GEOMETRY 80POINTS

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The measure of the interior angle at vertex F is 72 degrees.

A hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.

The angle of the hexagon is given in terms of x,

The sum of the angle is equal to 720 degrees

[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]

[tex]20\text{x} = 720[/tex]

[tex]\text{x} = 36[/tex]

[tex]\bold{2x = 72^\circ}[/tex]

Therefore, the measure of interior angle at vertex F is equal to 72 degrees.

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The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer:

x=50

Step-by-step explanation:

Make this equal to 180.

x+3x-35+x-35 = 180

5x = 180 + 70

5x=250

x=50

Answer:

B)  There are two solutions, but only one is viable.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}A=w^2+4w\\A=4w+45\end{cases}[/tex]

To solve the system of equations, substitute the first equation into the second equation:

[tex]w^2+4w=4w+45[/tex]

Solve for w using algebraic operations:

[tex]\begin{aligned}w^2+4w&=4w+45\\w^2+4w-4w&=4w+45-4w\\w^2&=45\\\sqrt{w^2}&=\sqrt{45}\\w&=\pm \sqrt{45}\\w &\approx \pm 6.71\; \sf cm\end{aligned}[/tex]

Therefore, there are two solutions to the given system of equations.

However, as length cannot be negative, the only viable solution is w ≈ 6.71 cm.

Answer: O (4, -4)

Step-by-step explanation:

To solve the system of equations using elimination, we can multiply the second equation by -3 to eliminate the y term:

Original equations:

5x + 3y = 8 (Equation 1)

4x + y = 12 (Equation 2)

Multiply Equation 2 by -3:

-3(4x + y) = -3(12)

-12x - 3y = -36 (Equation 3)

Now we can add Equation 1 and Equation 3 to eliminate the y term:

(5x + 3y) + (-12x - 3y) = 8 + (-36)

Simplifying:

5x - 12x + 3y - 3y = 8 - 36

-7x = -28

Divide both sides by -7:

x = -28 / -7

x = 4

Now substitute the value of x back into either of the original equations, let's use Equation 2:

4(4) + y = 12

16 + y = 12

y = 12 - 16

y = -4

Therefore, the solution to the system of equations is x = 4 and y = -4.

Answer:

the first 2

Step-by-step explanation:

let me know if it is wrong

Domain: The domain is the range of valid heights for the mountain, which is from 3300 feet to 8920 feet.

Range: The range is the set of all possible heights of the linear model, which in this case is also from 3300 feet to 8920 feet.

Domain: The domain of the linear model in this context would represent the possible values for the x variable, which is associated with the height of the mountain.

In this case, the meaningful domain would be the range of valid heights that the mountain can have.

Since the top of the mountain is at 8920 feet and the base is at 3300 feet, the meaningful domain would be the range of heights between 3300 feet and 8920 feet.

Therefore, the domain in this scenario would be [3300, 8920].

Range: The range of the linear model in this context would represent the possible values for the y variable, which is associated with the height of the mountain.

The range would be the set of all possible heights that the linear model can produce.

In this case, since the top of the mountain is at 8920 feet and the base is at 3300 feet, the range would encompass all the valid heights within this range.

Therefore, the range in this scenario would be [3300, 8920].

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The cost per trainee for the 5-week training course is $7,000.

To find the cost per trainee, we divide the total cost of the training course by the number of trainees.

Total cost of the training course = $140,000

Number of trainees = 20

Cost per trainee = Total cost of the training course / Number of trainees

Cost per trainee = $140,000 / 20

Cost per trainee = $7,000

Therefore, the cost per trainee for the 5-week training course is $7,000.

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The torque experienced by the rigid body is -17.10375 k N·m.

To determine the torque experienced by a rigid body when a force is applied, we need to calculate the cross product between the force vector and the radius vector from the point of application of the force to the point of rotation.

Since a force F = (4.501 - 3.25) N is applied and the radius vector is r = (1.801 + 2.50j) m, where j is the imaginary unit, we can calculate the cross product using the formula:

Torque = r x F

The cross product between two vectors is calculated as follows:

Torque = (r_x * F_y - r_y * F_x)k

Where r_x and r_y are the components of the radius vector and F_x and F_y are the components of the force vector. Furthermore, k is a unit vector in the direction of the axis of rotation.

Substituting the given values, we have:

Torque = ((1.801 * -3.25) - (2.50 * 4.501))k

Calculating the cross product:

Torque = (-5.85125 - 11.2525)k

Simplifying:

Torque = -17.10375k

Therefore, the torque experienced by the rigid body is -17.10375 k N·m.

The negative sign indicates that the torque is in the opposite direction to the axis of rotation. The magnitude of the torque is measured in newtons per meter (N·m) and represents the capacity of a force to produce a rotation in a rigid body around a specific axis.

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Answer:

Reflection Property.

All-zero Property.

Proportionality.

Switching property.

Factor property.

Scalar multiple properties.

Sum property.

Triangle property.

Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex]

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

[tex]x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72[/tex]

Answer:

there is no solution

Step-by-step explanation:

x + y = 6 → (1)

x + y = 4 → (2)

subtract (2) from (1) term by term

(x - x) + (y - y) = 6 - 4

0 + 0 = 2

0 = 2 ← false statement

this false statement indicates the equations have no solution

Answer:  [tex]x=200[/tex]

Step-by-step explanation:

    [tex]\frac{1}{5}x-\frac{2}{3}y=30[/tex]

[tex]\frac{1}{5}x-\frac{2}{3}(15)=30[/tex]

    [tex]\frac{1}{5}x-10=30[/tex]

            [tex]\frac{1}{5}x=40[/tex]

              [tex]x=\frac{40}{\frac{1}{5}}[/tex]

             [tex]x=40*\frac{5}{1}[/tex]

             [tex]x=200[/tex]

The product of the given fractions is 224/61.

To calculate the product of the given fractions, let's simplify and cancel out any common factors.

We have:

(4/5) x (5/7) x (7/9) x (9/11) x (11/13) x (13/15) x (15/17) x (17/19) x (19/21) x (21/23) x (23/25) x (25/27) x (27/28) x (29/37) x (31/35) x (33/33) x (35/31) x (37/29)

Starting from the numerator and denominator of the first fraction, we observe the following cancellations:

5 in the numerator and denominator cancel out.

7 in the numerator and denominator cancel out.

9 in the numerator and denominator cancel out.

11 in the numerator and denominator cancel out.

13 in the numerator and denominator cancel out.

15 in the numerator and denominator cancel out.

17 in the numerator and denominator cancel out.

19 in the numerator and denominator cancel out.

21 in the numerator and denominator cancel out.

23 in the numerator and denominator cancel out.

25 in the numerator and denominator cancel out.

27 in the numerator and denominator cancel out.

Now, let's multiply the remaining fractions:

(4/1) x (1/28) x (29/37) x (31/1) x (1/35) x (37/29)

This simplifies to:

(4 x 1 x 29 x 31 x 37) / (1 x 28 x 37 x 29 x 35)

Simplifying further:

(4 x 29 x 31) / (28 x 35)

We can calculate this to get the final result:

(4 x 29 x 31) / (28 x 35) = 3584 / 980 = 224 / 61.

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Answer:

arc VL = 91°

Step-by-step explanation:

the chord- chord angle WBF is half the sum of the arcs intersected by the angle and its vertical angle , that is

[tex]\frac{1}{2}[/tex] (WF + VL) = ∠ WBF

[tex]\frac{1}{2}[/tex] (143 + VL ) = 117° ( multiply both sides by 2 to clear the fraction

143° + VL = 234° ( subtract 143° from both sides )

VL = 91°

Ryan paid $5,560 in 2009.

Let's solve the problem using the given information: Amount paid in 2010 by Ryan = $1,112 Amount paid in 2010 is 80% less than the amount paid in 2009.

So, the amount paid in 2009 can be calculated as follows: Let x be the amount paid by Ryan in 2009.

Then we can write, $1,112 = x - 0.8x Simplifying this expression, we get:$1,112 = 0.2x Dividing both sides of the equation by 0.2, we get: x = $5,560

Therefore, Ryan paid $5,560 in 2009. I hope this helps.

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...................................................................

Answer:

Step-by-step explanation:

the answer is 13 remaining papers

The perimeter of the rectangle is 140 inches.

Let's denote the width of the rectangle as w. According to the given information, the length of the rectangle is six times its width, so we can express the length as 6w.

The area of a rectangle is given by the formula A = length × width. Substituting the values we have:

A = (6w) × w

600 = 6w^2

To solve for w, we divide both sides of the equation by 6:

w^2 = 100

Taking the square root of both sides:

w = ±10

Since width cannot be negative in this context, we discard the negative value and consider the positive value, w = 10.

Now that we have the width, we can find the length of the rectangle:

Length = 6w = 6 × 10 = 60

The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values:

P = 2(60 + 10)

P = 2(70)

P = 140

Therefore, the perimeter of the rectangle is 140 inches.

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Answer:

Step-by-step explanation:

This may be wrong but hear me out, 40+10 is 50 and 11+1 is 12, so 12:50?

Answer:

Step-by-step explanation:

Of course! I'd be happy to help you.

Let's simplify the expression f(x) + 8x - 8x^3 - x^4 + 6 step by step:

The given expression is: f(x) + 8x - 8x^3 - x^4 + 6

Since we don't have any specific information about f(x), we'll assume that f(x) is a constant or a function that doesn't depend on x. In that case, f(x) can be treated as a constant term.

Combining like terms, we have:

f(x) - x^4 - 8x^3 + 8x + 6

There is no further simplification we can do without additional information about the function f(x) or any specific values of x. Therefore, the simplified expression is:

f(x) - x^4 - 8x^3 + 8x + 6

Solution:

Formula: Total = Group 1 + Group 2 - Both + Neither

where:

- Total = total number of girls in the class (34)

- Group 1 = number of girls playing tennis (21)

- Group 2 = number of girls playing netball (18)

- Both = number of girls playing both games (what we want to find)

- Neither = number of girls playing neither game (0, since all the girls play at least one game)

Plugging in the values, we get:

34 = 21 + 18 - Both + 0

Simplifying:

34 = 39 - Both

Both = 39 - 34

Both = 5

The value of x that makes lines c and d parallel when cut by transversal p is 99 (option d).

To determine the value of x, we need to analyze the relationship between the given lines and transversal.

Recall that when two lines are cut by a transversal, the corresponding angles are congruent if the lines are parallel.

Since lines c and d are cut by transversal p, we need to find the corresponding angles that should be congruent.

Let's assume that angle 12 corresponds to angle 18. In order for lines c and d to be parallel, angle 12 must be congruent to angle 18.

However, angle 12 and angle 18 do not have equal values (12 ≠ 18). Therefore, we need to explore other possible values of x.

Let's try x = 81. With this value, angle 12 corresponds to angle 81. But again, angle 81 is not congruent to angle 18 (81 ≠ 18). Thus, x = 81 does not make lines c and d parallel.

Finally, let's try x = 99. With this value, angle 12 corresponds to angle 99. If angle 99 is congruent to angle 18, then lines c and d will be parallel.

Since 99 = 99, we can conclude that when x = 99, lines c and d are parallel when cut by transversal p.

Therefore, the value of x that makes lines c and d parallel when cut by transversal p is 99. Thus, the correct option is d.

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Answer:

We can construct only one triangle with the given description(this triangle is unique).

It is isosceles so the two sides are congruent(

4

4 cm) each. The angle they form is specified

80

°

80° so there is no way to construct one more with the same characteristics(we will have to change the angle or the length of the two sides).

Step-by-step explanation:

Answer:

One triangle

Step-by-step explanation:

By the Law of Cosines, given two side lengths of 3 inches and an included angle of 20°, then we are able to get the length of the third side using the formula [tex]a^2=b^2+c^2+2bc\cos(A)[/tex]

Hence, you can construct only one triangle because of SAS Theorem.

Answer:

$ 6.20 Cents

Step-by-step explanation:

17 - 5.50= 11.5

11.50 - 5.30= 6.2

Add A Zero at the end

You Get 6.20

Answer:

W = V/(LH)

Step-by-step explanation:

All we are doing is isolating W. Since V=LWH, then dividing both sides by LH will put W by itself on the right-hand side, you have V/(LH) = W as your equation

The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can use a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

From the given information, we can identify two data points:

(4, 31.00) and (8, 62.00)

Using these points, we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = (62.00 - 31.00) / (8 - 4)

m = 31.00 / 4

m = 7.75

Now, we can substitute one of the points and the slope into the equation to find the y-intercept (b).

Using the point (4, 31.00):

31.00 = 7.75(4) + b

31.00 = 31.00 + b

b = 0

Therefore, the equation that represents the relationship between the number of hours Steven babysits (x) and the amount he charges (y) is:

y = 7.75x

The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

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Answer:

To write the polynomial function m(x) = x + x^2 - 1 in standard form, we rearrange the terms in descending order of degree:

m(x) = x^2 + x - 1

Polynomial name: Quadratic polynomial

Degree: 2 (the highest exponent is 2)

Leading coefficient: 1 (the coefficient of the highest-degree term)

Constant term: -1 (the term without any variable)

Answer:

Step-by-step explanation:

To solve the equation (2/3)t - (1/5)t = 2 for t, we need to combine like terms and isolate the variable t. Here are the steps:

(2/3)t - (1/5)t = 2

To combine the fractions, we need to find a common denominator for 3 and 5, which is 15.

[(2/3)(5/5)]t - [(1/5)(3/3)]t = 2

(10/15)t - (3/15)t = 2

[(10 - 3)/15]t = 2

(7/15)t = 2

To isolate t, we can multiply both sides of the equation by the reciprocal of (7/15), which is (15/7).

[(7/15)t][(15/7)] = 2[(15/7)]

t = (2 * 15) / 7

t = 30/7

Therefore, the solution for t in the equation (2/3)t - (1/5)t = 2 is t = 30/7 or t ≈ 4.286.