6. A line passes through (1, -5) and (-3, 7).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in slope-intercept form.

Answer:

Value of Number = 8

Step-by-step explanation:

Consider the equation below;

[tex]If x - " A Number " -\\( 2 * x ) - 5 = x + 3,\\[/tex]

Now using this equation let us solve for x;

[tex]( 2 * x ) - 5 = x + 3 - Take ( 2 * x ) - 2x,\\2x - 5 = x + 3 - Add 5 on Either Side,\\2x = x + 8 - Subtract x From Either Side,\\\\x = 8, ( Solution )\\\\Conclusion ; x = 8[/tex]

Knowing this, we can say;

[tex]Value of Number = 8,\\if x - Value of Number ( Given ),\\\\Solution ; Value of Number = 8[/tex]

The value of unknown number x will be 8.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have been given a statement as;

"five less than 2 times a number is equal to the sum of the number and 3"

Let the unknown number be x.

So, from the given statement,

2x- 5 = x + 3

Subtract x on both sides;

2x- 5 = x + 3

2x- 5 -x = x + 3 - x

x - 5 = 3

Add 5 on both sides;

x - 5 = 3

x = 8

Therefore, the value of unknown number x will be 8.

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Answer:

Assuming the height is still 1 your answer would be 700

Step-by-step explanation:

Answer:

probably jay z albulm 4:44

Step-by-step explanation:

Step-by-step explanation:

f(x) = ax + b

a = -2/3

b = 6

f(x) = -2/3x + 6

Fx x

F(x) = -4/3x² + 6x

F(9) - F(0)

The area of the yellow part is 0.5 * 9 * 6 = 27

______________________________

Let the shares be X and 6x

X+6x=350

or,7x=350

or,X=350/7

X=50

Replacing value,

6x=6*50=300

So one person gets $ 50

Another person gets$300

Hope it helps

Good luck on your assignment

___________________________

Answer:

1/7 x 350 = £ 50

6/7 x 350 = £ 300

Answer:

Step-by-step explanation:

Denominators are 5 and ( x+2)

As there is no common factors, to find the lowest common denominator multiply them

LCD = 5*(x +2)

Answer:

To find the Hypotenuse the Pythagoras theorem is used

h² = a² + b²

h = hypotenuse

a = 15cm

b = 8cm

h = ?

h² = 15² + 8²

h = √225 + 64

h = √289

h = 17cm

The Hypotenuse is 17cm

Hope this helps.

Answer:

Step-by-step explanation:

6

Take the higher number and subtract the next lower value. It will tell you the difference.

17-11=6

Answer:

A) 6

Step-by-step explanation:

Answer:

The answer is option B.

Hope this helps.

Answer:

B

Step-by-step explanation:

Answer:

60 - 1/4x = 24

Step-by-step explanation:

Answer:

7,5 kg = 19,20.  

Step-by-step explanation:

19,20/7,5

= 2,56 $

(2,56 * 7,5 =19,20)

Answer:

the graph corresponds to function "D"  [tex]f(x)=3\,(\frac{1}{5} )^x[/tex]

Step-by-step explanation:

Since the graph shown corresponds to an exponential "decay" (the function decreases as we move from left to right), the base of the exponent has to be a number smaller than 1 (one). So we examine the only two options that give such (options C and D which have fractions as the base - 1/3 and 1/5 respectively)

From there, we analyze which of the two functions satisfies the crossing of the y-axis at (0,3) which is clearly shown in the graph:

We study both:

function C at x = 0 gives:

[tex]f(x)= 5\,(\frac{1}{3})^x\\f(0)=5\,(\frac{1}{3})^0 \\f(0)=5\,(1)\\f(0)=5[/tex]

while function D at x = 0 gives:

[tex]f(x)= 3\,(\frac{1}{5})^x\\f(0)=3\,(\frac{1}{5})^0 \\f(0)=3\,(1)\\f(0)=3[/tex]

Therefore, the graph corresponds to function "D"

A correct option is an option (d)

From the given graph the function is increasing, therefore the base of the exponent must be greater than 1

And the best suited is the first, as it passes through the point,

y = 3

If you substitute x = 0 in the function result you have to give,

y = 3 and intersect the y-axis at that point

So, the required function is [tex]f(x)=3\times (\frac{1}{5} )^x[/tex]

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Answer:

B. y ≥ 1/3 x - 1  

Step-by-step explanation:

y =  mx + b

b = - 1,

m = rise/ run = 1/3

y = 1/3 x - 1  is equation of the line.

Shading is over the line, so

y ≥ 1/3 x - 1  

Answer:

Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model).

Step-by-step explanation:

hope this helps

Answer:

x = 3 and x = 3

Step-by-step explanation:

The given equation is

2x² - 12x + 18 = 0

Divide both sides by 2:

x² - 6x + 9 = 0

We need two numbers that will add up to -6 and their product is 9.

The two numbers are -3 and -3.

=> x² - 3x - 3x + 9 = 0

x(x - 3) - 3(x - 3) = 0

(x - 3)(x - 3) = 0

x = 3 and x = 3

Answer:

[tex] \sqrt 54[/tex]

[tex] \sqrt 9.\sqrt 6[/tex]

[tex] \sqrt {27}.\sqrt 2 [/tex]

Step-by-step explanation:

[tex]3 \sqrt{6} = \sqrt{ {3}^{2} \times 6 } = \sqrt{9 \times 6} = \sqrt{54} \\ [/tex]

Also,

[tex] \sqrt 9.\sqrt 6[/tex]

&

[tex] \sqrt {27}.\sqrt 2 [/tex]

The right options are option B,D and F

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

A. y = -14

Step-by-step explanation:

Subtract 9 from its self and from 23 in order to isolate -y

-y + 9 = 23

- 9 -9

0 14

-y is now Isolated.

-y = 14

Generally, when you have a letter representing a number by itself such as -y, it is indicated that therecis always a 1, example -y = -1y, x = 1x, however 3y does not equal 13y or 31y. 3y already has a number in front of it so therefore, there is no need to include the number 1 in front of y.

Because -y is the same as -1y, that is a multiplation representation. -y is the same as -1 x y so the next step is to isolate y from -1. In order to do that, you will need to divide -1 by 1 and 14 by 1. (Remember, (-) (-) = + and (-) (+) = - and (+) (+) = +.)

-y = 14

-1 -1

y = -14

Answer:

20 servings

Step-by-step explanation:

Four quarters per pound

5(4)=20

Answer:

she can make 20 servings

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

it will be easier to do calculations later if you simplify first

in this case you did the best and shortest way

you could rewrite

(8-4√2) /2 + ( 6+4√2)/ 2 as

4-2[tex]\sqrt{2}[/tex]  + 3 + 2[tex]\sqrt{2}[/tex] and then 7 + 4[tex]\sqrt2[/tex]

Answer:

14/11

Step-by-step explanation:

A rational number times a rational number is rational

A rational number is written as a/b

14/11 * 1/2 = 7/11

This is rational

Answer:

84ft

Step-by-step explanation:

w = 2/3(L)

if 280 feet of fencing can enclose the garden,therefore the perimeter is 280 feet

perimeter = 2L + 2W

but W=2/3(L)

therefore, perimeter = 2L + 2(2/3L)

P= 2L + 4/3(L)

P= 10/3(L)

but P= 280

therefore 280= 10/3(L)

L = (3×280)÷10

L= 84 feet

He will require 2.79 cubic feet of potting soil to fill the planter, which is a rough estimate.

The product of a cylinder's base area and height provides the formula for calculating the cylinder's volume. A cylinder's volume is equal to πr²h cubic units.

Given, A gardener has a cylindrical planter that has a diameter of 16 inches and is 2 feet deep.

From the general formula of volume of cylinder =  πr²h cubic units

in our case

r = 16 / 2 = 8 inches

Since 1 feet = 12 inches

r = = 8/12 feet = 2/3 feet

h = 2 feet

The volume of platter = π * 2/3 * 2/3 *2

The volume of the platter = 2.79 ft³

Therefore, the approximate number of cubic feet of potting soil that he will need to fill the planter is 2.79 ft³.

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Answer:

308, 398, 421, 433, 570

Step-by-step explanation:

To start we know the smallest is 308 cans, so that is the first class.

Next, it says the range is 262. The range is maximum minus the minimum. Since we know the minimum(308), that means 308 + 262 = 570 and 570 is the maximum or the class with most collected cans.

Then, it says the median or the middle number is 421, the middle number in a class is 3. So, the third class collected a total of 421 cans.

After that, it says the two classes in the three hundred, or the first and second class, has a total of 706 cans. So, if we do 706 - 308 we get the second class. Which collected 398 cans.

Finally, it says the total all the class collected is 2130. So, if we add all the values we have know and subtract it from the total of all the class we get the missing class or the fourth class. So, 308 + 398 + 421 + 570 = 1697, and 2130 -1697 = 433. Which the fourth class.

Least to greatest:

308

398

421

433

570

Answer:

1000 seconds

Step-by-step explanation:

You can start by finding the unit rate for each of them to lay down a tile. That is, how many tiles they can lay down in one second. Ralph can lay one down in 1/5 of a second, while Bob takes 1/4. 1/5+1/4=4/20+5/20=9/20 of a tile per second. Dividing 450 by 9/20, you get 1000 seconds. Hope this helps!

Answer:

16 to 25 or 16/25 or 16:25

Step-by-step explanation:

Answer:

C!

Step-by-step explanation:

So, it's actually very simple!

If you don't know, the domain of a function is the set of x-values that make the equation true. The range, which we are trying to find, is the set of f(x), or y values that are possible.

Now, notice how in the graph, y-values don't go below 1. So there is our limit. There is nothing else limiting the y-values the other way, so its basically a single equality.

y=1 is included in the function, of course, as it goes on y=1.

So, it's [tex]y\geq 1[/tex]

Hope this helps!

Answer:

C

Step-by-step explanation:

the guy above me is right because i got a 100% on my test.

Answer:

1) Each group is composed of 10 people. They either saw results or don't saw results.

          saw results      no results   Total

A             6                        4              10  

B             7                         3              10  

C             5                         5             10  

D             4                         6              10  

Total      22                        18            40  

Probability of a group seeing results:

Group A: 6/10 = 0.6

Group B: 7/10 = 0.7

Group C: 5/10 = 0.5

Group D: 4/10 = 0.4

Probability of a group not seeing results:

Group A: 4/10 = 0.4

Group B: 3/10 = 0.3

Group C: 5/10 = 0.5

Group D: 6/10 = 0.6

2) Groups A and B  received the Power Pill.

What is the probability that a person saw results, given they received the power pill?

(6+7)/20 = 0.65

Groups C and D  received the placebo.

What is the probability that a person saw results, given they received a placebo?

(5+4)/20 = 0.45

3) What is the probability that a person received the placebo, given they did not see results?

(5+6)/18 = 0.61

What is the probability that a person received the power pill, given that they did not see results?

(3+4)/18 = 0.39

Answer:

Results

No Results

Totals

Group A

6

4

10

Group B

7

3

10

Group C

5

5

10

Group D

4

6

10

Totals

22

18

40

Using the data above, please calculate each probability:

The probability for Group A to see results ___15%___.  

The probability for Group A to see no result___10%____.  

The probability for Group B to see results __17.5%____.  

The probability for Group B to see no result___7.5%____.  

The probability for Group C to see results ___12.5%___.  

The probability for Group C to see no result___12.5%____.  

The probability for Group D to see results ___10%___.  

The probability for Group D to see no result___15%____.

TASK 2 Part 2

What is the probability that a person saw results given they received the power pill? __65%____  

What is the probability that a person saw results given they received the placebo? ___45%___  

Show your work and explain in terms of the study using the data from Part 1

The probability that a person saw results and a power pill is 65%. The probability that the person was given the placebo and saw results is 45%. 65% of the people that were given the pill saw results, and 45% did not.

TASK 2 Part 3

What is the probability that a person received the placebo given that they did not see results?  

61.111111%

What is the probability that a person received the power pill given that they did not see results?  

38.88888%

Show your work and explain in terms of the study using the data from Part 1

PB- (5+6)/18 = 0.61 x 100

PP- (3+4)/18 = 0.38 x 100

Step-by-step explanation:

Answer:

Surface are = 94.24 cm2

Cylinders =4,244

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Surface area of a cylinder = 2π (diameter/2) h + 2π (diameter /2)²  

Replacing with the values given

s = 2π (2/2) 14 + 2π (2/2)²

s = 87.96+ 6.28 =94.24 cm2

Since:

1 m2 = 10,000 cm2

40 m2 = 400,000 cm2 (area that one can of paint covers)

We have to divide the area that one can of paint covers by the surface area of each cylinder:

400,000/94.24 = 4244 cylinders