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3 years ago

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In a certain triangle the longest side is twice as long as the shortest side and the shortest side is 4 inches shorter than midd

le side. If the perimeter of the triangle is 52 inches how long is the longest side?

1 answer:

rodikova [14]3 years ago

5 0

Answer:

24 inches

Step-by-step explanation:

Let the longest side be x, the middle side be y and the shortest side be z

Rest is in the attached file

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The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge

Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

$5x+4y+5z=-1$

$x+y+2z=1$

$2x+y-z=-3$

Firs we find determinant of system of equations

Let a matrix A= $\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]$ and B= $\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]$

$\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}$

$\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0$

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply $R_1\rightarrow R_1-4R_2$ and $R_3\rightarrow R_3-2R_2$

$\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]$

Apply $R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]$

Apply $R_3\rightarrow R_3+R_2$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]$

Apply $R_3\rightarrow- \frac{1}{2}$ and $R_2\rightarrow R_2-R_3$

$\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Apply $R_1\rightarrow R_1-R_3$

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

4 0

3 years ago

Factor Completely: 10x + 15

tankabanditka [31]

Answer:

5(2x + 3)

Step-by-step explanation:

$10x + 15 \\ \\ = 2 \times 5 \times x + 3 \times 5 \\ ( take \: common \: factors \: out )\\ = 5(2 \times x + 3) \\ \\ = 5(2x + 3)$

3 0

2 years ago

Read 2 more answers

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a

belka [17]

Answer: third option 268.8

Explanation:

For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.

I have attached the figure for better understanding.

1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.

So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.

This is how you calculate the volume of the top portion:

1) The height of the cylinder is 54 mm - 18 mm = 36 mm

2) The formula for the volume of a cylinder is V = π (radius)^2 * height

radius = 8 mm
height = 36 mm

=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3

3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height

radius = 8 mm
height = 18 mm

V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3

4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:

Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3

5) To find the number of seconds <span>it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:

time in seconds = total volume of sand / rate of dripping

time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s

That is the answer: 268.8 s
</span>

4 0

3 years ago

Read 2 more answers

You have a total of 42 math and science problems for homework you have 10 more math problems and science problems how many probl

Kipish [7]

<span>X= math problems y= science problems x +y =42 x= y+10 Substitute: (y+10) + y =42 Combine y: 2y +10=42 Solve for y: y= 16 There are 16 science questions and 26 math questions</span>

3 0

3 years ago

Read 2 more answers

How much water must be evaporated from 130 gallons of a 9% acid solution to make a 12% acid solution?

Bad White [126]

Answer: 33 gallons

Step-by-step explanation:

We initially have 130 gallons of a $9\%$ acid solution and we need to change it to a $12\%$ acid solution, and for that it is necessary to evaporate $n$ gallons of water.

So, this situation can be mathemtically expressed as follows:

$(130)(9\%)=(130-n)(12\%)$

Then:

$(130)(\frac{9}{100})=(130-n)(1\frac{12}{100})$

Isolating $n$ :

$11.7=15.6-0.12 n$

$n=32.5 \approx 33$

Hence, we need to evaporate 33 gallons of water.

6 0

3 years ago