What is the equation of the line, in point-slope form, that passes through the points (-3, -1) and (-6, 8)?
A. y + 8 = -3(x - 6)
B. y - 8 = -3(x + 6)
C. y + 8 = 3(x - 6)
D. y - 8 = 3(x + 6)

Final answer:

To determine how many more minutes the water can continue to flow into the pool before it overflows, we need to find the value of m that satisfies the inequality 598 + x*m <= 850. The inequality can be rearranged to m >= (850 - 598) / x.

Explanation:

To answer this question, we need to set up an inequality to represent the situation. Let m represent the number of minutes the water can continue to flow into the pool before it overflows.

The pool can hold up to 850 gallons of water, and it currently has 598 gallons. If water is being filled at a certain rate, we can express the rate as gallons per minute. Let's say the rate is x gallons per minute.

So, in m minutes, the pool will have 598 + x*m gallons. To determine how many more minutes the water can continue to flow before it overflows, we need to find the value of m that satisfies the inequality 598 + x*m <= 850.

Now, we can solve this inequality for m by rearranging it: m >= (850 - 598) / x.

This means that water can continue to flow into the pool for m minutes as long as m is greater than or equal to (850 - 598) / x.

To determine how many more minutes water can be added to the pool before it overflows, subtract the current amount of water from the pool's capacity and set up an inequality with the rate of filling. Solve the inequality for the time, represented by 'm', to find the answer.

The student's question relates to finding out for how many more minutes, m, can water be added to a pool before it reaches its full capacity, using an inequality.

Firstly, we need to identify the amount of water the pool can still hold. The pool's total capacity is 850 gallons, and it already contains 598 gallons. Subtracting the current amount from the total capacity gives us the volume that can still be filled:

850 gallons - 598 gallons = 252 gallons

Next, we need to know the rate at which the pool is being filled. Since the rate isn't given in the student's question, let's assume the pool is being filled at the rate of R gallons per minute. We can then set up an inequality to represent the condition that the pool should not overflow:

252 gallons >= R * m

Where m is the number of minutes the water can continue to flow. Dividing both sides by R gives us:

m <= 252 gallons / R

This inequality can be used to solve for m once the actual rate (R) is known. To find the value of m, simply plug in the value of R and calculate.

Answer:

The system  that represent the scenario is

[tex]x+y\leq500[/tex]

[tex]215x+615y\leq 187,500[/tex]

The solution in the attached figure

Step-by-step explanation:

Let

x-----> the acres of corn

y----> the acres of cotton

we know that

[tex]x+y\leq500[/tex] ------> inequality A

[tex]215x+615y\leq 187,500[/tex] -----> inequality B

using a graphing tool

the solution is the shaded area in the attached figure

Answer:

x^2+x-6

Step-by-step explanation:

We just find the factored form of the equation which would be (x+3)(x-2).

Then we multiply it out to get x^2+x-6

Answer:

C. 8x+80.

Step-by-step explanation:

To make this a simple expression, we need to distribute the 8 into x+10. We do this by multiplication. 8*x=8x. 8*10=80. Our new equation is 8x+80.

So add them up you get

2y-2=0

2y=2

y=1

x=7/2

Answer:

the answer is 2y=2 the dude above me is right.

Answer: The correct answer is choice D.

Step-by-step explanation: In order to answer this question you need to calculate the volume of each of the cubes.

Cube A has a side which is 3 meters, so the volume = 3 x 3 x 3 = 27

Cub B has a side which is 6 meters, so the volume = 6 x 6 x 6 = 216

216/27 = 8. Therefore, the volume of cube B is 8 times the volume of cube a.

The volume of cube A is 27 cubic meters and the volume of cube B is 216 cubic meters. Cube B's volume is 8 times greater than cube A's. The correct answer is option D)

The volume of a cube is calculated by cubing the length of its side. So, the volume of cube A is 3 meters x 3 meters x 3 meters = 27 cubic meters. The volume of cube B is 6 meters x 6 meters x 6 meters = 216 cubic meters. Comparing the volumes, cube B's volume is 216/27 = 8 times greater than the volume of cube A. Therefore, the statement that accurately represents the relationship between the two volumes is option D) The volume of cube B is 8 times the volume of cube A.

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Answer:

10

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [1, 4 ]

f(b) = f(4) = 4² +5(4) = 16 + 20 = 36

f(a) = f(1) = 1² + 5(1) = 1 + 5 = 6, hence

average rate of change = [tex]\frac{36-6}{4-1}[/tex] = [tex]\frac{30}{3}[/tex] = 10

division property would help you solve this inequality

Step-by-step explanation:

6 units.

