Warren measured a rectangular window to find out how much plastic he would need to cover it. The window measured 5 ft 6 inches by 2 ft 9 inches. About how many square inches of plastic does Warren need to cover the window?

Answer:

# The general form of  x²/3² + (y - 2)²/2² = 1 is 4x² - 36y + 9y² = 0

# The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0

# The general form of x²/6² + (y + 4)²/4² = 1  is 16x² + 288y + 36y² = 0

# The general form of (x - 3)²/3² + y²/5² = 1  is 25x² - 150x + 9y² = 0

Step-by-step explanation:

* Lets revise the general form and the standard form of the ellipse

- The general form is Ax² + Bxy + Cy² + Dx + Ey + F = 0

- The standard form is (x - h)²/a² + (y - k)²/b² = 1

* Lets solve the problem

# x²/3² + (y - 2)²/2² = 1

∵ x²/9 + (y - 2)²/4 = 1 ⇒ multiply both sides by 9 × 4 (36)

∴ 4x² + 9(y - 2)² = 36 ⇒ open the bracket power 2

∴ 4x² + 9(y² - 4y + 4) = 36 ⇒ multiply the bracket by 9

∴ 4x² + 9y² - 36y + 36 = 36 ⇒ subtract 36 from both sides

∴ 4x² - 36y + 9y² = 0

* The general form of  x²/3² + (y - 2)²/2² = 1 is 4x² + 9y² - 36y = 0

# (x + 7)²/7² + y²/6² = 1

∵ (x + 7)²/49 + y²/36 = 1 ⇒ multiply both sides by 49 × 36 (1764)

∴ 36(x + 7)² + 49y² = 1764 ⇒ open the bracket power 2

∴ 36(x² + 14x + 49) + 49y² = 1764 ⇒ multiply the bracket by 36

∴ 36x² + 504x + 1764 + 49y² = 1764 ⇒ subtract 1764 from both sides

∴ 36x² + 504x + 49y² = 0

* The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0

# x²/6² + (y + 4)²/4² = 1

∵ x²/36 + (y + 4)²/16 = 1 ⇒ multiply both sides by 36 × 16 (576)

∴ 16x² + 36(y + 4)² = 576 ⇒ open the bracket power 2

∴ 16x² + 36(y² + 8y + 16) = 576 ⇒ multiply the bracket by 36

∴ 16x² + 36y² + 288y + 576 = 576 ⇒ subtract 576 from both sides

∴ 16x² + 288y + 36y² = 0

* The general form of x²/6² + (y + 4)²/4² = 1  is 16x² + 288y + 36y² = 0

# (x - 3)²/3² + y²/5² = 1

∵ (x - 3)²/9 + y²/25 = 1 ⇒ multiply both sides by 9 × 25 (225)

∴ 25(x - 3)² + 9y² = 225 ⇒ open the bracket power 2

∴ 25(x² - 6x + 9) + 9y² = 225 ⇒ multiply the bracket by 25

∴ 25x² - 150x + 225 + 9y² = 225 ⇒ subtract 225 from both sides

∴ 25x² - 150x + 9y² = 0

* The general form of (x - 3)²/3² + y²/5² = 1  is 25x² - 150x + 9y² = 0

Answer:In Plato this is the correct answer

Step-by-step explanation:

Answer:

e). 4

Step-by-step explanation:

45-45-90

x-x-xsquare root of 2

Final answer:

The measure of the leg of a 45-45-90 right triangle with a hypotenuse of 4√2 is 4 units.

Explanation:

The question asks for the measure of the leg of a 45-45-90 right triangle given that the hypotenuse is 4√2. In a 45-45-90 right triangle, both legs are of equal length and the hypotenuse is √2 times the length of a leg. Using the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a2 + b2), we can find the length of a leg when the hypotenuse is known.

Let the length of each leg be 'a'. Since the hypotenuse is 4√2, the equation according to the Pythagorean Theorem would be a2 + a2 = (4√2)2. This simplifies to 2a2 = 32, so a2 = 16, and thus a = √16. Therefore, each leg measures 4 units.

Answer: 7.5 hours

Step-by-step explanation:

750/50=15 to see how many times he climbed 15 feet

15 times 30=450 (total minutes)

450/60=7.5 hours

Answer:7.5

Step-by-step explanation:

450/60

A statistical question is a question asked with the goal of collecting data. You could rewrite the question so that it says something like, “How old were you when..” That way the responses will vary and you would be able to graph and compare them.

