Draw diagonal BD. how will this diagonal relate to the circumscribed circle. explain your reasoning

The solution to the equation 8^(2x) = 4096 is x = 2.

To solve the equation 8^(2x) = 4096, we can follow the steps outlined below:

Step 1: Recognize the base

The equation involves the base 8. Since 8 can be written as 2^3, we can rewrite the equation as (2^3)^(2x) = 4096.

Step 2: Apply the power rule

Using the power rule of exponents, we can simplify the equation further. By multiplying the exponents, we have 2^(3 * 2x) = 4096.

Step 3: Simplify the equation

Continuing from Step 2, we simplify the equation to 2^(6x) = 4096.

Step 4: Write 4096 as a power of 2

Since 4096 can be expressed as 2^12, we rewrite the equation as 2^(6x) = 2^12.

Step 5: Apply the exponent rule

Equating the exponents, we get 6x = 12.

Step 6: Solve for x

Dividing both sides of the equation by 6, we find x = 2.

Therefore, the solution to the equation 8^(2x) = 4096 is x = 2.

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The shape that can tessellate without leaving gaps is the hexagon (option A).

The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).

A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.

On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.

A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.

In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).

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The hyperbolas that open horizontally are equations are:

(x-1)²/6² - (2y+6)²/5² = 1

(2y-6)²/3² - (x+6)²/2² = 1

(2y-10)²/10² - (x+3)²/12² = 1

To identify the hyperbolas that open horizontally, we need to look at the equations and determine the orientation of the terms involving x and y.

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The triangle that has an angle greater than 90° and two congruent sides is a obtuse isosceles triangle.

An obtuse isosceles triangle is a triangle in which one of the three angles is obtuse (lies between 90 degrees and 180 degrees) and the other two acute angles are equal in measurement.

One example of obtuse isosceles triangle angles is 30°, 30°, and 120°.

An obtuse isosceles triangle can be considered as the triangle that contains the properties of both an isosceles triangle and an obtuse triangle.

Thus, the triangle that has an angle greater than 90° and two congruent sides is a obtuse isosceles triangle.

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The solution to the systems of equations graphically is (8, -1)

From the question, we have the following parameters that can be used in our computation:

y = -x + 7

y = 1/4x - 3

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This point is located at (8, -1)

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Question

Solve the following system of equations graphically on the set of axes below.

y = -x + 7

y = 1/4x - 3

Part A.

The probability of randomly selecting a student who is a girl that prefers the timber wolf is:

19/120

Part B.

The probability of randomly selecting a student who is not a boy that prefers the lion is:

2/3

Probability is the likelihood of a desired event happening. Mathematically:

Probability = Number of occurrence / Number of possible outcomes

Part A.

First, check the value that corresponds to girl and timber wolf in the table. The value is 19.

Also, the total number of students is 120.

Thus, probability of randomly selecting a student who is a girl that prefers the timber wolf is:

19/120

Part B.

The probability of randomly selecting a student who is not a boy that prefers the lion will be:

1 - (probability of randomly selecting a student who is a boy that prefers the lion)

1 - 40/120 = 2/3

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Noah earned $160 last month, and his income tax rate is 10%. To calculate how much he earns after tax, we need to subtract the tax amount from his earnings.

The tax amount is equal to 10% of his earnings, which is:

0.1

×

160

=

16

0.1×160=16

Therefore, Noah's earnings after tax is:

160

−

16

=

144

160−16=144

Noah earns $144 after tax.

The probability that at least one of the two students does not play a sport is:

(D) 88%

Probability is the likelihood of a desired event happening. Mathematically:

Probability = Number of occurrence / Number of possible outcomes

The probability that at least one of the two students does not play a sport is:

1 - (the probability that both students play a sport).

Since 35% of high school students play a sport. The probability that both students play a sport is:

0.35 * 0.35 = 0.1225.

Therefore, the probability that at least one of the two students does not play a sport is:

1 - 0.1225 = 0.8775

                = 87.75%

                ≈ 88%

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Answer:

0.2356, 0.1444

Step-by-step explanation:

Is 100 points even possible?
Here it states that 62% of them go on vacations. If 2 people are selected, each one ( technically ) has a 62/100 chance of going on a vacation. So the chance that one goes on vacation and one doesn't is .62 * .38 or .2356. The chance that none of them go on vacation is 0.38 * 0.38 or  0.1444.
Hope this helps

The equivalent expression in the context of this problem is given as follows:

A. 5k² - 3k + 1

The expression in the context of this problem is given as follows:

(15k³ - 9k² + 3k)/3k.

The common term in the numerator is given as follows:

3k.

The simplified numerator then is given as follows:

3k(5k² - 3k + 1).

Simplifying the common term 3k to the numerator and to the denominator, the simplified expression is given as follows:

A. 5k² - 3k + 1

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The resultant of the movement of the runner is 290.087 yards

The cosine rule states that if a , b ,c are sides of a triangle and A,B ,C are the opposite angles of the sides, then, c² = a² + b² − 2ab cos(C).

The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.

c² = 250² + 110² -2( 110) (250) cos 100

c² = 62500 + 12100 - 55000(-0.1738)

c² = 74600 + 9570

c² = 84170

c = √ 84170

c = 290.87 yards

Therefore the resultant of the runner pathway is 290.87 yards

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Answer:

109

Step-by-step explanation:

85-77=8

93-85=8

101-93=8

101+8=109

The predicted average score for persons taking a 47-hour review course is approximately 681.2

Given data points:

Review time (x1) = 30 hours, Score (y1) = 620

Review time (x2) = 70 hours, Score (y2) = 764

First, let's calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = (764 - 620) / (70 - 30)

m = 144 / 40

m = 3.6

Next, let's calculate the y-intercept (b) using the formula:

b = y - mx

Taking one of the data points (let's use (x1, y1) = (30, 620)):

b = 620 - 3.6 * 30

b = 620 - 108

b = 512

Now we have the slope (m = 3.6) and the y-intercept (b = 512), so the linear equation that fits this data is:

y = 3.6x + 512

To predict the average score for persons taking a 47-hour review course, we can substitute x = 47 into the equation:

y = 3.6 * 47 + 512

y = 169.2 + 512

y ≈ 681.2

Therefore, the predicted average score for persons taking a 47-hour review course is approximately 681.2 (rounded to the nearest tenth).

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The expression which would be easier to simplify if the associative property is applied to the grouping is (2 + 5/2) + (-1/2)

The associative property is a mathematical property that states that the grouping of numbers or terms in an addition or multiplication operation does not affect the result.

The expression (2 + 5/2) + (-1/2) would be re-written as follows :

(2 + 5/2) + (-1/2) = 2 + (5/2 + (-1/2))

A. (2 + 5/2) + (-1/2) can be simplified by associating the terms inside the parentheses differently:

(2 + 5/2) + (-1/2) = 2 + (5/2 + (-1/2))

This expression allows us to simplify the fractions with equal denominator more easily.

Hence, expression which would be easier to simplify if the associative property is applied to the grouping is (2 + 5/2) + (-1/2)

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Answer:

[tex](x+3)^2+\left(y-\frac{1}{2}\right)^2=\frac{85}{4}[/tex]

Step-by-step explanation:

Since the diameter of the circle has endpoints (-4,-4) and (-2,5), then the midpoint of these endpoints is the center of the circle as follows:

[tex](x_{c},y_{c})=\left(\frac{-4+(-2)}{2},\frac{-4+5}{2}\right)=\left(-3,\frac{1}{2}\right)\\[/tex]

Also notice that the radius of the circle is one-half of the distance from the point (-4,-4) to the point (-2,5) as follows:

[tex]r=\frac{1}{2}\sqrt{(-2-(-4))^2+(5-(-4))^2}\\r=\frac{1}{2}\sqrt{4+81}\\r=\frac{1}{2}\sqrt{85}\\\\r^{2}=\frac{85}{4}[/tex]

Then, the equation of the circle would be:

[tex](x-x_{c})^2+(y-y_{c})^2=r^2\\(x-(-3))^2+\left(y-\frac{1}{2}\right)^2=\frac{85}{4}\\(x+3)^2+\left(y-\frac{1}{2}\right)^2=\frac{85}{4}[/tex]

The graph initially increases from point A to point C

Based on the information provided, let's analyze the changes in the graph between point A and point C:

The graph increases from point A to point B: this means that as you move from point A to point B along the x-axis, the corresponding y-values on the graph increase.

