What is an equation of the line, in point-slope form, that passes through the given point and has the given slope?

Answer:

5

Step-by-step explanation:

D=[tex]\sqrt{(8-4)^2+(1-4)^2}[/tex]

D=[tex]\sqrt{4^2+(-3)^2}[/tex]

D=[tex]\sqrt{16+9}[/tex]

D=[tex]\sqrt{25\\}[/tex]

D=5

Answer: B

Step-by-step explanation:

Use the distance formula: [tex]d = \sqrt{(x_2 -x_1)^{2}+(y_2-y_1)^{2}}[/tex]

[tex]d_{PQ} = \sqrt{(8-4)^{2}+(1-4)^{2}}[/tex]

         [tex] = \sqrt{(4)^{2}+(-3)^{2}}[/tex]

         [tex] = \sqrt{16+9}[/tex]

         [tex] = \sqrt{25}[/tex]

         [tex] = 5[/tex]

Answer:

115+9=124 employees

Answer:

Adriano's this month earning is $1150

Step-by-step explanation:

Adriano's existing customers =200

Every customer Pays subscription fee = $5 per month

This month number of customers joined =40

And number of number of customers cancelled subscription =10

So this month addition of new customers = 40-10 =30

Therefore total numbers of subscribers =200+30 =230

And money earned this month = 230× $5

                                                   = $1150

Answer:

Step-by-step explanation:

Introduction:

Mixtures are not unique to chemistry; we encounter them on a daily basis. The food and drinks

we consume, the fuel we use in our vehicles, building materials, soil, air, and ordinary water are

all mixtures. In fact, very few common materials in the world are pure. Any material made up

of two or more substances that are not chemically combined is a mixture. It is not difficult to

separate the components of a mixture if you take advantage of differences in physical properties

of the components.

1. Sublimation. Some substances change directly from a solid to a gas when they

are heated. The reverse process, when the vapor goes back to the solid phase

without a liquid state in between, is called deposition. Some solids which sublime

are iodine, caffeine, and paradichlorobenzene (mothballs). Dry ice sublimes also.

2 Extraction. This uses a solvent to selectively dissolve one component of the

solid mixture. With this technique, a soluble substance can be separated from an

insoluble substance.

3. Decantation. This separates a liquid from insoluble solid sediment by carefully

pouring the liquid from the solid without disturbing the solid.

4. Filtration. This separates a solid from a liquid through the use of a porous

material as a filter. Paper, charcoal, or sand can serve as a filter. These materials

trap the solid but let the liquid pass through (see diagram in Procedure section).

5. Evaporation. This is the process of heating a mixture in order to remove a

liquid that evaporates easily, leaving a dry residue.  

Pure substances are further broken down into elements and compounds. Mixtures are physically combined structures that can be separated into their original components. A chemical substance is composed of one type of atom or molecule.

Answer:

[tex]12.5x-285[/tex].

Step-by-step explanation:

We are told that a man drove x miles per hour for 3 hours, so he traveled 3x miles in three hours.

We are also told that he drove (2x-60) miles per hour for the next 4.75 hours. So The distance traveled by in next 4.75 hours will be:

[tex]4.75\cdot (2x-60)=9.5x-285[/tex]  

To find the total distance traveled by man we will add distances traveled by him in first 3 hours and next 4.75 hours.

[tex]\text{The total distance traveled}=3x+9.5x-285[/tex]

Upon combining like terms we will get,

[tex]\text{The total distance traveled}=(3+9.5)x-285[/tex]

[tex]\text{The total distance traveled}=12.5x-285[/tex]

Therefore, the total distance traveled in terms of x will be [tex]12.5x-285[/tex].

The total distance traveled in terms of x is the sum of the distances for each part of the trip: 3x miles for the first part and 9.5x - 285 miles for the second part, equating to a total distance of 12.5x - 285 miles.

To express the total distance traveled in terms of x, we need to use the distance formula d = vt, which states that distance (d) is equal to velocity (v) multiplied by time (t).

For the first part of the trip, the man drove at x miles per hour for 3 hours. Therefore, the distance for this part is:

d1 = x miles/hour * 3 hours = 3x miles

For the second part of the trip, he drove at (2x-60) miles per hour for 4.75 hours. So, the distance for this part is:

d2 = (2x-60 miles/hour) * 4.75 hours = 9.5x - 285 miles

To find the total distance traveled, we add the two distances together:

Total Distance = d1 + d2 = 3x miles + 9.5x - 285 miles = 12.5x - 285 miles

Answer:

35

Step-by-step explanation:

It’s a 90 degree angle. 3x35=105 and 105-15=90

Answer:

x = 35

Step-by-step explanation:

Angle JML is 90 degrees

3x-15 = 90

Add 15 to each side

3x-15+15 = 90+15

3x = 105

Divide each side by 3

3x/3 =105/3

x = 35

Answer:

1.  P ( tails) = 1/2

2.P (number greater than 4)   = 1/3

3.  P (2 die sum to 8) = 5/36

Step-by-step explanation:

A coin only has 2 possibilities, head or tails, and they are equally likely

So the probability of getting a tails is 1/2

P ( tails) = 1/2

A die has the numbers 1,2,3,4,5,6 .  There are 2 numbers greater than 4.  They are 5 and 6.  So there are 2 of the 6 choices that work.

