Whats the value of x?

HELP PLEASE!!! I need help with this question!

AlexFokin [52]

Answer:

$\large\boxed{PS=10\sqrt5}$

Step-by-step explanation:

ΔPQS, ΔRQP and ΔRPS are similar (AA). Therefore the sides are in proportion:

$\dfrac{QR}{RP}=\dfrac{RP}{RS}$

We have:

$QR=5,\ RS=20$

Substitute:

$\dfrac{5}{RP}=\dfrc{RP}{20}$ <em>cross multiply</em>

$RP^2=(5)(20)\\\\RP^2=100\to RP=\sqrt{100}\\\\RP=10$

Use the Pythagorean theorem:

$PS^2=PR^2+RS^2$

Substitute:

$PS^2=10^2+20^2\\\\PS^2=100+400\\\\PS^2=500\to PS=\sqrt{500}\\\\PS=\sqrt{100\cdot5}\\\\PS=\sqrt{100}\cdot\sqrt5\\\\PS=10\sqrt5$

6 0

3 years ago

Find the prime factorization of 30

sattari [20]

Let us start dividing 30 by small prime numbers in increasing order .

the smallest prime number we use is 2

Let's divide 30 by 2 quotient is 15

so we get : 30 = 2* 15

15 is not a prime number , it can be factorized further .

now we start dividing 15

2 can not divide 15 so we move to next prime number that is 3

can 3 divide 15? yes .

we get a quotient 5

so 30 is now : 2* 15 = 2* 3*5

now we have to work on 5 but 5 is a prime number so we stop here .

the prime factorization of 30 is : 2* 3* 5

Answer : 2 *3*5

5 0

3 years ago

Read 2 more answers

Avery bought 6.5 pounds of produce. If the produce was priced at $1.88 per pound, how much change did Avery receive if she paid

Katarina [22]

Answer:

the answer is $7.78

Step-by-step explanation:

You multiply 6.5 times 1.88. Then you subtract that answer from 20.

7 0

3 years ago

You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

7 0

1 year ago

Can somebody help me with this math question, all you have to do is answer the equation, then it's described, and then it draw i

Jlenok [28]

Answer:

x=-2

Step-by-step explanation:

add 18 to both sides, simplify, add 6x to both sides, simplify, divide both sides by -12.then simplify again... I hope that helps...

7 0

3 years ago

Read 2 more answers