Which pairs of triangles appear to be congruent? Check all that apply.

Answer:

Step-by-step explanation:

{z+1}/{z-1} = i.

z+1 = i (z-1)

z+1 =iz -i

z - iz  = -1 -i

z ( 1 -i) = - 1 -i

z = (- 1 - i ) /(1-i) = - (1+i)/(1-i)

z = - (1+i)(1+i)/(1-i)(1+i)

z = - (1+2i +i²)/ ( 1²-i²).........i² = -1

z =-2i/2

z = - i      (one solution)

All the complex numbers z satisfying the equation {z+1}/{z-1} = i is z = -i.

Complex numbers are numbers which are of the form [tex]a + ib[/tex], where a and b are real numbers and i is the imaginary number called iota whose value is [tex]i^2[/tex]= -1.

Given equation is,

(z + 1) / (z - 1) = i

Multiplying both sides by (z - 1),

z + 1 = i (z - 1)

Let z = (a + bi)

Substituting,

(a + bi + 1) = i (a + bi - 1)

(a + bi + 1) - i (a + bi - 1) = 0

a + bi + 1 - (ai + b(i)² - i) = 0

a + bi + 1 - ai - b(i)² + i = 0

Now i² = -1

a + bi + 1 - ai + b + i = 0

Combining the like terms,

(bi - ai + i) + (a + 1 + b) = 0

i (b - a + 1) + (a + b + 1) = 0

Left hand side is a complex number.

A complex number is a + bi = 0, when a = 0 and b = 0.

So, we get,

(b - a + 1) = 0 and (a + b + 1) = 0

b - a = -1 and a + b = -1

So, combining,

a + b = b - a

a + a = b - b

2a = 0

a = 0

Substituting,

b = -1

So the complex number, z = a + bi = -i

Hence the complex number z = -i.

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Answer:

The translation is right 4 units and up 4 units

Step-by-step explanation:

we know that

The rule of the translation of the point V to V' is equal to

(x,y) ----> (x+4,y+4)

That means ----> The translation is right 4 units and up 4 units

Verify

V(-2,3) -----> V'(-2+4,3+4)

V(-2,3) -----> V'(2,7)

Is correct

The true statement is: The transformation is a vertical translation. (Statement 3)

Let's analyze each statement:

1. The point moves two units up and four units to the right.

  - This statement is incorrect. The point moves four units up, not two units up.

2. The transformation rule is (x, y) → (x + 0, y + 4).

  - This statement is incorrect. The transformation rule should be (x, y) → (x, y + 4) because the point moves vertically by adding 4 to the y-coordinate.

3. The transformation is a vertical translation.

  - This statement is correct. The point moves vertically, changing only the y-coordinate.

4. The image is four units to the right of the pre-image.

  - This statement is incorrect. The image is at the same x-coordinate as the pre-image (-2), so it's not four units to the right.

5. The translation can be described as (x, y) → (x - 2, y + 7).

  - This statement is incorrect. The translation rule should be (x, y) → (x, y + 4) because the point only moves vertically.

Complete question:A translation moves point V(-2, 3) to V prime (-2, 7). Which of the following statements are true about the translation?

1. The point moves two units up and four units to the right.

2. The transformation rule is (x, y) → (x + 0, y + 4).

3. The transformation is a vertical translation.

4. The image is four units to the right of the pre-image.

5. The translation can be described as (x, y) → (x - 2, y + 7).

(b^2+5)(−b^2+7)

Use the FOIL METHOD to expand.

-b^4 + 7b^2 - 5b^2 + 35

-b^4 + 2b^2 + 35

Did you follow?

Standard form (b^2+5)(−b^2+7) polynomial is = -b⁴+2b²+35

Using FOIL METHOD to expand.

(b²+5)(−b²+7)

=(b²+5)(7-b²)

=7b²-b⁴+35-5b²

=2b²-b⁴+35

= -b⁴+2b²+35

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Answer:

a=1, b=-12

Step-by-step explanation:

This is a rational function with a hole at x=3 and a vertical asymptote at x=-4.