P (number greater than 4)  = 2/6  = 1/3

See the dice chart

There are 36 possibilities when you roll the die.

There are 5 that sum to 8

P (2 die sum to 8) = 5/36

Answer:

Guy above is correct

Step-by-step explanation:

Answer:

Number of metric tons of corn produced by country A = 373 million MT

Number of metric tons of corn produced by country B = 234 million MT

Number of metric tons of corn produced by country C = 57 million MT

Step-by-step explanation:

From the given information we have

A+B+C = 664 ____equation(1)

A = B+C+82 ____equation(2)

B = C + 177 ____equation(3)

1) Plugging in B=C+177 into equation 2, we get

A = B+C+82

=> A = (C+177) + C +82

=> A = C+177+C+82

=> A = C +C +177+82

=> A= 2C +  259 ____let it be equation (4)

2) Plugging in A=2C+259 from equation 4 and B=C+177 from equation 3 into the equation 1, we get

A+B+C = 664

=> (2C+259)+(C+177)+C = 664

=> 2C+C+C+259+177 = 664

=> 4C + 436 = 664

3) Subtracting 436 from both the sides, we have

4C + 436 - 436 = 664 - 436

4) Cancelling out +436 and -436 from the left side, we get

4C = 228

5) Dividing both the sides by 4, we get

[tex]\frac{4C}{4} = \frac{228}{4}[/tex]

6) Cancelling out the 4's from the left, we get

C = 57

7) Plugging in C=57 into the equation 3, we get

B = C + 177

=> B = 57+177

=> B = 234

8) Plugging in B=234 and C=57 into the equation 1, we get

A+B+C = 664

=> A+234+57=664

=> A + 291= 664

9) Subtracting 291 from both the sides, we get

A + 291 - 291 = 664 - 291

10) Cancelling out +291 and -291 from the left side, we get

A = 373

So, A = 373, B= 234, C=57

Answer:

75%

Step-by-step explanation:

To calculate the percent increase or decrease, we:

The population of the town originally had 8,000 in 1992. In 1997, the population is 14,000.

The towns population increase by 75%

To find the percent increase in the population from 1992 to 1997, subtract the initial population from the final population, divide by the initial population, and multiply by 100, resulting in a 75% increase.

To calculate the percent increase in the population of the town from 1992 to 1997, follow these steps:

Therefore, the percent increase in the population from 1992 to 1997 was 75%.

w - width

2w - length (l)

30 cm - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 30    divide both sides by 6

w = 5 cm

2w = 2(5) = 10

l = 10 cm

The area of a rectangle: A = lw.

Substitute:

A = (5)(10) = 50

Answer:

y=-(3/4)x-5

Step-by-step explanation:

First we must write our equation in slope intercept form:

[tex]y=mx+b[/tex]

Where m is slope and b is the y-intercept.

[tex]4x-3y=12\\\\-3y=-4x+12\\\\y=\frac{4}{3}x-4[/tex]

Now we will find a line that is perpendicular to [tex]y=\frac{4}{3}x-4[/tex]

To do this we will get the negative inverse of our original slope which is 4/3 and the negative inverse is: [tex]-\frac{3}{4}[/tex].

Now we must determine our y-intercept for the perpendicular line by using the slope calculated above and plugging it in to the following equation:

[tex]y=m(x-x_1)+y_1[/tex]

Where m is the slope, x1 = -8 and y1=1 and so:

[tex]y=-\frac{3}{4}(x-(-8))+1\\\\y=-\frac{3}{4}x-\frac{24}{4}+1\\\\y=-\frac{3}{4}x-6+1\\\\y=-\frac{3}{4}x-5[/tex]

Answer:

The equation of the line would be y = -2x + 3

Step-by-step explanation:

In order to find the equation of the line, start by using point-slope form with the known information.

y - y1 = m(x -x1)

y - 1 = -2(x - 1)

Now that we have this, solve for y.

y - 1 = -2x + 2

y = -2x + 3

Answer:

∠6 > ∠3 is TRUE.

Step-by-step explanation:

We know that acute angle is less than 90 degree while obtuse angle is more than 90 degree. By looking at the given angles, we can easily determine which angle is obtuse or acute. then we can decide which angle is bigger to find the answer.

∠10 > ∠7

FALSE;

Because∠10 is acute while ∠7 is obtuse.

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

∠6 > ∠3

TRUE;

Because∠3 is acute while ∠6 is obtuse.

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

∠9 > ∠11

FALSE;

Because∠9 is acute while ∠11 is obtuse.

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

∠8 > ∠11

FALSE;

Because∠8 is acute while ∠11 is obtuse.

