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3 years ago

Answer the question below

Mathematics

1 answer:

lys-0071 [83]3 years ago

6 0

Answer:

A) -1

Step-by-step explanation:

$\frac{3 + 2\sqrt{5} }{2\sqrt{5}-3 } \\$

We can rewrite 2√5 - 3 as -(3 + 2√5)

Therefore,

$\frac{3+ 2\sqrt{5} }{-(3 + 2\sqrt{5} )} \\$

We can cancel out 3 + 2√5 both in the numerator and the denominator. So we get

= 1/-1

= -1

Answer : A) -1

Thank you.

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4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant

Ivan

Question:

The quantities x and y are in proportion

x y

4 6

30 45

8 b

a 15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

$a = 10$ and $b = 12$

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

$(x_1,y_1) = (4,6)$

$(x_2,y_2) = (30,45)$

The slope (m) is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{45 - 6}{30 -4}$

$m = \frac{39}{26}$

$m = 1.5$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

This gives:

$y - 6 = 1.5(x - 4)$

$y - 6 = 1.5x - 6$

$y = 1.5x$

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in $y = 1.5x$

$b = 1.5 * 8$

$b = 12$

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in $y = 1.5x$

$15 = 1.5 * a$

Solve for a

$a = \frac{15}{1.5}$

$a = 10$

Solving (b): The constant of variation.

This has been solved in (a) above as:

$m = 1.5$

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

<em>This shows direct variation</em>

3 0

2 years ago

Translate the sentence into an inequality. Twice the difference of a number and 8 is at least 26 . Use the variable w for the un

Olin [163]

"At least" refers to greater than or equal to (≥).
This is because "at least" means:
- it can't be less than
- it can be equal to
- it can be greater than
This is basically like saying no less than.
If you must have at least 10 oranges for some recipe, then you must have 10 oranges, but you can also have more.

"Twice the difference of a number and 8"
This means that 2 times a number minus 8.
This can be written as 2(w - 8), since w is unknown and it's the difference between w and 8.
The 2 is being multiplied by this because it's 2 times this difference.

"At least 26"
This means ≥ 26.

Now for the actual inequality.
"Twice the difference of a number and 8"
translates to 2(w - 8)
"is at least 26"
translates to ≥ 26
Now put them together.
2(w - 8) ≥ 26

So the answer is 2(w - 8) ≥ 26.

Hope this helps! :)

7 0

3 years ago

Robert drives 45 miles in 3 hours from New York City to New Jersey. How far will he drive in 5 hours?

fenix001 [56]

Ok so the awnser is 75 because 45 ÷ 3 is 15 and so 2 more hours so I added 30 to the 45 and I got 75 I think that's right please correct me

3 0

3 years ago

Your monthly living expenses are $1500 on an income of $1,650 per month. Your goal is to have an emergency fund of 4 times your

DochEvi [55]

Your end goal is to have $6000 total in 12 months. since you have $2400 already you can subtract that from 6000 leaving you with $3600 over the course of 12 months. since you already put $150 in a month over the course of 12 months you would have $1800 which is only half of the goal of $3600. in order for you to put in $3600 you would have to put an additional 150 in your savings along with your regular 150 making the answer b.

6 0

3 years ago

Read 2 more answers

What is the value of x in the equation x- 3/4 =5 1/6

Wewaii [24]

Answer:

5 11/12

Step-by-step explanation:

First convert the mixed number into an improper fraction: 31/6

Find a common denominator:

18/24 and 124/24

124/24+ 18/24 is 142/24 and that is the same as 5 11/12

Hopefully this helps and you can have a lovely day!

3 0

3 years ago