which diagram shows a pair of angle measures that prove lines a and b are parallel?

Answer:

A = 1.16d

Step-by-step explanation:

Multiplying by 1 + the percentage value is equivalent to adding the percentage.

The type of table that has the largest area is circular table

area of a square = l²

where

Therefore,

area of the square table = 39² = 1521 inches²

area of a rectangle = lw

where

Therefore,

area of the rectangular table = 23 × 71 = 1633 inches²

area of a circle = πr²

where

Therefore,

area of a circular table = π × (48 / 2)² = 576π = 1808.64 inches²

Therefore, the table that has the largest area is the circular table.

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Answer:

C.

Step-by-step explanation:

The boundary of a circle is the circle itself.

The radius of a circle is a segment from the center of the circle to any point of the circle.

In a circle, every radius has the same length.

Answer: C.

Answer:

Step-by-step explanation:

The volume of the cone is 4775.94 cu.cm

A cone is a three dimensional shape which has a circular base and then tapers down to a point called as Vertex.

It is given that the cone has

Height = 27 cm

Radius = 13 cm

The volume of the cone is given by

V = (1/3)πr²h

Volume = (1/3) * 3.14 * (13)² * 27

Volume = 4775.94 cu.cm

Therefore the volume of the cone is 4775.94 cu.cm

The complete question is

Find the volume of the cone of height = 27 cm and radius is 27 cm.

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Answer:

Let the angle be x

∘

. Then it's complement = (4x)

∘

.

We know that if the sum of two angles is equal to 90

∘

then the angles are said to be complementary.

Step-by-step explanation:

4x+x=90°

5x=90°

x=90°/5

x=18

4×18=72°

This is the complete solution!

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Answer:

B

Step-by-step explanation:

[tex](f-g)(x)=4x^2+5x-3-(4x^3-3x^2+5)\\\\=-4x^3+7x^2+5x-8[/tex]

Hence B is correct.

By using the given distances and directions, we have;

Part A: 1083.5 feet

Part B: 1921.37 feet

Part C: 58.05°

The distance between David and Lacey = 2000 feet

David's angle to the boat = 70°

Lacey's angle to the boat = 32°

Part A

The distance of the boat from David is found as follows;

Imaginary lines drawn from the boat to David and then to Lacey form a triangle.

In the triangle, let A = 70°

B = 32°

Therefore by the sum of angles in a triangle, we have;

C = 180° - (70° + 32°) = 78°

By using sine rule we have;

[tex] \frac{a}{sin(A)} = \frac{b}{sin( B )} = \frac{c}{sin(C)}[/tex]

David's distance from the boat, b, is therefore;

[tex] \frac{b}{sin( 32 )} = \frac{2000}{sin(78)}[/tex]

The angle subtended by the coastline, C, is therefore;

[tex] b = \frac{2000}{sin(78)} \times sin( 32 ) = 1083.5 [/tex]

Part B

The distance between the boat and Lacey is found as follows;

[tex] \mathbf{ \frac{a}{sin( 70)} }= \frac{2000}{sin(78)}[/tex]

[tex] a = \frac{2000}{sin(78)} \times sin( 70 ) = 1921.37 [/tex]

Part C

When b = 1200 feet, we have;

Finding the vertical distance of the boat from the coastline, we have;

1083.5 × sin(70) = 1018.17

We have;

[tex] \frac{1200}{sin(90)} = \frac{1018.17}{sin( B' )} [/tex]

[tex] {sin( B' )} = \frac{sin(90)}{1200} \times 1018.17 [/tex]

The angle between the coastline and his view to the boat, B', is therefore;

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The correct information based on the equation is that the functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

From the graph of f(x):

⇒ Axis of symmetry will be at x = 2

⇒ The maximum value of f(x) = 4

From the table of g(x):

⇒ Axis of symmetry will be at x = 2

⇒ The maximum value of g(x) = 3

The graph is attached.

The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

Here is the other part of the question:

Which statement is true?

The functions f and g have the same axis of symmetry, and the maximum value of f is less than the maximum value of g.

The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

The functions f and g have different axes of symmetry and different maximum values.

The functions f and g have the same axis of symmetry and the same maximum values.

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The miles Sophia drove is 60 miles

The distance Sophia drove is represented in fractions.

A number is expressed as a quotient where a numerator is divided by a denominator. In a simple fraction, both are integers.

A fraction consists of a numerator and a denominator. An example of a fraction is 1/2 where 1 is the numerator and 2 is the denominator.

In order to determine the miles Sophia drove, the total distance of the trip would be multiplied by the fraction of the time Sophia drove.

