ΔABC has been translated right to create triangle ΔXYZ. Based on this information, which of the following is a true statement? answers: A) ≅ B) ≅ C) ∠A ≅ ∠C D) ∠B ≅ ∠X

Answer:

[tex]\frac{x^{12}y^{4}}{z^3}[/tex]

Step-by-step explanation:

Step 1: Multiply exponents

[tex]\frac{y^{6/6}z^{-6/2}}{x^{-12}y^{-6/2}}[/tex]

Step 2: Simplify

[tex]\frac{yz^{-3}}{x^{-12}y^{-3}}[/tex]

Step 3: Flip the negative exponents

[tex]\frac{x^{12}y^{4}}{z^3}[/tex]

Step-by-step explanation:

[tex] log(x) = 2 \\ {10}^{2} = x \\ x = 100[/tex]

then for y:

[tex] log( y) = - 1 \\ {10}^{ - 1} = y \\ y = 0.1[/tex]

so:

[tex]xy - 100 {y}^{2} \\ = 100 \times 0.1 - 100 \times {(0.1)}^{2} \\ = 10 - 100 \times 0.01 \\ = 10 - 1 \\ = 9[/tex]

Answer:

Integers -3, 9, 5, 56/7, -1

Step-by-step explanation:

Integers are whole numbers that can be positive or negative. They do not have decimals.

Answer:

The first option from the picture

Step-by-step explanation:

In the picture attached, the question is shown.

In the first option:

The formula for calculating the standard deviation of sample data is expressed as    [tex]\sigma=\sqrt{\frac{\sum(x_1-\overline x)^2+(x_2-\overline x)^2+...(x_n-\overline x)^2)}{N} }[/tex]

The standard deviation is a measure of the amount of variation or dispersion of a set of values.

A lower value of the standard deviation shows that value is close to the mean otherwise it is far from the mean

The formula for calculating the standard deviation of sample data is expressed as:

[tex]\sigma=\sqrt{\frac{\sum(x_1-\overline x)^2}{N} }[/tex]

Assume we have the following data x1, x2, ....xn, the standard deviation will be given as:

[tex]\sigma=\sqrt{\frac{\sum(x_1-\overline x)^2+(x_2-\overline x)^2+...(x_n-\overline x)^2)}{N} }[/tex]

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Answer:

x= 70

Step-by-step explanation:

This question needs an attachment; see attached

Given

ABD = 55

Required

Find x?

In the figure shown in the attachment, angle b and ABD are alternate interior angles;

From parallel and perpendicular line theorems; alternate interior angles are equal.

This implies that <b = 55

Also; when a rectangle is divided by two diagonals, the resulting triangles are isosceles triangles;

where 2 sides and 2 angles are equal;

This implies that <b = <c = 55

Sum of angles in a triangle  = 180;

So,

<x + <b + <c = 55

x + 55 + 55 = 180

x + 110 = 180

Subtract 110 from both sides

x + 110 - 110 = 180 - 110

x = 180 - 110

x = 70

Answer:

5/14

Step-by-step explanation:

Multiply.

(-5 × -1 × 4) / (7 × 8)

20/56

Simplify.

5/14

Answer:

The answer is [tex]\frac{5}{14}[/tex].

Step-by-step explanation:

1. -5 × [tex]\frac{-1}{7}[/tex] =  [tex]\frac{5}{7}[/tex]

2.  [tex]\frac{5}{7}[/tex] · [tex]\frac{4}{8}[/tex] = [tex]\frac{20}{56}[/tex]

3. Simplify:

[tex]\frac{20}{56}[/tex]  = [tex]\frac{5}{14}[/tex]

Answer:

24

Step-by-step explanation:

Alright so the number has to be above 20 and below 35.

It has to be even, so our options are 22, 24, 26, 28, 30, 32, 34

Since the sum of the digits has to be 6, the only number from that list that it can be is 24.

This works because 24 is also evenly divisible by 4 (6x4=24) so it fits all of the criteria.

Hope this helps!

Answer:

24

Step-by-step explanation:

This works because 24 is also evenly divisible by 4 (6x4=24) so it fits all of the criteria.

Hope this helps!

