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2 years ago

Solve the inequality (n-7)>2n-3. Write the solution in set notation.

Mathematics

2 answers:

Elden [556K]2 years ago

5 0

Answer:

- 4 > n and Notion form : [ -4 , -∞).

Step-by-step explanation:

Given : (n-7)>2n-3.

To find : Solve the inequality.

Solution : We have given

(n - 7) > 2 n - 3.

On adding both sides by 3

n - 7+ 3 > 2n .

n - 4 > 2n .

On subtracting b both sides by n

-4 > 2n -n.

- 4 > n.

So, we can say value of n is less than - 4 like -5,-6, -7 ........-∞

Notion form : [ -4 , -∞).

Therefore, - 4 > n and Notion form : [ -4 , -∞).

belka [17]2 years ago

3 0

Answer:

n < -4

Step-by-step explanation:

To solve the inequality, use inverse operations.

(n-7) > 2n - 3

n - 7 > 2n - 3

-7 > 2n - n - 3

-7 > n - 3

-7 + 3 > n

-4 > n

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Alice should pick the enlarged-photo with dimensions of 8-inch by 10-inch.

Step-by-step explanation:

Step 1:

In order for a part of the photo to not be cut off, the enlarged photo's dimensions should be of a constant ratio with the original photo's dimensions.

We divide the dimensions of the enlarged-photo with the dimensions of the original photo to check which has a constant ratio.

Step 2:

The original photo was a 4-inch by 5-inch photo.

Option 1 is 7-inch by 9-inch, so the ratios are

$\frac{7}{4} = 1.75, \frac{9}{5} = 1.8.$ The ratios are different so this cannot be the enlarged photo's dimensions.

Option 2 is 8-inch by 10-inch, so the ratios are

$\frac{8}{4} = 2, \frac{10}{5} = 2.$ The ratios are the same so this can be the enlarged photo's dimensions.

Option 3 is 12-inch by 16-inch, so the ratios are

$\frac{12}{4} = 3, \frac{16}{5} = 3.2.$ The ratios are different so this cannot be the enlarged photo's dimensions.

So the enlarged-photo with dimensions of 8-inch by 10-inch should be picked.

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2 years ago

-67b + 6 ≤ 9b + 43 solve for b

qaws [65]

Answer:

b ≥ -(37/76)

Step-by-step explanation:

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2 years ago

Colin invests £2350 into a savings account. The bank gives 4.2% compound interest for the first 4 years and 4.9% thereafter. How

mixer [17]

To solve this, we are going to use the compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ is the final amount after $t$ years
$P$ is the initial investment
$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year

For the first 4 years we know that: $P=2350$ , $r= \frac{4.2}{100} =0.042$ , $t=4$ , and since the problem is not specifying how often the interest is communed, we are going to assume it is compounded annually; therefore, $n=1$ . Lest replace those values in our formula:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2350(1+ \frac{0.042}{1} )^{(1)(4)}$
$A=2350(1+0.042)^{4}$
$A=2770.38$

Now, for the next 6 years the intial investment will be the final amount from our previous step, so $P=2770.38$ . We also know that: $r= \frac{4.9}{100} =0.049$ , $t=6$ , and $n=1$ . Lets replace those values in our formula one more time:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2770.38(1+ \frac{0.049}{1})^{(1)(6)$
$A=2770.38(1+0.049)^6$
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We can conclude that Collin will have £3691.41 in his account after 10 years.

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2 years ago

A car rental firm has the following charges for a certain type of car: $25 per day with 100 free miles included, $0.15 per mile

Eddi Din [679]

y = 25 + 0.15x is the equation for relating the cost y to the number of miles x that you drive the car

Solution:

Let "y" be the total cost of car rental

Let "x" be the number of miles you drive the car for more than 100 miles

A car rental firm has the following charges for a certain type of car:

$25 per day with 100 free miles included, $0.15 per mile for more than 100 miles

Suppose you want to rent a car for one day, and you know you'll use it for more than 100 miles

Therefore,

Car is rented for one day

You will use it for more than 100 miles

Therefore, equation is framed as:

Total cost = $ 25 + 0.15(number of hours)

$Total\ Cost = 25 + 0.15x\\\\y = 25 + 0.15x$

Thus the equation for relating the cost y to the number of miles x that you drive the car

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2 years ago

489 to the nearest ten

sammy [17]

8 is in the tenth position.

In order to round up, the number behind it (in this case. 9) must be one of the numbers of 5-9. Because 9 meets this requirement, you can round 8 to 9 and this will make 9 to 0.

Your answer is 490

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2 years ago

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