THe 54th term of the sequence

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

Step-by-step explanation:

Answer:

improper fraction

Step-by-step explanation:

A mixed number has a whole number and a fraction.

An improper fraction is a fraction with a numerator bigger than the denominator.

Since 17 > 4 and there is no whole number,  this is an improper fraction.

It can be changed to a mixed number by dividing the numerator by the denominator

17 ÷4 = 4 and there is a remainder of 1.  The remainder goes over the denominator

4  1/4

Answer: It's an improper fraction

Step-by-step explanation: It's an improper fraction because an improper fraction is a fraction where the numerator is greater than the denominator, whereas a proper fraction is the opposite. A mixed number is when there is a whole number and then a regular (proper) fraction beside it. Here's an example:

[tex]5\frac{1}{7}[/tex]

Since 17 is greater than 4, 17/4 is an improper fraction. Now, if you wanted to find 17/4 as a fraction, you would divide the 17 by the 4, so the  whole number (4 in this case) would be the whole number, and the faction would be 1/4

So, [tex]\frac{17}{4}[/tex]= [tex]4\frac{1}{4}[/tex]

To check, you can multiply the 4 by the 4, which is 16, and add the numerator (1) to it, which would be 17/4. I hope this helps.

Answer:  True. In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the system before the collision is equal to the total momentum and total kinetic energy of the system after the collision.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

60% of the total calories is from fat

Step-by-step explanation:

We already have our first value 180 and the second value 108. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1Y =

108

180

By multiplying both numerator and denominator by 100 we will get:

STEP 2Y =

108

180

×

100

100

=

60

100

STEP 3Y = 60

Answer:

Step-by-step explanation:

It is impossible to accurately estimate the size of the crowd without knowing how many people are standing in each foot of space. However, if we assume that 16 people fit in a 9 ft x 8 ft area, then we can estimate the size of the crowd in a 2-mile section of the parade route that is 5 feet deep on both sides of the street.

Assuming a 5-foot deep crowd on both sides of the parade route, we can estimate that there would be 40 feet of crowd on one side of the parade route and 40 feet of crowd on the other side of the parade route. This means that there would be a total of 80 feet of crowd across the 2-mile parade route.

Using the assumption that 16 people fit in a 9 ft x 8 ft area, we can estimate that there would be 1280 people across the 2-mile parade route (80 feet x 16 people). This is a rough estimate, as it does not account for the gaps between people, which would likely reduce the total number of people in the parade route.

The value of x is 6

2/5 = 6/21-x

Cross multiply both sides

2(21-x)= 30

42-2x= 30

collect the like terms

-2x= 30-42

-2x= -12

Divide both sides by the coefficient of x which is 2

2x/2 = 12/2

x= 6

Hence the value of x is 6

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Answer:

To find out how many weeks it will take for the pea aphid population to reach 9,600 individuals, we need to determine how many times the population needs to double to reach that number.

We can use logarithms to find this out. Using the rule log(A) / log(B) = log(A) to base B, we can calculate the number of times the population needs to double.

log(9600) / log(2) = log(9600) to base 2 = 9.98

So the population needs to double 9.98 times.

Since the population doubles every week, it will take 9.98 weeks for the population to reach 9,600 individuals.

Vote Branliest!

Answer: 5 weeks

Step-by-step explanation: Based on the information given, let's conduct an equation. It'd look something like this:

300 * [tex]2^{x}[/tex] = 9600

Now, we need to "reduce" the greatest common factors on both sides of the equation. This is so we can find the value of "x" It should look like this:

[tex]2^{x}[/tex] = 32

Now, we need to covert both sides to have the same base, which should look like this:

[tex]2^{x} = 2^{5}[/tex]

Based on the information given, we now know that x = 5, making it have a constant rate of 5 weeks to reach 9,600 individuals. I hope this helped!

