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2 years ago

12

Mr. Sanchez earned a salary of $49,375 last year. He expects to earn 11% more this year. Which is closest to the salary Mr. Sanc

hez expects to earn this year? Select one:

1 answer:

Shkiper50 [21]2 years ago

5 0

49,375*0.11 = 5,431.25 , then add the original salary which is 49,375 and the answer is $54,806.25

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Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$

horrorfan [7]

Answer:

$A +B+C+D = 3$ is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

$A+B+C+D = ?$ if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under $\sqrt$ (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

$\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}$

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, $A +B+C+D = 5+6-10+2 = \bold3$

5 0

3 years ago

A ball is thrown into the air with an initial velocity of 22 meters per second.

lbvjy [14]

Answer:

27.4 metres

Step-by-step explanation:

Um, your question is missing the x's. I'm going to assume, -4.9x^2+22x+5.5

= -4.9(3)^2+22(3)+5.5

= 27.4

At 3 seconds the ball is 27.4 metres above the ground.

8 0

2 years ago

Yesterday it rained 5/8 inch. Today it rained 1/8 inch. What is the total amount of rain for the two days?

Alecsey [184]

The total amount is 0.75 inches or 3/4 inches.

7 0

2 years ago

PLZ I REALLY NEED HELP/ i'll give brainlist and 100 points PLZZZZZ

andrew11 [14]

Answer:

Question 1: Answer would be A.

Question 2: Answer would be B.

Question 3: I cannot answer this one because an image is not provided. I do not have the image of the original triangle LMN. If you message me with a photo of this question, I will be able to answer.

Question 4: This answer may be wrong, but I believe that it would be A. I don't know how to calculate dilation transformations, but after graphing out all the points, I found that (6,4) would be the correct point because the distance between Point S and (6,4) is even and is able to be divided by two.

Question 5: Again, I cannot answer this one because an image is provided. Message me with a photo, I'll answer.

Question 6: Answer would be C.

Question 7: Again, I cannot answer this one because an image is provided. Message me with a photo, I'll answer.

Question 8: Answer would be C.

Step-by-step explanation:

Question 1 Explanation: Answer would be A because the quadrilateral was rotated 180 degrees and dilated to be larger.

Question 2 Explanation: Quadrant IV is on the bottom right, Quadrant I is on the top right. If a triangle were to be rotated from the origin (0,0), it would have to rotate 270 degrees in order to reach Quadrant I.

Question 3 Explanation:

Question 4 Explanation:

Question 5 Explanation:

Question 6 Explanation: Using a rotation calculator, I input the degree of rotation as -90.

Question 7 Explanation:

Question 8 Explanation: Using a rotation calculator, I input the degree of rotation as -180.

7 0

3 years ago

9) v - 15 = -27 10) n + 16 = 9

Alik [6]

Answer:

9) v= -12

10) n= -7

Step-by-step explanation:

9) v - 15 = -27

Add 15 from both sides

i.e. v - 15 + 15 = -27 + 15

v = -12

10) n + 16 = 9

Subtract 16 from both sides

i.e. n + 16 - 16 = 9 - 16

n = -7

Hope this helps!!!

5 0

3 years ago