Consider the following number pattern: -7; 0; 9; 20; ... Show that the general term of this quadratic number pattern is given by T₁ = n² +4n-12. 2.1​

1. The function for this problem is given as follows: f(x) = x - 3.

2. The numeric value of the function at x = 2 is of f(2) = -1.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

We define the function in this problem as follows:

f(x) = x - 3.

The numeric value at x = 2 is found replacing the lone instance of 2 by 2, hence:

f(2) = 2 - 3

f(2) = -1.

We attribute the function in this problem as f(x) = x - 3.

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The solution to the inequality 7x + 9 ≤ 58 is given as follows:

x ≤ 7.

The inequality for this problem is defined as follows:

7x + 9 ≤ 58.

Isolating the variable x, we have that:

7x ≤ 58 - 9

7x ≤ 49

x ≤ 49/7

x ≤ 7.

Meaning that the inequality is solved similarly to an equality, with the difference that a range of values is obtained instead of a single value.

The problem asks for the solution to the inequality 7x + 9 ≤ 58.

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The answer to the inequality system is y > 2 – x, y < -1

Step 1: Formulate each inequality as y = x + b.

(1) x + y > 2

(2) 2x – y > 1

(3) y > 2 - x Each side of the equation had x subtracted (1)

-y > 1 - 2x 2x were taken out of either side of 2.

(4) y < 2x – 1 -1 multiplied each side, then the inequality was turned around.

Graphing the functions as equalities in step two

(5) y = 2 – x

(6) y = 2x - 1

The borders of the inequalities will be formed by the lines. On one side of a line, the condition will be true, but not on the other (see the diagram below).

Step 3: Highlight the graphs' areas where the inequalities exist.

The graph of y > 2 - x is shown by the red line.

Shade the area above the line because y exceeds a value on the high side of the line (red).

The graph of y = 2x - 1 is shown by the blue line.

Shade the area below the line because y is less than a value on the line's low side (blue).

Any location where the colored regions overlap constitutes the solution set for both inequality problems (purple).

4. Check the outcome.

Input a point in the shaded region, such as (2, 2), and confirm that each inequality is true.

(1) x + y > 2 (2) 2x – y >1

2 + 2 > 2 2(2) – 2 > 1

4 > 2 4 – 2 > 1

2 > 1

It verifies.

The answer to the inequality system is

y > 2 – x, y < -1.

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Correct option is A, (1,2) is the correct option for the given system of equations.

Equations occurring simultaneously, system of equations Algebraic equations involving two or more must be solved cooperatively (i.e., the solution must satisfy all the equations in the system).

For a system to have a single solution, the number of equations must equal the number of unknowns.

A set of simultaneous equations, often known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

A system of equations is a collection of equations with one or more variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.

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Answer:

11+x

Step-by-step explanation:

6 + (5 + x)

because you have a + between 6 and the parentheses then you can just add everything up without warring about them. so:

6+5+x which equals to 11+x

In ΔRST, the measure of angle R is  73.1°

Let us assume that r represents the opposite side of ∠R, and 't' represents the opposite side of ∠T

i.e., r = side ST and t = side RS

We know that the law of sine for triangle states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

i.e., for triangle ABC,

[tex]\frac{sin~A}{a} =\frac{sin~B}{b} =\frac{sin~C}{c}[/tex]

Using sine law for ΔRST,

[tex]\frac{sin~R}{r} = \frac{sin~S}{s} =\frac{sin~T}{t}[/tex]

Consider equation,

[tex]\frac{sin~R}{r} =\frac{sin~T}{t} \\\\\frac{sin~R}{79} = \frac{sin~(58)}{70}[/tex]

79 × 0.8481 = sin(R) × 70

sin(R) = 66.99 / 70

sin(R) = 0.9571

∠R = arcsin(0.9571)

∠R = 73.1°

Thus, measure of angle R = 73.1°

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The correct option that will make the inequality expression 2x - 3 > 11 - 5x true is when x is equal to 2.

We shall evaluate for the values of x to know that make the inequality expression true as follows;

2x - 3 > 11 - 5x

2x + 5x - 3 > 11 {add the 5x to both sides}

7x > 11 + 3 {add 3 to both sides}

7x > 14

x > 14/7 {divide through by 7}

x > 2

Therefore, the value for x that makes the inequality expression 2x - 3 > 11 - 5x true is 2.

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A control group is a group of individuals that is treated in exactly the same way as the experimental group in an experiment, except for the factor that is being manipulated.

This group is used as a comparison to measure the effects of the manipulated factor on the experimental group. The control group is key for determining the validity of the results of an experiment because it helps to ensure that any observed changes are actually due to the manipulated factor. A control group should be chosen at random from the same population as the experimental group and should be given the same conditions as the experimental group, except for the factor that is being manipulated. This helps to ensure that any observed differences in the experimental and control groups are due to the manipulation and not due to any other factor.

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Answer: 100

Step-by-step explanation:

x/2 = 50

Multiply both sides by 2:

x = 100

Answer:

Easy Peasy, MULTIPLY 2 by 50

Just type 100

Answer:

F(x)=-x^2

Step-by-step explanation:

The one example of function with range of only negative number is:

F(x)=-x^2

Why this? We know for every x, x^2 is positive. So -x^2 will be negative.

There are 6840 ways to choose a president, a vice-president, and a secretary from a committee of 20 members.

To choose a president, a vice-president, and a secretary from a committee of 20 members,

We will use the formula for combinations,

which is: C(n, k) = n! / (k! (n - k)!)

where n is the total number of members and k is the number of members being chosen.

So, for n = 20 and k = 1, we have:

C(20, 1) = 20! / (1! (20 - 1)!) = 20

This gives us 20 choices for the president.

For the vice president,

We need to choose 1 member from the remaining 19 members.

So, for n = 19 and k = 1,

we have:

C(19, 1) = 19! / (1! (19 - 1)!) = 19

This gives us 19 choices for the vice president.

Finally, for the secretary,

We need to choose 1 member from the remaining 18 members.

So, for n = 18 and k = 1,

we have:

C(18, 1) = 18! / (1! (18 - 1)!) = 18

This gives us 18 choices for the secretary.

Now for finding the total number of ways to choose the three positions, we multiply the number of choices for each position:

So, the required number of ways will be 20 * 19 * 18 = 6840

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Answer:The factors of 28 and 49 are 1, 2, 4, 7, 14, 28 and 1, 7, 49 respectively

Step-by-step explanation:Some numbers have 28 and 49 as answers

The probability of passing the practical test is 0.25. This is calculated by subtracting the probability of passing the theory test (0.75) from the probability of passing at least one of the two parts (0.36).

0.25

The probability of passing the practical test can be calculated by subtracting the probability of passing the theory test (0.75) from the probability of passing one of the two parts (0.36).

0.36 - 0.75 = 0.25

The probability of passing the practical test is 0.25. This is calculated by subtracting the probability of passing the theory test (0.75) from the probability of passing at least one of the two parts (0.36). The two events of passing the theory test and passing the practical test are independent, so their probabilities can be calculated separately.

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The domain of the quadratic function is x ≥ -6.

The correct option is C.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

Given:

The graph of quadratic function f is shown on the grid.

The domain of f(x) means,

all the values of x where function is defined.

From the graph,

the domain is, x ≥ -6.

Therefore, the domain is x ≥ -6.

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The number of customers are not exactly same in two cases.

In mathematics →

Given is the -

Number of customers this month -

{x} = 250 - {12% of 250}

{x} = 250 - {12/100 x 250}

{x} = 250 - 12 x 2.5

{x} = 250 - 30

{x} = 220

Number of customers last month -

250 = {x} + {12% of x}

250 = {x} + (12/100){x}

250 = {x} (1 + 3/25)

250 = {x} (28/25)

{x} = (250 x 25/28)

{x} = 223 {approx.}

Therefore, the number of customers are not exactly same in two cases.

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The graph of the exponential function y = 3(2)^x - 3 is given by the image presented at the end of the answer.

The parent function is given as follows:

y = 2^x.

Which has:

Then the transformations are given as follows:

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The correct answer is Number of science courses, discrete; time to complete homework, continuous.

Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.

The number of science courses enrolled in is likely a whole number, making it a discrete random variable. On the other hand, the time it takes to complete homework could be any value within a continuous range, such as minutes or hours, so it is a continuous random variable.

Hence, the number of science courses is discrete and time to complete homework is continuous.

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the value of x, y, and z are 2√14, √74, and √252.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, the right triangle that has two other right triangles inside it:

From the Pythagorean theorem:

Hyppotaneus ² = height ² + base²

from the Bigger triangle:

H = 14 + 4 = 18

b = y

h  = x

Thus,

y² + z² = 18*18

y² + z² = 324.....(1)

from the triangle with a height of 14,

z² = x² + 14²

z² = x² +  196....(2)

From the triangle with the base of 4:

y² = x² +  16...(3)

For equations 2 and 3 substitute the value in equation 1

2x² + 212 = 324

2x² = 112

x² = 56; x = 2√14

Thus,

y² = 56 +16

y² = 74; y = √74

z² = 56 + 196

z² = 252; z = √252

Therefore, the value of x, y, and z are 2√14, √74, and √252.

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The logarithmic form of the exponential expressions are;

1) log2 5 = x

2) log3 10 = y

3) logk 6 = 5

4) log2 32 = 5

5) log3 81 = 4

6) log 3 27 = 3

7) log10 100 = 2

8) logx y = 2

9) log10 x = 20

10) logp q = 10

11) logx y = 1/2

12) log9 3 = 1/2

We have to note that we can be able to write an exponential equation in the logarithmic form or in the exponential form. In the exponential form we we would have something like;

a^x = P

While in the logarithmic form we can be able to have something like;

logaP =x

These are the two forms that we can be able to write the equations that we have in the question.

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Inter-Item Reliability is a measure of how consistently different items within a measure are related to each other. It is used to assess the internal consistency of a measure.

An indicator of reliability based on the correlations of each item in a measure with every other item is called: Inter-Item Reliability.

