Number 9.
A recipe to make 3 apple pies requires
9 cups of flour. How many pies can be
made with 15 cups of flour?

Answer:

Recursive:

[tex]f(1)=4, f(n)=f(n-1)-4[/tex]

Explicit:

[tex]f(n)=4-4(n-1)[/tex]

And the 20th term f(20) is -72.

Step-by-step explanation:

We have the sequence:

4, 0, -4, -8...

Let’s find the recursive and explicit rule for the sequence.

Recursive Rule:

Let’s determine the factor by which the sequence is decreasing by. We see that each subsequent term is 4 less than the previous term. In other words, our common difference is -4.

So, this is a arithmetic sequence.

The standard format for an recursive rule for an arithmetic sequence is:

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

Where a is the initial term and d is our common difference.

From our sequence, we know that our initial term a is 4.

We also determined that our common difference is -4.

Substitute. Hence, our recursive rule is:

[tex]f(1)=4, f(n)=f(n-1)-4[/tex]

Explicit Rule:

The standard format for an explicit rule for an arithmetic sequence is:

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

Where a is the initial term and d is the common difference. So, again, let’s substitute 4 for a and -4 for d. Hence, our explicit formula is:

[tex]f(n)=4-4(n-1)[/tex]

To find f(20), we can use the explicit formula. It is possible to use the recursive formula, but it gets tedious. Therefore, we will substitute 20 for n for our explicit formula:

[tex]f(20)=4-4(20-1)[/tex]

Evaluate:

[tex]\begin{aligned} f(20)&=4-4(19) \\ f(20)&=4-76 \\ f(20)&=-72 \end{aligned}[/tex]

Hence, our 20th term is -72.

Answer:

C) 128

Step-by-step explanation:

Sum of all three angles of triangle = 180

Let the third angle be 'x'

x + 12 + 40 = 180

     x + 52 = 180

             x = 180 - 52

            x = 128

Answer:

(0,4) (3,5) (6,6)

Step-by-step explanation:

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shaded above

Answer:

A.

Step-by-step explanation:

Answer:

-96 :)

Step-by-step explanation:

12 x (-8) = -96

if there is one negative in the problem the answer will be negative.

I hope this is the way it must be calculated

Answer:

JKH and HKE, HKE and EKF, EKF and GKF, GKF and JKG

Step-by-step explanation:

i hope this is right, and helps lol

adjacent angles have a common vertex and side, so these should be correct

Answer:

{-6}

Step-by-step explanation:

Step 1 Raise both sides of the equation to the index of the radical in the case 2

[tex](\sqrt{2x+13} )^{2} =(x+7)^{2}[/tex]

[tex]2x + 13 = (x+7)(x+7)[/tex]

[tex]2x +13 = x^{2} + 14x + 49\\0=x^{2} +12x+36[/tex]

Step 2 Factor

(x + 6)(x + 6) = 0

x + 6 = 0

x = - 6

Step 3 Check -6

[tex]\sqrt{2(-6)+13} = -6 + 7\\\sqrt{-12+13} = 1\\\sqrt{1} = 1\\1 = 1[/tex]

Answer:

[tex]288 {x}^{2} + x + 18[/tex]

Step-by-step explanation:

Ayan po ang answer sana po makatulong

Paki heart nalang po kung nakatulong

#carrying learning

Answer:

Substitue 3 in for x...

Step-by-step explanation:

By substituting 3 in for x, you can solve for y. The result should be the same.

Answer:

9.55 hope this helps :)

Step-by-step explanation:

  1

  2.30

  2.50

+ 2.75

  2.00

-----------

  9.55

Answer:

G is the smallest

H is the largest

Step-by-step explanation:

Given

[tex]GH = 21[/tex]

[tex]HJ = 24[/tex]

[tex]GJ = 9[/tex]

Required

Which of the statements is true

First, we need to solve for G, H and J as follows:

[tex]G + H = 21[/tex] --- (1)

[tex]H + J = 24[/tex] --- (2)

[tex]G + J = 9[/tex] --- (3)

Make G the subject in (1)

[tex]G = 21 - H[/tex]

Substitute 21 - H for G in (3)

[tex]21 - H + J = 9[/tex]

Collect Like Terms

[tex]-H + J = 9 - 21[/tex]

[tex]-H + J = -12[/tex]

Make J the subject

[tex]J = H - 12[/tex]

Substitute H - 12 for J in (2)

[tex]H + H - 12 = 24[/tex]

[tex]2H - 12 = 24[/tex]

Collect Like Terms

[tex]2H = 24 + 12[/tex]

[tex]2H = 36[/tex]

Solve for H

[tex]H = 18[/tex]

Substitute 18 for H in [tex]J = H - 12[/tex]

[tex]J = 18 - 12[/tex]

[tex]J = 6[/tex]

Substitute 18 for H in [tex]G = 21 - H[/tex]

[tex]G = 21 - 18[/tex]

[tex]G = 3[/tex]

So, we have that:

[tex]G = 3[/tex]     [tex]J = 6[/tex]     [tex]H = 18[/tex]

Hence, we can conclude that:

G is the smallest

H is the largest

Answer:

2 glasses

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

6(2)

Answer:

10

Step-by-step explanation:

If ABCD is a rectangle, then AB=CD and AC=BD.

Check work:

Answer:

Step-by-step explanation:

square root of 25x^2 is 5x.  square root of 36 is 6

2(5x)(6)

60x

Answer: [tex]\frac{19}{39}[/tex]

Step-by-step explanation:

1. S(a+b) = 15/13

2. I tells us that sina = 2/3

3. 2/3 + sinb = 15/13

4. Solve for sinb which will be 19/39

I hope this is right.

Answer:

The correct option is;

26.8

Step-by-step explanation:

The given parameters are;

The perpendicular bisectors of the sides of ΔMNP = Segments OQ, OR, and OS

Therefore;

in Segment MN, segment QM = segment QN, by definition of bisected line

Segment OQ = Segment OQ by reflexive property

∠OQM = ∠OQN = 90° by definition of perpendicular bisector

∴ ΔOQN ≅ ΔOQM, by SAS rule of congruency

Segment MO ≅ Segment ON by Congruent Parts of Congruent Triangle are Congruent, CPCTC

Segment MO = Segment ON = 26.8, by definition of congruency

Segment MO = 26.8

Answer:

1h 18min

Step-by-step explanation:

Not sure if that is what the problem is asking you.

Answer:

An 1 hour and 18 minutes

Step-by-step explanation:

Yes uhmmm hope this helps I guess

Answer:

$901.9918

Step-by-step explanation:

$901.9918

Answer:

193.8

Step-by-step explanation:

a = 3.8 times 10^13 = 38,000,000,000,000

b = 5.1 times 10^-12 = 0.0000000000051

a times b = 193.8

Answer:

(8-3x)/4

Step-by-step explanation:

3x+4y=8

4y=8-3x

y=(8-3x)/4

So the answer is (8-3x)/4

Answer:

the first option has a sum of 20

Step-by-step explanation:

Answer:

the first one has a sum of 20

Step-by-step explanation:

Answer:

$1,605

Step-by-step explanation:

As, 7% of $1,500 is = $105

So, the investment is = Principcal + Interest.

= $1,500 + $105 = $1,605

The value of investment after one year will be $1,605.

Given that,

Principal[P] = $1,500.

Rate[R] = 7%.

Time[T] = 1 year.

Formula of simple interest[S.I] :

[tex]\text{ S.I.} = \dfrac{P\times R\times\ T}{100} .\\\\ \text{S.I.} = \dfrac{\$1,500\times7}{100}\\\\ \text{S.I. }=\$105.[/tex]

Investment after one year will be :

[tex]\text {Investment}= \text{Principal} +\text{Interest}.\\\text{Investment}=\$1,500+\$105\\\text{Investment} =\$1,605[/tex]

Hence, the worth of investment after one year will be $ 1,605.

Learn more about Simple Interest, refer:

https://brainly.com/question/2793278

9514 1404 393

Answer:

  k = -50

Step-by-step explanation:

The fraction denominators are 5 and 10. The least common multiple of those values is 10. This means we can eliminate fractions by multiplying both sides of the equation by 10:

  6k -50 = 7k

Subtracting 6k from both sides of the equation leaves you with the solution:

  -50 = k

Answer:

4/3 for slope.. I'm unsure if its also asking for y- intercept

Step-by-step explanation: