Which of the following is equidistant from a given directrix and focus?​

The dimensions the rug should have is 20 by 29

The dimension of the rug is given as:

22 ft by 31 ft

The area of the carpet is given as:

Area = 580

Represent the length of the empty space with x.

So, the dimension of the carpet is:

22 - 2x by 31 - 2x

The area is calculated as:

Area = (22 - 2x) * (31 - 2x)

Expand

Area = 682 - 62x - 44x + 4x^2

Evaluate the difference

Area = 682 -106x + 4x^2

Substitute Area = 580

682 -106x + 4x^2 = 580

Subtract 580 from both sides

102 -106x + 4x^2 = 0

Rewrite as:

4x^2 - 106x +102 = 0

Using a graphing calculator, we have:

x = 1 and x = 22.5

Substitute these values in 22 - 2x by 31 - 2x

So, we have:

Length = 22 - 2(1) = 20 or Length = 22 - 2(22.5) = -23

Width = 31 - 2(1) = 29 or Length = 31 - 2(22.5) = -14

The dimensions cannot be negative.

So, we have:

Length = 20 and Width = 29

Hence, the dimensions the rug should have is 20 by 29

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Answer:

option c and d are correct

Step-by-step explanation:

if there is only one choosing option you can choose option c

Using the binomial distribution, it is found that there is a 0.3438 = 34.38% probability that fewer than 3 of them are boys.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the values of the parameters are given as follows:

n = 6, p = 0.5.

The probability that fewer than 3 of them are boys is given by:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.5)^{0}.(0.5)^{6} = 0.0156[/tex]

[tex]P(X = 1) = C_{6,1}.(0.5)^{1}.(0.5)^{5} = 0.0938[/tex]

[tex]P(X = 2) = C_{6,2}.(0.5)^{2}.(0.5)^{4} = 0.2344[/tex]

Then:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0156 + 0.0938 + 0.2344 = 0.3438[/tex]

0.3438 = 34.38% probability that fewer than 3 of them are boys.

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Answer:

A- 17/24 sugar all together

B- yes the bowl would be big enough because when you add all the ingredients together it equals 3 5/24 and it's less than 3 1/2.

Answer:

Total, 2 milkshakes, and 3 cokes would cost $12.50

Step-by-step explanation:

The cokes cost $11.50 and the milkshakes $10.00

The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

From the given graph:

The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:

[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]

here:

Suppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8)  from the graph, we have:

[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]

y = 4x

Now, our region bounded by the three lines are:

Similarly, the change in polar coordinates is:

where;

Therefore;

Then:

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

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The rule for construction of Inscribed equilateral triangle

Means if marks are from 1 to 6 then

Or

Now

Here the rest two segments are

Answer:

FB and DB

Step-by-step explanation:

got it right on the test

Answer:

area = 62ft

Step-by-step explanation

so you section the polygon into a big rectangle and 2 small rectangles

the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft

the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft

now add the areas you got, 50+12 which is 62ft

hope this helps:)

The rate of change of this simple index over 1 week is - 8.81%

The rate of change is the ratio of the difference in the value of the simple index to the original value of simple index.

Total value of the simple index at day 1 = (8000 x $4.25) + (5000 x $2.90) + (2000 x $6.40) = $61,300

Total value of the simple index at day 8 = (8000 x $3.90) + (5000 x $2.50)+(2000*6.10)  = 55900

the rate of change of this simple index over 1 week

= (55900-61300)/ 61300          * 100 %

= -8.81 %

the rate of change of this simple index over 1 week is - 8.81%

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Answer:

Graph of Modulus

The graph of a modulus or absolute value function is in a form of a 'V' shape whose vertex depends upon the coordinates. The equation for the graph is given as,

where,

(a, b) are the coordinates of the vertex of 'v' in the form of (x, y),

And h shows how wider or lean will be the function, for h=0, it is a straight line, while for a negative value the graph will face downwards and opposite for a positive value.

