Amad was curious if triangles \triangle ABC△ABCtriangle, A, B, C, and \triangle EDF△EDFtriangle, E, D, F were congruent. He was able to map one figure onto the other using a reflection and a rotation. Amad concluded: "I was able to map \triangle ABC△ABCtriangle, A, B, C onto \triangle EDF△EDFtriangle, E, D, F using a sequence of rigid transformations, so the figures are congruent."

Answer:

[tex]Standard\ Form = {3n^2} m^{-2}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2}{3m^2n} * 4.5n^3[/tex]

Required

Write in Standard Form

To start with; the two monomials have to be multiplied together;

[tex]\frac{2}{3m^2n} * 4.5n^3[/tex]

[tex]Standard\ Form = \frac{2 * 4.5n^3}{3m^2n}[/tex]

Split the numerator and the denominator

[tex]Standard\ Form = \frac{2 * 4.5 * n^3}{3 * m^2 * n}[/tex]

Multiply Like terms

[tex]Standard\ Form = \frac{9 * n^3}{3 * m^2 * n}[/tex]

Divide 9 by 3 to give 3

[tex]Standard\ Form = \frac{3 * n^3}{m^2 * n}[/tex]

Divide n³ by n to n²

[tex]Standard\ Form = \frac{3 * n^2}{m^2 }[/tex]

Split fraction

[tex]Standard\ Form = {3 * n^2} * \frac{1}{m^2 }[/tex]

From laws of indices;

[tex]\frac{1}{a^n} = a^{-n}[/tex]

[tex]Standard\ Form = {3 * n^2} * \frac{1}{m^2 }[/tex] becomes

[tex]Standard\ Form = {3 * n^2} * m^{-2}[/tex]

Multiply all together

[tex]Standard\ Form = {3n^2} m^{-2}[/tex]

Answer: a simple interest rate of 3.2% will be the better deal.

Step-by-step explanation:

Hi, to answer this question we have to apply the compounded interest formula:  

A = P (1 + r/n) nt  

Where:  

A = Future value of investment (principal + interest)  

P = Principal Amount  

r = Nominal Interest Rate (decimal form, 3/100= 0.03)  

n= number of compounding periods in each year (1)  

Replacing with the values given  

A = 7000 (1+0.03/1)^(1x5)

A = 7000( 1.03)^5 = $8,114.92

For simple interest:

I = p x r x t  

Where:  

I = interest  

Replacing with the values given:

I = 7000 x (3.2/100) x 5 = $1,120

Adding the principal amount: 7000+1120 = $8,120

Since 8,120 (simple) >8,114.92(compound)

a simple interest rate of 3.2% will be the better deal.

solution,

X=5

[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]

hope this helps...

Good luck on your assignment..

Answer:

When x=5

Y=(5+9)÷(5-3)

= 14 ÷2

= 7

Answer:

We can prove that ΔTMB ≅ ΔTMD and ΔTMA ≅ ΔTMC by ASA. This means that BM = MD = BD / 2 = 8.5 and that AM = CM = 5 which means that CD = MD - CM = 8.5 - 5 = 3.5.

Answer:

132 degree

Step-by-step explanation: angle kjh is 132 degree and since lk is a straight line it is 180 degree. angle kjh is 132 degree so, angle LJM is 132 degree. This is because adjacent angles are equal as you can see, Angle LJM is adjacent to Angle KJH.

Answer:

g=number of girls in the class b=number of boy in the class

g+b=28

g=11+b

Answer:

21u-16v+18w

Step-by-step explanation:

(7u-4v+4w) 14u-12v+14w

21u-16v+18w

Answer:

= 21u−16v+18w

Step-by-step explanation:

Let's simplify step-by-step.

7u−4v+4w−2(−7u+6v−7w)

Distribute:

=7u+−4v+4w+(−2)(−7u)+(−2)(6v)+(−2)(−7w)

=7u+−4v+4w+14u+−12v+14w

Combine Like Terms:

=7u+−4v+4w+14u+−12v+14w

=(7u+14u)+(−4v+−12v)+(4w+14w)

=21u+−16v+18w

Answer:

=21u−16v+18w

Answer:

s = 4t

Step-by-step explanation:

Let number of shoelace produced be S and time taken to produce then be T

If the number of shoelaces it produces is proportional to the time, this can be expressed using a direct relationship as:

S∝T

S = kT where

k is the proportionality constant

If 12 laces of shoes can be produced in 3 minutes, then S = 12 and T = 3

The relationship above on substitution becomes

12 = 3k

k = 12/3

k = 4

If the proportionality constant is 4, then the equation representing the relationship will be:

s = 4t

please mark me brainliest!

Answer: y = 4x (y = shoelaces & x = minutes)

Step-by-step explanation: We know that 12 shoelaces are produced in 3 minutes and that the ratio of shoelaces produced to minutes spent is proportional. We can figure out, therefore, that if you multiply the number of minutes by 4, you will get the number of shoelaces. As an equation, this would be y = 4x (y = shoelaces & x = minutes).

Answer:

Step-by-step explanation:

Answer:

[tex] \sqrt{ {2}^{5} } [/tex]

Step-by-step explanation:

[tex]\huge \bigg( {2}^{ \frac{1}{2} }. {2}^{ \frac{3}{4}} \bigg)^{2} \\ \\ \huge = {2}^{ \frac{1}{2} \times 2 }. {2}^{ \frac{3}{4} \times 2} \\ \\ \huge = 2 \times {2}^{ \frac{3}{2} } \\ \\ \huge = {2}^{ \frac{3}{2} + 1 } \\ \\ \huge = {2}^{ \frac{3 + 2}{2} } \\ \\ \huge = {2}^{ \frac{5}{2} } \\ \\ \huge = \sqrt{ {2}^{5} } [/tex]

Answer:

One

Step-by-step explanation:

Through any 2 points, there is exactly one line.

Answer:

ONE

Step-by-step explanation:

Through any 2 points there is exaclty ONE line.

Answer:

704 pi in ^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

V = pi ( 8)^2 * 11

V = pi (704)

V = 704 pi in ^3

Answer:

Step-by-step explanation:

Solution,

Radius(R)= 8 in.

Height (h)= 11 in.

Volume of cylinder=?

Now,

Volume of cylinder:

[tex]\pi {r}^{2} h[/tex]

[tex]\pi \: {(8)}^{2} \times 11 [/tex]

[tex]\pi \times 64 \times 11[/tex]

[tex]704\pi \: {inches}^{3} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

CB = 3.6 cm

Step-by-step explanation:

Here, triangle ABC is rotated about point X which results in triangle EFD. Since triangle ABC is rotated it retains its shape and dimensions. This means that triangle ABC is parallel to triangle EFD ie, ABC≈EFD, also both dimensions will be congruent.

Thus

AB = EF

BC = FD

AC = ED

CB = DF

BA = FE

CA = DE

Since length of side DF = length of side CB, and DF = 3.6 cm. Therefore, CB = DF = 3.6 cm

Length of CB = 3.6 cm

Answer: B it's B

Step-by-step explanation: I got it right

Answer:

y=2 is the correct ans.

here, tge equn of st line passing through the point (3,2) and is also parallel to y axis.

we have, equn of st line parallel to y xaus is y= b

so , the equn of st line passing through the point (3,2) is y= 2 (where 2 is likely to b).

Answer:

A

Step-by-step explanation:

vol of a cylinder = pie* r^2×h

r= 5

h= 9

......vol= 9×5^2 pie= 225pie units ^3

Answer:

Translate 3 units to the left

Step-by-step explanation:

Answer:

0.03 feet

Step-by-step explanation:

d = 0.03r² + r

When d = 0: 0.03r² + r = 0

r(0.03r + 1) = 0

∴ r = 0

When r = 0: d = 0.03 feet

Answer:

The answer is A.

Step-by-step explanation:

The inequality states that the amount that Yvonne drives is more than 540 miles.  Since h represents the number of hours, we know that 69 probably means the number of miles Yvonne can drive per hour.  Finally, 126 shows the amount of miles that Yvonne has already driven.

Answer:

[tex]y = -2x - 8\\OR\\2x+y+8=0[/tex]

Step-by-step explanation:

Given that there are 2 points

[tex]A(-8,8)[/tex] and

[tex]B(1,-10)[/tex]

So, the coordinates are:

[tex]x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8[/tex]

Equation of a line is given as:

[tex]y =mx+c[/tex]

where 'm' is the slope of the line, formula for 'm' is given as:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex](x,y)[/tex] are the points that satisfy the equation of the line.

