Mackenzie wrote the following paragraph proof for the Vertical Angles Theorem: Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles. The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 _________________. Angle 1 is equal to angle 3 by the subtraction property of equality. Which phrase completes the proof? by construction using a straightedge by the definition of a perpendicular bisector by the transitive property of equality. by the vertical angles theorem

Answer:

3.60 pounds

Step-by-step explanation:

exchange rate of 1:.6 meaning .60 6 times,

2 is 1.20, 4 would be 2.40, meaning 6 is 3.60 pounds

Answer:

Step-by-step explanation:

Given is a function

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

This function is a parabola with vertex at (2,0) and axis of symmetry is x=2

Hence for x<2 the curve would be reflection of x>2

To get inverse we must get one to one funciton only.

So restrict the domain of f(x) to [tex][2,∞)[/tex]

Then we have f(x) as one to one with domain x≥2 and range is R+

[tex]f^{-1} (x)=+\sqrt{x} +2[/tex]

For this inverse domain is R+ and range is [tex][2,∞)[/tex]

Answer:

restriction of domain is x>=2

[tex]f^{-1}=\sqrt{x}+2[/tex]

Step-by-step explanation:

Restrict the domain of the function  [tex]f(x)=(x-2)^2[/tex] so it has an inverse

To restrict the domain we find the vertex

VErtex form of the equation is

[tex]y=(x-h)^2+k[/tex] vertex is (h,k). restriction of domain is x>=h

[tex]f(x)=(x-2)^2+0[/tex] , vertex is (2,0)

So restriction of domain is x>=2

now we find inverse function

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

Replace f(x) with y

[tex]y=(x-2)^2[/tex]

Replace x with y and y with x

[tex]x=(y-2)^2[/tex]

To remove square we take square root on both sides

[tex]\sqrt{x} =y-2[/tex]

Add 2 on both sides

[tex]\sqrt{x}+2 =y[/tex]

[tex]f^{-1}=\sqrt{x}+2[/tex]

Answer:

[tex]R-5=2C[/tex]

Step-by-step explanation:

Let C be the number of apps that Cora have.

We are told that Rita stared the day with R apps. Then she deleted 5 apps. So Rita is left with R-5 apps.

We are also told that after deleting 5 apps Rita still had twice as many apps as Cora has. We can represents this information as:

[tex]R-5=2C[/tex]

Therefore, the equation [tex]R-5=2C[/tex] represents the number of apps each girl has.

Answer:

Rita :R = 2C+5

Cora: C = (R-5)/2

Step-by-step explanation:

Hi, to answer this question we have to write an equation.

Rita has R apps and deletes 5, it means we have to subtract 5 to R. (R-5)

After that she has twice as many apps as Cora has. So, the previous expression is equal to the number of apps that Cora has (C) multiplied by 2.  

The whole equation:  

2C = R-5

For each girl we have to solve for each variable:

Rita's apps:  

2C = R-5

2C+5 =R

R = 2C+5

Cora's apps:

2C = R-5

C = (R-5)/2

2,8   2+8=10

4,6    4+6=10

Can’t be more than 10$’s. The multiples of 2 are 2,4,6,8,10. So you’re answering which 2 numbers add up to 10$. If it’s anything higher than that it’s not a possible price and if it’s lower than that then she would have payed less which also isn’t possible.

Answer: 93

Step-by-step explanation:

NOTE: "won" means add, "spent" means subtract

Monday: + 75

Tuesday: Monday + 105   = 75 + 105   = 180

Wednesday: Tuesday + 127 - 250   =   180 + 127 - 250   = 57

Jared has 57 but needs 150

(75+105)+127= 307

307-250=57

jared has 57 tickets he wants to 150 ticket prize

57-150=93

Jared needs 93 tickets to get the prize

Answer:

L is perpendicular to N

Step-by-step explanation:

M is perpendicular to N

L ll M

We can replace M with L since  they are parallel

L is perpendicular to N

Answer:

Option C

Step-by-step explanation:

It is given that M is perpendicular to N and L ║ M

Since M ║L

and N is perpendicular to line M So L will be perpendicular to N.

That means N will be perpendicular transverse of both the parallel lines M and L

Option C is the answer.

Answer:

[tex]t(c)=\frac{t-10}{8}[/tex] determines the time you used the kayak for at a specific cost you paid.

Step-by-step explanation:

The inverse of a function, is the function or rule formed by reflecting the line over y=x. This means essentially that all (x,y) values from the original function switch to (y,x).

(x,y)--->(y,x) in the new function.

If the function has points (-3,4) and (5,-2) then the inverse has points (4,-3) and (-2, 5).

For the original function, we used the time we had the kayak to compute the cost. For 3 hours, it cost c(3)=8(3)+10=$34. (3,34) for (t,c).

For the inverse, we will find the time we had the kayak for a specific cost. To write it we switch input(x) and output(y) and solve for y.

y=8x+10

x=8y+10

x-10=8y

[tex]\frac{x-10}{8} =y[/tex]

This is the inverse function, We replace (x,y) with (c,t).

[tex]t(c)=\frac{t-10}{8}[/tex]

Wanna try 40?

Step-by-step explanation:

To find the distance between Monica and Gina, the Pythagorean theorem is used because they form a right-angle triangle with Jodie. Calculating the hypotenuse of this triangle with sides of 6 and 7 meters results in a distance of approximately 9.2 meters between Monica and Gina.

The student has asked to find the distance between Monica and Gina, given the positions of three ballet dancers on stage. This problem can be solved using the Pythagorean theorem because Monica, Jodie, and Gina form a right-angle triangle on stage. Monica is behind Jodie and to the left of Gina, meaning that the line segment between Jodie and Monica is one leg of the right triangle, and the line segment between Jodie and Gina is the other leg of the triangle.

To find the distance between Monica and Gina, which is the hypotenuse of the right triangle, we apply the Pythagorean theorem (where d is the distance between Monica and Gina):

Therefore, the distance between Monica and Gina is approximately 9.2 meters.

Carmen can buy 4 tubes of paint at $4.80 each after purchasing 2 paint brushes at $6.70 each from her $35 winnings.

Carmen won a prize of $35 in a contest. To answer how many tubes of her favorite paint brand she can buy, first, we need to deduct the cost of the two paint brushes she needs, which are $6.70 each. The total cost for two brushes is:

2 brushes x $6.70 per brush = $13.40

Subtracting this amount from her winnings:

$35.00 - $13.40 = $21.60 remaining

Now, we divide the remaining money by the cost of each tube of paint, which is $4.80, to find out how many tubes she can purchase:

$21.60 / $4.80 per tube = 4.5 tubes

Since Carmen cannot buy half a tube, she can buy 4 tubes of paint and will have some money remaining.

Answer:

679959

Step-by-step explanation:

THE ANSWER IS 679959 BUT IF YOU ESTIMATE TO THE LAST DIGIT THE IT WOULD BE 700000 DUE TO 9 ROUNDING THE 7 TO A 8 AND THEN 8 EOUNDS THE 6 TO A 7 EVERYTHING ELSE BECOMES 0

To estimate 5,271 x 129, we round to the closest thousands and hundreds giving us 5,000 x 100, which equals 500,000. This is an estimation, the actual product of 5,271 and 129 is 679,859.

To estimate the product of 5,271 x 129, we can round each number to the nearest thousands and hundreds respectively. So, 5,271 can be rounded to 5,000 and 129 can be rounded to 100. Our estimation would then be 5,000 x 100 = 500,000.

Remember that this is an estimation. The actual product of 5,271 and 129 is 679,859, but for quick mental calculations or to get a sense of the size of the result, this type of estimation can be helpful.

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Answer:

im pretty sure its 1b 2a 3d 4c for the first row... if im reading it right. second row is 5c 6b 7a 8d i think. third row is 9b 10d 11a 12c. hope it helped :)

Step-by-step explanation:

i just plugged the functions into the y= in the calculator. i have the ti-84 plus ce calculator, but if you dont you can use one online

Answer:

The correct step will be [tex]5(\sqrt{164})=5(\sqrt{4*41})[/tex]

Step-by-step explanation:

We have been given that pond A has a radius of [tex]5\sqrt{(164)}[/tex] meters and radius of Pond B is [tex]\frac{(25\sqrt{200)}}{5}[/tex] meters. Todd simplifies the radius of pond A and we are asked to find out error in Todd's steps.

Step 1: [tex]5(\sqrt{100}+\sqrt{64})[/tex]

Since we know that [tex]\sqrt{ab}=\sqrt{a\times b}=\sqrt{a} \times \sqrt{b}[/tex]. We can see that Todd has made error in his very first step by splitting [tex]\sqrt{164}[/tex] as [tex]\sqrt{100+64}[/tex].

The correct step will be,

[tex]5(\sqrt{164})=5(\sqrt{4*41})[/tex]  

Therefore, the correct step 1 will be: [tex]5(\sqrt{4*41})[/tex].  

Now let us simplify our given radical expression.

[tex]5(\sqrt{4*41})=5(\sqrt{4}*\sqrt{41})[/tex]  

[tex]5\sqrt{4}*\sqrt{41}=5*2*\sqrt{41}[/tex]  

[tex]5*2*\sqrt{41}=10*\sqrt{41}[/tex]  

Therefore, our given radical expression simplifies to [tex]10*\sqrt{41}[/tex] meters.

The incorrect step in Todd's simplification is Step 1, which inaccurately breaks apart the square root of 164.

The step in Todd's simplification of the radius of Pond A that is incorrect is Step 1:

Incorrect Step 1: [tex]5(\sqrt{} 100 + \sqrt{ 64)[/tex]

This is incorrect because it suggests that √164 can be simplifed directly into the sum of the square roots of its components, which is not how square roots work.

The correct step should involve finding the prime factorization of 164 and then simplifying the square root.

Corrected Step 1: [tex]5\sqrt{} (4 x 41)[/tex]

Corrected Step 2: [tex]5(2\sqrt{} 41)[/tex]

Corrected Step 3: [tex]10\sqrt{} 41[/tex]

The fully simplified form of [tex]5\sqrt{} 164[/tex] meters would be [tex]10\sqrt{} 41[/tex] meters.

Answer:

the answer is B 2x-7

Step-by-step explanation:

-1 ║ 2               9                  7

                       -2                 -7

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

      2                7                  0

⇒ The Quotient is 2x + 7

Answer:

C.) if not b, then not a

Step-by-step explanation:

The formula for a contrapositive is:

a -> b to -b -> -a

Answer: I believe

the answer is C.

Step-by-step explanation:

Answer:

[tex]p=4h[/tex]    

Step-by-step explanation:

Let p be the number of trees Wangari plants, and h  be the time she spends planting them in hours.

We have been given that Wangari plants trees at a constant rate of 12 trees every 3 hours.    

Let us find number of trees planted in 1 hour by dividing 12 by 3.

[tex]\text{Number of trees planted in 1 hour}=\frac{12\text{ plants}}{3\text{ hour}}[/tex]

[tex]\text{Number of trees planted in 1 hour}=4\frac{\text{ plants}}{\text{ hour}}[/tex]

We can represent this information as: [tex]p=4h[/tex]

Therefore, the equation [tex]p=4h[/tex] relates the number of trees (p) Wangari plants, and the time (h) she spends planting them in hours.

Answer:

p=4h

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

A simple example would be picking  3 marbles ( of equal size) from a bag of 10 marbles previously shaken.

A simple random sample, by definition, is any sample selected in a manner that ensures every individual in the population has an equal chance of being selected. This method is commonly used in statistical studies and surveys to prevent bias and more accurately represent the larger population.

True, by definition, a simple random sample of size n is, indeed, any sample that is selected in a manner that guarantees every individual in the population an equal chance of being selected. This method is akin to drawing names out of a hat or using a random number generator, ensuring that all members of the population have an equal chance of selection. This approach is commonly implemented in statistical studies and surveys to avoid bias and to ensure that the sample accurately represents the broader population.

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The ratio of boys to girls is 2:3, which means for every 2 boys there are 3 girls.

There are 8 boys.

Divide the number of boys by 2 ( their ratio):

8/2 = 4

Multiply that by the part of the ratio for girls:

4 x 3 = 12

There are 12 girls

Answer:

Properties of isosceles triangle:

As per the given statement:

Congruent sides(a) = 3 feet And Vertex angle([tex]\angle QPR[/tex]) = [tex]35^{\circ}[/tex]

Let the length of the base(QR) of an isosceles triangle PQR be 2b.

By isosceles properties, in triangle PQR , the median of an isosceles triangle from its vertex angle is also the perpendicular bisector of the base.

Also, this  line divides the triangle into two congruent right angled triangles whose hypotenuse is 3 feet,

and  [tex]\angle QPS = \frac{\angle QPR}{2} = \frac{35}{2} = 17.5^{\circ}[/tex]

In a right angle triangle QSP

Using sine ratio formula;

[tex]\sin \theta = \frac{\text{opposite side}}{\text{Hypotenuse side}}[/tex]

Hypotenuse sides = PQ = 3 ft and Opposite side = QS = b ft

Solve for b using using sine ratio:

[tex]\sin (17.5^{\circ}) = \frac{b}{3}[/tex]

or

[tex]b = 3 \cdot \sin(17.5^{\circ})[/tex]

[tex]b = 3 \cdot 0.3007057995[/tex]

Simplify:

b = 0.902117398

Length of the base of an isosceles triangle PQR =  2b = 2(0.902117398) = 1.8042348

Therefore, the approximate length of the base of an isosceles triangle is, 1.8 feet

Answer:

 1.80 feet.

Step-by-step explanation:          

Please see the attachment.

Let c be the length of base of our given triangle.

We have been given that an isosceles triangle's congruent sides are 3 feet the vertex angle is 35 degrees. We are asked to find the length of the base of isosceles triangle.      

We will use law of cosine to find the length of our base.

[tex]c=\sqrt{a^2+b^2-2ab\text{ Cos(C)}}[/tex]

Upon substituting our given values in above formula we will get,

[tex]c=\sqrt{3^2+3^2-2\times 3\times 3\times\text{ Cos(35)}}[/tex]

[tex]c=\sqrt{9+9-18\times\text{ Cos(35)}}[/tex]

[tex]c=\sqrt{18-18\times 0.819152044289}[/tex]

[tex]c=\sqrt{18-14.744736797202}[/tex]

[tex]c=\sqrt{3.255263202798}[/tex]

[tex]c=1.8042347970255978\approx 1.80[/tex]

Therefore, the length of base of our given isosceles triangle is approximately 1.80 feet.

Yes it is possible for a geometric sequence to not outgrow an arithmetic one, but only if the common ratio r is restricted by this inequality: 0 < r < 1

Consider the arithmetic sequence an = 9 + 2(n-1). We start at 9 and increment (or increase) by 2 each time. This goes on forever to generate the successive terms.

In the geometric sequence an = 4*(0.5)^(n-1), we start at 4 and multiply each term by 0.5, so the next term would be 2, then after that would be 1, etc. This sequence steadily gets closer to 0 but never actually gets there. We can say that this is a strictly decreasing sequence.

If your teacher insists that the geometric sequence must be strictly increasing, then at some point the geometric sequence will overtake the arithmetic one. This is due to the nature that exponential growth functions grow faster compared to linear functions with positive slope.

Answer:

160 Sodas

80 Hot Dogs

Step-by-step explanation:

240=2x+x Given

240=3x Simplify

80=x Divide by 3

Now you would plug in the variable to solve

2(80) or 160 Sodas

(80) Hot Dogs

Answer:

The main difference between an observational study and an experiment is the inclusion of a random sample.

Step-by-step explanation:

In an observational study, the researchers do not interfere with the method the data is collected. In an investigation of how regularly the studying improves marks, the researchers sample people from the population who has studied regularly and those who haven't and then collect the average marks obtained by each of the groups. We can only accomplish an association among the response variable and the explanatory variables because there may be some other variable that may affect both the explanatory and the response variable, thus making it look as if there is a relationship among them.

But in an Experiment, the researchers actually interfere with the method the data is collected. In an experiment, each case is randomly assigned to the treatment groups, i.e. to say that each of the cases has an equal chance of being in both groups. These kinds of studies help us to establish causal connections between the response variable and the explanatory variables because random assignment makes sure that they are equally spread among both the groups.

So, the primary difference between an observational study and an experiment is that in case of an observational study there is no random assignment but in case of an experiment there is a random assignment.

Answer:

d^3 - 12d^2 b + 48db^2 - 64b^3

Step-by-step explanation:

(d - 4b)^3

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

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

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

Explanation

The general term of the binomial expansion is

Combination

[n! / (n - k)! k! ]

This means for the second term that k = 2 and n = 3

So the expansion becomes

3!/(3 - 1)!*1!

3!/1! 2!

3

Descending powers

In the second term

k = 1 ; n = 3

d^(n - k)*(-4b)^k

d^(3-1 ) * (- 4b)^(1)

d^2 * (-4b)^1

- 4 d^2 * b

Of course you have to put this together with the three

- 12 d^2 * b^1 or - 12d^2b

I know this looks awful (and it really is) but if you want the 5th term of (a - 2b)^10, you would go crazy trying to do this by expanding the binomial 10 times. So practice every one of these. Eventually it becomes mechanical. Mr. Miagi (karate kid) would say "Teacher teach. Pupil do."

Answer:

d^3 - 12d^2 b + 48db^2 - 64b^3

(d - 4b)^3

First term: [3!/(3 - 0!)*0!] = 3!/(3!)*1 = 1

1*d^(3 - 0)*(4b)^0

1*d^(3)*(4b)^0

1*d^(3)=d^(3)

d^(3)*(4b)^0

d^3

Second Term 3!/(3 -1 )!*1! * d^(3-1)*(-4b)^1

Second term 3 * d^2*(-4b)

Second term - 12d^2 * b

Third term 3!/[(3 - 2)!2!] * d^(3 - 2) (-4b)^2

Third term 3*d*16 b^2

Third term 48 db^2

Last term 3!/[(3 - 3)!(3!) ] * d^(3 - 3) (- 4b)^(3)

Last term 1*d^0*(-64b^3)

Last term - 64b^3

Answer:

the answer is 6.27

Step-by-step explanation:

all you have to do is divide 31.35 by 5

31.35/5 = 6.27

(unless your kind to pay the whole bill ;D)

Answer:

1.2 litres  more water should Josie drink.

Step-by-step explanation:

As given

It is recommended that an adult drink 64 fluid ounces of water everyday .

As given

1 ounce = 0.0296 litre .

Now convert 64 ounces into litre.

64 ounce = 64 × 0.0296

                = 1.9 litres (Approx)

As

1 litre = 1000 ml

[tex]1\ ml= \frac{1}{1000}\ litre[/tex]

Now convert 700 ml into litre.

[tex]700\ ml= \frac{700}{1000}\ litre[/tex]

[tex]700\ ml= \frac{7}{10}\ litre[/tex]

700 ml = 0 .7 litre

Thus

Recommended amount of water a adult should drink = Amount of water Josie already consumed + More water should Josie drink.

Putting the value

1.9 litres = 0 .7 litres +  More water should Josie drink.

More water should Josie drink = 1.9 - 0.7

More water should Josie drink = 1.2 litres .

Therefore 1.2 litres  more water should Josie drink.

Final answer:

To find the number of copies above which Company A's charges are higher than Company B's charges, set up an equation and solve for C. The number of copies above which Company A's charges are higher is 6000.

Explanation:

To find the number of copies above which Company A's charges are higher than Company B's charges, we need to set up an equation to represent the total charges for each company. Let C represent the number of copies. For Company A, the total charges can be represented as 360 + 0.12C. For Company B, the total charges can be represented as 720 + 0.06C. We can set these two expressions equal to each other and solve for C to find the number of copies above which Company A's charges are higher.

360 + 0.12C = 720 + 0.06C

0.06C - 0.12C = 720 - 360

-0.06C = 360

C = 360 / -0.06

C ≈ -6000

Since the number of copies cannot be negative, we can conclude that Company A's charges are higher than Company B's charges when the number of copies is greater than 6000.

Answer:

A: (-7x+10)(x-2)

Step-by-step explanation:

Given trinomial,

[tex]-7x^2-4x+20[/tex]

By middle term splitting,

[tex]=-7x^2-(14-10)x+20[/tex]

[tex]=-7x^2-14x+10x+20[/tex]  

[tex]=-7x(x+2)+10(x+2)[/tex]        

[tex]=(-7x+10)(x+2)[/tex]            

Since, further factorization is not possible,

Thus, the required factorized form of the given trinomial is,

[tex](-7x+10)(x+2)[/tex]    

Option A is correct.