What is 10 times 147

13. For what value of b would the following system of equations have an infinite number of solutions?

tiny-mole [99]

Answer:

b=2

Step-by-step explanation:

we have

9x+12y=21 -----> equation A

6x+8y=7b ----> equation B

we know that

If the system of equations have an infinite number of solutions then the equation A must be equal to the equation B

Multiply equation B by 1.5 both sides

1.5*[6x+8y[=7b*1.5

9x+12y=10.5b ----> equation C

Compare equation A and equation C

9x+12y=21 -----> equation A

9x+12y=10.5b ----> equation C

For the equations to be equal it must be fulfilled that

21=10.5b

solve for b

b=21/10.5

b=2

5 0

4 years ago

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

PLEASE ANSWER !! you went to Olive Garden with your family. The bill was $64.25. You left a 16% tip. How much money was your bil

irina [24]

Answer:

$74.53

Step-by-step explanation:

16%=0.16

0.16*64.25+64.25

=(0.16+1)*64.25

=$74.53

8 0

4 years ago

Pls help I need this and I don’t get it

Jobisdone [24]

Answer:

C.

Step-by-step explanation:

Hi there!

To find the answer to this, plug the number values in for n and then solve.

For the answer to be correct, the sum has to be less than 26.

Answers B and D both have numbers that would be equal to 26, so they aren’t right.

Answer A has numbers that would go over 26.

Every number in C can be added to 15 and the sum would be less than 26.

I hope this helps!

3 0

3 years ago

15/3 x 2/2= in fraction someone please help fast I’m going to get in trouble help help on fraction

Liono4ka [1.6K]

Answer

30/6

Step-by-step explanation:

you need to multiply 15 x 2 and 3 x 2 because 2 is your least common denominator and 2/2 is 1

sorry if that didn't make any sense

3 0

3 years ago