Regular hexagons have been used to tile floors. Can a floor be tiled using only regular​ pentagons? Why or why​ not?
Select the correct answer below.
A floor can or cannot be tiled using only regular pentagons. For a regular​ hexagon, the measure of each vertex angle is ___nothing°​, which means that 2,3,4,5 or 6 regular hexagons fit to form ____°​, and the plane can be filled. For a regular​ pentagon, the measure of each vertex angle is ____°​, so regular pentagons can or cannot be placed together to fill the plane because the measure of the​ plane, nothing____°​,is or is not divisible by the measure of each vertex angle.
​(Type integers or​ decimals.)

The equations y-6=x² and y=2x²+5-3x³ are non linear. Therefore, options D and F are the correct answers.

A linear function is a function that represents a straight line on the coordinate plane. The standard form of a linear function is y = mx + b.

Here, 'm' is the slope of the line, 'b' is the y-intercept of the line, 'x' is the independent variable and 'y' (or f(x)) is the dependent variable.

A) y=x

Here, degree of the equation is 1, so the equation is linear.

B) 2y=12x

Here, degree of the equation is 1, so the equation is linear.

C) y=8+x

Here, degree of the equation is 1, so the equation is linear.

D) y-6=x²

Here, degree of the equation is 2, so the equation is quadratic.

E) y=13-5x

Here, degree of the equation is 1, so the equation is linear.

F) y=2x²+5-3x³

Here, degree of the equation is 3, so the equation is cubic.

Therefore, options D and F are the correct answers.

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The inequality (x + 2)/(x - 7)>0 can be solved algebraically by first subtracting 2 from both sides. This results in the inequality (x - 7) > 2. By dividing both sides by (x-7), the inequality can be simplified to 1>2/x-7. This simplifies further to -7>2/x, or x>-7/2. Therefore, the solution to the inequality is x>-7/2.

In plain terms, this means that a value of x must be greater than -7/2 in order for the inequality to be true. This implies that the value of x must be a number greater than -3.5, since -7/2 is the same as -3.5. Thus, if x is any number greater than -3.5, then the inequality (x + 2)/(x - 7) > 0 will be satisfied.

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Answer: 75% of $13.50 is 10.125

Step-by-step explanation:

Answer:

10.125

Step-by-step explanation:

13.50 x .75 = 10.25

Answer:

72*price of pig= 54*560

price of pig=54*560/72

= 420

Answer: Total Lateral Area 96in^2^2 Surface Area 108in^2

Step-by-step explanation:

Lateral Areal:

LA=Ph

P=4+4+4=12 h=8 12(8)=96in^2

Surface Area:

B=1/2(4)(3)=6 SA=12(8)+2(6)=108in^2

[[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]]

The product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].

To calculate the product of two matrices, multiply each row of the first matrix with each column of the second matrix. Begin by multiplying the first row of the first matrix [-2, 0] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values -2, 0, 10, 2, 0 which will be the first row of the product matrix.

Next, multiply the second row of the first matrix [1, -1] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values 1, -1, 9, 2, -1 which will be the second row of the product matrix.

Therefore, the product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].
The given matrices are:
[[-2, 0],
[1, -1]]
[[-1, 0, 5, 1, 0],
[1, -1, 3, 1, -1]]

To find the product of two matrices, we need to follow a few steps:

Multiply the first row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the first row of the first matrix by the second column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the second column of the second matrix, and then add the results.

By following these steps, we can obtain the product of the matrices. So, we can proceed as follows:

-2×(-1) + 0×1 = 2
-2×0 + 0×(-1) = 0
1×(-1) + (-1)×1 = -2
1×0 + (-1)×(-1) = 1

Hence, the product of the given two matrices is:
[[2,0,10,2,0],
[-2,2,-8,-2,2]]

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Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.

To find the standard deviation of BMI for the 9 patients in the study, we need to follow these steps:
Find the mean of the BMI scores: (25 + 27 + 31 + 33 + 26 + 28 + 38 + 41 + 24) / 9 = 29.67
Subtract the mean from each BMI score to find the deviation: -4.67, -2.67, 1.33, 3.33, -3.67, -1.67, 8.33, 11.33, -5.67
Square each deviation: 21.81, 7.13, 1.77, 11.09, 13.45, 2.79, 69.43, 128.51, 32.15
Find the mean of the squared deviations: (21.81 + 7.13 + 1.77 + 11.09 + 13.45 + 2.79 + 69.43 + 128.51 + 32.15) / 9 = 32.12
Take the square root of the mean of the squared deviations to find the standard deviation: √32.12 = 5.67

Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.

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Answer: 5.25

Step-by-step explanation:

In the picture there is a smaller triangle inside a bigger triangle. You have to find the size it grows by dividing a side of the bigger triangle to the same side of the smaller triangle.

16.8/6.4 = 2.625

Then you find x by multiplying the adjacent side by the size it grows.

2*2.626 = x

2*2.626 = 5.25

Answer:

B. 3:1

Step-by-step explanation:

45 : 15

Divide both side by 15

= 3 : 1

The required measure of y in the given triangle is 14 cm.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
Following the property of proportionality of sides in similar triangles,
8 + 3.2 / 8 = y / 10
11.2/8 = y / 10
112 = 8y
y = 14

Thus, the required measure of y in the given triangle is 14 cm.

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Answer:

1.3 × .85 = 1.105

10.5% greater than original

The lateral and surface area of the given shape above in terms of π would be = 48π yd²:120π yd². That is option A.

To calculate the lateral surface area of the cylinder the formula below is used:

Lateral surface area = 2πrh

where;

r = diameter/2 = 12/2 = 6 yd

h = 4 yd

Lateral surface area = 2 ×π × 6×4 = 48π yd²

To calculate the surface area of the cylinder the following formula is used:

Surface area = 2πrh + 2πr²

r = diameter/2 = 12/2 = 6 yd

h = 4 yd

surface area = (2×π×6×4)+(2×π×36)

= 48π+72π

= 120π yd²

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The distance from the top of the cliff to the ship at C 373.4 m.

The angle of depression from the top of the cliff to the ship at C is 20.4 degrees

The distance BC = 200.2m

the distance is given as

[tex]\sqrt{130^{2} +350^{2} }[/tex]

= 373.4 m

The distance of the top of the cliff to the ship at c is 373.4 m

angle of depression is tan ∅ = 130 / 350

∅ = tan⁻¹  130 / 350

= 20.4 degrees

b. The distance BC

tan 33 = 130 / AB

AB = 130 / tan 33

= 200.2 m

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The length of the enlargement of the cube, given the scale factor and the length, would be 12 cm.

When a shape is enlarged by a scale factor of k, all its dimensions are multiplied by k. In this case, the scale factor is 1 1/2, which can be written as 3/2 in fraction form. Therefore, the length of the enlargement is:

Length of enlargement = Scale factor x Original length

Length of enlargement = (3/2) x 8 cm

Length of enlargement = 12 cm

So, the length of the enlargement is 12 cm.

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Answer: undefined

Step-by-step explanation:

(0+5)/(0+0)

Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds.

The function f(x) = 8192(0.05)^x represents exponential decay, where the number of players is decreasing by a factor of 0.05 in each round. However, in this tournament, the number of players is decreasing by a factor of 0.5 (half the players) in each round. Therefore, the correct function should be f(x) = 8192(0.5)^x.

To find the number of players remaining in the tournament at the end of x rounds, simply plug in the value of x into the function and solve.

For example, if we want to find the number of players remaining at the end of 3 rounds, we would plug in x = 3 and solve:

f(3) = 8192(0.5)^3
f(3) = 8192(0.125)
f(3) = 1024

Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds. Similarly, you can plug in any value of x to find the number of players remaining at the end of x rounds.

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we have proved that H ◃ G ↔ N(H) = G.

Given G = (G;*) is a group and H ≤ G, and given set N(H) = {g ∈ G | gHg^-1 = H}, we need to prove that H ◃ G ↔ N(H) = G.

First, let's assume that H ◃ G. This means that H is a normal subgroup of G. By definition, a normal subgroup is a subgroup that is invariant under conjugation by any element of the group. In other words, for any g ∈ G and h ∈ H, we have gHg^-1 = H. This is exactly the condition for an element to be in N(H), so we can conclude that N(H) = G.

Now, let's assume that N(H) = G. This means that every element of G is in N(H), which means that for any g ∈ G and h ∈ H, we have gHg^-1 = H. This is the definition of a normal subgroup, so we can conclude that H ◃ G.

