1) How does math of any kind affect your life on a daily basis? Please explain

2) How comfortable do you feel working with math skills, such as adding and subtracting up to finding sales tax or interest?

The solution is : equation for the perpendicular bisector of the line segment is:  7x -2y = 6

Here, we have,

The perpendicular bisector has a slope that is the opposite of the reciprocal of the slope of the segment between the two points. It must go through the midpoint of the segment.

The latter can be found by averaging the coordinates of the end points:

 ((-5, 6) +(9, 2))/2 = ((-5+9)/2, (6+2)/2) = (2, 4)

The difference in endpoint coordinates is ...

 (Δx, Δy) = (9-(-5), 2-6) = (14, -4)

For our purpose, we're only interested in the ratio of these values, so we can divide both by the common factor of 2:

 (Δx, Δy) = (7, -2)

A line perpendicular to this segment through the point (h, k) can be written as ...

 Δx·x +Δy·y = Δx·h +Δy·k

 7x -2y = 7(2) -2(4)

 7x -2y = 6 . . . . . . . standard form equation for the perpendicular bisector

Hence, The solution is : equation for the perpendicular bisector of the line segment is:  7x -2y = 6

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The given point (8, -15) is located in the third quadrant of the coordinate plane.

In this quadrant, the x-coordinate is negative and the y-coordinate is also negative.

Let us consider some common functions to determine which of them are positive in the third quadrant:

A linear function is of the form f(x) = mx + b,

where m is the slope and b is the y-intercept. In the third quadrant, both the slope and y-intercept are negative.

Therefore, if m > 0, then f(x) is negative for all x-values in the third quadrant.

If m < 0, then f(x) is positive for all x-values in the third quadrant.

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As we have proved that if p ≡ 1 (mod 4), then -r is also a primitive root of p.

Since r is a primitive root of p, we know that every non-zero integer modulo p can be written as a power of r. That is, for any integer a with gcd(a, p) = 1, there exists an integer k such that a ≡ rˣ (mod p). This follows from the fact that the order of the element r modulo p is φ(p) = p-1, where φ denotes the Euler totient function.

Now, let us consider the case where p ≡ 1 (mod 4). This means that there exists an integer x such that p = 4x + 1. We want to show that -r is also a primitive root of p.

To do this, we first observe that (-1)² ≡ 1 (mod p) since p is an odd prime. Therefore, (-1)^(4x) ≡ 1 (mod p), which implies that (-1)²ˣ ≡ 1 (mod p).

Now, if we can show that (-1)ˣ = -1, then we will have (-1)²ˣ = (-1)ˣ*(-1)ˣ = (-1)*(-1) = 1 (mod p), which will allow us to prove that -r is also a primitive root of p.

To see that (-1)ˣ = -1, we use the fact that p ≡ 1 (mod 4) and the properties of quadratic residues. Specifically, we know that -1 is a quadratic non-residue modulo p, since if -1 ≡ a² (mod p) for some integer a, then we would have

=> [tex](-1)^{((p-1)/2) }[/tex] ≡ [tex]a^{(p-1) }[/tex]≡ 1 (mod p),

which contradicts the fact that

=> [tex](-1)^{((p-1)/2) }[/tex]= -1.

Therefore, there exists an integer b such that b² ≡ -1 (mod p).

Now, consider the product brˣ. We claim that brˣ is a primitive root of p. To see this, note that for any integer a with gcd(a, p) = 1, we can write a ≡ rˣ (mod p) for some integer k. Then, we have:

(a*brˣ)² = a² * b² * r²ˣ ≡ r²ˣ * (-1) ≡ -r²ˣ (mod p)

Since r is a primitive root of p, we know that rˣ and r²ˣ cover all the non-zero residue classes modulo p. Therefore, we can choose k such that r²ˣ ≡ -1 (mod p), which implies that (a*brˣ)² ≡ -1 (mod p).

Since a was arbitrary, this shows that brˣ is a quadratic non-residue modulo p, and therefore a primitive root of p.

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The table that correctly represents the ratio is

Students           Adults

5                         2

15                       6

25                      10

(option d).