The denominator of this rational function must be:

[tex](x - 3)(x + 4)[/tex]

When we expand using the distributive property, we get:

[tex] {x}^{2} + 4x -3 x - 12[/tex]

This simplifies to

[tex] {x}^{2} + x - 12[/tex]

Therefore the graphed rational function is:

[tex]f(x) = \frac{ {x}^{2} - 4x + 3 }{ {x}^{2} + x - 12 } [/tex]

Comparing this to

[tex]f(x) = \frac{ {x}^{2} - 4x + 3 }{ {x}^{2} +a x + b} [/tex]

We have

[tex]a = 1[/tex]

and

[tex]b = - 12[/tex]

Answer:

w=6

Step-by-step explanation:

P=2(L)+2(w)

48= 2(18)+2w

48=36+2w

12=2w

w=6

checking;

48= 2(18)+2(6)

48= 36+12

48= 48

Answer:

[tex]x=e^3+4[/tex] (exact)

x = 24.0855 (rounded)

Step-by-step explanation:

We need to remember 3 rules:

1. ln means log_e (ln is log base e)

2. [tex]a^b=x\\SameAS\\log_ax=b[/tex]

3. [tex]aLogx=Logx^a[/tex]

Now we can write the equation as:

[tex]3Ln(x-4)=9\\3Log_e(x-4)=9\\Log_e(x-4)^3=9[/tex]

Now, we can convert it to exponential and solve:

[tex]Log_e(x-4)^3=9\\(x-4)^3=e^9\\\sqrt[3]{(x-4)^3}=\sqrt[3]{e^9} \\ x-4=e^3\\x=e^3+4[/tex]

This is the exact value of x, in 4 decimal places (by using calculator), it would be

x = 24.0855

Answer:

t = 1

Step-by-step explanation:

Given

16 - 2t = 5t + 9 ( subtract 5t from both sides )

16 - 7t = 9 ( subtract 16 from both sides )

- 7t = - 7 ( divide both sides by - 7 )

t = 1

Answer:

2.43

Step-by-step explanation:

16-2t=5t+2t

16-9=5t+2t

17÷7=7t

t=2.43

Answer:

D) 800

Step-by-step explanation:

5609/7 = 801.285

rounding to the nearest would be 800.

Anything below a 5 will go to the lower anything above a 5 will go higher:

ex: 804 would round nearest to 800

807 would round nearest to 810

Answer:

the answer is 12 days

Step-by-step explanation:

3×4=12

Answer:

C. positively skewed

Step-by-step explanation:

If a data set has more extremely large data values, the distribution is said to be positively skewed.

Have a great day!

A data set with more extremely large data values is said to be skewed right or positively skewed. This describes a distribution where the tail on the right side is extended due to a few high extreme values.

If a data set has more extremely large data values, the distribution is said to be skewed right or positively skewed. This occurs because the tail of the distribution on the right-hand side is longer or more drawn out compared to the left-hand side.

In a right-skewed distribution, the mean is typically larger than the median, and the mode lies to the left of the median. This asymmetry indicates a larger number of lower values and a few extreme higher values in the data set. For example, if we have a data set with the histogram showing a longer tail on the right, it suggests there are some very large values stretching the scale, resulting in a skewed right distribution.

Correct. We need a balance in order to answer the question.

Answer:

the rest of the question but the answer is $555.37

Step-by-step explanation:

[tex]\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ e^{\ln(3x)}\implies e^{\log_e(3x)}\implies 3x[/tex]

Answer:

3x

Step-by-step explanation:

e^ln3x

We know that e and ln are inverses of each other, so when we take e to the power ln, they cancel

e^ ln 3x

3x

Answer:

[tex]314.2cm^3[/tex]

Step-by-step explanation:

We use the formula below to find the volume:

[tex]\pi r^2\frac{h}{3}[/tex]

Note:

Simplify:

[tex]\pi 5^2\frac{12}{3}[/tex]

Solve the exponent first, then multiply the fraction:

[tex]\pi 5^2\frac{12}{3} \\\\ 5^2 = 25\\\\ 12/3 = 4\\\\ 25 * 4 = 100\\\\ 100\pi = 314.159[/tex]

Round:

314.15 -> 314.2

Our answer would be [tex]314.2cm^3[/tex]

Answer:

Question 1: 8

Question 2: -32.5

Step-by-step explanation:

Laura gets paid 8 dollars an hour to baby sit

8x represents how much Laura gets paid by the hour.

Laura owes her friend 32.50

-32.50 represents the amount she owes her friend

Combine

y = 8x - 32.50

Answer

Question 1: 8

Question 2: -32.5

Answer:

y = 8x-32.50

Step-by-step explanation:

She makes 8 dollars an hour babysitting.  She will work x hours

She makes 8x

She owes 32.50 to her friend.  This will be subtracted because she owes it

The amount of money she has at the end, y, is given by

y =8x-32.50

Answer:

[tex]\boxed{(-2,1)}[/tex]

Step-by-step explanation:

[tex]\left \{ {{5x+2y=-8} \atop {x+4y=2}} \right.[/tex]

I'll be solving this system of equations using the elimination method since the x and y values are neatly lined up.

I want to get a pair of x's or y's that cancel out, and it looks like the easiest way to start would be by multiplying the first equation by -2 (the y's will cancel).

I chose to multiply the first equation by -2 instead of multiplying the second equation by 5 because -2 is a smaller number and easier to multiply by.

[tex]-2\times(5x+2y=-8)[/tex]

Distribute -2 inside the parentheses. Now you've got:

[tex]\left \{ {{-10x-4y=16} \atop {x+4y=2}} \right.[/tex]

Add up the equations from top to bottom.

-10x plus x is -9x, the -4y and 4y cancel out, and 16 plus 2 is 18. Make this one single equation.

[tex]-9x=18[/tex]

Divide both sides by -9.

[tex]x=-2[/tex]

Substitute this value of x into the second equation (less to do with the x since it has no coefficient which means no multiplying).

[tex](-2)+4y=2[/tex]

Add 2 to both sides.

[tex]4y=4[/tex]

Divide both sides by 4.

[tex]y=1[/tex]

The final answer is [tex]x=-2, ~y=1[/tex].

Step-by-step explanation:

[tex]rise=y_2-y_1\\\\run=x_2-x_1\\\\slope=\dfrac{rise}{run}`\\\\\text{We have}\ (4,\ 6),\ (8,\ -8).\ \text{Substitute:}\\\\rise=-8-6=-14\\\\run=8-4=4\\\\slope=\dfrac{-14}{4}=-\dfrac{7}{2}[/tex]

Answer:

Part 1) The price will decrease $5,548

Part 2) The price of the next model is $32,452

Step-by-step explanation:

Let

x ----> the price of the next model

we know that

The current model costs $38,000 -----> represent the 100%

step 1

To find the price decrease in dollars multiply the current model price by 14.6%

14.6%=14.6/100=0.146

so

0.146*($38,000)= $5,548

step 2

Find the price of the next model

To find the price of the next model subtract the price decrease from the price of the current model

so

x=$38,000-$5,548=$32,452

just a quick note, that triangle is misleading some, since the HG side of 6 units, shows longer than GE which is 8, and of course 8 > 6.

Since GE is a perpendicular bisector, that means the angle at G is 90°.

Check the picture below.

To find the length of HE, we utilize the properties of a perpendicular bisector and trigonometry. Knowing that GE halves HF into two equal parts, we calculate HF using trigonometric concepts, then halve it to find HE.

In the question, it's mentioned that GE is a perpendicular bisector of HF. This means that GE bisects HF into two equal lengths. Therefore, the length of HE will be equivalent to half of the length of HF.

Since, HF can be calculated using trigonometry as mentioned. By definition, cose = x/h, so if we know the height 'h' and the angle, we can find 'x' which in this case would be HF, and subsequently HE would be HF/2.

Moreover, in trigonometry, the length of side opposite to the right angle in a right-angled triangle is calculated by the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We use this to find out HF if other two sides are known.

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Answer:

see explanation

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition x = 2.5 when y = 100

k = yx = 100 × 2.5 = 250

y = [tex]\frac{250}{x}[/tex] ← equation of variation

The constant of variation (k) in the inverse relationship equation (y = k/x) can be determined by multiplying the x and y values provided. In this case, k = 250. Therefore, the equation of variation would be y = 250 / x.

Given the inverse relationship where y varies inversely with x, it follows the general equation of y = k/x. This relationship is provided by the constant of variation (k). It can be determined by multiplying the given x and y values.

In this case, x = 2.5 when y = 100. We substitute these into our inverse relationship equation, yielding 100 = k/2.5. By multiplying both sides by 2.5, we are able to find that k = 250. Therefore, the equation of variation would be y = 250/x.

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Answer:

-11x-4 is the answer if the expression to simplify is (-7x+1)-(4x+5).

Step-by-step explanation:

We are first going to distribute to get rid of the ( ):

-7x+1-4x-5

Pair up like terms:

-7x-4x+1-5

Combine the like terms:

-11x-4

Answer:

[tex]y = \frac{1}{2}x+\frac{5}{2}[/tex]

Step-by-step explanation:

The perpendicular bisector of a line passes through the mid-point of the line and the product of slopes of the line and perpendicular bisector will be -1.

So,

[tex]Mid-point\ of\ BC = (\frac{6+8}{2},  \frac{8+4}{2})\\= (\frac{14}{2},  \frac{12}{2})\\= (7,6)[/tex]

The line will pass through (7,6)

Now,

[tex]Slope\ of\ BC = m_1 = \frac{y_2-y_1}{x_2-x_1} \\=\frac{4-8}{8-6}\\= \frac{-4}{2}\\= -2[/tex]

Let

m_2 be the slope of perpendicular bisector

So,

m_1*m_2 = -1

-2 * m_2 = -1

m_2 = -1/-2 = 1/2

The standard equation of line is:

y=mx+b

Where m is slope

So putting the value of slope and point to find the value of b

[tex]6 = \frac{1}{2}*7 +b\\ 6 = \frac{7}{2} + b\\b = 6 - \frac{7}{2}\\ b = \frac{12-7}{2}\\b = \frac{5}{2}\\So,\ the\ equation\ of\ perpendcular\ bisector\ of\ BC\ is:\\y = \frac{1}{2}x+\frac{5}{2}[/tex]

..

Answer:

C. The scientific revolution

Step-by-step explanation:

The scientific revolution led to new ways of studying and  thinking about the natural world.

The Scientific Revolution is the modern movement that led to new ways of studying and thinking about the natural world. It was characterized by advances in various fields of science, and marked a transformation in scientific thought and practice.

Among the options provided, option C -- The Scientific Revolution -- represents the modern movement that led to new ways of studying and understanding the natural world. The Scientific Revolution, which took place during the 16th and 17th centuries, was characterized by significant advances in physics, astronomy, biology, human anatomy, and chemistry. It marked a crucial period of transformation in scientific thought and practice, with philosophers and scientists starting to challenge traditional beliefs about nature and the universe, leading to the adoption of the scientific method.

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Answer:

51/7 = [tex]\frac7 {2}{7}[/tex]  31/9 = [tex]\frac3{4}{9}[/tex]

Step-by-step explanation: I hope this helps you!

Answer:

Step-by-step explanation:

51/7 = 7 2/7

31/9 = 3 4/9

Hope this helps!

