Which of the following is equivalent to
60 1/2

[tex]\left(\sqrt{z^{2}+8} \right)^{2}=(1-2z)^{2}\\\\z^{2}+8=4z^{2}-4z+1\\\\0=3z^{2}-4z-7\\\\0=(z+1)(3z-7)\\\\z=-1, z=\frac{7}{3}[/tex]

We know that if z=7/3, the right-hand side will be negative, which means it is an extraneous solution as square roots cannot be negative.

Answer:

  about 94.41°

Step-by-step explanation:

The Law of Cosines can be used to find an angle in a triangle with three sides given.

The law of cosines relation generally relates the side opposite the angle to the other measures in the triangle:

  r² = p² +q² -2pq·cos(R)

We want to find the measure of angle R, so we solve the equation for that:

  2pq·cos(R) = p² +q² -r² . . . . . . add 2pq·cos(R)-r²

  cos(R) = (p² +q² -r²)/(2pq) . . . . divide by the coefficient of the cosine

We can fill in the given side lengths at this point:

  cos(R) = (13² +10² -17²)/(2·13·10) = -20/260 = -1/13

Then the angle can be found using the arccos function:

  R = arccos(-1/13) ≈ 94.41°

The measure of angle R is about 94.41°.

__

Additional comment

When you have done a few of these, you recognize that the angle opposite side 'c' is ...

  C = arccos((a² +b² -c²)/(2ab))

A calculator can make short work of this. The second attachment shows the evaluation of this expression with a=10, b=13, c=17. The calculator angle mode is set to degrees. The arccos function is the 2ND function of the Cos key.

Answer:

12

Step-by-step explanation:

the number of the available cases is :

3 × 4 = 12

Answer:

The slope is 3

Step-by-step explanation:

it is 3 up and 1 across, which is 3/1 = 3

Answer:

3

Step-by-step explanation:

Look at the two lower dots shown on the line.

slope = rise/run

The vertical distance from the lower point to the higher point is 3. That is the rise.

The horizontal distance from the lower point to the higher point is 1. That is the run.

slope = 3/1 = 3

Answer: 3

The geometrical relationships between the straight lines AB and CD is that they are parallel to each other

It is important to note the following;

We  find the equation of AB by subtracting OB from OA, thus AB = (c - a)x + (d - b)y

The slope of line AB =

⇒ OA= 2 x + 9 y

⇒ OA = 4 x + 8 y

⇒AB = OB - OA

⇒AB = (4 x + 8 y) - (2 x + 9 y)

⇒ AB = 4 x + 8 y - 2 x - 9 y

Collect like terms

⇒ AB = (4 x - 2 x) + (8 y - 9 y)

⇒AB = 2 x + -y

⇒ AB = 2 x - y

⇒ Coefficient of x = 2

⇒ Coefficient of y = -1

⇒ The slope of ab = [tex]\frac{-2}{-1}[/tex] = 2

For CD

⇒ CD = 4 x - 2 y

⇒Coefficient of x = -4

⇒ Coefficient of y = -2

⇒The slope of cd = [tex]\frac{-4}{-2}[/tex] = 2

Note that Parallel lines have same slopes

And Slope of ab = slope of cd

AB // CD

Therefore, the geometrical relationships between the straight lines AB and CD is that they are parallel to each other

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Answer:

32

Step-by-step explanation:

YZ = ⅗XY.

XY = 20

20 / 5 x 3 = 12

YZ = 12

XZ = YZ + XY

XZ = 20 + 12

XZ = 32

Work is attached. Hope it helps!

Answer:

3/4

Step-by-step explanation:

The total number of children is 8 and the number of girls is 6. This can be represented as 6/8.

You would then need to simplify...

6/2=3

8/2=4

which which lead you to 3/4!

Answer:

d. vertical line

Step-by-step explanation:

A line with an undefined slope is a vertical line

Slope is the change in y over the change in x

When the slope is undefined, it means that the x does not change, which is a vertical line

Answer:

Line D

Step-by-step explanation:

Slope is defined as rise/run. Since a vertical line has zero run and infinite rise the equation is infinity/0 and anything divided by zero is undefined.

The option  that is shown to be congruent by a sequence of reflections and translations is Option B: Triangle ABC and Triangle MNO

Note that:

If ∆MNO  can be gotten  from ∆ABC  then ∆MNO ≅ ∆ABC  

To solve for Reflection (x axis), it will be:

The coordinate note for the reflection is (x, y) will be: (x,-y)

Since ∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).

Then the reflections will be:

M(-9, -4)- M1(-9,4)

N(-3, -4)- N1(-3,4)

O(-3,-15)-O1(-3,15)

To solve for Reflection (y axis), it will be:    

The coordinate note for the Reflection  is (x,y) will be (-x,y)

Since ∆M1N1O1  = M1(-9, 4), N1(-3, 4), and O1(-3, 15).

Then M1(-9, -4) - M2(9,4)

N1(-3, -4) - N2(3,4)

O1(-3,-15)- O2(3,15)

To solve for Translation

The coordinate note for the Translation is (x,y) will be (x+2,y+2)

Since ∆M2N2O2  = M2(9,4), N2(3,4), and O2(3, 15).

Then M2(9, 4) - M3(11,6)=A

N2(3,4) -  N3(5,6)=B

O2(3,15) - O3(5,17)=C

Hence  ∆MNO ≅ ∆ABC  

To know the congruent by a single rotation.

 If ∆JKL  can be gotten from ∆PQR

Then ∆JKL ≅ ∆PQR  

For Rotation of 90 degree in an anticlockwise position, then:

The coordinate note for the Rotation is (x,y) will be (-y, x)

So, ∆JKL  = J(17, -2), K(12, -2), and L(12, 7).

J(17, -2)-  J1(2,17)

K(12, -2) - K1(2,12)

L(12,7) - L1(-7,12)

To solve for translation

The coordinate note for the translation is (x,y) will be (x+10,y-14)

Then ∆J1K1L1 =  J1(2, 17), K1(2, 12), and L1(-7, 12).

Hence J1(2, 17) - J2(12,3) = P

K1(2, 12)- K2(12,-2) = Q

L1(-7, 12)- L2(3,-2) = R

So, ∆JKL ≅ ∆PQR.

So therefore, The option  that is shown to be congruent by a sequence of reflections and translations is Option B: Triangle ABC and Triangle MNO

See options below

___ can be shown to be congruent by a sequence of reflections and translations.

1)Pick one to go with the sentence.

a Triangle ABC and Triangle XYZ

b Triangle ABC and Triangle MNO

c Triangle JKL and Triangle ABC

d Triangle PQR and Triangle XYZ

___ can be shown to be congruent by a single rotation.

Pick one to go with the sentence.

a Triangle ABC and Triangle XYZ

b Triangle PQR and Triangle XYZ

c Triangle JKL and Triangle PQR

d Triangle JKL and Triangle XYZ

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The pair of the reciprocal function will be (7, 5) and (11, 9). Then the correct option is A.

Coordinate geometry is the study of geometry using the points in space.

If a linear function contains the pairs (5, 7) and (9, 11).

If the pairs should have the reciprocal function to this one. Then the coordinate gets swapped.

The pair of the reciprocal function will be (7, 5) and (11, 9).

Then the correct option is A.

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The value of y is increasing for x values in Graph C, the correct option is C.

A Linear Graph is the graphical representation of a Straight line equation.

From the graph attached with the answer, The x-y values for all the graphs are observed to determine the graph in which the y value goes up as the x value increases.

For the x value increasing, the value of y is decreasing in Graph A, B, and D.

The y value is rising only for Graph C.

Therefore, the correct option is C.

The complete question is attached with the answer.

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5000 square feet is the largest area that can be enclosed

It is given that a rectangular plot is to be fenced off and divided into three parts/plots on land that borders a barn there are and there is 200 feet of fence that is available.

One-fourth of the perimeter = 50

The other width also equals 50.

So the length of fencing = 200 - 50 - 50 = 100

So the area = 50 x 100 = 5000 square feet.

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Answer:

Law of large Numbers

Step-by-step explanation:

The Law of large numbers.

The law of large numbers plays the main role in probability and statistics. It means that if you repeat an experiment independently so many times and average the result, what you get has to be close to the expected value.

An example of the Law of Large Numbers:

Let's assume that you rolled the dice three times and the outcomes were 6, 6, and 3. Then the average result is 5.

So, according to the law of the large numbers, if we roll the dice a large no. of times, then the average result should be closer to the expected value.

It also states that probability and statistics set a sample size that grows, and the mean of the sample size gets closer to the average of the entire population.

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Since in each option, each input is mapped to only one output, all the options are correct.

A relationship represents a function when each input is mapped to only one output.

In this problem:

Thus all the options are correct.

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Las expresiones matemáticas descritas son: (x-1)4=-4³ y 1/3(x+1)=(-10)-1.

Para identificar las expresiones matemáticas debemos organizar los datos proporcionados en el fragmento de la siguiente manera:

Luego debemos solucionar las expresiones matemáticas para encontrar el resultado final:

A. (x-1)4 = -4³

4x-4 = -64

4x = -64+4

4x = -60

x = -60/4

x = -15

B. 1/3(x+1) = (-10)-1

1/3x+1/3 = -11

1/3x = -11-1/3

1/3x = -32/3

x = -32/3•3

x = -32

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The probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.

Given the true proportion is 0.07, sample size 289.

We have to calculate the probability that the sample proportion will differ from the population proportion by more than 0.03.

Probability is the likeliness or chance of happening an event among all the events possible. The probability lies between 0 and 1.

Probability=number of items/ total items.

True proportion=0.07

n=289

sample population mean=0.07

Sample proportion standard error=[tex]\sqrt{pq/n}[/tex]

=[tex]\sqrt{0.07*0.93)/289}[/tex]

=[tex]\sqrt{0.0651/289}[/tex]

=[tex]\sqrt{0.00022}[/tex]

=0.015

Probability that the sample proportion will differ from the population proportion by more than 0.03=P(I P-p I>0.03)

=P( I Z I>0.03*0.015)

=P ( I z I >0.0045)

=0.99968.

Hence the probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.

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Answer:

7/20

Step-by-step explanation:

15/25 * 14/24 = 210/600 = 21/60 = 7/20

The reflection over the y-axis only changes the sign of the x-component so the reflected point is A' (-3, -1)

Here we can't see the options, so I will teach you how to reflect any point over the y-axis.

Any point on the X-Y plane is defined by its coordinates (x, y).

If we reflect this point over the y-plane, we only change the sign of the x-component of the point.

So after the reflection, we get the point (-x, y).

Then if we apply that reflection to point A (3, -1). We will get the reflected point:

A' (-3, -1)

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Answer:

  100 m²

Step-by-step explanation:

The scale factor for volume of similar figures is the cube of the scale factor for linear dimensions. The scale factor for area is the square of that linear dimension scale factor.

If the ratio of volumes is the cube of the scale factor, then the scale factor for the smaller figure in terms of the larger is ...

  [tex]k=\sqrt[3]{\dfrac{125\text{ m}^3}{729\text{ m}^3}}=\sqrt[3]{\dfrac{5^3}{9^3}}=\dfrac{5}{9}[/tex]

The area of the smaller figure is found from ...

  [tex]\dfrac{A}{324\text{ m}^2}=\left(\dfrac{5}{9}\right)^2=\dfrac{25}{81}\\\\A=(324\text{ m}^2)\cdot\dfrac{25}{81}=\boxed{100\text{ m}^2}[/tex]

The surface area of the smaller solid is 100 square meters.

__

Additional comment

The least surface area for a given volume is that of a sphere. The larger volume given corresponds to a sphere with a radius of about 5.583 meters. Such a sphere will have an area of about 391.7 square meters. There is no known physical object with a volume of 729 m³ that can have a surface area as little as 324 m².

83 boxes are required to carry 800 books.

According to the question:

One Box can hold weight = 30 pounds

We know that ,  1 pound= 0.45 kg

hence, 30 pounds = 30 x 0.45 = 13.5kg  

hence,  one box can carry 13.5 kg of weight.

Now,

Weight of 1 book = 1.4 kg

So, Total Weight of 800 books= 1.4 x 800 kg

And , No. of boxes required to carry 800 books = (1.4 x 800)/13.5 = 82.96

                                                                             or approximately 83 boxes

Hence, 83 boxes are required to carry 800 books.

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The probability is P(X >= 2).

200 random people, n = 200

Let us consider the Binomial expression

i.e.,

P(X = r) = nCr*p^r*q^(n-r)

Here we have to assume that the 3 initials are equally likely events.

i.e.,

p = 1/3

q = 1 - 1/3

= 2/3

Required probability = P(X >= 2)

= 1 - [P(X = 0) + P(X = 1)]

= 1 - [200C0*(1/3)^0*(2/3)^200 + 200C1*(1/3)^1*(2/3)^199]

= 1 - [1*1*(2/3)^200 + 200*(1/3)*(2/3)^199]

= 1 - [(2/3)^200 + 200*(1/3)*(2/3)^199]

= 1 - (2/3)^200 - 200*(1/3)*(2/3)^199

Probability is truly how possibly something is to happen. every time we're unsure about the final results of an event, we will talk about the possibilities of certain consequences and how probably they are. The evaluation of events ruled by means of possibility is called records.

3 styles of probability

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Utilizando el triangulo rectangulo como contraejemplo, veremos que esto es falso.

Primero, sabemos que para todo triangulo la suma de sus angulos internos es igual que 180°.

Ahora, vamos a el triangulo más comun. El triangulo rectangulo.

Este es el triangulo que tiene uno de sus angulos internos igual a 90°.

Digamos que los otros dos angulos internos son A y B, entonces tendriamos:

A + B + 90° = 180°

Despejando A + B obtenemos:

A + B = 180° - 90° = 90°

A + B = 90°

Entonces vemos que la suma de estos dos angulos internos es igual que el tercer angulo.

Encontramos un contraejemplo de la proposición, asi, concluimos que la proposición es falsa.

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Answer:

232.28°

Step-by-step explanation:

Using N = 0 degrees

Arctan ( 12.8 / 9.9)   = 52.28    degrees   ( this A to C )

   C to  A  would be  232.28  °    ( just add 180 degrees)

Answer:

16.2

pls give brainlest

explanation:

lets use pythagorean theorem

12.8^2+9.9^2

which is 163.84+98.01=261.85

261.85 square root = 16.181177

round 16.18=16.2

answer 16.2

The answers to the questions are:

a. the straight-line method of depreciation

[tex]\frac{cost of machine - salvage}{useful life} * period[/tex]

= (240000 - 60000) / 4 * (9 / 12)

= $33,750

The debit is 33750 as well as the credit

b.  the units-of-production method of depreciation

(240000 - 60000) / 60000 * 12000

= $36000

c. the double-declining balance method of depreciation

(24000 *2 /4) * (9/12)

= $90000

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Answer:

y=mx+b

Step-by-step explanation:

Slope intercept form is y=mx+b where "m" should be substituted with the slope and "b" stands for the y-intercept value. "x" and "y" are your input and output values respectively.

The graph of the logarithmic function that passes through (-2,-2) and (1,0) is [tex]\log_2(x+3)-2[/tex].

Suppose that the function is

[tex]f(x)=\log_2(x+c)+d[/tex]

Then there are two observations that we must consider from the figure

So,

[tex]-2=\log_2(-2+c)+d[/tex]

[tex]\implies -2+c=e^{-2-d} ...~...~(1)[/tex]

And,

[tex]0=\log_2(1+c)+d\\\implies 1+c=e^{-d} ~...~...~(2)[/tex]

Observe the figure given below we see that the graph of

[tex]\log_2(x)[/tex] passes through (1,0) but does not pass through (-2,-2) and the graph is to the right of (-2,-2) hence, we need the graph to move left.

When we increase c the graph  [tex]\log_2(x+c)+d[/tex]  moves left and

When we decrease d then the graph  [tex]\log_2(x+c)+d[/tex]  moves down.

That makes the graph required to be   [tex]\log_2(x+3)-2[/tex].

Hence, the graph of the logarithmic function that passes through (-2,-2) and (1,0) is [tex]\log_2(x+3)-2[/tex].

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