Miles Sophia drove = 3/5  x 100

                                = 60 miles

So sophia drove 60 miles in 500 miles.

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Answer:

option D. DE = 11

Step-by-step explanation:

The line DF is equivalent in length to the blue line,

(x + 7) + 7 = 4x + 2

Solve:

x + 14 = 4x + 2

subtract 14 from both sided to get x alone,

x + 14 - 14 = 4x + 2 - 14

x = 4x - 12

subtract 4x from both sided,

x - 4x = 4x - 4x - 12

-3x = -12

divided both sides by -3,

-3x / 3 = -12 / -3

x = 4

Plug in x into DE equation:

x + 7: (4) + 7 = 11

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This is a very simple transformation problem and can be solved by observation. The correct answer is Option D where g(x) = f(x-3) + 6. See the attached graph for the full question.

In mathematics, transformation is the process of converting one figure, expression, or function into another of equivalent value.

Note that on an x-axis, moving past zero to the left gets you into the negative, and vice versa.

On the y-axis moving upwards past zero gets you into the positive.

Recall that g(x) is a transformation of f(x). This means that the original image is f(x).

Notice that F(x) is transformed three degree beyond 0 on the -axis and 6 degrees beyond zero on the y-axis. Hence the correct equation is:

g(x) = f(x-3) + 6.

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An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.

We have been given a rational function:

[tex]f(x)=\frac{x^{2} -81}{x^{2} -11x+18}[/tex]

And we are required to determine an appropriate viewing rectangle for the graphing calculator.

Hence, An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.

For the given function, an appropriate viewing rectangle will be [-20,20,2]  by [-20,20,2].

This function, when graphed using a graphing calculator on the said viewing rectangle, it appears as attached.

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Answer:16.67

Step-by-step explanation:

880 of 5280 can be written as:

880

5280

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

880

5280

×

100

100

= (

880 × 100

5280

) ×

1

100

=

16.67

100

Therefore, the answer is 16.67%

If you are using a calculator, simply enter 880÷5280×100 which will give you 16.67 as the answer.

Answer: D. all negative and positive angle measures.

A percentage is a way to describe a part of a whole. The percetage decrease in the price of CD is 33.33%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The price of the CD decreases from $18 to $12. Therefore, the percentage decrease is,

Percentage Decrease = ($18-$12)/$18 × 100% = 33.33%

Hence, the percetage decrease in the price of CD is 33.33%.

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Given that the AC and BC are perpendicular, their slopes are the negative inverse of each other which gives that the product of the slopes of AC and BC is -1

The completed proof is presented as follows;

The slope of AC or GC is GF/FC by definition of slope. The slope of BC or CE is DE/CD by definition of slope.

<FCD = <FCG + <GCE + <ECD by angle addition property <FCD = 180° by the definition of a straight angle, and <GCE = 90° by definition of perpendicular lines. So by substitution property of equality 180° = <FCG + 90° + <ECD. Therefore 90° - <FCG = <ECD, by the subtraction property of equality . We also know that 180° = <FCG + 90° + <CGF by the triangle sum theorem and by the subtraction property of equality 90° - <FCG = <CGF, therefore <ECD = <CGF by the substitution property of equality. Then <ECD ≈ <CGF by the definition of congruent angles. <GFC ≈ <CDE because all right angles are congruent. So by AA ∆GFC ~ ∆CDE. Since the ratio of corresponding sides of similar triangles are equal then GF/CD = FC/DE or GF•DE = CD•FC by cross product. Finally, by the division property of equality GF/FC = CD/DE. We can multiply both sides using the slope of using the multiplication property of equality to get GF/FC × -DE/CD = CD/DE × -DE/CD. Simplify so that GF/FC × -DE/CD = -1. This shows that the product of the slopes of AC and BC is -1.

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Calculations:

Normal pop has mean of 20.0

standard deviation = 4.0

XNN(20.0, 4.0)

a).

[tex]z=\frac{x-h}{z}[/tex]

[tex]=\frac{25-20}{4.0} =\frac{5}{4} =1.25[/tex]

Z = 1.25

b).

The proportion between 20 and 25 is P(20 <x<25.0)

[tex]=p(\frac{20-20}{4} < z < \frac{25-0}{4} )[/tex]

[tex]=P(0 < z < 1.25)[/tex]

[tex]=P(Z < 1.25)-P(z < 0)[/tex]

[tex]=0.8944-0.5000[/tex]

P(20 < x < 25)=0.3944

c).

The proportion value is less than 18 when

[tex]P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}[/tex]

[tex]=P(z < \frac{-2}{4})[/tex]

[tex]=P(z < -0.5)[/tex]

P(x<18) = 0.3085

0.16 = 0.16161616... as a ratio of integers is 16 : 99

The equation is given as:

0.16 = 0.16161616...

The above is a non-terminating decimal.

It can be represented as:

a/b - 1

Where

a = 16

b = 100

So, we have:

16/100 - 1

Evaluate the difference

16/99

Express as ratio

16 : 99

Hence, 0.16 = 0.16161616... as a ratio of integers is 16 : 99

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The measure of an interior angle of a regular nonagon (9-sided polygon) is 140°

The formula for sum of interior angles of a polygon is given as;

= ( n -2) × 180

Recall that a nonagon has nine sides, so , n = 9

Substitute the value into the formula

= ( 9 -2) × 180

= 7× 180

= 1260°

Since the sum of the angles =  1260°

One of the angles = 1260/ 9 = 140°

Therefore, the measure of an interior angle of a regular nonagon (9-sided polygon) is 140°

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Answer:

(x-{-2})^2+(y-{4})^2={36}

Equation:

x^2+y^2=r^2

r=radius

Blank following x/y is flipped center(of circle) coordinate for x/y

Using the hypergeometric distribution, it is found that there is a 0.0002 = 0.02% probability that exactly 6 patients will die.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

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

The parameters are:

The values of the parameters for this problem are:

N = 25, k = 6, n = 8.

The probability that exactly 6 patients will die is P(X = 6), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 6) = h(6,25,8,6) = \frac{C_{6,6}C_{19,2}}{C_{25,8}} = 0.0002[/tex]

0.0002 = 0.02% probability that exactly 6 patients will die.

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Answer:

-0.61

Step-by-step explanation:

0.55/2=0.275

Read 0.275 from normal distribution tables

Gives -0.61

Answer:

A 256/3

Step-by-step explanation:

1/3 * 4^4 =

1/3 * (4*4*4*4) =

1/3 * 256 = 256/3

Answer:

A = 256/3

Step-by-step explanation:

F(x) = 1/3 × 4ˣ = 4ˣ/3

F(4) = 4⁴/3 = 256/3

Answer:

3 nikels and 2 cents

Step-by-step explanation:

1 niquel = 5 cents

5+5+5= 15

15+ 2= 17

Answer:

90

Step-by-step explanation:

slope

Answer:

formula is equal to rice run is equal to y 2 -y 1 X2 minus X1

The correct option is the second one:

We know that:

We have the operation:

x - y + (-z)

Notice that because y is negative, then -y is positive.

Because z is positive, -z is negative.

Then we have:

positive + positive + negative

Or, in the number line:

right, right, left.

Second question:

Can we conclude the sign of the outcome?

No, we can't, the sign will depend on the values of x, y, and z.

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Answer:The correct option is the second one:i) right, right, left.ii) Undefined.

Step-by-step explanation:

The area of the base of cube B is 25/9 times larger than the area of the base of cube A.

Because the cubes are similar, then we know that the dimensions of cube B are a dilation of scale factor K of the dimensions of cube A.

Then, the volume of cube B is K³ times the volume of cube A.

The area of any face of cube B is K² times the area of any face of cube A

From this we can write:

125 in³ = K³*27in³

(125/27) = K³

If we apply the cubic root in both sides, we get:

∛(125/27) = K = 5/3

Then the relation between the areas is equal to:

K² = (5/3)^2 = 25/9

The area of the base of cube B is 25/9 times larger than the area of the base of cube A.

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Answer:

25/9

Step-by-step explanation:

I Just Took the Test.

Answer:

Mikhail is 44 years old.

Step-by-step explanation:

Set both Gabrielle and Mikhail's age to a variable.

Gabrielle is x, Mikhail is also x.

Now create an equation using the variables with the sum.

Age1 + Age2 + 15 = 103

x + x + 15 = 103

Now we solve.

1. Combine like terms

2x + 15 = 103

2. Make all the numbers on one side of the equation, and the variables of the other, so subtract.

2x + 15 - 15 = 103 - 15

2x = 88

3. Simplify further by dividing.

x = 44

Mikhail is 44 years old.

Check your work:

44 + (x + 15) = 103

x + 15 = 59

x = 44

Answer:

Step-by-step explanation:

Let Gabrielle's age be x.

The age of the milk will be x - 15.

x + (x - 15) = 103.

2x - 15 = 103

2x = 118

x = 59

The milk's age = x - 15 = 59 - 15 = 44.

Answer: False

Step-by-step explanation:

[tex]\sqrt{5x}=\sqrt{x} \sqrt{5} \neq x\sqrt{5}[/tex]