write the slope-intercept form of the equation of each line.

8x + 3y = -9

this is becoming a serious problem. my math teacher CANNOT teach.

please help.

(a) <TOR=pi/3 radians

To determine <TOR we use the fact that in the right-angled triangle ORT we know two sides:

|OT|=radius=8cm and |OR|=radius/2=4cm

and can use the sine:

[tex]\sin \angle OTR=\frac{r/2}{r}=\frac{1}{2}\implies \angle OTR =\frac{\pi}{6}[/tex]

and since <TRO=pi/2, it must be that

[tex]\angle TOR =\pi-\frac{\pi}{2}-\frac{\pi}{6}=\frac{\pi}{3}[/tex]

(b) The arc length is approximately 7.255 cm

In order to calculate the arc length QT, we need to first determine the length |ST| and the angle <OST.

Towards determining angle <OST:

[tex]\angle SOT = \pi - \angle TOR = \pi - \frac{\pi}{3} = \frac{2}{3}\pi[/tex]

Next, draw a line connecting P and T. Realize that triangle PTS is right-angled with <PTS=pi/2. This follows from the Thales theorem. Since R is a midpoint between P and O, it follows that the triangles ORT and PRT are congruent. So the angles <PTR and <OTR are congruent. Knowing <PTS we can  determine angle <OTS:

[tex]\angle OTR \cong \angle PTR=\frac{\pi}{6}\implies\angle OTS=\angle PTS -\angle PTR -\angle OTR\\\angle OTS = \frac{\pi}{2}-\frac{\pi}{6}-\frac{\pi}{6}=\frac{\pi}{6}[/tex]

and so the angle <OST is

[tex]\angle OST = \pi - \angle TOS - \angle OTS = \pi -\frac{2}{3}\pi - \frac{1}{6}\pi=\frac{\pi}{6}[/tex]

Towards determining |TS|:

Use cosine:

[tex]\cos \angle OST =\frac{|RS|}{|ST|}\implies |ST|=\frac{\frac{3}{2}r}{\cos \frac{\pi}{6}}=\frac{12\cdot 2}{\sqrt{3}}=8\sqrt{3}cm[/tex]

Finally, we can determine the arc length QT:

[tex]QT = {\angle OST}\cdot |ST|=\frac{\pi}{6}\cdot 8 \sqrt{3}=\frac{4\pi}{\sqrt{3}}\approx 7.255cm[/tex]

Answer:

5m-50

Step-by-step explanation:

Let Diego current age be x,

Given that Diego’s current age is five times Martina’s age ten years ago

Martina current age = m years

10 years ago Martina's age = m-10

Hence we have

x = 5(m-10) = 5m-50

So we find that Diego's current age can be expressed in terms of m as

Deigo's current age= 5m-50

Verify:

Deigo current age = 5m-50

Hence Martina age 10 years ago = 5m-50 divided by 5 = m-10

Martina current age = m-10+10 = m

Verified.

The current age of Diego in terms of m is expressed as:  [tex]5m - 50[/tex]

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given condition, we can take Diego's current age represented by a symbol.

Then, converting the statement "Diego’s current age is five times Martina’s age ten years ago." in mathematical terms,

Diego's current age = 5 times (Martina's age 10 years ago)

[tex]D = 5 \times (m - 10)\\\\or\\\\D = 5m - 50[/tex]

( sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)

Therefore, The current age of Diego in terms of m is expressed as:  [tex]5m - 50[/tex]

Learn more about forming equations here:

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Answer:

For minimum cost  the number of speedboats produced would be 4,000.

Step-by-step explanation:

That would be the value of x which minimises the cost C(x).

You can find this by converting the function to vertex form.

C(x) = 3x^2 - 24x + 144

= 3(x^2 - 8x) + 144

= 3[ (x - 4)^2 - 16] + 144

= 3(x - 4)^2 -48 + 144

= 3(x - 4)^2 + 96

For this to be a minimum x must be = 4.

That is 4,000 speedboats.

The actual minimum cost of producing theses is  is  96 million dollars.

Answer:

4 thousand speedboats

Step-by-step explanation:

The minimum/maximum point on a parabola is just another name for that parabola's vertex. A parabola can be defined in a few different ways, but one is as the curve described by a quadratic function, a function of the form [tex]y=ax^2+bx+c[/tex] where a, b, and c ≠ 0. To see how we can get a vertex out of this, we can start with the simpler function [tex]y=ax^2[/tex]. Here, the vertex is simply the origin, (0, 0). If we shift the graph horizontally by h units, replacing x with (x - h), we get the function [tex]y = a(x-h)^2[/tex] and the vertex (h, 0), and if we shift it vertically by k units, we get the equation [tex]y-k=a(x-h)^2[/tex] and the vertex (h, k). We can, of course, add k to either side to obtain the function [tex]y=a(x-h)^2+k[/tex], also known as the general vertex form of a quadratic function.

