A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one-
quarter of the second number and 5. The situation can be represented by using the graph below, where x
represents the second number.
16
14
12+
10
2-
4-22-
2 4 6 8 10 12 14 16 X
Which equations represent the situation?
8
64

The following is deduced from the equation f(x)=(x - 1)^3 + 5

Horizontal shift: 1 left

Vertical shift: 5 down

Vertical stretch factor: 1

Vertical compression factor: 1

Axis of reflection: -x + 6

Domain: all real numbers

Range: all real numbers

Inflection Point: (1, 5)

The vertical stretch factor is a term used in mathematics to describe the transformation that changes the height of a graph while leaving the horizontal axis unchanged. In other words, it's a factor by which the y-values of a function are multiplied to produce a new, stretched or compressed version of the original graph.

The stretch factor is usually represented by the symbol "k". For example, if the equation of a function is y = f(x), then the equation of its vertically stretched image would be y = k * f(x). A positive value of k stretches the graph upward, while a negative value of k compresses the graph downward. If k > 1, the graph is stretched vertically; if 0 < k < 1, the graph is compressed vertically; if k = 1, the graph remains unchanged.

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The determinant of the 3*3 matrix A where A = [[1,2,3], [4,5,6], [7,8,9]] is zero (0).

A matrix's determinant refers to the scalar value calculated for a given square matrix. The determinant is a concept in linear algebra, and its components are square matrixes. It may be viewed as the matrix transformation's scaling factor.

To find the determinant of the given matrix A = [[1,2,3], [4,5,6], [7,8,9]];

From the attached steps in the image below, the next following step would be to add the determinants;

= 1 ×(−3)−2×(−6)+3×(−3)

= -3 + 12 - 9

= 12 - 12

= 0

Therefore, we can conclude that the determinant of the 3*3 matrix A where A = [[1,2,3], [4,5,6], [7,8,9]] is zero (0).

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1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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Answer:

3+ 0 = 3

( 4+7) + 3.0 × 1 = 4 + (7+3)

9 + 8 = 8 + 9

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer:

C

Step-by-step explanation:

please mark brainliest if correct

To find the value of x, we can set the two angle measures equal to each other and solve for x.

Given:

mZA = (4x - 2)°

mZB = (6x - 20)°

Setting them equal to each other:

4x - 2 = 6x - 20

Now, we can solve for x:

4x - 6x = -20 + 2

-2x = -18

Dividing both sides by -2:

x = -18 / -2

x = 9

Therefore, the value of x is 9.

Answer:

The answer is 9.

Step-by-step explanation:

We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:

mZA + mZB + mZC = 180°

Substituting the given values, we get:

(4x - 2)° + (6x - 20)° + mZC = 180°

Simplifying the left side, we get:

10x - 22 + mZC = 180°

Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:

mZA = mZB

Substituting the given values and simplifying, we get

4x - 2 = 6x - 20

Solving for x, we get:

x = 9

Therefore, the value of x is 9.

Answer:

I don't have a clue

Step-by-step explanation:

movies 1.75 each

games 5.75 each

Answer:

Option B

Step-by-step explanation:

704 cubic centimeters

Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

The prime factorization of 45 written as exponents from least to greatest is 45 = 3² × 5¹

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.

Using prime factorisation, we shall consider the first five prime numbers which are; 2, 3, 5, 7, and 11.

45 cannot be divided by 2 without a remainder so we use 3;

45/3 = 15

15 can also be divided by 3 so;

15/3 = 5

3 cannot divide 5 without a remainder so we use 5;

5/5 = 1

hence;

45 = 3 × 3 × 5

45 = 3² × 5¹

Therefore, the prime factorization of 45 written as exponents from least to greatest is 45 = 3² × 5¹

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Answer:

A

Step-by-step explanation:

For a right triangle

\(A=\frac{ab}{2} \\\frac{(10.4)(15.3)}{2} =79.56\)

This is the same as the other triangle because they are the same size because of congruency

Area of the rectangle

\(a^2+b^2=c^2\\\)

\(\sqrt{(10.4^2+15.3^2} =c\)

\(c= 18.5\)

18.5 x 7 = 129.5

Add them all up

129.5+79.56+79.56= 288.62

Answer:

B

Step-by-step explanation:

each side is corresponded to the other so Q=U and P=S

The correct option for the congruency of triangle by using ASA congruent theorem is,

⇒ ∠Q ≅ ∠T

We have to given that,

Two triangles PQR and STU are shown in figure.

Now, We have;

⇒ PQ ≅ ST

⇒ ∠P ≅ ∠S

To show the congruency of triangle by using ASA congruent theorem, we need;

⇒ ∠Q ≅ ∠T

As, PQ = ST

Therefore, The correct option for the congruency of triangle by using ASA congruent theorem is,

⇒ ∠Q ≅ ∠T

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Answer:

\(E(x) = 4.500\) --- Expected value

\(SD(x) = 2.872\) --- Standard deviation

Step-by-step explanation:

Given

\(\begin{array}{ccccccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} & {7} & {8} & {9} \ \\ P(X=x) & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}}& {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} \ \end{array}\)

Solving (a): Expected value

This is calculated using:

\(E(x) = \sum\limits^{9}_{i=0} x_i * P(X = x_i)\)

Since they all have the same probability, the formula becomes:

\(E(x) = \frac{1}{10}\sum\limits^{9}_{i=0} x_i\)

\(E(x) = \frac{1}{10}(0+1+2+3+4+5+6+7+8+9)\)

\(E(x) = \frac{1}{10}*45\)

\(E(x) = \frac{45}{10}\)

\(E(x) = 4.500\)

Solving (b): Standard Deviation

First, we calculate the variance using

\(Var(x) = E(x^2) - (E(x))^2\)

In (a), we have:

\(E(x) = 4.500\)

\(E(x^2)\) is calculated as:

\(E(x^2) = \sum\limits^{9}_{i=0} x_i^2 * P(X = x_i)\)

Since they all have the same probability, the formula becomes:

\(E(x^2) = \frac{1}{10}\sum\limits^{9}_{i=0} x_i^2\)

So, we have:

\(E(x^2) = \frac{1}{10}(0^2+1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2)\)

Using a calculator

\(E(x^2) = \frac{1}{10}(285)\)

\(E(x^2) = 28.5\)

So:

\(Var(x) = E(x^2) - (E(x))^2\)

\(Var(x) = 28.5 - 4.5^2\)

\(Var(x) = 28.5 - 20.25\)

\(Var(x) = 8.25\)

The standard deviation is then calculated as:

\(SD(x) = \sqrt{Var(x)}\)

\(SD(x) = \sqrt{8.25}\)

\(SD(x) = 2.872\) ---- approximated

The first step would be to multiply the bottom equation by -1 to eliminate x, then you would combine like terms, like 5y + 2y, and 16 + 10.

Answer:

Subtracting the 2 equations

Step-by-step explanation:

3x + 5y = 16

3x + 2y = 10

Subtract it;

3y = 6

Divide both sides b 3;

y = 2

Substitute y;

3x + 5y = 16

3x + 5(2) = 16

3x + 10 = 16

Subtract 10 from both sides;

3x = 6

Divide both sides by 3;

x = 2

(x, y) = (2, 2)

Is not possible to define a radius  nor a diameter in a trapezium.

Radius and diameter are two measures defined for circles.

Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).

At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.

To get the area use the formula:

Area = (base1 + base2)*height / 2

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Answer:

1/3

Step-by-step explanation:

y=1/3x+5

This is written in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 1/3

Answer:

The answer would lie within 31 degrees of MP and also as in PM.

Answer:

central m arc MP=118°

Step-by-step explanation:

here

central m arc MN=2* inscribed m arc MN=2*31=62°

again

central m arc MN+ central m arc MP=180° being linear pair

substituting value

62°+central m arc MP=180°

central m arc MP=180°-62°

central m arc MP=118°

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 solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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The probability of matching x successes on n further trials in an experiment with two possible outcomes. There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.

Given that,

The probability of matching x successes on n further trials in an experiment with two possible outcomes is known as the binomial probability (commonly called a binomial experiment).

The following formula gives it:

\(P=C_{n,x}p^{n}.(1-p)^{n-x}\)

Where is the number of distinct combinations of x items drawn from a set of n elements, as determined by the formula below.

\(C_{n,x}=\frac{n!}{x!(n-x)!}\)

And p is the probability that anything will happen.

Being aware that employers are monitoring phone calls is a victory in this issue.

43% of adults fear that their employers are listening to their phone calls,

p=43%=0.43

We must locate Four persons were questioned, and none expressed concern about phone call monitoring by companies.

We count four adults, n=4.

Is there a probability of success of 0? If so, then x = 0.

\(P=C_{n,x}p^{n}.(1-p)^{n-x}\)

\(P=C_{4,0}(0.43)^{0}.(0.57)^{4}\)

P=0.0488

Therefore, There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.

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\(\begin{align}\sf\:\Phi_1 &= \iint_{S_1} (-2u^6\cos(v) - 2u^3\sin(v)) \, du \, dv \\ &= \int_{0}^{1} \int_{0}^{2\pi} (-2u^6\cos(v) - 2u^3\sin(v)) \, dv \, du \end{align} \\\)

Answer: "The pyramid and the cone have the same volume despite their different shapes."

Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

"The pyramid and the cone have the same volume despite their different shapes."

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Answer:

4

Step-by-step explanation:

2x - 3 = 5

add 3 to both sides

2x - 3 + 3 = 5 + 3

Simplify

2x = 8

divide

x = 4

Answer:

\( \boxed { \sf{x = 4}}\)

Step-by-step explanation:

Solution:

Verification:

So in a gumball machine there are 6 gumballs (3+3)

\( \frac{2}{6} \)

because you buy 2 gumballs, which means you bought 2 gumballs out of 6.

Answer:

Range = Highest - Lowest

= 12 - 0

= 12