Choose the expressions that are perfect cubes.
–3
125a^6
8m^20
100w^24x^3
–64q^12
–c^30d^9f^18g^3

The 1:3 ratio means that the distance from A to the point is 1/4 of the distance from A to B.

The difference of y-coordinates is 10-8 = 2. 1/4 of that is 2·1/4 = 1/2, so the point of interest will have y-coordinate 8 + 1/2 = 8 1/2. This apparently corresponds to the first selection:

... (6 1/2, 8 1/2)

The first quartile (Q1) in a box-and-whisker plot is the value at the left boundary of the box, which represents the median of the lower half of the dataset. According to the information provided, Q1 is 80, but none of the given answer options (A, B, C, D) match this value.

In the context of your question, which examines a box-and-whisker plot, the first quartile (Q1) corresponds to the value at the left boundary of the box. The first quartile represents the median of the lower half of the dataset, excluding the overall median. From the information provided, we can deduce that the first quartile (Q1) is 80, as represented by the left boundary of the box in a box plot provided elsewhere.

Therefore, the correct answer to your question would be the option that most closely matches the value of 80. However, since none of the options (A. 43.5, B. 47.5, C. 41.5, D. 50.0) match this value, there appears to be a discrepancy. It's possible that there is an error in the question options, or there might be a misinterpretation regarding the information provided. Make sure that you are referring to the correct box plot.

To use the AA postulate directly, you need to show that two corresponding angles are congruent. In order to show that here, you must calculate the value of one of the missing angle measures. Either of the missing angles can be found by invoking the fact that the sum of angles in a triangle is 180°.

After finding either missing angle, you can show that the measures of two angles in one triangle are identical to the measures of two angles in the other triangle, hence the triangles are similar by the AA postulate.

Answer:

I wrote the answer below :)  hope it makes sense

Step-by-step explanation:

The Angle-Angle Similarity postulate can be used to prove that these two triangles are similar. To demonstrate I will use an example, and try to make sense to the reader. on triangle ABC, the 2 angles that are given to us are 32 degrees and 49 degrees. Since all triangles have an angle sum of 180 degrees, the missing degree would have to be 99 degrees. Same for the triangle A'B'C'. The 2 angles given are 99 degrees and 49 degrees, which means the missing angle has to be 32 degrees. Therefore, the triangles are similar.

I just took the test and this is correct.

Happy Holidays!

The slope of your line is the x-coefficient: 5.

The slope of a perpendicular line is the negative reciprocal of that: -1/5.

Answer:

parallel

Step-by-step explanation:

Translation moves each point the same amount in the same direction. Essentially, the original segment becomes the side of a parallelogram, whose other side is the image, and whose ends are the vectors specifying the translation.

In the attachment, we have designated (a, b) as point A, and (c, d) as point B. We had to choose specific values for these in order to plot them, but the description of the effect of translation applies no matter what the point coordinates are chosen to be.

y=x^2 - 10x +2

Use the form ax^2 + bx + c to find the values of a, b,and c.

a = 1 ( no number in front of the x^2)

b = 10

c = 2

Vertex form is a(x+d)^2 + e

Solve for d using d= b/2a

d = 10 / 2

d = 5

Find e using e = c - b^2/4a

e = 2 - 10^2/4

e = 2 - 25

e = -23

Vertex = d,e

Vertex = (5, -23)

Let x be the bigger number and y be the smaller number.

One number is 11 more than twice another number. Thus,

x = 2y + 11

The sum of the numbers is twice their difference, thus,

x + y = 2(x-y), which simplifies to:

x + y = 2x - 2y

3y = x  (Now plug this back to the first equation:

3y = 2y + 11, and solve:

y = 11

Plug in y = 11 to the first equation:

x = 2(11) + 11 = 22 + 11 = 33

Thus the numbers are: x = 33, y = 11.

Answer:

1. Put the numbers in order.

2. Cross off high/low pairs.

3. Add the leftover numbers.

4. Divide the sum by 2.

Step-by-step explanation:

We know that the median represent the middle value in a data which gives the center of the measure.

Whenever we calculate the median of a data the first step we need to follow is to arrange the a data in either ascending or descending order.

After that choose that center-most data value (in odd number of data value) or calculate the mean of the center-most 2 numbers ( if even) which will be the median of the  data.

Given data: 24, 16, 23, 30, 18, 29

Number of numbers = 6 (even)

1. Put the numbers in order.

16,18,23,24,29,30

2. Cross off high/low pairs., we left with the numbers :-

23,24

3. Add the leftover numbers.

23+24=47

4. Divide the sum by 2.

[tex]\dfrac{47}{2}=23.5[/tex]

Answer:

A.

Step-by-step explanation:

The product of the two roots is c/a.

_____

Consider the equation

... a(x -p)(x -q) = 0

which has solutions x=p and x=q.

When multiplied out, it becomes ...

... a(x² -(p+q)x +pq) = ax² -a(p+q)x +apq = 0

When apq = c, the product pq is c/a.

Given

Lee converted 500 U.S. dollars to 625 Singapore dollars.

x represents U.S. dollars and s represents Singapore dollars.

Find out equations represents the relationship between the two currencies.

To proof

As given in the question

x represents U.S. dollars and s represents Singapore dollars.

converted 500 U.S. dollars to 625 Singapore dollars

500 x = 625 s

[tex]x = \frac{625}{500} s[/tex]

x = 1.25 s

This shows that the U.S dollars is equal to 1.25 times of singapore dollars.

Hence proved

9 + 5 = x - 11

combine like terms

14 = x - 11

add 11 to both sides

25 = x

or

x = 25

answer

x = 25

9+5=x-11

14=x-11

+11    +11

24=x

Amount needed for down payment = $650

Amount charged by Jordan for mowing 1 lawn = $25

Amount charged by Sharla for 1 necklace = $ 15

Let the number of lawns mowed by Jordan = x

Let the number of necklace made by Sharla = y

Part A:

[tex]25x+15y=650[/tex]

As it is given, Sharla can make 40 necklace so,

[tex]25x+15(40)=650[/tex]

Or it could be 25x=650 and 15y=650

Part B:

No, Sharla cannot afford the down payment because she makes $15 for every necklace and she only has 40 necklaces which is [tex]15*40=600[/tex]

The associative property allows you to change the grouping of addends or factors without changing the value of the expression.

The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.The associative property allows you to change the grouping of addends or factors without changing the value of the expression.

Solution: We have to find the Frequency and Relative frequency of the given data:

Frequency is the number of times a number occurs.

Relative Frequency is the number of times a number occurs divided by the total number of items.

Therefore, the frequency and relative frequency are calculated as below:

Number       Frequency          Relative Frequency

20                       1                     [tex]\frac{1}{31} \times 100 =3.2\%[/tex]

21                        4                    [tex]\frac{4}{31} \times 100 =12.9\%[/tex]

22                       2                    [tex]\frac{2}{31} \times 100 =6.5\%[/tex]

23                       4                    [tex]\frac{4}{31} \times 100 =12.9\%[/tex]

24                       3                    [tex]\frac{3}{31} \times 100 =9.7\%[/tex]

25                       2                    [tex]\frac{2}{31} \times 100 =6.5\%[/tex]

26                       3                    [tex]\frac{3}{31} \times 100 =9.7\%[/tex]

27                       5                    [tex]\frac{5}{31} \times 100 =16.1\%[/tex]

28                       3                    [tex]\frac{3}{31} \times 100 =9.7\%[/tex]

29                       4                    [tex]\frac{4}{31} \times 100 =12.9\%[/tex]

Total                  31

false

under the given translation

the point (1, 6 ) → (1 - 7, 6 + 3 ) → (- 6, 9 )

Matrix multiplication is defined for M×K and K×N matrices to give an M×N result. Note that the middle two numbers (K) are the same.

Matrix multiplication of a 2×2 and 2×3 matrix will give a 2×3 matrix result. It is defined.

Ok, so what this question is really asking you is: [tex]2/5=0.4[/tex]

What is [tex]6*0.4[/tex] and that equals [tex]6*0.4=2.4[/tex]

Now because the the number is 2.4 plot that point

[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{7})~\hspace{10em} slope = m\implies -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-7=-2(x-4)[/tex]

Answer:

The equation in point-slope is [tex]y-7=-2(x-4)[/tex].

Step-by-step explanation:

Point-slope is a specific form of linear equations in two variables:

[tex]y-b=m(x-a)[/tex]

When an equation is written in this form, m gives the slope of the line and (a, b) is a point the line passes through.

We want to find the equation of the line that passes through (4, 7) and whose slope is -2. Well, we simply plug m = -2, a = 4, and b = 7 into point-slope form.

[tex]y-7=-2(x-4)[/tex]

Answer:

 PK=8.49m

Explanation:

We have sine formula

     [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

By sine formula we have

    [tex]\frac{PS}{sinK} =\frac{PK}{sinS} =\frac{KS}{sinP}[/tex]

    We have PS = 12, ∠P=105° and ∠S=30°, so ∠K=180°-(105°+30°)=45°

 Substituting

        [tex]\frac{12}{sin45} =\frac{PK}{sin30} \\ \\ PK=8.49m[/tex]      

Answer:

The Answer is B

Step-by-step explanation:

Subtract f-g

4x + 1 - x^2 - 5

Distribute the - sign

4x + 1 - x^2 + 5

Combine like terms

-x^2 + 4x + 1 + 5

-x^2 + 4x + 6

y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{15}{2}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = 4x + 5 is in this form with slope m - 4

Given the slope of a line m, then the slope ([tex]m_{2}[/tex]) of a line perpendicular to it is

[tex]m_{2}[/tex] = - (1 / m ) = - [tex]\frac{1}{4}[/tex]

y = - [tex]\frac{1}{4}[/tex] x + c is the partial equation of the perpendicular line

to find c, substitute ( 2, 7 ) into the partial equation

7 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = [tex]\frac{15}{2}[/tex]

y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{15}{2}[/tex] ← equation of perp. line

A number added to its opposite is zero (0). No exponent is needed.

7^4 - 7^4 = 0

f(3) = -9 for the function [tex]\( y = f(x) = -3x \) when \( x \) is 3.[/tex]

To find f(x) when ( x ) is 3 for the given function [tex]\( y = f(x) = -3x \),[/tex] you substitute 3 for ( x ) in the function:  [tex]\[ f(3) = -3 \times 3 \][/tex]

Now, calculate the value: [tex]\[ f(3) = -9 \][/tex]

Therefore, when ( x ) is 3, f(x) is -9 for the function [tex]\( y = f(x) = -3x \).[/tex]

In more detail, this means that if you plug ( x = 3 ) into the function, it will result in ( y = -9 ). The function ( y = -3x ) represents a linear relationship where the coefficient of ( x ) is -3. This indicates that for each unit increase in ( x ), ( y ) decreases by 3 units. In the specific case of ( x = 3 ), substituting this value into the function gives [tex]\( y = -3 \times 3 = -9 \).[/tex]

This kind of analysis is fundamental in understanding the behavior of linear functions. It provides insight into how the function's output (y) changes in response to changes in the input ( x ). In this case, when ( x ) increases by 1, ( y ) decreases by 3, leading to the slope of -3 in the function ( y = -3x ).

Angles on the same side are the same, so angle 1 is 110°.

Angle 1 and 2 are supplementary, so they add up to 180. Since we know angle 1 is 110, angle 2 must be 70°

1/2 = 3/6

2/3 = 4/6

2/3 is greater than 1/2, so is to the right of 1/2 on the number line.

The difference is (4/6) -(3/6) = (4-3)/6 = 1/6.

2/3 is 4/3 times 1/2.

The population is multiplied by 100% -2.2% = 97.8% each year. After 5 years, the population will have been multiplied by this value 5 times, so will be ...

... 3500×0.978⁵ ≈ 3132

The appropriate choice is ...

... C. 3132