How many integral solution(s) is/are there for x if -69 ≤ 7x + 9 ≤ 49?​

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

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Answer:

scale factor of 3

Step-by-step explanation:

[character limit pass]

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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The domain is the set of all values in the set (- ∞, ∞).

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a quadratic function as follows -

ax² + bx + c

For any quadratic equation (with vertex at origin), the value of [y] or the range is either the set of all positive values from 0 to infinity when the quadratic function open upwards and  the set of all negative values from 0 to -infinity when the quadratic function open downwards. The domain is the set of all values in the set (- ∞, ∞).

Therefore, the domain is the set of all values in the set (- ∞, ∞).

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{Question in english language is as follows -

How the domain of the quadratic function is determined.}

9514 1404 393

Answer:

  F.  30·tan(52°)

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between the opposite and adjacent sides in a right triangle.

  Tan = Opposite/Adjacent

  tan(52°) = BD/DL

  BD = DL·tan(52°)

The boat-to-dock distance is ...

  30·tan(52°) . . . . matches F

Answer:

-13

Step-by-step explanation:

-2x6 = -12

-9+8= -1

-1+-12=-13

Hope this helps

Answer:

  x = 50

  y = 65

Step-by-step explanation:

The marked sides show you that the triangle is isosceles. That means the base angles, y° and 65°, are congruent.

  y = 65

__

The sum of the angles in a triangle is 180°.

  65° +65° +x° = 180°

  x° = 180° -130° = 50° . . . . . . subtract 130°

  x = 50

Answer:

2,1

Step-by-step explanation:

Find where both lines meet. Then the x coordinate comes first then the y .

Answer:

C. The percentage of people who prefer spring is similar for the two age groups, but the percentages of people who prefer winter and fall differ between the age groups.

Answer: C. The percentage of people who prefer spring is similar for the two age groups, but the percentages of people who prefer winter and fall differ between the age groups.

Step-by-step explanation:

For the information given in the statement, you have that the horses that remain in the stable are

Because initially there are h horses in the stable and 6 of them are going to exercise, then h-6 horses remain in the stable.

Answer:

a) 0.06 = 6% probability that a person has both type O blood and the Rh- factor.

b) 0.94 = 94% probability that a person does NOT have both type O blood and the Rh- factor.

Step-by-step explanation:

I am going to solve this question treating these events as Venn probabilities.

I am going to say that:

Event A: Person has type A blood.

Event B: Person has Rh- factor.

43% of people have type O blood

This means that \(P(A) = 0.43\)

15% of people have Rh- factor

This means that \(P(B) = 0.15\)

52% of people have type O or Rh- factor.

This means that \(P(A \cup B) = 0.52\)

a. Find the probability that a person has both type O blood and the Rh- factor.

This is

\(P(A \cap B) = P(A) + P(B) - P(A \cup B)\)

With what we have

\(P(A \cap B) = 0.43 + 0.15 - 0.52 = 0.06\)

0.06 = 6% probability that a person has both type O blood and the Rh- factor.

b. Find the probability that a person does NOT have both type O blood and the Rh- factor.

1 - 0.06 = 0.94

0.94 = 94% probability that a person does NOT have both type O blood and the Rh- factor.

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, we only have to sum all 6 triangles and the base area :

6 × 6×8/2 + 93.5 = 36×4 + 93.5 = 144 + 93.5 =

= 237.5 in²

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer:

x = 5, y = 13

Step-by-step explanation:

Solve for x:
42 = 8x + 2

40 = 8x

x = 5

This is solved using the alternate interior angles theorem, which states that alternate interior angles (in this case, the 42-degrees and 8x + 2 degree angles) are the same.

Solve for y:

180 = 42 + 6(2y - 3)

180 = 42 + 12y - 18

180 = 24 + 12y

156 = 12y

y = 13

This is solved using the same-side interior angles theorem, which states that same-side interior angles (in this case, the 42-degrees and 6(2y-3)-degree angles) add up to 180 degrees.

Answer:

Monmon is a Beast Digimon. It is a Digimon that has the appearance of an infant monkey. It has enough strength to wield a slingshot the size of its body with ease, and confidence in its abilities to prevent its prey from escaping. It often falls from treetops due to its careless personality. Its stylish traits are its tiger-printed outfit and its white-tipped tail

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

  $28

Step-by-step explanation:

Each round trip will be double the price of a one-way trip, so will be ...

