Based on the graph which congruence theorems or postulates are reasons why these graphs are equal?

simplifying 1,615×10 to the 2 power would give 161500

Index notation is known as a way of representing numbers (constants) and variables (e.g. x and y) that have been multiplied by themselves a number of times.

Index notations, or indices are use to simplify expressions or solve equations involving powers.

For instance;

8 × 8 × 8 × 8

8 is multiplied by itself 4 times

In index form , it is written as 8 ^4, that is, 8 to the 4 power

From the information given, we have to simply 1,615×10 to the 2 power

It can be written as;

= 1, 615 × 10 × 10

= 1, 615 × 100

= 161500

Thus, simplifying 1,615×10 to the 2 power would give 161500

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By definition of perimeter, direct observation and Pythagorean theorem, the perimeter of kite OBDE is 38 units. (Correct choice: C)

In geometry, the perimeter is the sum of the lengths of the sides of a figure.  Herein we must determine the perimeter of a quadrilateral, the kite OBDE, that is, the sum of the lengths of its four sides:, which can be found both by direct observation or by the use of the Pythagorean theorem.

Please notice that the quadrilateral has an axis of symmetry passing through the points O and D, which implies that OB = OE and BD = DE. The length of sides BD and DE is 6 units and the length of the sides OB and DE are:

OB = DE = 0.5 · √(24² + 10²)

OB = DE = 13

Lastly, the perimeter of kite OBDE is p = 2 · 6 + 2 · 13 = 38 units.  

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Answer:  C. 38 units

Step-by-step explanation:  TRUST ME!!! Answer is correct on Edge!!!  :)

Just did it and got it correct!

Answer:

  12 in, 7 in

Step-by-step explanation:

The area of a rectangle is the product of length and width. Here, you are given the area, and an additional relation between length and width.

The two relations between length and width described by this problem are ...

  A = LW . . . . . . . dimensions are of a rectangle

  L = W +5 . . . . . . length is 5 inches more than width

  A = 84 . . . . . . . . area in square inches

Substituting for L and A in the area formula, we have ...

  84 = (W +5)(W)

We can solve this as a quadratic in any of several ways. One of those ways is by factoring.

Essentially, we're looking for factors of 84 that differ by 5. We can consider different factorizations of 84 to see what we get:

  84 = 84×1 = 42×2 = 28×3 = 21×4 = 14×6 = 12×7

The differences between the factors in these pairs are 83, 40, 25, 17, 8, 5.

This means the last pair, with a difference of 5, is the one we're looking for.

 W+5 = 12, W = 7

The rectangle is 12 inches long and 7 inches wide.

__

Additional comment

As a quadratic in standard form, we would have ...

  W² +5W -84 = 0   ⇒   (W +12)(W -7) = 0   ⇒   W = {7, -12}

If you were to solve this by completing the square, you would have ...

  (W +2.5)² = 90.25   ⇒   W = -2.5 ±9.5 = {7, -12}

Taking into account the definition of a system of linear equations, 240 stamps are in Will’s collection.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know that:

So, the system of equations to be solved is

[tex]\left \{ {{30=\frac{1}{3}C } \atop {W=2(C+30)}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

Solving the first equation:

30= [tex]\frac{1}{3}[/tex]C

30÷[tex]\frac{1}{3}[/tex]= C

90= C

Substituting the value in the second equation:

W= 2(90 + 30)

W= 2×120

W=240

Finally, 240 stamps are in Will’s collection.

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The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.

Note that this is simple probability.

Hence probability of the 75% football starts selected randomly where the chance is 93% =

75% x 93%

= 69.75%

The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:

Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.

Recall that the total population is 100%.

From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.

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The height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches. This can be obtained by using the ratio of scale drawing to the real drawing.

Here in the question it is given that,

Thus we can say that, scale of the painting is 2 cm : 7 in

Ratio of scale drawing and real painting is 2 : 7

⇒ Similarly here height of the painting in the scale drawing to the height of the painting in the real drawing will be in the ratio 2 : 7.

We can say that,

2 cm/7 in = x cm/35 in

where x is the height of the painting in the scale drawing

2 cm × 35 in /7 in = x cm

x = 2 × 5 cm

x = 10 cm

Hence the height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches.

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By using the compound interest model, the initial deposit required to receive $ 5 000 every 6 months is $ 125 000.

In this problem we must apply the compound interest model, which represent a periodic accumulation of interest according to the following formula:

C' = C · (1 + r/100)ˣ     (1)

Where:

If we know that x = 1, r = 4, C = x and C' = x + 5 000, then the initial deposit is:

x + 5 000 = x · (1 + 4/100)

x + 5 000 = 1.04 · x

0.04 · x = 5 000

x = 125 000

By using the compound interest model, the initial deposit required to receive $ 5 000 every 6 months is $ 125 000.

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The grid of numbers with a row and column sum of 30 is

3   15  12

17   11   2

10  4   16

The grid in the question has a row sum and column sum of 15

The question implies that we create a similar grid with a row sum and column sum of 30

Represent the grid as follows:

a    b   c

d    e    f

g   h    j

So, we have the following sum of rows

a + b + c = 30

d + e + f = 30

g + h + j = 30

And, we have the following sum of rows

a + d + g = 30

b + e + h = 30

c + f + j = 30

Using trial by error, we have:

3 + 15+ 12  = 30

17 + 11 + 2 = 30

10 + 4 + 16 = 30

When the columns are added, we have

3 + 17 + 10 = 30

15 + 11 + 4 = 30

12 + 2 + 16 = 30

Hence, the grid of numbers is

3   15  12

17   11   2

10  4   16

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Answer:

Step-by-step explanation:

Answer:

i think no 3 hasexactly one 0

Option A is correct. The type of construction that we have here is the bisection of the <D.

The bisection of angle can be defined to be the construction of a ray that would help to divide a particular angle into two equal halves.

In this diagram we can see that the angle here is at D. Hence the construction is aimed at dividing this particular angle into 2. Therefore the answer to the question is The bisection of ∠D.

The bisector does the job of creating an equal measure. The given bisector is known to have the midpoint of the segment. It cuts through this angle and creates two different angles that are of the same size.

If we draw the line in that shape, we will be having the division of that angle. From the explanation here, we can see the answer is the first option

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Answer:

a^2+b^2=c^2

Step-by-step explanation:

leg1=a

leg2=b

hypotenuse=c

a^2+b^2=c^2

Answer:

u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

Step-by-step explanation:      

Step-by-step explanation:

1. Entrance of Head of State and IOC President

2. Playing of the national anthem

3. The parade of the athletes

4. The symbolic release of doves

5. Olympic Laurel Award

6. Official Speeches

7. Opening of the Games

8. Raising the Olympic flag and playing the Olympic Anthem

9. Athletes, judges and coaches’ oath

10. Lighting of the Olympic flame

11. The artistic programme

The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.

Hence, f(-3/5) = 101/25.

Given the function; f(x) = ( 8x² - 2x + 4 ) / 2

To determine the value of the function when x = -3/5, we simply replace the variable x with -3/5 in the function.

f(x) = ( 8x² - 2x + 4 ) / 2

f(-3/5) = ( 8(-3/5)² - 2(-3/5) + 4 ) / 2

Divide each term by 2

f(-3/5) = 4(-3/5)² - (-3/5) + 2

f(-3/5) = 4(9/25) - (-3/5) + 2

f(-3/5) = 36/25 +3/5 + 2

f(-3/5) = ( 36 + 3×5 + 2×25 ) / 25

f(-3/5) = ( 36 + 15 + 50 ) / 25

f(-3/5) = 101/25

The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.

Hence, f(-3/5) = 101/25.

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To solve this question, we simply need to divide the total amount of students by 8% to find out how many students were absent and how many were present.

However, we can't simply multiply it by 8%, so we need to turn that into a decimal.

8% - 0.08

Multiply:

355 x 0.08

= 28.4

Round:

28 kids were absent

Subtract:

355 - 28

= 327

This means that 28 kids were absent, and 327 kids were present.

Answer:

The scale factor is 1/5.

Step-by-step explanation:

You can find the side length of triangles by looking at the points or it might be easier to see if you look at the graphs that I have attached.  I can see that the legs of the small triangle are 3 and the legs of the large triangle are 15.  What do I need to multiple 3 by to get 15?  5.  That is the scale factor from the little triangle to the big triangle.  If I go the other way, the scale factor is the reciprocal of 5 or 1.5

The angle the pole makes with the tent is 39.7°.

Trigonometric ratio: the trigonometric ratio is used to demonstrate the relationship between the sides and angles of a right-angled triangle.

Let θ represent the angle the pole makes with the tent.

Using trigonometric ratios:

Therefore, the angle the pole makes with the tent is 39.7°.

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Z = 1.555 should be used

If we seek an 88% confidence interval, that means we only want a 12% chance that our interval does not contain the true value.

Assuming a two-sided test, that means we want a 6% chance attributed to each tail of the Z-distribution.

the zα/2 value of z0.06.

This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. We find this z-value by reverse-lookup in a z-table.

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.

The standard score (more commonly referred to as a z-score) is a very useful statistic because it

(a) allows us to calculate the probability of a score occurring within our normal distribution and

(b) enables us to compare two scores that are from different normal distributions.

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Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.

Given the data in the question;

Since angle ABD and angle DBC are adjacent angle, there addition will give us the value of angle ABC.

∠ABD + ∠DBC = ∠ABC

We substitute in the given values

61° + 59° = ∠ABC

∠ABC = 120°

Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.

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The remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)

The expression is given as:

x^2y - 2xy - 24y

Factor out y from the expression

y(x^2 - 2x - 24)

Expand the equation

y(x^2 + 4x - 6x - 24)

Factorize

y(x - 6)(x + 4)

Hence, the remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)

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The average rate of change of [tex]f(x)[/tex] on [tex]12\le x\le36[/tex] is the difference quotient

[tex]\dfrac{f(36) - f(12)}{36 - 12} = \dfrac{28 - 34}{24} = \boxed{-\dfrac14}[/tex]

Cheetahs population will be more affected by genetic drift

Genetic drift is the change in a population's frequency of an existing gene variant brought on by chance. Gene variations may totally vanish due to genetic drift, hence reducing genetic variation. Additionally, it may lead to the considerably greater frequency and even fixation of previously rare alleles.

Random drift is a result of recurrently small populations, drastic population reductions known as "bottlenecks," and founder events in which a new population is created from a small number of individuals.

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The probability that the machine produces fewer than 5 defective widgets in a production run of 100 items is 0.10

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 5 widgets.

It has a 0.07 defective rate.

Defective rate fewer than 5

Total Probability = P of 4 defective + P for 3 defective + P for 2 defective + P for  1 defective.

Total Probability = 4/100 + 3/99 + 2/98 + 1/97

Total Probability ≈ 0.10

Therefore, the required probability for fewer than 5 defective rate is 0.10

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It is to be noted that at the seven and half year, is when the revenue of both ads became equal. This is a graph problem. See the explanation below.

Step 1:

Note that the amount of money earned by routine company activities is known as revenue, which is calculated by dividing the average sales price by the number of units sold.

Step 2:

Note that the graph is to be used to justify the statement by the lead executive.

Step 3

From the graph, we know that the revenue in the 10th year for printed ads was $ 2,000,000 and $ 3,000,000 for online ads. Represented on as coordinates, that would be (0,3); (10, 2).

Thus, we can create an equation that states:

(y-2) = [(3-2)/(0-10)] * (x - 10)

⇒ y - 2

= [-1/10] * [x - 10]

Hence,

10y - 20 = - x + 10

10 y + x = 30 ........Lets call this equation A

We can also state that:

Online revenue coordinates on the graph are (0,0,) (10, 3)

Thus,

(y-0) =

[(3-0)/(10-0)] (x -0)

⇒ y = [3x/10]  [10y - 3x] = 0.........Lets make this equation B

For printed Ad Revenue:

Year 12= x

10y + 12 = 30

Y = 18/10

y = 1.8

For online Ad revenue

Year = 12 = x

10y = 36

Y = 36/10

y = 3.6

From the above, it is clear that in year 10, the online ad revenue got doubled as same as that of revenue from printed ads.

In order to get the year in which the revenue were equal, we solve both equations simultaneously:

+ 10y + x = 30

±  10y ≠ 3x = 3

4x = 30

x thus, = 30/4

= 7.5

Thus, it is correct to state that both revenue's became equal by the mid of the 7th year going to the eight year.

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Full Question:

Missing graph is attached.

Answer: 2

Step-by-step explanation:

Each of the two sides of the equation is set equal to y

Answer:

120

Step-by-step explanation:

seema 150 marbles

rani 20 more marbles

alok 50 less marble

150+20=170_rani

170-50=120_alok

correct answer is 28.

If the mean of four numbers is 25 and three numbers are 36, 12 and 24 then fourth number is 28.

given terms are:

first number =36

second number=12

third number=24

fourth number=?

let us assume the fourth number be x.

we know the formula to find mean is:

Mean=addition of given terms / total number of terms

According to given statement, we put the values in above equation and we get,

25=(36+12+24+x) / 4

By rearranging, we get

36+12+24+x=100

72+x=100

x=100-72

x=28

so, the fourth number is 28.

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(a) Let [tex]C(t)[/tex] denote the amount (in grams) of copper (II) sulfate (CuSO₄) in the tank at time [tex]t[/tex] minutes. The tank contains only pure water at the start, so we have initial value [tex]\boxed{C(0)=0}[/tex].

CuSO₄ flows into the tank at a rate

[tex]\left(20\dfrac{\rm g}{\rm L}\right) \left(4\dfrac{\rm L}{\rm min}\right) = 80 \dfrac{\rm g}{\rm min}[/tex]

and flows out at a rate

[tex]\left(\dfrac{C(t)\,\rm g}{400\,\mathrm L + \left(4\frac{\rm L}{\rm min} - 4\frac{\rm L}{\rm min}\right) t}\right) \left(4\dfrac{\rm L}{\rm min}\right) = \dfrac{C(t)}{100} \dfrac{\rm g}{\rm min}[/tex]

and hence the net rate of change in the amount of CuSO₄ in the tank is governed by the differential equation

[tex]\boxed{\dfrac{dC}{dt} = 80 - \dfrac C{100}}[/tex]

(b) This ODE is linear with constant coefficients and separable, so we have a few choices in how we can solve it. I'll use the typical integrating factor method for solving linear ODEs.

[tex]\dfrac{dC}{dt} + \dfrac C{100} = 80[/tex]

The integrating factor is

[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{100}\right) = e^{t/100}[/tex]

Distributing [tex]\mu[/tex] on both sides gives

[tex]e^{t/100} \dfrac{dC}{dt} + \dfrac1{100} e^{t/100} C = 80 e^{t/100}[/tex]

and the left side is now the derivative of a product,

[tex]\dfrac d{dt} \left[e^{t/100} C\right] = 80 e^{t/100}[/tex]

Integrate both sides. By the fundamental theorem of calculus,

[tex]e^{t/100} C = e^{t/100}C\bigg|_{t=0} + \displaystyle \int_0^t 80 e^{u/100}\, du[/tex]

The first term on the right vanishes since [tex]C(0)=0[/tex]. Then

[tex]e^{t/100} C = 8000 \left(e^{t/100} - 1\right)[/tex]

[tex]\implies \boxed{C(t) = 8000 - 8000 e^{-t/100}}[/tex]

Answer:

option 4

Step-by-step explanation:

F = [tex]\frac{kxy}{z}[/tex]

k is the constant of variation

• if the variables are on the numerator they vary directly

• if the variables are on the denominator they vary inversely

In this case F varies directly with x and y ( variables on numerator ) and inversely with z ( variable on denominator )

Answer:

Option A

Step-by-step explanation:

The solution is in the image

The value of x from the given data is 2

Mean is the ratio of sum of numbers to the total samples. Given the following data

15,19,23,41, and Z

The mean is calculated as

Mean = 15+19+23+41+z/5

Since the mean the of the data is given as 20. Substitute

20 = 15+19+23+41+z/5

Cross multiply

20*5 = 15+19+23+41+z

100 = 15+19+23+41+z

100 = 98 + z

z = 100- 98

z = 2

Hence the value of x from the given data is 2

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