Therefore, we have proved that H ◃ G ↔ N(H) = G.

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These are the Critical numbers of the function within the given interval.
Therefore, the answer is \(x=\frac{\pi }{6}, \frac{5 \pi }{6}\).

The Critical numbers of a function are the values of x that make the derivative of the function equal to zero. To find the eritical numbers of the given function, we need to find the derivative of the function and set it equal to zero.

The derivative of the function \(f(x)=-x+\sin (2 x)\) is \(f'(x)=-1+2\cos (2 x)\).

Setting the derivative equal to zero, we get:

\(-1+2\cos (2 x)=0\)

\(\cos (2 x)=\frac{1}{2}\)

Using the inverse cosine function, we get:

\(2 x=\cos ^{-1}\left(\frac{1}{2}\right)\)

\(2 x=\frac{\pi }{3}\) or \(2 x=\frac{5 \pi }{3}\)

Dividing both sides by 2, we get:

\(x=\frac{\pi }{6}\) or \(x=\frac{5 \pi }{6}\)

These are the Critical numbers of the function within the given interval.

Therefore, the answer is \(x=\frac{\pi }{6}, \frac{5 \pi }{6}\).

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The exact value of the expression is √3.

To find the exact value of the given expression, we can use the sum formula for tangent. The formula is:

Tan (A + B) = (tan A + tan B) / (1 - tan A tan B)

Where A and B angle.

In this case, A = 41° and B = 19°. Plugging these values into the formula, we get:

Tan (41° + 19°) = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)Simplifying the left side of the equation gives us:

Tan 60° = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)We know that tan 60° = √3.

Substituting this value into the equation gives us:√3 = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)

Cross-multiplying and simplifying gives us:

√3 (1 - tan 41° tan 19°) = tan 41° + tan 19°√3 - √3 tan 41° tan 19° = tan 41° + tan 19°

We can rearrange the terms to get:

√3 = tan 41° + tan 19° + √3 tan 41° tan 19°

This is the same expression that we were given in the question.

Therefore, the exact value of the expression is √3.

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The general solution of a fifth order linear ODE with one real root r and two complex roots a ± bi and c ± di can be determined by using the fact that the general solution of a linear ODE is the sum of the solutions corresponding to each of the roots.

For the real root r, the solution is given by:
y1 = C1 * e^(r*x)

For the complex roots a ± bi, the solution is given by:
y2 = C2 * e^(a*x) * cos(b*x) + C3 * e^(a*x) * sin(b*x)

For the complex roots c ± di, the solution is given by:
y3 = C4 * e^(c*x) * cos(d*x) + C5 * e^(c*x) * sin(d*x)

The general solution of the fifth order linear ODE is the sum of these solutions:
y = y1 + y2 + y3
= C1 * e^(r*x) + C2 * e^(a*x) * cos(b*x) + C3 * e^(a*x) * sin(b*x) + C4 * e^(c*x) * cos(d*x) + C5 * e^(c*x) * sin(d*x)

This is the general solution of the fifth order linear ODE with one real root r and two complex roots a ± bi and c ± di.

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1.....30 | 18.97
     50 | 24.49
     60 | 26.83
     90 | 32.87

2..... 54.77 mph

a. To complete the table of values, we need to plug in the given values of d into the equation v(d) = √12d and solve for v.

For d = 30:
v(30) = √12(30) = √360 = 18.97 mph

For d = 50:
v(50) = √12(50) = √600 = 24.49 mph

For d = 60:
v(60) = √12(60) = √720 = 26.83 mph

For d = 90:
v(90) = √12(90) = √1080 = 32.87 mph

So the completed table of values is:

d | v
---|---
30 | 18.97
50 | 24.49
60 | 26.83
90 | 32.87

b. To evaluate v(250), we simply plug in the value of d into the equation and solve for v:

v(250) = √12(250) = √3000 = 54.77 mph

So the velocity of the car when the length of its skid marks is 250 feet is 54.77 mph.

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The volume of the sunglasses case is 292.5 cm^3 and the surface area is 324 cm^2.

The volume and surface area of the sunglasses case can be calculated using the following formulas:

[tex]Volume = Length * Width * Height[/tex]

[tex]Surface Area = 2(LW + LH + WH)[/tex]

Plugging in the given values:

[tex]Volume = 15 cm * 3.0 cm * 6.5 cm[/tex]

[tex]Volume = 292.5 cm^3[/tex]

[tex]Surface Area = 2(15 cm * 3.0 cm + 15 cm * 6.5 cm + 3.0 cm * 6.5 cm)[/tex]

[tex]Surface Area = 2(45 cm^2 + 97.5 cm^2 + 19.5 cm^2)[/tex]

[tex]Surface Area = 2(162 cm^2)[/tex]

[tex]Surface Area = 324 cm^2[/tex]

Therefore, the volume of the sunglasses case is 292.5 cm^3 and the surface area is 324 cm^2.

The volume of a cube is calculated by multiplying the three (3) sides of the figure, that is, height times length times width. This is given by the expression: [tex]V = a*b*h[/tex].

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Fraction in simplest form is (3)/(4).

To add or subtract fractions with the same denominator, you simply add or subtract the numerators and keep the same denominator. Then, simplify the fraction if possible.

In this case, the fractions have the same denominator of 8, so we can simply add the numerators:

(1)/(8) + (5)/(8) = (1 + 5)/(8) = (6)/(8)

Now, we need to simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator. The GCF of 6 and 8 is 2, so we can divide both the numerator and denominator by 2 to get:

(6)/(8) = (6/2)/(8/2) = (3)/(4)

So the final answer is (3)/(4).

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Answer:

To simplify the expression, we need to distribute the negative sign to all the terms inside the parentheses, and then combine like terms.

Starting with:

(5x^4-4x^3-2x^2+x-19)-(x^4+5x^3+8x^2+x+5)

Distribute the negative sign inside the parentheses:

5x^4 - 4x^3 - 2x^2 + x - 19 - x^4 - 5x^3 - 8x^2 - x - 5

Now we can combine like terms:

(5x^4 - x^4) + (-4x^3 - 5x^3) + (-2x^2 - 8x^2) + (x - x) + (-19 - 5)

Simplifying further:

4x^4 - 9x^3 - 10x^2 - 24

Therefore, the simplified expression is:

4x^4 - 9x^3 - 10x^2 - 24.

The Degree of the polynomial 6, Leading Coefficient of the polynomial -7 .

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of the variables. It can have constants and/or variables, and can represent equations, functions, or graphs.

The degree of a polynomial is the highest exponent of the variable in the polynomial. The leading coefficient is the coefficient of the term with the highest degree.

In the polynomial -8y⁴+12y-7y⁶-6y²+, the highest exponent is 6, so the degree of the polynomial is 6. The coefficient of the term with the highest degree is -7, so the leading coefficient is -7.

Therefore, the degree of the polynomial is 6 and the leading coefficient is -7.

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The equation (1 + 4/a+4/a²)/ (1- 8/a - 20/a² simplifies to  -(a-10)/(a+2) . (C)

The given expression can be simplified by using the distributive law of multiplication over addition and the inverse law of multiplication to simplify the denominator.

By applying these laws, the given expression becomes: (1 + 4/a+4/a²)/ (1- 8/a - 20/a² = (1 + 4/a+4/a²)/ (a² - 8a - 20) = (a+2)/(a² - 8a - 20). By further simplifying it, we get (a+2)/(a-10). Hence, the answer is C. -(a-10)/(a+2).

In order to simplify the given expression, the distributive law of multiplication over addition is used by multiplying the numerator and denominator separately with the denominator's terms.

The inverse law of multiplication is then used to simplify the denominator. This gives us the simplified expression of (a+2)/(a-10).

By substituting the values of a in the expression, we can verify the answer. If a = 5, then the expression simplifies to

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Complete question:

[tex]\[ \frac{1+\frac{4}{a}+\frac{4}{a^{2}}}{1-\frac{8}{a}-\frac{20}{a^{2}}} \] a. \( \frac{a+2}{a-10} \) b. \( \frac{a+2}{a^{2}} \) c. \( -\frac{a-10}{a+2} \) d. \( \frac{4}{a-10} \)[/tex]

(1 + 4/a+4/a²)/ (1- 8/a - 20/a²) = ?

A. (a+2)/(a-10) b. (a+2)/a² C. -(a-10)/(a+2) D. 4/(a-10)