Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. -91, -194, -291, -388

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Explanation:

The old dimensions of the rectangle were 30 by 15.

The new dimensions are 30+x by 15+x, where x is some positive number.

The new rectangle dimensions multiply to 1000

(30+x)(15+x) = 1000

Use the FOIL rule to expand out the left side like so

(30+x)(15+x) = 1000

450+30x+15x+x^2 = 1000

450+45x+x^2 = 1000

x^2+45x+450

Then lets get everything to one side

x^2+45x+450 = 1000

x^2+45x+450-1000 = 0

x^2+45x-550 = 0

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From here we use the quadratic formula

Plug in a = 1, b = 45, and c = -550.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(45)\pm\sqrt{(45)^2-4(1)(-550)}}{2(1)}\\\\x = \frac{-45\pm\sqrt{4225}}{2}\\\\[/tex]

[tex]x = \frac{-45\pm65}{2}\\\\x = \frac{-45+65}{2} \ \text{ or } \ x = \frac{-45-65}{2}\\\\x = \frac{20}{2} \ \text{ or } \ x = \frac{-110}{2}\\\\x = 10 \ \text{ or } \ x = -55\\\\[/tex]

Earlier we defined x to be a positive number. This means we ignore x = -55. It makes no sense to add on a negative amount to each dimension.

The only practical answer is x = 10.

So each dimension is increased by 10 feet.

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If x = 10, then the old dimensions of 30 by 15 bump up to 30+10 = 40 by 15+10 = 25

Then note how 40*25 = 1000, which helps confirm we have the correct dimensions.

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Now go back to the question at hand: we want to find the new width. The old width was 30 feet. The new width is 30+x = 30+10 = 40 feet

Answer:

The number of clay flower pots = x = 19

The number of ceramic flower pots = y = 16

Step-by-step explanation:

Let

The number of clay flower pots = x

The number of ceramic flower pots = y

Tara bought 35 flower pots

= x + y = 35

x = 35 - y

The gardening store sells clay flower pots, which hold 2 litres of dirt, and ceramic flower pots, which hold 7 litres. Tara bought 35 flower pots, which will hold a total of 150 litres of dirt.

Hence:

2x + 7y = 150.... Equation 2

Substitute 35 - y for x in Equation 2

2 (35 - y) + 7y = 150

70 - 2y + 7y = 150

-2y + 7y = 150 - 70

5y = 80

y = 80/5

y = 16 flower pots

x = 35 - y

x = 35 - 16

x = 19 flower pots

The number of clay flower pots = x = 19

The number of ceramic flower pots = y = 16

Answer:

The number of clay flower pots = 19

The number of ceramic flower pots = 16

Step-by-step explanation:

Answer:

yes its linear

Step-by-step explanation:

Answer:

[tex]\sqrt{12}[/tex] units

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the other leg, then

x² + 2² = 4²

x² + 4 = 16 ( subtract 4 from both sides )

x² = 12 ( take the square root of both sides )

x = [tex]\sqrt{12}[/tex] units

which can be simplified to 2[tex]\sqrt{3}[/tex] units , if required.

Answer:

y= -5/1 + 1.90

Step-by-step explanation:

The y-intercept is hard to tell

But the rest is right

Answer:

I have a picture if that helps

Step-by-step explanation:

Answer:

The average speed of the athlete for the entire competition is approximately 21.23 km/hr

Step-by-step explanation:

The given parameters of the athlete performance in the triathlon are;

The length the athlete swims = 750 m = 0.75 km

The time the athletes spends swimming = 15 minutes = 0.25 hours

The speed with which the athlete cycles = 40 km/hr.

The time the athletes spends while cycling = 30 minutes = 0.5 hours

The distance the athlete ran = 5 km

The average speed with which the athlete ran = 3 m/s = 10.8 km/hr.

The formula for average speed, s is Average speed = Total distance/(Total time)

The distance, ∑d, the athlete covered in the entire competition is given as follows;

∑d = 0.75 km + 0.5 hr. × 40 km/hr. + 5 km = 0.75 km + 20 km + 5 km = 25.75 km

The distance, ∑t, the athlete spends in the entire competition is given as follows;

∑t = 0.25 hr. + 0.5 hr. + 5 km/(10.8 km/hr.) = 0.25 hr. + 0.5 hr. + 0.463 hr. ≈ 1.213 hr.;

Therefore;

The average speed of the athlete for the entire competition, s = ∑d/∑t = 25.75 km/(1.213 hr.) ≈ 21.23 km/hr.

Answer:

A or B

Step-by-step explanation:

Also i need help to

Answer:

A. [tex]\sqrt{16}[/tex] × [tex]\sqrt{4}[/tex]  

I hope this helps!

Answer:

The equation of the linear relationship is y = 3x + 2 ⇒ B

Step-by-step explanation:

To solve the question substitute the x in the equation by the x-coordinate of each point to find y, if y equals the y-coordinate of the point, then the point is on the graph of the equation

A.

∵ y = 2x + 3

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 2(0) + 3

∴ y = 0 + 3 = 3

∵ The y-coordinate is 2

∴ The point (0, 2) does not lie on the graph of the relationship

∴ The equation y = 2x + 3 doesn't represent the equation of the relationship

B.

∵ y = 3x + 2

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 3(0) + 2

∴ y = 0 + 2 = 2

∵ The y-coordinate is 2

∴ The point (0, 2) lies on the graph of the relationship

→ Use the second point (1, 5)

∵ x = 1

→ Substitute x by 1 in the equation

∴ y = 3(1) + 2

∴ y = 3 + 2 = 5

∵ The y-coordinate is 5

∴ The point (1, 5) lies on the graph of the relationship

→ Use the third point (3, 11)

∵ x = 3

→ Substitute x by 3 in the equation

∴ y = 3(3) + 2

∴ y = 9 + 2 = 11

∵ The y-coordinate is 11

∴ The point (3, 11) lies on the graph of the relationship

→ Use the fourth point (2, 7)

∵ x = 2

→ Substitute x by 2 in the equation

∴ y = 3(2) + 2

∴ y = 6 + 2 = 8

∵ The y-coordinate is 7

∴ The point (2, 7) doesn't lie on the graph of the relationship

∴ The equation of the linear relationship is y = 3x + 2

Answer:

b

Step-by-step explanation:

Answer:

the answer is D.

Step-by-step explanation:

Answer: Option B.

Step-by-step explanation:

A linear function can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

if the line passes through the points (ax, ay) and (bx, by) then the slope is:

a = (bx - ax)/(by - ay)

In this case, we can see that the line passes through the points:

(1, 3) and (2, 1)

Then the slope is:

a = (1 - 3)/(2 - 1) = -2

y = -2*x + b

In the graph we also can see that the line intersects the y-axis at y = 5, then b = 5.

The line is:

y = f(x) = -2*x + 5.

the inverse function is such that:

g( f(x)) = x

to find the inverse function of a linear equation, we just could isolate x.

y - 5 = -2x

-y/2 + 2.5 = x

Then we could write the inverse function as:

g(x)  = - x/2 + 2.5

Now we need to see which pairs belong to this line. I just will evaluate the function g(x) in different values of x, and see which points belong to the line.

g(9) = -9/2 + 2.5 = -4.5 + 2.5 = -2

(9, -2) belongs to the line.

g(7) = -7/2 + 2.5 = -3.5 + 2.5 = -1

Then (7, -1) belongs to this line.

g(5) = -5/2 + 2.5 = 0

Then the point (5, 0) belong to this line.

We can already see that all these points are in option B, then option B is the correct one.

Step-by-step explanation:

Alex buys x oranges and Bobbie buys x + 2 oranges. Together they buy 2x + 2 oranges.

$4.20 / $0.21 = 20 oranges.

2x + 2 = 20

2x = 18

x = 9

Hence the value of x is 9.

Answer:

x=9

Step-by-step explanation:

The total number of oranges purchased is x + x+2 =  2x+2

They cost 21 cents each

(2x+2) *.21

This is equal to 4.20

(2x+2) *.21 =4.20

Divide each side by .21

(2x+2) *.21/.21 =4.20/.21

2x+2 = 20

Subtract 2 from each side

2x+2-2 =20-2

2x= 18

Divide by 2

2x/2 =18/2

x =9

Answer:

Step-by-step explanation:

Let football cost be f and basketball cost be b

We have two equations as per given:

We need to find b, therefore we'll eliminate f

To do so we'll double the first equation and subtract the second one:

Each basketball costs $6.25

Question:

Coach purchased footballs and basketballs from two different stores.

Each football costs the same amount, and each basketball costs the same amount.

At the first store, the coach paid $110 for 5 footballs and 14 basketballs.

At the second store, the coach paid $82.50 for 10 footballs and 6 basketballs.

What was the cost in dollars of Each basketball?

Answer:

Probably 7

REAL Answer:
6.25

Your Welcome! (^·^)

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Step-by-step explanation:

Since Angle DAE = Angle BCE, lines AD amd BC are parallel (by Z-angles).

This means that Angle ADE = Angle CBE (by Z-angles).

We have 2 congruent angles and 1 congruent side (AD = BC, given).

By ASA congruence, triangles AED and CEB are congruent.

B.P. Mathur v. Union Of India

Answer:

a. are for the same time period

Answer:

y=-7x-2

Step-by-step explanation:

I assume you need the equation for the line, so that's what I'm solving for here.

1. Start by putting the slope and the coordinates into point slope form, which is y-y1=m(x-x1)

y+30=-7(x-4)

2. Distribute -7 to (x-4) (or multiply x and -4 by -7).

y+30=-7x+28

3. Subtract 30 from both sides to get y by itself.

y=-7x-2

Answer:

the first one

Step-by-step explanation:

☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️

Answer:

[tex]x=12(\sqrt2-1)[/tex]

Step-by-step explanation:

The given equation is :

[tex]\sqrt{2} x-7+x=5[/tex]

Add 7 to both sides of the equation.

[tex]\sqrt{2} x-7+x+7=5+7\\\\\sqrt{2} x+x=12[/tex]

Taking x common from both sides of the equation.

[tex]x(\sqrt{2} +1)=12\\\\x=\dfrac{12}{\sqrt2+1}[/tex]

Multiplying both numerator and denominator by [tex]\sqrt2-1[/tex]

[tex]x=\dfrac{12}{\sqrt2+1}\times \dfrac{\sqrt2-1}{\sqrt2-1}\\\\=\dfrac{12(\sqrt2-1)}{2-1}\\\\=12(\sqrt2-1)[/tex]

Hence, the value of x is [tex]12(\sqrt2-1)[/tex].

Answer:

8 pounds

Step-by-step explanation:

3 ft board = 2lb

12 ft board is 4 times more so

2x4 = 8 lb

Step-by-step explanation:

4x+2+95=-7+17x

104=13x

x=8

for angle U=34 degrees

the answer is C

Answer:

R=-4

Step-by-step explanation:

-3(2r+7)=3

-6r-21=3

-6r=24

r=-4

I hope this is correct and have a great day

Answer:

$50

Step-by-step explanation:

Change 250 to a decimal:

250/100 = 2.50

multiple the price by this decimal to find the new price:

$20 x 2.50 = $50

Answer:

the answer is 12k²r¹⁴.........

Answer:

x+9

Step-by-step explanation:

I got it right on the quiz

Given:

A line is perpendicular to the given line and having negative slope.

To find:

The slope of the line.

Solution:

We know that, product of slopes of two perpendicular lines is -1.

[tex]m_1\cdot m_2=-1[/tex]

[tex]m_1=-\dfrac{1}{m_2}[/tex]

It means, one slope is opposite and reciprocal of other.

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the given graph it is clear that, blue line passes through (0,3) and (2,4). So, slope of blue line is

[tex]m_B=\dfrac{4-3}{2-0}[/tex]

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

The slope of blue line is [tex]\dfrac{1}{2}[/tex]. So, slope of the line which is perpendicular to the blue line is -2, which is negative.

From the given graph it is clear that, red line passes through (0,4) and (4,3). So, slope of red line is

[tex]m_R=\dfrac{3-4}{4-0}[/tex]

[tex]m_R=\dfrac{-1}{4}[/tex]

The slope of blue line is [tex]-\dfrac{1}{4}[/tex]. So, slope of the line which is perpendicular to the blue line is 4, which is positive.

Therefore, the slope of the line which is perpendicular to the given line and having negative slope, is -2.

Answer:

B

Step-by-step explanation:

The pattern is x/-3

Answer:

take one finger and than the other and how may fingers do you have now 2