Which graph is defined by the function given below? y=(x+2)(x+7)

To find the formula for the nth term of a quadratic or cubic sequence, we can analyze the differences between consecutive terms and use a corresponding formula. For quadratic sequences, the second differences should be the same, while for cubic sequences, the second differences will differ.

To find the formula for the nth term of a quadratic sequence, we need to examine the differences between consecutive terms. Let's analyze each given sequence:

a) 15, 19, 25, 33

The first differences are 4, 6, and 8. Notice that the second differences are the same, which means the formula is quadratic. To find the formula, we can use the quadratic formula:

an = dn2 + cn + b

By substituting the values, we can solve for d, c, and b:

Solving this system of equations will give us the formula for the nth term.

b) 19, 15, 9, 1

The first differences are -4, -6, and -8. Again, the second differences are the same, indicating a quadratic sequence. Following the same process as above, we can solve the equation to find the formula for the nth term.

c) -2, -1, 1, 4

In this case, the first differences are 1, 2, and 3, while the second differences differ. This tells us that the sequence is not quadratic, but rather cubic. To find the formula for the nth term, we need to use a cubic formula instead.

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To find the formula for the nth term of a quadratic sequence, look for a pattern in the differences between consecutive terms. Sequence a) 15, 19, 25, 33 has the formula n^2 + 2n - 2. Sequence b) 19, 15, 9, 1 has the formula -n^2 + 4n + 15. Sequence c) -2, -1, 1, 4 has the formula n^2 - 3n - 2.

To find the formula for the nth term of a quadratic sequence, we need to look for a pattern in the differences between consecutive terms. Let's analyze each given sequence:

Sequence a) 15, 19, 25, 33:

The differences between consecutive terms are 4, 6, and 8. Notice that these differences are increasing by 2 each time. This indicates a quadratic sequence with a common second difference of 2. The formula for this sequence is n^2 + 2n - 2.

Sequence b) 19, 15, 9, 1:

The differences between consecutive terms are -4, -6, and -8. Again, these differences are decreasing by 2 each time. This indicates a quadratic sequence with a common second difference of -2. The formula for this sequence is -n^2 + 4n + 15.

Sequence c) -2, -1, 1, 4:

The differences between consecutive terms are 1, 2, and 3. Just like sequence a), these differences are increasing by 1 each time, indicating a quadratic sequence with a common second difference of 1. The formula for this sequence is n^2 - 3n - 2.

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Answer:

D. 14 small bottles and 5 large bottles

Step-by-step explanation:

[tex]\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-5\\ n=10\\ a_{10}=13 \end{cases} \\\\\\ a_{10}=a_1+(10-1)d\implies 13=-5+(10-1)d \\\\\\ 13=-5+9d\implies 18=9d\implies \cfrac{18}{9}=d\implies 2=d[/tex]

Answer:

Common difference = 2

Step-by-step explanation:

[tex]n^{th}[/tex] term of an arithmetic progression is given by a + (n-1)d, where a is the first term and d is the common difference.

Here first term is given as -5

           a = -5

Tenth term is 13

           n = 10

          [tex]n^{th}[/tex] term = 13

We have

       -5 + (10-1)d = 13

         9 d = 13 + 5

            9 d = 18

               d = 2

Common difference = 2

Every two triangles are similar. Therefore the sides of triangles are in proportion.

We have the equations:

1.

[tex]\dfrac{3}{5}=\dfrac{3+x}{20}[/tex]    cross multiply

[tex]5(3+x)=(3)(20)[/tex]      divide both sides by 5

[tex]3+x=(3)(4)[/tex]

[tex]3+x=12[/tex]      subtract 3 from both sides

[tex]\boxed{x=9}[/tex]

--------------------------------------

2.

[tex]\dfrac{3}{4}=\dfrac{9}{y}[/tex]      cross multiply

[tex]3y=(4)(9)[/tex]

[tex]3y=36[/tex]      divide both sides by 3

[tex]\boxed{y=12}[/tex]

------------------------------------------

3.

[tex]\dfrac{3}{5}=\dfrac{3+9+u}{60}[/tex]

[tex]\dfrac{3}{5}=\dfrac{12+u}{60}[/tex]    cross multiply

[tex]5(12+u)=(3)(60)[/tex]      divide both sides by 5

[tex]12+u=(3)(12)[/tex]

[tex]12+u=36[/tex]      subtract 12 from both sides

[tex]\boxed{u=24}[/tex]

----------------------------------------------

4.

[tex]\dfrac{3}{4}=\dfrac{24}{v}[/tex]              cross multiply

[tex]3v=(4)(24)[/tex]

[tex]3v=96[/tex]      divide both sides by 3

[tex]\boxed{v=32}[/tex]

Answer:

See below.

Step-by-step explanation:

There is no statement given so we can only guess. There is a way of finding out.

Slope ZY = - 1/2

Slope XY = 2

Those two slopes (when multiplied) will equal - 1 (2 * -(1/2) = - 1). That is the definition of two lines meeting at right angles or one line being perpendicular to another.

Answer:

The slopes of XY and ZY are opposite reciprocals.

Step-by-step explanation: Hope this helps

Answer:

The first one

Step-by-step explanation:

The given expression is simplified as x² + 3x - 4.

What is an Algebraic expression?

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

((4x²+ 12x - 16) / (2x + 10)) / ((6x + 24) / (x ²+ 9x + 20))

It can be simplified as,

((4x²+ 12x - 16) (x ²+ 9x + 20)) / (2x + 10) (6x + 24)

Now, (4x²+ 12x - 16)  and  (x ²+ 9x + 20) can be factorised as,

4x²+ 12x - 16 = 4x²+ 16x - 4x - 16

                   = 4x(x + 4) - 4(x + 4)

                   = (4x - 4) (x + 4)

And, x ²+ 9x + 20 = x ²+ 5x + 4x + 20

                           = x(x + 5) +4(x + 5)                            = (x + 4) (x + 5)

Substitute the factors to get the expression as,

(4x - 4) (x + 4) (x + 4) (x + 5) /  (2x + 10) (6x + 24)

= (4x - 4) (x + 4) (x + 4) (x + 5) /  2 × 2(x + 5) (x + 4)

=  (4x - 4) (x + 4) / 4

= 4(x - 1) (x + 4) / 4

= (x - 1) (x + 4)

= x² + 3x - 4

Hence, the given expression can be simplified as  x² + 3x - 4.

Answer:

C. 4x + y = 21

Step-by-step explanation:

(4 x 3) + 9

12 + 9 = 21

Answer:

It's C.

Step-by-step explanation:

It's right on edmentum. Also, just use substitution. Not that hard.

The minute hand has turned 450 degrees and 1.25 of a full turn.

To find the angle the minute hand has turned, we need to find the elapsed time in minutes and convert it to degrees. Since Brent started his homework at 4:00 pm, we need to determine the elapsed time from 4:00 pm to the completion time. Let's say he completed his homework at 5:15 pm, which means 1 hour and 15 minutes have passed. There are 60 minutes in an hour, so the total elapsed time is 60 minutes + 15 minutes = 75 minutes.

To convert minutes to degrees, we need to know that the minute hand completes a full revolution (360 degrees) in 60 minutes. Therefore, we can set up a proportion: 75 minutes is to x degrees as 60 minutes is to 360 degrees. Solving for x, we get:

x = (75 minutes * 360 degrees) / 60 minutes = 450 degrees

So, the minute hand has turned 450 degrees.

As a fraction of a full turn, we can divide the angle turned in degrees (450 degrees) by 360 degrees (a full turn), giving us:

450 degrees / 360 degrees = 1.25

Therefore, the minute hand has turned 1.25 of a full turn.

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We need the time Brent completed his homework to calculate the angle turned by the minute hand and express it as a fraction of a full turn.

To determine the angle turned by the minute hand and express it as a fraction of a full turn, we need to know the time taken to complete the homework. Without that information, we cannot calculate the angle and fraction accurately. Please provide the time Brent completed his homework so we can calculate the desired values.

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Answer:

40.5 g

Step-by-step explanation:

Find how much salt is in 450 g of a 9% salt solution.

Note that

450 g - 100%,

x g - 9%,

then

[tex]\dfrac{450}{x}=\dfrac{100}{9},\\ \\x=\dfrac{450\cdot 9}{100}=40.5\ g.[/tex]

If you evaporated all water from this solution, then you would get 40.5 g of salt.

Answer:

40.5g

Step-by-step explanation:

RSM anyone?

Answer:

D. -1,1,-2i, 2i

Step-by-step explanation:

We should have 4 roots since this is a 4th degree polynomial.  We just have to watch since some of them may be multiple roots.

x^4+3x^2-4 = 0

Factoring this equation

(x^2 - 1) (x^2+4) = 0

We can factor the first term

(x-1) (x+1) (x^2+4) =0

Using the zero product property

x-1 =0  x+1 = 0  x^2+4 =0

x=1        x=-1        x^2 = -4

                            Taking the square root of each side

                           sqrt(x^2) =± sqrt(-4)

                                     x =± sqrt(-1) sqrt(4)