Answer:

Step-by-step explanation:

5x3= 15

8x9=72

12x11=132

14x17=138

9x17=153

15+72+132+138+153=510

510/50=10.2= mean

[tex]answer \\ 5 \\ solution \\ let \: the \: points \: be \: a \: and \: b \\ a(3 , 8) = > (x1 , y1) \\ b(1 , - 2) = > (x2 , y2) \\ slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: = \frac{ - 2 - 8}{1 - 3} \\ \: \: \: \: \: = \frac{ - 10}{ - 2} \\ \: \: \: \: \: \: = 5 \\ hope \: it \: helps[/tex]

To find the slope of the line, I will be showing you the table method.

To find the slope of the line using the table method,

we start by making a table for our ordered pairs.

We will put the x values in the left column

and the y values in the right column.

Our first ordered pair is (3, 8), so we put a

3 in the x column and a 8 in the y column.

Our second ordered pair is (1, -2), so we put a

1 in the x column and a -2 in the y column.

Next, remember that the slope or m, is always equal to

the rate of change or the change in y over the change in x.

Using our table, we can see that the y values

go from 8 to -2 so the change in y is -10.

The x values go from 3 to 1 so the change in x is 2.

Therefore, the rate of change, or the change in y

over the change in x is -10/2 which reduces to 5.

This means that the slope is also equal to 5.

Answer:

Option B is the correct answer.

Step-by-step explanation:

B= {- 5, - 4.5, - 3}

Answer:

It's (B) [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Hope this helped you!

Answer:

f^-1(8) = 3/2

Step-by-step explanation:

f(x) = 2x + 5

y = 2x + 5

x = 2y + 5

2y = x - 5

y = (x - 5)/2

f^-1(x) = (x - 5)/2

f^-1(8) = (8 - 5)/2

f^-1(8) = 3/2

Answer:

7

Step-by-step explanation:

Answer: domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

Step-by-step explanation:

DOMAIN: {4}

RANGE: {2,5,7,9}

FUNCTION? NO!

Your domain is always your x-coordinates, which are the first coordinates in a pair.

Your range is always your y-coordinates, which are the second coordinates in a pair.

When listing the points, it's important to remain a relation CANNOT be a function if the x's repeat, so luckily, they do not repeat.

Also, when listing points for your range, remember, if they repeat, you should only count one of the numbers, as you can see from the answer, there were two nines, but instead, I put one.

Answer:

(3, -3)

Step-by-step explanation:

If a point is dilated about the origin rule to be followed,

(x, y) → (kx, ky)

where k is a scale factor by which the point is being dilated.

If a point R having coordinates (1, -1) is dilated by scale factor of 3, coordinates of the image will be [3×1, 3(-1)]

Therefore, coordinates of the image R' will be (3, -3)

Answer:

Distance = 162.5 to 2dp.

Step-by-step explanation:

Alex car drives 65km = 40mins we round up to 1hr

= 1/2 x 65 + 65 = 32.5 +65 = 97.5  km p/h

Roy is 1/4 faster (As Alex speed is 3/4 of Roy)

To find 3/4 we divide by 3  then, add the 97.5  km etc..

97.5/3 =  + 32.5km = 130 km/ph

To check we only have to divide by 4

130 / 4  = 32.5

We know 32.5 is 1/4 we can add this on as 15minutes.

130 km = 1hr +

32.5 km = 15 mins

Distance = 162.5 km

Answer:

162.50 km

Step-by-step explanation:

Alex: 40 minutes for 65 km

speed = distance/time = (65 km)/(40 min) * (60 min)/(1 hr) = 97.5 km/h

Alex's speed = 3/4 of Roy's speed

Roy's speed = (Alex's speed)/(3/4) = (97.5 km/h)/(0.75) = 130 km/h

speed = distance/time

distance = speed * time

time = 1 hour + 15 minutes = 1 hour + 15/60 hour = 1.25 hour

distance = 130 km/h * 1.25 hour = 162.50 km

Answer:

6.9 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/hyp

sin 35 = x/12

12 sin 35 = x

6.882917236 = x

To the nearest tenth

6.9 =x

Answer:

48 degrees

Step-by-step explanation:

Angle 2 is a right angle.

Right angles are 90 degrees.

A line is 180 degrees.

Angle 1, 5, and 2 form a line.

180-90=90

That means that Angles 1 and 5 add up to 90 degrees.

We know that Angle 3 is 42 degrees.

Angle 3 and 5 are Vertical angles.

Vertical angles are always congruent.

This means that Angle 5 is also 42 degrees.

As we discussed earlier, Angles 1 and 5 are complementary. (Add up to 90 degrees)

42+x=90

Subtract 42 from both sides.

x=48

m<1=48

Answer:

It is 48 degrees because I took the test

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

Answer:

70 fewer refrigerators  than television

Step-by-step explanation:

Answer:

I would think it is supplementary.

Step-by-step explanation:

If 2 angles equal 180 degrees, then they are supplementary.

Answer:

c

Step-by-step explanation:

In the given line the relationship between angle w and z is Measure of angle w + measure of angle z = 180 degrees.

This is the type of angle that when measured, two of the angles would sum up to 180 degrees.

The supplementary angle is the sum of angle w + angle z = 180 degrees. Hence c is correct.

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Answer:

axis of symmetry: x=-1

Step-by-step explanation:

Answer:

C) None of the above

Step-by-step explanation:

Reason is V is a shorter distance and q is longer they need to be subtraction but the other way round to enable the correct subtraction we can show (q-V) which means the longer distance minus the shorter distance.

Answer:

D

Step-by-step explanation:

Its a straight line, and remember, you ALWAYS read graphs from left to right, so its linear increasing. :)

Answer:

Standard deviation  for the number of people with the genetic mutation = 4.178

Step-by-step explanation:

Explanation:-

Given random sample size 'n' =600

proportion of the Population 'p'=3% or  0.03

Let 'X' be the random variable in binomial distribution

Mean of the  binomial distribution

                              μ = n p

                                 = 600 X 0.03

                                = 18

Mean of the  binomial distribution ' μ ' =18

Standard deviation of the binomial distribution

                                σ = [tex]\sqrt{npq} = \sqrt{600 X 0.03 X 0.97} = \sqrt{17.46} = 4.178[/tex]

Conclusion:-

Standard deviation  for the number of people with the genetic mutation = 4.178

Answer:

Option C.

Step-by-step explanation:

It is given that James earns $1000 weekly base pay as a sales-person.

We know that, we have 4 weeks in a month. So, monthly salary of james is

Monthly income [tex]=\$1000\times 4=\$4,000[/tex]

It is said that he sold $20,000 worth of merchandise last month and he gets a 10% commission on everything he sells.

Commission [tex]=\$20,000\times \dfrac{10}{100}=\$2,000[/tex]

Total amount = Monthly income + Commission

          [tex]=\$4,000+\$2,000[/tex]  

          [tex]=\$6,000[/tex]  

Therefore, the correct option is C.

Answer:

Solution,

Hypotenuse(h)=X

Perpendicular (p)=9

Base(b)=12

Now,

Using Pythagoras theorem,

[tex] {h}^{2} = {p}^{2} + {b}^{2} \\ or \: {x}^{2} = {(9)}^{2} + {(12)}^{2} \\ or \: {x}^{2} = 81 + 144 \\ or \: {x}^{2} = 225 \\ or \: x = \sqrt{225} \\ or \: x = \sqrt{ {(15)}^{2} } \\ x = 15[/tex]

hope this helps...

Good luck on your assignment...

The length of the hypotenuse in the given triangle is A. 15 units.

This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, the base of the triangle is 12 units and the height is 9 units.

∴ x² = 9² + 12².

x² = 144 + 81.

x² = 225.

x = + 15 units.

So, the length of the hypotenuse is 15 units.

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Answer:

A. [tex] x = \frac{5}{p} [/tex]

Step-by-step explanation:

[tex]px + 12 = 17 \\ px = 17 - 12 \\ px = 5 \\ x = \frac{5}{p} [/tex]

Answer:

John's initial investment is Rs.150000

Step-by-step explanation:

Let the principal amount be a

We are given that John wants to invest in a simple interest savings account .The interest rate on this account is 0.7%.

Now to find simple interest in x years

Formula : [tex]Si = P \times T \times R[/tex]

Where P = Principal

T= time

R = rate of interest in decimals

So,[tex]SI=a \times 0.007 \times x[/tex]

Amount = Principal+Interest

Amount = [tex]a+a(0.007)x[/tex]

We are given that The account balance y can be modeled by the following linear equation y=150,000+150,000(0.007)x

So, On comparing a = 150000

Hence John's initial investment is Rs.150000