write an equation of a line in standard form
passes through (35,42) and (15,-2)

Answer:

23 degrees

Step-by-step explanation:

We can use basic trigonometric equations to solve for the angle x because we are given a right triangle.

I will use the sin x = opposite / hypotenuse

sin x = 5 / 13

x = sin^-1 (5 / 13)

x = 22.61986 degrees

The question requires us to round to the nearest degree which is 23.

Other alternative methods you can use include the tangent and cosine functions or the law of cosines.

Answer:

x = 23°

Step-by-step explanation:

I will use

[tex]tanx=opposite/adjacent[/tex]

[tex]tanx=\frac{5}{12}[/tex]

[tex]x=tan^{-1} (\frac{5}{12} )=tan^{-1} (0.417)=22.62^{o}[/tex]

rounded to the nearest degree : 23°

Hope this helps

Answer:

6 hours

Step-by-step explanation:

Let the smaller pipe fill the pool in x hours and the bigger pipe y hours.

x-y=4

1/x+1/y=4/15

x=10, y=6

so 6 hours

Step-by-step explanation:

l = large pipe

s = small pipe

s needs x hours alone to fill the pool.

l needs x-4 hours alone to fill the pool.

s does 1/x of the work in 1 hour.

l does 1/(x-4) of the work in 1 hour.

3 hours 45 minutes = 3.75 hours

3.75 × 1/x + 3.75 × 1/(x-4) = 1 (= the whole work)

3.75 + 3.75 × x/(x-4) = x

3.75×(x-4) + 3.75×x = x(x-4) = x² - 4x

3.75x - 15 + 3.75x = x² - 4x

7.5x - 15 = x² - 4x

-15 = x² - 11.5x

0 = x² - 11.5x + 15

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -11.5

c = 15

x = (11.5 ± sqrt(132.25 - 4×1×15))/(2×1) =

= (11.5 ± sqrt(72.25))/2 = (11.5 ± 8.5)/2

x1 = (11.5 + 8.5)/2 = 20/2 = 10

x2 = (11.5 - 8.5)/2 = 3/2 = 1.5

x = 1.5 would turn l = 1/(x-4) negative, which does not make sense.

so, x = 10 is our solution.

that means

s does 1/10 of the work in 1 hour.

so, the small pipe alone fills the pool in 10 hours.

l does 1/(10-4) = 1/6 of the work in 1 hour.

so, the large pipe alone fills the pool in 6 hours.

Answer:

f(-14) = -6

f(-4) = 6

f(12) = 6

f(0) = -3

negative

Step-by-step explanation:

f(-14) = -6

This is because when x is -14, y is -6, as seen in the graph

f(-4) = 6

This is because when x is -4, y is 6, as seen in the graph

f(12) = 6

This is because when x is 12, y is 6, as seen in the graph

f(0) = -3

This is because when x is 0, y is -3, as seen in the graph

is f(4) positive or negative?
negative

This is because when x is 4, y is -6, as seen in the graph

Answer:

x=1/3

Step-by-step explanation:

-4(3x-2)=6x+2

or,-12x+8=6x+2

or,-12x-6x=2-8

or,-18x=-6

or,x=-6/-18

or,x=1/3

The area of the shaded face of the cylinder with the given radius is approximately 1520cm².

This question is incomplete, the missing diagram is uploaded along the answer below.

From the diagram, the shaded region is a circle with radius 22 meters.

Area of a circle is expressed as;

A = π × r²

r is radius and π is constant pi ( π = 3.14 )

We substitute our values into the equation above.

A = π × r²

A = 3.14 × (22m)²

A = 3.14 × 484m²

A = 1519.76 ≈ 1520cm²

Therefore, the area of the shaded face of the cylinder with the given radius is approximately 1520cm².

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Answer:

  (a) No; rainfall amounts are positive

Step-by-step explanation:

Rainfall amounts are measured using a gauge that reports the amount as zero when the gauge is empty. Any rainfall adds to the amount in the gauge, so is reported as a positive number. There is no way to remove more rainfall than is in the gauge, so there is no way to have a negative rainfall amount

A prediction of a negative rainfall amount makes no sense, because you can't have a negative amount of rainfall.

Answer:

4x+2y=4

3x-y=-7

first one by 3

second by 4

12x+6y=12

12x-4y=-28

subtract

10y=40

y=4

plug in

3x-4=-7

add 4

3x=-3

x=-1

(-1,4)

c

Hope This Helps!!!

Answer: third option

Step-by-step explanation:

There are 2 ways to go about systems of equations normally, and that's elimination and substitution. For this particular problem, I would recommend elimination.

we see the first equation 4x+2y=4

we want to be able to simplify it as much as possible (so it's easier to solve)

so we divide all the terms by 2, giving 2x+y=2.

the second equation can't be simplified, so we set up the elimination method.

   2x+y=2

  -3x-y=-7

multiplying both equations by 2 and 3, we subtract them and get that y equals 4, which is clearly the answer.

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Answer:  [tex]\textsf{285 total calories}[/tex]

-------------------------------------------------------------------------------------------------------------

Given: [tex]\textsf{1 egg = 95 calories}[/tex]

Find: [tex]\textsf{Calories in 3 eggs}[/tex]

Solution: In order to determine the total amount of calories in 3 eggs we must multiply the amount of calories in one egg by 3.  So we do 95 * 3 which gives us 285 total calories.

Step-by-step explanation:

If you roll the die once, the probability of getting a 3 is 1/6

If you roll the die twice and get a three both times, the probability of that happening is 1/6 * 1/6 or 1/36

and so on...

The probability of rolling a 3 is 1/6.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

A number cube is rolled several times.

There are a total of 6 numbers in a number cube.

Total outcomes = 6

We have to find the probability of rolling a 3.

Probability = 1/6

Hence the required probability is 1/6.

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1) If the limit [tex]L[/tex] is

[tex]L = \displaystyle \lim_{\Delta x\to0} \frac{\sin\left(\frac\pi3 + \Delta x\right) - \sin\left(\frac\pi3\right)}{\Delta x}[/tex]

then using the hint as well as [tex]\sin\left(\frac\pi3\right)=\frac{\sqrt3}2[/tex] and [tex]\cos\left(\frac\pi3\right)=\frac12[/tex] we have

[tex]\displaystyle L = \lim_{\Delta x\to0} \frac{\sin\left(\frac\pi3\right)\cos(\Delta x) + \cos\left(\frac\pi3\right)\sin(\Delta x) - \sin\left(\frac\pi3\right)}{\Delta x}[/tex]

[tex]\displaystyle L = \sin\left(\frac\pi3\right) \lim_{\Delta x\to0} \frac{\cos(\Delta x) - 1}{\Delta x} + \cos\left(\frac\pi3\right) \lim_{\Delta x} \frac{\sin(\Delta x)}{\Delta x}[/tex]

[tex]L = \dfrac{\sqrt3}2 \times 0 + \dfrac12\times1 = \boxed{\dfrac12}[/tex]

which follows from the well-known limits,

[tex]\displaystyle \lim_{x\to0} \frac{1-\cos(x)}x = 0 \text{ and } \lim_{x\to0} \frac{\sin(x)}x=1[/tex]

Alternatively, if you already know about derivatives, we can identify the limit as the derivative of [tex]\sin(x)[/tex] at [tex]x=\frac\pi3[/tex], which is [tex]\cos\left(\frac\pi3\right)=\frac12[/tex].

2) It looks like you may be using double square brackets deliberately to denote the greatest integer or floor function which rounds the input down to the nearest integer. That is, [tex][\![x]\!][/tex] is the greatest integer that is less than or equal to [tex]x[/tex]. The existence of [tex]L[/tex] depends on the equality of the one-sided limits.

Suppose [tex]3\le x<4[/tex]. Then [tex]2[tex]\displaystyle \lim_{x\to4^-} [\![x - 1]\!] = 2[/tex]

Now suppose [tex]4\le x<5[/tex], so that [tex]3\le x-1 < 4 \implies [\![x-1]\!]=3[/tex] and

[tex]\displaystyle \lim_{x\to4^+} [\![x-1]\!] = 3[/tex]

The one-sided limits don't match so the limit doesn't exist.