                                       x =±i *2

                                       x = ±2i

So firstly, I will be factoring by grouping. Firstly, what two terms have a product of -4x⁴ and a sum of 3x²? That would be -x² and 4x². Replace 3x² with -x² + 4x²:

[tex]0=x^4-x^2+4x^2-4[/tex]

Next, factor x⁴ - x² and 4x² - 4 separately. Make sure that they have the same quantity on the inside:

[tex]0=x^2(x^2-1)+4(x^2-1)[/tex]

Now you can rewrite it as:

[tex]0=(x^2+4)(x^2-1)[/tex]

However, we can simplify it even further. With the second factor, apply the difference of squares rule (x² - y² = (x + y)(x - y)):

[tex]x^2-1=(x+1)(x-1)\\\\0=(x^2+4)(x+1)(x-1)[/tex]

Now it's fully factored. With this, apply the zero product property and solve:

[tex]x^2+4=0\\x^2=-4\\x=\pm \sqrt{-4}=\pm \sqrt{4}i\\x=\pm\ 2i\\x=2i,-2i\\\\x+1=0\\x=-1\\\\x-1=0\\x=1[/tex]

In short, your answer is D. -1, 1, -2i, 2i

Final answer:

We find that there are 6 rows in the array.

Explanation:

To solve the student's question, we need to find the number of rows in an array made with 24 tiles, where the number of rows is 2 more than the number of tiles in each row.

Let's denote the number of tiles in each row as x, and the number of rows as y.

According to the problem statement, y = x + 2.

Also, the total number of tiles in the array is the product of the number of rows and the number of tiles per row, hence 24 = x * y.

Substituting the expression for y from the first equation into the second equation, we have

24 = x * (x + 2).

To find the value of x, we need to solve this quadratic equation. Starting with simplification, we get

x^2 + 2x - 24 = 0.

This factors to (x + 6)(x - 4) = 0, so x could be -6 or 4.

Since the number of tiles in a row can't be negative, we disregard -6, leaving us with x = 4.

Hence, y = 4 + 2 = 6 rows.

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} \stackrel{-3\cdot 2}{-6}&2\\ \stackrel{-3\cdot 3}{-9}&3\\ \stackrel{-3\cdot 5}{-15}&5\\ \cline{1-2} \end{array}~\hspace{5em}\textit{we know that } \begin{cases} y=3\\ x=-9 \end{cases}\implies 3=k(-9) \\\\\\ \cfrac{3}{-9}=k\implies -\cfrac{1}{3}=k\qquad therefore\qquad \blacktriangleright y=-\cfrac{1}{3}x \blacktriangleleft[/tex]

as you can see above, we can see that "x" can be a product of whatever "y" happens to be, so we know each variable is just a factor away from the other.

Answer:

Direct variation; k = -3; y = -3x  

Step-by-step explanation:

The formula for direct variation is

y = kx     Divide both sides by x

k = y/x

For x = -6, y = 2:

k = -6/2

k = -3

=====

For x = -9, y = 3:

k = -9/3

k = -3

=====

For x = -15, y = 5:

k = -15/5

k = -3

y = -3x

y and x are always in the same ratio, so y varies directly with x.

Answer:

Step-by-step explanation:

Diagonal =9cm

Diagonal of a square is  √2 x length of the side

 √2 x side =9

side =9/ √2

√2 =1.414

side =9 / 1.414 =6.364 cm

The side length of a square with a 9cm long diagonal can be estimated to be approximately 6.36cm using the Pythagorean theorem.

To answer your question about estimating the side length of a square with a 9cm long diagonal, we will make use of the Pythagorean theorem. The Pythagorean theorem is applied in a right-angled triangle and states that the square of the hypotenuse side (the side opposite the right angle, or in this case, our square's diagonal) is equal to the sum of the squares of the other two sides. In case of a square, these two sides are equal in length. So, if we call one of these sides 'a', we can write the theorem as a² + a² = 9². Solving this equation leads us to approximately 6.36cm as the side length of the square.

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Answer:

Volume = 7.66* side^3

side^3 = Volume / 7.66

side^3 = 30 / 7.66

side^3 = 3.9164490862

side = 1.5762707925

side = 1.58 feet (rounded)

Step-by-step explanation:

1.38 feet rounded to the nearest hundredth is correct actually :)

Answer: 13

Step-by-step explanation:

3X5=15, (0+2)=2, -4

15+2-4=13

Answer:

.23  ,1/5  , 1/8 ,.01

Step-by-step explanation:

.I will put them all in decimal form

.01 = .01

1/8 = .125

.23  = .23

1/5 = .2

largest to smallest

.23 >..2  < .125  < .01

Put them back in their original form

.23  >1/5  > 1/8  >.01

.23  ,1/5  , 1/8 ,.01

Answer:

D: 54 Divided by 6

Step-by-step explanation:

To find out how many 6 pound bags of food we can give away, we take the total amount of food and divide by 6

54/6

Answer:

Step-by-step explanation:

1 mph = 1.6 kph

30 ÷ 1.6 = 18.75 mph

18.75 mph x 4 hours = 75 miles

The speed of the cyclist is 18.75 miles per hour and he will travel 75 miles in 4 hours.

