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3 years ago

Four more than twice a number is 8

Mathematics

1 answer:

zzz [600]3 years ago

5 0

let x is the number

twice a number is 2x

Four more than twice a number: 2x + 4

Four more than twice a number is 8 :

2x +4 = 8

If solve for x then

2x + 4 = 8

subtract 4 to both sides

2x +4 - 4 = 8 -4

Simplify

2x = 4

Divide both sides by 2

2x/2 = 4/2

Simplify

x = 2

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Which is the correct label of the parallel lines? (4 points) Parallel lines a and b are shown. Points A and B lie on line a whil

ddd [48]

The same way you number

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2 years ago

The sum of two numbers is -6. The difference is 16. Find the two numbers.

Bess [88]

Answer:

$-5\:\mathrm{and}\: 11$

Step-by-step explanation:

We can write the following system of equations:

$\begin{cases}x+y=6\\x-y=16\\\end{cases}$

Adding both equations together, we isolate $x$ and get:

$2x=22,\: x=11$

Plugging $x=11$ in any of the equations, we can solve for $y$ :

$11+y=6,\: y=-5$

Verify that the solution pair $(11, -5)$ works $\checkmark$

Therefore, the two numbers are $\fbox{$-5\:\mathrm{and}\: 11$}$ .

7 0

3 years ago

If 40% of a number is 80 what is 25% of that number?

olga2289 [7]

Answer:

25% of 200 is 50

Step-by-step explanation

40% of a number is 80

.40 * n = 80

Divide each side by .4

.40 n/.4 = 80/.4

n = 200

The number is 200

Now lets find 25 percent of that number

.25 * 200 = 50

7 0

3 years ago

out of 45 times at bat, Raul got 19 hits.Find Rauls batting average as a decimal rounded tothe nearst thousandth.

kati45 [8]

19/45=0.422222222........
Therefore rounded to the nearest thousandth his batting average is 0.422

3 0

3 years ago

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