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, - 3) and (x₂, y₂ ) = (- 7, 4)

m = [tex]\frac{4+3}{-7+2}[/tex] = [tex]\frac{7}{-5}[/tex] = - [tex]\frac{7}{5}[/tex]

We can use either of the 2 points for (a, b)

Using (a, b) = (- 7, 4), then

y - 4 = -[tex]\frac{7}{5}[/tex](x - (- 7)), that is

y - 4 = - [tex]\frac{7}{5}[/tex](x + 7) ← in point- slope form

Answer: Last Option

[tex]P=0.4125[/tex]

Step-by-step explanation:

In this case we have a uniform probability. In the graph the horizontal axis represents the possible values of the variable x and the vertical axis represents the probability P(x).

To calculate the probability that x is between 4.71 and 7.4 we calculate the area under the curve.

The horizontal length between 4.71 and 7.4 is:

[tex]7.4-4.1 = 3.3[/tex].

Then notice that the vertical length in this interval is 0.125.

Then the area of a rectangle is:

[tex]A = lw[/tex]

Where l is the length and w is the width.

In this case we have to:

[tex]l = 3.3[/tex]

[tex]w = 0.125[/tex]

So

[tex]P = A = 3.3 * 0.125[/tex]

[tex]P=0.4125[/tex]

Answer:

3y-x= -6

4y-x=44 ....

Step-by-step explanation:

Let y= 1/3x-2

Let y= 1/4x+11

Now we are required to arrange them in standard form.

So,

y= 1/3x-2

Combine the variable terms:

-1/3x+y=-2

Multiply both sides by 3

3(-1/3x+y)=3* -2

-x+3y= -6

3y-x= -6 ---------equation 1

y= 1/4x+11

Combine the variable terms:

-1/4x+y = 11

Multiply both sides by 4

4(-1/4x+y) = 4*11

-x+4y=44

4y-x=44 -----------------equation 2

Therefore the system of equations is:

3y-x= -6

4y-x=44 ....

Answer: Hello there!

we have that "one thirdx − 2 = one fourthx + 11"

this means  (1/3)x - 2 = (1/4)x + 11

now, we also can write this as:

(1/3)x - 2 = y = (1/4)x + 11

and now we have a system of equations:

(1/3)x - 2 = y

(1/4)x + 11 = y

or

(1/4)x - y = -11

(1/3)x - y = 2

Answer:

0

Step-by-step explanation:

Each time two cubes are rolled, the sum can be a number from 2 (rolling 1 and 1) to 12 (rolling 6 and 6). It is impossible to get a sum of more than 12, so there is zero probability of getting a sum of 47.

Answer: 0

Hello There!

the distance between 0 and -53 on a number line would be 53 spaces. This is because they are exactly 53 spaces away from each other.

Answer:

Its a kite

Step-by-step explanation:

Answer:

kite

Step-by-step explanation:

try not to get it confused with a rhombus

Answer:

The order pair of point Q' is (-21/4 , -7/2)

Step-by-step explanation:

* Lets explain the dilation

- A dilation is a transformation that changes the size of a figure.  

- The figure can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much the image will be larger

 or smaller  

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- The center of dilation is a fixed point in the plane about which all

 points are expanded or contracted

* Lets solve the problem

- The pentagon OPQRS is dilated by a scale factor 7/4

- The center of dilation is the origin

- The image of the pentagon after the dilation is O'P'Q'R'S'

∵ The coordinates of the vertices of the pentagon OPQRS are

  O (-1 , 2) , P (-5 , 3) , Q (-3 , -2) , R (2 , 1) , S (2 , 5)

- To find the image of each point after the dilation multiply each

  coordinates of the points by the scale factor of dilation

∵ The scale factor is 7/4

∵ The coordinates of point Q are (-3 , -2)

∴ The image of point Q after dilation is (-3 × 7/4 , -2 × 7/4)

∴ The image of point Q after dilation is (-21/4 , -7/2)

∵ Q' is the image of Q

∴ Q' = (-21/4 , -7/2)

* The order pair of point Q' is (-21/4 , -7/2)

Answer:

The answer is (−5.25, −3.5)

Step-by-step explanation:

-3 times 7/4 is -5.25. -2 times 7/4 is -3.5.