Simplify the following expression: 27x12−−−−−√3 . What elements appear in the simplified expression? Select all that apply.

Applying the angle of intersecting secants theorem, the missing information is: a. m(XY) = 42°       b. m(PR) = 18°

To find the missing information, use the angle of intersecting secants theorem to create an equation, then solve accordingly.

a. 31 = 1/2(104 - m(XY)) [based on the angle of intersecting secants theorem]

31 * 2 = 104 - m(XY)

62 = 104 - m(XY)

62 - 104 = -m(XY)

-42 = -m(XY)

m(XY) = 42°

b. 34 = 1/2(m(PR - 50) [based on the angle of intersecting secants theorem]

34 = 1/2(m(PR - 50)

68 = m(PR) - 50

68 - 50 = m(PR)

m(PR) = 18°

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Answer:

[tex]3x - 3 < 9[/tex]

[tex]3x < 12[/tex]

[tex]x < 4[/tex]

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{5}) \\\\\\ y-3=-2x+10\implies {\Large \begin{array}{llll} y=-2x+13 \end{array}}[/tex]

Answer:

Step-by-step explanation:

center=(-1,1)

radius=√16=4

distance between (-1,1) and (3,1)=√[(3+1)²+(1-1)²]=√[16+0]=√16=4=radius

Hence point lies on the circle.

A square cannot be drawn with the same area as the parallelogram and with its vertices at the intersections of grid lines because the sides of the square would have to be diagonal to the grid lines.

What is square?

A square is a geometrical shape with four equal sides and four equal angles, each of which is a right angle (90 degrees).

A parallelogram can be drawn on a grid by connecting its vertices with line segments that are parallel to the grid lines. However, a square cannot be drawn with the same area as the parallelogram and with its vertices at the intersections of grid lines because the sides of the square would have to be diagonal to the grid lines.

This means that the sides of the square cannot be parallel to the grid lines. If the sides of the square are not parallel to the grid lines, then it cannot be drawn on the grid in a way that all of its vertices lie at the intersections of grid lines.

Therefore, a square with the same area as the parallelogram and with its vertices at the intersections of grid lines cannot be drawn.

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Answer:

402,124 cubic inches

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.

Substituting the given radius of 41.8 inches into the formula, we get:

V = (4/3)π(41.8 in)^3

V = (4/3)π(75,927.832 in^3)

V = 402,123.732 in^3

Step-by-step explanation:

Volume of a sphere = 4/3 pi r^3  = 4/3 pi (41.8)^3 = 305,926.7511 in^3

     (round as needed)

In the triangle PQR, let X represent the point where angle P and side QR connect, and let Y represent the foot of the perpendicular that runs from X to side PR. The length of XY is  2.25 × √(3) units.

By drawing straight lines from three non-collinear points, a triangle is a three-sided polygon.

It is a basic geometric shape having several properties and applications in science, technology, engineering, and other fields.

Depending on the size of their angles and side lengths, triangles can be divided into different categories.

Due to the fact that PQ = QR = PR, triangle PQR is an equilateral triangle.

Let's write x as the length of each angle in this triangle. Since the angle P is divided into two equal halves by the angle bisector, the measures of the angles PXQ and QXR are both x/2.

Let's write d to represent XY's length. Trigonometry can be used to determine the length of XY since triangle PXY is a right triangle. Specifically, we have

tan(30) = XY / PY

Since PY = PQ - QY and PQ = QR = 9, we have PY = 9 - QY. Therefore:

tan(30) = XY / (9 - QY)

Solving for XY, we get:

XY = (9 - QY) tan(30)

QY needs to be located. The Pythagorean theorem can be used to determine QY because triangle QYX is also a right triangle:

QY² + XY² = QX²

Triangle QRX being a 30-60-90 triangle gives us:

QX = QR / 2 = 4.5

Therefore:

QY² + XY² = 4.5²

QY² + (9 - QY)² tan²(30) = 4.5²

The result of simplifying and solving for QY is:

QY = 2.25

Inputting this value into the XY expression yields the following result:

XY = (9 - 2.25) tan(30) = 2.25 × √(3)

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad E(\stackrel{x_2}{5}~,~\stackrel{y_2}{-10}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +x}{2}~~~ ,~~~ \cfrac{ -10 +y}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE D} }{(11~~,~~4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ 5 +x }{2}=11\implies 5+x=22\implies \boxed{x=17} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -10 +y }{2}=4\implies -10+y=8\implies \boxed{y=18}[/tex]

The volume of cone B is of 2.37π cubic centimeters.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor in this problem is given as follows:

k = 3/2.