[tex]c[/tex] is the [tex]y -[/tex] intercept.

Calculating the value of m using the given coordinates:

[tex]m=\dfrac{-10-8}{1-(-8)}\\\Rightarrow m=\dfrac{-18}{9} = -2[/tex]

So, the equation of line becomes:

[tex]y =-2x+c[/tex]

Now, putting the coordinates of point [tex]A(-8,8)[/tex]

[tex]8 =-2\times (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8[/tex]

Please refer to the graph of given equation of line.

The equation of line is:

[tex]y =-2x+-8\\OR\\2x+y+8=0[/tex]

Answer:

Choice 3

Step-by-step explanation:

A(-5,-1) and B(4, 1)

Distance AB is calculated as x²+y², where x= 4-(-5)=9 and y= 1-(-1)=2

Point P is at 1/4 of distance from point A, so its coordinates will be at 1/4 of full distance from A to B in term of both coordinates:

So P= (-11/4, -1/2) and choice 3

Answer: I = $ 19.53

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 25%/100 = 0.25 per year,

then, solving our equation

I = 312.5 × 0.25 × 0.25 = 19.53125

I = $ 19.53

The simple interest accumulated

on a principal of $ 312.50

at a rate of 25% per year

for 0.25 years is $ 19.53.

Answer:

P = 5000

You need to multiply r and T together, then divide 312.50 by that.

Answer:

The 18th term of the sequence is -117.

Step-by-step explanation:

The given sequence is 2,-5,-12,-19

From this AP,

First term, a = 2

Common difference, d = -5-2 = -7

It is required to find the 18th term of the sequence. The nth term of an AP is given by :

[tex]a_n=a+(n-a)d\\\\a_{18}=a+17d\\\\a_{18}=2+17\times (-7)\\\\a_{18}=-117[/tex]

So, the 18th term of the sequence is -117.

Answer:

only the inverse is a function

Answer:

40

Step-by-step explanation:

Once you plot the data, the middle values will be 39 and 41. To calculate the median, you add them up and divide by two, which will result in 40!

Median is the middle value.

Write the numbers out from smallest to largest:

35, 38, 38, 39, 39, 41, 42, 43, 43, 44

There are 10 total numbers, find the middle two:

39 and 41

Add them Together and divide by 2:

39 + 41 = 80

80/2 = 40

Median = 40

Answer:

The answer is given below

Step-by-step explanation:

a) What is the probability that a randomly selected pregnancy lasts less than 242 days

First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,

[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]

From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783

(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]

c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]

From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985

d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]

From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143

(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?

It would be unusual if it came from mean of 247 days

f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean

For x = 236 days

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]

For x = 258 days

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]

From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939

Answer:

Range = [5, ∞)

Step-by-step explanation:

The initial  number of snakes is 5 and it is increasing at a high rate so the maximum number is infinite. The population is increasing exponentially according to the equation  P = 5(2)^t  where t = the number of years.

Answer: No solution

Step-by-step explanation:

This system of equation has no solution because...

-3x+4y=12

1/4x-1/3y=1

[tex]-3x+4y-4y=12-4y[/tex]

[tex]-3x=12-4y[/tex]

[tex]\frac{-3x}{-3}=\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]x=-\frac{12-4y}{3}[/tex]

substitute

[tex]\frac{1}{4}\left(-\frac{12-4y}{3}\right)-\frac{1}{3}y=1[/tex]

[tex]-1=1[/tex]

-1=1 is false so therefore this system has no solution

Answer:

The answers are options A and E

x² + 4x-9 = 5x + 3

Group like terms

x² + 4x - 5x - 9 - 3 = 0

x² - x - 12 = 0

Using factorization method

(x + 3)( x - 4) = 0

x = - 3 x = 4

Hope this helps

Answer:

The equation above represents the total time the play director spent preparing for a play.

Step-by-step explanation:

The time spent by the play director for preparing for a play is, 190 hours.

Of these 190 hours, the director spent varying amounts of time attending 35 rehearsals for the play.

Let the varying amounts of time be denoted by, x.

The director also spent 3/4th of an hour, i.e. 45 minutes, on other responsibilities related to the play.

The equation provided is:

[tex]35x+\frac{3}{4}=190[/tex]

The equation above represents the total time the play director spent preparing for a play.