For part a), sketch the figures on your own paper. Then, answer part b) below.
8
Figure 1
a. On your paper, sketch Figures 4 and 5.
b. How does the pattern grow? Explain how you know.
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Figure 2
insert into paragraph
Figure 3

Answer:

25.6

Step-by-step explanation:

x=(20)tan52

x=25.6(correct to nearest tenth)

Answer:

Function 1

Step-by-step explanation:

I got it correct on khan academy

The function defined on the graph by the equation y = (-1/4)r -5 and line p has slope which is represented by option C. The functions have same slope.

Let the two coordinate on the line p of the function 2 on the graph.

( x₁ , y₁ ) = (-4, -6)

(x₂ , y₂ ) = ( 4 ,-8 )

Slope of the line = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value in the formula we get,

Slope of line p = ( -8 + 6 ) / ( 4 + 4 )

                         = -2/8

                        = -1/4

Slope of the function 1

y = -(1/4)r -5

When r = 8 ⇒ y = -7

r = -8 ⇒ y = -3

( x₁ , y₁ ) = (8, -7)

(x₂ , y₂ ) = ( -8 ,-3 )

Slope of the function 1  = ( -3 + 7 ) / ( -8  - 8 )

                         = 4/ -16

                        = -1/4

Therefore, slope of the both the function 1 and function 2 represented by line p are given by option C. the functions have same slope.

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Answer:

48

Step-by-step explanation:

The given parameters are;

The activities in which the students of the school participate = 1) Debate, 2) Music, and 3) Community services

The number of students that do all three activities = 3

The number of students that do two or more activities = 21

The number of the students that participate in music = Half of the students

The ratio of the students that take part in debate, music, and community service = 5 : 4 : 3

Let x represent a common number factor of participants in each of the given three activities, we have;

5·x participate in debate, A

4·x participate in music, B

3·x participate in community service, C

We get;

The sum of the students in the school = A∪B∪C = A + B + C - A∩B - A∩C - B∩C + A∩B∩C

Given that the number of students that do two or ore activities = 21, we have;

(A∩B)∪(A∩C)∪(B∩C) = 21

However, we have;

(A∩B)∪(A∩C)∪(B∩C) = (A∩B) + (A∩C) + (B∩C) - A∩B∩C - B∩A∩C - C∩B∩A + A∩B∩C

∴ 21 = (A∩B) + (A∩C) + (B∩C) - 3 - 3 - 3 + 3

(A∩B) + (A∩C) + (B∩C) = 21 + 3 + 3 + 3 - 3 = 21 + 6 = 27

∴ -(A∩B) - (A∩C) - (B∩C) = -27

Therefore;

A + B + C - A∩B - A∩C - B∩C + A∩B∩C = 5·x + 4·x + 3·x - 27 + 3

5·x + 4·x + 3·x - 27 + 3 = 12·x - 24

The total number of students = A∪B∪C = 12·x - 24

The number of students participating in music, B = 4·x = Half the total number of students = (12·x - 24)/2

∴ 4·x = (12·x - 24)/2

8·x = 12·x - 24

12·x - 8·x = 24

4·x = 24

x = 24/4 = 6

The total number of students at the school = 12·x - 24 = 12 × 6 - 24 = 48

Answer:

x = 2.6

Step-by-step explanation:

–4.8(6.3x – 4.18) = –58.56

-30.24x + 20.064 = -58.56

-30.24x = -78.624

x = 2.6

So, x = 2.6 is the answer.

Answer:

2n-3

Step-by-step explanation:

three less so -3

Julie runs three less than 2 times what Hannah ran

Hannah ran n miles

so Julie ran three less than 2n

Answer:

Deck | 60 zed

wheels | 14 zed

trucks. | 16+16 32 zed

Hardware | 10 zed

total. | 116 zed

remaining 4 zed

Step-by-step explanation:

hope this helps

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\({{ \Large{ \blue{ \rm{{⇛}}}}}} \rm \Large \: \: (2x + 9) \: (3x - 5)\)

\({{ \Large{ \blue{ \rm{{⇛}}}}}} \rm \Large \: \:2x \: (3x - 5) \: + \: 9 \: (3x - 5)\)

\({{ \Large{ \blue{ \rm{{⇛}}}}}} \rm \Large \: \: {6x}^{2} \: - \: {10x} \: + \: 27x \: - \: 35\)

\({{ \Large{ \blue{ \rm{{⇛}}}}}} \rm \Large \: \: {6x}^{2} \: + \: 17x \: - \:35\)

Answer: 0.47 is equal to 47/100

Step-by-step explanation:

1.00=100 Is like pennies, if you have a hundred of them you have 1 dollar but since there’s only 47 it’s out of a hundred

Answer:

0.47 as a fraction equals 47/100

Step-by-step explanation:

Write 0.47 as  

Multiply both the numerator and denominator by 10 for each digit after the decimal point.

\(\frac{0.47}{1}\) = \(\frac{0.47 x 100 } {1x100}\) = \(\frac{47}{100}\)

So, 0.47 as a fraction  in simpliest form equals 47/100

Answer:

There is no error, Amad is correct.

Step-by-step explanation:

Khan Academy Checked.

Amad had done no error. His conclusion is true.

Two triangles are said to be congruent if their sides are equal in length, the angles are of equal measure, and they can be superimposed on each other.

For example,

In the figure given above, Δ ABC and Δ PQR are congruent triangles. This means that the corresponding angles and corresponding sides in both the triangles are equal.

Sides: AB = PQ, BC = QR and AC = PR;

Angles: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.

Therefore, Δ ABC ≅ Δ PQR

The following are the congruence theorems or the triangle congruence criteria that help to prove the congruence of triangles.

As, from the given cases the prediction of congruency of two triangles is correct. There is no error he made.

Hence, Amad had not made any error.

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4/a) The equation of the line through D and C is simply x = 2.5, which represents a vertical line passing through the midpoint of AB.

4/b) The equation of the line through B and C is y = -2.4x + 1.

5) the equation of the perpendicular bisector of PQ is: y = 2x

4/a) We know that the line passing between A and C is vertical since they share the same x-coordinate of 0. In order to find the equation of the line passing between points D and C, one must first determine the value of x at point D and then use that value to formulate the equation of the line.

We can determine the x-coordinates of D and B by solving the equation of the line through A and B for x when y = 6, since ABCD is a rectangle and we know that AD is parallel to BC and has the same length as B.

6 = 2x + 1

5 = 2x

x = 2.5

Therefore, In order to illustrate a vertical line travelling through the centre of AB, the equation for the line via D and C is simply x = 2.5.

4/b) The line through B and C can be found by determining its slope and y-intercept using the coordinates of B and C.

The slope of the line can be found by taking the difference in y-coordinates divided by the difference in x-coordinates:

Slope \(= \frac{(Y_C - Y_B)}{(X_C - X_B)} = \frac{(6 - 1)}{(0 - 2.5)} = -2.4\)

To find the y-intercept, we can use the point-slope form of the equation for a line:

\(Y - Y_B\) = slope * \((X - X_B)\)

Using point B and the slope we just found, we get:

y - 1 = -2.4 * (x - 0)

y - 1 = -2.4x

y = -2.4x + 1

Therefore, the equation of the line through B and C is y = -2.4x + 1.

5) To find the equation of the perpendicular bisector of PQ, we first need to find the midpoint of PQ. The midpoint M is given by:

\(M = (\frac{(X_P + X_Q)}{2}, \frac{(Y_P + Y_Q)}{2})\)

\(= (\frac{(2 + (-2))}{2}, \frac{(1 + (-1))}{2})\)

= (0, 0)

So the midpoint of PQ is the origin (0, 0).

The slope of the line PQ can be found using the two points P and Q:

Slope of PQ  \(= \frac{(Y_Q - Y_P)}{(X_Q - X_P)}\)

\(= \frac{(-1 - 1)}{(-2 - 2)}\)

= 1/2

The perpendicular bisector of PQ will have a slope that is the negative reciprocal of the slope of PQ. Therefore, the slope of the perpendicular bisector is:

slope(perp) = -1 / slope(PQ)

= -1 / (1/2)

= -2

So the equation of the perpendicular bisector of PQ will be of the form y = mx + b, where m is the slope and b is the y-intercept. We already know that the slope is 2 and that the midpoint of PQ lies on the line, so we can use this information to find the y-intercept:

0 = (-2)*(0) + b

b = 0

Therefore, the equation of the perpendicular bisector of PQ is: y = 2x

Which represents a line passing through the origin and having a slope of 2.

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9514 1404 393

Answer:

  {58, 59, 60} kg

Step-by-step explanation:

Let x represent the mass of the heavier cow. Then the mass of the lighter cow is 96 -x.

The inequalities regarding the relative masses are ...

  x ≥ 96-x +20 . . . . . the heavy cow is at least 20 kg heavier

  96 -x > 35 . . . . . . . the lighter cow is more than 35 kg

__

Adding x to the first inequality makes it ...

  2x ≥ 116

  x ≥ 58

Adding x-35 to the second inequality makes it ...

  61 > x

So the mass of the heavier cow must be in the range ...

  58 ≤ x < 61

Possible whole-number masses for the heavier cow are ...

  58 kg, 59 kg, 60 kg

               - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\(\diamond\large\textsf{\textbf{Question:-}}}}\)

-7n-15≤21. find n

\(\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\)

 ❖ Add 15 to both sides:-

      -7n≤21+15

        -7n≤36

❖ Now divide by -7 on both sides:-

               n≥-5.14 or

                n≥-5

The inequality sign changed because we divided both sides by a negative number.

        - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - -

Answer:

35 / 9.99 = can buy 4 rounded

paragraph: To find how many pairs of shorts we can buy, we must divide our total money with the cost. We are diving because we need to find how many times 35 can go into 9.99 to find our number. 35 / 9.99 = 3.5035035035035. Our answer must be rounded now because shorts are in whole numbers and can't be in decimals. Take the tenth place of the decimal and round it to the nearest number. 5 is closer to 10 than 0 so we just round it to 4 and there is our answer.

Answer:

E. X= 5+ (gcf)37/6

F. x= 5 - (gcf)37/6

Step-by-step explanation:

put in calculator MOD 5 3

write the values: -

                             a= 3    b= -5    c= -1

Answer:

x = 69

Step-by-step explanation:

since AB is parallel to CD we can find the value of y with the following equation :

2y - 40 = 66 add 40 to both sides

2y = 110 divide both sides by 2

y = 55

from supplementary angles, we know that the exterior angle's measure is 124

since the sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle

y + x = 124 we found value of y earlier

55 + x = 124 subtract 55 from both sides

x = 69

Answer:

10 units

Step-by-step explanation:

this is right answer

The equation of the line in slope-intercept form is y = (1/√3)x + 2.

Let's start by drawing a diagram. We have a line with a slope of 1/2 passing through the point (0,2). We can find another point on the line by moving 2 units up and 1 unit to the right (since the slope is 1/2).

This gives us the point (1,3). We can now draw a right triangle with the line, the y-axis, and the segment connecting (0,2) and (1,3) as the legs, and the segment connecting (0,0) and (1,0) as the hypotenuse.

Since the line has a slope of 1/2, the angle between the line and the y-axis is 30 degrees. This means that the angle between the line and the hypotenuse is also 30 degrees.

We can now use similar triangles to find the equation of the line. The two small triangles in our diagram are similar, so we can set up the following proportion:

y-2 / x = 1/ tan(30)

Simplifying this equation, we get:

y-2 = (1/√3)x

Adding 2 to both sides, we get:

y = (1/√3)x + 2

This is the equation of the line in slope-intercept form.

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Answer:

The answer is B.

Step-by-step explanation:

You have to use area of trapezoid formula, A = 1/2×(a+b)×h where a, b are the side lengths and h is height :

\(area = \frac{1}{2} \times (a + b) \times h\)

\(let \: a = 6,b = 16,h = 5\)

\(area = \frac{1}{2} \times (6 + 16) \times 5\)

\(area = \frac{1}{2} \times 22 \times 5\)

\(area = 11 \times 5\)

\(area = 55 \: {cm}^{2} \)

Answer:

Solving steps:

Question:5 boys and 4 girls are randomly arranged to sit in a row. find the probability that all girls sit together.

Find:the probability that all girls sit together.

Solution: 5 boys and 4 girls, 9 kids in all, can be seated in a row in 9! ways. In order to find the number of ways, where the 4 girls are seated together, we place them in an imaginary group Z, so that they are not separated in the seating arrangements. Now we have 6 entities, namely 5 boys and one group of girls, and the number of ways of their seating is 6!. For each of these 6! ways, the 4 girls can be seated within the group Z in 4! ways. So the number of ways in which the 4 girls are seated together, is 6!/4!.

So the probability, as requested, is (6!4!)/9! = 24/(7x8x9) = 1/21

Answer:

$11.75

Step-by-step explanation:

In order to solve this problem, you divide $47.00/4. When you do that, you get $11.75

The polynomial f(x) of degree 4 can have at most 3 turning points.

The number of turning points in a polynomial function is determined by its degree. The degree of a polynomial represents the highest power of x in the polynomial expression.

In this case, the degree of f(x) is 4, which means the highest power of x is \(x^4\).

A turning point is a point on the graph of a function where the function changes from increasing to decreasing or from decreasing to increasing. It corresponds to a change in the concavity of the function.

For a polynomial of degree n, the maximum number of turning points is n-1.

Therefore, for a polynomial of degree 4, the maximum number of turning points is 4-1=3.

It is important to note that this is the maximum number of turning points, and the actual number of turning points can be less depending on the specific coefficients and factors of the polynomial.

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Answer:

x=12

Step-by-step explanation:

25°+114°+(5x-19)°=180°

139°+(5x-19)=180°

5x-19=180-139

5x-19=41

5x=41+19

5x=60

x=60/5

x=12

Answer:

p=19

Step-by-step explanation:

since the instructions say that (\(x^{13}\))(\(x^{6}\)) is equivalent to \(x^{p}\), we can make the equation:

(\(x^{13}\))(\(x^{6}\))=\(x^{p}\)

now, apply the laws of exponents; \(a^{m} * a^{n} =a^{m+n}\)

in that case, since we're multiplying x to the 13th power by x to the 6th, the result is \(x^{13+6}\), which is \(x^{19}\)

the equation now:

\(x^{19}\)=\(x^{p}\)

since the exponents are at the same base, we can solve the equation

19=p

so p is 19

hope this helps :)

By using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.

In Mathematics, there are different types of functions and these include the following;

A logarithm function can be defined as a type of function that represents the inverse of an exponential function. Mathematically, a logarithm function is written as follows:

y = logₐₓ

y = log₁₀10

y = log₁₀10 = 1.  

Therefore, if log₁₀x < 1, then, x < 10.  Also, if log₁₀x > 1, then, x > 10.

For this exercise, you should take note of this deductive points:

In conclusion, by using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

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The slope of a beer's law plot represents that one can quantitatively determine the molar absorptivity of a substance, which is essential for accurately determining concentrations of unknown samples using spectrophotometric methods.

In Beer's law, the relationship between the concentration of a substance and its absorbance is described by the equation A = εbc, where A is the absorbance, ε is the molar absorptivity (also known as the molar absorptivity coefficient), b is the path length of the sample, and c is the concentration of the substance.

When plotting a graph of absorbance versus concentration, the slope of the line represents the molar absorptivity (ε). The molar absorptivity is a constant that reflects the substance's ability to absorb light at a specific wavelength. A higher molar absorptivity indicates that the substance has a greater tendency to absorb light and is more sensitive to changes in concentration.

Conversely, a lower molar absorptivity indicates weaker absorption characteristics.

In summary, by measuring the slope of the Beer's law plot, one can quantitatively determine the molar absorptivity of a substance.

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The final expression of the function f(x) is

f(x) = x + 2/5 (37x³/²) - 166.6

To find f(x), we need to integrate f'(x) with respect to x:

where C is the constant of integration.

To determine the value of C, we can use the initial condition f(9) = 65:

f(9) = 9 + 2/5 (37(9)³/²)) + C = 65

Simplifying, we get:

Therefore, the function f(x) is:

f(x) = x + 2/5 (37x³/²) - 166.6

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When we rotate a figure 90° counterclockwise each point changes thorugh the following rule.

then, since the initial coordinates of the figure are given, apply the transformation to each point

If we look at the flags shown, the correct ubication of the flag is: