3/5 intoconvert to decimal
​

The area of the triangle spanned by the vectors u and v can be calculated by taking the magnitude of the cross product of the two vectors. The cross product of u and v is (6, 4, -8) and the magnitude of this vector is 10, so the area of the triangle is 10.

The area of a triangle spanned by two vectors u and v can be calculated by taking the magnitude of the cross product of the two vectors. To calculate the cross product of two vectors u and v, we use the formula u x v = (u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1). For our vectors, u = (1, 2, -2) and v = (0, -1, 3), the cross product is (6, 4, -8). We then calculate the magnitude of the cross product, which can be done using the formula |u x v| = √(u2v3 - u3v2)2 + (u3v1 - u1v3)2 + (u1v2 - u2v1)2. Substituting in the values for our vectors gives |u x v| = √62 + 42 + (-8)2, which is equal to 10. Therefore, the area of the triangle spanned by the vectors u and v is 10.

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Answer:

see explanation

Step-by-step explanation:

11

the sum of the 3 angles in a triangle = 180° , then

∠ B + 75° + 90° = 180°

∠ B + 165° = 180° ( subtract 165° from both sides )

∠ B = 15°

12

using the sine ratio in the right triangle

sin75° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{125}{x}[/tex] ( multiply both sides by x )

x × sin75° = 125 ( divide both sides by sin75° )

x = [tex]\frac{125}{sin75}[/tex] ≈ 129.4 ( to 1 decimal place )

13

using the tangent ratio in the right triangle

tan75° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{125}{y}[/tex] ( multiply both sides by y )

y × tan75° = 125 ( divide both sides by tan75° )

y = [tex]\frac{125}{tan75}[/tex] ≈ 33.5 ( to 1 decimal place )

A sense of 3 dimensional space on a 2 dimensional surface be created using flat shapes by Overlapping , Shadows and Volume and shading .

A sense of three-dimensional space on a two-dimensional surface can be created using flat shapes by using various techniques that give the illusion of depth and volume.

Some of the techniques are :

(i) Overlapping : This involves placing objects on top of one another to create a sense of depth and hierarchy.

(ii) Shadows : The Shadows can be used to create a sense of depth by suggesting that objects are casting a shadow on each other, which implies that they exist at different levels of the image.

(iii) Volume and shading: Adding volume to shapes by shading and adding highlights can help to create the illusion of three-dimensional space on a two-dimensional surface.

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The line segment with endpoints (0, -5) and (5, 0) is (5/2, 5/2) and has integer coefficients.

A line is an enormously long object without any width, depth, or curvature. A line is therefore a one-dimensional object, even if it can also exist in two-, three-, and far more spaces. In everyday language, a line is defined as an integrand with two points operating as its ends. A line is an open, straight form that has no thickness and can extend in both directions indefinitely. It is common that the terms "straight line" or "ancient correct line" to describe a line that has no "wobble" anything along its length. (Casey 1893)

given

line segment ( 0,-5) and ( 5,0)

mid - point coordinate of x = x2 - x1 /2 = 5/2

mid - point coordinate of y = y2 - y1 / 2 = 5/2

The line segment with endpoints (0, -5) and (5, 0) is (5/2, 5/2) and has integer coefficients.

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Answer:

x=66

Step-by-step explanation:

A quadrilateral is 360 degrees

you add all of the other angles and subtract it from 360 to find x

103+133+58 = 294

360-294 = 66

x = 66

Answer:

x = 66

Step-by-step explanation:

The interior angles of a 4 sided shape always add up to 360 degrees. This means that the sum of the angles in the shape = 360. Using this information we can create an equation to solve for x

103 + 133 + 58 + x = 360

==> combine like terms

294 + x = 360

==> subtract both sides by 294

x = 66

Answer:

ask your teacher it's the best answer

Exactly 195 more blue marble are there than red marble in the jar

Total marble in a jar = 520

The ratio of blue marble to red marble is 5:3.

To find the number of red marble and blue marble,

Let the number of blue marble is 5x.

Let the number of red marble is 3x.

We add the number of red marble and blue marble. Then we equal the total number equal to 520. Then after solving we determine the value of x. Then we put the value of x in the number of red marble and the number of blue marble. This way we can determine the value of total number of blue and red marble.

Now adding the red and blue marble and equating equal to 520.

5x + 3x = 520

8x = 520

Divide by 8 on both side, we get

x = 65

Now putting the value of x in the number of blue marble and red marble.

The number of blue marble = 5x = 5×65 = 325

The number of blue marble = 2x = 2×65 = 130

Now determining exactly how many more blue marble are there than red marble in the jar.

More Blue Marble = The number of blue marble - The number of blue marble

More Blue Marble = 325 - 130

More Blue Marble = 195

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The value of g of (-12)​ is -7

What is Function?

A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

g(x) = x +5

substitute x= -12

g(-12) = -12 +5 = -7

The value of g of (-12)​ is -7

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The solution of the given differential equation is [tex]y=2e^x-1[/tex].

A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a place is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others. Studying equation-satisfying solutions and the solutions' characteristics is the main goal of differential equations.

We have the differential equation -

[tex]\frac{dy}{dx}-y=1\\\\\frac{dy}{1+y}=dx\\\\log(1+y)=x+c\\1) y(0)=1\\log2=c\\\\1+y=e^{x+c}\\y=2e^x-1[/tex]

2)

y(1)=0

log(1+0)=1+c

c=-1

[tex]y=e^{x-1}\\[/tex]

3)

y(0)=6

log7=c

[tex]y=e^{x+log7}-1\\y=7e^x-1[/tex]

4)

c=log5

[tex]y=5e^x-1[/tex]

The complete question is-

The given differential equation is [tex]\frac{dy}{dx}-y=1[/tex],

find the particular solution on ivp y(0)=1,y(1)=0 ,y(0)=6 and y(0)=5

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The event that the card is a queen, denoted as e, and the event that the card is a heart, denoted by f, are not independent.

Independent events are events where the occurrence or outcome of one event does not affect or influence the occurrence or outcome of another event. In other words, the outcome of one event has no effect on the probability of the other event happening. For example, flipping a coin and rolling a dice are independent events, because the outcome of one event (e.g., heads on a coin flip) does not affect the outcome of the other event (e.g., rolling a six on a dice).

The event "the card is a queen" reduces the number of cards in the deck, while the event "the card is a heart" also reduces the number of cards in the deck. The intersection of these two events, "the card is a queen of hearts," is a smaller set of cards than either event individually, so these events are dependent.

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The vertices of the image of the quadrilateral after rotation are C'(-6, 6), D'(-8, 6), E'(-10, 8) and F'(-8, 10).

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

Given that,

The coordinates of the vertices of quadrilateral CDEF are C(6, 6), D(6, 8), E(8, 10), and F(10, 8).

This is rotated 90° about the origin.

Any point (x, y) after a rotation of 90° about the origin changes to the point (-y, x).

C(6, 6) changes to C'(-6, 6)

D(6, 8) changes to D'(-8, 6)

E(8, 10) changes to E'(-10, 8)

F(10, 8) changes to F'(-8, 10)

Hence the coordinates of the vertices of the image are C'(-6, 6), D'(-8, 6), E'(-10, 8) and F'(-8, 10).

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The new cost equation is y=36x+44

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

A computer technician charges a flat base fee plus an hourly rate for all repairs. Last year, she used the formula  y= 18x+ 22  to determine the cost in dollars, y, of a repair that required x hours of work.

From the given equation, the base fee= 22

she doubles her base fee this year, double of 22= 2*22=44

So base fee of new cost is 44

There is no information about hourly rate. so hourly rate can be any number

So, new cost equation is  y=36x+44

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Answer:

The answer is 2. sin2A-cosA. This can be seen by using the trigonometric identities sin2A=2sinAcosA and cos2A=cos2A-sin2A. The expression tanA-secA can then be simplified to sinA/cosA-1/cosA, which can be further simplified to (2sinAcosA-cos2A)/cosA, which can be further simplified to 2sinAcosA-cosA, which can finally be simplified to sin2A-cosA.

