Item 6 Your friend earns $10.50 per hour. This is 125% of her hourly wage last year. How much did your friend earn per hour last year?

Multiplying a complex number by -1 flips it across the origin on the complex plane, changing its direction by 180 degrees but not its magnitude, resulting in a point directly opposite to the initial position.

The question asks about the effect of multiplying a complex number by -1 in the complex plane. Multiplying a complex number by -1 essentially flips the point representing the complex number across the origin. If Point A represents a complex number on the complex plane, multiplying that complex number by -1 will result in a point that lies exactly opposite of Point A with respect to the origin. This operation does not change the magnitude of the complex number but changes its direction by 180 degrees. This is because the complex plane is analogous to a two-dimensional Cartesian coordinate system where complex numbers are represented as vectors. The multiplication by -1 is a reflection across the origin in such a plane.

For example, if a complex number z is represented by the point (a, b) where a is the real part and b is the imaginary part, then multiplying z by -1 gives us the point (-a, -b). This operation is similar to rotating the vector z 180 degrees around the origin or mirroring it across both the x and y axes.

Answer:

The correct answer option is: it is a difference of squares:  (y – 15)(y + 15)

Step-by-step explanation:

We are given a polynomial and we are to determine if it is a difference of squares.

Let us recall the algebraic formulas which include:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

[tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex](a+b)(a-b)=a^2-b^2[/tex]

So if we look closely, we can conclude that the given polynomial observes the third formula of the perfect squares.

Hence, we can say that it is a difference of squares:  (y – 15)(y + 15)

[tex]y^2-225 = (y-15)(y+15)[/tex]

B - Brandon's age

4B - Michael's age

B + 27 - Michael's age

The equation:

4B = B + 27       subtract B from both sides

3B = 27      divide both sides by 3

B = 9

4B = 4(9) = 36

You are given the height of the building and the length of the shadow the building gives, so you can set that up as a proportion of Height of building over the length of the shadow so 31/28.

Now you can set the same proportion for Julian, using X for her height, so you would have x/6.

To solve for her height, set the two proportions equal and solve for x:

31/28 = x/6

Cross multiply:

31 * 6 = 28 *x

186 = 28x

Divide both sides by 28:

x = 186 / 28

x = 6.64 feet tall

To find Julian's height using the proportion between the building's height and shadow length and Julian's shadow length, we set up a proportion as follows: 31 feet (building height) / 28 feet (building's shadow) = Julian's height / 6 feet (Julian's shadow). Solving for Julian's height, we determine it is approximately 6.64 feet.

The question pertains to similar triangles and proportionality in shadows cast by objects. Using the concept of similar triangles, we can set up a proportion to find Julian's height. The shadows and the objects (Julian and the building) form two sets of similar triangles because the angles of the sunshine are the same for both objects, and thus their corresponding sides are proportional.

To set up the proportion, we use the building's shadow and height relation and compare it to Julian's shadow and unknown height. So, we write:

Building's height / Building's shadow length = Julian's height / Julian's shadow length
31 feet / 28 feet = Julian's height / 6 feet

To generate an accurate answer, we solve for Julian's height as follows:

Julian's height = (31 feet / 28 feet) \ 6 feet = (31 / 28) \ 6
Julian's height = 6.64 feet (approximately)

This proportional relationship can be used to find unknown heights or lengths of shadows when a reference object is used, provided the angle of light is the same.

Answer:

Length of AC = 48 units.

Step-by-step explanation:

Given in parallelogram ABCD , diagonals AC and B intersects at a point E.

Length of AE = [tex]x^2-16[/tex] units and CE = 6x.

We have to find the length of AC.

According to the property of parallelogram:

Diagonals are intersecting each other at their midpoint.

Since, E is the midpoint AC ;

so, AE = CE

[tex]x^2-16[/tex] =6x

or we can write this as;

[tex]x^2-6x-16[/tex]=0

[tex]x^2-8x+2x-16[/tex]=0

[tex]x(x-8)+2(x-8)[/tex]=0

[tex](x-8)(x+2)[/tex] = 0

Zero product property states that if ab = 0 , then either a=0 or b =0.

By zero product property, we have;

(x-8) = 0 and (x+2) = 0

x = 8 and x = -2

Since, length x cannot be negative so we ignore x = -2.

then;

x = 8

AC = [tex]x^2-16[/tex] = [tex]8^2 -16 = 64- 16 =48[/tex] units.

Therefore, the length of AC = 48 units.

Answer:

I just took the test and got the answer AC=96.

Answer:

P(1+r) = p(1+0.11)= p+0.11p=1.11p

Step-by-step explanation:

The merchandise is marked up 11%. This means you pay 100% of the price plus 11%. We can represent that as (1+r) where r is the percent marked above. For 11%, this expression would be 1+0.11. We multiply that by the price p. p(1+0.11). This simplifies to p+0.11p. We can further simplify it to 1.11p.

Answer:

p + 0.11p

i did the test

The correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].

The correct option is (a).

To use the distributive property to simplify the expression (9(x+3) + 15x), we need to distribute the terms outside the parentheses to each term inside the parentheses.

The given expression is [tex]\(9(x+3) + 15x\)[/tex].

1. Distribute 9 to (x) and (3):

[tex]\[ 9(x+3) = 9 \times x + 9 \times 3 \][/tex]

2. Distribute 15 to (x):

[tex]\[ 15x \][/tex]

So, after using the distributive property, the expression becomes:

[tex]\[ 9 \cdot x + 9 \cdot 3 + 15x \][/tex]

Now, let's compare this with the options:

a. [tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex] - This matches our result.

b. [tex]\(9(x+3+15)x\)[/tex] - This option seems incorrect as it doesn't distribute 9 to each term inside the parentheses correctly.

c. [tex]\(9:x+3+15x\)[/tex] - This option doesn't seem to use the distributive property correctly.

d. [tex]\(9x+9 \cdot 3+9 \cdot 15x\)[/tex] - This option distributes 9 correctly but includes an extra term (9x) that doesn't appear in the original expression.

Therefore, the correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].

Which expression is equivalent to the given expression after using the distributive property? 9(x+3)+15x

a.9· x+9· 3+15x

b.9(x+3+15)x

c.9: x+3+15x

d.9 x+9· 3+9· 15x

Answer:

24x + 15

Step-by-step explanation:

9(x+3)+15x

Use the distributive property.

9*x +9*3 + 15x

9x + 15 + 15x

Combine the like terms.

24x + 15

Answer:

f(-2)= -8

f(-1) = -1

f(0)= 0

Step-by-step explanation:

f(x) = x^3

if x =-2

f(-2) = (-2) ^3 = -2*-2*-2 = -8

if x =-1

f(-1) = (-1) ^3 = -1*-1*-1 = -1

if x =0

f(0) = (0) ^3 = 0*0*0 = 0

Answer:

Graph 4

Step-by-step explanation:

for part B

1. You are trying to isolate "F" in the equation

[tex]C=\frac{5}{9}(F-32)[/tex]      Multiply 9/5 on both sides

[tex](\frac{9}{5})C=(\frac{9}{5}) \frac{5}{9} (F-32)[/tex]

[tex]\frac{9}{5}C=F-32[/tex]    Add 32 on both sides

[tex]\frac{9}{5}C+32=F-32+32[/tex]

[tex]\frac{9}{5}C+32=F[/tex]

THIS IS WRONG

2. You are trying to isolate "y" in the equation

[tex]m=\frac{x+y+z}{3}[/tex]   Multiply 3 on both sides

3m = x + y + z        Subtract x and z on both sides

3m - x - z = y

THIS IS CORRECT

3. Isolate "r"

[tex]s=\frac{r}{r-1}[/tex]   Multiply (r - 1) on both sides

s(r - 1) = r    Distribute s into (r - 1)

sr - s = r     Subtract sr on both sides

-s = r - sr    Factor out r from (r - sr)

-s = r(1 - s)    Divide (1 - s) on both sides

[tex]\frac{-s}{1-s}=r[/tex]

