Two of the vertices of a triangle are located at (6,0) and (5,10) on the coordinate plane. The third vertex is located at (x,20), where x is a negative value. The area of the triangle is 60 square units

From the given information provided, the number of students who brought a packed lunch and did not visit the gift shop is 32.

The number of students who brought a packed lunch and did not visit the gift shop can be calculated by subtracting the number of students who visited the gift shop from the number of students who bought a packed lunch:

32 - 0 = 32

A frequency tree is a visual representation of data that shows how the total number of individuals or items is distributed among different categories or groups. It is commonly used in statistics and probability to organize and analyze data in a hierarchical structure.

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a) The sum of their times is of 4x + 3.

b) The property used is the combination of like terms, which we use to add the terms with the variable x.

c) If Doug ran the race in 27 minutes, the total time for the team is of 111 minutes.

Doug finished first, and the times of the other two athletes are as function of Doug, hence the variable x represents the time needed for Doug to finish the race, that is:

D = x.

Kim finished 3 minutes after Doug, hence:

K = D + 3

K = x + 3.

Conner finished with a time that was twice Doug’s time, hence:

C = 2x.

Then the total time is given as follows:

T = D + K + C

T = x + x + 3 + 2x

T = 4x + 3.

If Doug ran the race in 27 minutes, the total time for the team is obtained as follows:

T = 4 x 27 + 3

T = 111 minutes.

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Given:

5yd

To find:

The area of the hexagon

Solution:

Answer: Option B is the correct answer

Step-by-step explanation:

Area of lateral surface = 3 x Area of rectangle

The rectangle is of  5 inches wide and 14 inches long.

Area of rectangle =  5 x 14 = 70 square inches

Area of lateral surface = 3 x Area of rectangle

Area of lateral surface = 3 x 70 = 210 square inches

Option B is the correct answer.

The desired solution is to the nearest quarter of a unit, the approximate solution is x=2.25.

A quarter is a fraction that represents one-fourth of a whole number or quantity. It can be written as a ratio, a decimal, or a percentage. A quarter is one of the simplest fractions, and it can be used to divide an object or number into four equal parts. It is also used to calculate percentages and proportions.

A table of values is a great way to approximate a solution to an equation. To approximate a solution to the equation f(x)=g(x) to the nearest quarter of a unit, the table of values must contain the x-values and the corresponding f(x) and g(x) values.

For example, if the equation was f(x)=2x+3 and g(x)=x+2, the table of values would look like this:

x f(x) g(x)

0 3 2

1 5 3

2 7 4

3 9 5

4 11 6

To find the approximate solution to f(x)=g(x), the table must be examined for the first x-value where the f(x) and g(x) values are equal. In this case, the x-value is 2 and the corresponding f(x) and g(x) values are both 7. Since the desired solution is to the nearest quarter of a unit, the approximate solution is x=2.25.

This method of using a table of values to approximate a solution to an equation is very simple and quick. It is a great way to get a rough answer to an equation without having to solve it. It is also a useful tool for double-checking the exact solution to an equation.

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Answer:

70 and 2.91 days

hope this helped

The vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.

If k is a real number, then the vectors (1,k), (k,3k+18) are linearly independent precisely when k≠a,b, where a=-18 and b=1/3. This is because for the vectors to be linearly independent, the equation c1(1,k) + c2(k,3k+18) = (0,0) should only have the trivial solution of c1 = c2 = 0. If k = a or k = b, then there will be nontrivial solutions for c1 and c2, making the vectors linearly dependent.

To find the values of a and b, we can set the equations for the x and y components equal to 0 and solve for k:

c1 + c2k = 0

c1k + c2(3k+18) = 0

From the first equation, we can solve for c1 in terms of c2 and k:

c1 = -c2k

Substituting this into the second equation:

-c2k^2 + c2(3k+18) = 0

c2(-k^2 + 3k + 18) = 0

Since c2 cannot be 0, we can divide both sides by c2 and solve the quadratic equation for k:

-k^2 + 3k + 18 = 0

(k-1/3)(k+18) = 0

So k = 1/3 or k = -18. Therefore, the vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.

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The exact values are sin 195 = 0.9763, cos 165 = 0.6088, cos θ/2 = 0.8944, and cot θ/2 = -0.2764.

To find the exact value of sin 195 and cos 165 using a half-angle identity, we need to use the following formulas:

sin(x/2) = √[(1-cosx)/2] and cos(x/2) = √[(1+cosx)/2]

For sin 195, we can use the half-angle identity for sine:

sin(195/2) = sin(97.5) = √[(1-cos195)/2] = √[(1+0.9063)/2] = √(0.9532) = 0.9763

For cos 165, we can use the half-angle identity for cosine:

cos(165/2) = cos(82.5) = √[(1+cos165)/2] = √[(1-0.2588)/2] = √(0.3706) = 0.6088

For question 8, we can use the given values and the half-angle identities to find the exact values of cos θ/2 and cot θ/2.

For cos θ/2 given sin θ = -4/5 with 180º < θ < 270º, we can use the half-angle identity for cosine:

cos(θ/2) = √[(1+cosθ)/2] = √[(1+√(1-sin^2θ))/2] = √[(1+√(1-(-4/5)^2))/2] = √[(1+√(1-(16/25)))/2] = √[(1+√(9/25))/2] = √[(1+(3/5))/2] = √(0.8) = 0.8944

For cot θ/2 given tan θ = -√5/2 with 90° < θ < 180°, we can use the half-angle identity for cotangent:

cot(θ/2) = (1+cosθ)/sinθ = (1+√(1-sin^2θ))/sinθ = (1+√(1-(1/tan^2θ)))/(1/tanθ) = (1+√(1-(1/(-√5/2)^2)))/(-√5/2) = (1+√(1-(4/5)))/(-√5/2) = (1+√(1/5))/(-√5/2) = (1+(1/√5))/(-√5/2) = (1-(1/√5))/(-√5/2) = -0.2764

Therefore, the exact values are sin 195 = 0.9763, cos 165 = 0.6088, cos θ/2 = 0.8944, and cot θ/2 = -0.2764.

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The nearest value of x is 56°. We solve this question using Pythagoras theorem for that we also find one of its side which is not given.

The square on the hypotenuse of a right-angled triangle has the same area as the sum of the squares on the other two sides, according to a Pythagorean theorem.

Given AB = 5 and AC = 9

By Using Pythagoras theorem,

AB² + BC² = AC²

5² + BC² = 9²

BC² = 9² - 5²

BC² = 81 - 25

BC = 7.48 (Approx.)

Now, we will find the value of x°

[tex]So, tan\ x^{\circ} = \frac{BC}{AB}[/tex]

[tex]tan \ x^{\circ} = \frac{7.48}{5}[/tex]

[tex]tan\ x^{\circ} = 1.496[/tex]

[tex]x^{\circ} =tan^{-1} 1.496[/tex]

[tex]x^{\circ} = 56.24^{\circ}[/tex] , which is close to 56°

So the nearest value of x is 56°.

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Rows of chairs that are needed to make 48 musicians sit is 8 rows.

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers.

Given,

Number of musicians in orchestra

18 string musicians, 9 percussion musicians,

15 brass musicians, and 12 woodwind musicians

Total number of musicians

= 18 + 9 + 15 + 12

= 54

Six of the musicians cannot play in the next performance

Number of musicians playing in next performance

= 54 - 6

= 48

48 musicians will sit on 48 chairs

Number of chairs in one row = 6

Number of rows for 48 chairs = 48/6 = 8

Hence, 8 rows of chairs are needed to make 48 musicians sit.

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Answer:

1. What is the maximum length of a chess table that is still within the tolerance limit?

To find the maximum length of a chess table that is still within the tolerance limit, we add the tolerance to the average length:

110 cm + 16.5 cm = 126.5 cm

Therefore, the maximum length of a chess table that is still within the tolerance limit is 126.5 cm.

2. What is the minimum length of a chess table that is still within the tolerance limit?

To find the minimum length of a chess table that is still within the tolerance limit, we subtract the tolerance from the average length:

110 cm - 16.5 cm = 93.5 cm

Therefore, the minimum length of a chess table that is still within the tolerance limit is 93.5 cm.

Step-by-step explanation:

The Rational Roots Theorem states that the possible rational roots of a polynomial equation are the factors of the constant term divided by the factors of the leading coefficient. Therefore, the possible rational roots of P(x) are ±1, ±2, ±4, and ±4.

To find the exact roots of P(x), we can use synthetic division. Synthetic division is an efficient way of dividing a polynomial by a number. Using this method, we can determine that there are three roots for P(x): 1, -2, and -3. To verify this, we can evaluate P(x) for each of the three roots and confirm that the result is zero.

