When navigating the maze, the robot will only need to go north, south, east, and west. It can be useful to use the complex plane to represent these directions. When using the complex plane this way, we use numbers such that their magnitude is equal to 1. If we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west?

Answers:

Angle A = 62.1 degrees

Angle X corresponds to angle A

The triangles are not similar

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

Explanation:

To find angle A, subtract the given angles B and C from 180 to get 180 - B - C = 180 - 60.8 - 57.1 = 62.1 degrees

Notice how none of the angles of triangle ABC have a measure of 59.1, so this means that angle Y cannot be congruent to any of A, B or C. This is why the triangles are not similar. We would need 2 pairs of congruent angles to use the AA (angle angle) similarity theorem.

If the triangles were similar, then we can say triangle ABC is similar to triangle XYZ. The letters A and X are the first letters mentioned of the trio of letters, which means that they correspond to one another.

Answer:

D- -50.76

Step-by-step explanation:

Answer:

Erin must first reconcile her bank account:

She must add to her bank balance all the deposits in transit = $125.56 + $50 + $212.34 = $387.90

then she should subtract all outstanding checks = $15 + $78.25 = $93.25

reconciled bank statement = $844.93 + $387.90 - $93.25 = $1,039.58

if her check register shows a $1,150.34 balance and her reconciled bank statement is $1,039.58, then there is a $10.76 difference that must be accounted for.

The $10.76 are probably bank fees and charges that Erin has not recorded yet. Therefore, she should check her bank statement and look for any charged fees (ATM withdrawal charges + account fees) and then record them properly.

*ATM withdrawals are automatically recorded by the bank, so they do not have to be considered in the reconciliation, there is no such thing as outstanding ATM withdrawal.

Answer:

true statement

Step-by-step explanation:

Substituting a solution back into the original equation will make the equation true.

Answer: Choice D) x intercept of f(x) is larger then the x intercept of g(x)

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

Explanation:

A) False. The x intercept of f is 1 while the x intercept of g is -1. The x intercept happens when y = 0. Visually, this is where the graph crosses the x axis.

B) False. The y intercept of f(x) is -1, compared to the y intercept of g(x) is +1. The y intercept happens when x = 0, which is when the graph crosses the y axis.

C) False. The y intercept of f(x) is actually smaller than the y intercept for g(x)

D) True. The x intercept of f(x) is larger than the x intercept of g(x). Compare 1 and -1, which are the x intercepts for f and g in that order.

Answer: D

Step-by-step explanation:

NOTES:

          f(x)        g(x)

x-int:     1          -1

y-int:    -1           1

A) x-intercepts are not equal so FALSE

B) y-intercepts are not equal so FALSE

C) y-intercept of f(x) is not greater than g(x) so FALSE

D) x-intercept of f(x) is greater than g(x) so TRUE

Answer:

its called line FGH

Step-by-step explanation:

its because the line is FGH

Hope this helps :)

A line is named by two of the points on the line, with a line drawn above the letters.

For the line in the attached image, the answer would be the first choice.

Answer:

D

Step-by-step explanation:

First, he parabola has a sideways orientation. This signals that x and y have been reversed within the equation meaning  [tex]x^{2} --->y^{2}[/tex]. We first look for answers for which y has been raised to the seocnd power instead of x. This leaves answer choice a, b, and d.

Second, we find the vertex of the parabola (center point of the U) at (2,-3). We write them with inverse signs. (x-2) since 2 is the x-coordinate. (y+3) since -3 is the y-coordinate.

The only answer choice meeting these requirements is D.

D. x-2 = (-2/9)(y +3)^2

The parent function, x = y^2 is translated 2 units to the right and 3 units down. This means x is replaced by x-2, and y is replaced by y+3.

There is also a horizontal scale factor involved. It is useful to use the point (0, 0) to determine what it is.

... (x -2) = a(y +3)^2 . . . . . the translated function with unknown factor "a"

... 0 -2 = a(0 +3)^2 . . . . . .substitute (x, y) = (0, 0)

... -2 = 9a . . . . . . . . . . . . . simplify

... a = -2/9 . . . . . . . . . . . . .divide by the coefficient of "a"

So, the graph is described by ...

... (x-2) = (-2/9)(y+3)^2 . . . . . matches selection D

Answer:

the answer is d

Step-by-step explanation:

you can tell because it's past 2 and close to 3. it's -5 because it's past -4. so their is your answer to why it's d

The ordered pair that represents point P on the graph is **D) (3, -5)**. Point P lies in the fourth quadrant, where both the x-coordinate (3) and the y-coordinate (-5) are positive.

Answer:

DE = 6 cm

Step-by-step explanation:

Let DE = x cm.

Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)

As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.

Therefore, from (1) We get ,  m∠EAD = m∠ADE and m∠EBD = m∠BED.

So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.

So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then

12 + x + x + x = 30

⇒ 12 + 3x = 30

⇒ x = 6

Hence, the length of DE is 6 cm.

Answer:

DE=6cm

Step-by-step explanation:

Let x=DE, since AB║DE, therefore ∠BAD=∠ADE and ∠ABE=∠BED.        (1)

Also, we are given that AD is the angle bisector of ∠A and BE is the angle bisector of ∠B,

Therefore, ∠EAD=∠DAB and ∠ABE=∠EBD                                             (2)

From (1) and (2), ∠EAD=∠ADE and ∠EBD=∠BED

⇒The ΔADE and ΔEDB then becomes the isosceles triangle with AE=Ed and ED=DB (Sides opposite to equal angles are always equal)

Therefore, AE=DE=DB=x

We are given that the perimeter of ABDE is 30 cm, therefore,

Perimeter of ABDE= sum of all the sides of ABDE

⇒30=AB+BD+DE+AE

⇒30=12+3x

⇒30-12=3x

⇒x=6cm

Therefore, the length of DE= 6cm

Final answer:

Writing a linear equation requires knowing the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, and the point-slope form (y - y1 = m(x - x1)), useful when a point on the line and the slope are known.

Explanation:

The ability to write a linear equation involves understanding different forms, such as standard form, point-slope form, and slope-intercept form. The slope-intercept form of a linear equation is commonly written as y = mx + b, where m represents the slope and b represents the y-intercept. The slope is the rate of change, indicating how much y increases for a one-unit increase in x. The y-intercept is the point where the line cuts the y-axis, which means when x=0.

It's important to note some variations in notation, such as y = a + bx, which is another way to express the slope-intercept form, where a is the y-intercept and b is the slope. When converting between forms, it's essential to identify these components correctly to maintain the equation's integrity.

In point-slope form, an equation of a line is written as y - y1 = m(x - x1), where (x1, y1) is a known point on the line, and m is the slope. This form is particularly useful when you have a point and a slope and need to write the equation of the line.

Answer:

Step-by-step explanation:

factor the trinomial: (3x-1)(2x+1)=0

x = 1/3 or -1/2

Answer:

x = 6

Step-by-step explanation:

The midsegment of a trapezoid is the line parallel to the parallel sides of the trapezoid, which connects the midpoints of the non-parallel sides.

The length of the midsegment of the trapezoid is half the sum of the length of the parallel sides.

i.e,

Length of the midsegment = (1/2) *(Length of base1 + Length of base2)

6x - 24 = (1/2) * (5 + 2x + 7)

12x - 48 = 2x + 12

10x = 60

x=6

∴ x = 6

Answer: The correct answer for number 1. is 11

Answer:

If you round the answer it is 2 miles

Step-by-step explanation:

You multiply the fractions in fraction or decimal form

With decimal form you get 1.995, rounded up to 2

Answer:

2 miles

Step-by-step explanation:

hope this helps

The correct answer is A, 1440 guppies.

Answer:

Option A. 1440 guppies

Step-by-step explanation:

In an appropriate environment, the population of breeding guppies doubles every 2 months.

Initial population of guppies = 180

after 2 months they doubles = 180 × 2 = 360

after 4 months they doubles  = 360 × 2 = 720

after 6 months they doubles again = 720 × 2 = 1440

After 6 months guppies population would be 1440.

Answer:

Option A is correct.

Inequality represents the sale s in dollars:

[tex]0.025s\geq 100[/tex]

[tex]s> 4000[/tex]

Step-by-step explanation:

Let s represents the sales in dollars.

Given :A salesperson at a clothing store earns a commission of 2.5% on all the sales he makes.

Earns a  Commission = 2.5% of s = [tex]\frac{2.5}{100} \times s = \frac{25s}{1000} = 0.025s[/tex]

It is also given that he needs to make to earn a commission of more than $100

then, we have an inequality:

[tex]0.025s\geq 100[/tex]

divide both sides by 0.025 we get;

[tex]s> 4000[/tex]

Therefore, an inequality represents the sales in dollar ; [tex]0.025s\geq 100[/tex] or [tex]s> 4000[/tex]

Answer:

s > 4,000, s > 4,000

Step-by-step explanation:

Since he needs to make $100 the choices that give him $100 or more are correct.

Answer: A bond purchased at $500.00 now has a value of $650.00 what is the percent increase of its value?

To make it simple for you, the final ANSWER is a 30% increase, due to the fact that taking $500.00 and multiplying that by 0.3 gives you 150, which you add on to 500, giving you 650. Hope that helps!

Answer:  The required percent increase in the bond's value is 30%.

Step-by-step explanation:  Given that a bond purchased at $500.00 now has a value of $650.00.

We are to find the percent increase of the value of bond.

According to the given information, we have

Purchasing value of the bond = $500.00

and

present value of the bond = $650.00.

So, increase in the value of the bond = $(650.00 - 500.00) = $150.00.

Therefore, the percent increase of the bond's value is given by

[tex]\dfrac{150.00}{500.00}\times 100\%=\dfrac{3}{10}\times 100\%=30\%.[/tex]

Thus, the required percent increase in the bond's value is 30%.

Answer:

Im assuming youre trying to answer what is the 60% height, it would be 3ft

Step-by-step explanation:

The height of the ball follows a geometric sequence where each subsequent bounce reaches 60% of the height of the previous bounce. The height continues to decrease but does so following a consistent pattern of 60% reduction with each bounce.

The problem presented involves the bouncing of a ball and is described as a geometric sequence because each bounce is a constant ratio (60% or 0.6) of the previous height. To understand this sequence, we need to look at it step by step.

Initially, the ball is dropped from a height of 5ft therefore, the initial height is 5ft. With each subsequent bounce, the ball bounces to 60% of its previous height. The height after the first bounce would be 0.6 times the initial height, which equals to 0.6*5 = 3ft. After the second bounce, the height would be again 60% of the previous height, which calculates to 0.6*3 = 1.8ft. This continues for each subsequent bounce.

So, the height of the ball after each bounce decreases but it follows a constant pattern - every next height is 60%, or 0.6, of the previous one, which is a characteristic of geometric sequences.

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Answer:it’s B

Step-by-step explanation:

Answer:

Answer D. "ASA"

Step-by-step explanation:

Answer:

ASA

Step-by-step explanation:

When looking at the postulates, we need to know what they stand for

SSS, is side side side

SAS is Side angle side

AAS is angle angle side

ASA is Angle side angle  (the side is between the angles)

In the picture we know 2 angles and the included side

so we will use ASA

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Jane mixes 3 pints of blue paint with 4 pints of red paint to get her desired color.

So, the ratio will be

[tex]3:4[/tex]

We have 16 pints of red paint and we have to find the pints of blue paint 'say x'.

According to question,

Since there is "direct variation" . So,our equation becomes,

[tex]\frac{3}{16}=\frac{4}{x}\\\\x=\frac{16\times 4}{3}\\\\x=\frac{64}{3}\\\\x=21.34[/tex]

Hence, Option 'C' is correct.

Answer:

3

4

=  

x

16

given ratio =  

3

4

and,

3

4

=  

12

16

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

i took a test with this question

We want to see which one of the given relations is a function.

The correct options are:

B and C.

To see this, we first need to define what a function is.

A function is a relationship that maps elements from one set, the domain, into another set, the range.

Such that each element in the domain can be mapped into only one element on the range.

The standard notation to these relations is (x, y).

This means that x, from the domain, is being mapped into y, from the range.

Now let's analyze the given options:

A) {3,7,-7,9}

This is just a set of values, no relation there, so this is not a function.

B)  { (3,9), (7,-4), (-7,7) }

Here we have a relation, and we can see that each element on the domain is being mapped into only one element from the range, so this is a function.

C)  { (3,9), (7,-4), (-7,7) }

This is the exact same set as the one on B.

D)  { (3,9), (7,-4), (7,6), (-7,7) }

Here we can see that the element x = 7 is mapped into two different values, so this is not a function.

Then the options that represent functions are B and C.

If you want to learn more, you can read:

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Answer:

P = 124 inches

Step-by-step explanation:

We will need to use the Pythagorean theorem to find the bottom of the rectangle.

a^2 + b^2 = c^2

14^2 + b^2 = 50^2

196 + b^2 = 2500

Subtract 196 from each side

b^2 = 2500 -196

b^2 =2304

Take the square root of each side

sqrt(b^2) =sqrt(2304)

b=48

The perimeter is equal to

P =2(l+w)

P =2(14+48)

  = 2(62)

   = 124

Answer:

Step-by-step explanation:

Any angles on opposite sides of the intersection point of crossing lines are "vertical" angles, and they have identical measure.

Any angles along the same side of the same line are "linear" angles, and they are supplementary (add to 180°).

The angles inside a triangle add to 180°.

Using these relationships, work from the given information to find the rest of the angles.

Answer:

Side DF = 4 units

Step-by-step explanation:

Similar triangles states that the triangles with equal corresponding angles and proportionate sides.

Given: ΔABC and ΔDEF are similar

Corresponding angles are;

[tex]\angle A = \angle D[/tex] ,  

[tex]\angle B = \angle C[/tex] ,

[tex]\angle C= \angle F[/tex]

Proportionate sides are;

[tex]\frac{AB}{DE} =\frac{BC}{EF} =\frac{AC}{DF}[/tex]

It is also given BC = 6 units , EF = 8 units and DF -AC = 1

Let AC = x units then;

DF = x +1 units.

Then, by definition of similar triangle ;

[tex]\frac{BC}{EF} =\frac{AC}{DF}[/tex]

[tex]\frac{6}{8} =\frac{x}{x+1}[/tex]

By cross multiply we have;

[tex]6(x+1) = 8x[/tex]

Using distributive property;  [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]

6x + 6 = 8x

Subtract 6x on both sides we get;

6x + 6 -6x = 8x -6x

Simplify:

6 = 2x

Divide by 2 on both sides we get;

x = 3

DF = x +1  = 3+1 = 4

Therefore, the side DF is, 4 units

Answer: 200 messages

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Plan A's cost equation is y = 0.10x + 30

Plan B's cost equation is y = 50

Equate the two right hand sides, then solve for x

0.10x + 30 = 50

0.10x = 50-30

0.10x = 20

x = 20/0.10

x = 200

If you send/receive 200 messages, then the two plans will both cost the same ($50) per month.

Answer:

Therefore, the correct option is OPTION C.

Step-by-step explanation:

If Orlando had not made his early withdrawal, the amount of money he would have earned is:

F = 0.065($16,000)(8) = $8.320

Given that he withdraw $3500, he now earns:

F1 = (0.065)($16,000)(5) + ($12,500)(0.065)(3)

F1 = $5200 + $2437.5 = $7637.5

And now we have to take into acount the year of penalty, which is one year’s worth of interest on the amount withdrawn.

Penalty= $3500(0.065)(1) = $227.5

So the total money he earns now is: $7637.5 - $227.5 = $7410

Then, the amunt of money he could have earn but he didn't is:

Money = $8.320 - $7410 = $910

Therefore, the correct option is OPTION C.

Answer:

Its C

Step-by-step explanation:

Answer:

D) Only (-1,9) is a solution.

Step-by-step explanation:

x+y =8

x^2 + y = 10

Lets check the first point (-1,9)

Put in x =-1 y =9

x+y =8

-1+9 = 8

8 =8

This works

x^2 + y = 10

(-1)^2 +9 =10

1+9 = 10

10 = 10

This works

Lets check the second point (-2,6)

Put in x =-2 y =6

x+y =8

-2+6 = 8

4=8

This  does not work

We can stop now.  (-2,6) cannot be a solution

After substituting the given pairs into both equations, only the pair (-1,9) satisfies the system of equations, meaning Only (-1,9) is a solution (D).

To determine if the given pairs (-1,9) and (-2,6) are solutions to the system of equations x + y = 8 and x² + y = 10, we need to plug the x and y values from each pair into the equations and check for their validity.

Checking Pair (-1,9):

For the first equation:

For the second equation:

Checking Pair (-2,6):

For the first equation:

For the second equation, the check is unnecessary as the pair already failed the first equation.

Therefore, the correct answer is D) Only (-1,9) is a solution.

Answer:

   = 11.4%

Step-by-step explanation:

Percent error = (target - actual)/target * 100

target = 2500

actual = 2215

Lets substitute in

Percent error = (2500-2215)/2500 * 100

                        = 285/2500*100

                       =.114 * 100

                      = 11.4%

Answer:

11.4%

Step-by-step explanation: