If a spring stretches 6 meters when a 7-kilogram weight is attached to it, how much will it stretch when a 42-kilogram weight is attached to it?

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

[tex] \frac{2}{3} x = 1 - 5[/tex]

[tex] \frac{2}{3} x = ( - 4)[/tex]

[tex]x = ( - 4) \div \frac{2}{3} [/tex]

[tex]x = ( - 4) \times \frac{3}{2} [/tex]

[tex]x = \frac{ - 12}{ \: \: \: 2} [/tex]

[tex]x = ( - 6)[/tex]

[tex]∴ \frac{2}{3} \times ( - 6) + 5 = 1[/tex]

Answer:

x = 40 + -1.5y

Step-by-step explanation:

Simplifying

2x + 3y = 80

Solving

2x + 3y = 80

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3y' to each side of the equation.

2x + 3y + -3y = 80 + -3y

Combine like terms: 3y + -3y = 0

2x + 0 = 80 + -3y

2x = 80 + -3y

Divide each side by '2'.

x = 40 + -1.5y

Simplifying

x = 40 + -1.5y

Final answer:

The x-value 6.5 in the quadratic function's vertex represents the price of the headphones in dollars at which the company's expected revenue is maximized, according to the revenue function [tex]R= - 5x^2 +65x + 700[/tex].

Explanation:

The question involves understanding the meaning of the x-value in the vertex form of a quadratic function, which in this context represents the price of the headphones for which the company expects to make the maximum revenue. The given function is [tex]R= - 5x^2 +65x + 700[/tex], and the vertex of the graph of this function is given as (6.5, 911.25). The x-value, 6.5, therefore represents the price in dollars at which the revenue of the company is maximized. This is because, in the context of a quadratic revenue model, the vertex represents the maximum point when the parabola opens downwards (which it does, since the coefficient of x² is negative), meaning that increasing or decreasing the price from this point will lead to a decrease in the total revenue.

Answer:

It would take approximately 6.50 second for the cannonball to strike the ground.

Step-by-step explanation:

Consider the provided function.

[tex]h(t)=-4.9t^2+30.5t+8.8[/tex]

We need to find the time takes for the cannonball to strike the ground.

Substitute h(t) = 0 in above function.

[tex]-4.9t^2+30.5t+8.8=0[/tex]

Multiply both sides by 10.

[tex]-49t^2+305t+88=0[/tex]

For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Substitute a = -49, b = 305 and c=88

[tex]t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}[/tex]

Ignore the negative value of t as time can't be a negative number.

Thus,

[tex]t=\frac{305+\sqrt{110273}}{98}\approx6.50[/tex]

Hence, it would take approximately 6.50 second for the cannonball to strike the ground.

Answer:

Therefore,

[tex]x=y= 4\sqrt{2}=5.6568\ units[/tex]

Step-by-step explanation:

Given:

Consider In Right Angle Triangle ABC

∠B = 90°

∠C = ∠A = 45°

AB = y

BC = x = adjacent side

AC = 8 = hypotenuse

To Find:

x = ?

y = ?

Solution:

In Right Angle Triangle ABC by Cosine Identity we have

[tex]\cos C = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}\\[/tex]

substituting the above given values we get

[tex]\cos 45 = \dfrac{BC}{AC}=\dfrac{x}{8}[/tex]

[tex]\dfrac{1}{\sqrt{2} } =\dfrac{x}{8}\\\therefore x=\dfrac{8}{\sqrt{2} } \\Rationalizing\ we\ get\\\therefore x=\dfrac{8}{\sqrt{2}}\times \dfrac{\sqrt{2} }{\sqrt{2}}}\\\therefore x=4\sqrt{2}=4\times 1.4142=5.6568\ units[/tex]

As The triangle is 45 - 45 - 90

It is an Isosceles Right triangle

[tex]x=y[/tex]..... Isosceles Triangle property

[tex]\therefore y=4\sqrt{2}=4\times 1.4142=5.6568\ units[/tex]

Therefore,

[tex]x=y= 4\sqrt{2}=5.6568\ units[/tex]

Answer:

49 cm²

Step-by-step explanation:

The volume (V) of a cube is calculated as

V = s³ ← s is the length of the side, thus

s³ = 343 ( take the cube root of both sides )

s = [tex]\sqrt[3]{343}[/tex] = 7, thus

area of base = s² = 7² = 49 cm²

Rajeev will pay Rs 6876.10 for the goods.

Step-by-step explanation:

Given,

Worth of goods = Rs 6650

Rebate = 6%

Amount of rebate = 6% of worth of goods

Amount of rebate = [tex]\frac{6}{100}*6650=0.06*6650[/tex]

Amount of rebate = Rs 399

Amount after rebate = 6650 - 399 = Rs 6251

Sales tax = 10%

Amount of sales tax = 10% of amount after rebate

Amount of sales tax = [tex]\frac{10}{100}*6251=0.1*6251[/tex]

Amount of sales tax = Rs 625.10

Total amount of goods paid = Amount after rebate + sales tax

Total amount of goods paid = 6251+625.10 = Rs 6876.10

Rajeev will pay Rs 6876.10 for the goods.

Keywords: addition, percentage

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Answer:

[tex]a - 6 \leqslant 15 + 8a[/tex]

[tex] - 7a \leqslant 21[/tex]

[tex]a \geqslant - 3[/tex]

Answer:

It is B.   (36√5 + 36) ft^2.

Step-by-step explanation:

Total area = area of the base +  4 * area of the triangular side.

The slant height of a triangular side =  √(6^2 + 3^2)

= √45

= 3√5

The area of this side = 3 * 3 √5

= 9√5.

Therefore the total area of the pyramid

=  6^2 + 4*9√5

= (36 + 36√5) ft^2.

Grant needs to ride at least 13.33 miles to male at least $ 15.00 a day

Solution:

Given that Grant has an agreement with Brian to rent the bike for $35.00 a night

He charges customers $3.75 for every mile he transports them

Grant needs to make at least $15.00 a day

To find: miles needed to ride

From given question, He charges customers $3.75 for every mile he transports them

So if he transports for "x" miles he would get,

[tex]\$ 3.75 \times x = \$ 3.75x[/tex]

So the profit he gets is $ 3.75 and initial cost invested to rent bike is $ 35. Also, Grant needs to make at least $15.00 a day

So we can frame a inequality as:

[tex]3.75x - 35 \geq 15\\\\3.75x\geq 35 + 15\\\\3.75x\geq 50\\\\x \geq 13.33[/tex]

So he needs to ride atleast 13.33 miles to male atleast $ 15.00 a day

Answer:

The amount of tax paid is C. $3.20

Step-by-step explanation:

If we take $50.00 and give a 20% discount, we're taking 20% of 50 and then subtracting it from the origional price (50) which brings us down to 40, because 20% of 50 is 10 and we subtract.

Now that we have $40.00, sales tax comes in at a whopping 8%. To calculate the solution of a price with sales tax, we need to find what 8% of $40 is, which after calculations will be 3.20.

Since this question is asking on tax only, our answer is $3.200, C.

There is no graph, so it is impossible to answer this question. I apologise.

Answer:

x=-17/19, y=131/19. (-17/19, 131/19).

Step-by-step explanation:

-19x=26-9

-19x=17

x=-17/19

9(-17/19)=54-9y

-153/19=54-9y

9y=54-(-153/19)

9y=54+153/19

9y=1026/19+153/19

9y=1179/19

y=(1179/19)/9

y=(1179/19)(1/9)

y=1179/171

y=131/19

Good evening ,

Answer:

Step-by-step explanation:

255 = 3×5×17

726 = 2×3×11^2

Then HCF(255,726) = 3.

:)

Answer:

8.76

Step-by-step explanation:

Simplifying

15.00 + -6.24 = b

Combine like terms: 15.00 + -6.24 = 8.76

8.76 = b

Solving

8.76 = b

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-1b' to each side of the equation.

8.76 + -1b = b + -1b

Combine like terms: b + -1b = 0

8.76 + -1b = 0

Add '-8.76' to each side of the equation.

8.76 + -8.76 + -1b = 0 + -8.76

Combine like terms: 8.76 + -8.76 = 0.00

0.00 + -1b = 0 + -8.76

-1b = 0 + -8.76

Combine like terms: 0 + -8.76 = -8.76

-1b = -8.76

Divide each side by '-1'.

b = 8.76

Simplifying

b = 8.76

Answer:

[tex]x^{2} +7x-170=0[/tex]

Step-by-step explanation:

Here is the complete question: The width of a rectangle is 7 meters greater than its length . If the area of the rectangle is 170 m², write the quadratic equation in standard form for the equation that would represent the area of the rectangle. Let x equal to the length of the rectangle.

Given: Width of rectangle is 7 meter greater than length

           Length of rectangle is x.

           Area of rectangle= 170 m²

Now as given, length is x meter and width is (x+7) meter

we know that, area of rectangle= [tex]length\times width[/tex]

∴ substitute the values to get correction equation.

⇒170= [tex]x\times (x+7)[/tex]

now distributing x into (x+7).

⇒ [tex]170= x^{2} +7x[/tex]

subtracting 170 both side.

[tex]x^{2} +7x-170=0[/tex]

∴ [tex]x^{2} +7x-170=0[/tex] is the quadratic equation in standard form for the equation that would represent the area of the rectangle.

Answer:

The number of adult tickets sold is 894 and the number of kid tickets is 750.

Step-by-step explanation:

Given:

A Six Flags theme park charges $30 for adults and $15 for kids.

Total of 1,644 tickets were sold.

Total amount of tickets $11,250.

Now, to find the number of adult tickets and kid tickets.

Let the number of kid tickets be [tex]x.[/tex]

And the number of adult tickets be [tex]y.[/tex]

So, the total number of tickets:

[tex]x+y=1644.[/tex].....(1)

Solving the equation we get the value of [tex]x[/tex]:

[tex]x=1644-y.[/tex]

Now, the total amount of tickets of adult and kids:

[tex]15x+30y=11250.[/tex]

So, by putting the value of [tex]x[/tex] we get:

[tex]15(1644-y)+30y=11250[/tex]

[tex]24660-15y+30y=11250[/tex]

[tex]24660+15y=11250[/tex]

Subtracting both sides by 24660 we get:

[tex]15y=-13410[/tex]

Dividing both sides by -15 we get:

[tex]y=894[/tex]

Thus number of adult tickets = 894.

Now, putting the value of [tex]y[/tex] in equation (1):

[tex]x+894=1644[/tex]

On solving we get:

[tex]x=1644-894[/tex]

[tex]x=750.[/tex]

So. the number of kid tickets = 750.

Therefore, the number of adult tickets sold is 894 and the number of kid tickets is 750.

Answer: 750

Step-by-step explanation:

Answer:

[tex]a=2s-b-c[/tex]

Step-by-step explanation:

Given formula:

[tex]s=\frac{a+b+c}{2}[/tex]

To solve for [tex]a[/tex]

In order to solve for [tex]a[/tex] we will try to isolate [tex]a[/tex] on one side of the equation.

Steps to isolate [tex]a[/tex].

1) Multiplying both sides by [tex]2[/tex] to remove fractions.

[tex]2\times s=2\times \frac{a+b+c}{2}[/tex]

[tex]2s=a+b+c[/tex]

2) Subtracting both sides by [tex]b[/tex]

[tex]2s-b=a+b-b+c[/tex]

[tex]2s-b=a+c[/tex]

3) Subtracting both sides by [tex]c[/tex]

[tex]2s-b-c=a+c-c[/tex]

[tex]2s-b-c=a[/tex]

Thus, we successfully isolated [tex]a[/tex] on one side. The formula for [tex]a[/tex] can be given as:

∴ [tex]a=2s-b-c[/tex]

The new mean is 11

Step-by-step explanation:

The mean = sum of the numbers ÷ numbers

∵ The set has 5 numbers

∵ The mean of the 5 numbers is 12

- Substitute these values in the rule of the mean above

∴ 12 = sum of the numbers ÷ 5

- Multiply both sides by 5

∴ 60 = sum of the numbers

∵ One of the number is 16

∵ 16 is removed from the set of the number

- Subtract 16 from the sum and the numbers will be four numbers

∵ The new sum = 60 - 16

∴ The new sum = 44

∵ The set has 4 numbers

∴ The new mean = 44 ÷ 4 = 11

The new mean is 11

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Answer:

The correct answer is A. 4,818'000,000 kilowatt-hours per year and B. 481,800 households.

Step-by-step explanation:

1. Let's review the information provided to us for solving the questions:

Power capacity of the wind farms = 2,200 Megawatts or 2.2 Gigawatts

2. Let's resolve the questions A and B:

Part A

Assuming wind farms typically generate 25​% of their​ capacity, how much​ energy, in​ kilowatt-hours, can the​ region's wind farms generate in one​ year?

2,200 * 0.25 = 550 Megawatts

550 Megawatts = 550 * 1,000 Kilowatts = 550,000 Kilowatts

Now we calculate the amount of Kilowatts per hour, per day and per year:

550,000 Kw generated by the farms means that are capable of produce 550,000 kw per hour of energy

550,000 * 24 = 13'200,000 kilowatt-hours per day

13'200,000 * 365 = 4,818'000,000 kilowatt-hours per year

Part B

Given that the average household in the region uses about​ 10,000 kilowatt-hours of energy each​ year, how many households can be powered by these wind​ farms?

