….: 5 : 6 : 7= 24 :15 : …. :…. What is the missing number?

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

For the following equations, by the trial and error method in 2(p-3) =6  the value of p is 9

Trial and error is assuming a value for a unkown variable, observing if it works, and if it doesn't trying a new value for the variable.

2p-3 = 15

p=6

2(6) -3 = 9

p=7

2(7)-3 = 11

p=8

2(8)-3 = 13

p=9

2(9)-3 = 15

so, p is 9

For the following equations, by the trial and error method in 2(p-3) =6  the value of p is 9

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Given the following quadratic expression:

Let's check if the given equation can be solved by factoring.

a.) Let's determine the original equation.

From the original equation, we observed that the constant 155/9 is not a perfect square. For the original quadratic equation to be factorable, we must apply the method of completing the square.

Therefore, we can say that the original quadratic equation can't be solved by factoring.

We have to find the equation of a circunference with:

As it is a circunference that passes through a point, we know that the distance between the center and the point must be the radius, as all points in a circunference are at the same distance from the center.

We will find then the radius, by calculating the distance:

Now, this means that the radius is √90.

We use the standard form for the equation of a circle:

where (h,k) is the center of the circle. In this case,

And replacing, we obtain that the equation of the circle is:

f(x) is a linear function whose slope is equal to -1 and y-intercept is equal to -7.

Here we have f(x) defined as:

f(x) = -x - 7

Now, we define a general linear function as:

g(x) = m*x + b

Where m is the slope and b is the y-intercept.

Now, we can rewrite f(x) as:

f(x) = (-1)*x +  (-7)

So f(x) is a linear function with a slope of -1 and a y-intercept of -7.

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step 1

the probability of get 4 in one dice is

P=1/6

so

the probability of get 4 in two dices is

(1/6)*(1/6)=1/36

The length of the guy wire, using similar triangles, is of:

43 feet.

Similar triangles are triangles that share these two features listed as follows:

The height h of the tower can be found using similar triangles, as the two right triangles are similar.

The equivalent measures are given as follows:

Hence the proportional relationship is:

h/7 = 17/3

Applying cross multiplication:

3h = 17 x 7

h = 17 x 7/3

h = 39.67 ft.

Then, applying the Pythagorean Theorem, the length of the guy wire is of:

l² = 39.67² + 17²

l = sqrt(39.67² + 17²)

l = 43 feet. (rounded down).

(the pythagorean theorem is applied as the length of the guy wire is the hypotenuse of the right triangle).

The problem is given by the image at the end of the answer.

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There are 144 players in the 12-team league.

Given:

In one basketball league, there are 96 players on 8 teams.

In another basketball league, there are 12 teams.

All of the teams in both leagues have the same number of players.

we are asked to determine the  number of players in the 12-team league.

⇒ 96 player - 8 teams

⇒ 12 team player = ?

⇒ 96/8 = 12 player.

each team:

⇒ 12 × 12

= 144 players in 12 teams.

Hence we get the answer as 144 players.

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To be able to make x/y table, we substitute any number as x in the given equation y = -1/3x - 2.

Let's create a table,

x solution y

-6 -1/3(-6) - 2 = 2 - 2 0

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

0 -1/3(0) -2 = 0 - 2 -2

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

6 -1/3(6) - 2 = -2 - 2 -4

First, let's draw a sketch of the problem to better understand it:

Since the distances 20, 4√7 and x create a right triangle, we can use the Pythagorean theorem to calculate the value of x.

The Pythagorean theorem states that the length of the hypotenuse squared is equal to the sum of each leg squared.

So we have:

Therefore the wanted distance is 12√2 feet (16.97 ft).

(x-3) is not a factor of [tex]2x^3-4x^2-6[/tex]

and the Remainder is 32 .

Using the remainder theorem, which asserts that if x is a factor in a polynomial p(x), then p(a) = 0, we may say that.

Therefore, p(x) = 2x3 - 4x2 - 6 p(3) = 0 if x - 3 is a factor.

So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then

p(3) = 0

So, substituting x = 3 into the equation, we have

p(3) = 2x³ - 4x² - 6

= 2(3)³ - 4(2)² - 6

= 2(27) - 4(4) - 6

= 54 - 16 - 6

= 54 - 22

= 32

Since p(3) ≠ 0.

x - 3 is not a factor

2. Since p(3) = 32,

Thus the required remainder is 32.

