If a1=
1 and an=
(an-1)^2 + 2 then find the value of a4

The answer is

X= 3 and Y= -4

Answer:

If you are solving for substitution then the anwser is x+3, and y = -4 (3, -4)

Step-by-step explanation:

First you solve for x

x-2y=11 to x = 11 + 2y

Then you plug it in to the first equation.

-7 (11 + 2y)- 2 = -13 Then Simplify. -77 - 16y= -13

Solve for Y.

Add 77 to both sides. -16y= 64

Divide both sides by -16

y= -4

The Solve for X

x=11 + 2 x -4

X=3

Therefore the anwser is (3, -4)

Answer:

9

Step-by-step explanation:

\(2 + ( - 5) + 15 + ( - 3)\)

\(2 - 5 + 15 - 3\)

Add the negative and the positive numbers seperately:

\(17 - 8 = 9\)

There are no solutions to the system of inequalities Option (d)

Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.

A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is

y > 3x + 1

y < 3x - 3

The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.

The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.

Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.

To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.

When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.

There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.

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Complete Question :

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Options:

a)Only values that satisfy y > 3x + 1 are solutions.

b)Only values that satisfy y < 3x – 3 are solutions.

c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

d)There are no solutions.

Answer:

D

Step-by-step explanation:

Answer:

3) Equation of line is: 5x-8y+34=0

4) Equation of line is: 5x+y+5=0

Step-by-step explanation:

3) Equation of line parallel to \(5x-8y+12=0\) and through point (-2,3)

When two lines are parallel they have same slope.

Converting the given equation \(5x-8y+12=0\) to Slope intercept form i.e \(y=mx+b\)

\(5x-8y+12=0\\-8y=-5x-12\\y=-\frac{5x}{-8}-\frac{12}{-8}\\y= \frac{5x}{8}+\frac{3}{2}\)

Now comparing with \(y=mx+b\) we get value of m i.e 5/8 which is slope of line.

Now, finding y-intercept using point (-2,3) and slope 5/8

\(y=mx+b\\3=\frac{5}{8}(-2)+b\\3=-\frac{5}{4}+b\\b=3+\frac{5}{4}\\b=\frac{3*4+5}{4}\\b=\frac{12+5}{4}\\b=\frac{17}{4}\)

So, y-intercept is b= 17/4

The required equation is:

\(y=mx+b\\y=\frac{5x}{8}+\frac{17}{4}\)

Writing in Standard form

\(y=\frac{5x}{8}+\frac{17}{4}\\y=\frac{5x+17*2}{8} \\y=\frac{5x+34}{8} \\8y=5x+34\\5x-8y+34=0\)

So, Equation of line is: 5x-8y+34=0

4) Equation of line perpendicular to \(x-5y+2=0\) and through point (-2,5)

When two lines are perpendicular they have opposite slope i.e m=-1/m.

Converting the given equation \(x-5y+2=0\)  to Slope intercept form i.e \(y=mx+b\)

\(x-5y+2=0\\-5y=-x-2\\y=-\frac{x}{-5}-\frac{2}{-5}\\y= \frac{x}{5}+\frac{2}{5}\)

Now comparing with \(y=mx+b\) we get value of m i.e 1/5 which is slope of given line.

Slope of required line will be: m=-1/m = -5

Now, finding y-intercept using point (-2,5) and slope -5

\(y=mx+b\\5=-5(-2)+b\\5=10+b\\b=5-10\\b=-5\)

So, y-intercept is b= -5

The required equation is:

\(y=mx+b\\y=-5x-5\)

Writing in Standard form

\(y=-5x-5\\5x+y+5=0\)

So, Equation of line is: 5x+y+5=0

Answer:

Step-by-step explanation:

to find this answer you have to know how to make a percent of something to a normal value so to make 91% to a decimal value you divide by 100. That is 0.91. Then you multipy 0.91 x 80=72.8

He got 72 questions right

The correct answer is option C which is the degree of ab⁴ will be 5.

The maximum power of the variable in the polynomial is called the degree of the polynomial.

Here in the question, we have to find the polynomial with the degree of 5 so we can see that the degree of the polynomial ab⁴. Here a have one degree and the power of b is 4.

Therefore the degree of the variable ab⁴ is 5 the correct answer is option C which is the degree of ab⁴ will be 5.

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Given:

Differentiate with respect to t

The rate of change of elevation when x=25 is decreasing 5 feet/s .

Answer:

5.25

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

I will do 9 only. You can do 11.

Question 9

sin(60) = x/8

sin(60)(8) = x

4•sqrt{3} = x

x^2 + y^2 = 8^2

(4•sqrt{3})^2 + y^2 = 64

16(3) + y^2 = 64

48 + y^2 = 64

y^2 = 64 - 48

y^2 = 16

sqrt{y^2} = sqrt{16}

y = 4

Do 11 the same way.

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

90

Step-by-step explanation:

5+6+4=15

15 x 6=9

You can use the following formula:

a/b ÷ c/d = (a*d)/(b*c)

So:

Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

Answer: There is 1 compounding period for this investment.

Step-by-step explanation: To determine the number of compounding periods, we can use the following formula:

n = (t / p) * m

where:

n = number of compounding periods

t = time period in years

p = payment frequency per year

m = compounding frequency per payment period

In this case, we have:

Principal = $1832

Future value = $2193

Interest rate = 8.1%

Payment frequency = 12 (monthly)

First, let's calculate the time period in years:

t = 1 year / 12 months = 0.0833 years

Next, let's determine the compounding frequency per payment period:

m = 12 (since interest is compounded monthly)

Now we can calculate the number of compounding periods:

n = (t / p) * m = (0.0833 / 1) * 12 = 1

Therefore, there is 1 compounding period for this investment.

To find the number of compounding periods, we can use the formula:

n = (t x f)

where:

n = number of compounding periods

t = time in years

f = frequency of conversion

We are given that the principal is $1832, the future value is $2193, the interest rate is 8.1%, and the frequency of conversion is monthly. We need to find the time in years.

To find the time in years, we can use the formula:

FV = PV x (1 + r/n)^(nt)

where:

FV = future value

PV = present value

r = interest rate

n = number of compounding periods per year

t = time in years

Substituting the given values, we get:

$2193 = $1832 x (1 + 0.081/12)^(12t)

Simplifying this equation, we get:

1.1971^(12t) = 1.1971

Taking the natural logarithm of both sides, we get:

12t x ln(1.1971) = ln(1.1971)

Solving for t, we get:

t = ln(1.1971) / (12 x ln(1.1971))

t = 3 years

Now that we know the time in years, we can find the number of compounding periods:

n = (t x f)

n = (3 x 12)

n = 36

Therefore, the number of compounding periods is 36.

Answer: 15

Step-by-step explanation:

The range is the set of all Y values, in this question -8 is the minimum and +7 is the maximum, therefore the range is (-8-7) = -15, but range is not negative so we get 15

Answer:

c) 5x + 13x = 180

Step-by-step explanation:

c) 5x + 13x = 180

c) 5x + 13x = 180

Hey there!

We simply have to do 182/2.8, and you will get the area (65m^2).

We know that the formula for area is length x width, and the formula for volume is length x width x height. In the volume formula, we can see it can also be area x height to get volume. So, we know that area x height = volume, right? And in this equation, we are given volume and height. If          V = ha, with V = volume; h = height; a = area, we can divide "h" on both sides, and we get V/h = a, or volume divided by height is area. To solve for the above equation, we can plug the numbers in the formula: 182/2.8 = a, or 65 = a.

Hope this helps! Have an amazing day, and remember, you've got this!

a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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Answer:

6 black marbles

Step-by-step explanation:

19+1=20

120/20=6

6×19=114

120-114=6

Step-by-step explanation:

You want to find the equation for a line that passes through the point (4,21) and has a slope of 01.

First of all, remember what the equation of a line is:

y = mx+b

Where: m is the slope, and b is the y-intercept

To start, you know what m is; it's just the slope, which you said was 01. So you can right away fill in the equation for a line somewhat to read:

y=01x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(4,21). When x of the line is 4, y of the line must be 21.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the 1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (4,21).

Answer:

(f - g)(x) = -x² + 2x + 3

Step-by-step explanation:

Step 1: Define

f(x) = 2x + 3

g(x) = x²

(f - g)(x) = f(x) - g(x)

Step 2: Set up expression (Substitute)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 2x + 3 - x²

Step 3: Simplify

(f - g)(x) = -x² + 2x + 3

\( \qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

Let's solve ~

\(\qquad \sf \dashrightarrow \: \dfrac{2x - 1}{5} = \dfrac{x - 2}{2} \)

\(\qquad \sf \dashrightarrow \: 2(2x - 1) = 5(x - 2)\)

\(\qquad \sf \dashrightarrow \: 4x - 2 = 5x - 10\)

\(\qquad \sf \dashrightarrow \: 5x - 4x = -2 + 10\)

\(\qquad \sf \dashrightarrow \: x = 8\)

Value of x is 8

From the steps shown in the solution below; the solution to the problem is x = -1.

An equation is any mathematical statement that contains the equality sign.

The first step here is to obtain the LCM of 2 and 5 which is 10. The next step is to multiply each term with the LCM of 2 and 5 which is 10. So;

10( 2x - 1)/5 = 10 (x - 2)/5

4x - 2 = 2x - 4

4x - 2x = -4 + 2

2x = -2

x = -1

The solution to the problem is x = -1.

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Option (b) is the correct answer: Perpendicular segments.

Perpendicular rays, perpendicular segments, perpendicular lines, and parallel lines are important concepts in geometry that describe the relationship between lines and line segments.

1. Perpendicular Rays: Perpendicular rays are two rays that intersect at point and form a right angle (90 degrees) at the point of intersection. The rays extend indefinitely in opposite directions from the point of intersection.

2. Perpendicular Segments: Perpendicular segments are line segments that intersect at a right angle. They share a common endpoint but do not extend indefinitely like rays. The right angle is formed at the point of intersection.

3. Perpendicular Lines: Perpendicular lines are lines that intersect at a right angle. They continue indefinitely in opposite directions and form four right angles at the point of intersection. Perpendicular lines are often denoted by a symbol ⊥.

4. Parallel Lines: Parallel lines are lines that never intersect. They remain equidistant from each other at all points. Parallel lines have the same slope and do not converge or diverge. In Euclidean geometry, parallel lines are denoted by a double vertical line symbol (||).

Understanding these concepts is fundamental in geometry as they help define angles, shapes, and spatial relationships. The properties of perpendicular and parallel lines play a crucial role in various geometric theorems and applications.

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Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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