Find the value of x needed to make the equation True. 3/4(20x-8)-3=54

3.

natima [27]

Answer:

See explanation

Step-by-step explanation:

Let x be the number of spade shovels, y -the number of flat shovels and z - the number of square showels sold that day.

The store keeps an inventory of 80 shovels, then

x+y+z=80

The store always buy twice as many spade shovels as square, so

x=2z

The total cost of all shovels is

16x+9.60y+12.80z=1,072

a) The system of three equations is

$\left\{\begin{array}{l}x+y+z=80\\ \\x=2z\\ \\16x+9.60y+12.80z=1,072\end{array}\right.$

b) In matrix form this is

$\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}80\\0\\1,072\end{array}\right)$

c) The determinant is

$\left\|\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right\|=0-32+9.60-0+19.20-12.80=-16$

d) Find three determinants:

$\left\|\begin{array}{ccc}80&1&1\\ 0&0&-2\\ 1,072&9.60&12.80\end{array}\right\|=0-2,144+0-0+1,536-0=-608$

$\left\|\begin{array}{ccc}1&80&1\\ 1&0&-2\\ 16&1,072&12.80\end{array}\right\|=0-2,560+1,072-0+2,144-1,024=-368$

$\left\|\begin{array}{ccc}1&1&80\\ 1&0&0\\ 16&9.60&1,072\end{array}\right\|=0+0+768-0-0-1,072=-304$

So,

$x=\dfrac{-608}{-16}=38\\ \\y=\dfrac{-368}{-16}=23\\ \\z=\dfrac{-304}{-16}=19$

e) If the store doubled all prices and inventory, then the new matrix is

$\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 32&19.20&25.60\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}160\\0\\2,144\end{array}\right)$

7 0

3 years ago

Im confused (pIcTuRe aTtAcHeD)

vodka [1.7K]

well, let's take a peek, "m" is drawn on the x-axis most likely and H(m) is drawn on the y-axis, making a straight line.

so at m = -5, namely 5 minutes before he was told to go home, the kite was 375 meters up.

then he was told to go home, when m = 0, and the kite was 300 meters up.

now, as far as the other numbers, m = 5, 5 minutes after he was told, the kite was 225 m up, then 10 minutes later, then 15 minutes later then 20 minutes later m = 20, the kite was at 0, namely on the ground, he already had rolled up all the kite string that he was coiling up, so he can pack it in his carriage bag and go home.

5 0

3 years ago

The function f(x)=2x−5 is a linear function. Let g(x) represent f(x) after a horizontal translation 3 units to the right.

trapecia [35]

G. (x)=2x-11

how u get the answer is:
$\frac{x}{y} \sqrt{x} x^{2} \left \{ {{y=2} \atop {x=2}} \right.$

4 0

3 years ago

Read 2 more answers

The radius of a cone is 10 units and the<br> height is 5 units. What is the volume?

kumpel [21]

Answer:

523.6

Step-by-step explanation:

V=πr^2(h/3)=π*10^2*(5/3)=523.59878

3 0

3 years ago

What is five and five eighths plus 11 and five eighths

mihalych1998 [28]

To add mixed numbers like you have here, you first have to convert them into fractions.

To do this, multiply the whole number part of the mixed number by the denominator, and add that value to the numerator.

So, 5 5/8 would become 45/8, because 5 x 8 = 40, and 40 + 5 = 45.
Likewise, 11 5/8 would become 93/8, because 11 x 8 = 88, and 88 + 5 = 93.
This gives us 45/8 + 93/8.

Now, to add the fractions. The two fractions have the same denominator already, so it is easy to add them. Simply add the numerators and keep the denominator the same.
The result of this is 143/8.

To simplify this to mixed number form, divide the numerator by the denominator. This results in 17.875. This means that 17 is your whole number part of the mixed number.
To find out how many eighths you'll have, multiply the 17 you just got by the denominator (8), and subtract the result from your large numerator. 17 x 8 = 136, and 143 - 136 = 7.

Your final result is 17 and 7/8.

4 0

3 years ago

Read 2 more answers