The income tax of Rebecca and Steve will be $27020 and $20625.

Rebecca has an income of $96500. The income tax will be:

= 28% × $96500

= 27020

Steve has an income of $82500. The income tax will be:

= 25% × $82500

= 20625

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The weight of relish prepared after the evaporation of water is 2,226.02 pounds

Total = 1000 + 500 + 900 + 75 + 5

= 2,480 pounds

pickles are 92% water

= 92/100 × 1000

= 920 pounds

onions are 85% water

= 85/100 × 500

= 425 pounds

salt brine is 88% water

= 88/100 × 75 pounds

= 66 pounds

Total water in the mixture = 920 pounds + 425 pounds + 66 pounds

= 1,411 pounds

Amount of water evaporated = 18/100 × 1,411 pounds

= 253.98 pounds

Weight of the relish prepared = 2,480 pounds - 253.98 pounds

= 2,226.02 pounds

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Answer: 1.59375. Round to 1.6 if need be.

Step-by-step explanation:

Their are 384oz in 3 gallons (multiply gallons by 128)

Their are 120 seconds in 2 minutes (multiply minutes by 60)

Multiply 1.5 * 120 = 180 to get how many oz have drained after 2 minutes.

Subtract 384 - 180 = 204 to get how many oz left in the milk container.

Convert 204oz to gallons by dividing by 128. 204 / 128 = 1.59375gallons.

The length of the altitude to the hypotenuse of the right triangle is 3 / 5

A right triangle has one of it's angle as 90 degrees. Therefore,

area of right triangle = 1 / 2 bh

where

Hence,

6 = 1 / 2 × 4 × h

6 = 4h / 2

cross multiply

12 = 4h

divide both sides by 4

h = 12 / 4

h = 3 units

Hypotenuse² = 4² + 3²

c² = 16 + 9

c = √25

c = 5

Therefore, the length of the altitude to the hypotenuse of the right triangle is 3 / 5

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Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

first find g(-2) by plugging in -2 as x in the g(x) equation

g(-2) = 3(-2)+5

g(-2) = -6+5

g(-2) = -1

then plug that value (-1) as x in the f(x) equation

f(-1) = 4-(-1)^2

f(-1) = 4-1

f(-1) = 3

It really depends what situation you are trying to set goals at,

Trying to understand math concept or any really concept, I would set little goals such as " Study for 15 mins a day" or something and the big goal would be "UNDERSTAND THE CONCEPT"

for goals, I would set small goals that work towards your main goal.

Answer:

Marriage and Family Harmony. ...

Proper Mindset and Balance. ...

Commitment to Improved Physical Health. ...

Career Passion and Personal Satisfaction. ...

Develop Empathy and Gentleness. ...

Financial Stability. ...

Service and Social Responsibility.

Answer:

Step-by-step explanation:

The area of a parallelogram is h*b where h is the height/altitude and b is the base.

The base is 27 millimeters and the altitude is 18 millimeters, so we multiply those together.

27*18= 486.

The area of the parallelogram is 486mm²

Hope this helps!

Answer:

Law of sines

Step-by-step explanation:

The law of sines is a formula used to find either an angle or side in a non-right triangle.

You have to have at least three parts to use it.

For example, if you have angle A and its side (a) along with angle B, you can use it to find side b.

The perimeter of the hollow shape is 16d + 4(a + b + c)

The question is incomplete, and the missing parameters cannot be found.

So, I will give a general explanation on how to determine perimeter.

The given information are:

The perimeter of a right triangle that has sides a, b and c is:

P = a + b + c

Since there are 4 triangles, the perimeter of the 4 triangles is:

P = 4(a + b + c)

The perimeter of a square that has side length d is:

P = 4d

Since there are 4 squares, the perimeter of the 4 triangles is:

P = 4 * 4d

P = 16d

Add the perimeters of the squares and the triangles

P = 16d + 4(a + b + c)

Hence, the perimeter of the hollow shape is 16d + 4(a + b + c), where a, b, c and d are the unknown variables

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Answer: Segment AD

Reason:

Any diameter goes through the center of a circle, with both endpoints on the circle edge.