Inter-Item Reliability is a measure of how consistently different items within a measure are related to each other. This is assessed by calculating the correlations between each item and every other item in the measure.

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Answer: 16

Step-by-step explanation:

1/5 x 70 = 14
70 - 14 = 56
5/7 x 56 = 40
56 - 40 = 16

Answer:

16

Step-by-step explanation:

Yesterday, the bookstore sold 1/5 of the 70 copies, which is 70 * 1/5 = 14 copies.

After selling 14 copies, the bookstore was left with 70 - 14 = 56 copies.

Today, the bookstore sold 5/7 of what remained, which is 5/7 * 56 = 40 copies.

So, the bookstore has 56 - 40 = 16 copies left.

The rental cost for each movie and each video game are  $1.25 and $5.25 respectively

An algebraic expression can be defined as an expression that is usually composed of terms, variables, constants, factors and coefficients.

These expressions are also made up of some mathematical operations, such as;

From the information given;

Let movies be x

Let the video games be y

We have that;

3x + 5y = 30

6x + 2y = 18

Make 'x' the subject from equation 1

x = 30-5y/3

Substitute the value

6(30-5y/3) + 2y = 18

expand the bracket

180 - 30y/3 + 2y = 18

-24y + 180/3 = 18

-24y + 180 = 54

y = $5.25

Then, x = $1.25

Hence, the values are $1.25 and $5.25

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The ASA and AAS theorems are used in the proof as explained below for each given statements.

A proof is a logical argument that demonstrates the truth of a mathematical statement.

The proof that can be used to prove each given statements are demonstrated below.

14. Proof for ∆UVY ≅ ∆XVW:

Statement Reason

1. V is the midpoint of YW. 1. Given

2. UY || XW 2. Given

3. YV ≅ WV. 3. Def. of midpoint

4. <UYV ≅ <XWV. 4. Alternate <s theorem

5. <UVY ≅ <XVW 5. Vertical<s theorem

6. ∆UVY ≅ ∆XVW 6. ASA

15. Proof for ∆MSP ≅ ∆RQP:

Statement Reason

1. MS ≅ RQ 1. Given

2. MS || RQ 2. Given

3. <MSP ≅ <RQP. 3. Alternate <s theorem

5. <MPS ≅ <QPR 4. Vertical<s theorem

6. ∆MSP ≅ ∆RQP 6. AAS

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A plot of the two points, where x is the time in minutes and y is the number of pages is shown in the graph attached below.

First of all, we would convert the value of time in hours to minutes as follows;

Conversion:

60 minutes = 1 hour.

x minutes = 2 hours.

Cross-multiplying, we have:

x minutes = 60 minutes × 2 hours

x minutes = 120 minutes.

In this scenario, the time in minutes would be plotted on the x-axis (x-coordinate) of the graph while the number of pages would be plotted on the y-axis (y-coordinate) of the graph.

Next, we would use an online graphing calculator to plot the points representing the time in minutes and the number of pages on a coordinate axes as shown in the image attached below.

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Answer:

input, output

Step-by-step explanation:

A function is a rule that assigns each input exactly one output.

Some questions that have you check a list of points, a table of values, a graph or an equation, to figure out if its a function... you check to see if every x only has one y to go with it. This is what the vertical line test does also.

The graph is a step function with a horizontal jump at x=7, where the cost changes from $350 to $10 per day.

What is the Graph?

The graph of the step function that represents the cost of renting a dumpster for x days is a graph that shows how the cost of the rental changes based on the number of days. The x-axis represents the number of days, and the y-axis represents the cost in dollars.

To write the step function that represents the cost of renting a dumpster for x days, we can use the information provided in the problem statement. The cost for the first week is $350, and the cost for each additional day is $10.

We can write the step function as:

y = 350, if x <= 7

y = 350 + 10(x-7), if x > 7

In the first case, if x is less than or equal to 7 (i.e. within the first week), the cost is $350. In the second case, if x is greater than 7 (i.e. more than one week), the cost is $350 for the first week plus $10 for each additional day.

To graph the step function, we can start by plotting the two points on the graph:

(7,350) represents the point at which the cost changes from $350 to $10 per day

(x,y) = (7,350) + (x-7,10x-70)

The graph is a step function with a horizontal jump at x=7, where the cost changes from $350 to $10 per day.

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Rotate 90 clockwise around E, then reflected over the vertical line K

The slope and y intercept for y-5=2(x-5) is 2 and -5 respectively.

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given

expression

y- 5 = 2(x-5)

y - 5 = 2x - 10

y = 2x+5-10

y = 2x-5

Its in the form of y = mx+c

where m is slope

and c is y intercept.

So,

From the equation ,

we can say that  m = 2 that is slope = 2 and y intercept is -5.

Therefore, The slope and y intercept for y-5=2(x-5) is 2 and -5 respectively.

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Answer:

$327.73

Step-by-step explanation:

$25,800 - $8,000 = $17,800

The car loan is a total of 60 months (so at 60 her payment will be $0) and the interest rate is 3.99%

Growth formula: A = P(1+r)^t

We're asking for what value at x = 60 would make P(1+r)^60 = 0?

As such, $327.73