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vladimir2022 [97]

3 years ago

13

Sebastian was in a hotel lobby and took the elevator up 7 floors to his room. Then he took the elevator down 9 floors to the par

king garage. He described his movement with the expression below.

1 answer:

chubhunter [2.5K]3 years ago

7 0

Answer:

7-9

Step-by-step explanation:

Sebastian goes up from 0 by 7 floors. Then, he goes down by 9.

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The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number

andreyandreev [35.5K]

Answer:

39

Step-by-step explanation:

let the 2 digit number be ab = 10a + b ( considering place value )

The reversed 2 digit number is ba = 10b + a

The sum of the 2 digit number is

a + b = 12 ( subtract b from both sides )

a = 12 - b → (1)

Expressing as an equation

ba = ab + 54 , that is

10b + a = 10a + b + 54

Substitute a = 12 - b into the equation

10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides

9b + 12 = 120 - 10b + b + 54

9b + 12 = - 9b + 174 ( add 9b to both sides )

18b + 12 = 174 ( subtract 12 from both sides )

18b = 162 ( divide both sides by 18 )

b = 9

Substitute b = 9 into (1)

a = 12 - 9 = 3

Thus

the original 2 digit number = ab = 39

The reversed 2 digit number = ba = 93

which is 54 more than the original number

7 0

3 years ago

The temperature falls from 10°F to -15° F. What is the difference in these<br> temperatures?

nadya68 [22]

Answer:

the difference is 25

Step-by-step explanation:

to get from 10 to 0 is 10 units and from 0 to -15 is 15

10+15 = 25

8 0

3 years ago

Helppppp me plzzzzzzzzzzz

Iteru [2.4K]

Answer:

congruent

Step-by-step explanation:

4 0

3 years ago

For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of

Katena32 [7]

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is $(-1)^{k+1}(\frac{1}{2^{k}})$ .

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as $(-1)^{k+1}(\frac{1}{2^{k}})$ .

where k is from 1 to 10.

By the given expression sequence will be $\frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......$

In this sequence first term "a" = $\frac{1}{2}$

and common ratio in each successive term to the previous term is 'r' = $\frac{\frac{(-1)}{4}}{\frac{1}{2} }$

r = $-\frac{1}{2}$

Since the sequence is infinite and the formula to calculate the sum is represented by

$S=\frac{a}{1-r}$ [Here r is less than 1]

$S=\frac{\frac{1}{2} }{1+\frac{1}{2}}$

$S=\frac{\frac{1}{2}}{\frac{3}{2} }$

S = $\frac{1}{3}$

Now we are sure that the sum of infinite terms is $\frac{1}{3}$ .

Therefore, sum of 10 terms will not exceed $\frac{1}{3}$

Now sum of first two terms = $\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$

Now we are sure that sum of first 10 terms lie between $\frac{1}{4}$ and $\frac{1}{3}$

Since $\frac{1}{2}>\frac{1}{3}$

Therefore, Sum of first 10 terms will lie between $\frac{1}{4}$ and $\frac{1}{2}$ .

Option D will be the answer.

3 0

3 years ago

I NEED HELP!!!!!! 4x+2x-5=7x-1

yan [13]

Let's solve your equation step-by-step.

4x+2x−5=7x−1

Step 1: Simplify both sides of the equation.

4x+2x−5=7x−1

4x+2x+−5=7x+−1

(4x+2x)+(−5)=7x−1(Combine Like Terms)

6x+−5=7x−1

6x−5=7x−1

Step 2: Subtract 7x from both sides.

6x−5−7x=7x−1−7x

−x−5=−1

Step 3: Add 5 to both sides.

−x−5+5=−1+5

−x=4

Step 4: Divide both sides by -1.

−x

−1

=

4

−1

x=−4

Answer:

x=−4

i hope this helps you

3 0

3 years ago