What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1?

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

–8
–5
0
6

Answer:

9/16

Step-by-step explanation:

18522/32928= 0.5625 which can be reconverted to a fraction, which in this case that fraction is 9/16

Answer:

1451/31914

Step-by-step explanation:

hope this helps :) have a nice day

Answer:

c= 9

Step-by-step explanation:

first you would need to get the variable alone

next you would take the one and since it is subtraction you would do the opposite addition

then you would add one to each side and the two ones cancel each other out so the you add 8 and 1 and get nine so c would equal 9

Steps to solve:

c - 1 = 8

~Add 1 to both sides

c - 1 + 1 = 8 + 1

~Simplify

c = 9

Best of Luck!

Answer:

C

Step-by-step explanation:

Given the logarithmic equation

[tex]\log_4x+\log_4(x-3)=\log_4(-7x+21)[/tex]

First, notice that

[tex]x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x<21\ x<3[/tex]

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

[tex]\log_4x+\log_4(x-3)=\log_4x(x-3),[/tex]

then

[tex]\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3[/tex]

Hence, [tex]x=3[/tex] and [tex]x=-7[/tex] are extraneous solutions

Answer:

x=4

Step-by-step explanation:

6k-25=7-2k

6k-25+25=7-2k+25

6k=7-2k+25

6k+2k=7-2k+2k+25

6k+2k=8k

7+25

8k=32

x=32÷8

x=4

Final answer:

The maximum number of volts that can be placed across the resistor is 20 volts.

Explanation:

The maximum number of volts, E, that can be placed across a resistor is given by the formula E = √(P * R), where P is the number of watts of power that the resistor can absorb and R is the resistance of the resistor in ohms. To find E, we can substitute the given values for P and R into the formula and solve:

E = √(2 * 200) = √(400) = 20 volts

Therefore, the maximum number of volts that can be placed across the resistor is 20 volts.

The maximum number of volts E that can be placed across the resistor is 20 volts.

The maximum number of volts, E, that can be placed across the resistor is given by the square root of the product of power P and resistance R. Therefore, E can be calculated as follows:

[tex]\[ E = \sqrt{P \times R} \][/tex]

[tex]\[ E = \sqrt{2 \text{ watts} \times 200 \text{ ohms}} \][/tex]

[tex]\[ E = 20 \text{ volts} \][/tex]

 The formula provided in the question is [tex]\( E = \sqrt{P \times R} \),[/tex] where E is the maximum number of volts that can be placed across a resistor, P is the power in watts, and R is the resistance in ohms.

This formula is derived from the power equation [tex]\( P = \frac{V^2}{R} \),[/tex]where V is the voltage across the resistor.

Given that the power P is 2 watts and the resistance R is 200 ohms, we substitute these values into the formula to find E:

[tex]\[ E = \sqrt{2 \times 200} \][/tex]

[tex]\[ E = \sqrt{400} \][/tex]

 The square root of 400 is 20, so the maximum number of volts E that can be placed across the resistor is 20 volts.

This is the voltage at which the resistor will absorb the maximum power of 2 watts without being damaged, assuming the resistor is operating at its maximum power rating.

Answer:

vertical

Step-by-step explanation:

Answer:

4x + 184 = 360

4x = 176

x = 44

Step-by-step explanation:

Lets check!

88 + 88 + 100 + 84 = 360

176 + 184 = 360

360 = 360

Answer:

im not sure sure but by the looks of it i think thats 3,6

Step-by-step explanation:

Answer:

slope of the given straight line in graph is -2

Step-by-step explanation:

Explanation:-

in given graph we have to choose points are A(0,3) on y-axis and B(1.5 , 0) on x- axis

let m be the slope of a line

by using slope formula is

[tex]m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

m = [tex]\frac{0-3}{1.5-0}[/tex]

m= -2

another points we have choose

in given graph we have to choose points are A(0,3) on y-axis and B(2.5 , -2)

slope of a line :-

let m be the slope of a line

by using slope formula is

[tex]m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

[tex]m = \frac{-2-3}{2.5-0}[/tex]

m= -2

where ever you will take point the slope of given straight line is

m = -2

Answer:

[tex]\large \boxed{\text{ 0.4 lb/ft}^{3}; 5}[/tex]

Step-by-step explanation:

1. Density

[tex]\begin{array}{rcl}\text{Density} & = & \dfrac{\text{Mass}}{\text{Volume}}\\\\& = & \dfrac{\text{4 lb}}{\text{10 ft}^{3}}\\\\& = &\textbf{0.4 lb/ft}^{\mathbf{3}}\\\end{array}\\\text{The density of the gas is $\large \boxed{\textbf{ 0.4 lb/ft}^{\mathbf{3}}}$}[/tex]

2. Specific gravity

Specific gravity (sp gr) is the ratio of the density of the density of a gas to the density of dry air at standard temperature and pressure.

At IUPAC standard temperature and pressure (0 °C and 100 kPa), dry air has a density of 0.080 lb/ft³.

[tex]\begin{array}{rcl}\text{Sp gr}& = & \dfrac{\rho_{\text{gas}}}{\rho_{\text{dry air}}}\\\\& = & \dfrac{\text{0.4 lb/ft}^{3}}{\text{0.080 lb/ft}^{3}}\\\\& = &\mathbf{5}\\\end{array}\\\text{The specific gravity of the gas is $\large \boxed{\mathbf{5}}$}[/tex]

The density is the ratio of mass to volume, while the specific gravity is the ratio of two densities

The values required are;

Given:

Mass of the gas = 4 lb

Volume occupied by the gas = 10 ft.³

Required:

Find the density and the specific gravity of the gas

Density:

[tex]Density = \dfrac{Mass}{Volume}[/tex]

Therefore, the density of the mass of gas is given as follows;

[tex]Density = \dfrac{4 \ lb}{10 \ ft.^3} = 0.4 \ lb/ft.^3[/tex]

The density of the gas = 0.4 lb/ft.³

Specific gravity:

The specific gravity, s.g. of a gas is the ratio of the density of the gas to the density of air

The density of air ≈ 0.0765 lb/ft.³

The specific gravity of the gas is therefore;

[tex]s.g. = \dfrac{0.4 \ lb/ft.^3}{0.0765 \ lb/ft.^3} = \dfrac{800}{153} \approx 5.23[/tex]

The specific gravity of the gas is approximately 5.23

Learn more about density and specific gravity here:

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Answer:

2/5

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

40%=40/100=4/10=2/5

Answer:

(2, - 3 )

Step-by-step explanation:

Given the 2 equations

2x - 3y = 13 → (1)

x + 2y = - 4 → (2)

Rearrange (2) expressing x in terms of y by subtracting 2y from both sides

x = - 4 - 2y → (3)

Substitute x = - 4 - 2y into (1)

2(- 4 - 2y) - 3y = 13 ← distribute and simplify left side

- 8 - 4y - 3y = 13

- 8 - 7y = 13 ( add 8 to both sides )

- 7y = 21 ( divide both sides by - 7 )

y = - 3

Substitute y = - 3 into (3) for corresponding value of x

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

Solution is (2, - 3 )

Answer:

37.5%

Step-by-step explanation:

1/8 is 12.5% so multiply 12.5 x 3.

Answer:62.5

Step-by-step explanation:

1. if 3/8 is gone, that means 5/8 is present , which would make it 62.5 percent

the LCM of 21 and 105 is 105.

Answer:

The answer to your question is 105

Step-by-step explanation:

To get the least common factor dividing both numbers by the prime numbers starting from 2.

But these numbers are not multiples of 2, try 3

                                                           21   105   3

These numbers are not multiples of 3 let's try 5                                                                    

                                                            7     35  5  

These numbers are multiples of 7     7       7   7

                                                            1        1

The LCM is the product of the prime numbers = 3 x 5 x 7 = 105

Answer:

Carlos would pay lower out-of-pocket costs if he picks over plan B.

Step-by-step explanation:

Let's make the comparison between plan A and plan B, this way:

Medicals bills = US$ 6,350

Plan A

6,350 - 1,200 = 5,150 * 30% = 5,150 * 0.3 = 1,545

Total out-of-pocket costs = 1,200 + 1,545 = $ 2,745

Plan B

6,350 - 1,500 = 4,850 * 25% = 4,850 * 0.25 = 1,212.50

Total out-of-pocket costs = 1,500 + 1,212.50 = $ 2,712.50

Carlos would pay lower out-of-pocket costs if he picks over plan B.

Answer:

Part A) [tex]A_s=\frac{\pi r^{2}}{360^o}{\theta}[/tex]

Part B) option 1,option 4

Step-by-step explanation:

Part A) Derive the formula for the area of a sector

we know that

The area of circle is equal to

[tex]A=\pi r^{2}[/tex]

The area of circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector  [tex]A_s[/tex]  by a central angle of ∅ degrees

[tex]\frac{\pi r^{2}}{360^o}=\frac{A_s}{\theta}[/tex]

[tex]A_s=\frac{\pi r^{2}}{360^o}{\theta}[/tex]

Part B) Verify each case

case 1) we have

radius = 5 cm

angle = 120°

area = 26.2 cm 2

Find the area of the sector and then compare with the value of the given area

assume

[tex]\pi=3.14[/tex]

substitute the given values

[tex]A_s=\frac{(3.14)(5)^{2}}{360^o}{120^o}[/tex]

[tex]A_s=26.2\ cm^2[/tex]

so

The given value of area is correct

case 2) we have

radius = 4 cm

angle = 105°

area = 16.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

[tex]\pi=3.14[/tex]

substitute the given values

[tex]A_s=\frac{(3.14)(4)^{2}}{360^o}{105^o}[/tex]

[tex]A_s=14.7\ cm^2[/tex]

so

The given value of area is not correct

case 3) we have

radius = 6 cm

angle = 85°

area = 23.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

[tex]\pi=3.14[/tex]

substitute the given values

[tex]A_s=\frac{(3.14)(6)^{2}}{360^o}{85^o}[/tex]

[tex]A_s=26.7\ cm^2[/tex]

so

The given value of area is not correct

case 4) we have

radius = 7

angle = 75°

area = 32.1 cm 2

Find the area of the sector and then compare with the value of the given area

assume

[tex]\pi=3.14[/tex]

substitute the given values

[tex]A_s=\frac{(3.14)(7)^{2}}{360^o}{75^o}[/tex]

[tex]A_s=32.1\ cm^2[/tex]

so

The given value of area is correct

Answer:

It would be 4 to 80

Step-by-step explanation:

Answer:

28 boys

Step-by-step explanation:

For every 7 boys there are, there are 20 girls. It is given to us that there are 80 girls. To solve, divide 80 with 20:

80/20 = 4

Next, multiply 4 with 7:

4 x 7 = 28

There are 28 boys at the school dance.

Answer:

600

Step-by-step explanation:

first you need to find the calories for the entire batter:

12 muffins x 250 cal = 3000 cal

then you divide the total calories by 20:

3000/20 = 150

then multiply 150 by 4:

150 x 4 = 600

To find the caloric content of each mini-muffin, divide the total calories in the recipe by the new yield to find that each mini muffin is 150 calories. Consuming 4 mini muffins will total 600 calories.

The caloric content of a full-size muffin is 250 calories. If we reduce the size of the muffins we make from the recipe, it doesn't alter the total caloric content of the whole batch – it just redistributes those calories across more muffins. To calculate the number of calories in one mini-muffin, we need to divide the total number of calories in the entire recipe (250 calories/muffin * 12 muffins = 3000 calories) by the total yield of mini-muffins, which is 20. This results in 3000 calories/20 mini-muffins = 150 calories per mini-muffin. If you consume 4 mini-muffins, you'd be consuming 4 * 150 calories = 600 calories.

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#SPJ3

Answer:

1.28

Step-by-step explanation:

0.4 x 3.2 = 1.28

$50,000 is 0.881 % of $5,670,000

Solution:

We have to find what percentage is $50,000 of $5,670,000

Let "x" be the required percentage

Then, by given, we can say,

"x" percent of 5,670,000 is 50000

Here, "of" means multiplication

So the statement goes like this:

"x" percent multiplied with 5,670,000 is equal to 50000

Thus finally the expression becomes:

[tex]x \% \times 5670000 = 50000\\\\\frac{x}{100} \times 5670000 = 50000\\\\\text{Simplify the above expression }\\\\56700x = 50000\\\\567x = 500\\\\x = 0.881[/tex]

Thus $50,000 is 0.881 % of $5,670,000

Answer:

6/10

Step-by-step explanation:

#1. It helps to write everything out:

Sell price for boxes of cookies: $4.25x (x representing number of boxes)

Cost of each carton: $30y (y representing number of cartons)

The group bought 6 cartons, so we substitute y for 6:

30(6) = $180 they spent on the cartons.

Each carton contains one dozen boxes of cookies. In other words, 12 boxes of cookies. WIth 6 cartons purchased, we multiply 6 with 12 to get 72 boxes of cookies total they sold. Now we substitute x for 72:

4.25(72) = $306 they earned.

#2. The pattern is 2x + 5 = y where x represents the number of rides and 5 represents the admission. The y represents the total cost. Simply plug in the x's in the table into this equation to get the answer for y.

Answer:

no

Step-by-step explanation:

3=5(3)

3=15

false

Answer:

no

Step-by-step explanation:

Answer:

Step-by-step explanation:

think of any number : x

add 3 : x+3

double that : 2(x+3)

subtract 4 : 2(x+3)-4

cut in half (divide by 2) : (2(x+3)-4)/2

subtract original number : (2(x+3)-4)/2-x

if you simplify, you will end up with 1

Step by Step simplification

2(x+3) = 2x+6   double that

2x+6-4=2x+2    subtract 4 : 2(x+3)-4

(2x+2)/2 = x+1     cut in half (divide by 2)

x+1-x = 1      subtract original number

Answer: slope = 0

Step-by-step explanation:

The formula for calculating slope is given as :

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = 2

[tex]x_{2}[/tex] = 1

[tex]y_{1}[/tex] = 0

[tex]y_{2}[/tex] = 0

Substituting into the formula , we have

m = [tex]\frac{0}{-1}[/tex]

m = 0

The slope of the line passing through (2, 0) and (1, 0) is 0, indicating that the line is horizontal.

The slope of a line that passes through the points (2, 0) and (1,0) can be determined using the formula for slope, which is (y2 - y1) / (x2 - x1).

Plugging in the coordinates, we get (0 - 0) / (1 - 2), which simplifies to 0/-1.

The slope of this line is 0. This indicates that the line is horizontal because there is no change in the y-value as the x-value changes.

Option E

The sum of all possible values of y is 20

Solution:

Given that,

6x + 2y = 25

Where, xy > 0

We have to find the sum of all possible values of y if x is a positive integer

We can use values of x = 1, 2, 3, 4

For x = 5 and above, y will be negative

Substitute x = 1 in given equation

6(1) + 2y = 25

6 + 2y = 25

2y = 25 - 6

2y = 19

Divide both the sides of equation by 2

[tex]y = \frac{19}{2}[/tex]

Substitute x = 2 in given equation

6(2) + 2y = 25

2y = 25 - 12

2y = 13

Divide both the sides of equation by 2

[tex]y = \frac{13}{2}[/tex]

Substitute x = 3 in given equation

6(3) + 2y = 25

2y = 25 - 18

2y = 7

Divide both the sides of equation by 2

[tex]y = \frac{7}{2}[/tex]

Substitute x = 4 in given equation

6(4) + 2y = 25

24 + 2y = 25

2y = 25 - 24

2y = 1

Divide both the sides of equation by 2

[tex]y = \frac{1}{2}[/tex]

Now add all the values of "y"

[tex]\text{Sum of possible values of y } = \frac{19}{2} + \frac{13}{2} + \frac{7}{2} + \frac{1}{2}\\\\\text{Sum of possible values of y } = \frac{19+13+7+1}{2}\\\\\text{Sum of possible values of y } = \frac{40}{2}=20[/tex]

Thus sum of all possible values of y is 20

In this question, you're simplifying the expression.

Simplify:

2(x- 5) + 7x + 4

use distributive property

2x - 10 + 7x + 4

combine like terms

2x - 10 + 7x + 4

9x - 10 + 4

9x - 6

Answer:

9x - 6

Answer:

12 meter = 129.167

48 = 516.668

121  =1302.43

144 =1550

169 = 1819.1

Step-by-step explanation:

Final answer:

The area of a 12 meter square is calculated by squaring the length of the side, which results in 144 square meters.

Explanation:

The area of a square can be found by squaring the length of one of its sides. Since the given square has a side length of 12 meters, the area can be calculated as follows:

Area = side length * side length

Area = 12 m * 12 m

Area = 144 square meters

Answer:

It could be 9 or 23. It could also be many other things.

Step-by-step explanation:

The other side of the triangle has to be greater than 15 when added to 7 or greater than both when they are added together.