Write the point slope form of the equation of the line passing through the points (-5, 6) and (0.1).

Answer:

d. 8

Step-by-step explanation:

The volume of a sphere = 4/3πr³

Let the radius of the smaller sphere be r, then the volume of the large sphere will be 2 r

Finding the volumes of the 2 gives:

volume of large sphere = 4/3π (2r)³

= 32/3πr³

Volume of the smaller sphere = 4/3πr³

Dividing the two volumes we get the ratio of their volumes

32/3πr³÷4/3πr³= 8

Answer: Option d

[tex]\frac{V_2}{V_1}=8[/tex]

Step-by-step explanation:

The volume of a sphere is calculated using the following formula

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where r is the radius of the sphere and V is the volume.

If the radius of the small sphere is r and the volume is [tex]V_1[/tex] then:

[tex]V_1=\frac{4}{3}\pi r^3[/tex]

Let's call [tex]V_2[/tex] the volume of the large sphere. We know that it has a radius of 2r. So:

[tex]V_2=\frac{4}{3}\pi (2r)^3[/tex]

[tex]V_2=\frac{4}{3}*8\pi r^3[/tex]

Now we calculate the quotient of the volumes

[tex]\frac{V_2}{V_1}=\frac{\frac{4}{3}*8\pi r^3}{\frac{4}{3}\pi r^3}\\\\\frac{V_2}{V_1}=\frac{8r^3}{r^3}\\\\\frac{V_2}{V_1}=8[/tex]

The answer is the option d

Final answer:

A system of equations will have the solution (2,0) if, when substituting x=2 and y=0, both equations are satisfied. This can be a linear equation where the y-intercept is set to be the negative double of the slope, or a conic section represented by a quadratic equation that intersects the x-axis at x=2.

Explanation:

Systems of equations that will have a solution of (2,0) must satisfy the condition that when x=2 and y=0, both equations are true. Considering the information provided about quadratic and differential equations, to find a system with the solution (2,0), one can set up a system of any two equations and test if the point (2,0) satisfies them. For instance, any linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept, will have a solution of (2,0) if b is set to -2m. Similarly, a second-order differential equation can be constructed with known solutions, including the point (2,0).

A system with a linear equation y = mx - 2m, where m can be any value.

A homogeneous linear differential equation with boundary conditions that result in the point (2,0) being a solution.

A conic section represented by a quadratic equation that intersects the x-axis at x=2.

For example, the quadratic equation ax² +2hxy+by² = 0, can be factored into two linear factors with no constant term, which means it represents two lines intersecting at the origin. If one of these lines passes through the point (2,0), it would confirm that our solution fits this system as well.

Answer: 317.93

Step-by-step explanation:

317.93371 when rounded off to nearest hundred, we get 317.93.

Rounding off is the method by which a decimal integer is reduced to its nearest closer value of the next number . After the decimal point, if the value is greater than 5 we increment the numerical value by 1 and if the value is less than 5 we keep the numerical value intact.

The given value is 317.93371 .

Rounding off to nearest hundred means that we will get the rounded off value up to two decimal places.

We can see that the third decimal place is 3 which means that the second decimal place of the number will be kept intact.

Rounded off value is -  317.93 .

Thus, 317.93371 when rounded off to nearest hundred, we get 317.93.

To learn more about rounding off, refer -

https://brainly.com/question/48768

#SPJ2

The equation representing the population of the city is P = 50t + 8500. Substituting t=7 in this equation gives the estimated population in year 2017 as 8850 people.

The question is asking for the population of the town in a given year, given it's steadily increasing each year. The original population, in 2010, is 8500 people and each year the number of people increases gradually by 50.

The general equation for a line is y = mx + c, where m is the slope (the rate of change), c is the y-intercept (the initial value), x is the input (in this case, the number of years since 2010), and y is the output (the population).

In this case, m = 50 (because the population increases by 50 people per year), c = 8500 (the population in 2010) and x will be the number of years since 2010. Therefore, the equation for the population of the town is: P = 50t + 8500

To find the population in 2017, you substitute t=7 (because 2017 is 7 years after 2010) into the equation: P = 50*7 + 8500 = 8850

So the estimated population in 2017 would be 8850 people.

https://brainly.com/question/34334668

#SPJ2

Answer:

14.4 in

Step-by-step explanation:

2160/ 150= 14.4

Answer:

8,640 ft^2

Step-by-step explanation:

There are 144 square inches per square foot, therefore 144x60=8,640 ft^2

Step-by-step answer with explanations:

Recall that a coordinate pair such as (5,-1) has two components.

The first (5, -1) means that the point is situated at x=5.

The second (5, -1) means that the point is situated at y=-1.

Now, a horizontal line through (5,-1) means that ALL points on the line have y-coordinate equal to -1, so that any point with y=-1 will lie on this horizontal line.  An example would be (-2,-1).

A vertical line through (5, -1) means that ALL points on the line have x-coordinate equal to 5, so that any point with x=5 will lie on this vertical line.  An example would be (5,4).

Answer:

its D

Step-by-step explanation:

ur welcome =)

Answer:364.6

Step-by-step explanation:

Answer:

You MUST use parentheses around denominator 8+x, or ANY denominator that consist of more than a single number of variable. 

Also, don't use lower case and upper case interchangeably. 

In algebra, x and X are different, as are y and Y. 

f(x) = y = 3x/(8+x) 

Switch x and y, solve for y: 

x = 3y/(8+y) 

x(8+y) = 3y 

8x+xy = 3y 

8x = 3y−xy 

8x = y(3−x) 

y = f⁻¹(x) = 8x/(3−x)

I hope this helps, love 

Step-by-step explanation:

For this case we can raise a rule of three:

$ 58 ----------> 100%

$ 63 ----------> x

Where "x" represents the percentage equivalent to $ 63.

[tex]x = \frac {63 * 100} {58}\\x = \frac {6300} {58}\\x = 108.62[/tex]

Thus, the percentage increase is 8.62%

Answer:

The percentage of increase is 8.62%

Answer: 1 day, 21 hours, and 40 minutes

Step-by-step explanation: To make it less confusing, you can convert all of the days into hours (24 hours in a day)...

126 hours and 20 minutes-80 hours and 40 minutes

7580 minutes-4840 minutes=2740 minutes

We can convert 2740 minutes back into hours and days now...

1 day, 21 hours, and 40 minutes

Or....

Step-by-step explanation: Or you can just subtract, start with minutes and go up from there...

20-40 would be in the negatives and time can’t be negative, so you need to borrow from the hours. So hours is now at 5 and minutes is at 20+40 which is 80. And 80-40=40

We now have...

5 days, 5 hours, and 40 minutes-3 days and 8 hours.

Now we can do the hours...

5-8 also is negative, so we need to borrow from the days. Days is now at 4. There are 24 hours in a day so 24+5=29. Now we can subtract 29-8=21

Now we have 4 days, 21 hours, and 40 minutes

And 4-3 is 1, which means we have 1 day,

21 hours, and 40 minutes as our answer!

The difference between the given time frames 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes after performing the subtraction operation is 1 day, 13 hours, and 40 minutes.

The question is about an arithmetic operation involved in time. This arithmetic operation is subtraction. Given the time frames are 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes. Let's subtract the smaller time frame from the larger one.

So, the difference between 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes is 1 day, 13 hours, and 40 minutes.

https://brainly.com/question/10627828

#SPJ11

Answer:

D y= -2 (x-8)2 -3

Step-by-step explanation:

The equation of the new parabola will be y = -2(x + 2)² + 1. Then the correct option is A.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation of the parabola is given below.

y = -2(x - 3)² + 4

If this parabola is shifted 5 units to the left and 3 units down. Then replace x with x + 5 and subtract 3 from the equation.

Then the equation of the new parabola will be given as,

y = -2(x + 5 - 3)² + 4 - 3

y = -2(x + 2)² + 1

The condition of the new parabola will be y = - 2(x + 2)² + 1. Then, at that point, the right choice is A.

More about the equation of the parabola link is given below.

https://brainly.com/question/20333425

#SPJ2

To find the percentage of the monthly budget that housing represents in a circle graph, divide the housing cost ($175) by the total monthly expenses ($500) and multiply by 100. This calculation shows that housing accounts for 35% of the monthly budget.

When representing a monthly budget on a circle graph, or pie chart, you need to find out what percentage of the total budget each category represents. In this case, a young single person spends $150 on food, $175 on housing, and $175 on other items. To find the percentage that represents housing, we first need to calculate the total amount of monthly expenses which are $150 for food, $175 for housing, and $175 for other items, adding up to a total of $500.

Next, we calculate the percentage that the housing expense represents by dividing the housing cost by the total expenses and then multiplying by 100 to get a percentage:

Therefore, housing represents 35% of the total monthly budget on the circle graph.

ANSWER

[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]

EXPLANATION

The given equation is

[tex] {x}^{2} - 5x - 5 = 0[/tex]

The solution is given by the formula

[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

where a=1, b=-5, c=-5

We substitute into the formula to get;

[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)( - 5)} }{2(1)} [/tex]

We simplify to get,

[tex]x = \frac{ 5 \pm \sqrt{ 45} }{2} [/tex]

The solutions are:

[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]

The equation has no complex roots.

Answer:

x =  [5 + 3√5]/2   or x =  [5  -3√5]/2

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

To find the solutions of given equation

It is given  x² - 5x - 5 = 0

here a = 1, b = -5 and c = -5

x = [-b ± √(b² - 4ac)]/2a

 =  [--5 ± √((-5)² - 4*1*-5)]/2*1

 = [5 ± √(25 + 20)]/2

 =  [5 ± √(45)]/2

 =  [5 ± 3√5]/2

x =  [5 + 3√5]/2   or x =  [5  -3√5]/2

Answer:

9

Step-by-step explanation:

negative times a negative is a positive. Negative three squared is 9.

Answer:

[tex]e^{ln(12)}=12[/tex]

Step-by-step explanation:

I suppose your intended expression is;

[tex]e^{ln(12)}[/tex]

The exponential function, e, and the natural logarithm function, ln, are inverses of each other;

[tex]e^{lnx}=x\\\\lne^{x}=x[/tex]

Therefore, our expression becomes;

[tex]e^{ln(12)}=12[/tex]

Answer:

Both the lines would have the same slope since they are parallel. The lines would not however have the same y-intercept.

Step-by-step explanation:

This is because in order for lines to be parallel the lines must have the same slope, otherwise they would meet at some point. They would not have the same y-intercept because if both the y-intercept and the slope were the same it would be the same line.

Answer:

Both lines are parallel, so they have the same slope. However, the y-intercepts of the lines are not the same. For the lines to be parallel, the slopes of the lines must be the same. If both the y-intercept and slope are the same, they are the same line, so they do not have the same y-intercept.

Answer:

P(A|B) = 0.30

Step-by-step explanation:

P(A) = 0.30

P(B) = 0.60

To Find:

P(A|B) = ?

P(A|B) means probability of occurring of event A when event B has occurred.

P(A|B) = P(A∩B)/P(B)

We know that for independent events;

P(A∩B) = P(A).P(B)

So, we have:

P(A|B) = P(A).P(B)/P(B)

P(A|B) = P(A)

So, probability of occurrence of an independent event does not depend on the probability of a different event.

The answer is:

The velocity with which the ball can be thrown to have a maximum range of 20 meters is equal to 14 m/s.

[tex]u=14\frac{m}{s}[/tex]

To solve the problem and find the velocity, we need to isolate it from the equation used to calculate the maximum horizontal range.

We have the equation:

[tex]R=\frac{u^{2} }{g}[/tex]

Where,

R is the maximum horizontal range.

u is the initial velocity.

g is the gravity acceleration.

Also, from the statement we know that:

[tex]R=20m\\g=9.8\frac{m}{s^{2} }[/tex]

So, using the given information, and isolating, we have:

[tex]R=\frac{u^{2} }{g}[/tex]

[tex]R*g=u^{2}[/tex]

[tex]u^{2}=R*g=20m*9.8\frac{m}{s^{2} }=196\frac{m^{2} }{s^{2} }\\\\u=\sqrt{196\frac{m^{2} }{s^{2}}}=14\frac{m}{s}[/tex]

Hence, we have that the velocity with which the ball can be thrown to have a maximum range of 20 meters is equal to 14 m/s.

[tex]u=14\frac{m}{s}[/tex]

Have a nice day!

Answer:

The velocity with which a ball must be thrown to have a maximum range of 20 m is 14 m/s.

Note that this problem means to find the magnitude of the velocity and not the direction (it is implicit in the formula that the angle of the launch is 45°).

Explanation:

You just must use the given equation for the maximum horizontal range of a projectile and solve for u which is the unknwon:

Solve for u:

Take square root from both sides:

Answer:

The correct option is C.

Step-by-step explanation:

In a right triangle, the hypotenuse has endpoints XY as shown in the given graph.

Since XY is hypotenuse and Z is third vertex in the triangle, therefore XZ and YZ must be perpendicular at point Z.

The coordinates of X are (-4,2), so draw a vertical line x=-4 and a horizontal line y=2.

The coordinates of Y are (-1,-3), so draw a vertical line x=-1 and a horizontal line y=-3.

From the below figure it is clear that the vertcal and horizontal lines intersect each other at [tex]Z_1[/tex] and [tex]Z_2[/tex].

It is given that Z is located in the second quadrant with integer coordinates, therefore the only possible location of Z is

[tex]Z=Z_2(-1,2)[/tex]

Since the length of YZ₂ is 5 units and Z=Z₂, therefore the length of YZ is 5 units.

Hence the correct option is C.

Hello There!

There are 32.5 kilograms in 32,500 grams.

STEPS

Write the number of grams

Divide by 1,000 because a kilogram is 1,000 grams

Answer: infinite solutions

Step-by-step explanation:

If the left side equals the right side, then every value you input for the variable will make a TRUE statement --> which means there are infinite solutions.

For example: x + 1 = x + 1

Any value you choose for "x" will result in a true statement.

This is because they are the same line, which is another way of showing that they have infinite solutions.

The linear equation is an identity, which means that it has infinite solutions.

We define an identity as an equation where we have the exact same expression in both sides of the equation.

For example, in:

f(x) = f(x).

Where f(x) is a function.

A easier example can be:

x + 5 = x + 5

Notice that we have the exact same thing in both sides, this is what Jilana gets when solving her linear equation.

This means that for any given value of x, the equation will be true. So, x can be any real value, which means that there are infinite solutions for the equation.

If you want to learn more about linear equations, you can read:

https://brainly.com/question/4074386

Answer:

it is :119.5714

Step-by-step explanation:

15 3/14+24 1/14+12 2/7+12 2/7+10 1/7+10 1/7+35 3/7=

step by step now:

15 3/14+24 1/14+12 4/14+12 4/14+10 2/14+10 2/14+35 6/14=118 22/14=118+1.5714=119.5714

Final answer:

The sum of the given mixed numbers is 119 and 2/7 after adding the whole numbers separately and then the fractions.

Explanation:

To calculate the sum of the given numbers, we start by adding the whole numbers and the fractions separately. All the fractions have a common denominator, which simplifies the process. Let's proceed with the calculation:

Adding the whole numbers: 15 + 24 + 12 + 12 + 10 + 10 + 35 = 118.

Adding the fractions: 3/14 + 1/14 = 4/14, simplifies to 2/7 because 4/14 is dividable by 2. Then, we add 2/7 + 2/7 + 1/7 + 1/7 + 3/7 = 9/7. But 9/7 is more than 1, so we rewrite 9/7 as 1 whole and 2/7.

Now let's combine the sums of whole numbers and fractions: 118 + 1 = 119.

Thus, the total sum is 119 and 2/7.

Answer:

15 litres

Step-by-step explanation:

129.6 m² needs 8L

1m² needs 8/129.6L

243m² needs (8/129.6)×243 = 15L

To calculate the amount of paint required for a 243m² area, determine the coverage rate from the given data (16.2 m² per litre) and then divide the desired area by the coverage rate. We find that 15 litres of paint are necessary to cover 243m².

To find out how much paint is required to paint an area of 243m² when 8 litres of paint can cover 129.6 m², we need to calculate the paint coverage ratio and then apply it to the desired area.

First, we calculate the coverage rate of the paint:

Next, we use this rate to determine the amount of paint needed for 243m²:

Therefore, 15 litres of paint are required to paint an area of 243m².

https://brainly.com/question/14687962

#SPJ2

Answer:

B) The scale on the y-axis could be changed to 25–40.

Answer:

B the scale on the y-axis could be changed from 25-40

Step-by-step explanation:

just took test on edg and got a 100

Answer:

[tex]\large\boxed{(f\cdot g)(x)=2x^3+x^2-14x-7}[/tex]

Step-by-step explanation:

[tex](f\cdot g)(x)=f(x)\cdot g(x)\\\\f(x)=2x+1;\ g(x)=x^2-7\\\\(f\cdot g)(x)=(2x+1)(x^2-7)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(2x)(x^2)+(2x)(-7)+(1)(x^2)+(1)(-7)\\\\=2x^3-14x+x^2-7[/tex]

False.

This is not a function because for something to be a function each x value can only have one y value. In this case two of the points have a value of 1 and their y are different, making them NOT a function

(1, 3)

(1, 2)

Hope this helped!

~Just a girl in love with Shawn Mendes

Final answer:

The 9th term of the geometric sequence -1, -5, -25, -125 is found to be -390625, using the formula for a geometric sequence nth term with a common ratio of 5.

Explanation:

To find the 9th term of the geometric sequence -1, -5, -25, -125, we need to determine the common ratio and apply the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and r is the common ratio.

The common ratio (r) is the factor that each term is multiplied by to get the next term. In this sequence, r is obtained by dividing the second term by the first term: r = -5 / -1 = 5. Therefore, to find the 9th term, we use the formula with a1 = -1, r = 5, and n = 9:

a9 = -1 × 5(9-1) = -1 × 58 = -390625

So, the 9th term of the geometric sequence is -390625.

Answer:

-15

Step-by-step explanation:

Note that it says x = -9. Plug in -9 for all x inside the expression and solve.

(x² + 9)/(x + 3) = (-9² + 9)/(-9 + 3)

Solve. First, solve the parenthesis, then divide:

(-9² + 9) = (81 + 9) = 90

(-9 + 3) = (3 - 9) = -6

Divide:

(90)/(-6) = -15

-15 is your answer.

~

Answer:

1,715

Step-by-step explanation:

So, we have a product that is sold for $0.85 and costs $0.50 to produce, and we need to find the number is items needed to cover the $600 fixed costs of the company.

We can model this like that, where x is the number of items to make:

0.85x - 0.5x = 600

0.35x = 600

x = 1,714.29

So, to cover the fixed overhead/fixed expenses, they need to make at least 1,715 items, each day.