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

Answers:

a) Choice D -- Graph is discrete due to b only taking on whole number values (b = 0, b = 1, b = 2, etc)

see the attached image below for the graph

---------

b) She bought 9 basketballs

====================================================

Explanation for part A

To make a table, we simply replace every copy of 'b' with a positive whole number. So for instance, replace b with 0 and we get

a = 18*b = 18*0 = 0

Therefore b = 0 leads to a = 0 meaning buying 0 basketballs cost the coach $0

If b = 1, then a = 18 because

a = 18*b = 18*1 = 18

So 1 basketball costs $18 as expected

2 basketballs cost a total of $36 and we see that as shown below

a = 18*b = 18*2 = 36

This pattern continues however long as you need. Each row of the table represents an ordered pair of (b,a) values. Unfortunately your teacher made 'b' the independent variable meaning that it must come first even if the temptation is to put 'a' first in the ordered pair due to alphabetical order.

To graph this function, we just plot the points from the table. Each row is an ordered pair so it represents 1 point. We do NOT connect the dots with a straight line. Why not? Because we can't buy half a basketball, so the point with b = 1/2 = 0.5 wouldn't make any sense, so it's no use to us. The fact we have disconnected points as the graph shows visually tells us that we have a discrete graph. Connecting the dots would make the graph continuous.

Once again, have a look at the image attached below for the table and graph.

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

Explanation for part B

The equation in part A helps us find the pre-tax total cost. If that cost is $162, then a = 162 and b is...

a = 18*b

162 = 18*b

18*b = 162

18*b/18 = 162/18

b = 9

So she bought 9 basketballs

This is represented as point J(9,162) on the graph below.

Answer:

m∡1 + m∡2 = 180

Step-by-step explanation:

m∡1 + m∡2 = 180

This is because supplementary means they add up to 180°.

Answer:

$33,476.00

Step-by-step explanation:

Just add them all together

Answer:

it is a fifty fifty chance

Step-by-step explanation:

if they are the same number it is always a fifty fifty chance

Answer:

10.82 is the answer

Step-by-step explanation:

Answer:

Motorcycle will complete the 540 mile trip in 11.25 hr.

The car will complete it 2.25 hours less, or 9 hours.

The speed of the car therefore is 540/9 = 60 mph.

60t + 48t = 540

108t = 540

t = 5

So they will meet in 5 hours, after which time the motorcycle will have traveled 48*5 = 240 miles

and the car will have traveled 60*5 = 300 miles.

Hope this help

Step-by-step explanation:

Answer:

Total = 686000 meters for 10 weeks 7 days a week.

Step-by-step explanation:

Let's solve this by doing the increase on just 1 training day per week. Then we can find the grand total for 7 days a week by multiplying by 7

a = 8000

n = 10

d = 400

Sum = (a + L)*n/2

Sum = (8000 + 11600)*10/2

Sum = 19600 * 10/2

Sum = 98000 meters.

This total represents 1 training day a week.

The total amount is 7 times this figure.

Total = 7 * 98000 = 686 000 meters.

[tex]\begin{cases}4x+2\ge14\\-21x+1<22\end{cases}[/tex]

In the first inequality, we have

[tex]4x+2\ge14\implies4x\ge12\implies x\ge3[/tex]

In the second, we have

[tex]-21x+1<22\implies-21x<21\implies x>-1[/tex]

The solution to the system is the intersection of these two intervals, which would be [tex]x\ge3[/tex].

Answer:

3 and 4

Step-by-step explanation:

We apply 2 transformations here.

f(x)  ----> f(x + a) - this is  a shift of a units to the left.

f(x) ---- > f(x) + a - this is a shift of a units vertically up.

x - 1  ----> x + 2  shifts  it 3 units to the left.

3 ---->5  shifts it 2 units up.

Answer:

Options 3 & 4

Step-by-step explanation:

Recall, an exponential function has the basic form  

[tex]y=ab^{x+h}+k[/tex].

Thus [tex]f(x)=2^{x-1} +3[/tex] is shifted to the right 1 unit and up 3 units.\\

This means that [tex]g(x)=2^{x+2}+5[/tex] is shifted to the left 2 units and up five units.

Remember it had already been shifted up 3 so, moving up to 5 is a movement of 2 units. Option 3 is correct.

Also, remember the function started 1 unit to the right and then shifted left to 2. This would be 1--2=3 units in total were shift from f(x) to g(x). This makes Option 4 correct too.

Answer:

-15 is how many tests per hour i think, and 78 is how many tests total

Step-by-step explanation:

= 78 − 15ℎ

1 hour would be

78-(15x1)=63

2 hours would be

78-(15x2)=48

and so on.

Final answer:

The value 78 represents the initial number of tests Mrs. Hool has, while -15 represents the rate at which she grades tests per hour.

Explanation:

The values 78 and -15 in the equation represent the initial number of tests that Mrs. Hool has and the rate at which she grades the tests per hour, respectively.

The value 78 is the initial number of tests that Mrs. Hool has left to grade. This means that when she starts grading, she has 78 tests remaining.

The value -15 represents the rate at which Mrs. Hool grades the tests per hour. It indicates that for every hour she works on grading, she is able to complete 15 fewer tests than what she started with. In other words, the number of tests she has left decreases by 15 for every hour she works.

than anwser is 22% or 0.22