(3*2)+2x=3x

Set the perimeter equal to the area

x(length)=6 units

Answer:

Part a) In the procedure

Part b) Line A and Line B are different parallel lines

Step-by-step explanation:

Part a) we have

[tex]3x-6y=-12[/tex] ----> equation A

[tex]x-2y=-8[/tex] ----> equation B

Isolate the variable x in the equation B

[tex]x=2y-8[/tex]

Substitute the value of x in the equation A

[tex]3(2y-8)-6y=-12[/tex]

[tex]6y-24-6y=-12[/tex]

[tex]-24=-12[/tex] ------> is not true

therefore

The system of equations has no solutions

Part b) What do you know about the two lines in this system of equations?

[tex]3x-6y=-12[/tex] ------> equation A

isolate the variable y

[tex]6y=3x+12[/tex]

[tex]y=(1/2)x+2[/tex]

[tex]x-2y=-8[/tex] -------> equation B

isolate the variable y

[tex]2y=x+8[/tex]

[tex]y=(1/2)x+4[/tex]

Line A and Line B are parallel lines, because their slopes are the same

Line A and Line B are different lines because their y-intercept is not the same

Answer:

The total value is £268.20.

Step-by-step explanation:

Given : There are 495 coins in a bottle.

1/3 of the coins are £1 coins.

124 of the coins are 50p coins.

The rest of the coins are 20p.

To find : Work out the total value of the 495 coins?

Solution :

According to question,

Total coins = 495

[tex]\frac{1}{3}[/tex] of the coins are £1 coins.

i.e.  The number £1 coins are

[tex]\frac{1}{3}\times 495 =165[/tex]

So, We have £165

124 of the coins are 50p coins.

50p=£0.50

Number of coins were

[tex]124\times0.50 =62[/tex]

So, We have £62 .

Remaining coins were,

[tex]495-(124+165)=206[/tex]

i.e. remaining coins are 206 are of 20p.

20p=£0.20

Number of coins were

[tex]206\times0.20 =41.20[/tex]

So, We have £41.20 .

Now, Adding all of them together,

i.e. £165+£62+£41.20=£268.20

So, The total value is £268.20.

Answer:

B

Step-by-step explanation:

Adams headed the Commission that negotiated the Treaty of Ghent in 1814, which ended the War of 1812 with Great Britain.

Answer:

The percentage increase in the cost of her car insurance is 260.4%

Step-by-step explanation:

First, we are going to find by how much the insurance increased:

We know that this year she pays £883 and the last year she paid £245, so

insurance increase = £883 - £245

insurance increase = £638

Now, we are going to find what percentage of the last year price is the insurance increase. So, to find the percentage increase in the cost of the car insurance, we need to divide the insurance increase by the last year price and multiply the result by 100%

percentage increase = [tex](\frac{638}{245} )[/tex](100%)

percentage increase = (2.604)(100%)

percentage increase = 260.4%

We can conclude that Jo's car insurance cost increased 260.4%

A) You would use the two points that are closest to the graphed line

(2,7) and (8,13)

B) Slope = change in Y over the change in X:

Slope = (13-7) / (8-2) = 6/6 = 1

Slope = 1

c) Point slope is written as y -y1 = m(x-x1) where m is the slope y1 is the first Y value and x1 is the first x value.

Equation is: y-7 = x-2

d) To rewrite y -7 = x-2 in slope intercept form, you need to isolate y.

To isolate Y add 7 to both sides:

y = x +5

Step a is (2,7)/(8,13).

Step b is 1

Step c is y-7 = x-2

Step d is y = x +5

Answer:

v = -1

Step-by-step explanation:

Solve for v:

7 v = 8 v + 1

Subtract 8 v from both sides:

7 v - 8 v = (8 v - 8 v) + 1

7 v - 8 v = -v:

-v = (8 v - 8 v) + 1

8 v - 8 v = 0:

-v = 1

Divide both sides by -1:

Answer:  v = -1

Answer:   [tex]\bold{\sqrt[4]{2} }[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{2}\sqrt[4]{32} =\dfrac{1}{2}\sqrt[4]{2\cdot 2\cdot 2\cdot 2\cdot 2}=\dfrac{1}{2}\cdot 2\sqrt[4]{2}=\boxed{\sqrt[4]{2} }[/tex]

Answer: Last option.

Step-by-step explanation:

To find the inverse of the function f(x), you must follow the proccedure shown below:

- Rewrite the function,as following:

[tex]y=4x+12[/tex]

- Solve for x. Then:

[tex]y-12=4x\\x=\frac{1}{4}y-\frac{12}{4}\\\\x=\frac{1}{4}y-3[/tex]

- Now, substitute y with x.

