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katrin2010 [14]
3 years ago
6

3.

Mathematics
1 answer:
natima [27]3 years ago
7 0

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)

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djyliett [7]

Answer:

x= 6 ± √31

Step-by-step explanation:

x^2-12x=-5

x^2 -12x +36= -5 +36

(x -6)^2= 31

√(x -6)^2= ±√31

(x-6)= ±√31

x= 6 ± √31

3 0
2 years ago
van someone please help me with this i dont need an explaination i just need a. b. c. or d. please and thank you
Talja [164]

Answer:

option C

f(x)=-\sqrt{x+3}+8

Step-by-step explanation:

we have

f(x)=-2\sqrt{x-3}+8

using a graphing tool

see the attached figure N1

The range is the interval--------> (-∞,8]

y\leq 8

case A) f(x)=\sqrt{x-3}-8

using a graphing tool

The range is the interval--------> [-8,∞)

y\geq -8

case B) f(x)=\sqrt{x-3}+8

using a graphing tool

The range is the interval--------> [8,∞)

y\geq 8

case C) f(x)=-\sqrt{x+3}+8

using a graphing tool

The range is the interval--------> (-∞,8]

y\leq 8

case D) f(x)=-\sqrt{x-3}-8

using a graphing tool

The range is the interval--------> (-∞,-8]

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5 0
3 years ago
The length of a rectangle is 8cm and the height is 16cm find the answer of the above figures using this formular...
notsponge [240]
  • Length=8cm
  • Breadth=16cm(Height)

<h3>Perimeter:-</h3>

\\ \sf\longmapsto Perimeter=2(L+B)

\\ \sf\longmapsto Perimeter=2(16+8)

\\ \sf\longmapsto Perimeter=2(24)

\\ \sf\longmapsto Perimeter=48cm

Area:-

\\ \sf\longmapsto Area=Length\times Breadth

\\ \sf\longmapsto Area=8(16)

\\ \sf\longmapsto Area=128cm^2

3 0
3 years ago
-9(m+3) +14=-49 please show work
yKpoI14uk [10]

Answer:

m=4

Step-by-step explanation:

−9(m+3)+14=−49

Step 1: Simplify both sides of the equation.

−9(m+3)+14=−49

(−9)(m)+(−9)(3)+14=−49(Distribute)

−9m+−27+14=−49

(−9m)+(−27+14)=−49(Combine Like Terms)

−9m+−13=−49

−9m−13=−49

Step 2: Add 13 to both sides.

−9m−13+13=−49+13

−9m=−36

Step 3: Divide both sides by -9.

−9m

−9

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−36

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8 0
3 years ago
Quadrilateral A has side lengths 2,3,5 and 6. Quadrilateral B has side lengths 4,5, 8 and 10. Could one of the quadrilaterals be
Makovka662 [10]

Answer:

No

Step-by-step explanation:

Given

Quadrilateral A: 2,3,5 and 6

Quadrilateral B: 4,5, 8 and 10

Required

Determine if one is a scale of another

To do that, we have to divide the corresponding lengths to give ratio.

Considering Side of A = 2 and Side of B = 4

Ratio = \frac{B}{A}

Ratio = \frac{4}{2}

Ratio = 2

Considering Side of A = 3 and Side of B = 5

Ratio = \frac{B}{A}

Ratio = \frac{5}{3}

Ratio = 1.67

There's no need to check further, since the two ratios calculated so far do not have the same value;

<em>Hence, one quadrilateral is not a scale of the other</em>

7 0
3 years ago
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