Answer:

Mean: [tex]14 \frac{11}{207}[/tex]

Median: 14.5

Mode: 6, 13, and 15

Step-by-step explanation:

We will start by arranging these numbers from smallest to greatest to get the median and mode:

6, 6, 11, 12, 13, 13, 14, 15, 15, 17, 19, 20, 22, 24

To get the mode, we will look. There are two 6, 13, and 15. So those three are our modes. Then, since there are 14 numbers, we will split the list in half and find the average of the two most inward numbers. We get:

6, 6, 11, 12, 13, 13, 14     15, 15, 17, 19, 20, 22, 24

Our two most inward numbers are 14 and 15, so we add the two together and then divide by 2, giving us:

14 + 15 = 29/2 = 14.5

So our median is 14.5.

Finally, we will add up all the numbers together, then divide by 14 to get our mean. We get:

6 + 6 + 11 + 12 + 13 + 13 + 14 + 15 + 15 + 17 + 19 + 20 + 22 + 24 = 207

Then we divide by 14:

[tex]\frac{207}{14} = 14 \frac{11}{207}[/tex]

So, our median is [tex]14 \frac{11}{207}[/tex].

Hope this helped!

The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.

The rate of change is $ 0.75 per attraction.

The table on the number of tickets and total cost is:

Number of tickets                 1                        5                 10               15

Total cost                          $ 10. 75             $ 13.75       $17.50        $ 21. 25

The number of tickets that Sam can buy when he has $ 37 is:

= (Amount to spend - Cost of admission ) / Cost per ticket

= ( 37 - 10 ) / 0.75

= 36 tickets

The rate of change is therefore the $ 0.75 charged per ticket per event.

The number of tickets for $ 10. 75 is:

= ( Total cost - Cost of admission ) / cost per ticket

= ( 10. 75 - 10 ) / 0.75

= 1 ticket

The cost of 5 tickets :

= ( Number of tickets x cost per ticket) + cost of admission

= (5 x 0. 75 ) + 10

= $ 13. 75

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19.63

Step-by-step explanation: area of circle=pi*r^2

3.14*2.5^2

3.14*6.25

=19.625 rounded to nearest tenth is 19.63

The graphs of the functions f(x) and g(x) are attached with the answer.

       [tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]

Given are the functions f(x) and g(x).

The given functions are -

f(x) = [tex]$100(\frac{3}{5})^{x}[/tex]

g(x) = [tex]$100(\frac{2}{5})^{x}[/tex]

Refer to the graphs of the function f(x) and g(x).

Therefore, the graphs of the functions f(x) and g(x) are attached with the answer.

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To answer this, you get to pick any x-value and then solve for y OR you can pick any y-value and solve for x.

For this one, let's pick x = 3.  We'll then substitute 3 in for x in the equation:

       - (3) + 2y = 7

and then solve for x:

       -3 + 2y = 7

Add 3 to both sides:
              2y = 10

Divide by 2 on both sides:
                y = 5

This shows that (3,5) is a solution for the equation.

Again, you could pick any x-value and solve for y OR pick any y-value and solve for x.  There are an infinite number of solutions.

Answer:

the building is approximately 28.3 feet tall, accurate to the nearest tenth of a foot.

Step-by-step explanation:

The height of the building can be found using the Pythagorean theorem, which states that in a right 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. In this case, the building is the hypotenuse, and the base of the ladder and the top of the ladder form the other two sides.

The height of the building can be found using the following formula:

h = √(32^2 - 15^2)

h = √(1024 - 225)

h = √(799)

h ≈ 28.3 ft

Answer:

Step-by-step explanation:

Answer:

0.5 is the answer

Step-by-step explanation:

2 clearly cannot be divided by 4

So what we have to do is put a 0 over the 2 and a decimal in the place after the 2 and bring down a 0 making it 20÷4=5

Don't forget the decimal point that was necessary to create the 20

That makes the answer 0.5

The average rate of change of g(x) =5x^3+4/x^2 on the interval [-1,2] is -2

A function can be defined as a law, rule or expression explaining the relationship between two variables.

These variables are called;

From the information given, we have the function;

g(x) =5x^3+4/x^2

For the interval, {1, -2}

Let's substitute the value of x as 1

g(1) = 5(1)³ + 4/(1)²

find the values

g(1) = 5 + 4/1

g(1) = 9/1 = 9

For x = -2

g(-2) = 5(-2)³ + 4/(-2)²

find the values and substitute

g(-2) =5(-8) + 4/ -8

g(-2) = -40 + 4/-8

add the numerators

g(-2) = -36/8

divide the values

g(-2) = -9/2

The average change = 9 ÷ -9/2 = 9 × 2/-9 = -2

Hence, the value is -2

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Answer:

The equation that this graph corresponds to is y -3/4x + 8

Step-by-step explanation:

The answer choice you chose is correct.

The measure of side KL from triangle KLM is 22 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle HIJ is similar to triangle KLM.

From the similar triangles,

JH/MK =HI/KL

31/13.9 =49/KL

31KL=49×13.9

31KL=681.1

KL=681.1/31

KL=21.97

KL≈22

Therefore, the measure of side KL is 22 units.

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A coefficient is a number that is multiplied by a function or an expression.

A coefficient is a multiplier to a function or an expression.

For example, in a polynomial function, the coefficients are the terms that multiply the powers of x.

Taking the standard quadratic function as follows:

y = ax² + bx + c.

The coefficients are a, b and c.

Considering this concept, the blanks are completed on the answer at the beginning.

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Using Squeeze theorem, the limit of the function is 0

The Squeeze Theorem states that if f(x,y) <= g(x,y) <= h(x,y) for all x,y in a region around (x0,y0) and lim (x,y)->(x0,y0) g(x,y) = L, then lim (x,y)->(x0,y0) f(x,y) = lim (x,y)->(x0,y0) h(x,y) = L.

We can use the Squeeze Theorem to find the limit of the given function by finding two other functions that bound it and have known limits as (x,y) approaches (0,0).

We can see that

(x^2+y^2)/(x^2+y^2) <= 3x^2y/(x^2+y^2) <= (3xy)/(x^2+y^2)

As x,y approaches 0, the first inequality approaches 1 and the second one approaches 0, so the limit of the given function is also 0.

Therefore, lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2)) = 0.

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The given system of equations has infinitely many solutions. Option A is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Given equation,
- 6x - 2y = 10 - - - -1

y = - 3x - 5  - - - -2

From equation 1
-6x - 2y = 10
Reform the equation,
-2y = 6x + 10

Divide the above equation by -2,
y = -3x - 5

Since the above equation is equivalent to equation 2, therefore the system of equations has infinitely many solutions.

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Answer:

total probability (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)

3/36=1/12

Step-by-step explanation:

Therefore , to calculate the  average AVC, use the formula: TC at 0 output is 5, which equals fixed cost (FC) of 5.

The fixed cost per unit of output is known as the AFC, and the variable cost per unit of output is known as the AVC. We previously stated that Bob's Bakery can produce 100 loaves with FC = 40, VC = 500, and TC = 540. ATC = TC/Q = 540/100 = 5.4 as a result. Additionally, AVC = 500/100 = 5 and AFC = 40/100 = 0.4.

Here,

Total cost is equal to total fixed cost plus total variable cost, or TC.

In order to obtain the VC at each output, we must first subtract 5 from the TCs for all subsequent output levels.

AVC is now equal to VC divided by Q.

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If the brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. For such data: it is significantly low for a brain because 1386.4 cm³ is less than the upper limit.

Mean = 1085.2 cm³

Standard deviation = 125.6 cm³

Hence,

Lower limit = Mean - 2 x Standard deviation

Lower limit  =1085.2 - 2 x 125.6

Lower limit =1161.2 - 251.2

Lower limit  =910

Upper Limit = Mean + 2 x Standard deviation

Upper Limit = 1161.2 +  2 x 125.6

Upper Limit =1161.2 +251.2

Upper Limit =1412.4

The limit of values is from 910 to 1412.4.

A value below 910 will be is considered low and a value above 1412.4  will be considered high

Therefore 1386.4 cm³ is less than the upper limit. Thus it is significantly low for a brain.

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The number of different sequences of tosses could there have been, if the number of tosses was even 1/2

You should understand that the tosses involves a sequence which is an array of numbers in a particular order

The question reads thus How many different sequences of tosses could there have been, if the number of tosses was even.

Number of tosses = 12

The tosses are 1,2,3,4,5,6,7,8,9,10,11,12 = 12 Times

The even numbers are

2,4,6,8,10,12 = 6 times

The Probability of the toss is 6/12

Therefore the number of tosses equals 1/2

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