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3 years ago

What is the value of X?

Mathematics

1 answer:

Ugo [173]3 years ago

4 0

∆ABC similar to ∆CBD

DB/AC = CB/AB

$\frac{x}{7.5} = \frac{7.5}{x + 3} \\ x(x + 3) = {7.5}^{2} = { (\frac{15}{2}) }^{2} \\ {x}^{2} + 3x = \frac{225}{4} \\ 4 {x}^{2} + 12x = 225 \\ 4 {x}^{2} + 12x + 9 = 216 \\ {(2x + 3)}^{2} = 216 \\ 2x + 3 = 6 \sqrt{6} \\ x = - 1.5 + 3 \sqrt{6}$

approximately 6.1485

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A swimming pool is represented on a coordinate grid with the following vertices: Vertex A is at (−2,−3) . Vertex B is at (−2,

Semmy [17]

Answer:

26 yards.

Step-by-step explanation:

We can find the distance walked by Jared by finding the distances between each of the given vertex of swimming pool. We will use distance formula to find the distances between each vertex.

$\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(-2--2)^{2}+(-3-5)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(-2+2)^{2}+(-8)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(0)^{2}+(-8)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{64}=8$

Now let us find distance between vertex B and vertex C.

$\text{Distance between vertex B and vertex C}=\sqrt{(-2-3)^{2}+(5-5)^{2}}$

$\text{Distance between vertex B and vertex C}=\sqrt{(-5)^{2}+(0)^{2}}$

$\text{Distance between vertex B and vertex C}=\sqrt{25}=5$

Now let us find distance between vertex C and vertex D.

$\text{Distance between vertex C and vertex D}=\sqrt{(3-3)^{2}+(5--3)^{2}}$

$\text{Distance between vertex C and vertex D}=\sqrt{(0)^{2}+(5+3)^{2}}$

$\text{Distance between vertex C and vertex D}=\sqrt{64}=8$

Now let us find distance between vertex D and vertex A.

$\text{Distance between vertex D and vertex A}=\sqrt{(3--2)^{2}+(-3--3)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{(3+2)^{2}+(-3+3)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{(5)^{2}+(0)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{25}=5$

Now let us add all these distances to find the total distance walked by Jared.

$\text{Total distance walked by Jared}=8+5+8+5$

$\text{Total distance walked by Jared}=26$

Since we have been given that one unit on the grid equals 1 yard, therefore, Jared walked a distance equal to 26 yards.

3 0

2 years ago

The combined mass of two children is 75lbs. The first child is four times the mass of the second child. What are the masses of t

gayaneshka [121]

The second child is about 19lbsif you want to round it otherwise it's 18 something lbs, so the first child is about... 57.

3 0

2 years ago

Read 2 more answers

Evaluate −3w − 6p for w=2 and p = −7

kap26 [50]

-3w-6p when w=2 and p=-7

-3(2)-6(-7)

= -6 + 42

= 36

7 0

2 years ago

Read 2 more answers

Is fge and egc supplementary angles

morpeh [17]

Answer:

yes sry if i am wrong

5 0

2 years ago

A chemist wants to make 100 liters of a 44% acid solution. She has solutions that are 20% acid and 60% acid.

alexgriva [62]

the first solution is 20% acid, and say we'll be using "x" liters, so how many liters of just acid are in it? well 20% of "x" or namely 0.2x. Likewise for the 60% acid solution, if we had "y" liters of it, the amount of only acid in it is 0.6y.

$\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{liters of }}{amount}\\ \cline{2-4}&\\ \textit{1st solution}&x&0.20&0.2x\\ \textit{2nd solution}&y&0.60&0.6y\\ \cline{2-4}&\\ mixture&100&0.44&44 \end{array}~\hfill \begin{cases} x+y=100\\\\ 0.2x+0.6y=44 \end{cases}$

$x+y=100\implies y=100-x~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.2x+0.6(100-x)=44} \\\\\\ 0.2x+60-0.6x=44\implies -0.4x+60=44\implies -0.4x=-16 \\\\\\ x=\cfrac{-16}{-0.4}\implies \boxed{x=40}~\hfill \boxed{\stackrel{100-40}{y=60}}$

7 0

1 year ago