All categories

2 years ago

Five times the smallest of three consecutive odd integers is seven more than twice

Mathematics

1 answer:

Fantom [35]2 years ago

4 0

Answer:

5, 7, 9

Step-by-step explanation:

Using the information given we get:

$5x-7=2z$

$x+2=y\\y+2=z\\x+4=z$

$5x-7=2(x+4)\\5x-7=2x+8\\$

Add 7 to both sides

$5x=2x+15$

Subtract 2x from both sides

$3x=15$

Divide both sides by 3

$x=5$

Using these equations:

$x+2=y\\y+2=z\\x+4=z$

and

$x=5$

We get:

$x=5\\y=7\\z=9$

You might be interested in

Find the values of x and y.

Papessa [141]

Step-by-step explanation:

x=20

y=100

solution in image

6 0

2 years ago

Please answer asap!!!!!!!!!!!!!!!!!!!!!!!!!

Vilka [71]

Answer:

x=60

Step-by-step explanation:

right angle is 90 degrees +30 degrees equals 120 so 180-120 gives you 60 degrees

4 0

2 years ago

Read 2 more answers

Find the value of x in the triangle... Then classify the triangle as acute, right or obtuse

ddd [48]

Answer:

x = 44

right

Step-by-step explanation:

The sum of the angles in a triangle add to 180

90+ 46+x = 180

Combine like terms

136+x = 180

Subtract 136 from each side

136+x-136=180-136

x =44

Since we have a 90 degree angle it is a right triangle

4 0

3 years ago

8m+3n-4m+7n help please

Lilit [14]

$8m+3n-4m+7n =\\
4m+10n$

7 0

2 years ago

Read 2 more answers

g Given the system of equations: 15 c1 – 5 c2 – c3 = 2400 - 5 c1 + 18 c2 – 6 c3 = 3500 - 4 c1 - c2 + 12 c3 = 4000 (a) Calculate

denpristay [2]

Answer

(a)

$A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}$

(b)

$A^{-1} b = \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}$

Step-by-step explanation:

Remember that when you want to solve a problem like this, you express the equation as following

$Ax = b$

So, if you know the inverse of $A$ then

$x = A^{-1} b$

For this case

$A = \begin{pmatrix} 15 && 5 && -1 \\ -5 && 18 && -6 \\ -4 && -1 && 12 \end{pmatrix}$

Now for this case the inverse of A would be

$A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}$

Then when you multiply with the vector solution

$A^{-1} b = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix} * \begin{pmatrix} 2400 \\ 3500 \\ 4000 \end{pmatrix} = \frac{1}{3493} \begin{pmatrix} 249500 \\ 1197600 \\ 1347300 \end{pmatrix}\\\\\\= \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}$

So from that information you can conclude that the solution to the system of equations is x = 500/7 y = 2400/7 and z = 2700/7

7 0

2 years ago