The graph is constant between points B and C: this indicates that the y-values on the graph remain the same as you move from point B to point C along the x-axis.

Therefore, between point A and point C, the graph initially increases from point A to point B and then remains constant between points B and C.

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Answer:

£16

Step-by-step explanation:

Let's assume the normal price of the coat is represented by the variable "P."

According to the information given, the normal price of the coat is reduced by £12. This can be expressed as:

P - £12

Additionally, in the sale, normal prices are reduced by 25%. This reduction can be calculated by multiplying the normal price by 25% (or 0.25):

0.25P

To find the sale price after the 25% reduction, we subtract the reduction amount from the normal price:

P - 0.25P = £12

Simplifying the equation:

0.75P = £12

To solve for P, we divide both sides of the equation by 0.75:

P = £12 / 0.75

Performing the calculation:

P = £16

Therefore, the normal price of the coat is £16.

The answer to all parts is shown below.

a. To combine the two chemicals, we need to add them together. Therefore, the rational expression for C(z) is:

C(z) = C₁(z) + C₂(z)

C₁(z) = z / (z + 1)

C₂(z) = 2 / (z - 3)

Combining the two chemicals, we have:

C(z) = C₁(z) + C₂(z)

= z / (z + 1) + 2 / (z - 3)

b. To find the simplified equation of V(x), we substitute the expressions for C(z) and H(x) into the formula:

V(x) = C(x) + C₂(x) H(x)

= (z / (z + 1) + 2 / (z - 3)) (x³ - x) / x

Simplifying further, we have:

V(x) = (z(x³ - x) + 2x (z - 3)) / ((z + 1) x)

c. To find the volume when a specific number of units are produced, we substitute the value into the equation V(x) and simplify.

Let's calculate the volume for 50, 100, and 1000 units:

For z = 50:

V(x) = (50 (x³ - x) + 2x (50 - 3)) / ((50 + 1) x)

For z = 100:

V(x) = (100 (x³ - x) + 2x (100 - 3)) / ((100 + 1) x)

For z = 1000:

V(x) = (1000 (x³- x) + 2x (1000 - 3)) / ((1000 + 1) x)

d. To find the number of units needed to achieve a volume of 3000 c³, we set V(x) equal to 3000 and solve for x:

3000 = (z (x³ - x) + 2x (z - 3)) / ((z + 1) x)

Solving this equation for x will give us the number of units needed to produce a volume of 3000 c³.

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Hello!

x = the intersection

5x + 3 = 2x + 15

5x - 2x = 15 - 3

3x = 12

x = 12/3

x = 4

Answer: X=4

Step-by-step explanation: 5x + 3 and 2x + 15 are congruent. sub tract 3 from each side, 5x and 2x + 12 are equal. Subtract 2x from each side, 3x and 12 are equal. Divide each side by 3 and get X=4

The height needed to reach the desired volume is given as follows:

h = 4 ft.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

V = 168, l = 7, w = 6.

Hence the height of the prism is obtained as follows:

7 x 6 x h = 168

h = 168/42

h = 4 ft.

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Answer: 4

Step-by-step explanation:

1 third of 30 is 10 and 2/5s of 10 is 4

Given,

Two functions f(x) and g(x) are inverses if the composite functions are equal to the identity.

This means that:

f(g(x)) = g(f(x)) = x.

Now,

In this problem, we know that  f(x) and g(x) are inverse functions,

Using the above relation, we know that:

f(g(x)) = x

Hence the equation that satisfies the inverse relation between two functions is f(g(x)) = x

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The volume of the given three dimensional figure is 14352 cubic inches.

From the given three dimensional figure, dimensions in rectangular prism are Length = 23 inches, Breadth = 16 inches and Height = 18 inches.

So, volume of rectangular prism = Length×Breadth×Height

= 23×16×18

= 6624 cubic inches

Volume of triangular prism = Area of base × Height

= (23×16) × Height

= 368 × Height

= 368 × 21

= 7728 cubic inches

Total volume = 6624 + 7728

= 14352 cubic inches

Therefore, the volume of the given three dimensional figure is 14352 cubic inches.

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Juan will have more amount money after a year and with a difference of $2048.3.

Compound interest is the interest you earn on interest.

For example if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

The total amount in compound interest is expressed as;

A = P( 1+r/n)^{nt}

where p is the principal, r is the rate and n is the interval at which its compounded.

For Jon

P = $7050, r = 5% = 0.05, n = 1/4 of 12 = 3

A = 7050( 1+0.05/3)^{3×1}

A = 7050( 1.017)³

A = 7050 × 1.052

A = $7416.6

Therefore the total amount for Juan after a year is $7416.6

For Sara,

P = $4867, r = 10% = 0.1 , t = 1.,.n = 365

A = 4867( 1+ 0.1/365) ^{365×1)

A = 4867( 1.00027)^365

A = 4867 × 1.103

A = $5368.3

therefore the total amount for Sara after a year is $5368.3

Therefore Juan will have more money after a year and with a difference of $2048.3

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The Area of Square is 81 cm².

let the side of the square which is length for both rectangles be a.

let the width of rectangle be x and y.

So, x+ y= a

sum of perimeters= 54

2 (a +x ) + 2 (a+ y) = 54

2a+ 2x + 2a+ 2y = 54

2a + 2a + 2(x+ y) = 54

4a + 2 (a) = 54

4a + 2a = 54

6a = 54

a= 54/6

a= 9

So, area of square

= 9 x 9

= 81 cm²

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The force of the rock as it hits the river is 17.15 N.To find the force of the rock as it hits the river, we need to use the formula F=ma (force equals mass times acceleration).

For the first part of the question, when Camille throws the rock at the tree with an acceleration of 2.45 m/s2, we can plug in the given values to get:

F = (1.75 kg) x (2.45 m/s2)
F = 4.29 N

So the force of the rock as it hits the tree is 4.29 N.

For the second part of the question, when Camille drops the rock from the bridge with an acceleration 4 times greater than her throw, we can calculate the acceleration by multiplying 2.45 m/s2 by 4, which gives us 9.8 m/s2 (the acceleration due to gravity).

Then, using the same formula, we can find the force when the rock hits the river:

F = (1.75 kg) x (9.8 m/s2)
F = 17.15 N

So the force of the rock as it hits the river is 17.15 N.

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Answer:

b. no

Step-by-step explanation:

This is not a random sample of the soccer players in the league. A random sample would involve selecting players from the entire population of soccer players in the league using a random and unbiased method. In this case, Donald surveyed only his 3 favorite soccer players, which introduces bias and does not represent the entire population of players in the league.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Average velocity of Julian = -21.4 km / 0.25 hours= -85.6 km/hour Julian's average velocity is -85.6 km/hour.

Given: Julian sets the simulated biker to a speed of 20km/h. After he rides his bike for 15 minutes, Julian's app reports a position of -21.4 km.

To find: What is Julian's average velocity?

Solution:We know that,velocity = displacement/time or velocity = (final position - initial position) / time.

Since Julian started from 0 km and after 15 minutes he reached at -21.4 km. So,-21.4 km - 0 km = -21.4 km (Final position - Initial position)Also, time = 15 minutes.

Converting minutes into hours, 15 minutes = 15/60 hours = 0.25 hours.

Therefore, average velocity of Julian = -21.4 km / 0.25 hours= -85.6 km/hour Julian's average velocity is -85.6 km/hour.

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The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

From the question, we have the following parameters that can be used in our computation:

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

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