THIS IS WRONG

4. Isolate "b"

[tex]A=\frac{1}{2}(a+b)[/tex]    Multiply 2 on both sides

2A = a + b     Subtract a on both sides

2A - a = b

THIS IS CORRECT

5. Isolate "y"

[tex]m=\frac{x+y}{2}[/tex]    Multiply 2 on both sides

2m = x + y    Subtract x on both sides

2m - x = y

THIS IS WRONG

The 2nd and 4th one is right

Answer:

. You are trying to isolate "F" in the equation

     Multiply 9/5 on both sides

   Add 32 on both sides

THIS IS WRONG

2. You are trying to isolate "y" in the equation

  Multiply 3 on both sides

3m = x + y + z        Subtract x and z on both sides

3m - x - z = y

THIS IS CORRECT

3. Isolate "r"

  Multiply (r - 1) on both sides

s(r - 1) = r    Distribute s into (r - 1)

sr - s = r     Subtract sr on both sides

-s = r - sr    Factor out r from (r - sr)

-s = r(1 - s)    Divide (1 - s) on both sides

THIS IS WRONG

4. Isolate "b"

   Multiply 2 on both sides

2A = a + b     Subtract a on both sides

2A - a = b

THIS IS CORRECT

5. Isolate "y"

   Multiply 2 on both sides

2m = x + y    Subtract x on both sides

2m - x = y

THIS IS WRONG

The 2nd and 4th one is right

Step-by-step explanation:

The measure of the angle 1 cannot be determined

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

The pentagons ABCDE and FGHIJ

Given that pentagon ABCDE ≅ pentagon FGHIJ

We can see that there is no occurrence of the angle 1 in both figure

This means that the measure of the angle 1 cannot be determined

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Answer:

There are 272 students going on the field trip.

Step-by-step explanation:

68 students on each bus. 4 busses. 68 x 4 = 272

Answer:

The answer is 272 students.

Step-by-step explanation:

1. First, I looked at how many students and buses are there.

2. I looked at the question, "How many students are going on the field trip?"

3. Next, I will multiply the number of students on each bus by the number of buses on there.

4.   68

   x  4

   272

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

Hope this helped! Your answer is 272 students. ❤️

Answer:  10

Step-by-step explanation:

Answer:

x) =g(x) -1  shifts the graph g(x) down 1 unit

Step-by-step explanation:

g(x) = 3x

When we add  to g(x) and make it g(x) +c, we shift the graph vertically,

+c shifts the graph up

-c shifts the graph down

h(x) =g(x) -1  shifts the graph g(x) down 1 unit

Answer:

Both A and D are false

Step-by-step explanation:

We expect lower academic performance when unemployment is high, so a lower graduation rate. Dropouts—those who don't graduate—tend to have a higher unemployment rate, so there is cause/effect working in both directions. Thus graduation rate and unemployment would be negatively correlated. (One study showed the correlation coefficient to be about -0.11.)

Because D is false, A is also false.

Answer: 4.5kg = 9.9208lbs

4.5kg = 158.733oz

The watermelon weighs approximately 4.5 kg, which can be converted to pounds and ounces by using the conversion factors. It is approximately 9 pounds and 15 ounces after conversion.

A watermelon at the grocery store weighs 4.5 kg. To convert this weight into pounds and ounces, we can use the fact that 1 kg is equivalent to 2.205 pounds (lb) and 1 pound equals 16 ounces.

First, let's find out how much the watermelon weighs in pounds:

Since we want the weight in pounds and ounces, we'll convert the decimal part of the pounds to ounces:

Therefore, the watermelon weighs approximately 9 pounds and 15 ounces (rounding 14.76 ounces to the nearest whole number).

Answer:

Expenses for purchasing is $245 ,Revenue $479 and Total profit $ 234

Step-by-step explanation:

Cost of two blouses = 2× 25 = $50

Revenue from blouses = 2× 38 = $76

Profit of blouses = 76- 50 = $26

Similarly cost of 3 skirts = 3×15 = $45

Revenue from Skirts = 3×26 =$78

Profit from skirts = 78-45 =$33

Now cost price of pants = 5×30 =$150

Revenue from Pants = 5×65 =$325

Profit from pants = 325-150 = $175

So Jayla's expenses for purchasing = 50+45+150

                                                           = $245

                                           Revenue = 76+78+325

                                                           = $479

                                        Total Profit = 479 -245

                                                            = $234

Jayla's total expenses were $245, she made $479 in revenue through sales, making her resultant profit $234. This is calculated by subtracting the total expenses from the total revenue.

The subject of this problem deals with the concepts of expenses, revenues, and profit in a small business setting. Jayla spent $50 on the blouses (2 x $25), $45 on the skirts (3 x $15), and $150 on the pants (5 x $30), adding up to a total expense of $245. She sold these items for total revenues of $76 for the blouses (2 x $38), $78 for the skirts (3 x $26), and $325 for the pants (5 x $65), giving her a total revenue of $479. The total profit can be calculated by subtracting the total expenses from the total revenue, and therefore, Jayla made a profit of $234 ($479 - $245).

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Answer:

617.5

Step-by-step explanation:

If you expand the series by putting in [tex]n=1,n=2,n=3...[/tex] values, you will see:

68.7, 66.4, 64.1, ....

To find common difference (d) (difference in a term and its previous term) we take any term and subtract from it the term before it:

[tex]66.4-68.7=-2.3[/tex]

The sum of arithmetic series formula is:

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

Where,

Substituting these values, we get:

[tex]S_{50}=\frac{50}{2}[2(68.7)+(50-1)(-2.3)]\\S_{50}=25[137.4+(49)(-2.3)]\\S_{50}=25[24.7]\\S_{50}=617.5[/tex]

Last answer choice is right.

Answer: D. 617.5 hope that helps !

The total number of observations is

2+9+16+12+8+6+4+2+1=60

The first five counts refer to 0 to four cars:

2+9+16+12+8=47

The probability is the fraction less than five,

p= 47/60 = 0.783333...

Answer: 78%

Answer:

59%

Step-by-step explanation:

First let us work out the total number of cars waiting in the  given period.

= 0 *2 + 1*9 + 2*16 + 3*12 + 4*8 + 5*6 + 6*4+7*2+8*1

= 185

Now the number when there are less than 5 cars in line ( that is when there are 0 - 4 cars in line) =

0*2 + 1*9 + 2*16 +3*12+4*8

= 109

Thus the required probability = 109/185

= 0.589

= 59%  (answer)

Answer:

The focii are 8 feet apart

Step-by-step explanation:

You can use the formula

F = √(a^2 - b^2)   where F is the distance of the focii from the center , a = length of the semi major axis and b = length of the semi minor axis)

So here it is  √(5^2 - 3^2)

= √16 = 4

So the distance is 2*4 = 8

Quadratic relations and comic sections unit test part 1

12. b. 8 feet

1. b ellipse

domain -4<=x<=4

range -3<=y<=3

2. c. x^2/3

3. c. 1/10 x^2

4. b. 5 inches

5. d. x=1/12 (y-4)^2 +2

6. b. (x-4)^2 + (y-5)^2 =49

7. b. (x+8)^2 + (y+4)^2 =25

8. d. (x+3)^2 + (y+2)^2 =9

9. a. center at (7,-6); radius 4

10. b. x^2/25 + y^2/169 =1

11. a. (0, +/- 6)

12. b. 8 ft

13. c. (put equation in graphing calculator to see graph)

14. d. (0, +/-5)

Answer: Our function will be

[tex]d=180-9.2t[/tex]

Step-by-step explanation:

Since we have given that

Distance of the entrance = 180 meters

Speed of Nala who is running towards the entrance of the lair = 9.2

As we know the "Distance-Speed formula":

[tex]Time=\frac{Distance}{Speed}\\\\t=\frac{180}{9.2}\\\\t=19.565\\\\t=19.57\ seconds[/tex]

So, our required function will be

[tex]d=180-9.2t[/tex]

As we increase the time distance get reduced from 180 which is the distance of the entrance .

Hence, our function will be

[tex]d=180-9.2t[/tex]

Answer:

length of each plan A work out: 1 hour

length of plan B work out: [tex]\frac{1}{2}[/tex] hours

Step-by-step explanation:

Let x represents the time taken to do plan A

y represents the time taken to do plan B

On Monday there were 5 clients who did Plan A and 2 who did Plan B.

Miguel trained his Monday clients for a total of 6 hours

5x + 2y = 6 -----------> equation 1

On Tuesday there were 3 clients who did Plan A and 8 who did Plan B. .He trained his Tuesday clients for a total of 7 hours

3x + 8y = 7  -------------------> equation 2

Now we solve for  x  and y

Let multiply the first equation by -4 to eliminate y

-20x -8y = -24

  3x + 8y = 7

------------------------ (add both equations)

-17x    = -17

Divide both sides by -17

So x= 1

Plug in 1 for x  in first equation and  solve for y

5x + 2y = 6

5(1) + 2y = 6

5 + 2y =6

Subtract 5 on both sides

2y = 1

y = 1/2

length of each plan A work out: 1 hour

length of plan B work out: [tex]\frac{1}{2}[/tex] hours

Answer:

All the fields will be harvested in 6.25 days

Step-by-step explanation:

because 75 ÷ 12 and 62.5 ÷ 12 is 6.25

Answer:

Step-by-step explanation:

84-90=90-96=96-102=102-108=-6

its a sequence where A(1)=84 n A(n+1)-A(n)=6

A(n)=84+(n-1)*6; n=1,2,3,4,5

Answer:

f(x) = 84 + 6x where x=0, 1, 2, 3, 4, ...

Step-by-step explanation:

Given 84, 90, 96, 102, 108, ...

the numbers are a sequence with 84 as the initial value and in increment of 6s. So the function can be written as:

f(x) = 84 + 6x where x=0, 1, 2, 3, 4, ...

Answer:

No

Step-by-step explanation:

Let us consider two positive radicals first,

[tex]\sqrt{3} , \sqrt{5}[/tex]

We know that [tex]\sqrt{3}[/tex] is an irrational number and [tex]\sqrt{5}[/tex] is also an irrational number.

So the sum of two positive radicals does not always have a rational solution.

There are examples when the some of adding positive radicals can get us a rational solution. For example,

[tex]\sqrt{4}+\sqrt{4}  =4[/tex]

So if the radicand is a perfect square then the solution is rational.

Answer:

1. 24 outcomes

2. 3

3. A= 1/4

   Odd = 1/2 (reduced from 12/24 chances)

   A/Odd = 1/8

4. 50% the letter chosen doesn't affect the outcome of the roll of the dice

5. i believe they are independent

6. 1/8

Hope that helps!

Answer:

3/4

Step-by-step explanation:

Answer:

A quadrilateral has 4 right angles

Step-by-step explanation:

In a conditional statement

If hypothesis, then conclusion

OR

Conclusion, if hypothesis.

The hypothesis goes with the if part.

Answer:

Option B is correct.

By ASA rule are these triangles are congruent

Step-by-step explanation:

In triangle JMK and triangle JMN

[tex]\angle KJM \cong \angle NJK[/tex]   [Angle]         [Given]

[tex]JM \cong JM[/tex]   [Common Side]  

[tex]\angle JMK \cong \angle JMN [/tex]   [Angle]

ASA(Angle-Side-Angle) theorem states that if two angles and the included  side of one triangle are congruent to the corresponding parts of another triangle, then these triangles are congruent.

then, by ASA theorem;

[tex]\triangle JMK \cong \triangle JMN[/tex]

Therefore, by ASA rule are these triangles are congruent.

The rules AAS, ASA, SAS, SSS are a set of criteria that can determine if two triangles are congruent. They need accurate measurements of angles and sides of the triangles to be applied. Without these specifics, it's hard to identify which rule applies.

In order to answer which rule makes the triangles congruent, we would need more specific information about these triangles, such as the measures of their angles and sides. However, let me explain what each of these rules represents:

Without specific information about your triangles, it's difficult to conclusively establish which rule applies.

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