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Answer:

There are 3 common factors of 63 and 54, that are 1, 3, and 9. Therefore, the greatest common factor of 63 and 54 is 9.

Step-by-step explanation:

In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match.

Hope this helped:)

Yes, Because the amount charged grows by $35, a fixed amount, every time the number of months increases by 1.

Direct proportion, also known as direct variation, is a relationship between two quantities when their ratio equals a fixed number. The proportional symbol is used to denote it. The fact that the other quantity is inverted here means that the same symbol is really employed to denote inverse proportional.

Direct proportionality applies. This is so that the cost of the membership remains constant no matter how many months you choose to pay for. For instance, the cost is 1 x $35 if you pay for one month. The price increases to 2 x $35 if you pay for two months, which is twice as expensive.

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Next two terms of the sequence 4, 8, -16, -32, 64, ?, ? are 128 and -256.

How to solve question in sequence?

Every sequence has certain logic which can be used to find next terms.

Mainly operations like addition, subtraction, multiplication, squares and cubes are used to find the logic.

Trial and error method is applied to comprehend the logic of sequence.

4, 8, -16, -32, 64, A, B.

According to the given question, the sequence can be split in two separate sequences by taking alternate terms -

1) 4, -16, 64, B

2) 8, -32, A

Now clearly the logic is:

Next term is obtained by multiplying the previous term with -4.

Let's check 4x(-4) = -16x(-4) = 64

∴ B = 64x(-4) = -256

Similarly, 8x(-4) = -32

∴ A = -32x(-4) = 128

Hence completed sequence is 4, 8, -16, -32, 64, 128, -256.

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x = 10 is the value of x as per given in the question.

3x + 6  = 36

3x = 30

x = 10

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A sandwich store charges a $10 delivery fee and $4.50 for each sandwich.

a) If an office order 6 sandwiches, the total cost is:

10 + 6(4.50) = 10 + 27 = 37

Then, the cost of the order is $37

b) The total cost of x sandwich is given by the following algebraic equation:

f(x) = 10 + 4.50x

because 10 from the delivery fee and x sandwiches cost 4.50x dollars, f(x) is the total cost.

c) The relationship between the number of sandwiches and the cost of the order is proportional, because if the numbers of sandwiches increases, the cost increases too. It can be appreciated in the function f(x), which is a linear function with a unit rate of 4.50.

Answer: y=2x

Step-by-step explanation:

The equation of the line is y=2x.

Answer:

Explanation:

The median is the value corresponding to the line inside the box. Looking at the box plot, the line is between 8 and 9. Thus,

Median = 8.5

To find the measure of variability, we would find the interquartile range, IQR

IQR = third quartile(Q3) - first quartile(Q1)

The first quartile is the value corresponding to the left end of the box. From the box plot, it is between 5 and 6. Thus,

Q1 = 5.5

The third quartile is the value corresponding to the right end of the box. From the box plot,

Q3 = 11

Thus,

IQR = 11 - 5.5

IQR = 5.5

The range is the difference between the minimum and maximum values. On the box plot,

maximum value = 13

minimum value = 1

Range = 13 - 1

Range = 12

Given the table:

X -3 , 0 , 3 , 6

Y 3, 7, 11, 15

We can write the ordered pairs of the function:

(-3, 3), (0, 7), (3, 11), (6, 15)

Any pair of ordered pairs can be used to calculate the slope, assuming they all belong to the line.

Let's pick the points (-3, 3) and (0, 7). The formula to calculate the slope is:

Substituting:

It can be verified that the slope is 4/3 regardless of the points selected to calculate it.

Answer: 4/3

Answer: I suppose it is still 60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

becaus eit the whole nimber

a) The proportional relationship is: M = 2.4R.

b) The graph of the proportional relationship is given by the first image at the end of the answer, and they would raise $2,400 selling 1000 tickets.

3. The slope of the function, and the relation with the graph, is as follows:

4. The graph is given by the second image at the end of the answer.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

A proportional relationship is a linear function with intercept zero, hence it is given as follows:

y = mx.

Item a states that the students collect $24 for selling 10 raffles, hence the slope is:

m = 24/10 = 2.4.

Hence the equation is:

M = 2.4R.

If they sold 1000 tickets, the amount they would raise is of:

y = 2.4 x 1000 = $2,400.

The domain of this graph excludes negative values, as the number of raffles sold cannot be negative.

The function for item 4 is:

y = 3/11(x - 2).

Hence the intercepts are:

The graph connecting these poins is the second one at the end of the answer.

The text before item a is:

The students collect $24 for selling 10 raffles.

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The greatest common factor or GCF in the expression  4y + xy² + 6y is y.

The given expression is 4y + xy2 + 6y

GCF stands for greatest common factor

Among these three numbers ;

the variable y is common in all three of them

The factors of 4 y = 4 and y

the factors of xy² are x and y

and the factors of 6y are 6 and y

This can also be simply written by taking y common in this

for example; y ( 4 + xy + 6 )

From the above mentioned proof we can establish the fact that the variable y is common in all three of them

Thus the greatest common factor among them is y

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First, let's calculate the Profit functions which is P(x)=R(x)-C(x)

Let's continue simplifying the function

The profit function is a polynomial function, so the domain is all the real numbers which means x can be any real number

Domain=(-∞,∞)

Calculating x=-10 doesn't make sense because x in all the functions is the number of items, and doesn't make sense to have -10 items, so x shouldn't be negative numbers.

And Calculating x=1000 doesn't make sense either because the problem says "The maximum capacity of the company is 110 items" so if we have x=1000 we are exceeding the limit of items that the company can handle.

Now let's calculate the profit when producing 40 and 50 items (we just need to evaluate those values in the function):

The profit when the company produces 50 items is 500 and the profit when the company produces 40 items is 550.

The company should choose to produce 40 items because is a higher profit in contrast to making 50 items.

According to the function, when we replace the values in X we can see that the term (X^2) grows more than the term X and as you can see the term X^2 is negative which decreases the final result of the profit. Another way to see this is by drawing the function

As you can see the function is a parable and when the number of items "X" is very high the function tends to decrease. The function starts to grow in profit until 40 items (when you find the maximum value of profit) and then the profit function decreases.

The coordinates of A' is (-0.5, 1)

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size.

Given:

A (-1,2) B(4,-3) and C (0,0)

First ABC is dilated by 0.5.

The transformation rule of this dilation is:

(x, y)--> 0.5 (x, y)--> (0.5x, 0.5y)

So, the coordinate of A' after dilation is

(-1, 2 ) --> 0.5(-1, 2)--> (-0.5 , 1)

Hence, the coordinates of A' is (-0.5, 1)

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From the given question

The volume of a cone is:

Now,

We are given with radius and the height of the cone

So,

We can solve for the radius as a function of water level using ratio and proportion

Then,

Substitute the value of r into the above formula

So,

Then,

Taking derivatives

The,

Solving for the dh/dt

So,

Hence, the answer is 9.55.

Answer:

2, 3, 5

Step-by-step explanation:

There is no side-side congruence theorem.

There is also no angle-side-side congruence theorem.

That eliminates choices 1 and 4.

The triangles show side-angle-side-angle as congruent corresponding parts.

Also using the vertical angles at vertex C, you get angle-side-angle.

Answer: choices 2, 3, and 5.

We need to operate the next matrixes.

First, subtract the next matrixes:

13 10 7

6 8 1

2 5 0

-

3 -2 6

14 -6 11

8 -12 9

=

13-3 10-(-2) 7-6

6-14 8-(-6) 1-11

2-8 5-(-12) 0-9

=

10 12 1

-8 14 -10

-6 17 -9

Now, the result adds to the next matrix:

10 12 1

-8 14 -10

-6 17 -9

+

6 10 15

10 0 9

1 0 7

=

10+6 12+10 1+15

-8+10 14+0 -10+9

-6+1 17+0 -9+7

=

16 22 16

2 14 -1

-5 17 -2

Therefore, the correct answer is the first one.

Answer:

The second scale gives us a bigger drawing than the first scale.

Explanation:

Let's draw the initial scale figure with its measures in centimeters:

So, if the scale is 1 cm to 30 meters, the true length of side A will be:

In the same way, the true length of sides B and D of a playground is:

Now, if we scale the length in meters to centimeter but using the new scale 1 cm to 20 meters, we get that the new scale lengths will be:

So, the new scale drawing is:

Then, we can compare both scale drawing and observe that the second scale gives us a bigger drawing than the first scale.

Answer:

A//F

CE

BD

Step-by-step explanation:

since its an equilateral triangle you can split in half easily