Write an equation in standard form for the line that has an undefined slope and passes through (–6, 4).

The amount of cost to carpet the entire rectangular living room floor of the cabin is given by A = $ 420

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular living room be A

The scale factor is 1 cm of graph = 4 feet

Now , the length of rectangular floor be L = 5 cm

So , the length of the rectangular floor L = 20 feet

And , the width of the rectangular floor W = 3.5 cm

So , the width of the rectangular floor W = 14 feet

The cost per unit area of carpet = $ 1.50

The area of rectangular floor = L x W

On simplifying , we get

The area of rectangular floor = 20 x 14 = 280 feet²

Now , the cost to carpet 280 feet² of living room = 280 x cost per unit area of carpet

The amount of cost to carpet the entire living room floor = 280 x 1.5

The amount of cost to carpet the entire living room floor = $ 420

Hence , the cost to carpet the living room is $ 420

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The complete question is :

If carpet cost s $1.50 per square foot including the cost of installation how much would it cost to carpet the entire living room floor of the cabin shown at the right?

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Given :

Tomas combined 7.28 ounces of strawberries with 8.06 ounces of blueberries to make fruit bowls.

He pours the fruit equally into four bowls and has a 1.58 ounces of fruit left over.

To Find :

Weight of each ounces of fruit bowl.

Solution :

Sum of fruits , S = 7.28 + 8.06 = 15.34 ounces.

Weight of put he filled in 4 bowls, W = 15.34 - 1.58 = 13.76 ounces.

So, weight of each fruit bowl is :

\(w=\dfrac{13.76}{4}\\\\w=3.44\ pounds\)

Hence, this is the required solution.

Refer to the images attached. Now I am guessing when it says "use geometry" was to graph it? I wasn't completely sure. I attached how I would normally evaluate that problem and a graph of the piecewise function. It has been a while since I have dealt with integrating piecewise function, please let me know what process you were supposed to use if you figure it out. Hope this helps you a bit, have a good one!

1. Volume of Water= 35.25 unit³

2. Volume of 1 ice = 1.4 unit³

3. Volume of 3 ice cubes submerged = 3.78 unit³

1. Volume of Water

= πR²H

= 3.14 x 3/2 x 3/2 x 5

= 3.14 x 45/4

= 35.25 unit³

2. Volume of 1 ice

= π(r2² - r1²)h

= 3.14 x [(4/6)² - (2/6)²] x 4/3

= 3.14 x 12/36 x 4/3

= 3.14 x 1/3 x 4/3

= 1.395

= 1.4 unit³

3. Volume of 3 ice cubes submerged

= 3 x (9/10 x 1.4)

= 3.78 unit³

4 . Total Height displacement

= 5 - 4/3

= 11/3 unit

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Answer:

Step-by-step explanation:

In this type of question , if the difference b/w the numerator and the denominator is 1 , then simply check the numerator . Whichever is big , it will be the larger .

In this question ,

           \(\frac{8}{9} \\\frac{7}{8} \\\\\)

here , we can see that 9 - 8 = 1  &  8 - 7 = 1

∵  8 > 7

∴   \(\frac{8}{9} > \frac{7}{8}\)

For common denominator , find its LCM : LCM(8,9) = 72

∴  Common denominator is 72 .

Answer:

Step-by-step explanation:

S.I= PTR/100

=9000*(15/12)*2/100

=90*5/2

=450/2

=225

Answer:

The slope is -2 and y-intercept is (0, 5/4).

Step-by-step explanation:

-8x-4y=-5

4y=-8x-(-5)

4y=-8x+5

y=-8/4x+5/4

y=-2x+5/4

y=mx+b where m=slope and b=y-intercept.

Thus, m=-2 and b=5/4.

Answer:

difference between x and 2

Step-by-step explanation:

x-2< 9

x< 11

Answer:

-√26, 5.15, 5.2, 16/3

Step-by-step explanation:

-√26 = -5.09

16/3 = 5.33

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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The system of equations is.

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

And the solutions are y = 50 and x = 10.

Let's define the two variables:

With the given information we can write two equations, then the system will be:

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

Now let's solve it.

We can isolate x on the first  to get:

\(\text{x} = 60 - \text{y}\)

Replace that in the other equation to get:

\(15\times(60 - \text{y}) + 10\text{y} = 800\)

\(-2\bold{y} = 900 - 800\)

\(-2\bold{y} = 100\)

\(\text{y} = \dfrac{100}{-2} = \bold{50}\)

Then \(\bold{x=10}\).

Therefore, the solutions are y = 50 and x = 10.

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Answer:

-0.2857

Step-by-step explanation:

\(\frac{3-5}{9-2}\)  

= -2/7

= -0.2857

Answer:

the slope is 1/2

Step-by-step explanation:

the formula you use for this is (x1 - y1)/(x2 - y2) then after subtracting you will have a fraction and you will have to simplify, so (2-5)/(9-3) + -3/6, then you simplify that to 1/2 and that should give you your answer!

Answer:

The answer is 20/3

Step-by-step explanation:

(5 x 1 ) + ( 5 x 1/3)

5 + ( 5 × 1/3 )

5 + 5/3 = 20/3

Answer:

\(Opposite = Adjacent= 5\)

Step-by-step explanation:

Given

\(Hypotenuse^2 = 50\)

\(Opposite = Adjacent\)

Required

Find the length of each leg

This is calculated using Pythagoras Theorem

\(Opposite^2 + Adjacent^2 = Hypotenuse^2\)

\(Opposite^2 + Adjacent^2 = 50\)

Represent the opposite and adjacent with x

\(x^2 + x^2= 50\)

\(2x^2 = 50\)

Divide both sides by 2

\(x^2 = 25\)

Take square roots

\(x = 5\)

Hence:

\(Opposite = Adjacent= 5\)

We know that two vertical angles are equal.

\(108° \: = \: (12x \: + \: 24)°\)

\( - 12x \: = \: 24 \: - \: 108\)

\( - 12x \: = \: -84\)

\( \boxed{ \bold{x \: = \: 7°}}\)

We know that a complete angle measures 360°.

\(108° \: + \: 108° \: + \: z \: + \: z \: = \: 360°\)

\(216 \: + \: 2z \: = \: 360\)

\(2z \: = \: 360 \: - \: 216\)

\(2z \: = \: 144\)

\( \boxed{ \bold{z \: = \: 72°}}\)

Answer:

80 feet

Step-by-step explanation:

6 cm = 15 feet

1 cm = 5/2 feet

32 cm = 90 feet

The actual perimeter of the room is 90 feet.

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

The scale drawing of a rectangular room measures 10 cm long by 6 cm wide.

The actual width of the room is 15 feet.

This means,

6cm = 15 feet

1 cm = 15/6 feet

1 cm = 5/2 feet

Now,

The perimeter of the rectangular room.

= 2(10 + 6)

= 2 x 16

= 32 cm

1 cm = 5/2 feet

So,

32 cm = 32 x 5/2 feet

32 cm = 16 x 5 feet

32 cm = 90 feet

Thus,

The actual perimeter of the room is 90 feet.

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Using the volume of the rectangular prism, it is found that it takes 7 hours to fill the pool.

The volume of a rectangular prism of dimensions l, w and h is given by the multiplication of it's dimensions, that is:

V = lwh.

In this problem, the dimensions in meters are: l = 7, w = 3, h = 0.75. Hence, the volume in cubic meters is:

V = lwh = 7(3)(0.75) = 15.75.

It fill 2.25 cubic meters per hour, hence, for 15.75 cubic meters, the time taken is:

15.75/2.25 = 7 hours.

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Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

Given:

The given radical expression is,

Required:

To find the expression equivalent to the given radical expression when

Explanation:

Let us solve the given expression.

Final Answer:

The expression equivalent to the given radical expression when

is given by,

Option D is correct.

the answer is 5 cuz the gcf of the given numbers is 5

Answer:

19cm

Step-by-step explanation:

The volume of the give cone is 21.40 cm³

A cone is a shape formed by using a set of line segments  or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.

Given that, A right circular cone has a height of 10 centimetres and a base of 9 cm.

The circumference of the base is 9 cm

Therefore, 2πr = 9

r = 9/3.14×2

r = 1.43 cm

Volume of a cone = πr²h/3

V = 3.14(1.43)²10/3

V = 21.40 cm³

Hence, The volume of the give cone is 21.40 cm³

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The tree is approximately 12 feet tall to the nearest tenth of a foot.

We have,

To find the height of the tree, we can set up a proportion using the measurements of the shadow.

Since we know that Tyler is 6 feet tall and his shadow is 10 ½ feet long, we can set up the following expression:

Tyler's height / Tyler's shadow length = Tree's height / Tree's shadow length

6 feet / 10.5 feet = Tree's height / 21 feet

To find the tree's height, we can cross-multiply and solve for it:

6 feet x 21 feet = 10.5 feet x Tree's height

126 feet = 10.5 feet x Tree's height

Dividing both sides of the expression by 10.5 feet:

126 feet / 10.5 feet = Tree's height

12 feet = Tree's height

Therefore,

The tree is approximately 12 feet tall to the nearest tenth of a foot.

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Answer:

Letter (C)

Step-by-step explanation:

The chart shows the Growth of dollars 1,000 in years on the x-axis and on the y-axis is the account balance. The account balance was 1000 dollars on year 1 and at the end of 18 years, it was 58,000 dollars. This type of data is best modeled by an exponential function because it shows a continuous increase in the account balance over time.

Answer: 17

Step-by-step explanation:

Answer:

12.5

Step-by-step explanation:

To evaluate an algebraic expression, you have to substitute a number for each variable ( y for 4.5 as in the question ) and perform the arithmetic operations ( then add 4.5 + 8 )

4.5 + 8 = 12.5

HOPE THIS HELPED

Answer:

x =23

Step-by-step explanation:

ok first, the full degree of a straight line is 180°

subtract 38° out of 180°

180-38= 142

so 6x+4= 142°

subtract 4 from both sides of the equation

6x +4 -4= 142-4

6x=138

divide 6 from 6x and 138

x=23

Step-by-step explanation:

No Not an answer

21=x-5

x=26

a)

i) The mean number of refunds given in the summer is 21.

ii) The mean number of refunds given in the winter is 20.

b) The answer to part a) does NOT support the hypothesis.

To calculate   the mean number of refunds given in the summer and winter,we need to find the average of the  values for each season over the given years. Let's calculate  -

a) Mean number of refunds given in the summer  -

(20 + 15 + 10 + 15 + 32 + 34) / 6

= 126 / 6

 = 21

b) Mean number of refunds given in the winter   -

(24 + 10 + 15 + 18 + 26 + 27) / 6

= 120 / 6

= 20

The mean   number of refunds given in thesummer is 21, and the mean number of refunds given in the winter is 20.

b) Based on the calculated means, the answer to part a) does NOT support the hypothesis.

The mean number   of refunds given in the summer (21) is greater than the mean number of refunds given in thewinter (20), indicating that more refunds are   given in the summer than in the winter, contrary to the hypothesis.

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