We can also use the quadratic formula to find the remaining two roots. Since P(x) is a 5th degree polynomial, the two remaining roots are complex and can be found using the quadratic formula. The complex roots of P(x) are -0.5 ± 0.5i.

In conclusion, the roots of P(x) are 1, -2, -3, -0.5 ± 0.5i. All of these results can be verified by evaluating P(x) and confirming that the result is zero.

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For the given function we have:

domain  [0, 76,867] and range [$0, $12,375,587]

We know that x represents the number of people in atendance, then:

R(x) = 161*x

Represents the revenue.

The domain is the set of possible inputs, and it will go between 0 and 76,867 (total number of seats).

The range will go between:

R(0) = 161*0 = 0

R(76,867) = 76,867*161 = 12,375,587

Then the domain is all the integers in [0, 76,867] and the range is [$0, $12,375,587]

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The length of the base of the parallelogram is 10.25 inches.

given that,

the area of parallelogram=102 1/2 square inches

height=10 inches

The following formula determines the area of a parallelogram:

Base + height = area.

The parallelogram's area and height are provided. By entering these values in the above formula we obtain:

102 1/2 = base × 10

We can divide both sides by 10 to find the base:

102 1/2 ÷ 10 = base

By dividing 1 by 2, we may convert the mixed number 1/2 to a decimal:

102 1/2 ÷ 10 = 102.5 ÷ 10 = 10.25

therefore, the length of the base of the parallelogram is 10.25 inches long.

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The value of x in the triangle based on Pythagoras Theorem will be 13

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a²+b²=c². However, it can also be written in the form of c²=a²+b²

This will be:

x² = 12² + 5²

x² = 144 + 25

x² = 169

x = ✓169

x = 13

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The relative maxima.

To find the relative maxima and minima of the function f(x) = x + 9/x + 5, we need to first find the derivative of the function.

The derivative of f(x) is f'(x) = 1 - 9/x^2.

Next, we need to set the derivative equal to zero and solve for x to find the critical points.

1 - 9/x^2 = 0

9/x^2 = 1

x^2 = 9

x = ±3

So, the critical points are x = 3 and x = -3.

To determine if these are relative maxima or minima, we need to use the second derivative test.

The second derivative of f(x) is f''(x) = 18/x^3.

Plugging in x = 3, we get f''(3) = 18/27 = 2/3, which is positive. This means that x = 3 is a relative minima.

Plugging in x = -3, we get f''(-3) = 18/-27 = -2/3, which is negative. This means that x = -3 is a relative maxima.

Therefore, the relative maxima is at x = -3 and the relative minima is at x = 3.

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There are three recipes provided to mention the fractional amounts of ingredients:

Recipe for Chicken Curry:

2 teaspoons of turmeric

1/2 teaspoon of cumin

1/4 spoon of any type of pepper

If you were to double this recipe, you would use:

4 teaspoons of turmeric

1 teaspoon of cumin

1/2 teaspoon of pepper

To double the amount of the ingredients, you would multiply each fraction by 2.

Chocolate chip cookies:

1/4 teaspoon of baking soda

1/2 teaspoon of salt

double the quantities if u want to make more or huge quantities

Tomato soup recipe

half a spoonful of dried basil

1/4 teaspoon of dried thyme

for this recipe, we will need

1 spoon of basil

1/2 teaspoon of dried thyme

Recipe for Pasta Salad:

fourth cup of Olive oil

1/3 cup of red wine vinegar

1/2 teaspoon of dried oregano

1/4 teaspoon of salt

1/8 teaspoon of black pepper

We can multiply by 2 if we increase the quantity.

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Answer:

Keith bought 14 gallons of paint, and each classroom requires 7/4 gallons of paint.

To find how many classrooms can be painted, we can divide the total amount of paint by the amount of paint needed per classroom:

14 ÷ (7/4) = 8

Therefore, Keith can paint 8 classrooms in total.

Answer:

8

Step-by-step explanation:

Let's call the unknown side [tex]c[/tex].

The Pythagorean Theorem states that in any right triangle, [tex]a^{2} + b^2 = c^2[/tex]

Now plug in the known values.

[tex]6^2 + (2\sqrt 7)^2 = c^2\\36 + 4(7) = c^2\\36 + 28 = c^2\\64 = c^2\\c = \sqrt{64} = 8[/tex]

Local Minima is 5 and 80

The critical numbers, a and b, of f'(x)=x^4−19x^3+135x^2+2 can be found by setting the derivative f'(x) = 0 and solving for x.

The derivative is: f'(x) = 4x^3 − 57x^2 + 270x

By setting the derivative equal to 0, we get:
4x^3 − 57x^2 + 270x = 0

Solving for x, we get:
x = 0, x = 5, x = 9

The critical numbers of f'(x) are 0, 5 and 9. The second derivative f''(x) is undefined at x = 0, so this is a local maximum point, while x = 5 and 9 are local minimum points.

Table:
Critical number | Second derivative (f''(x)) |  Value
0 | Undefined | Local Maximum
5 | -80 | Local Minimum
9 | 80 | Local Minimum

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Answer:

Step-by-step explanation:

Im not really sure what the heck you doing because im only in 8th grade but right now im in central and i'm kind of good at math but i'll try. Lets see........ I think they would all just be $11.50, but like i said im only in 8th grade and not that good at this kind of math so before you answer it please check with someone else to see if i got it right for you, cause i don't want to give you the wrong answer and you fail it.

The value shown on the number line is 3 8/10

The number line represents the given parameter

On the number line, we have the point located between 3 and 4

Such that the point is at 0.8 between 3 and 4

When the above expression is represented as a number, we have

Number = 3 + 0.8

Express the decimal as a fraction

So, we have

Number = 3 + 8/10

Evaluate

Number = 3 8/10

Hence, the solution is 3 8/10

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The solutions to the given trigonometric equations are:
i. θ = π/4, 3π/4, 5π/4, 7π/4
ii. θ = π/2, 3π/2
iii. θ ≈ 76.96º, 13.04º

To solve the given trigonometric equations using algebra, we need to rearrange the equations and use trigonometric identities to find the values of θ that satisfy the equations.

i. 2 sin^2 θ = 1, 0 < θ < 2π
First, we rearrange the equation to isolate sin^2 θ:
sin^2 θ = 1/2
Next, we take the square root of both sides:
sin θ = ±√(1/2)
Using the identity sin θ = cos (π/2 - θ), we can find the values of θ that satisfy the equation:
θ = π/4, 3π/4, 5π/4, 7π/4

ii. sin 1/2 θ = 1, - π < θ < 2π
First, we rearrange the equation to isolate θ:
sin θ = 2
Next, we use the identity sin θ = 1/csc θ to find the values of θ that satisfy the equation:
θ = π/2, 3π/2

iii. 4 cos(θ-45º) + 7 = 10, 0 < θ < 360 º
First, we rearrange the equation to isolate cos(θ-45º):
4 cos(θ-45º) = 3
cos(θ-45º) = 3/4
Next, we use the identity cos θ = sin (π/2 - θ) to find the values of θ that satisfy the equation:
θ = 45º + cos^-1(3/4), 45º - cos^-1(3/4)

Using desmos, we can verify our solutions and find the approximate values of θ:
θ ≈ 76.96º, 13.04º

Therefore, the solutions to the given trigonometric equations are:
i. θ = π/4, 3π/4, 5π/4, 7π/4
ii. θ = π/2, 3π/2
iii. θ ≈ 76.96º, 13.04º

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There will be about 111.25 square feet of space remaining in the room after the ping pong table is put in.

First, we need to convert the scale of the blueprint to a real-world scale. Since the scale is 1.5 in 5 feet, we can write this as:

1.5 inches : 5 feet

To convert this to a ratio that we can use, we can divide both sides by 1.5 inches:

1 inch : 3.33 feet

Now we can use this ratio to convert the dimensions of the room from the blueprint to real-world dimensions:

3 inches x 3.33 feet/inch = 9.99 feet

4.8 inches x 3.33 feet/inch = 15.96 feet

So the room is approximately 10 feet by 16 feet.

Next, we need to see if the ping pong table will fit in the room. The table is 9 feet by 5 feet, which means it needs at least a space of 9 feet x 5 feet = 45 square feet. To convert this to the scale of the blueprint, we can use the inverse of the ratio we calculated earlier:

1 foot : 1/3.33 inches

So the table needs at least a space of 9 feet x (1/3.33 inches/foot) = 27 inches by 5 feet x (1/3.33 inches/foot) = 15 inches on the blueprint.

The space in the room is 3 inches x 4.8 inches on the blueprint, which is equivalent to 3 inches x (1/1.5 inches/foot) = 2 feet and 4.8 inches x (1/1.5 inches/foot) = 1 foot 7.8 inches in real-world dimensions.

Since the table will fit on the blueprint, we can now calculate the remaining space in the room. The total area of the room is approximately 10 feet x 16 feet = 160 square feet.

The area taken up by the ping pong table is approximately 9 feet x 5 feet = 45 square feet, or 27 inches x 15 inches on the blueprint. To convert this to square feet, we can use the ratio we calculated earlier:

27 inches x (1/12 feet/inch) x 15 inches x (1/12 feet/inch) = 3.75 square feet

So the remaining space in the room is approximately 160 square feet - 45 square feet = 115 square feet - 3.75 square feet

= 111.25 square feet.

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The area of the pond after rounding to the nearest hundredth is 39 feet²

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

To find the area of a semicircle, we need to first find the radius of the pond.

Let's assume the diameter of the pond is 10 feet.

Since a semicircle is half of a circle, the radius of the pond is half the diameter, which is 5 feet.

Now we can use the formula for the area of a semicircle, which is:

A = (1/2)πr²

where A is the area and r is the radius.

Plugging in the values, we get:

A = (1/2) × 3.14 × 5²

A = 39.25

Rounding to the nearest whole number, the area of the pond is approximately 39 square feet.

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The surface areas of these cylinders are 75.39 cm, 835.76 cm,  1324.11 cm, and 3543.71 cm.

The surface area of a cylinder can be calculated by using the formula  2π r h + 2π r², which means we need the radius and the height to calculate the area. Let's now use this formula to know the area of each cylinder:

Cylinder 1:

2π 2 4+ 2π 2² = 75.39 cm

Cylinder 2:

2π 7 12+ 2π 7² = 835.76 cm

Cylinder 3:

2π 8.2  17.5+ 2π 8.2² = 1324.11 cm

Cylinder 4:

2π 12 35 + 2π 12r² = 3543.71 cm

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The expressiοn (B) 2 × 4 × 5 × 1/3 × 1/3 × 1/3 can be used tο find the vοlume οf the rectangular prism is cubic yards.

A mathematical equatiοn links twο statements and utilises the equals sign (=) tο indicate equality. In algebra, an equatiοn is a mathematical assertiοn that prοves the equality οf twο mathematical expressiοns. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical fοrmula may be used tο determine hοw the twο sentences οn either side οf a letter relate tο οne anοther. The lοgο and the particular piece οf sοftware are usually identical. like, fοr instance, 2x - 4 = 2.

Vοlume is calculated using the fοrmula LWH

Here each cube has side 1/3 yd

Sο vοlume = (2 × 1/3) × (4 × 1/3) × (5 × 1/3)

It can be written as 2 × 4 × 5 × 1/3 × 1/3 × 1/3

Thus, οptiοn B is cοrrect.

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Complete question:

The amount of cost for the fabric is given by A = $ 13

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the total cost of red fabric be represented as A

Now , the amount of red fabric be = 6 1/2 yards

And , the cost of red fabric per yard = $ 2

So , the total cost of red fabric A = amount of red fabric x cost of red fabric per yard

On simplifying the equation , we get

The total cost of red fabric A = ( 6 1/2 ) x 2

The total cost of red fabric A = ( 13/2 ) x 2

The total cost of red fabric A = $ 13

Therefore , the value of A is $ 13

Hence , the total cost of red fabric is $ 13

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The final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.

To determine the indicated angle, we can use the Law of Cosines, which states that: \[ c^2 = a^2 + b^2 - 2ab\cos(C) \]We can rearrange this equation to solve for the cosine of the indicated angle: \[ \cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \]Plugging in the given values for a, b, and c, we get: \[ \cos(C) = \frac{69.01^2 + 39.28^2 - 42.65^2}{2(69.01)(39.28)} \]Simplifying the expression, we get: \[ \cos(C) = 0.7664 \]Now, we can use the inverse cosine function to find the indicated angle: \[ C = \cos^{-1}(0.7664) \]This gives us an angle of 40.32 degrees. However, the question asks us to round our answer to two decimal places, so the final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.

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