The statistical question of the given statement is How old were you then.

Hence, the statistical question of the given statement is How old were you then.

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Answer:

yes

Step-by-step explanation:

A = 1/2aP

P = number of sides x length of each side

P = 8 x 5.8

P = 46.4

A= 1/2 x 7 x 46.4

A = 162.4

Sphere = 4PiRsquared

Radius = 13

13 x 13 = 169

169 x 4= 676 Pi

5e surface is 676Pi

Answer:

The correct answer is option B.   676π units²

Step-by-step explanation:

Formula:-

The surface area of a sphere = 4πr²

Where r is the radius of sphere

To find the surface area of given sphere

Here r = 13 units

Surface area = 4πr²

 = 4 * π * 13²

 = 4 * π * 169 = 676π units²

Therefore the  correct answer is option A.   676 units²

Answer:

C

Step-by-step explanation:

Draw in <QOS. That's the central angle. It is also 60 degrees.

<R  which has Q and S as its end points, = 1/2 the central angle (always) so <R = 30 degrees.

C

the center is : (-8 , 12)

Answer:

the interquartile range is 13.5

minimum 16

maximum 43

medium 29

lower  Q1  24

upper Q3  37.5 or 38

Range 27

Answer: 120

Step-by-step explanation:

ANSWER

Option B

EXPLANATION

The equation given to us is;

[tex] {(x - 2)}^{2} = 12(y - 3)[/tex]

Comparing this to the general parabolic equation:

[tex] {(x - h)}^{2} = 4p(y - k)[/tex]

We have h=2 and k=3.

The vertex of this parabola is (h,k) which is (2,3).

This parabola also opens upwards because the value of p is positive.

The correct graph is B.

Hello there! Here are your answers:

Does Kerri's dot plot match the data in the tally table? No.

Look at any of the hours on the chart vs dot plot. Let's take 4 for example. In the tally table, there are 6 class mates. In the plot, there are 3. So no, it is not the same.

The answers for the other problems are in this order (since it's the number of circles on the dot plot at the given hour):

5 - classmates spent 3 hours at the park

3 - classmates spent 4 hours at the park

6- classmates spent 5 hours at the park

4 - classmates spent 6 hours at the park

I hope this was helpful and let me know if you need more help! :) Have a great day! :)

Answer:

the other guy is right

Step-by-step explanation:

-~- boiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii laggy

Answer:21

Step-by-step explanation:

if there are 21 feet of ribbon and we need it in foot long pieces there are 21

Answer:

35

Step-by-step explanation:

Answer:

D

Explanation:

A is the same thing as the statement, only that it says if the polygon is convex. Same thing for B. C could've worked if it said exterior instead of interior. D is basically the converse of the statement.

A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D

Each interior angle of a convex polygon is less than 180° while in the case of the concave polygon at least one angle is more than 180°.

In the diagram attached,

We can see in the case of a convex polygon if we join any two vertices, a line segment joining two vertices never passes through the exterior or interior of the polygon.

In the case of a concave polygon, at least a line segment joining two vertices passes through the exterior of a polygon.

Therefore, A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D

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[tex]V=209.44[/tex] | Formula for the volume of a cone: [tex]V=\pi r^2\frac{h}{3}[/tex]

Answer:

the correct answer would be c, g(x)=2^x+2

Step-by-step explanation:

We can eliminate the first and the last option because the line is going upwards, not downwards(it would if it was negative or had the negative sign in front). We can cross out the second option because if it was 2^x+3, then it would be crossing (0,4) on the y-axis. Therefore the correct option is C, since it crosses right at (0,3).

hope this helps :)

Answer:

"Membership decreased by an average of 6,600 people per year from year 3 to year 5"

Step-by-step explanation:

To get average rate of change from year 3 to year 5, we need to divide the change from year 3 to 5 by 2 (because from year 3 to 5 is 2 years).

THe change is:

83.6 - 96.8 = -13.2

We divide by 2 to get per year average rate of change:

-13.2 / 2 = -6.6

In thousands, that is 6600 decrease.

2nd answer choice is right.

Answer:

12.3

Step-by-step explanation:

cos(35) = y/15

y = 15 * cos(35) = 12.3

Answer:

y = 12.3 cm

Step-by-step explanation:

Since the triangle is right with hypotenuse 15, use the cosine ratio to solve for y, that is

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{15}[/tex]

Multiply both sides by 15

15 × cos35° = y, hence

y ≈ 12.3

Answer:

Find the GCF

Step-by-step explanation:

When multiplying the following polynomials:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5)

1.     First we need to use the distributive property:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 2x^3 * 9x^2  - 2x^3 * 4x  + 2x^3 * 5 + 2x^2 * 9x^2 - 2x^2 * 4x + 2x^2 * 5 - 3x * 9x^2 + 3x * 4x - 3x * 5.

2.   Second, we need to use the multiplication property of exponents:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 - 8x^4 + 10x^3 + 18x^4 - 8x^3 + 10x^2 - 27x^3 + 12x^2 - 15x.

3. We need to combine like terms:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 +10x^4 -25x^3 + 22x^2 - 15x.

We don't need to find the GCF.

Answer:

Option A, 7 and Option B, -2

(7,0) and (-2,0)

Step-by-step explanation:

Given in the question a function f(x) = (x+2)(x-7)

Step 1

Expand the function (x+2)(x-7)

x(x-7)+2(x-7)

x² - 7x + 2x - 14

x² - 5x - 14

Step 2

To find the x-intercepts we will substitute y with 0

y = x² - 5x - 14

0 = x² - 5x - 14

(x-7)(x+2) = 0

x = 7

x = -2

Answer:

The x-intercepts would be 7 and -2.

Step-by-step explanation:

Answer: [tex]3\sqrt{2}\ m[/tex]

Step-by-step explanation:

The perimeter of a square is:

[tex]P=4s[/tex]

Where "s" is the lenght of a side of the square.

Then, if the perimeter of this square is 12 m, you can solve for "s" and find its value:

[tex]s=\frac{P}{4}\\\\s=\frac{12\ m}{4}\\\\s=3\ m[/tex]

You can calculate the length of the diagonal with this formual:

[tex]d=s\sqrt{2}[/tex]

Where "s" is the lenght of a side of the square.

Substituting the value of "s" into the formula  [tex]d=s\sqrt{2}[/tex], you get that the lenght of the diagonal of this square is:

[tex]d=3\sqrt{2}\ m[/tex]

Answer:

  1.3×10⁻² = 0.013

Step-by-step explanation:

The "E" stands for "×10^", so 1.3E-2 means 1.3×10^-2.

Of course 10^-2 = 1/10^2 = 1/100 = 0.01, so

  1.3E-2 = 1.3×10^-2 = 1.3×0.01 = 0.013

_____

This notation was used by early computers to print results where the character set was limited and superscripts could not be printed.

To obtain a mixture of 200 liters with an average cost of 0.50, we need to start with approximately 133 liters of the wine with a price of 0.35 and approximately 67 liters of the wine with a price of 0.80.

To solve this problem, we will call "x" the quantity of liters of the wine with a price of 0.35, and "y" the quantity of liters of the wine with a price of 0.80 that we need to obtain the desired mixture.

We know that we want to obtain 200 liters of mixture, and the average cost of the mixture should be 0.50.

We can establish the following equations:

x + y = 200 (equation for the total quantity of mixture)

(0.35 * x + 0.80 * y) / 200 = 0.50 (equation for the average cost of the mixture)

Now  solve this system of equations to find the values of "x" and "y".

From the first equation, we can solve for "x" in terms of "y" as follows:

x = 200 - y

Substitute this expression for "x" in the second equation

(0.35 * (200 - y) + 0.80 * y) / 200 = 0.50

Solving this equation, we can find the value of "y":

(0.35 * 200 - 0.35 * y + 0.80 * y) / 200 = 0.50

(70 - 0.35y + 0.80y) / 200 = 0.50

(0.45y + 70) / 200 = 0.50

0.45y + 70 = 0.50 * 200

0.45y + 70 = 100

0.45y = 100 - 70

0.45y = 30

y = 30 / 0.45

y = 66.67

Now that we have the value of "y,"  find the value of "x" by substituting it into the first equation:

x = 200 - y

x = 200 - 66.67

x = 133.33

However, we cannot have a fractional quantity of liters, so we must round these values to whole numbers.

Therefore, to obtain a mixture of 200 liters with an average cost of 0.50, we need to start with approximately 133 liters of the wine with a price of 0.35 and approximately 67 liters of the wine with a price of 0.80.

We have wine of two different qualities with prices of 0.35 and 0.80. If we want to obtain a mixture of 200 that results in 0.50, how many liters of each class do we need to start with?

Answer:

Step-by-step explanation:

Formula

a^2 + b^2 = c^2

Givens

a = x

b = 20.2

c = 14.7 + x

Solution

x^2 + 20.2^2 = (14.7 + x)^2                       Expand the brackets

x^2 + 408.04 = 14.7^2 + 29.4x + x^2       Cancel the x^2

408.04 = 216.9 + 29.4x                            Subtract 216.9 from both sides.

191.98 = 29.4x                                           Divide by 29.4

6.52993 = x                                               Answer.

6.5 to the nearest tenth.

Answer:

x = 6.5 cm

Step-by-step explanation:

The tangent to the circle forms a right angle with the radius x

Using Pythagoras' identity on the right triangle

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

The hypotenuse is (x + 14.7) ← opposite the right angle, hence

(x + 14.7)² = x² + 20.2² ← expand parenthesis on left side

x² + 29.4x + 216.09 = x² + 408.04 ( subtract x² from both sides )

29.4x + 216.09 = 408.04 ( subtract 216.09 from both sides )

29.4x = 191.95 ( divide both sides by 29.4 )

x ≈ 6.5 cm

Answer:

True

Step-by-step explanation:

A plane is a flat, infinite 2D surface, so when we say two things are coplanar, they can all fit on a single plane. In this case, all three lines a, b, c, and d lie on the same 2D surface, so we'd consider them coplanar. True.

Answer:

We have 8 cups of orange juice

Step-by-step explanation:

orange juice:  water:  total

1                     : 3         : 4

Multiply everything by x

1x                 3x             4x

We have 32 cups total

4x = 32

Divide each sice by 4

4x/4 = 32/4

x = 8

We have 8 cups of orange juice

3*8 = 24

We have 24 cups of water

The ratio of orange juice to water in the punch is 1:3, which means that for every single cup of orange juice, there are 3 cups of water. To find out how many cups of orange juice were used to make 32 cups of punch, we find out what 1 part out of the total 4 parts is, which is 32 ÷ 4 = 8. Therefore, James used 8 cups of orange juice for the punch.

The subject of the question is Mathematics and it pertains to the concept of ratios in particular. The ratio of orange juice concentrate to water is given as 1:3. This means that for every 1 cup of orange juice, James uses 3 cups of water. So, the total parts in the punch are 1 (for orange juice) + 3 (for water) = 4 parts.

However, James made 32 cups of punch. Hence, to find out how many cups of orange juice he used, we need to find out what 1 part out of the total 4 parts is. To do this, you divide the total punch made (32 cups) by the number of total parts (4).

Therefore, 32 cups divided by 4 equals 8 cups. Hence, James used 8 cups of orange juice to make the punch.

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Answer:

x  = 3

Step-by-step explanation:

Given in the question an equation,

[tex]2lne^{ln5x}=2ln15[/tex]

Step 1

[tex]e^{lnx}=x[/tex]

so,

[tex]2ln(5x)=2ln15[/tex]

Step 2

cancel 2 on both sides of the equation

[tex]ln{5x}=ln15[/tex]

Step 3

[tex]ln{5x}-ln15=0[/tex]

[tex]ln\frac{5x}{15}=0[/tex]

Step 4

[tex]ln\frac{x}{3}=0[/tex]

Step 5

[tex]e^{ln\frac{x}{3}}=e^{0}[/tex]

Step 6

x/3 = 1

x = 3(1)

x = 3

Answer:

(a, 0)

Step-by-step explanation:

As S is on the x-axis, its y-coordinate will be zero.

And since this is a right trapezoid, ∠QPS and ∠PSR are right angles, so S and R will have the same x-coordinate, which is a.

Therefore, the coordinate of Point S is (a, 0)

Answer:

±4

Step-by-step explanation:

The margin of error in a confidence interval is half the range:

(84 - 76) / 2 = 4

So the margin of error is ±4.

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The margin of error of the survey will be ±4%.

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

The results of a survey indicate that between 76% and 84% of the season ticket holders are satisfied with their seat locations. Therefore, the margin of error can be written as,

Margin of Error = (84%-76%)/2 = 8%/2 = ±4%

Hence, the margin of error of the survey will be ±4%.

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