Given to us

y = |x-3|

On the coordinate plane

The graph will be in the shape of a 'V' whose vertex will lay at the coordinates (3, 0). As the value of a is 1 the graph will face upwards. As shown below on the graph.

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Step-by-step explanation:

Answer:

C

Step-by-step explanation:

edge 23

Answer:

Point C

Step-by-step explanation:

At point C, the graph is changing from decreasing to increasing.

Answer:

See below

Step-by-step explanation:

You will just need to use your protractor to measure the given angles..

  Here is some gross guesses  starting with top row

      45     120   100  25   90   80  135  120 °

The attached figure represents the sketch of the graph

The complete question requires that we sketch the graph that follows the given parameters

The given parameters are:

To start with, we plot the points on an empty coordinate plane.

Next, we connect the points using a rough curve

Lastly, the points are labelled

See attachment for the sketch of the graph

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To Find = Diameter, Area

Solution :

Diameter = 2 × Radius

Diameter = 2 × 6cm

Diameter = 12 cm

Area = 2πr

[tex]area \: = 2 \times \frac{22}{7} \times 6cm[/tex]

[tex]area \: = \frac{264}{7} [/tex]

[tex]area \: = 37.7 \: cm[/tex]

2. Given : Diameter = 8 DM

( 1dm = 10 cm

8dm = 8 × 10 = 80cm )

To find : Radius , area

Solution :

[tex]raduis \: = \frac{1}{2} \times diameter[/tex]

[tex]radius \: = \frac{1}{2} \times 80cm[/tex]

[tex]radius \: = 40 \: cm \: or \: 4dm[/tex]

Area = 2πr

[tex]area \: = 2 \times \frac{22}{7} \times 40[/tex]

[tex]area \: = \frac{1760}{7} [/tex]

[tex]area \: = 251.4cm \: \: \: or \: 25.14dm[/tex]

3. Given : Radius = 2.5m

To find : Diameter , Area

Solution :

Diameter = 2 × radius

Diameter = 2 × 2.5m

Diameter = 5m

Area = 2πr

Area = 2 × 22/7 × 5m

Area = 220/7

Area = 31.4m

The approximate area that is within range of the motion sensor is 4975 square meters

The figure is not given, however the area of the range can be calculated without the figure.

The given parameters are:

Angle, ⊕ = 135°

Radius, r = 65 meters

The area of the range is calculated using the following sector area

[tex]A = \frac{\theta}{360} * \pi r^2[/tex]

This gives

[tex]A = \frac{135}{360} * 3.14 * 65^2[/tex]

Evaluate

A = 4974.9375

Approximate

A = 4975

Hence, the approximate area that is within range of the motion sensor is 4975 square meters

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Answer:

perpendicular

Step-by-step explanation:

x = -2    is a vertical line at   x   =  -2

y is a horizontal line          the two lines are perpindicular

the lines  x=−2, y=10 are perpendicular to each other.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Here, The given equations are :

x=−2 and y=10

First, consider x = -2 equation :

equation x = -2 is a vertical line, parallel to x = 0 line and perpendicular to line y = 0.

Consider second line y = 10 :

line y = 10 is horizontal line and is parallel to line y = 0 and is perpendicular to line x = 0.

Therefore, the lines  x=−2, y=10 are perpendicular to each other.

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Answer:

84 circular tiles are needed to make pattern number 20

4(20+1)

Step-by-step explanation:The number of circular tiles is 1 more than the pattern number on each side of the square.

circular tiles = 4(n +1)

Answer:

your answers are 5.5 and 2.5 as they both have a half extra

Answer:

g(x) = 1/3 • |x|

Step-by-step explanation:

To stretch a parent function, you multiply by whatever you want to stretch it with. If you multiplied by 3, it would be a vertical stretch... if you multiplied by 1/3, it makes it horizontal.

Hope this helps!

Answer:

Step-by-step explanation:

The first shape has 6 sides. Hence, it is called a hexagon.

The second shape has 7 sides. Hence, it is called a heptagon.

The mathematical name for the given 2 polygons.

The first polygon has 6 sides with an angle sum of 720°, which means the mathematical name given for this polygon is,

[tex]\large\boxed {Hexagon}[/tex]

The second polygon has 7 sides with an angle sum of 900°, which means the mathematical name given for this polygon is,

[tex]\large\boxed {Heptagon}[/tex]

Hence, the first polygon is a hexagon and the second polygon is a heptagon.

Answer:

I think that the answer is 432.

Step-by-step explanation:

6x2y3.We have x as 6 and y as 2.So we replace them with their numbers.

We'll have 6*6*2*2*3 which will give us 432. I HOPE THIS HELPS.

The equation that can be used to represent the situation is y = 5.5 + x

The equation:

Total flour = Whole wheat flour + White flour

y = 5.5 + x

Therefore, the equation that can be used to represent the situation is y = 5.5 + x

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Answer:

C

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

By the geometric mean theorem, if we let the length of the altitude to the hypotenuse be [tex]y[/tex], this means that [tex]y^{2}=84 \longrightarrow y=\sqrt{84}[/tex].

So, by the Pythagorean theorem, [tex]x=\sqrt{(\sqrt{84})^{2}+4^{2}}=\boxed{10}[/tex]

Step-by-step explanation:

hope this will help you....

Answer:

\begin{gathered}\\1) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\end{gathered}

1)

Alternateinteriorangles:

\begin{gathered} \sf \implies \: 2\: \: and \: \: 7\\\end{gathered}

⟹2and7

\begin{gathered} \sf \implies \: 6\: \: and \: \: 3\\\\\end{gathered}

⟹6and3

\begin{gathered}\\2) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\\\end{gathered}

2)

Alternateinteriorangles:

\begin{gathered} \sf \implies \: 1\: \: and \: \: 8\\\end{gathered}

⟹1and8

\begin{gathered} \sf \implies \: 5\: \: and \: \: 4\\\\\end{gathered}

⟹5and4

\begin{gathered}\\3) \: \: \underline{ \sf{ Corresponding \: angles \: \: : }}\\\end{gathered}

3)

Correspondingangles:

\begin{gathered} \sf \implies \: 3\: \: and \: \: 1\\\end{gathered}

⟹3and1

\begin{gathered} \sf \implies \: 5\: \: and \: \: 7\\\end{gathered}

⟹5and7

\begin{gathered} \sf \implies \: 4\: \: and \: \: 2\\\end{gathered}

⟹4and2

\begin{gathered} \sf \implies \: 6\: \: and \: \: 8\\\\\end{gathered}

⟹6and8

\begin{gathered}\\4) \: \: \underline{ \sf{ Consecutive\: Interior \: angles \: \: : }}\\\end{gathered}

4)

ConsecutiveInteriorangles:

\begin{gathered} \sf \implies \: 2\: \: and \: \: 3\\\end{gathered}

⟹2and3

\begin{gathered} \sf \implies \: 6\: \: and \: \: 7\\\\\end{gathered}

⟹6and7

\begin{gathered}\\5) \: \: \underline{ \sf{ Consecutive\: Exterior \: angles \: \: : }}\\\end{gathered}

5)

ConsecutiveExteriorangles:

\begin{gathered} \sf \implies \: 1\: \: and \: \: 4\\\end{gathered}

⟹1and4

\begin{gathered} \sf \implies \: 5\: \: and \: \: 8\\\\\end{gathered}

⟹5and8

Answer:

2,160 ÷ 36 = 60

Step-by-step explanation:

The division problem that this area model represents is,

2,160 ÷ 36 = 60

Answer:

f(-3) = -6

Step-by-step explanation:

f(x) = x^2 + 4x - 3

f(-3) means to put -3 in place of x and then do the calculation.

f(-3)

= (-3)^2 + 4(-3) - 3

= 9 - 12 - 3

= -3 - 3

= -6

First square -3, its 9. Then multiply -3 and 4, that's -12. Then add everything.

f(-3) = -6