To convert the speed from kilometers per hour to miles per hour, we divide the speed in kilometers per hour by 1.6 (since 1 mile is equal to 1.6 kilometers). So, the speed of the cyclist in miles per hour is 30 / 1.6 = 18.75 miles per hour. Cyclist rides at this speed.

To find out how many miles the cyclist will ride in 4 hours, we multiply the speed in miles per hour by the number of hours. So, in 4 hours, the cyclist will travel 18.75 * 4 = 75 miles.

Remember, these answers are precise as we did not round them.

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Answer:

BC = 25

Step-by-step explanation:

If the base angles are equal, then the sides opposite them are as well.

But that's not what you are asked for. You want the value of 2x + 7

Answer:

y = [tex]\frac{3}{2}[/tex] x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c (m is the slope and c the y-intercept )

to calculate m use the gradient formula

y = (y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 3)

m = [tex]\frac{3-0}{0+2}[/tex] = [tex]\frac{3}{2}[/tex]

the line crosses the y-axis at (0, 3) ⇒ c = 3

y = [tex]\frac{3}{2}[/tex] x + 3

A fraction will be bigger than another if for the same denominator the numerator is bigger therefore fraction 7/8 will be bigger than 13/15.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.

As per the given fractions 7/8 and 13/15

Multiply 15 numerators and denominators to 7/8

(7/8) × 15/15 = (7 × 15/8)/15

⇒ 13.125/15

Since 13.125 > 13

Since A fraction will be bigger than another if for the same denominator the numerator is bigger.

So 7/8 > 13/15.

Hence " A fraction will be bigger than another if for the same denominator the numerator is bigger therefore fraction 7/8 will be bigger than 13/15".

For more about fractions,

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Answer:

Step-by-step explanation:

Answer with explanation:

x        -7        -1     3     4       7    

f(x)     -11       1     9    11      17

Slope between two points

     [tex]m=\frac{1-(-11)}{-1+7}\\\\=\frac{9-1}{3-(-1)}\\\\=\frac{11-9}{4-3}\\\\=\frac{17-11}{7-4}\\\\=2[/tex]

Equation of line will be

  ⇒y-(-11)=2×[x-(-7)]

  →y+11=2×(x+7)

 →y+11=2x+14

 →2x-y+14-11=0

→2x-y+3=0

 →y=2x+3

Option B

Answer:

the answer is y=8

Step-by-step explanation:

i hope this help u

Answer:

Answer is 17.088 seconds

Step-by-step explanation:

We have given,

Speed of helicopter while going down = 10.5feet/sec

Time taken to travel down = 100 sec

Distance covered while going down = speed * time

Distance covered while going down  = 10.5 * 100

Distance covered while going down  = 1050 feet

Now,

Speed of helicopter while going up = 5.2feet/sec

time taken to travel up = 150 sec

Distance covered while going up = 5.2 * 150 =  780 feet

After this 250 second period , the position of helicopter will be:

Position of helicopter = distance covered in downward - distance covered upward

Position of helicopter = 1050 - 780 = 270 feet

That means we need to travel upward a distance of 270 feet at a maximum speed of 15.8feet/sec to reach sea level.

Time taken to reach sea level = distance/ speed = 270/15.8 = 17.088 sec

Hence time taken to reach at sea level with maximum speed is 17.088 seconds.

Answer: 2/3

Step-by-step explanation:

Slope Intercept Form: y = mx + b

m = slope

So, since 2/3 fits the form above, 2/3 is the slope in this equation.

The slope of the given line equation is [tex]m=\frac{2}{3}[/tex]. Since the given equation is in the form of slope-intercept form of a line y=mx+c.

The slope-intercept form of a line is expressed by the equation y=mx +c. where m is the slope and c is the y-intercept of the line.

Give that the equation of the line is y=2/3x+1

Comparing this equation with the standard form, we get

m = 2/3 and c=1

So, the slope of the given equation of the line is 2/3.

Learn more about slope-intercept form here:

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Answer: 24480

Step-by-step explanation:

just multiply the two numbers since 24 is distributing to 1020...24 times 1020

Answer:

the answer is 24480

Step-by-step explanation: