What is the slope of the line that contains the points in the table?
х
У
15
-2
9
ON
3
4
-3
O A. 3
O B. -6
O c. 2
O D. -3

Answer:

total candy = 54 bags

y=17

x=37

Step-by-step explanation:

5x + 4y = 253

x-y = 20

x = 20+y

5(20+y) + 4y = 253

100 + 9y = 253

9y = 153

y=17

x=37

Given:

The recursive formulae.

To find:

The correct explicit formulae for the given recursive formulae.

Solution:

If the recursive formula of a GP is [tex]f(n)=rf(n-1), f(1)=a, n\geq 2[/tex], then the explicit formula of that GP is:

[tex]f(n)=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

The first recursive formula is:

[tex]f(1)=5[/tex]

[tex]f(n)=3f(n-1)[/tex] for [tex]n\geq 2[/tex].

It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:

[tex]f(n)=5(3)^{n-1}[/tex]

Therefore, the required explicit formula for the first recursive formula is [tex]f(n)=5(3)^{n-1}[/tex].

If the recursive formula of an AP is [tex]f(n)=f(n-1)+d, f(1)=a, n\geq 2[/tex], then the explicit formula of that AP is:

[tex]f(n)=a+(n-1)d[/tex]

Where, a is the first term and d is the common difference.

The second recursive formula is:

[tex]f(1)=5[/tex]

[tex]f(n)=f(n-1)+5[/tex] for [tex]n\geq 2[/tex].

It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:

[tex]f(n)=5+(n-1)5[/tex]

[tex]f(n)=5+5(n-1)[/tex]

Therefore, the required explicit formula for the second recursive formula is [tex]f(n)=5+5(n-1)[/tex].

The third recursive formula is:

[tex]f(1)=5[/tex]

[tex]f(n)=f(n-1)+3[/tex] for [tex]n\geq 2[/tex].

It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:

[tex]f(n)=5+(n-1)3[/tex]

[tex]f(n)=5+3(n-1)[/tex]

Therefore, the required explicit formula for the third recursive formula is [tex]f(n)=5+3(n-1)[/tex].

Answer: u = [tex]\frac{7}{8}[/tex] or 0.875

Step-by-step explanation:

Let us convert this statement to a question

[tex]4^{2}[/tex]-8u-9 = 0

16-8u-9 = 0

-8u = 0+9-16

-8u = -7

u = -7 ÷ -8

u = [tex]\frac{7}{8}[/tex] or 0.875

Answer:

Ishaan is currently 15 years old.

Step-by-step explanation:

Let B represent Ben's current age and I represent Ishann's current age.

Ben is four times as old as Ishaan. In other words:

[tex]B=4I[/tex]

Six years ago, Ben was six times as old as Ishaan. In other words:

[tex]B-6=6(I-6)[/tex]

Solve for I. Substitute:

[tex](4I)-6=6(I-6)[/tex]

Distribute:

[tex]4I-6=6I-36[/tex]

Subtract 4I from both sides and add 36 to both sides:

[tex]2I=30[/tex]

And divide both sides by two. Hence:

[tex]I=15[/tex]

Ishaan is currently 15 years old.

Answer:

Age of Ishaan = 15 years

Step-by-step explanation:

Let Ishaan's age = x years

Age of Ben = 4 * x = 4x years

6Years ago:

Age of Ishaan = x - 6

Age of Ben = 4x - 6

6 years ago, Ben was 6 times as old as Ishaan

So, Age of Ben = 6 * Ishaan's age

     4x - 6 = 6 *(x-6)

4x - 6 = 6x - 36

Add 36 to both sides

4x - 6 + 36  = 6x  

4x + 30 = 6x

Subtract '4x' from both sides

30 = 6x - 4x  

30 = 2x

2x = 30

Divide both by 2 sides

x = 30/2

x = 15

Answer:

Whether her conversion is correct or not, you can just base it on the true answer. For this problem, we apply the technique of dimensional analysis. You can like units if they both appear on the numerator and the denominator side. The solution is as follows:

Mass in ounces = 3 kg * (1,000 g/ 1 kg) * (1 ounce/28.35 g) = 105.82 ounces

Step-by-step explanation:

The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.

Answer:

56

Step-by-step explanation:

Zoe : hanna

3         7

Zoe got 24

3*8 = 24

so multiply each side by 8

Zoe : hanna

3*8         7*8

24           56

Hanna got 56

Answer:

17424

Step-by-step explanation:

(6.6 x 10(-2) ( 3.3 x 10(-4))

(6.6 x - 20) ( 3.3 x -40)

(-132) (-132)

=17424

Answer:

[tex]\displaystyle d = \sqrt{29}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

*Note:

The distance formula is derived from the Pythagorean Theorem.

Step 1: Define

Identify

Point (5, 10)

Point (10, 12)

Step 2: Find distance d

9514 1404 393

Answer:

  -19.2

Step-by-step explanation:

Fill in the given values and do the arithmetic.

  [tex]\displaystyle x\ \blacksquare\ y=\frac{x}{y}-xy\\\\4\ \blacksquare\ 5=\frac{4}{5}-4\cdot5=0.8-20\\\\\boxed{4\ \blacksquare\ 5=-19.2}[/tex]

Given:

The polygon in the given figure are similar.

To find:

The missing side length.​

Solution:

We know that the corresponding sides of similar figures are proportional.

The given polygons are similar, so the their corresponding sides are proportional.

[tex]\dfrac{x}{15}=\dfrac{32}{40}=\dfrac{32}{40}[/tex]

So, the missing values in the equation of proportion are 15, 40, 32 respectively.

On solving the above equation, we get

[tex]\dfrac{x}{15}=\dfrac{4}{5}=\dfrac{4}{5}[/tex]

[tex]\dfrac{x}{15}=\dfrac{4}{5}[/tex]

[tex]x=\dfrac{4}{5}\times 15[/tex]

[tex]x=12[/tex]

Therefore, the value of x is 12.

Answer:

Take the gross amount of any sum (items you sell or buy) – that is, the total including any VAT – and divide it by 117.5, if the VAT rate is 17.5 per cent. (If the rate is different, add 100 to the VAT percentage rate and divide by that number.)

Answer:

divide by 117.5 if the rate different, add 100 to the percentage and divide by the number therefore multiply by 100 to get the total

Step-by-step explanation:

the formula to calculate vat percentage

Answer:

Step-by-step explanation:

days in september=30

salry paid per day=Rs.160

salary paid in 30 days=160×30=Rs.4800

Answer:

4800

Step-by-step explanation:

In the month of September there are only 30 days. So assuming Sohanlal works the entire month of September we will multiply how much he makes daily which is 160 times the amount of days he works which is 30. this will look like this:

160 × 30 = 4800

Answer:

x=-1  y = 1/3

x = 1  y = 3

x = 3  y = 27

Step-by-step explanation:

y = 3^x

Let x = -1

y = 3^-1 = 1/3^1 = 1/3

Let x = 1

y = 3^1 = 3

Let x = 3

y = 3^3 = 27

Answer:

Equation:  [tex]70=(x+3)x[/tex]

x = -10 or x = 7

x = 7 (width can't be negative)

x + 3 = 10

Step-by-step explanation:

Represent the width of the rectangle by  x.  "The length of a rectangle EXCEEDS the width by 3" means the length is 3 LONGER than the width, so the length is represented by the expression  x + 3.

Area = (length)(width)

70 = (x + 3)x

Multiply out the right side.

[tex]70=x^2+3x\\x^2+3x-70=0[/tex]

Factor the left side.

[tex](x+10)(x-7)=0[/tex]

Each binomial could equal 0, so

[tex]x+10=0 \text{ or }x-7=0\\x=-10\text{ or }x=7[/tex]

The negative solution does not make sense as the width of a rectangle.

x = 7, making the length, x + 3 = 10

Answer:

Pls mark this as brainiest

Step-by-step explanation:

Area of the rectangle = length x breadth

consider 'x' to be width

therefore length = x+3

area = (x+3)*x

Area = 70 square

x = 7

x+3 = 7+3

      = 10

verification

7 x 10

= 70

Answer:

Volume is equal to

L×W×H

=(10×9×7)cm

=90×7

=630

The volume of the prism is 980cm3.

We are given that;

The dimensions= 4*7*9*2*10cm

Now,

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

Volume of upper prism;

=5*4*40

=800cm3

Volume of lower prism;

=2*9*10

=180cm3

Total volume= upper volume + lower volume

=980cm3

Therefore, by the rectangular prism the answer will be 980cm3.

Learn more about a rectangular prism;

https://brainly.com/question/21308574

#SPJ2

Answer:

[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]

Or about 15.136 centimeters by 7.136 centimeters.

Step-by-step explanation:

Recall that the area of a rectangle is given by:

[tex]\displaystyle A = w\ell[/tex]

Where w is the width and l is the length.

We are given that the length is 8 centimeters longer than the width. In other words:

[tex]\ell = w+8[/tex]

And we are also given that the total area is 108 square centimeters.

Thus, substitute:

[tex](108)=w(w+8)[/tex]

Solve for w. Distribute:

[tex]w^2+8w=108[/tex]

Subtract 108 from both sides:

[tex]w^2+8w-108=0[/tex]

Since the equation is not factorable, we can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:

[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]

So, our two solutions are:

[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]

Since width cannot be negative, we can eliminate the second solution.

And since the length is eight centimeters longer than the width, the length is:

[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]

So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.

Answer:

The graph that have 2 lines is for Question 21 and the graph with three lines is for Question 22

Step-by-step explanation:

=======================================================

Explanation:

Extend segment MN such that it intersects side ST. Mark the intersection as point A. See the diagram below.

We're given that angle MNT is 72 degrees. The angle TNA is equal to 180-(angle MNT) = 180 - 72 = 108 degrees, since angles MNT and TNA add to 180.

For now, focus entirely on triangle TNA. We see from the diagram that T = 34 and we just found that N = 108. Let's find angle A

A+N+T = 180

A+108+34 = 180

A+142 = 180

A = 180-142

A = 38

So angle NAT is 38 degrees.

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

Since segment MA is an extension of MN, and because MN || SQ, this means MA is also parallel to SQ.

We found at the conclusion of the last section that angle NAT was 38 degrees. Angles QST and NAT are corresponding angles. They are congruent since MA || SQ. This makes angle QST to also be 38 degrees

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

The angles QSR and QST are a linear pair, so they are supplementary

(angle QSR) + (angle QST) = 180

angle QSR = 180 - (angle QST)

angle QSR = 180 - 38

angle QSR = 142 degrees

Answer:

I Will explained you youuuuuu<uuuuuuuuuu

Answer:

angle bisector

Step-by-step explanation:

Since the line divided the top angle into two equal pieces we call this an angle bisector.

Answer:

−48x+112

Step-by-step explanation:

evatulate: −16  (3−7)

                -48+112

Answer:

G. 4 cm

Step-by-step explanation:

28 divided by 7 equals 4.

So, 16 divided by 4 equals 4, which is the answer.

4 is the multiple that relates AABC to ADEF.

Answer:

Hello,

Answer B (-5/3,-4/3)

Step-by-step explanation:

I am going to use the substitution 's method.

[tex]\left\{\begin{array}{ccc}x+y&=&-3\\y&=&2x+2\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&2x+2\\x+2x+2&=&-3\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&2x+2\\3x&=&-5\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x&=&-\dfrac{5}{3} \\\\y&=&2*(-\dfrac{5}{3})+2\\\end {array} \right.\\\\\\\boxed{\left\{\begin{array}{ccc}x&=&-\dfrac{5}{3} \\\\y&=&-\dfrac{4}{3}\\\end {array} \right.\\}[/tex]

Answer:

y + 2.3 = 0.45x

y = 0.45x - 2.3

-2y = 4.2x - 7.8

-2(0.45x - 2.3) = 4.2x - 7.8

-0.90x + 4.6 = 4.2x - 7.8

-0.90x - 4.2x = -7.8 - 4.6

-5.1x = - 12.4

x = -12.4 / -5.1

x = 2.4

y + 2.3 = 0.45x

y = 0.45(2.4) - 2.3

y = 1.08 - 2.3

y = -1.2

solution is : (2.4, - 1.2)

Step-by-step explanation:

Answer:

(x, y) = (5,8)

Step-by-step explanation:

Comparing the ordered pairs we get, x+y=13 and 2=2x-y. Solving it we will get, x=5 and y=8

Answer:

reflection over Y axis

Step-by-step explanation:

Answer:

I believe it is D) a reflection over the Y-axis

Step-by-step explanation

it is going over the Y-axis as if it is a sort of mirror, if it were going over the x-axis it would be flipped upside down, if it was A the shape would be going over the original shape. I don't know how to explain C. (I hope this helped and I hope it was correct lol)

Answer: £21007.22

Step-by-step explanation:

First, find the interest amount using the formula SI = (P × R × T) / 100.

SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22

The total amount = principle amount + interest amount

= £18790 + £2217.22 = £21007.22

The functions f and g have different axis of symmetry

The y-intercept of f is higher than the y-intercept of g

Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g

The known value in the question includes the following

The given table of f(x) and x, from which we have;

The point of the minimum value, which is the vertex = (-3, -10)

The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3

The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)

Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6

From the graph of g(x), we have;

The axis of symmetry is the line x = -3

The y-intercept = (0, -2)

Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3

Therefore, we have the correct options as follows;

The functions f and g have different axis of symmetry

The y-intercept of f is higher than the y-intercept of g

Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g

Learn more about parabola here;

https://brainly.com/question/22213822