Answer:

Step-by-step explanation:

you need to fiqure out wich numbers go were by matching the numbers

If  tree casts a shadow of 30 m, when a 9 m post nearby casts a shadow of 90 m, then the height of the tree is 3 meter

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

A tree casts a shadow of 30 m

when a 9 m post nearby casts a shadow of 90 m

Suppose, the height of the tree = x

So, value of elevation angle will be equal in the both cases,

Elevation angle for a post =  height/shadow

                                tanα   =   9/90

Elevation angle for a tree =  height/shadow

                                 tanα   =  x/30

Both the angles are equal, So

x/30 =  9/90

x  = (9 x 30)/90

x  =  3

Hence, the height of tree is 3 meter

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Answer:2.94642857143

Step-by-step explanation:

Sally and Mike have set up a corporation, Green Gra Inc., which is a business entity that offers limited liability protection and is separate from its owners.

Depending on the type of corporation they choose, they can be taxed as a C corporation, S corporation, or LLC. Each type of corporation has its own advantages and disadvantages, such as taxation, management structure, and liability, so they should review the various options and decide which one is best suited for their business.

Additionally, the agreement they have established in the event that either of them wishes to leave the corporation is known as a buy-sell agreement. This agreement will help ensure that both parties have the necessary funds to buy out the other's shares if either decides to leave the business.

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The number of fifty dollar bill is 15

Let a represent the number of twenty dollar bill
Let b represent the number of fifty dollar bill

a + b= 46.......equation1

20a + 50b= 1370..........equation 2

From equation 1

a + b= 46

a= 46-b

Substitute 46-b for a in equation 2

20(46-b) + 50b= 1370

920 - 20b + 50b= 1370

30b= 1370-920

30b= 450

b= 450/30

b= 15

Substitute 15 for b in equation 1

a + 15= 46

a= 46-15

a= 31

Hence the number of fifty dollar bill is 15

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Answer: e = $14.50

Step-by-step explanation: :)))

The diagonals of a parallelogram bisect each other. Therefore, the intersection of the diagonals of parallelogram GHJK is the midpoint of each diagonal.

What is math in coordinates?

A point or form in a two-dimensional plane is located using a pair of numbers called coordinates. A point's position on a 2D plane is indicated by two numbers called the x- and y-coordinates.

The midpoint of diagonal GH is given by the average of their endpoints:

G = (1,3), H (2,1)

Midpoint = ((1+2)/2, (3+1)/2) = (1.5, 2)

The midpoint of diagonal JK is given by the average of their endpoints:

J = (-1,-5), K = (-2,-3)

Midpoint = ((-1-2)/2, (-5-3)/2) = (-1.5, -4)

Since the two diagonals intersect at the same point, the coordinates of the intersection are (1.5, 2) and (-1.5, -4).

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Answer:

12 bunches

The easiest way by far, that you can solve for questions like this is to put the amount of money (m) over the price of each item (p). The fraction would look like this:

[tex]\frac{m}{p}[/tex]

Insert your numbers into the fraction:

[tex]\frac{24}{2}[/tex]

Now, just solve.

 [tex]\frac{24}{2}[/tex] = 12

Therefore, you can buy 12 bunches of seedless red grapes for $24.

Jessica can wax around 33.3 square meters.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jessica is a custodian at Oracle ArenaShe waxes 20 m2 of the floor in 3/5 of an hour Jessica waxes the floor at a constant rate.

If Jessica waxes 20m² of the floor in 3/5 of an hour, then;

20m² = 3/5 hr

To get the area that she waxes in an hour

x = 1 hr

Divide both expressions,

20/x = 3/5

3x = 20 * 5

3x = 100

x =100/3

x = 33.3 square meters

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Between Kalamazoo to Ann Arbor, the actual driving distance is roughly 62.5 miles.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller). By multiplying each side by a certain number, say 2, we can increase the size of a rectangle with sides of 2 cm and 4 cm.

The scale factor and the in-scale distance are combined to create the true distance. The scale factor is 50 miles per centimeter, and the in-scale distance is roughly 1.25 centimeters, as seen in the picture. So, this is how far Kalamazoo is from Ann Arbor really is:

[tex]& d \approx\left(50 \frac{\mathrm{mi}}{\mathrm{cm}}\right) \cdot(1.25 \mathrm{~cm}) \\[/tex]

[tex]& d \approx 62.5 \mathrm{mi}[/tex]

The actual distance in miles between Kalamazoo and Ann Arbor is about 62.5.

The complete question is:

Use the map and the provided ruler to find the actual distance between cities. The actual distance between Kalamazoo and Ann Arbor is ___ miles.

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If they plan to randomly select 30 parents and send them a survey and follow up with a phone call , then type of sampling strategy being used is (a) Cluster Sampling.

The Cluster Sampling is defined as a sampling technique where the entire population is divided into groups or clusters, and then a sample is taken from each cluster.

In this case, the entire population of the school system is divided into 10 elementary schools, and a sample of 30 parents from each school is selected.

The idea behind cluster sampling is that it is often easier and more efficient to obtain a sample from a smaller group rather than trying to select a sample from the entire population. The key feature of cluster sampling is that the units selected from the population are groups rather than individuals.

The given question is incomplete , the complete question is

In a large city school system with 10 elementary schools in a variety of neighborhoods, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. They plan to randomly select 30 parents from every elementary school, then send them a survey and follow up with a phone call or home visit if the survey is not returned within a week.

Which type of sampling strategy is being used ?

(a) Cluster Sampling

(b) Convenience Sampling

(c) Stratified Sampling

(d) Voluntary Sample .

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The distance between 1.5 and any point,n,on a number line is |1.5 - n|

From the question, we have the following parameters that can be used in our computation:

Points = n and 1.5

The distance between these points is the absolute difference between them

This is represented with the following equation

Distance = |1.5 - n|

Hence, the distance is |1.5 - n|

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Answer:

y = x + 14

Step-by-step explanation:

plug any two x and y coordinates into y = mx + b, then simplify

=> 14 = m(0) + b => b = 14

=> 15 = m(1) + b => 15 = m + b

solve for m by plugging b

=> 15 = m + 14 => m = 1

plug in the values of b and m into y = mx + b, then simplify

=> y = (1)x + 14 => y = x + 14

A combination of carnations and roses that does not meet the restrictions is given as follows:

r = 80, c = 0.

The are four restrictions in the problem, given as follows:

Hence the combinations that meet these restrictions are the combinations that are between these four curves, which are the amounts below the blue line and above the red line, as the graph is composed by the first quadrant.

Then one combination that does not meet the restrictions is given as follows:

r = 80, c = 0.

As it is not on the region between the red line and the blue line.

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The value of x in the diagram is 24°. Option C

Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line. Angles on a straight line add to 180° .

To find the value of x,

58 + 5x + 2 = 180

60+5x=180

5x=180-60

5x=120

Divide both sides of the equation by 5

5x/5=120/5

x = 24°

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The simplified power of [tex](\frac{\sqrt[4]{m} }{6\sqrt[4]{m^3} })^{-1}[/tex]⁻¹ is 6√m and a = 1/2.

To simplified the power of the equation, we have to do some converstion to the equation.

Remember that:

[tex]x^{-1}=\frac{1}{x}[/tex]

[tex]\sqrt[b]{x^a} =x^{\frac{a}{b} }[/tex]

[tex]\frac{x^{a} }{x^{b} }[/tex] = xᵃ⁻ᵇ

Notice that the power outside the brackets are negative, then we need to flip the equation to eliminate the negative sign:

[tex](\frac{\sqrt[4]{m} }{6\sqrt[4]{m^3} })^{-1}[/tex] = [tex]\frac{6\sqrt[4]{m^3} }{\sqrt[4]{m} }[/tex]

               = [tex]\frac{6m^{3/4} }{m^{1/4} }[/tex]

               = [tex]6m^{(3/4 - 1/4)}[/tex]

               = [tex]6m^{2/4}[/tex]

               = [tex]6m^{1/2}[/tex]

6mᵃ = [tex]6m^{1/2}\\[/tex]

a = 1/2

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The student completed 9 courses worth 4 credits. The solution has been obtained by using the linear equation.

What is a linear equation?

It follows that a linear equation has the highest degree of one. As a result, it is evident that there are no variables in a linear equation with an exponent bigger than one. A straight line is produced by this equation on the graph.

Let the courses worth 3 credits be 'x' and worth 4 credits be 'y'.

We are given that the student earned a total of 54 credits.

So,

3x + 4y = 54   ...(1)

Also, we are given that in total 15 courses were completed.

So,

x + y = 15   ...(2)

From (2), we get

x = 15 - y

Substituting this value in (1), we get

⇒3(15-y) + 4y = 54

⇒45 - 3y + 4y = 54

⇒45 + y = 54

⇒y = 9

Therefore, x = 15-9 = 6

Hence, the student completed 9 courses worth 4 credits.

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