Hence:

The scale factor measures the ratio of the side lengths, in units, while the volume is given in cubic units, hence the ratio of the volumes is given as follows:

Vb/Va = (2/3)³

Vb/Va = 4/27

Hence the volume of solid B is given as follows:

Vb = 4/27 x 16π

Vb = 2.37π.

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Answer:

Answer:

169.65

Step-by-step explanation:

Solving ones like these, I use the formula: Volume b/Volume a=k^3. I will be using “•” to represent multiplication, “^” is used for exponent. 16•pie is the volume for shape A, and k is 3/2. The reason why k is exponent by 3 is because this is for volume. Then, plug in the values, Volume B/16•pi=3/2^3 is what we have. With the piwer of inverse operations, we can isolate for Volume B. By multiplying 16•pi by each side, Volume B=16•pi•3/2^3. Lets do 3/2^3 first since it is following the order of PEMDAS. To recall what PEMDAS is, it is a method my school uses for solving equations. Parentheses first, Exponent next, then Multiply, Divide, Add, and subtract. Basically the order of solving any equation. 3/2^3= 27/8. Now, back to multiplying! I use desmos scientific calculator. 27/8•16•pi= =169.6460033. The qeustion says to round to the nearest hundreth, so it would be 169.65. Have a great day everybody

Step-by-step explanation:

Answer:

It would take the company 11.25 days to repave the road.

Step-by-step explanation:

27 miles to repave total

2.4 repavement per day

27 / 2.4 = 11.25

Therefore, it would take the company 11.25 days to repave the road.

Solution of system is p = 3 and q = -3.

The given system of equation is

4p+9q = -15

3p-7q = 30

The augmented matrix of this system be

[tex]\left[\begin{array}{ccc}4&9&-15\\3&-7& 30\\\end{array}\right][/tex]

Now use echelon method to convert it into reduced form,

So perform [tex]R_{2}[/tex] ⇒ 3x[tex]R_{1}[/tex] - 4x[tex]R_{2}[/tex]

 [tex]\left[\begin{array}{ccc}4&9&-15\\0&55& -165\\\end{array}\right][/tex]

Now the reduced system be

4p+9q = -15  ...(i)

   55q = -165

⇒     q = -165/55 = -3

Put   q = -3 into equation (i)

⇒ 4p + 9x(-3) = -15

⇒   p = 3

Hence p = 3 and q = -3

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The polyhedron Marguerite get from the net diagram is square based pyramid.

Given that, the net has 1 square face and 4 triangular faces.

A square pyramid characterized by a square base is a three-dimensional shape having five faces, thus called a pentahedron. The most famous example of such a square pyramid is the Great Pyramid of Giza.

Marguerite drew a net of a tetrahedron; a polyhedron with four faces, all of which are triangles. A net is a two-dimensional figure that can be folded to form a three-dimensional shape. A tetrahedron has four faces, all of which are triangles, and four vertices. It is one of the simplest polyhedral and is comprised of four triangular faces that meet at a single point, called the vertex.

Therefore, the polyhedron Marguerite get from the net diagram is square based pyramid.

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The domain of the equation include the following: D. all real numbers.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-4, ∞}

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The requried total amount of metal needed for the project is 4 1/2 yards.

The first piece of metal measures 1 1/5 yards, which is equivalent to 6/5 yards. The second piece of metal measures 3/10 yards. To find the total amount of metal needed, we need to multiply the sum of the two pieces by 3:

Total amount of metal = 3 x (6/5 + 3/10) yards

Simplifying the expression inside the parentheses, we have:

Total amount of metal = 3 x (12/10 + 3/10) yards

Total amount of metal = 3 x 15/10 yards

The total amount of metal = 9/2 yards

Total amount of metal = 4 1/2 yards

Therefore, the total amount of metal needed for the project is 4 1/2 yards.

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The integral of the rational expression is equal to I = - 1.414 · ㏑ |x + 3.372| + 2.194 · ㏑ |x - 2.372| + 0.219 · ㏑ |x - 1| + C.

In this problem we find the case of a rational expression, whose integral must be determined. This can be done by means of partial fractions method, that is, decompose the rational expression into a sum of fractions. First, write the entire rational expression and use partial fractions method:

(x² - 9) / (x³ - 9 · x + 8)

[(x - 3) · (x + 3)] / [(x + 3.372) · (x - 2.372) · (x - 1)]

A / (x + 3.372) + B / (x - 2.372) + C / (x - 1)

(x - 3) · (x + 3) = A · (x - 2.372) · (x - 1) + B · (x + 3.372) · (x - 1) + C · (x + 3.372) · (x - 2.372)

x² - 9 = A · (x² - 3.372 · x + 2.372) + B · (x² - 2.272 · x - 3.372) + C · (x² + x + 7.998)

x² - 9 = (A + B + C) · x² + (- 3.372 · A - 2.272 · B + C) · x + (2.372 · A - 3.372 · B + 7.998 · C)

Solve the system of linear equations:

A + B + C = 1

- 3.372 · A - 2.272 · B + C = 0

2.372 · A - 3.372 · B + 7.998 · C = - 9

(A, B, C) = (-1.414, 2.194, 0.219)

(x² - 9) / (x³ - 9 · x + 8) = - 1.414 / (x + 3.372) + 2.194 / (x - 2.372) + 0.219 / (x - 1)

Second, integrate the resulting equation:

I = - 1.414 ∫ [1 / (x + 3.372)] dx + 2.194 ∫ [1 / (x - 2.372)] dx + 0.219 ∫ [1 / (x - 1)] dx

I = - 1.414 · ㏑ |x + 3.372| + 2.194 · ㏑ |x - 2.372| + 0.219 · ㏑ |x - 1| + C

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Answer: The solutions to the equation sin x - 1 = cos x in the interval [0, 2) are x = -π/2 and x = 3π/4, in radians in terms of π.

Step-by-step explanation:sin x - 1 = cos x

Subtracting cos x from both sides:

sin x - cos x - 1 = 0

Using the identity sin(x - π/4) = sin x cos π/4 - cos x sin π/4, we get:

sin(x - π/4) = -1/√2

Taking the inverse sine of both sides, we get:

x - π/4 = -π/4 - π/2 = -3π/4

or

x - π/4 = π/2 + π/4 = π/2

Adding π/4 to both sides:

x = -3π/4 + π/4 = -π/2

or

x = π/2 + π/4 = 3π/4

Note that the interval [0, 2) contains 0, π/2, and π, but none of these values satisfy the equation. Therefore, the solutions in the given interval are:

x = -π/2 and x = 3π/4.

Hence, the solutions to the equation sin x - 1 = cos x in the interval [0, 2) are x = -π/2 and x = 3π/4, in radians in terms of π.

In the given graphs, the second graph is a connected graph.

A connected graph is a type of graph in which there is a path between every pair of vertices. In other words, it is a graph in which every vertex is reachable from any other vertex.

A graph is composed of vertices, which are points or nodes, and edges, which are the lines connecting the vertices.

In a connected graph, there are no isolated vertices or disjoint subsets of vertices, and every vertex is connected to at least one other vertex.

Here we have 3 graph

In the first graph, there are 3 individual graphs that are not connected.

Hence, The first graph is not connected graph

In the second graph, there are no isolated nodes or vertices as the graph is connected at every node

Hence, The Second graph is connected graph

In the third graph, there are 2 graphs that are not connected,

Hence, The third graph is not a connected graph.  

Therefore,

In the given graphs, the second graph is a connected graph.

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The figures can be evaluated as composite figures, which indicates;

16. The surface area composite solid is about 125.65 yd²

17. The surface area of the composite solid is about 210·π yd²

A composite solid is a solid that comprises of two or more regular solids.

16. The formula for the surface area the pyramid are;

Surface area, S.A. = π·r·l + Base Area

Where;

Base Area = π·r²

l = The slant height

r = The radius of the base = 3 yd

l = √(4² + 3²) = 5

S.A. = π × 3 × 5 = 15·π

Area of the pyramid at the bottom is therefore;

l = √(8² + 3²) = √(73)

S.A. = π × 3 × √(73) = 3·√(73)·π

The surface area is therefore; 15·π + 3·√(73)·π ≈ 127.65

18. The surface area of the cylinder = π × 10²/4 + π × 10 × 12 = 145·π

The surface area of the circular pyramid is therefore;

S.A. = π × r × l

l = √((10/2)² + 12²) = 13

r = 10/2 = 5

S.A. = π × 5 × 13 = 65·π

The surface area of the figure is therefore; 145·π + 65·π = 210·π

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Step-by-step explanation:

To find the equation of the parabola with focus (-3,2) and directrix x-y+1=0, we can use the definition of a parabola: the set of all points that are equidistant to the focus and directrix.

Let P(x, y) be an arbitrary point on the parabola, and let d(P, directrix) be the distance from P to the directrix. The distance from P to the focus is given by the distance formula:

d(P, focus) = √[(x - (-3))^2 + (y - 2)^2] = √[(x + 3)^2 + (y - 2)^2]

Since P is equidistant from the focus and directrix, we have:

d(P, directrix) = |x - y + 1| / √(1^2 + (-1)^2) = |x - y + 1| / √2

Therefore, the equation of the parabola is given by:

d(P, focus) = d(P, directrix)

√[(x + 3)^2 + (y - 2)^2] = |x - y + 1| / √2

Squaring both sides and simplifying, we get:

(x + 3)^2 + (y - 2)^2 = (x - y + 1)^2 / 2

Expanding the right-hand side and simplifying, we get:

2(x + 3)^2 + 2(y - 2)^2 = (x - y + 1)^2

Expanding the right-hand side again and simplifying, we get:

2x^2 + 8xy + 2y^2 - 8x - 12y + 20 = 0

Therefore, the equation of the parabola is:

2x^2 + 8xy + 2y^2 - 8x - 12y + 20 = 0

which is in general form.

If triangle XYZ is isosceles, then the two sides (XY and YZ) are congruent in addition to the two base angles.

Angle Y (the one at the top of the triangle) = 42 degrees

Angles X and Z are congruent because of the properties of an isosceles triangle. Let's call both angle measures "x" in our equation.

x + x + 42 = 180

2x + 42 = 180

2x = 138

x = 69

Answer: The measure of Angle Z is 69 degrees.

Hope this helps!

Let x be the number of gallons consumed by the first car.

Then, the number of gallons consumed by the second car is 65-x (since the total gas consumption is 65 gallons).

Using the formula distance = fuel efficiency x gas consumption, we can set up two equations:

First car: distance = 30x

Second car: distance = 20(65-x)

Since the total distance is 1700 miles, we can set up another equation:

Total distance: 30x + 20(65-x) = 1700

Simplifying this equation, we get:

30x + 1300 - 20x = 1700

10x = 400

x = 40

Therefore, the first car consumed 40 gallons and the second car consumed 65-40 = 25 gallons.

Let's assume that the first car traveled x miles and the second car traveled y miles during that week. We can set up two equations based on the given information:

x + y = 1700 (the combined total of miles traveled by both cars)

x/30 + y/20 = 65 (the total gas consumption)

To solve for x and y, we can use the first equation to express one variable in terms of the other. For example, we can solve for y as follows:

y = 1700 - x

Substituting this into the second equation, we get:

x/30 + (1700 - x)/20 = 65

Multiplying both sides by the common denominator 60, we can simplify the equation:

2x + 3(1700 - x) = 3900

2x + 5100 - 3x = 3900

-x = -1200

x = 1200

So the first car traveled 1200 miles during the week. We can use this value to find the second car's mileage:

y = 1700 - x = 1700 - 1200 = 500

Therefore, the second car traveled 500 miles during the week. To find the gallons of gas consumed by each car, we can use the fuel efficiency rates:

Gallons used by first car = 1200 miles / 30 mpg = 40 gallons

Gallons used by second car = 500 miles / 20 mpg = 25 gallons

So the first car consumed 40 gallons of gas and the second car consumed 25 gallons of gas during that week.

There are 48 students.

To find the number of students, we need to divide the total amount of clay by the weight of each portion.

We are given that there are 30kg of clay. We are also told that the clay is divided into portions of 5/8kg each.

To divide one quantity by another, we can use the following formula:

quantity ÷ weight per portion = number of portions

In this case, we can write:

30kg ÷ (5/8)kg per portion = number of portions

30kg × (8/5) portions per kg = number of portions

Simplifying, we get:

48 portions = number of portions

Therefore, there are 48 portions of clay in total. To find the number of students, we need to divide the number of portions by the number of portions per student.

Since each portion weighs 5/8kg, we can write:

1 portion = 5/8kg

number of portions per student = 1 portion/student

So, the number of students would be:

48 portions ÷ 1 portion per student = 48 students

Therefore, there are 48 students.

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Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a translation of 2 units to the right and 5 units to left.

Given information:

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD.

In Euclidean geometry, a translation is a geometric transformation that entails shifting each point in a figure, shape, or space by the same amount in one direction.

A translation may also be conceived of as changing the coordinate system's origin or as adding a constant vector to each point.

As per the diagram:

A(-5, 3) translates to A'(-3, -2).

As per the translation rule:

A translates to A' as per the rule of 2 units to the right and 5 units to left.

Similarly, all the remaining coordinates follow the same translation rule.

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The probability that exactly 2 of the pencils in the package are painted green is given as follows:

p = 9/30.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

In this problem, we have a set of 30 outcomes, in which the number of outcomes in which the letter G appears exactly twice is given as follows:

9.

Hence the probability that exactly 2 of the pencils in the package are painted green is given as follows:

p = 9/30.

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The composite solid has a volume of 224 inches³.

Volume is a mathematical notion that indicates how much space in three dimensions a solid, liquid, or gas occupy.

It is commonly measured in cubic length units like cubic metres, cubic feet, or cubic centimetres.

The volume of the cube must be subtracted from the volume of the rectangular prism in order to determine the volume of the composite solid.

Volume of the rectangular prism = length x width x height = 8 x 6 x 6 = 288 cubic inches

Volume of the cube = side [tex]length^3[/tex] = [tex]4^3[/tex] = 64 cubic inches

The composite solid's volume is thus:

Volume of rectangular prism - Volume of cube = 288 - 64 = 224 cubic inches.

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There are 48 students in the pottery class

30kg of clay is divided into 5/8kg chunks, and there is just enough for all of the kids. To find the number of students in the class, we need to divide the total amount of clay by the amount of clay per student.

The amount of clay per student is 5/8kg.

So, number of students = (total amount of clay) / (amount of clay per student)

Dividing the total amount of clay by the amount of clay per student, we get:

30 / (5/8) = 30 x 8/5

= 48

Therefore, there are 48 students in the pottery class

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[tex]\cfrac{7\times 10^{5}}{2\times 10^{3}}\implies \cfrac{7}{2}\times\cfrac{10^5}{10^3}\implies \cfrac{7}{2}\times 10^5\cdot 10^{-3}\implies \cfrac{7}{2}\times 10^{5-3} \\\\\\ \cfrac{7}{2}\times 10^2\implies 3.5\times 100\implies 350[/tex]

The value of the expression  p + (-q) - 2p for the value p = -3 and q = 5 is equals to -2.

The expression is equal to,

p + (-q) - 2p

Where 'p' and 'q' are the two variables.

To evaluate p + (-q) - 2p with p = -3 and q = 5,

Substitute the values into the given expression, we get,

= p + (-q) - 2p

= ( -3 ) + ( -5 ) - 2 × ( -3 )

As minus multiply by minus is plus.

And minus multiply by plus is minus.

= -3 - 5 + 6

= -8 + 6

Put the sign of greatest integer.

= -2

Therefore, value of p + (-q) - 2p = -2 when p = -3 and q = 5.

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The above question is incomplete, the complete question is:

Evaluate p+(−q)−2p where p = -3 and q = 5.

Answer:

The x-coordinate stays the same, so the starting point is at (-3, -5) since 4 - 9 = -5.