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11111nata11111 [884]

3 years ago

10

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2,5

)?

1 answer:

KonstantinChe [14]3 years ago

6 0

Answer:

C

Step-by-step explanation:

The point slope form of a line is $y - y_1 = m(x-x_1)$ . If the point is (2,5) then the equation will be $y - 5=m(x-2)$ . Only option C matches this equation.

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I will use fancy gold and red wrapping paper for two packages i have to wrap. I will use 1 2/4 yard of paper for one of the boxe

Allisa [31]

Well you need first 1 2/4 of a yard. Then you will need 5/6 of a yard. But first you need to put them together. So we need to find the common denominator. Six and four both share which multiple? Twelve. So let's rewrite that. You need 1 6/12 yards + 10/12 yards of wrapping paper. But before we do anything else we need to fix the mixed number. 1 6/12 isn't as easy to add ad 18/12 is. So 18/12 + 10/12 = 28/12
That can simplify as well. Now it's 14/6 which is equivalent to the fraction we had before. But it can also go down to 2 2/6. Now we can simplify it even further. By dividing it by two we can get 2 1/3. These are the measurements we need. So you would need how many thirds? Seven. (2 1/3 is seven thirds) This is your final answer.

You would need to have seven peices of wrapping paper cut to wrap both gift boxes.

6 0

3 years ago

All angle values for cos0=1

vagabundo [1.1K]

Cos 0° = Sin 90°

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byjus dot com

6 0

2 years ago

Read 2 more answers

Find the number of terms, n, in the arithmetic series whose first term is 13, the common difference is 7, and the sum is 2613.

siniylev [52]

Answer:

A

Step-by-step explanation:

Recall that the sum of an arithmetic series is given by:

$\displaystyle S = \frac{n}{2}\left(a + x_n\right)$

Where <em>n</em> is the number of terms, <em>a</em> is the first term, and <em>x</em>_<em>n</em> is the last term.

We know that the initial term <em>a</em> is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find <em>n</em>.

First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:

$x_n=a+d(n-1)$

Since the initial term is 13 and the common difference is 7:

$x_n=13+7(n-1)$

Substitute:

$\displaystyle S = \frac{n}{2}\left(a + (13+7(n-1)\right)$

We are given that the initial term is 13 and the sum is 2613. Substitute:

$\displaystyle (2613)=\frac{n}{2}((13)+(13+7(n-1)))$

Solve for <em>n</em>. Multiply both sides by two and combine like terms:

$5226 = n(26+7(n-1))$

Distribute:

$5226 = n (26+7n-7)$

Simplify:

$5226 = 7n^2+19n$

Isolate the equation:

$7n^2+19n-5226=0$

We can use the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, <em>a</em> = 7, <em>b</em> = 19, and <em>c</em> = -5226. Substitute:

$\displaystyle x =\frac{-(19)\pm\sqrt{(19)^2-4(7)(-5226)}}{2(7)}$

Evaluate:

$\displaystyle x = \frac{-19\pm\sqrt{146689}}{14} = \frac{-19\pm 383}{14}$

Evaluate for each case:

$\displaystyle x _ 1 = \frac{-19+383}{14} = 26\text{ or } x _ 2 = \frac{-19-383}{14}=-\frac{201}{7}$

We can ignore the second solution since it is negative and non-natural.

Therefore, there are 26 terms in the arithmetic series.

Our answer is A.

6 0

2 years ago

A town has a population of 17000 and grows at 2.5% every year. To the nearest year, how long will it be until the population wil

andre [41]

Answer:

6 years

Step-by-step explanation:

we know that

The equation of a exponential growth is equal to

$y=a(1+r)^x$

where

y ----> is the population

x ---> is the number of years since now

a ---> is the initial value or y-intercept

r ---> is the rate of change

we have

$a=17,000\ people$

$r=2.5\%=2.5/100=0.025$

substitute

$y=17,000(1+0.025)^x$

$y=17,000(1.025)^x$

For y=19,600

substitute in the exponential equation and solve for x

$19.600=17,000(1.025)^x$

$(19.600/17,000)=(1.025)^x$

apply log booth sides

$log(19.600/17,000)=log(1.025)^x$

$log(19.600/17,000)=xlog(1.025)$

$x=log(19.600/17,000)/log(1.025)=6\ years$

8 0

3 years ago

The average American consumes about 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will 50 Amer

love history [14]

1 year has around 52.1429 weeks
We are given that one American consumes around 20 gallons of ice cream in a year. This means that the consumption is 20 gallons in 52.1429 weeks.
Now, first we will calculate the amount consumed by 1 American in one week using cross multiplication as follows:
consumption per week = (1*20) / (52.1429) = 0.38356 gallons

Now, to know the consumption of 50 Americans in one week, we will simply multiply the consumption of one American by 50 as follows:
consumption of 50 Americans = 0.38356 * 50 = 19.18 gallons/week

3 0

3 years ago