1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stiks02 [169]
3 years ago
5

A rectangle has a height of t^2+7t+6t

Mathematics
1 answer:
jek_recluse [69]3 years ago
4 0

Answer:

2t^3+15t^2+19t+6

Step-by-step explanation:

Height of the Rectangle=t^2+7t+6

Width of the Rectangle=2t+1

Area of the Rectangle = Height X Width

=(2t+1)(t^2+7t+6)\\=2t(t^2+7t+6)+1(t^2+7t+6)\\=2t^3+14t^2+12t+t^2+7t+6\\$Collect like terms\\=2t^3+14t^2+t^2+12t+7t+6\\Area=2t^3+15t^2+19t+6\\

The area of the rectangle is 2t^3+15t^2+19t+6

You might be interested in
Gallon of gas cost 4$ carols car can drive 20 miles per gallon. what is the cost to drive 30 miles
almond37 [142]

Answer: It costs $6 to drive 30 miles.

Step-by-step explanation:

$4 per 20 miles

20/4 = 5

1$ per 5 miles

30/5 = 6

6 * 5 = 30

3 0
3 years ago
A list contains twenty integers, not necessarily distinct. Does the list contain at least two consecutive integers?
algol13

Answer:

Answer c is correct. Both statements arent sufficient separately, but together they are sufficient.

Step-by-step explanation:

Neither of the statments are sufficient alone. Lets first analyze why statment (1) alone is not sufficient.

If we suppose that our list is scattered, so our values are pretty distant one to the other, one value increasing by one wont change this. The list will still be scattered and our values will remain distant one to the other.

For a concrete example, consider a list with values multiples of a thousand. Our list can look this way {1000,2000,3000, ....., 19000, 20000}. So we have 20 distinct values. Adding one to any of this 20 values wont change the fact that we have 20 different values. However, our list doesnt have 2 consecutive integers.

Proving (2) not being sufficient is pretty straightfoward. If our list contains 20 equal values it wont have 2 consecutive values, because all values are equal. For example the list with values {0, 0, 0, 0, ....., 0} will have the value 0 occuring more than once but it doesnt have 2 consecutive values.

Now, lets assume both statements (1) and (2) are valid.

Since (2) is valid there is an integer, lets call it <em>k</em>, such that <em>k</em> appears on the list at least twice. Because (1) is True, then if we take one number with value <em>k </em>and we increase its value by one, then the number of distinct values shoudnt change. We can observe a few things:

  1. There are 19 numbers untouched
  2. The only touched value is <em>k</em>, so our list could only lost <em>k </em>as value after adding 1 to it.
  3. Since <em>k</em> appears at least twice on the list, modifying the value of one<em> number</em> with value <em>k</em> wont change the fact that the rest of the numbers with value <em>k</em> will <em>preserve</em> its value. This means that k is still on the list, because there still exist numbers with value k.
  4. The only number that <em>could</em> be new to the list is k+1, obtained from adding 1 to k

By combining points 2 and 3, we deduce that the lists doesnt lose values, because point 2 tells us that the only possible value to be lost is k, and point 3 says that the value k will be preserved!

Since the list doesnt lose values and the number of different values is the same, we can conclude that the list shoudnt gain values either, because the only possibility for the list to adquire a new value after adding one to a number is to lost a previous value because the number of distinct numbers does not vary!

Point 4 tells us that value k+1 was obtained on the new list after adding 1 to k. We reach the conclusion that the new list doesnt have new values from the original one, that means that k+1 was alredy on the original list.

Thus, the original list contains both the values k (at least twice) and k+1 (at least once), therefore, the list contains at least two consectutive values.

8 0
3 years ago
Triangle ABC with coordinates A (3,-2), B (5,5), and C (-4, 2) is reflected across
son4ous [18]

Step-by-step explanation:

the formula of coordinates (x, y) that reflected across the x-axis : (x, y) => (x, -y)

so,

A(3, -2) => A'(3, 2)

B(5, 5) => B'(5, -5)

C(-4, 2) => C'(-4, -2)

5 0
2 years ago
Read 2 more answers
Find the mean of the data in the dot plot below.
NemiM [27]

Answer:

2.5 is the mean

3 0
2 years ago
Read 2 more answers
A line that intersects one of two parallel lines intersects the other also.
IceJOKER [234]

Answer:

Never

Step-by-step explanation:

It is not possible for one out of two parallel lines to be cut by a transversal, because eventually it would have to intersect

8 0
3 years ago
Other questions:
  • A satellite dish shaped like a paraboloid, has diameter 2.4 ft and depth 0.9 ft. If the receiver is placed at the focus, how far
    13·1 answer
  • Z - 3( z + 2 ) = -6 - 2z
    7·2 answers
  • How do you find the total surface area of a 3-D composite figure? Do you subtract one base from one of the figures or both of it
    6·1 answer
  • 4/5 of the 315 members of a book club are male.How many female members are there in the club?
    15·1 answer
  • For small changes in temperature, the formula for the expansion of a metal rod under a change in temperature is: g-L=aL(t-T), wh
    15·1 answer
  • WIll give brainley<br><br>1/3x = 6
    11·1 answer
  • Please help me. i don’t know how to do this at all
    11·1 answer
  • John went shopping for a pair of jeans.
    8·1 answer
  • 8x-4y=-96 in slope intercept form
    14·1 answer
  • Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answerbox. Also, s
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!