Ratios are a way of comparing two quantities by expressing their relationship in a simplified form. They are commonly used in various real-life situations, such as determining the student to adult ratio on a field trip. In this case, the ratio of students to adults is given as 5 to 2, which means that for every 5 students, there are 2 adults present on the trip.

To represent this ratio in a table, we need to choose values that are in the same proportion as the given ratio. For example, if we have 10 students, we need to have 4 adults (since 5 to 2 is equivalent to 10 to 4). Similarly, if we have 15 students, we need to have 6 adults.

Looking at the given tables, we can see that only option D correctly represents the ratio of 5 to 2. In this table, for every 5 students, there are 2 adults, and the other values in the table are also in the same proportion as the ratio.

Therefore, option D is the correct table that represents the ratio of students to adults on the field trip.

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I think it is C.

C. 2 tons = 64, 000 ounces

Answer:

line RQ

Step-by-step explanation:

The points on a line can be flipped when naming. For example, line AB is the same as line BA.

As we have shown that matrix multiplication is associative.

Let us start by computing the products (AB) and (BC) separately. To multiply matrix A by matrix B, we need to take the dot product of each row of A with each column of B.

Simplifying the above expression, we get:

A*B = [11 -10 39] *  [21 28 13]

Similarly, to multiply matrix B by matrix C, we need to take the dot product of each row of B with each column of C. Thus, the resulting matrix (B*C) will have the same number of rows as B and the same number of columns as C. Using the given matrices B and C, we have:

B*C = [1 -2 5] * [1    -2      10]

Simplifying the above expression, we get:

B*C = [39 18]

Thus, the resulting matrix (A(BC)) will have the same number of rows as A and the same number of columns as (BC). Using the given matrices A, B, and C, we have:

A*(B*C) = [7 1] * [39  18]

Simplifying the above expression, we get:

A*(B*C) = [327 489]

Now, let us compute the product ((AB)C) by multiplying the matrix (AB) with matrix C. To do this, we need to take the dot product of each row of (AB) with the only column of C. Thus, the resulting matrix ((A*B)C) will have the same number of rows as (AB) and the same number of columns as C. Using the given matrices A, B, and C, we have:

(A*B)*C = [11 -10 39] * [1      -2       10]

Simplifying the above expression, we get:

(A*B)*C = [327     489]

As we can see from the above calculations, both the products (A*(BC)) and ((AB)*C) have the same result, which is [327 489]. Therefore, we can conclude that matrix multiplication is associative.

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The volume of the hexagonal pyramid is 508.93 cubic inches.

The formula for the volume of a pyramid is:

Volume = (1/3) x base area x height

In this case, we are given that the base of the pyramid is a regular hexagon with an area of 92 square inches, and the height is 6 inches.

To find the volume of the pyramid, we need to first find the area of one of the triangles that make up the hexagonal base. Each of the six triangles in the base is an equilateral triangle, so we can use the formula for the area of an equilateral triangle to find the area of one of the triangles:

Area of an equilateral triangle = ([tex]\sqrt{3}[/tex]/4) x [tex](side)^{2}[/tex]

Since the base of the pyramid is a regular hexagon, all six sides are equal. Let's call the length of one side "s". Then we have:

Area of one triangle = ([tex]\sqrt{3}[/tex]/4) x [tex]s^{2}[/tex]

To find the total area of the hexagonal base, we can multiply the area of one triangle by the number of triangles in the base:

Area of hexagonal base = 6 x([tex]\sqrt{3}[/tex]/4) x [tex]s^{2}[/tex]

We are given that the area of the hexagonal base is 92 square inches, so we can solve for "s":

6 x ([tex]\sqrt{3}[/tex]/4) x [tex]s^{2}[/tex] = 92

([tex]\sqrt{3}[/tex]/4) x [tex]s^{2}[/tex] = 92/6

[tex]\sqrt{3}[/tex]  x [tex]s^{2}[/tex] = 46

[tex]s^{2}[/tex]  = 46/[tex]\sqrt{3}[/tex]  

s ≈ 6.21 inches

Now that we know the length of one side of the hexagonal base, we can find the area of the base by using the formula for the area of a regular hexagon:

Area of hexagonal base = (3[tex]\sqrt{3}[/tex]  /2) x  [tex]s^{2}[/tex]  

Area of hexagonal base ≈ 254.47 square inches

Finally, we can use the formula for the volume of a pyramid to find the volume of the hexagonal pyramid:

Volume = (1/3) x base area x height

Volume = (1/3) x 254.47 x 6

Volume ≈ 508.93 cubic inches

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The inequality that can be used to find the number of sales she needs to make is D. 100 + 15x ≥ 500.

In this scenario, Aaliyah wants to earn at least $500. The fixed amount she earns is $100, and she earns $15 for each sale.

Therefore, the total amount she earns can be represented as 100 + 15x, where x is the number of sales she makes. To ensure that she earns at least $500, we can set up the inequality 100 + 15 x ≥ 500.

With this inequality, we can see that the sum of the $ 100 base salary and the $ 15 per sale would add up to a sum that is either $ 500 or above.

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The type of graph would have the title, "Monthly Company Profit for the Year?" is line graph (option a).

Using a line graph to display monthly company profits allows for the visualization of the overall trend and any fluctuations or changes in the profits over the year. It also allows for easy comparison of the profits from one month to another, as well as identifying which months were particularly profitable or unprofitable.

In mathematical terms, a line graph can be defined as a graph in which the data points are plotted as individual points, and a line is drawn to connect the points.

The line represents a mathematical function that can be used to model the relationship between the variables being plotted. In the case of the monthly company profits, the function would model the relationship between time and profit.

Hence the correct option (a).

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Answer:

Step-by-step explanation:

Quadratics Practice (Up to Quiz 8-1) Flashcards

its on quizlet<3

The value of x is 18.9( 1 decimal place).

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

The inverse of sin , cos and tan are cosec, sec and cot respectively.

Here, opposite side to the angle is x and the adjascent is 17, therefore to calculate the value of x, we use tan function.

tan 48 = x/17

x = tan48 × 17

x = 1.111 × 17

x = 18.9( 1 d.p)

therefore the value of x is 18.9

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The experimental probability of the next balloon sold being green is 4/15.

Probability is a crucial concept in the field of mathematics that is used to measure the likelihood of an event happening.

According to the information given, the number of green balloons sold is 20, and the total number of balloons sold is the sum of all the colors, which is:

20 + 17 + 12 + 19 + 7 = 75

Now we can use these numbers to calculate the experimental probability of a green balloon being sold:

Experimental probability of a green balloon being sold = Number of green balloons sold / Total number of balloons sold

Experimental probability of a green balloon being sold = 20 / 75

Experimental probability of a green balloon being sold = 4/15

This means that if we randomly select a balloon from the store, the likelihood of it being green is 4 out of 15 or approximately 0.27 or 27%.

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Answer:

4/15

Step-by-step explanation:

Answer:

0.75

Step-by-step explanation:

P(A) = 9+9 = 18

P(B) = 9+9 = 18

P(A and B) = 9

P ( A or B) = 18+18-9 = 27

Probability = ans / total = 27/36 = 0.75

The probability that either event will occur is given as follows:

P(A or B) = 0.75.

We have,

The figure about the possible outcomes are shown in image.

Now, The formula used to calculate the probability is given as follows:

P(A or B) = P(A) + P(B) - P(A and B).

The total number of events from the Venn's diagram is given as follows:

4 x 9 = 36.

Hence the probability of each outcome is given as follows:

P(A) = (9 + 9)/36 = 0.5.

P(B) = (9 + 9)/36 = 0.5.

P(A and B) = 9/36 = 0.25.

Hence the or probability is given as follows:

P(A or B) = P(A) + P(B) - P(A and B).

P(A or B) = 0.5 + 0.5 - 0.25

P(A or B) = 0.75.

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The expression factoring out the greatest common factor is  (3pf - 21p²)(f + 2).

We have the expression as

3pf² - 21p²f + 6pf - 42p²

Now, factorising the expression as

= 3pf² + 6pf - 21p²f - 42p²

= 3pf(f +2) - 21p²(f + 2)

= (3pf - 21p²)(f +2)

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The volume of the solid is 94.375 ft³.

We have,

From the figure,

We can have three rectangles.

So,

Rectangle A area.

= 2 x 6

= 12 ft²

Rectangle B area.

= (9 - 2 - 3) x (6 - 2(1/2))

= (4 x 12 - 2.5)

= (48 - 2.5)

= 45.5 ft²

Rectangle C area.

= 3 x 6

= 18 ft²

Now,

Adding the area of the rectangles.

= 12 + 45.5 + 18

= 75.5 ft²

This is our base area.

Now,

The volume of the solid.

= 75.5 ft² x 1(1/4) ft

= 94.375 ft³

Thus,

The volume of the solid is 94.375 ft³.

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The desired outcomes use in finding the probability of blue pens is 7.

Given that a bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato wants to pull a blue pen from the bag.

We need to find desired outcomes for him to use in finding the probability of blue pens,

We know that the desired outcomes or the favorable outcomes are the same thing which is the number of the element of whose probability is to be find,

Here we are to find the probability of getting a blue pen and the number of blues pen is 7.

Hence the desired outcomes use in finding the probability of blue pens is 7.

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Answer:

22 m^2

Step-by-step explanation:

multiply the sides

Answer:

The volume is 200.7 cm^3

Step-by-step explanation:

The volume of a cylinder is:

Vol = pi•r^2•h

The radius and height were given, so fill them in.

V = pi • (4.4)^2 • 3.3

V = 200.710071

This is the answer you get if you use the pi key on the calculator.

Round to the nearest tenth.

V = 200.7

The volume is 200.7cm^3.

***(If your teacher/class/text/program says to use 3.14 for pi, the answer will come out as 200.6)

The value of the index form is x¹³/11

Index forms are simply described as mathematical forms or expressions that are used to represent numbers or variables that are too large or too small to be written conveniently.

Some rules of index forms are;

From the information given, we have that;

x⁹/11 × x⁴/11

Since they are of the same bases, add the exponent values

x¹³/11

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The equation of the line which passes through the points (-4,-5) and (6,4) is [tex]y = \frac{9}{10}x - \frac{7}{5}[/tex].

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

The line passes through the points (-4,-5) and (6,4).

First, detremine the slope of the line using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 4 - (-5) ) / ( 6 - (-4) )

m = ( 4 + 5 ) / ( 6 + 4 )

m = ( 9 ) / ( 10 )

m = 9/10

Next, using the point-slope form, plug in one of the given points and slope m = 9/10 to find the equation of the line.

Using the point (-4,-5):

y - y₁ = m(x - x₁)

[tex]y - (-5) = \frac{9}{10}( x - (-4))\\ \\ y + 5 = \frac{9}{10}( x + 4)\\\\ y + 5 = \frac{9}{10}x + \frac{18}{5}\\\\ y = \frac{9}{10}x + \frac{18}{5} - 5\\ \\ y = \frac{9}{10}x - \frac{7}{5}[/tex]

Therefore, the equation of line is [tex]y = \frac{9}{10}x - \frac{7}{5}[/tex].

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There are 10 pentagons to form close ring.

In the pentagon

The number of sides = 5

Let interior angles of pentagon = q degree

Therefore,

p = (5-2)x180/5 = 108

q = 360 -2p = 360- 2x108 = 144

Now, q = (n-2)x180/n

 ⇒ 144 = (n-2)x180/n

 ⇒  -36n = -360

 ⇒ n = 10

Hence, n = 10

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The a whole number or in simplest form is 2.2.

We are given that;

Right rectangle length=33 and height=11, left triangle length=11 height=5

Now,

The length of the right rectangle is 33 and the length of the left rectangle is 11. To find the scale factor, we divide the length of the right rectangle by the length of the left rectangle:

33 / 11 = 3

This means that the right rectangle is 3 times as long as the left rectangle. The scale factor is 3.

We can check our answer by comparing the heights:

The height of the right rectangle is 11 and the height of the left rectangle is 5. To find the scale factor, we divide the height of the right rectangle by the height of the left rectangle:

11 / 5 = 2.2

Therefore, by fraction the answer will be 2.2.

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Based on the information, the regular polygon has 35 sides.

In order to determine the number of sides that a regular polygon has if the sum of the interior angles is given, you can use the formula:

sum of interior angles = (n - 2) x 180°

solve for n, you can rearrange the formula as:

n = (sum of interior angles ÷ 180°) + 2

Then, plug in the given sum of interior angles and solve for n.

b. Using the formula above, we can find the number of sides of the regular polygon with a sum of interior angles of 6,300°:

n = (6300° ÷ 180°) + 2

n = 35

The regular polygon has 35 sides.

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The solution is : the value of y is 7.

Here, we have,

The perimeter of a rectangle is found by

P = 2 (l+w)

P = 2( 3y+3+2y)

Combine like terms

P = 2(5y+3)

We know the perimeter is 76

76 = 2(5y+3)

Divide each side by 2

76/2 = 2/2(5y+3)

38 = 5y+3

Subtract 3 from each side

38-3 = 5y+3-3

35 = 5y

Divide each side by 5

35/5 = 5y/5

7 =y

We want the length of AD = BC = 2y

AD = 2y=2*y = 14

Hence, The solution is : the value of y is 7.

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The required surface area of the given rectangular prism is 202 square yd.

Here, we have,

Given that,

the surface area of a rectangular prism with a base length of 9 yd, a base width of 5 yd, and a height of 4 yd is to be determined.

We have,

Surface area is defined as the measure of a region or surface is called as surface area.

Here,

The surface area of the rectangular prism is given as,

S = 2(lw + lh + wh)

S = 2 [9×5 + 5×4 + 4×9]

S = 202 square yd.

Thus, the required surface area of the given rectangular prism is 202 square yd.

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The following statements are true:

Line AB and line CG are parallel.

Line CG and line RS are perpendicular.

Line segment CG lies in plane X.

Given information:

Planes X and Y intersect at a right angle.

Lies in plane X and do not intersect.

A) Line AB and Line CG are parallel: As both lines, AB and CG lie in plane X.

Thus, both are parallel and options A is the correct option.

B) Line AB and Line RS are parallel: As the line, AB lies in the plane X and the line RS lies in the plane Y.

Thus both are perpendicular and not parallel. Option B is the incorrect option.

C) Line CG and Line RS are perpendiculars: As the line CG lies in the plane x and the line RS lies in the plane Y.

Thus both are perpendicular. Option C is the correct option.

D) Line AB and Line RS must intersect: line RS passes from the middle of the plane Y and line AB passes from the left of the plane X centre.

Thus they do not intersect each other. Option D is the incorrect option.

E) Line segment CG lies in plane X: As shown in the diagram, line CG lies in plane X. Thus option E is the correct option.

F) Line segment RS lies in plane X: As shown in the diagram, and the line lies RS in plane Y. Thus option F is the incorrect option.

Hence, the following statements are true:

Line AB and line CG are parallel.

Line CG and line RS are perpendicular.

Line segment CG lies in plane X.

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The complete question is =

Planes X and Y intersect at a right angle. Line A B and Line C G lie in plane X and do not intersect. Line R S lies in plane Y.

Vertical plane x intersects horizontal plane y. Line R S is horizontal on plane y. Lines A B and C G are vertical and beside each other on plane x. A right angle is indicated between the lines on the y plane and x plane. Lines A B and D G are parallel.

Which statements are true? Select three options.

Line A B and Line C G are parallel.

Line A B and Line R S are parallel.

Line C G and Line R S are perpendicular.

Line A B and Line R S must intersect.

Line segment C G lies in plane X.

Line segment R S lies in plane X.

David is studying Giraffe.

The correct option is (d)

Here, The table of the given information is:

Animal                      speed               Type                Habitat

Elephant                   25 mph            Mammal           Grassland

Sailfish                      68 mph            Fish                   Oceans

Giraffe                       32 mph            Mammal           Grassland

Dolphin                     30 mph            Mammal           Oceans

And, The options are given :

David is studying a mammal, but Ping is not.

Therefore, Ping is studying Sailfish.

The animal that Mandy is studying can be found in the ocean.

Therefore, Mandy is studying Dolphin.

The animal that Alan is studying is slower than the animal that David is studying,

Therefore, Alan is studying Elephant which is slower than Giraffe.

Finally David is studying Giraffe.

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