can someone tell me what the asnwer is thanks (geometry)

The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Answer:

Step-by-step explanation:

z is a non negitave real number

The measure of the side length labelled x is 23.3 units.

The figure in the image is right triangle.

To find x, we use trigonometric ratio

Sine = Opposite / Hypotenuse

Hence;

sin( 42 ) = 15.6 / x

Solve for x

x = 15.6 /  sin( 42 )

x = 23.3

Therefore, the value of x is 23.3.

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The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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Answer:

picture?

Step-by-step explanation:

Answer:

Visualise the answer as a 90 degree angle, pointing downward (left side going up/left at 45 degrees, and right side going up/right at 45 degrees), with the corner falling on point 0, 3.

The probability of rolling a sum from 2 to 12 on 2 dices is 100%

Given the data,

The two dice should be rolled.

Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).

The resultant 36 results are as follows:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6

2-1, 2-2, 2-3, 2-4, 2-5, 2-6

3-1, 3-2, 3-3, 3-4, 3-5, 3-6

4-1, 4-2, 4-3, 4-4, 4-5, 4-6

5-1, 5-2, 5-3, 5-4, 5-5, 5-6

6-1, 6-2, 6-3, 6-4, 6-5, 6-6

When using two dice, there are a total of 36 possibilities that might occur.

As a result, the results' total ranges from 2 to 12.

Hence , the probability is 100 %

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Where the above relations are given, note that Options A,  D, and E are the relations that represents a function. The others are just relations.

To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.

Note that where you are given domain and range, only the range is represented on the x-axis.

Some of the x values may be seen repeated in B, and C.

How is this so?

B) In a coordinate system, values are represented as (x, y). so

In relations, B 2 is repeated twice to in connection with -5, and -6. That is:

(2, -5) , (2, -6)

Since two is x, then its repetition nullified the relation as a function.

C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.

As a result, Options A,  D, and E are the relations that represent a function.

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Answer:

common ratio =r=3

Step-by-step explanation:

Answer:

−4194304

Step-by-step explanation:

Answer:

  y = 1/2x +7/2

Step-by-step explanation:

The two marked points are 2 units apart vertically, and 4 units apart horizontally. The slope of it is ...

  m = rise/run = 2/4 = 1/2

The value of the y-intercept can be found from

  b = y -mx . . . . . . where (x, y) is a point on the line

Using the point (-1, 3), we find the y-intercept to be ...

  b = 3 -(1/2)(-1) = 3 1/2 = 7/2

Then the slope-intercept equation is ...

  y = mx +b

  y = 1/2x +7/2

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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the approximate solution for the initial conditions x(0)=-2.1, y(0)=0.1 is (-2.1, -1.91). To find the equilibrium points of the system, we set x' and y' equal to zero:

x' = y = 0

\(y' = -6x - y - 3x^2 = 0\)

From the first equation, we get y = 0. Substituting into the second equation, we have \(-6x - 3x^2 = 0\) , which gives us x = -2 or x = 0.

Therefore, the equilibrium points are (-2,0) and (0,0).

To find the linearization at each equilibrium point, we calculate the Jacobian matrix:

J = [0 1; -6-6x -1]

At (-2,0), J = [0 1; -6 -1] and at (0,0), J = [0 1; 0 -1].

To determine the type and stability of each equilibrium point, we calculate the eigenvalues of the Jacobian matrix. At (-2,0), the eigenvalues are -3 and 2, which means it is a saddle point. At (0,0), the eigenvalues are 0 and -1, which means it is a degenerate node.

To find the approximate solution of the system for the initial conditions x(0)=-2.1, y(0)=0.1, we can use numerical methods such as Euler's method or Runge-Kutta method. Here, we will use the Euler's method with step size h=0.1.

We have x(0) = -2.1 and y(0) = 0.1. Using the system of differential equations, we have:

x(0+h) = x(0) + hy(0) = -2.1 + 0.10 = -2.1

\(y(0+h) = y(0) + h*(-6x(0) - y(0) - 3x(0)^2) = 0.1 + 0.1*(-6*(-2.1) - 0.1 - 3*(-2.1)^2) = -1.91\)

Therefore, the approximate solution for the initial conditions x(0)=-2.1, y(0)=0.1 is (-2.1, -1.91).

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A dilation by a scale factor of 5 centered at the  origin simply multplies by 5 the coordinates of every point. So, the new coordinates are (-5, -25)

Answer:

115.24

Step-by-step explanation:

15.35*4.25=65.2375

65.2375+50=115.2375

115.2375≈ 115.24

Answer:

$84.95

Step-by-step explanation:

50+15.35=65.35

15.35+4.25=19.6

65.35+19.6=84.95

Answer:

a

Step-by-step explanation

The plotted upon graph function is y = {x² + 2, x < 1 and -x + 2, x ≥ 2}.

The correct option is A.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

The graph of the function is given:

And function is a piecewise function.

The upper quadratic function defined over the domain x < 1.

And line function define over the domain x ≥ 2.

The function that satisfies the domain is,

y = {x² + 2, x < 1 and -x + 2, x ≥ 2}

Therefore, the function is y = {x² + 2, x < 1 and -x + 2, x ≥ 2}

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The measure of the vertex angle of the isosceles triangle is 96 degrees.

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

Area: ½ × base × height

Perimeter: (2 x length of one of the long sides) + base of the isosceles triangle

We are given that;

The base angle= 42°

If an isosceles triangle has two equal angles, then the third angle (the vertex angle) must also be equal to those angles.

In this case, one of the equal angles measures 42°, so the other equal angle must also measure 42°. The sum of the angles in any triangle is 180°, so we can find the measure of the vertex angle by subtracting the sum of the two equal angles from 180°:

Vertex angle = 180° - 2(42°) = 96°

Therefore, the measure of the vertex angle in the isosceles triangle will be 96 degrees.

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The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

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Answer:

Let the length of the rectangle be L. Then we can use the formula for the area of a rectangle:

Area = Length x Width

Substituting the given values, we get:

16 1/3 = L x 4 2/3

To solve for L, we can first convert the mixed numbers to improper fractions:

16 1/3 = 49/3

4 2/3 = 14/3

Substituting these values, we get:

49/3 = L x 14/3

To solve for L, we can multiply both sides by the reciprocal of 14/3:

49/3 ÷ 14/3 = L

Simplifying, we get:

L = 49/3 x 3/14

L = 7/1

L = 7

Therefore, the length of the rectangle is 7 inches.

Step-by-step explanation:

The equations that can be used to solve for y, the length of the room, are: y(y + 5) = 750, y² – 5y = 750, and y(y – 5) + 750 = 0.

It states that when multiplying a number by a group of numbers added together, you can multiply the number by each individual number in the group and add the products together to get the same answer.

In order to find the length of the room, we need to solve for y in each of the equations given.

First, let's solve for y in the equation y(y + 5) = 750. We can use the distributive property to expand the equation to y² + 5y = 750.

Then, we can subtract 750 from both sides of the equation to get y² + 5y - 750 = 0.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

Second, let's solve for y in the equation y² – 5y = 750.

To solve this equation, we can add 5y to both sides to get y² = 5y + 750. Then, we can divide both sides by y to get y = 5y + 750.

We can then subtract 5y from both sides to get y - 5y = 750. Finally, we can divide both sides by 5 to get y = 150.

Third, let's solve for y in the equation y(y – 5) + 750 = 0.

To solve this equation, we can use the distributive property to expand the equation to y² – 5y + 750 = 0.

Then, we can subtract 750 from both sides to get y² – 5y = -750.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

In conclusion, the equations that can be used to solve for y, the length of the room, are y(y + 5) = 750, y2 – 5y = 750, and y(y – 5) + 750 = 0. The solutions for y are y = -25 and y = 30.

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:  115,151,115,133,313,331

Step-by-step explanation:

The Andre's  number can consist from 1+1+5 or 3+3+1. There are no any other sets of 3 odd digit to get 7.

Lets prove this statement.

Lets 1 of the digit is bigger than 5. However the digit is odd so it can be 7 only. However in this case the residual 2 digits are 0 . This is not possible so the gigits are odd however 0 is even.

Lets check the case when the biggest digit in the set is smaller than 3.

So it can be 1 only.

So the residual 2 digits can be 1 only. The sum of 1+1+1<7 .

SO we've  prooven that the only sets of the digits are 1;1;5 or 3;3;1

The set   1;1;5 can give 3 numbers:

115,151,115

The set   1;3;3 can give 3 numbers as well:

133,313,331

Answer:

DOMAIN : x ∈ (-∞ , -3 )U (4 , ∞) or {x | x ∈ R where x ≠ -3 and 4}

REAL ZEROS : x = 5/3

Step-by-step explanation:

\(f(x) = \frac{3x -5}{x^{2} -x-12}\)

factorize the bottom part

\(x^{2} - x - 12\)

product = -12 , sum = -1 , factors = -4 and 3

\(x^{2} +3x-4x-12=0\)

x (x + 3) - 4(x + 3) = 0

(x - 4) ( x + 3) = 0

x - 4 = 0 and x + 3 = 0

x = 4 and x = -3

for the function f(x) the domain is all real numbers ( R ) except - 3 and 4

Domain = x ∈ (-∞ , -3 )U (4 , ∞)

TO FIND THE ZEROS LET f(x) be equal to zero

\(0 = \frac{3x - 5}{x^{2} - x - 12}\)

cross multiply

0 = 3x - 5

find x

3x = 5

\(x = \frac{5}{3}\)

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

Solve the equation using the quadratic formula ⇨ x² + 11x + 9 = 0

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \sf \: x ^ { 2 } + 11 x + 9 = 0\)

All equations of the form \(\sf\:ax^{2}+bx+c=0\) can be solved using the quadratic formula: \(\sf\frac{-b±\sqrt{b^{2}-4ac}}{2a}\). The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

\( \sf \: x^{2}+11x+9=0 \)

This equation is in standard form: ax² + bx + c = 0. Substitute 1 for a, 11 for b and 9 for c in the quadratic formula \(\sf\frac{-b±\sqrt{b^{2}-4ac}}{2a}\).

\( \sf \: x=\frac{-11±\sqrt{11^{2}-4\times 9}}{2} \\ \)

Square 11.

\( \sf \: x=\frac{-11±\sqrt{121-4\times 9}}{2} \\ \)

Multiply -4 times 9.

\( \sf \: x=\frac{-11±\sqrt{121-36}}{2} \\ \)

Add 121 to -36.

\( \sf \: x=\frac{-11±\sqrt{85}}{2} \\ \)

Now solve the equation \(\sf\:x=\frac{-11±\sqrt{85}}{2}\) when ± is plus. Add -11 to √85.

\( \boxed{ \boxed{\bf \: x=\frac{\sqrt{85}-11}{2} }}\)

Now solve the equation \(\sf\:x=\frac{-11±\sqrt{85}}{2}\) when ± is minus. Subtract √85 from -11.

\( \boxed{ \boxed{\bf \: x=\frac{-\sqrt{85}-11}{2}} } \\ \)

The equation is now solved. The solution set is :-

\(\bf \: x=\frac{\sqrt{85}-11}{2} \\ \\ \sf \: and \\ \\ \bf \: x=\frac{-\sqrt{85}-11}{2} \)

The proper steps for the construction are given as 1, 2 4, and then 3.

The proper steps for the construction are;

1. Place the compass needle on the external point R. Make the compass width greater than the distance from R to the given line.

2. Draw an arc cutting the given line at two points. Mark and label the points of intersection P and Q.

3. Move the compass needle to P and make an arc below the line. Keep the compass width, and move the compass needle to Q. Draw an arc below the line crossing the other arc. Mark and label the point of intersection S.

4. Draw a line from the external point R to the points where the arcs intersect, S. Line RS is perpendicular to line PQ and passes through the external point R.

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Answer:

\(y = {(x + 8)}^{3} - 9\)

the function that connects the point (0;1) with the point (-1;0) is the graph

Explanation:

The equation of the line is:

y = mx + b

Where m is the slope and b is the y-intercept. So, replacing m = -1/42 and b = 2, we get:

y = (-1/42)x + 2

Then, to graph the function, we need to indentify two points. So, given the values of x, we can calculate y as follows

If x = 0

y = (-1/42)(0) + 2

y = 0 + 2 = 2

If x = 42

y = (-1/42)(42) + 2

y = -1 + 2 = 1

Therefore, the graph passes through the points (0, 2) and (42, 1).

Answer:

So, the graph is:

500 represents the initial amount of medication, since when t=0, a=500.

Answer:

Step-by-step explanation:

Y =  Ax2 Bx C

Enter coefficients here >>>  4 7 -20

Standard Form: y = 4x²+7x-20    

1.75 0.875 0.765625 3.0625 -23.0625

Grouped  Form: No valid Grouping      

Graphing Form: y = 4(x+0.88)²-23.06    

Factored Form: PRIME    

Solution/X-Intercepts: -3.28 AND 1.53    

Discriminate =369 is positive, two real solutions    

VERTEX: (-0.88,-23.06)     Directrix: Y=-23.13