Write the quotient as a mixed number. 15 ÷ 7 = 2 R1

Answer:

1 is p,l and n,m

2 is a,h and s,f

Step-by-step explanation:

Answer:

E) \(x = 4\:\:y=2\sqrt3\)

Step-by-step explanation:

\(cos \: 60 \degree = \frac{2}{x} \\ \\ \frac{1}{2} = \frac{2}{x} \\ \\ \bold{ \purple{ \boxed{ \bold{x = 4}}}} \\ \\ tan \: 60 \degree = \frac{y}{2} \\ \\ \sqrt{3} = \frac{y}{2} \\ \\ \bold{ \red{ \boxed{ \bold{y = 2 \sqrt{3} }}}} \\ \\ \)

Mean = Sum of points/ number of points

Median

A hyperbola is a kind of conic section that can be either right or oblique. A hyperbola with vertices at (0, −6) and (0, 6) has a vertical axis of symmetry and is centred at (0, 0).

The standard form of the equation for a vertical hyperbola is given by;

\($$\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1$$\)

The equation for a vertical hyperbola whose center is at the origin $(0, 0)$ and whose vertices are located at $(0, a)$ and $(0, -a)$ is given by;

\($$\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$$\)

Here a is the distance from the center to the vertices and b is the distance from the center to the end of the transverse axis. To get the values of a and b, note that the distance from the center to the vertices is 6, and b is the distance from the center to the asymptote, which has the equation y = (3/5)x.

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Answer:

1.19

Step-by-step explanation:

1) Shift the decimals of both 0.8449 and 0.71 to the right by 2 decimal places. (This is needed to convert 0.71 to 71, since long division must divide by a whole number.)

84.49 ÷ 71

2)  Use the algorithm method.

1 . 1 9

7 1 | 8 4 . 4 9

7     1 .  

1 3 . 4

7 . 1

6 . 3 9

6 . 3 9

3) Therefore,  0.8449 ÷ 0.71 = 1.19.

1.19

Answer:

1. x = 6.5

2. x = 5

Step-by-step explanation:

The value of b from the inequality is 8, 8.1, 9 and 13

An equation is an expression showing the relationship between two or more numbers and variables.

An inequality is used to show that two numbers or variables are non equal to each other.

Dividing an inequality by negative 1, changes the inequality sign.

Given that:

-b ≤ -8

Dividing both sides of the inequality by -1:

-b / -1 ≤ -8/-1

b ≥ 8 (the inequality sign changes)

b = [8, ∞)

The value of b from the inequality is [8, ∞)

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The solution to the linear functions as represented by the table is: D. (-14, -54).

Write the linear equations for each table in the slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.

First table:

Slope (m) = change in y / change in x = 14 - 2 / 3 - 0 = 4

b = 2 (value of y when x is 0)

The equation would be: y = 4x + 2 (equation 1).

Second table:

Slope (m) = change in y / change in x = -3 -(-12) / 3 - 0 = 3

b = -12 (value of y when x is 0)

The equation would be: y = 3x - 12 (equation 2).

Solve both equations, y = 4x + 2 and y = 3x - 12, simultaneously:

To solve the equations y = 4x + 2 and y = 3x - 12 simultaneously, we can set the expressions for y equal to each other and solve for x.

Setting the two equations equal to each other:

4x + 2 = 3x - 12

Next, we can subtract 3x from both sides:

4x - 3x + 2 = 3x - 3x - 12

Simplifying the equation:

x + 2 = -12

x + 2 - 2 = -12 - 2

x = -14

Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the equation y = 4x + 2:

y = 4(-14) + 2

y = -54

Therefore, the solution to the system of linear functions is: (-14, -54).

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Answer:

a. 54.75

b. 2.64

Step-by-step explanation:

The length of line CD is 15 cm.

To calculate the length of line CD, we can use the property of similar triangles.

In triangle ABC, we can see that triangle ABE is similar to triangle ACD.

Using the property of similar triangles, we can set up the following proportion:

AB/AC = BE/CD

Substituting the given values:

12/18 = 10/CD

To solve for CD, we can cross-multiply and solve the resulting equation:

12 × CD = 18 × 10

CD = (18 × 10) / 12

CD = 180 / 12

CD = 15

Therefore, the length of line CD is 15 cm.

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Answer:

d

Step-by-step explanation:

Answer:

7 nights

Step-by-step explanation:

Tamika:          Mark:

20                   30

24                   32

28                   34

32                   36

36                   38

40                   40

44                   42

48  

52  

56  

60  

Answer:

kilometres our parents print events at 30 seconds cat 1 run to distance which a sprinter venture xxxii xxxii xxxii xxxii xxxii

Step-by-step explanation:

to him and his wife i y

The Alternate Exterior Angles Theorem states that when a pair of parallel lines is intersected by a transversal, the pairs of alternate exterior angles formed on opposite sides of the transversal are congruent.

If line AB and line CD are parallel, and line EF intersects both lines at points G and H respectively, then the angles formed on opposite sides of line EF and on the exterior of the parallel lines are congruent.

The Alternate Exterior Angles Theorem states that when a pair of parallel lines is intersected by a transversal, the pairs of alternate exterior angles formed on opposite sides of the transversal are congruent.

In symbols, the theorem can be written as:

∠1 ≅ ∠4

where ∠1 and ∠4 are alternate exterior angles.

This theorem is useful in solving problems involving angles and parallel lines, and it is commonly used in geometry proofs.

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Answer:

- In a 3-D setting, straight line aa can be perpendicular or parallel to straight line cc.

- In a 2-D setting, straight line aa can only be parallel to straight line cc.

- W ustawieniu trójwymiarowym linia prosta aa może być prostopadła lub równoległa do linii prostej cc.

- W ustawieniu 2-D linia prosta aa może być równoległa do linii prostej cc.

Step-by-step explanation:

English Translation

Straight line aa and straight line bb are perpendicular to each other, as well as straight line bb and straight line cc are perpendicular to each other. Choose the correct completion of the sentence. Line aa is perpendicular / parallel to line cc.

Solution

If the frame of reference for the lines is in 3-D, then, it is the straight line aa can also be perpendicular to the straight line cc in the same vein as the x, y and z component lines are usually all perpendicular to one another. Note that straight line aa could also be parallel to straight line cc in a 3-D frame of reference.

But in a 2-D frame of reference, straight line aa can only be parallel to straight line cc. This is because the only directions that straight line bb can be perpendicular to, in a 2-D setting, are all in the same parallel direction.

In Polish/Po polsku

Jeśli układ odniesienia dla linii jest w 3-D, to jest to linia prosta aa może być również prostopadła do linii prostej cc w tej samej żyle, ponieważ linie składowe x, y i z są zwykle wszystkie prostopadłe do jednego inne. Należy zauważyć, że linia prosta aa może być również równoległa do linii prostej cc w trójwymiarowym układzie odniesienia.

Ale w dwuwymiarowym układzie odniesienia linia prosta aa może być tylko równoległa do linii prostej cc. Jest tak, ponieważ jedyne kierunki, w których prosta bb może być prostopadła, w ustawieniu 2-D, wszystkie są w tym samym kierunku równoległym.

Hope this Helps!!!

Mam nadzieję że to pomoże!!!

The probability that the sum is 4 or higher is 11/12.

Probability in mathematics is the possibility of an event in time. In simple words, how many times does that incident is happening in any given time interval.

Given:

You rolled two fair 6 sided dice.

The total number of outcomes = 6 x 6 = 36.

The sample space that does not satisfy the condition,

S = {1 + 1, 1 + 2, 2 + 1}

The possible outcomes = 36 - 3 = 33

The probability that the sum is 4 or higher,

= 33/36

= 11/12

Therefore, 11/12 is the probability.

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The corresponding CDF is:F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6.

The value of the constant A can be obtained by using the normalization condition that the integral of the PDF function over the entire possible range of X must be equal to 1. So, we can write the following integral to solve for

A:(∫f(x) dx) from 0 to π/2=∫A sin(x) dx= A [-cos(x)] evaluated at π/2 and 0= -A(cos(π/2) - cos(0))= A (1 - 0) =1. Therefore, the value of the constant A is 1. b. The CDF of the given random variable X is given as follows:

F(x)=∫f(x)dx from 0 to x, for 0 < x < π/2=∫sin(x) dx from 0 to x= [-cos(x)] evaluated at x and 0= -cos(x) - (-cos(0))= 1 - cos(x) for 0 < x < π/2=1 for x ≥ π/2. So, the corresponding CDF is as follows:

F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X can be obtained using the following formula:

E(X) = ∫xf(x)dx from 0 to π/2=∫x sin(x) dx from 0 to π/2= [-x cos(x)] evaluated at π/2 and 0 - ∫-cos(x) dx from 0 to π/2= -0 + cos(0) - ([-cos(x)] evaluated at π/2 and 0)= 0 + 1 - (-1)= 2. So, the expected value of the given random variable X is 2.

d. The variance of the given random variable X can be obtained using the following formula:

Var(X) = E(X²) - [E(X)]²=∫x² f(x)dx from 0 to π/2 - [E(X)]²=∫x² sin(x)dx from 0 to π/2 - (2)²= [-x² cos(x)] evaluated at π/2 and 0 + ∫2x cos(x)dx from 0 to π/2 - 4= -0 + π²/4 - 4 + (2 sin(x) + 2x cos(x)) evaluated at π/2 and 0= π²/4 - 2 - 4 + 2 + 2π= π²/4 + 2π - 6. So, the variance of the given random variable X is π²/4 + 2π - 6

Hence, the answer is: a. The value of the constant A is 1.b. The corresponding CDF is : F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6

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The range are    {0,300,600,900,1200} in function .

Describe domain and range?

The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x). The collection of numbers that the function assumes is known as its range.

                            The values that the function outputs when we enter an x value are in this set. The range is the set of y -coordinates, which are 0, 1, 2, and 7, 8, 9, 10, respectively, while the domain is the set of x -coordinates.

since for the given table we have unique output for each input.

the given table hour worked versus salary is a function.

Domain - set of input values

          {0,10,20,30,40 }

Range - set of output values

         {0,300,600,900,1200}

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MY WORK:

First, you would cut it up into different parts/shapes

(I cut it up into rectangles)

Then, you would find the area of each.

The bottom rectangle: 10 ( 5 times 2 )

The middle rectangle: 12 ( 6 times 2 )

The top rectangle: 8 ( 4 times 2 )

Lastly, you would add!

10 + 12 + 8 = 30

Therefore, the answer is...

30!

My apologies if this is wrong but I hope I helped a little bit!

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Considering the data:

Dilation by a scale factor of 4 from the origin in the form of an A'B'C' reflection over x = 1

<=> The two triangles are comparable to one another since triangles can have the same shape but differ in size, so A′′B′′C′′ is 4 times larger than ABC.

=> the connection between "ABC" and "A"B"C" .

\(\frac{AB}{A"B"} = \frac{1}{4}\)

We settle on C.

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

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Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 \(\(\int_{0}^{\pi /3}\) ½ (4 cos (θ)² − ½ (2)² dθ

  =  \(\(\int_{0}^{\pi /3}\) 16 cos2 (θ) − 4dθ

  = \(\(\int_{0}^{\pi /3}\) 8 (1+cos(2θ)) − 4dθ

  =\(\(\int_{0}^{\pi /3}\) 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] \(\(\int_{0}^{\pi /3}\)

  = 4π/3 + 2√3

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Answer:

Step-by-step explanation:

Follow (PEMDAS) order of operations

\(3-5+3\left(2-1\right)+4\div \:2\\\\3-5+3\cdot \:1+4\div \:2\\\\3-5+3+4\div \:2\\\\3-5+3+2\\\\3\)

~

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

-14+8q

Step-by-step explanation:

Open the prentheses by using distributive property.

\(( - 7 + 4q)2 \\ - 14 + 8q\)

The equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16x - 8y + 8z = 32

We know that the equation of plane passing through point (x₁, y₁, z₁) is given by,

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0

where, A, B, and C are direction ratios

In the question,  the plane passes through point (0, -3,1)

Let (x₁, y₁, z₁)  = (0, -3,1)

Using above formula the equation of the plane will be in the form,

A(x -0) + B(y - (-3))+C(z - 1) = 0            

Ax + B(y + 3)+C(z - 1) = 0                   ..........(1)

The required plane is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.

So, their normal to the required plane would be perpendicular to the normal of both the planes.

The normal to the required plane is a cross-product of the normals of planes.

A cross-product of the normals of planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16i - 8j + 8k

So, the direction ratios,

A = 16, B = -8, C = 8

So equation (1) becomes,

16x - 8(y + 3) + 8(z - 1) = 0  

16x - 8y - 24 + 8z - 8 = 0

16x - 8y + 8z - 32 = 0 is the required equation of the plane

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To bisect a segment, Jessica should place the compass on one endpoint, open it to a width larger than half of the segment, draw two intersecting arcs with the compass, and draw a straight line through the intersection points to bisect the segment.

To bisect a segment, Jessica should first place the compass on one endpoint of the segment and open it to a width larger than half of the segment. She should then draw an arc that intersects the segment at two points. Next, she should place the compass on the other endpoint of the segment and draw a similar arc that intersects the first arc she drew.

Finally, she should draw a straight line through the two points where the arcs intersect to bisect the segment into two equal parts. This method is based on the concept of congruent triangles, as the two arcs create two congruent triangles with the segment as their base.

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Answer:

-7/8

Step-by-step explanation:

If two lines are parallel, they have the same slope. The slope of p is -7/8 (y=mx+b), so the slope of q is also -7/8.

Problem 1

Explanation:

Use the difference of squares rule here.

That rule says (a-b)(a+b) = a^2-b^2

In this case, a = x and b = 2.

===========================================================

Problem 2

Work Shown:

(2x+5)(x+1)

y(x+1) ..... let y = 2x+5

xy+y

x(y) + 1(y)

x(2x+5) + 1(2x+5) ... plug in y = 2x+5

2x^2+5x+2x+5

2x^2+7x+5

===========================================================

Problem 3

Explanation:

The standard form of a quadratic is ax^2+bx+c, where a,b,c are real numbers. In the case of choice A, we have a = -1, b = -5, c = 7.

===========================================================

Problem 4

Explanation:

Along the top we have three green rectangles. If each of them are of length x, then we have x+x+x = 3x so far. Then adding on a yellow piece of 1 unit leads to 3x+1 as the total horizontal width across the top.

Similarly, along the left side we have 1 green portion and 2 yellow leading to x+2. So this shows why this diagram represents (3x+1)(x+2)

A rectangle must be formed with the smaller pieces glued together. We cannot have any gaps or overlaps. The reason we're aiming for a rectangle is because the area of a rectangle is length*width. Think of (3x+1) as the length and (x+2) as the width.

Answer:

right angle

Step-by-step explanation: