The princess traces one plant’s roots to discover that it has exactly 5 roots. One of the roots she can trace to 2−3√5. At least two of the roots are the same and labeled −4.

What conclusions can the princess draw about the other two roots?

There may be more than one correct answer. Select all correct answers.

-One of the other roots is 2+ 3√5
-One of the other roots could be another −4.
-One of the other roots could be another 2− 3√5
-One of the other roots is 3+ 2√5
-One of the other roots is 3− 2√5

C'(2, 3 )

under a counterclockwise rotation about the origin

a point (x, y ) → (- y, x ) hence

C(3, - 2 ) → C'(2, 3 )

Answer:

C' (2, 3)

Step-by-step explanation:

Remember that when you are rotating something 90 degrees and counter clockwise you just need to interchange the X and Y values, and change the value of the new X to a negative position because it woul be located in the second quarter:

(x,y) rotated 90º counter clockwise= (-y,x)

(3,-2)=(-(y),x)=(-(-2),(3)=(2,3)

So the answer would be C' (2, 3)

to answer this question, you would need the Least Common Denominator.

6, 12, 18, 24, 30

10, 20, 30

So the LCD, Least Common Denominator, is 30.

How many packs of hot dogs did he buy?

5 packs.

How many packs of buns did he buy?

3 packs.

How many hot dogs did he buy?

30 hot dogs.

Hoped this helped,

-Anime

Answer: option. y=-1.33x; 2.67

Solution:

If y varies directly with x, the relation between y and x is:

y=kx

where k is a constant of proporcionality.

We know y=8 when x=-6. Replacing these values in the equation above:

8=k(-6)

8=-6k

Solving for k: Dividing both sides of the equation by -6:

8/(-6)=-6k/(-6)

-1.33=k

k=-1.33

Then the relation between y and x is:

y=kx→y=-1.33x

What is the value of y when x=-2?

Replacing x by -2 in the formula:

y=-1.33x→y=-1.33(-2)→y=2.66

Here we need to find the average rate of change of [tex]f(x)[/tex].

Now,

[tex]f(x)=-2x^2+4x+2[/tex]

Let us find out the value of [tex]f(x)[/tex] at the point [tex]x=1.2[/tex].

Plugging [tex]x=1.2[/tex] in the equation we get:

[tex]f(1.2)=-2(1.2)^2+4(1.2)+2=-2\times 1.44+4.8+2=-2.88+4.8+2=3.92[/tex]

So,

[tex]f(1.2)=3.92[/tex]

Now calculating the value of [tex]f(x)[/tex] at [tex]x=3.8[/tex].

[tex]f(3.8)=-2(3.8)^2+4(3.8)+2=-2(14.44)+15.2+2=-28.88+15.2+2=-11.68[/tex]

So,

[tex]f(3.8)=-11.68[/tex]

Now that we have the values of the function at two distinct points, we can find the average by using the formula given below:

[tex]Avg= \frac{sum}{n}[/tex], where 'n' represents the number of values and that is two in our case and sum represents the sum of the values of the function.

Therefore,

[tex]Avg= \frac{3.92+(-11.68)}{2} =\frac{-7.76}{2} =-3.88[/tex]

So, the average rate of change of the function [tex]f(x)[/tex] from 1.2 to 3.8 is [tex]-3.88[/tex].

she needs to count how much 90% is so

85.00 times 90%

or 8500 times 0.9

Answer:

B) .95(53.75)

Step-by-step explanation:

5% is equal to 0.05. So the following expressions are equivalent.

5% × 53.75 = 0.05 × 53.75

To find the final price, she first takes the 5% and then subtracts the amount from 53.75. That is,

53.75 - 5% × 53.75 = 53.75 - 0.05 × 53.75

We can take out the common factor 53.75

53.75 . (1 - 0.05) = 53.75 . 0.95 = 0.95 . 53.75 = 0.95 (53.75)

Here we are given the inequality:

[tex]y\geq4x-5[/tex]

Let us check for each ordered pair that satisfies the given inequality.

1. (3,0)

LHS: y

here y is 0.

So LHS is 0.

RHS: 4x-5

plugging x as 3,

4(3)-5 = 7

0≥7

False

So (3,0) does not satisfy the inequality.

2. (1,1)

LHS: y

here y is 1.

So LHS is 1.

RHS: 4x-5

plugging x as 1,

4(1)-5 = -1

1≥-1

True

So (1,1)  satisfy the inequality.

1. (3,4)

LHS: y

here y is 4.

So LHS is 4.

RHS: 4x-5

plugging x as 3,

4(3)-5 = 7

4≥7

False

So (3,4) does not satisfy the inequality.

1. (2,1)

LHS: y

here y is 1.

So LHS is 1.

RHS: 4x-5

plugging x as 2,

4(2)-5 = 3

2≥3

False

So (2,1) does not satisfy the inequality.

Answer: (1,1) is the solution of the given inequality.

Since all triangles in these questions are similar, we use that the ratios of corresponding sides are equal

(1)

[tex]\frac{y}{6}[/tex] = [tex]\frac{9}{x}[/tex] = [tex]\frac{5}{4}[/tex]

solving [tex]\frac{9}{x}[/tex] = [tex]\frac{5}{4}[/tex] ( cross-multiply )

5x = 36 ( divide both sides by 5 )

x = [tex]\frac{36}{5}[/tex]

solving [tex]\frac{y}{6}[/tex] = [tex]\frac{5}{4}[/tex]

4y = 30 ⇒ y = [tex]\frac{15}{2}[/tex]

(2)

let h be the height of the flagpole, then

[tex]\frac{h}{5.5}[/tex] = [tex]\frac{50}{4}[/tex]

4h = 275 ⇒ h = 68.75 feet

(3)

[tex]\frac{x}{6}[/tex] = [tex]\frac{93.5}{12.75}[/tex]

12.75x = 561 ⇒ x = 44 feet

The correct answer is option B.

Let the basic calendars be = x

Let the deluxe calendars be = y

Total calendars are = 72 , so equation becomes:

[tex]x+y=72[/tex]  .............(1)

Cost of 1 basic calendar = $10

So, cost of all basic calendars will be = 10x

Cost if 1 deluxe calendar = $15

So, cost of all deluxe calendars = 15y

As given, the number of deluxe calendars must be greater than or equal to 3 times the number of basic calendars, the equation becomes

y=3x ...............(2)

Putting the value of y from (2) in (1)

[tex]x+y=72[/tex]

[tex]x+3x=72[/tex]

[tex]4x=72[/tex]

x=18

As, y=3x

y=[tex]3\times18=54[/tex]

So we have 18 basic calendars and 54 deluxe calendars.

Cost of 18 basic calendars will be= [tex]18\times10=180[/tex]

Cost of 54 deluxe calendars will be = [tex]54\times15=810[/tex]

So total amount is = $990

Hence, the maximum revenue is $990.

Answer:

The CORRECT answer is $1080

Step-by-step explanation:

Your answer would be choice C

The distributive property tells you the product is found by multiplying each term inside parentheses by the factor outside.

... 4 -6n = 8n +8·7

... 4 = 14n +56 . . . . . . . add 6n to both sides

... -52 = 14n . . . . . . . . . subtract 56 from both sides

... -52/14 = -26/7 = n . . . divide by 14, reduce the fraction

The solution is ...

... n = -26/7 = -3 5/7

Answer:

The vertices are (0,0), (3,0), (1.5,2) and (0,2.5)

Step-by-step explanation:

We are given the constraints of the problem as,

[tex]4x+3y\leq 12[/tex]

[tex]2x+6y\leq 15[/tex]

[tex]x\geq 0[/tex]

[tex]y\geq 0[/tex]

Using 'Zero Test', which states 'If after substituting (0,0) in the inequalities the result is true, the solution region is towards the origin and if the result is false, the solution region is away from the origin'

So, after plotting the graph, we see that,

The end-points of the feasible region are given by,

(0,0), (3,0), (1.5,2) and (0,2.5)

Answer:

A (0, 0), (0, 2.5), (1.5, 2), (3, 0)

Step-by-step explanation:

edg 2022

Answer:

a

Step-by-step explanation:

If you divide by 8, you can put the equation into intercept form. That form is ...

... x/a + y/b = 1

where a and b are the x- and y-intercepts, respectively.

Here, your equation would be

... x/(-2) + y/(-4) = 0

The graph with those intercepts is not shown with your problem statement here. See the attachment for the graph.

The correct answers are;

A. [tex]3x^{2} =9[/tex]

C. [tex]4x^{2} =16[/tex]

E. [tex]13x^{2} =169[/tex]

F. [tex]25x^{2} =625[/tex]

Hope this helps!!!!

The numbers that are perfect squares include 9, 16, 169, and 625.

In conclusion, the numbers that are perfect squares include 9, 16, 169, and 625.

Learn more about square on:

https://brainly.com/question/8422946

y = 4

first note that the right side simplifies to 12, equation can be written

[tex]\frac{2y+1.6}{0.8}[/tex] = 12 ( multiply both sides by 0.8 )

2y + 1.6 = 9.6 ( subtract 1.6 from both sides )

2y = 8 ( divide both sides by 2 )

y = 4

Hey there!!

We have:

... (2y+1.6)/0.8 = 30/2.5

... (2y+1.6)/0.8 = 12

Multiplying 0.8 on both sides.

... (2y+1.6) = 12×0.8

... 2y+1.6 = 9.6

Subtracting 1.6 on both sides:

... 2y = 9.6-1.6

... 2y = 8

Dividing by 2 on both sides:

... y = 8/2

... y = 4

Hence, the required answer is 4.

Hope my answer helps

Answer:

204 students

just do 7140/35= 204

Step-by-step explanation:

Number of students who can get craft sticks are 204 .

To determine how many students can get craft sticks from the teacher, we need to divide the total number of craft sticks by the number of craft sticks each student needs.

Step-by-Step Solution

The total number of craft sticks is 7,140.

Each student needs 35 craft sticks.

To find out how many students can get the craft sticks, divide the total number of craft sticks by the number of craft sticks each student needs:

7,140 ÷ 35 = 204

Therefore, 204 students can get craft sticks from the teacher.

Estimation and Checking

To estimate the quotient, you can round the numbers to make the division easier. For example, round 7,140 to 7,000 and 35 to 30:

7,000 ÷ 30 ≈ 233.33

This estimation tells us that our division answer is reasonable, falling close to this rounded solution.

To check the division, multiply the quotient by the divisor and see if you get the original dividend:

204 × 35 = 7,140

Since the result matches the original number of craft sticks, the answer is verified as correct.

since both points have a y- coordinate of zero, this is a horizontal line parallel to the x- axis

hence slope = 0

We want to find the slope of a line given that we know two points on the line.

We will see that the slope of the line is 0.

Generally, if we know that a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we know that the line passes through (-4, 0) and (2, 0) then the slope will be:

[tex]a = \frac{0 - 0}{2 - (-4)} = 0[/tex]

The slope is equal to zero, meaning that this is a horizontal line (as you can see in the points, the y-component does not change).

If you want to learn more, you can read:

https://brainly.com/question/16180119

Dana wants to find the sum

  3 4 6

  4 2 1

+1 5 2

________

We will not regroup this ones place because the sum of the digits in the ones place is not up to. It's just 6+1+2 = 9.

Therefore, 13a) No.

There is no regrouped tens to add, so we would not able to regroup the ones place.

Therefore, 13b) No.

We regroup the tens place because the sum of the digits in the ones place is upto to 10.

And 13c) Yes.

We add the regrouped hundred as we regrouped the ones place.

Therefore,

13 D) Yes.

Since, there are 6 science fiction stories, 4 adventure stories, 3 historical stories and 2 sport stories.

So, total number of stories = 6+4+3+2 = 15 stories

Probability that Artie selects a science fiction story = [tex]\frac{6}{15}[/tex]

Probability that Artie selects an adventure story = [tex]\frac{4}{15}[/tex]

Probability that story selected is either a science fiction or adventure fiction = P(Science) + P(Adventure)

= [tex]\frac{6}{15} + \frac{4}{15}[/tex]

= [tex]\frac{10}{15}[/tex]

= 0.66

=0.67

Therefore, the probability that the story Artie selects is either a science fiction story or an adventure story is 0.67.

Answer:Probability of selecting either A or B P(A∩B)=2/3.

Step-by-step explanation:

Total number of story books=6+4+3+2=15

Let A be the event of selecting science fiction story

then its probability P(A)=number of science stories/total stories=6/15

Now let B be the event of selecting adventure story P(B)=number of adventure stories/total stories

=4/15

thus Probability of selecting either A or B P(A∩B)=P(A)+P(B)=6/15+4/15=10/15=2/3.

Answer: The number of pages in the U.S. tax code x=20000 and the number of pages in the King James Bible y = 1472

Step-by-step explanation:

Let the number of pages in the U.S. tax code be x and the number of pages in the King James Bible be y.

According to the given problem , we have the following system

x - y = 18528    ..............(1)

x + y = 21472     ..............(2)

Adding (1) and (2) , we get

2x = 18528 +21472 = 40000

⇒ 2x =40000

⇒ x =20000

Putting value of x = 20000 in (2) ,we get

20000 + y =21472

⇒ y = 1472

Ans  the number of pages in the U.S. tax code x=20000 and the number of pages in the King James Bible y = 1472

Final answer:

By setting up an equation and solving for B, which represents the number of pages in the Bible, it is determined that the King James Bible has 1,472 pages.

Explanation:

To determine how many pages are in the King James Bible, we need to set up an equation based on the information given in the problem. We know that the number of pages in the U.S. tax code exceeds the number of pages in the King James Bible by 18,528 and the combined total of pages in both the tax code and the Bible is 21,472.

Let's let B represent the number of pages in the Bible. Then the number of pages in the U.S. tax code would be B + 18,528. The total number of pages in both is given to be 21,472, so we can write the following equation:

B + (B + 18,528) = 21,472

Simplifying the equation, we get:

2B + 18,528 = 21,472

Subtract 18,528 from both sides to get the number of pages in the Bible:

2B = 2,944

Divide by 2 to solve for B:

B = 1,472

Therefore, the King James Bible has 1,472 pages.

Answer:

$75.19

Step-by-step explanation:

Let 'x' be the cost of remote keyless entry.

And [tex]8x[/tex] be the cost of 4-way power front passenger seat.

Total cost = destination charge + title fee + taxes

So we have the equation:

[tex]20,000 = (17,980+x+8x)+0.072(17,980+x+8x)[/tex]

Now solving for 'x', we get:

[tex]20,000 = (17,980+9x)+0.072(17,980+9x)[/tex]

[tex]20,000=17,980+9x+1294.56+0.648x[/tex]

[tex]20,000=19274.56+9.648x[/tex]

[tex]725.44=9.648x[/tex]

[tex]x=\frac{725.44}{9.648} =75.19[/tex]

Therefore, the cost of remote keyless entry is $75.19.

Answer:

$601.53

Step-by-step explanation:

just do what the person did but all they forgot to do was to multiple for the "8 times" so take 75.19*8 to get 601.53.

Answer:

B) x = -1 and x = 6

Step-by-step explanation:

The values that must be excluded from the domain are the values for which f(x) is undefined. Those values are the ones that make the denominator be zero.

We can find the zeros of the denominator by factoring.

... x² -5x -6 = (x +1)(x -6)

The product is zero when either factor is zero, so when x=-1 or x=6.

Answer:

c

Step-by-step explanation:

-2 & 6

Answer:

The distance between these two is 3 3/5

Step-by-step explanation:

In order to find the distance between two points, we subtract one from the other. Then if the result is negative, we take the absolute value.

2 3/5 - -1

2 3/5 + 1

3 3/5

1. a= 60 (vertically opposite angles)

b= 360-(60+60)=240/2= 120 (angles at a point)

c= 120 (vertically opposite angles with b)

2. c= 90-40= 50 (vertically opposite angles)

b=a=360-90-90=180/2=90 (angles at a point)

3. a= 180-52-51= 77 (angles on a straight line)

b=52 (angles at a point)

d=51 (angles at a point)

c=77 (angles at a point)

4. a= 60 (vertically opposite angles)

b= 360-(60+60)=240/2= 120 (angles at a point)

c= 120 (vertically opposite angles with b)

e=65

d=f= 360-65-65=230/2=115

h=55

i=g=360-55-55=250/2=125

5. b=163

a=90

e=70

d=360-70-70=220/2=110

c=360-163-163=34/2=17

Hope this helps!

Yes, the S. A. S. postulate is correct, because his proof stated two sides and the angle between those sides are congruent.

You're right. There is nothing in the text about a third side or a second angle, and doesn't say anything about the hypotenuse.

Answer:

137.4 feet

Step-by-step explanation:

Consider the attached diagram. The given angle of depression from the lighthouse to the boat is the same as the angle of elevation from the boat to the lighthouse. The trig relationship for tangent tells you ...

... tan(20°) = opposite/adjacent = AL/AB = 50'/AB

Solving for AB, we get

... AB = 50'/tan(20°) ≈ 50'/0.36397

... AB ≈ 137.4'

Answer:

137.373871

Rounded to the 10th place

137.4

Rounded to the whole number

137

Step-by-step explanation:

There are a few methods for solving this type of problem. Please view the images I have provided. I gave two methods for solving this problem.

Answer:

20%

Step-by-step explanation:

i did it and got it right

the picture is my evidence.

Assuming that you meant "11 plus 1/6" written as the equivalent decimal expression, then it'd be 11.16666....     Here the 6 repeats indefinitely.

Answer:

Rational

Step-by-step explanation:

Any number you can write out completely, or that has a repeating decimal fraction, is a rational number. 291.7 is the entire number, so is rational.

√61 ≈ 7.8

√101 ≈ 10.05

The integers between these numbers are 8, 9, 10. The product of these is 720.

It's a 3rd grade problem in addition and subtraction, or number lines. As a college-level problem, it might be described as ...

... a part-whole problem, because the length of the third table is part of the total length of the long table