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3 years ago

Two times the greater of consecutive integers is 9 less than three times the lesser integer. What are the integers?

Mathematics

1 answer:

BigorU [14]3 years ago

6 0

Answer:

The integers are 11 and 12.

Step-by-step explanation:

Let x be the greater integer, then the lesser is x - 1, so:

2x = 3(x -1) - 9 Distribute the 3:

2x = 3x - 3 - 9 Subtract 3x from both sides:

-x = -3 - 9

-x = -12

x = 12.

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Please help me quick with it

n200080 [17]

Answer:

the answer is C

Step-by-step explanation:

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3 years ago

Read 2 more answers

(1 point) find the equation of the sphere centered at (−9,4,1)(−9,4,1) with radius 4. normalize your equations so that the coeff

CaHeK987 [17]

The equation of a sphere centered at (h, j, k) with radius r is

... (x -h)² +(y -j)² +(z -k)² = r²

Your sphere has center (-9, 4, 1) and radius 4, so its equation is

... (x +9)² +(y -4)² +(z -1)² = 16

This can be written in general form as

... x² + y² + z² +18x -8y -2z +82 = 0

5 0

3 years ago

A rectangular price tag has a perimeter of 28 centimeters. Its area is 40 square centimeters.

kirill [66]

Answer:

10 x 4

Step-by-step explanation:

what factors are there for 40?

1, 2, 5, 8, 10, 20, 40

A rectangle has 2 equal long sides and 2 equal short sides. The area is the short times the long.

10 plus 10 and 4 plus 4 equals 28. 4 x 10 equals 40.

5 0

3 years ago

Keiko the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the

soldier1979 [14.2K]

Hey!

Hope this helps....

~~~~~~~~~~~~~~~~~~~~~~~~~

Given Information:

No client can do both Plans

On Wednesday: 3 clients did Plan A, and 2 clients did Plan B

On Thursday: 5 clients did Plan A, and 6 clients did Plan B

Keiko was training for a total of 6 hours on Wednesday, and training for a total of 12 hours on Thursday

------------------------------

We'll let t stand for length of time

Wednesday:

3t + 2t = 6

5t = 6

t = 1.2 hours > translates to 1 hour, and 12 minutes

On Wednesday, she was with her clients individually for 1 hour and 12 minutes

Thursday:

5t + 6t = 12

11t = 12

t ~ 1.1 hours > translates to about 1 hour and 6 minutes

On Thursday, she was with her clients individually for about 1 hour and 6 minutes

-----------------------

We'll let A stand for total length of time for Plan A, and B stand for total length of time for Plan B

We'll let W stand for Wednesday, and T stand for Thursday...

We'll let z stand for total amount of clients for that plan...

~~~~

We know, for Plan A, on Wednesday there were 3 clients, and Thursday there were 5 clients

We also know for Plan B, on Wednesday there were 2 clients, and Thursday there were 6 clients

~~~~~

(3W + 5T)/z = A

(3(1.2) + 5(1.1))/8 = A

(3.6 + 5.5)/8 = A

9.1/8 = A

Plan A = 1.1375 hours > 1 hour 8 minutes 15 seconds

(2W + 6T )/z ~ B

(2(1.2) + 6(1.1))/8 ~ B

(2.4 + 6.6)/8 ~ B

9/8 ~ B

Plan B ~ 1.125 hours > 1 hour 7 minutes 30 seconds

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

When ever the symbol " ~ " is used in an equation, it stands for "About"...

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Sorry for the mess up before....

8 0

4 years ago

Give a power series representation for the function f(x) x^3/(1 + 9x^2)

Nata [24]

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n\ge0}x^n$

Replace $x$ with $-9x^2$ and we get

$\displaystyle\frac1{1-(-9x^2)}=\sum_{n\ge0}(-9x^2)^n=\sum_{n\ge0}(-9)^nx^{2n}$

Lastly, multiply this by $x^3$ , so that

$\boxed{f(x)=\displaystyle\sum_{n\ge0}(-9)^nx^{2n+3}}$

6 0

4 years ago