For calculating the amount of households we divide the total amount of energy the wind farms can generate (4,818'000,000 kilowatt-hours) and we divide it by the average household consumption (10,000 kilowatt-hours)

Amount of households =  4,818'000,000/10,000 = 481,800

Answer:

y = mx + b

Step-by-step explanation:

m is slope

b is y-intercept

Answer:

y = 90°

Step-by-step explanation:

You do 110° + 80° which is 180 divides by two because there is a straight line in the middle of it. I don't know how to explain it.

Answer:

90 degrees

Step-by-step explanation:

you have angles of 110 and 70 on the sides. The triangle altogether equals 180 but that doesn't matter in this equation. Since y is directly between the two angles that are given, it is 90.

110-70=40/2=20 so add 20 to 70 and subtract 20 from 110 so you get 90.

Answer:

x>-4

Step-by-step explanation:

13-2x > 21

-13 -13

-2x >8

(-2x)/(-2) >(8)/(-2)

x>-4

Answer:

Step-by-step explanation:

Divide 7,200 by 45

The number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

A clothing factory makes 7,200 t-shirts in one week on average there are 45 employees at the factory.

Let x be the number of t-shirts each employee make in one week

The value of x can be calculated as follows:

x = 7,200/45

x = 160

Thus, the number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.

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Answer:

y+1=-3/2(x-3)

Step-by-step explanation:

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

m=(5-(-1))/(-1-3)

m=(5+1)/-4

m=6/-4

simplify

m=-3/2

y-y1=m(x-x1)

y-(-1)=-3/2(x-3)

y+1=-3/2(x-3)

Answer:

Substitute the slope  and the coordinates of point D in the equation of the line  y=mx+b and then solve for b in each equation

Step-by-step explanation:

we know that

The first step is calculate the slopes of these two lines. Remember that if two lines are parallel then the slopes are the same (m1=m2) and if two lines are perpendicular then the slopes is equal to m1*m2=-1

The second step is substitute the slope m2 and the coordinates of point D in the equation of the line in slope-intercept form y=mx+b and then solve for b in each equation

Answer:

$.56 per can; $.49 per can; 5 cans for $2.45

Step-by-step explanation:

If it were a dollar for two cans, it's pretty easy to figure out each can is 50 cents.  So you use the same idea.  if you have x cans for y dollars, if you divide both numbers by x you get the price of 1 can.

3 cans for 1.68 is 1 can for 1.68/3 = .56 so 56 cents

5 cans for 2.45 is 1 can for 2.45/5 = .49 so 49 cents.

You could use this trick dividing by the price and find how many cans you need to but to pay 1 dollar.

3 cans for 1.68 is 3/1.68 for 1 dollar or 1.786 cans for 1 dollar.  Doesn't make a lot of sense since you can't but part of a can, but I wanted to show you how you could use the logic for other things.

Answer:

x= 1; y= 0; z= -2 and w= 3.

Step-by-step explanation:

Given that,

1) x + 2y - z = 3

2) 2x - y + z - w = -3

3) y + 2z - w = -7

4) x + 3y + 2z + 2w = 3 ​

now, from 1) z = x + 2y -3 →→(5)

from 2) w = 2x -y + z +3

         ⇒w = 2x -y + x + 2y -3 +3  (from (5))

            w = 3x + y →→(6)

Now substitute (5) and (6) in 3), we get

y +2(x + 2y -3) - (3x + y) = -7

⇒ 4y - x = -1 →→→(7)

Now substitute (5) and (6) in 4), we get

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

⇒ 9x +9y = 9

⇒ x + y =1 →→→(8)

⇒ x= 1-y , substituting this in (7) gives 5y -1 = -1

⇒ y = 0 and x = 1

substituting these values in

(5) and (6) gives, z = -2 and w = 3

⇒ x= 1; y= 0; z= -2 and w= 3.

Answer:

For x = 10,  the value of the given function f(x)= 4(x − 11) − 9 is -13.

Step-by-step explanation:

Here, the given expression is:

f(x) = 4(x − 11) − 9

Now, given: f(x)  = -13

⇒ -13  = 4(x − 11) − 9

Now, solving for the value of x, we get:

-13  = 4(x-11) -9

⇒ -13 = 4 x - 44 - 9

or, -13 + 44  + 9 =  4x

or, 4 x = 40

or, x = 40/4 = 10

or, x = 10

Hence, for x = 10,  the value of the given function f(x)= 4(x − 11) − 9 is -13.

Answer:

The answer is B. 6 and 8.

Answer:

B) 6 and 8

Step-by-step explanation:

[tex]3 \times 8 = 24[/tex]

[tex]4 \times 6 = 24[/tex]

[tex]2 \times 12 = 24[/tex]