Therefore, you obtain that the inverse function g(x) is the following:

[tex]g(x)=\frac{1}{4}x-3[/tex]

Then, the answer is the last option.

Answer:

Last choice is the answer.

Step-by-step explanation:

We have given a function.

f(x) = 4x+12

We have to find the inverse of given function.

Let y  = f(x)

y = 4x+12

Solving for x, we have

x = 1/4y-3

Since, x =  f⁻¹(y)

 f⁻¹(y) =  1/4y-3

Replacing y with x , we have

f⁻¹(x) = 1/4x-3

Given that g(x) = f⁻¹(x)

g(x) = 1/4x-3 which is the answer.

Answer:

[tex]\large\boxed{y=a(x+8)(x+1)(x-3)}[/tex]

Step-by-step explanation:

[tex]\text{Factored form:}\\\\y=a(x-x_1)(x-x_2)(x-x_3)\\\\x_1,\ x_2,\ x_3-zeros\\\\\text{We have}\ x_1=-8,\ x_2=-1\ \text{and}\ x_3=3.\ \text{Substitute:}\\\\y=a(x-(-8))(x-(-1))(x-3)\\\\y=a(x+8)(x+1)(x-3)\\\\\text{Where}\ a\neq0\ (\text{any real number except 0})[/tex]

Final Answer:

The exact value of [tex]\(\tan\left(\frac{-x}{3}\right)\)[/tex] is [tex]\(-\tan\left(\frac{x}{3}\right)\).[/tex]

Explanation:

To find the exact value of [tex]\(\tan\left(\frac{-x}{3}\right)\),[/tex] we can use the periodicity property of the tangent function. The tangent function has a period of [tex]\(\pi\),[/tex] which means that [tex]\(\tan(\theta) = \tan(\theta + \pi)\)[/tex].

Therefore, [tex]\(\tan\left(\frac{-x}{3}\right)\)[/tex] is equivalent to [tex]\(\tan\left(\frac{-x}{3} + \pi\)\).[/tex] Additionally, the tangent function is an odd function, so [tex]\(\tan(-\theta) = -\tan(\theta)\). Combining these properties, we get \(\tan\left(\frac{-x}{3}\right) = -\tan\left(\frac{x}{3}\right)\).[/tex]

In summary, the exact value of [tex]\(\tan\left(\frac{-x}{3}\right)\) is \(-\tan\left(\frac{x}{3}\right)\)[/tex] due to the periodicity and odd function properties of the tangent function.

Answer:

Step-by-step explanation:

1/4x20=5 so Maria ate 5 slices of pizza.

he spent 15 mins for lunch. I wish you used a comma for 3, 70 min classes lol. tripped me up a sec

Final answer:

Bennett spent 20 minutes eating lunch, which was calculated by subtracting the time he spent in classes and during breaks from his total time at school.

Explanation:

To determine how long Bennett spent eating lunch, we need to subtract the time he spent attending classes and the breaks between classes from the total time he was at school. Bennett attended 3 classes, each lasting 70 minutes, so the total class time is 3 classes × 70 minutes/class = 210 minutes. There are 2 breaks between classes, each lasting 5 minutes, adding up to 2 breaks × 5 minutes/break = 10 minutes.

Total time spent on classes and breaks is 210 minutes + 10 minutes = 220 minutes or 3 hours and 40 minutes. Since Bennett was at school for 4 hours (or 240 minutes), the time spent eating lunch can be calculated by subtracting the class and break time from the total time at school: 240 minutes - 220 minutes = 20 minutes.

Therefore, Bennett spent 20 minutes eating lunch.

Answer:

Step-by-step explanation:

A diameter is two times longer than a radius. Therefore, if the diameter

d = 15cm, then the radius r = (15cm) : 2 = 7.5cm.

The formula of an area of a circle:

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

Substitute:

[tex]A=\pi(7.5)^2=56.25\pi\ cm^2[/tex]

[tex]\pi\approx3.14[/tex]

Then

[tex]A\approx(56.25)(3.14)\approx177\ cm^2[/tex]

Answer:  [tex]\bold{\bigg(\dfrac{1}{2},2\dfrac{1}{2}\bigg)}\qquad \implies \qquad \bold{\bigg(\dfrac{1}{2},\dfrac{5}{2}\bigg)}[/tex]

Step-by-step explanation:

y = x + 2       x + y = 3

Solve using Substitution Method by replacing y with x + 2:

                    x + (x + 2) = 3

                         2x + 2 = 3

                         2x       = 1

                           x        = [tex]\dfrac{1}{2}[/tex]

Next, replace x with 1/2 in one of the original equations and solve for y:

y = x + 2

  = [tex]\dfrac{1}{2}[/tex] + 2

  = [tex]2\dfrac{1}{2}[/tex]

Answer:

x = 1/2

y = 5/2

Step-by-step explanation:

So we're gonna use the elimination method, by eliminating one of x or y to find the value of the other one.

y = x + 2 --------------(1)

x + y = 3 --------------(2)

In (1), x is in LHS and y is in RHS. To make things simpler, we take both x and y to the same side.

y           = x + 2

y - x      = x + 2 - x ( take x to the other side)

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

Note that in (2), x is positive and in (3), x is negative. So by adding these two, we can single out y because +x and -x cancels out. So we can eliminate x.

(3) +  (1) : (x+y) + (y- x) = 3 + 2

              2y                 = 5

              y                   = 5/2

Substituting y = 5/2 for (1),

5/2 - x  = 2

5/2       = 2 + x

5/2 - 4/2 = x

x   = 1/2

∴ x = 1/2

  y = 5/2

Hope i helped you :)

no, the angles in triangles have to add up to 180 deg. but this adds up to 190

Answer:

Which of what following? There's no options.

Step-by-step explanation:

The constant term is "240." The number represents the daily revenue when the price of a taco is 0 dollars.

Answer:

The constant term is 240. It represents the initial daily revenue.

Step-by-step explanation:

It is given that Tico's Taco Truck is trying to determine the best price at which to sell tacos, the only item on the menu,  to maximize profits.

The owner can calculate the daily revenue using the polynomial  expression

[tex]-7x^2+32x+240[/tex]

where x is the number of $1 increases in the taco price.

Constant term does not contain any variable.

In the given expression 240 is free from variable x. So, the constant term is 240.

The value of expression is 240 for x=0. Since x is the number of $1 increases in the taco price, therefore 240 is the daily revenue when the taco price is not increased or the taco price increased by 0.

Therefore the constant term is 240 and it represents the initial daily revenue.

Answer:

Choices A and C

Step-by-step explanation:

Answer:

A, C

Step-by-step explanation:

We can see in the graph that it is done by ticks of 1/10s

Therefore we can determine that point A is on 1.6.

Since 1.6 > 1.27, this is true.

1 one and 7 hundreths is 1.07

And since 1.07 < 1.27, this is not true.

Finally 27 tenths is the equivalent of 2.7

2.7 > 1.27 so this is true.

Answer:

10 -6x

Step-by-step explanation:

We cannot solve since there is no equal sign, we can only simplify

(-3 + 5) - (6x - 8)

Combine the like terms in parentheses

(2) - (6x - 8)

Distribute the minus sign

2 -6x --8

2 -6x +8

Combine like terms

2+8 -6x

10 -6x

set it equal to 0

(-3+5)-(6x-8)=0

2-6x+8=0

isolate x

-6x=-2-8

-6x=-10

cancel negatives

6x=10

divide by 6

x= 10/6

reduce:

x = 5/3

Answer:

Just took the test test it is A 100%

Step-by-step explanation:

The relationship between the two triangles can be described as ΔMLN ~ ΔFGH by the third angle theorem, ∠M ≅ ∠F, ∠L ≅ ∠G, and ∠N ≅ ∠H.

Given two triangles.

The triangles are named as LMN and FGH.

Also, two of the angles of each triangle is given.

For triangle LMN,

∠L = 36° and ∠M = 51°

Similarly, for triangle FGH,

∠G = 36° and ∠F = 51°

So, for both triangles,

∠L = 36° = ∠G

∠M = 51° = ∠F

Using the angle sum property of triangles,

∠N = ∠H = 180° -(36° + 51°) = 93°

That is, all three angles of triangle LMN is equal to triangle FGH.

So, by the third angle theorem, ΔMLN is similar to ΔFGH.

Hence, the correct option is A.

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[tex]\bold{Hey\ there!} \\ \\ \bold{Combine\ like\ terms\downarrow} \\ \bullet\bold{35x\ \&\ 10x} \\ \bold{35x+10x=45x} \\ \\ \bold{Since,\ -5\ doesn't\ have\ any\ like\ terms\ it\ stays\ the\ same!} \\ \\ \\ \boxed{\boxed{\bold{Answer:45x-5}}}\checkmark[/tex]

[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ day!} \\ \\ \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]