This problem asks us to find a value for x which would minimize the C(x) in the function [tex]C(x)=3x^2-24x+144[/tex]. This essentially boils down to getting C(x) in vertex form and finding the x coordinate of the vertex from there. To do this, we can utilize an algebraic technique called completing the square to transform the expression on the right side into the form we want. Our task then is to somehow manipulate [tex]3x^2-24x+144[/tex] so that it resembles the form [tex]a(x-h)^2+k[/tex], where a, h, and k are constants, and (h, k) is the vertex of the parabola.

The first thing we can do with our expression is pull out a 3 from all three terms:

[tex]3x^2-24x+144\rightarrow3(x^2-8x+48)[/tex]

What we'd like now is to somehow turn that expression in the parentheses into something resembling [tex](x-h)^2[/tex]. To do this, we can recall that

[tex](x-y)^2=x^2-2xy+y^2[/tex].

If we rewrite [tex](x^2-8x+48)[/tex] as [tex](x^2-2\cdot4\cdot x+48)[/tex], we can see that this almost resembles [tex](x-4)^2=x^2-2\cdot4\cdot x+4^2=x^2-8x+16[/tex]. The only difference is between the 48 and the 16. To fix this, we can subtract 32 from the 48:

[tex]3(x^2-8x+48-32)[/tex]

However, to balance this subtraction out, we'll need to add 96 (which is 32 × 3) on to the end:

[tex]3(x^2-8x+16)+96[/tex]

Finally, we can rewrite our function C(x) as

[tex]C(x)=3(x-4)^2+96[/tex]

This gives us a vertex/minimum point of (4, 96), which means we need to produce 4 thousand speedboats to minimize its costs.

Answer:

$13.72

Step-by-step explanation:

To get the answer, we need to find out how much one bag costs. We can divide 5.88 by 3 and get 1.96. One bag is $1.96. To find out how much seven bags cost, we can multiply 1.96 x 7 to get 13.72. It costs $13.72 for 7 bags of popcorn.

ANSWER: The length of the entire dash is 700 meters.

EXPLANATION:

Because 20% of the dash equals 140 meters, we can use a variable to figure out the length of the entire dash.

Let x be the length of the entire dash.

[tex].2x = 140\\\\x = 700[/tex]

The length of the entire dash is 700 meters.

Answer: -12

Step-by-step explanation: 24 divided by -2 = -12

Answer:

-12

Step-by-step explanation:

Divide. 24÷(−2)

Dividing a positive number with a negative number results to a negative number.

24 is positive and 2 is negative.

24 ÷ 2 = 12

But since 2 is negative;

24 ÷ -2 = -12

24 ÷ (-2)

Answer:

x = -2, y = 0

Step-by-step explanation:

This is a systems of equations. Using substitution, we solve for a single variable, plug it in to solve for the other, and solve that one back in to solve for the original. Let's solve it.

5x + y = -10

Subtract 5x from both sides.

y = -5x - 10

Now that we have y isolated, we can plug it in to the other equation.

4x - 7(-5x-10) = -8

Distribute.

4x + 35x + 70 = -8

Subtract 70 from both sides and simplify.

39x = -78

Divide both sides by 39.

x = -2

Now that we have x as -2, we plug it in to the original.

5(-2) + y = -10

Simplify.

-10 + y = -10

Add 10 to both sides.

y = 0

x = -2, y = 0

[tex]\left\{\begin{array}{ccc}5x+y=-10&|\text{subtract 5x from both sides}\\4x-7y=-8\end{array}\right\\\left\{\begin{array}{ccc}y=-5x-10&|\text{substitute to the second equation}\\4x-7y=-8\end{array}\right\\\\4x-7(-5x-10)=-8\qquad\text{use distributive property}\\\\4x+(-7)(-5x)+(-7)(-10)=-8\\\\4x+35x+70=-8\qquad\text{subtract 70 from both sides}\\\\39x=-78\qquad\text{divide both sides by 39}\\\\\boxed{x=-2}\\\\\text{Put the value of x to the first equation}\\\\y=-5(-2)-10\\\\y=10-10\\\\\boxed{y=0}[/tex]

[tex]Answer:\ \boxed{x=-2\ and\ y=0}[/tex]

Question

6v²+ 4v²  please solve this equation

Answer:

Step-by-step explanation:

6v²+ 4v² =

(6 + 4)v² =

10v²

Answer:

Band A:  

Linear equation: y = 600  

Band B:  

Linear equation: y = 1.25x + 350  

The cost will be equal at 200 tickets.  

The cost when they are equal is $600.

use desmos copy and paste the graph

Answer:

15/216 (6.944%)

Tienes suerte, me tomé 5 años de español! Hoep me ayudó!

Answer:

Suceso A= (6;4) (5;5) (4;6)

n(A)= 3

Suceso B= (5;5)

n(B)= 1

P(AnB)= (5;5)= 1

Espacio muestral= 36

P(B/A)= 1/36 / 3/36= 0.33= 33%

Suceso C= (4;6) (6;4)  

n(C)= 2

P(AnC)= (4;6) (6;4)

P(AnC)= 2

P(C/A)=2/36 / 3/36= 2/3= 0.66= 66%

Answer:

y^2 +8y + 16

Step-by-step explanation:

 6y^2 +2y +5  - (5y^2 -6y -11)

I distribute the minus sign

6y^2 +2y +5  - 5y^2 +6y +11

Then I put them vertical.

6y^2 +2y +5  

-5y^2 +6y +11

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

y^2 +8y + 16

This is in standard from since the exponential decreases.

Answer:

Step-by-step explanation:

Factor out 6

I assume you mean 6x^2+30x+36, because that makes far more sense

6(x^2+5x+6) = 6(x^2 + 2x +3x +6)

(To find that it is 2x and 3x: 2 +3 = 5, 2 * 3 = 6)

Factor by grouping:

6* x(x+2) +3(x+2) = 6(x+3)(x+2)

For binomials, it could be either (6x+18) (x+2) or (x+3) (6x+12), depending on where you multiply the 6.

Answer:x+2

Step-by-step explanation:

x = number of hours after 9 am (eg: x = 1 means 1 hr after 9 am, so 10 am)

f(x) = population count x hours after 9 am

f(1) = population count at 10 am (1 hour later)

f(2) = population count at 11 am (2 hrs after 9 am)

f(2) - f(1) represents the difference in population counts from 10 am to 11 am, or put another way, how much the population increased during that time interval.

f(2)-f(1) represents the change in the population of bacteria from the first to the second hour after 9 a.m., giving us the rate of population growth over that one-hour period.

The expression f(2)-f(1) in the function f(x), where x represents the hours after 9 a.m., illustrates the change in the population of the bacteria between the first and second hour after 9 a.m. Population growth in bacteria usually follows a logarithmic scale where it doubles every given time period, typically every hour. Thus, by calculating the difference between the population at the second hour (f(2)) and the first hour (f(1)), we can get the increase in the population of bacteria over that one-hour period.

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Answer: k = -12

The mixed number -1 & 1/3 converts to the improper fraction -4/3

Let r be the common ratio. To go from one term to the next, we multiply by this common ratio. So,

second term = (first term)*(common ratio)

4 = (-4/3)*r

3*4 = 3*(-4/3)*r

12 = -4r

-4r = 12

r = -3

We multiply each term by -3 to get the next term. The third term is therefore,

third term = (second term)*(common ratio)

third term = 4*r

third term = 4*(-3)

third term = -12

and if we keep going...

fourth term = (third term)*(common ratio)

fourth term = -12*(-3)

fourth term = 36

So it matches up

If a, b, c are the geometric sequence, then

[tex]ac=b^2[/tex]

We have a = 4, b = k, c = 36. Substitute:

[tex](4)(36)=k^2\\\\k^2=144\to k=\pm\sqrt{144}\to k=-12\ \vee\ k=12[/tex]

First term is negative, therefore it's the alternating sequence. Therefore your answer is

Answer:

speed = 67/6 miles per hour

Step-by-step explanation:

To find the average speed, we divide the distance by the time

d/t = 134 miles/ 12 hours

speed = 134/12 miles per hour

We can simplify this fraction  by dividing the top and bottom by 2

speed = 67/6 miles per hour

Answer:

11.16 mph

Step-by-step explanation:

You divide Distance by Time to get the speed.

134/12= 11.1667

Answer:

$2

Step-by-step explanation:

$40 * 0.02 = 5

Answer:

1) Increased by 2 times then 16 hours

2) Increased by 4 times then 8 hours

Step-by-step explanation:

Given :-

==> 4 construction crew members need 32 hours to pour concrete foundations.

==> All the members work at a same pace.

1) If the numbers of workers are increased by 2 time i.e., 4 workers × 2 = 8 workers. It would take half of the time that is taken now i.e., 32 hours ÷ 2 = 16 hours.

2) If the numbers of workers are increased by 4 time i.e., 4 workers × 4 = 16 workers. It would take 1/4th of the time that is taken now i.e., 32 hours ÷ 4 = 8 hours.

Answer:

30

Step-by-step explanation:

To find the area of a triangle you need to multiply base times height. Which in this case is 6 times 10 equals 60. Then you just need to simplify it and it equals 30.

Answer:

A=m-n-p

Step-by-step explanation:

So solve for a, we have to isolate it on one side, so -a=n+p-m. So a=m-n-p

Answer:

a = m - n - p

Step-by-step explanation:

isolate the term in a by subtracting m from both sides

- a = n + p - m ( multiply through by - 1 )

a = - n - p + m = m - n - p

Answer:

If Aaron leaves one city at noon and has to be at another city at 3:00pm traveling at a rate of 65km/h, he will arrive to the second city on time.  

Step-by-step explanation:

Aaron has three hours (from noon to 3:00pm) to travel a distance of 186km.  If he travels at a speed of 65km per hour, then we can multiply 65 km times the number of hours he has available, three, to get a total of 195km.  So, Aaron can travel up to 195 km in the three hour period and since the city is only 186km away, he has time to make it there before the 3:00pm deadline.  

Answer:

Yes, he can.

Step-by-step explanation:

From noon to 3:00 pm, it's 3 hours.

If he drives on the speed limit with 65 km/h, andhas 186 kilometers to drive, he can make it on time.

3(65)=195 km.

195 is greater than 185, so he can make it on time.

3*x*x*5*x

If x=3 then:

3*3*3*5*3

=27*15

= 405

Hope this helps! <3

Answer:

120

Step-by-step explanation:

Answer:

$104.738

Step-by-step explanation:

Let's work out the stock plan first:

$2,000 - 7% in the first year = $1,860

$1,860 + 10% = $2,046 in the second year

Savings account:

$2,000 + 3.7% = $2,074 in the first year

$2,074 + 3.7% = $2,150.738 in the second year

The difference:

$2,150.738 - $2,046 = $104.738

At the end of the second year, the savings account earns $104.74 more than the stock plan.

We are required to calculate the difference in earnings between a stock investment and a savings account after two years. To do this, we need to account for the changes in the stock plan's value and the compound interest from the savings account.

For the stock plan:

Year 1: $2,000.00 - (7% of $2,000.00) = $2,000.00 - $140.00 = $1,860.00

Year 2: $1,860.00 + (10% of $1,860.00) = $1,860.00 + $186.00 = $2,046.00

For the savings account:

Year 1: $2,000.00 + (3.7% of $2,000.00) = $2,000.00 + $74.00 = $2,074.00

Year 2: $2,074.00 + (3.7% of $2,074.00) = $2,074.00 + $76.74 = $2,150.74

The difference in earnings at the end of the second year is the amount in the savings account minus the amount in the stock plan:

$2,150.74 - $2,046.00 = $104.74.

Answer:

Sphere Volume = (4/3) * PI * radius^3

Sphere Volume = (4/3) * PI * radius^3

11,488 = ((4/3) * 3.14) * radius^3

radius^3 = 11,488 / 4.1866666667

radius^3 = 2,743.9490445641

radius = 14 cm

diameter = 28 cm

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

average = [tex]\frac{sum of patients}{number of assistants}[/tex]

             =  [tex]\frac{7+8+5+9+10+10+14}{7}[/tex] = [tex]\frac{63}{7}[/tex] = 9

To get this answer you need to find the average. To find the average, you need to add the number of patients for each assistant together.

7 + 8 + 5 + 9 + 10 + 10 + 14 = 63

Then divide the answer by the number of assistants.

63 / 7 = 9

So, the answer is 9. There are an average of 9 patients per nurse.

The answer is George Washington.

Answer:

The first president was George Washington. Hope this helps you out.

Step-by-step explanation:

Answer:

295.16 feet

Step-by-step explanation:

We need to find the length of the diagonal of a right angled triangle with equal length legs.

Length of each leg = √(43560)

Using the Pythagoras theorem:-

x^2 = (√(43560))^2 + (√(43560))^2    (where x = length of the diagonal)

x^2 = 43560 + 43560

x = √(87120) = 295.16 feet

Answer:

distance from corner to corner = 295.16 ft

Step-by-step explanation:

Given the land is square, then its area is computed as:

Area = (length of a side)^2

Replacing with area = 1 acre =  43560 sq. ft.

43560 = (length of a side)^2

length of a side = √43560

length of a side = 208.71 ft

The distance from corner to corner and two sides of the square form a right triangle, where the distance from corner to corner is the hypotenuse and the square sides are the legs. From Pythagorean theorem:

(distance from corner to corner)^2 = 208.71^2 + 208.71^2

distance from corner to corner = √(208.71^2 + 208.71^2)

distance from corner to corner = 295.16 ft

Answer:

125%

Step-by-step explanation:

The old population was 100% of the old population since 100% means a whole amount.

Since the population increased by 25%, the new population is 125% of the old population.

Answer:

15377.34375

Step-by-step explanation:

10800*((224+1)/2)/100*((224+1)/2)/100*((224+1)/2)/100

=108 * (225/2)  * ( 225/200)*(225/200)

=15377.34375