  2 × $3.50 = $7.00

Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...

  4 × $7.00 = $28.00

Answer:

∠6 = 57°

Step-by-step explanation:

∠6 = 180° - 123° = 57°

The FOIL method to find the product (x + 5)(x² - 3x) is x³ + 2x² - 15

You should note the following about FOIL method

It stands for "First, Outer, Inner, Last"

It is the sum of:

· multiplying the First terms,

· multiplying the Outer terms,

· multiplying the Inner terms, and

· multiplying the Last terms

That is  (a+b)(c+d) = ac + ad + bc + bd

Use FOIL (First, Outside, Inside, Last)

The give expression is

x(x²) = x³

x(-3x) = -3x²

5(x²) = 5x²

5(-3x) = -15x

Combine like terms:

x³ - 3x² + 5x² - 15x

x³ + 2x² - 15

Therefore the FOIL method is x³ + 2x² - 15

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Answer:

No she does not.

Step-by-step explanation:

6 3/4 x 4 2/3 = 31 1/2, so there is not enough.

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Answer:

11x - 16

Step-by-step explanation:

3x + (8x-16)

3x + 8x-16

11x - 16

The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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hello how are you? I am fine

Answer:

   quotient: x+5     ||       remainder: 3

Explanation:

                     ____x_+_5______ ............this is quotient

__\(\left(x+5\right)\)___|   \(x^2+\:10x\:+\:28\)

  |                 -----------------------------

  |                    \(x^2 +5x\)

  |               -----------------------------

  |                     5x + 28

  |                     5x + 25

  |                 -----------------------

  |                          3  ...............................this is remainder.

  |

this is the dividend

The solution to the given inequality -3(x - 2) ≤ 1/3 is x ≤ 17/9

-3(x - 2) ≤ 1/3

-3x + 6 ≤ 1/3

-3x ≤ 1/3 - 6

-3x ≤ (1-18) / 3

-3x ≤ -17/3

x ≤ -17 /3 ÷ -3

x ≤ -17/3 × 1/-3

x ≤ -17/-9

x ≤ 17/9

A verbal statement describing the solution to the inequality is x is less than equal to 17 over 9

Verifying the solution of the inequality:

-3(x - 2) ≤ 1/3

-3x + 6 ≤ 1/3

-3(17/9) + 6 ≤ 1/3

-51/9 + 6 ≤ 1/3

(-51+54) / 9 ≤ 1/3

3/9 ≤ 1/3

1/3 ≤ 1/3

Therefore, the -3(x - 2) ≤ 1/3 to the inequality -3(x - 2) ≤ 1/3 in verbal statement is x is less than equal to 17 over 9.

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To find the volume of the solid, you need to calculate the area of each cross-section and then multiply that by the thickness of the section (which is the distance along the y-axis).

(a) Squares: The cross-sections are squares with sides of length y. The area of a square is side^2, so the area of each square is y^2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the square cross-sections is y^2 * y

(b) Semicircles: The cross-sections are semicircles with radii of length y. The area of a semicircle is (pi * r^2) / 2 , so the area of each semicircle is (pi * y^2) / 2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semicircular cross-sections is (pi * y^2) / 2 * y

(c) Equilateral triangles: The cross-sections are equilateral triangles with side length of y. The area of an equilateral triangle is (s^2 * √3)/4. so the area of each equilateral triangle is (y^2 * √3) / 4. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the equilateral triangle cross-sections is (y^2 * √3) / 4 * y

(d) Semi-ellipses: The cross-sections are semi-ellipses whose heights are twice the lengths of their bases. The area of a semi-ellipse is πab/2, where a and b are the lengths of the semi-major and semi-minor axes respectively. Therefore the area of each semi-ellipse will be (πy^2)/2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semi-ellipse cross-sections is (πy^3)/2

It is important to note that this is a theoretical volume calculation, as the shape of the solid does not have a closed form representation by these functions, but rather, these are an approximation.

Also, for any of these volumes to be meaningful, we have to integrate over the range of the variable y, since it is bounded by the equations y=x, y=0 and x=1, the variable y is limited.

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      410.4

5|2,052.00

2,502/5 = 410.4

410.4 rounded is 410.

The average is 410.