Why does the range of this function include negative values? What is the significance of the point where the graph crosses the horizontal axis?

Answer:

Hello,

Step-by-step explanation:

Let's say 2x the smaller number,2x+2 the greater.

2x*(2x+2)=12+(2x)²

2x²+4x=12+4x²

4x=12

x=3

The smaller numbre is 2x=6 and the greater is 8

6*8=48 =12+6²

At a point on the ground 15ft from the base of a​ tree, the distance to the top of the tree is 1 ft more than 2 times the height of the tree. Find the height of the tree.

The height of the tree is 8ft.

Given that,

A right triangle has two legs, which are height and (15 feet) from the base.

The hypotenuse is 15 feet from the base to the top of the tree.

or 2(height) + 1ft.

Let us take a as height of the tree; b=distance from base=15 ft; c=hypotenuse=2a+1ft

The area of the square created on the hypotenuse of any right triangle is equal to the sum of the areas of the squares formed on the triangle's legs:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]a^{2} +(15ft)^{2}=(2a+ 1ft) ^{2}[/tex]

[tex]a^{2} +225ft^{2}=4a^{2} +4a+1\\ 0=3a^{2}+4a-224\\ 0=(a-8)\times(3a+28)\\[/tex]

Now,

a-8=0 (or) 3a+28=0

a=8 (or) a=[tex]\frac{-28}{3}[/tex]

Therefore, The height of the tree is 8ft.

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Answer:

4x+8+7x-8

Step-by-step explanation:

4x+7x+8-8

11x+0

11x.

Answer:

1.5 teaspoons for each dozen

Step-by-step explanation:

A recipe calls for 4.5 teaspoons of sugar for 3 dozen cookies explain the process to find how much is needed for each dozen?

Divide 4.5 teaspoons by 3:

4.5/3 = 1.5 teaspoons for each dozen

since 4.5 teaspoons of sugar will make 3 dozen, we divide 4.5 by 3 to find for each dozen.

Answer: The 12 songs for $10

Step-by-step explanation: 12 / 10 = 1.2 while 12 / 0.85 = 14.11

See attachment for the graphs of the inequalities

To do this, we analyze and plot each inequality at a time

Having said that, we have

Inequality 1: y > -3x - 2

Here, we have

y > -3x - 2

The inequality > implies that the right-hand side of the origin will be shaded

Also, it means that the line of the inequality will be a dotted line

Inequality 2: 4x + 5y ≤ 20

Here, we have

4x + 5y ≤ 20

The inequality ≤ implies that the left-hand side of the origin will be shaded

Also, it means that the line of the inequality will be a closed line

Inequality 3: y > -4

Here, we have

y > -4

The inequality > implies that the upper part of the origin will be shaded

Also, it means that the line of the inequality will be a dashed line

See attachment for the graphs of the inequalities

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Numbers that can be written as a power in more than one way is known as exponents .

A sign that denotes raising to a power that is placed above and to the right of a mathematical expression. for example , [tex]2^{a}[/tex].

The mathematical procedure known as exponentiation, abbreviated as bn, involves the base number (b) and the exponent (or power) number (n). In English, it is pronounced "b (raised) to the (power of) n." [1] Exponentiation is the process of repeatedly multiplying bases, where n is a positive integer, and the product is known as bn.

The exponent is typically denoted by a superscript to the right of the base. The term "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most simply, "b to the nth," is used to describe bn.

Numbers that can be written as a power in more than one way is known as exponents .

These numbers are basically written to save time to multiply the same number multiple times .

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Answer:

x + y ≤ 7

(if that doesn't work, 0 ≤ x + y ≤ 7)

Rew wants to buy 7 items or less, so the number of dubbles and totts combined can't be bigger than 7, and is therefore less than or equal to 7.

The capacity of the full tank is 16 hectolitre. percentage problem.

A gasoline tank contains 9.6 hectolitres (hL) when it is 60% full. when the tank is 100% full that is the capacity of the tank.

so, the capacity of the full tank is 9.6x(100/60) = 16 hL.

this a percentage problem. In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". A percentage is a dimensionless number; it has no unit of measurement.

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Answer:

  5%

Step-by-step explanation:

You want the interest rate that makes the difference between compound and simple interest on ₹8000 for two years be ₹20.

The formula for the value of an account earning simple interest is ...

  A = P(1 +rt) . . . . P earning interest rate r for t years

The formula for the value of an account earning compound interest is ...

  A = P(1 +r)^t . . . . P earning interest rate r for t years

We want the difference in these amounts over 2 years to be ₹20.

  8000(1 +r)^2 -8000(1 +2r) = 20

  1 +2r +r^2 -(1 +2r) = 20/8000 . . . . . divide by 8000, expand the square

  r^2 = 1/400 . . . . . . simplify

  r = 1/20 = 5% . . . . . take the square root

The rate of interest is 5% per year.

Answer:

The correct answer would be,

= 10m^3 + 8m^2 - 10m - 0.8

Step-by-step explanation:

First you subtract the m^3 terms :

> 7m^3 + 3m^3

> 10m^3

Then you subtract m^2 , in this case we only have 1 m^2 :

> 8m^2

Then you subtract the m terms :

> -m - 9m

> -10m

The lastly you subtract the last terms :

> 2.8 - 3.6

> -0.8

= 10m^3 + 8m^2 -10m -0.8

(Make sure to distribute the negative before you solve it.) Just a point!!

Answer:

10m³+8m²-10m-0.8

Step-by-step explanation:

(7m³ +8m²-m+2.8)-(-3m³ +9m+3.6)

Use the sign to open the bracket we have;

7m³ +8m²-m+2.8+3m³-9m-3.6

bring like terms together

7m³+3m³+8m²-9m-m-3.6+2.8

Simplifying we have;

10m³+8m²-10m-0.8

hope it helps...

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Miraawesome

Answer:

Step-by-step explanation:

Let the time for cold tap be c and hot tap be h.

The cold water tap can fill a container two hours faster than the hot water tap:

The two taps together can fill a container in 80 minutes:

Answer:

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

[tex]y < \frac{3x}{2} +6[/tex]

Answer:

9 Pizzas

Step-by-step explanation:

Answer:

you're answer will be 2 hours and 30 minutes

Step-by-step explanation:

i hope that helps you! :))

The equation of the future value function if x represents the number of weeks is [tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex].

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

Robbie depositing= $100

Interest=2.4%

Time=3 years.

According to given question we have

P = periodic payment = $100 / week

r = interest rate = 2.4%, compounded weekly

t = 3 years

x = 52 weeks (# of times interest is compounded per year)

To write a equation we have

B = Future Value

[tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex]

Therefore, the equation of the future value function if x represents the number of weeks is [tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex].

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Answer:

[tex] \sf (- \infty, 58] [/tex]

Step-by-step explanation:

Express as interval = [tex] \sf (- \infty, 58][/tex]

The first angle will be 77.33°.

It should be noted that the total angles will be 180°.

This will be illustrated as:

8x + 8 + 8x + 8 + 2x + 8 = 180

18x + 24 = 180

18x = 180 - 24

18x = 156

x = 8.667

The first angle will be

= 8x +8

= 8(8.667) + 8

= 77.33°

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Answer: 1 1/4 batches of muffins

Step-by-step explanation:

Answer:

y = - 3x + 12

Step-by-step explanation:

Slope intercept form of line

y = mx + b where m = slope, b = y-intercept

==> y = -3x + b is the equatin

To find b, plug in values for point x = 9, y =-15 and solve for b

-15 = -3(9) + b

-15 = -27 + b

Add 27 both sides

-15 + 27 = b

12 = b

b = 12

Equation is
y = - 3x + 12

Answer: full house,fairly oddparents, the simsons

edit^^^ a movie is clueless or even mean girls

Step-by-step explanation:

An all-terrain vehicle can travel the fastest.

Speed can be define as the time rate by which an object is moving or running along a path. A speed is the quantity which describes the moving rate of any object. We can define the speed with respect to distance and time . Or we can say speed is distance per unit of time . It is calculate in term of kilometers per hour.

Mathematically, we can write:

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

where, distance is measured in km

           and Time is measured in hours

In the question, the distance for three different types of vehicles are given and we have to find fastest vehicle for which we need to find the speed.

For  self-balancing scooter

Time = 1 hour

Distance = 12 miles

Therefore, Speed = 12 miles/h

For all-terrain vehicle

Time = 1 hour

Distance = 12 . 6 = 72 miles

Therefore, speed = 72 miles/h

For a go-kart

Time = 1 hour

Distance = 67 miles

Therefore, speed = 67 miles/h

Hence it is cleared that An all-terrain vehicle can travel the fastest.

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Answer:

1/243

Step-by-step explanation:

Each denominator is multiplied by 3 from the last one

3 x 3 = 9

9 x 3 = 27

27 x 3 = 81

81 x 3 = 243

The range of the data is 5.

Ensure that the score column entries are listed in ascending numerical order. The entries in our example are listed in numerical order.

According to the definition, range is determined for continuous frequency distribution as the difference between the upper limit of the maximum interval and lower limit of the minimum interval of the grouped data.

1. Find the score column entry with the lowest value (with a Frequency greater than 0).

here we have 1 as the lowest entry. The lowest test score is 1.

2. Find the highest entry in the Score column (with a Frequency greater than 0).

here, we have 6 as the highest entry  The highest test score is 6.

Subtract the lowest number (1) from the highest number (6).

6 - 1 = 5

The range of the test scores is 5.

Hence we get the range of the given data as 5.

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[tex](\stackrel{x_1}{4.5}~,~\stackrel{y_1}{3.5})\qquad (\stackrel{x_2}{9.5}~,~\stackrel{y_2}{5.5})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5.5}-\stackrel{y1}{3.5}}}{\underset{run} {\underset{x_2}{9.5}-\underset{x_1}{4.5}}}\implies \cfrac{2}{5}[/tex]

Answer:

G(0) = 3

Step-by-step explanation:

g(0) means what is the value of g(x) when x = 0

substitute x = 0 into g(x)

g(0) = 2(0) + 3 = 0 + 3 = 3