\\\
thus\qquad y=3x$

3 0

3 years ago

Charlotte has 12 t-shirts one fourth of her t-shirts are green how many of Charlotte's t-shirts are green draw a quick picture t

Ivan

A fourth of 12 is 3 so if you draw a picture of 12 shirts and color 3 green then you get there answer

7 0

3 years ago