Another diameter is segment FC.

Answer:

CF and AD

Step-by-step explanation:

Hello!

Given the definitions, we are simply looking for any line that goes through the center of the circle, and touches twice on the circumference of the circle.

There are only two lines that seem to go through the circle, and have endpoints on the circle:

Step-by-step explanation:

The figure below shows a portion of the graph of the function [tex]j\left(x\right) \ = \ 4^{x-2}[/tex], hence the average rate of change (slope of the blue line) between the [tex]x[/tex] and [tex]x+h[/tex] is

                     [tex]\text{Average rate of change} \ = \ \displaystyle\frac{\Delta y}{\Delta x} \\ \\ \rule{3.7cm}{0cm} = \dsiplaystyle\frac{f\left(x+h\right) \ - \ f\left(x\right)}{\left(x \ + \ h \right) \ - \ x} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{f\left(x + h\right) \ - \ f\left(x\right)}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{4^{x+h-2} \ - \ 4^{x-2}}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{4^{x-2+h} \ - \ 4^{x-2}}{h}[/tex]

                                                            [tex]\\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{\left(4^{x-2}\right)\left(4^{h}\right) \ - \ 4^{x-2}}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{\left(4^{x-2}\right)\left(4^{h} \ - \ 1 \right)}{h}[/tex]

Answer:

help to others the exact amount u have

Answer:

He can watch 8 movies

Step-by-step explanation:

100-40.66=59.34

6.71 x 8 = 53.68

therefore the most amount of movies he can watch is 8

Answer:

Step-by-step explanation:

Nines: (3,6), (4,5), (5,4), (6,3)

Tens: (4,6), (5,5), (6,4)

Elevens: (5,6), (6,5)

Twelves: (6,6)

4 + 3 + 2 + 1 = 10 outcomes possible

36 outcomes total for rolling two dice.

P(sum > 8) = 10/36 or 5/18 simplified.

Answer:

0.350  (3 d.p.)

Step-by-step explanation:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student owns a credit card

Use the given table to calculate the probability that the student is a freshman:

[tex]\implies \sf P(A)=\dfrac{60}{100}=0.6[/tex]

And the probability that the student is a freshman and owns a credit card:

[tex]\implies \sf P(A \cap B)=\dfrac{21}{100}=0.21[/tex]

To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of B given A is:

[tex]\sf P(B|A)=\dfrac{P(A \cap B)}{P(A)}[/tex]

Substitute the found values into the formula:

[tex]\implies \sf P(B|A)=\dfrac{0.21}{0.6}=0.35[/tex]

Therefore, the probability that the student owns a credit card given that they are a freshman is 0.35

The ending inventory using LIFO is $920.

The ending inventory using FIFO is $1,472.

LIFO means last in first out. It means that it is the last purchased inventory that is the first to be sold. Ending inventory would consist of first purchased inventory.

23 x $40 = $920

FIFO means first in, first out. It means that it is the first purchased inventory that is the first to be sold. Ending inventory would consist of last purchased items in inventory.

23 x $64 = $1,472

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Answer:

2h 1' 1"

Step-by-step explanation:

1h = 1 hora

1' = 1 minute

1" = 1 secind

The sum of the three days is:

  58'  45"

+ 40'  40"

  20'  36"

= 118'  121"

118' 121" = 118' + 121"

1' = 60"

121" = 120" + 1"  = (120/60) + 1 = 2' + 1"

Then:

118' + 121" = 118' + 2' ´+ 1" = 120' + 1"

1 h = 60'

(120/60) + 1 = 2h + 1'

then:

118' + 121" = 2h + 1' + 1"

= 2h 1' 1"

Considering the sample mean, the best estimate for the mean monthly electric bill for all residents of the local apartment complex is of $86.

The point estimate for the population parameter is found according to the parameter for a sample from the population. For example:

In this problem, the mean bill for 132 residents is of $86, hence the best estimate for the mean monthly electric bill for all residents of the local apartment complex is of $86.

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