Find a formula for an for the arithmetic sequence.

Answer:

11.43

Step-by-step explanation:

80÷7= 11.428571428571428571428571428571

i hope this helps

Answer: You have the correct answer. It is y = 150x-50

Nice work on getting the correct answer. For anyone curious, the explanation is below.

=============================================

x = number of hours the stand is open

y = amount earned

(1,100) is from the fact the stand is open 1 hour and earns $100

(3,400) is due to the stand earning $400 after 3 hours.

Slope Formula

m = (y2 - y1)/(x2 - x1)

m = (400-100)/(3-1)

m = 300/2

m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.

Use m = 150 and (x,y) = (1,100) to find the value of b as shown below

y = mx+b

100 = 150(1) + b

100 = 150 + b

100-150 = b

-50 = b

b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.

So we have m = 150 as the slope and b =  -50 as the y intercept.

Therefore, y = mx+b turns into y = 150x-50.

-------

As a check, plugging in x = 1 should lead to y = 100

y = 150x-50

y = 150(1)-50

y = 150-50

y = 100 and indeed it does

The same should be the case with (3,400). Plug in x = 3 and we should get y = 400

y = 150x-50

y = 150(3)-50

y = 450-50

y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).

The equation for revenue earned from being opened for x hours will be y=150x-50 so it is absolutely correct.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given,

$100 for 1 hour

So,

x = 1 and y = 100

And,

$400 for 3 hour

So,

x = 3 and y = 400

Now the slope of the linear equation is given by

m = difference in ys coordinate / difference in xs coordinate  

m = (400 - 300)/(3-1) = 150

So equation become

y = 150x + b

Now put (3,400) to find out b

400 = 150(3) + b

b = -50

So, equation

y = 150x - 50

Hence " The equation for revenue earned from being opened for x hours will be y=150x-50".

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Answer:

P(A) = 0.5

Step-by-step explanation:

Look from the tree root (left) and find A.  

When you reach the first branch that shows A, the probability is on it's left, so

P(A) = 0.5

Answer:

center : (-2, -2.5)

Step-by-step explanation:

Midpoint point formula says that if there are two points (x1,y1) and (x2,y2) then

coordinate of midpoint is given by

midpoint (x1+x2)/2 , (y1+y2)/2

_______________________________________________

In the problem, we have to find the center of circle of by using the midpoint formula.

Since the circle is circumscribed in square. Its center will be midpoint of either of the diagonal.

To find the center we can take coordinate of any of two diagonal points of square and find midpoint for this and that will be center of circle.

_________________________________________________

1st diagonal pair(4,8) and (-8,-3)

Then midpoint is (4 + -8)/2 , (8+ -3)/2  

midpoint (-2, -2.5)

Thus, center of circle is (-2,-2.5)

we can verify this by using other diagonal pair (-8,8) and (4,-3)

Midpoint in this case can be calculated as

midpoint (-8+4)/2 , (8 + -3)/2

midpoint (-2,-2.5)

Thus, we see that in both cases Midpoint is same and hence center is (-2, -2.5)

Answer:

(C) Translation of 2 units right, 1 up, and a reflection over the y-axis.

Step-by-step explanation:

Ideally, we are looking for a reflection of the red image over the y-axis, and to do that, we can see how we need to move the black image.

In order for points Q and Q' to be a reflection of each other, they need to have the same y value, and be the exact same distance from the y axis, so the point that Q has to be at is (-1,-3).

Q is right now at (-3,-4) so we can translate this.

To get from -3 to -1 in the x-axis, we go right by 2 units.

To get from -4 to -3 in the y-axis, we go up one unit.

Now, if we reflect it, the triangles will be the same.

Hope this helped!

Answer:

C.

Step-by-step explanation:

When you study the images, it is clear that the black triangle has to be reflected over the y-axis to face the same direction as the red triangle. So, choice A is eliminated.

Once you reflect the black triangle across the y-axis, you have points at (-1, -1), (3, -4), and (3, -2). Meanwhile, the red triangle's coordinates are at (-3, 0), (1, -3), and (1, -1). From these points, you can tell that the x-values differ by 2 units and the y-values differ by 1 unit.

All of these conditions match the ones put forth in option C, so that is your answer.

Hope this helps!

Answer:

11 children sitting

Step-by-step explanation:

3+8=11

Answer:

x=1

y=1

Step-by-step explanation:

Please look at the image below for solutions⬇️

Answer:

Step-by-step explanation:

Add the equations in order to solve for the first variable . Plug this value into the equations in order to solve for the remaining variables.

Point form

(x, 2-x)

Answer:

Y = 40

Step-by-step explanation:

First find the measure of V

The sum of the angles of a triangle equal 180

U+V+W =180

70+Y+70 =180

140+U =180

U = 180-140

U = 40

Since the triangles are similar

V = Y

40 = Y

Answer:

Step-by-step explanation:

w - 3 = 15

Add 3 to both sides to make w stand alone

That's

w - 3 + 3 = 15 + 3

w = 15 + 3

We have the final answer as

w = 18

Hope this helps you

Answer: w = 18

Step-by-step explanation: To solve for w in this equation, we want to get w by itself on the left side of the equation.

Since 3 is being subtracted from w, to get w by itself,

we need to add 3 to the left side of the equation.

If we add 3 to the left side, we must also add 3 to the right side.

Notice that on the left side, -3 and +3 cancel

each other out so were simply left with w.

On the right side, 15 + 3 is 18.

So we have w = 18.

Answer:

Q= 8

The amount emptied is 8 gallons of water

Step-by-step explanation:

First we need to create the equation for the above statement.

Q is directly proportional to the square of d

Q= kd²

Q= 50

d= 5

50= k5²

50 = k25

K = 50/25

K = 2

K is the constant of proportionality.

Now our equation is

Q= 2d²

Where Q = volume in gallons

d = pipe diameters in inch

For a pipe of diameter 2 inch

The amount of gallons of water emptied assuming the same kinf of flow is

Q= 2d²

Q= 2(2)²

Q= 2(4)

Q= 8

The amount emptied is 8 gallons of water

Answer:

1 1/3 ft

Step-by-step explanation:

12 inches in a foot, so 16/12, or 1 4/12 feet, or 1 1/3 feet

Answer:

0.5 seconds and 1.5 seconds.

Step-by-step explanation:

h(t) = -16t^2 + 32t + 2

14 = -16t^2 + 32t + 2

16t^2 - 32t - 2 + 14 = 0

16t^2 - 32t + 12 = 0

8t^2 - 16t + 6 = 0

4t^2 - 8t + 3 = 0

(2x - 3)(2x - 1) = 0

2x - 3 = 0

2x = 3

x = 3/2

x = 1.5

2x - 1 = 0

2x = 1

x = 1/2

x = 0.5

So, the ball was at 14 feet at 0.5 seconds and 1.5 seconds.

Hope this helps!

Answer:

x = 1 3/22

Step-by-step explanation:

1/2 x + 3/5 x = 5/4

We need to get rid of the fractions by multiplying by 20 on each side

20 (1/2 x + 3/5 x) = 20 * 5/4

Distribute

10x + 12x = 25

Combine like terms

22x = 25

Divide each side by 22

22x/22 = 25/22

x = 22/22 + 3/22

x = 1 3/22

Answer:

[tex]x = 1\frac{3}{22}[/tex]

Step-by-step explanation:

=> [tex]\frac{1}{2} x + \frac{3}{5} x = \frac{5}{4}[/tex]

LCM = 20

So, Multiplying both sides by 20

=> [tex]20 (\frac{x}{2} + \frac{3x}{5}) = 5 * 5[/tex]

[tex]10 * x + 4*3x = 25\\10x+12x = 25\\22x = 25[/tex]

Dividing both sides by 22

[tex]x = \frac{25}{22}[/tex]

[tex]x = 1\frac{3}{22}[/tex]

Answer:

price per pound of apple = $1.25

price per pound of banana = $0.75

Step-by-step explanation:

Your first question is what value should you multiply the second equation by in order to eliminate the y terms.

The number should be 3.  Let us multiply the first equation by 2 and the second equation by 3 and see how y will be eliminated.

10x + 6y = 17...............(i)

9x + 6y = 15.75...........(ii)

10x - 9x  = x

6y - 6y = 0

17 - 15.75 = 1.25

x = 1.25

let us find y

10x + 6y = 17...............(i)

10(1.25) + 6y = 17

12.5  + 6y = 17

6y = 17 - 12.5

6y = 4.5

divide both  sides by 6

y = 4.5/6

y = 0.75

In order to eliminate y term from the system of equations we multiply equation 2 by -3.

The price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.

Given equations,

[tex]5x + 3y = 8.5[/tex].........(1)

[tex]3x + 2y = 5.25[/tex].......(2)

Here x is the cost per  pound of apples, and y is the cost per pound of bananas.

According to the question, multiply the first equation by 2, we get

[tex]10x+6y=17[/tex].....(3)

So, in order to eliminate y term from the system of equations we multiply equation 2 by -3, we get

[tex]-9x-6y=15.75[/tex].....(4)

Now Adding (3) and (4) equation, we get

[tex]x=1.25[/tex]

Putting the above value of x in equation 3 we get,

[tex]10\times1.25+6y=17\\12.5+6y=17\\6y=17-12.5\\6y=4.5\\y=\frac{4.5}{6} \\y=0.75[/tex]

Hence the price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.

For more details follow the link:

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Answer:

[tex]\left(-\dfrac{7}{2},\dfrac{7\sqrt{3}}{2}\right)[/tex].

Step-by-step explanation:

The given point is

[tex]\left(7,\dfrac{2\pi}{3}\right)[/tex]

We need to find the rectangular coordinates of the given point.

If a polar coordinate is [tex](r,\theta)[/tex], then  

[tex]x=r\cos theta[/tex]

[tex]y=r\sin theta[/tex]

In the given point [tex]\left(7,\dfrac{2\pi}{3}\right)[/tex],

[tex]r=7,\theta=\dfrac{2\pi}{3}[/tex]

Now,

[tex]x=7\cos \dfrac{2\pi}{3}[/tex]

[tex]x=7\cos \left(\pi-\dfrac{\pi}{3}\right)[/tex]

[tex]x=-7\cos \left(\dfrac{\pi}{3}\right)[/tex]

[tex]x=-7\left(\dfrac{1}{2}\right)[/tex]

[tex]x=-\dfrac{7}{2}[/tex]

and,

[tex]y=7\sin \dfrac{2\pi}{3}[/tex]

[tex]y=7\sin \left(\pi-\dfrac{\pi}{3}\right)[/tex]

[tex]y=7\sin \left(\dfrac{\pi}{3}\right)[/tex]

[tex]y=7\left(\dfrac{\sqrt{3}}{2}\right)[/tex]

[tex]y=\dfrac{7\sqrt{3}}{2}[/tex]

Therefore, the required point is [tex]\left(-\dfrac{7}{2},\dfrac{7\sqrt{3}}{2}\right)[/tex].

Answer:  = approx 0.2006

Step-by-step explanation:

The probability that first 1 randomly selected  calculator is defective is

P(1st defect)= 42/(42+20)=42/62=21/31

If the first calculator is defective the residual number of defective calculators is 42-1=41. The residual total number  number of calculators is 62-1=61

So the probability that second calculator is defected

P(2nd defective)=41/61

If both previous calculators are defective the residual number of defective calculators is 42-2=40.  Total residual number of calculators is 62-2=60

So the probability that third calculator is defected

P(3rd defective)=40/60=2/3

Finally the probability that also fourth calculator is defective is 39/59

P(4th defective)=39/59

The resulted probability that all 4 calculators are defective is

P(all 4 are defective)= P(1st defect)* P(2nd defect) * P(3rd defect)* P(4th defect)=21*41*2*39/(31*61*3*59)=67158/334707=0.200647... = approx 0.2006

Answer:

Step-by-step explanation:

(3 +3 - 3 -3) / 3 = 0

3 - 3/3 - 3/3 = 1

3 + 3 - 3  - 3/3 = 2

(3*3*3/(3*3) = 3

(3 + 3+ 3+ 3) / 3  = 4

(3 * 3) - (3 + 3/3) = 5

((3*3*3)/ 3))  - 3 = 6

(3 * 3) - 3 + 3/3 = 7

(3*3*3 - 3) / 3 = 8

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

3 + 3 + 3 + 3/3 = 10.

