Add 13.2 and 0.9,and then divide by 0.6.

[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:-8 and 2

Step-by-step explanation:

graph it

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 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:

D - 37 degrees

Step-by-step explanation:

Sin = opp / hyp

Cos = adj / hyp

Tan = opp / adj

Tan(x) = 29/38

~37.34 degrees

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 difference between the number of actual outcomes and the number of expected outcomes is given as follows:

3 outcomes.

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.

The probabilities are given as follows:

Hence the composite probability of the two independent events is given as follows:

1/2 x 1/4 = 1/8.

The expected number of outcomes in 40 trials is given as follows:

1/8 x 40 = 5 outcomes.

Hence the difference is of:

8 - 5 = 3 outcomes.

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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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Answer:

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

Step-by-step explanation:

The formula for the circumference of a circle :

circ = pi * d      <======you need to remember this

circ = pi * 5.52 mm = 17.34 cm

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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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.

The constant of variation for the

number of hummingbirds per flower is 0.75.

From the information, Daniel recorded the number of hummingbirds (B) and the number of red flowers (F) for each quarter of a field.

For the first observation, we have 6 hummingbirds and 8 flowers. So the ratio of hummingbirds to flowers is 6/8 = 0.75.

For the second observation, we have 12 hummingbirds and 16 flowers. So the ratio of hummingbirds to flowers is 12/16 = 0.75.

Hence, the constant of variation for the

number of hummingbirds per flower is 0.75.

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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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Answer:

  B.  7

Step-by-step explanation:

You want the value of b from the choices {5, 7, 8, 10} that will satisfy both inequalities ...

You are asked to find the answer by substitution. This means you put the offered value of 'b' into the inequality where 'b' is, then simplify and see if you have a true relation.

In the first inequality, this is ...

  2·5 -8 > 5

  10 -8 > 5

  2 > f . . . . . . . false — not a solution

In the first inequality, this is ...

  2·7 -8 > 5

  14 -8 > 5

  6 > 5 . . . . . . True

In the second inequality, we have ...

  3·7 -13 < 9

  21 -13 < 9

  8 < 9 . . . . . . True — this is the solution you want

The choice b = 7 satisfies both inequalities.

__

Additional comment

We generally find it easier to compare to zero, rather than some constant. In the attached, we evaluated the left-side expressions ...

The first inequality is true for b = {7, 8, 10}. The second inequality is true for b = {5, 7}. The only value of b that satisfies both inequalities is b=7.

You will notice we also find it easier to try all the choices at once, rather than retype the calculator input for each one.

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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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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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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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 graph of the system is on the image at the end, there we can see that it has no solutions.

The two linear equations are:

y = (1/2)*x - 6

y = (1/2)*x - 4

First we can see that the two lines are parallel, thus, the lines never do intercept, so that is enough to know that the system of equations has no solutions.

We can graph both of the lines in the same coordinate axis and we wil see that the lines never intercept, as you can see in the graph at the end of this answer.

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Answer:

it's correct because when you plug in the value of 2 and check, you get 1. try it yourself and you'll see!

Step-by-step explanation:

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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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.

Answer:

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

[tex]3x < 12[/tex]

[tex]x < 4[/tex]

Answer:

The volume of the pyramid is approximately 25,920,000 cubic feet.

Step-by-step explanation:

The Great Pyramid of Khufu is one of the most famous pyramids in Egypt, located in Giza. Its original height was 146.7 meters (481 feet), but due to erosion and the loss of its outer casing, it now stands at a height of 138.8 meters (455 feet). The base of the pyramid is a square with sides measuring 230.4 meters (755.9 feet).

To find the volume of the pyramid, we can use the formula:

V = (1/3)Bh

where V is the volume, B is the area of the base, and h is the height of the pyramid.

First, we need to convert the dimensions of the pyramid to feet. The height of the pyramid is 455 feet, and the base of the pyramid is a square with sides of 755.9 feet.

The area of the base is:

B = side^2 = (755.9 ft)^2 = 571536.81 sq ft

The volume of the pyramid is:

V = (1/3)Bh = (1/3) × 571536.81 sq ft × 455 ft ≈ 2.592 × 10^7 cubic feet

Therefore, the dimensions of the Great Pyramid of Khufu are approximately 755.9 feet for each side of the base, and 455 feet for the height. The volume of the pyramid is approximately 25,920,000 cubic feet.

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)

Answer:

3. 2(π)(4)

Step-by-step explanation:

The expression for the circumference of a circle is 2πR.

The R stands for the radius which is 4.

Hope this helps...

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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 solution is :

So, you need 3 days approximately.

Here, we have,

We will use Chain Rule to solve this question.

According to Chain Rule, the work efficiency remains constant.

• WWF×TWWF×T= Constant

• Here W = Work Done, WF = Workforce, T = Time.

Let the number of days needed be 'x'.

Applying Chain Rule,

10×9×6= 15×12×(x)

Or, x=3x=3 day

So, you need 3 days approximately.

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