Greetings from Brasil...

We need to use just GCD (greatest common divisor)

MDC in Brasil

GCD 1200, 1100 and 550 = 50

So we have to use bags with capacity of 50kg

In total we have (weight):

(1200 + 1100 + 550)kg

2850kg

total of bags:

Total Weight ÷ GDC

2850 ÷ 50

57 bags

  1 bag = U$5

57 bag = X

X = 57.5

Answer:

a) 3x^2-6x-3

b) 6

Step-by-step explanation:

f(x)=2x^2−4x+3

g(x)=x^2−2x−6

a)  (f+g)(x) = (2x^2−4x+3) + (x^2−2x−6)

             collect like terms

   (f+g)(x) = 2x^2+x^2-4x-2x+3-6

   (f+g)(x) = 3x^2-6x-3

b) (f+g)(3). This implies that x=3

  recall (f+g)(3) = 3x^2-6x-3

   (f+g)(3) = 3(3)^2-6(3)-3 = 27-18-3

   (f+g)(3) = 27-21 =6

Answer:

Step-by-step explanatiio:

Ep is when Qd=Qs

400-4p=6p-10

-4p-6p=-10-400

-8p=-410

P=51.25frs

EQ=400-4(51.25)

400-205

=125kg

Answer:

Pii is equAAAaaaaallLLLL to 3.14(rounded)

Step-by-step explanation:

Here listed are some formulas which can help you with your problems:

circumference of a circle=C=2πr

however, you can also write it as dπ, since  is two d times r.

area of a circle= πr^2

simply plug in your values, and solve them

you have all the materials you need to know

Further assistance/spoonfeed time:

We know the formulas for the circumference and area.

We also have the values of the circles A and B.

C=2πr

That's the formula, and now I'm gonna plug in the values given to me for A, which is 21.98 for circumference, and 7 for diameter.

(21.98)=2πr

Like I said before, the radius multiplied by 2 is the diameter, which is 7. But if you actually want the radius for some reason, just divide the diameter by 2.

let's update the equation: 21.98= 7π

now divide both sides by seven, and you'll get 3.14=π

area=π^2

now do what i just did, according to this formula

Answer:

16

Step-by-step explanation:

1x to 2x ratio

total is 24 oz, aka 3x or 1x+2x

24oz=3x

do some math

x=8oz

raisins = 2x = 16 oz

Answer:

Step-by-step explanation: 2x-16 oz

Answer:

7 square root x = 14​

Step-by-step explanation:

A radical equation will have the variable inside the radical

Answer:

D

Step-by-step explanation:

A radical equation persists when a radical includes a variable within it. In this case the x is in the radical, times 7. The rest of the answers do not have a variable in a radical.

Answer:

"Compactness" is the right answer.

Step-by-step explanation:

So that the above would be the correct answer.

The answer is 47 pounds

Explanation:

1. First, let's calculate the amount of money that was spent on chicken

$5 per pound of chicken x 25 pounds = $125

2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.

$454 (total) - $125 (chicken)  =  $329

3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.

$329 / $7 = 47 pounds

Add the top and bottom numbers together, divide that by 2 then multiply by the height.

15.3 + 19.5 = 34.8

34.8/2 = 17.4

17.4 x 11.1 = 193.14

Answer is 193.1 m^2

Answer:

The answer is option A.

Step-by-step explanation:

To find the length of AB we use sine

sin∅ = opposite / hypotenuse

From the question

AB is the hypotenuse

AC is the opposite

sin 36 = AC / AB

sin 36 = 20/ AB

AB = 20 / sin 36

AB = 34.026

Hope this helps you

Answer:

The correct answer is option a.

a. 5( √3+ 1 )

Step-by-step explanation:

Given that the angle changes from 45° to 60° in 10 minutes.

This situation can be represented as right angled triangles [tex]\triangle[/tex]ABC (in the starting when angle is 45°)and [tex]\triangle[/tex]ABD (after 10 minutes when the angle is 60°).

AB is the tower (A be its top and B be its base).

Now, we need to find the time to be taken to cover the distance D to B.

First of all, let us consider [tex]\triangle[/tex]ABC.

Using tangent property:

[tex]tan\theta =\dfrac{Perpendicular}{Base}\\\Rightarrow tan 45=\dfrac{AB}{BC}\\\Rightarrow 1=\dfrac{h}{BC}\\\Rightarrow h = BC[/tex]

Using tangent property in [tex]\triangle[/tex]ABD:

[tex]\Rightarrow tan 60=\dfrac{AB}{BD}\\\Rightarrow \sqrt3=\dfrac{h}{BD}\\\Rightarrow BD = \dfrac{h}{ \sqrt3}\ units[/tex]

Now distance traveled in 10 minutes, CD  = BC - BD

[tex]\Rightarrow h - \dfrac{h}{\sqrt3}\\\Rightarrow \dfrac{(\sqrt3-1)h}{\sqrt3}[/tex]

[tex]Speed =\dfrac{Distance }{Time}[/tex]

[tex]\Rightarrow \dfrac{(\sqrt3-1)h}{10\sqrt3}[/tex]

Now, we can say that more distance to be traveled to reach the base of tower is BD i.e. '[tex]\bold{\dfrac{h}{\sqrt3}}[/tex]'

So, more time required = Distance left divided by Speed

[tex]\Rightarrow \dfrac{\dfrac{h}{\sqrt3}}{\dfrac{(\sqrt3-1)h}{10\sqrt3}}\\\Rightarrow \dfrac{h\times 10\sqrt3}{\sqrt3(\sqrt3-1)h}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{(\sqrt3-1)(\sqrt3+1)} (\text{Rationalizing the denominator})\\\Rightarrow \dfrac{10 (\sqrt3+1)}{3-1}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{2}\\\Rightarrow 5(\sqrt3+1)}[/tex]

So, The correct answer is option a.

a. 5( √3+ 1 )

Answer:

Point of faulty equipment car = 0.2614 (Approx)

Step-by-step explanation:

Given:

Total number of car = 700

Faulty equipment car = 183

Find:

Point of faulty equipment car

Computation:

Point of faulty equipment car = Faulty equipment car / Total number of car

Point of faulty equipment car = 183 / 700

Point of faulty equipment car = 0.261428571

Point of faulty equipment car = 0.2614 (Approx)

========================================================

Explanation:

The angle 945 degrees is not between 0 and 360. We need to adjust it so that we find a coterminal angle in this range. To do this, subtract off 360 repeatedly until we get into the right range

945 - 360 = 585, not in range, so subtract again

585 - 350 = 225, we're in range now

Since 945 and 225 are coterminal angles, this means cos(945) = cos(225)

From here, we use the unit circle. Your unit circle should show the angle 225 in quadrant 3, which is the lower left quadrant. The terminal point here at this angle is [tex]\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]

The x coordinate of this terminal point is the value of cos(theta). Therefore  [tex]\cos(225^{\circ}) = -\frac{\sqrt{2}}{2}[/tex] and this is also the value of cos(945) as well

Using the periodic property of cos function, you can evaluate the value of cos(945°).

The value of cos(945°) is given by:

[tex]cos(945^\circ) = -\dfrac{1}{\sqrt{2}}[/tex]

A function returning to same value at regular intervals of specific length(called period of that function).

It is [tex]2\pi[/tex]

Thus, we have:

[tex]cos(x) = cos(2\pi +x) \: \forall \: x \in \mathbb R[/tex]

[tex]cos(945^\circ) = cos(2 \times 360^\circ + 225^\circ) = cos(2\pi + 2\pi + 225)\\ cos(945^\circ) = cos(2\pi) + 225) = cos(225^\circ)[/tex]

[tex]cos(\pi + \theta) = -cos(\theta)[/tex]

Thus:

[tex]cos(945^\circ) = cos(225^\circ) = cos(180^\circ + 45^\circ) = -cos(45^\circ) = -\dfrac{1}{\sqrt{2}}\\ cos(945^\circ) = -\dfrac{1}{\sqrt{2}}[/tex]

Note that wherever i have used [tex]\pi[/tex], it refers to [tex]\pi ^ \circ[/tex] (in degrees).

Thus, the value of cos(945°) is given by:

[tex]cos(945^\circ) = -\dfrac{1}{\sqrt{2}}[/tex]

Learn more about periodicity of trigonometric functions here:

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