A strip of wood 78 inches long is to be cut into pieces 3 3/4 inches long. How many pieces can be cut?

F(t) = -(t-2) (t-15)

Goryan [66]

Answer:

smaller (t) = 2 and this in coordinates form (2,0)

larger (t) = 15 and this in coordinates form (15,0)

the vertex of the parabola = $(\frac{17}{2} ,\frac{169}{4} )$ or in decimals (8.5, 42.25)

Step-by-step explanation:

For the zeros of the function take each bracket and make it equal to zero.

SMALLER (t):

(t-2)=0

(add 2 for both sides)

t=2

LARGER (t):

(t-15)=0

(add 15 for both sides)

t=15

For the vertex of the parabola you do:

step1: expand the brackets:

f(t)=-(t-2)(t-15)

f(t)= $-t^{2} +17t-30$

step2: define a,b and c using the expression $ax^{2} +bx+c$ :

a= -1 (the coefficient of $t^{2}$ )

b= 17 (the coefficient of t)

c= -30 (the single number without a letter)

step3: sub the values in the formula $-\frac{b}{2a}$ to find the x coordinate of the vertex :

$-\frac{b}{2a}$

= $- \frac{17}{2*-1}$

= $\frac{17}{2}$ or in decimals 8.5

step4: sub the value of t (the x-coordinate) in equation f(t):

f(t)= $-t^{2} +17t-30$

f ( $\frac{17}{2}$ ) = - $(\frac{17}{2} )^{2}$ + 17× $\frac{17}{2}$ - 30

= $-\frac{289}{4}$ + $\frac{289}{2}$ -30

= $\frac{169}{4}$ or in decimals 42.25

(THIS IS A PICTURE OF THE GRAPH↓)

6 0

3 years ago

HELP WILL GIVE BRANLIEST

Nitella [24]

Answer:

328

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

You know how to play 21 songs on your guitar. (a) If you want to choose 8 of the songs to make a setlist to play for a small gat

UNO [17]

Answer:

(a) 8,204,716,800

(b) 5,985

Step-by-step explanation:

Combinations and Permutations

Combinatorics is the part of the discrete mathematics that studies the enumeration of groups or sorting of a determined number of elements. The concept of combinations is tied to the different forms to group elements where the order of their arrangements is not important or does not differentiate from the very same set of elements picked in a different order.

The concept of combinations is tied to the differents forms to group elements where the order of their arrangements is not important or does not differentiate from the very same set of elements picked in different order.

On the other hand, permutations or variations are sets selected in a specific order and another set with the same element but in different order is considered a different set.

If we have n elements available to pick from in sets of m elements each, there can be C(n,m) different combinations, and it's given by

$\displaystyle C(n,m)=\frac{n!}{m!(n-m)!}$

Similarly the number of permutations is given by

$\displaystyle P(n,m)=\frac{n!}{(n-m)!}$

(a) I have n=21 songs to pick from and I want to choose m=8 of them where the order matters, so it's a permutation:

$\displaystyle P(21,8)=\frac{21!}{(13)!}=\frac{51,090,942,171,709,440,000}{6,227,020,800}=8,204,716,800$

I can make more than 8 billion different setlists

(b) To choose m=4 songs from n=21 songs where the order does not matter, we compute the combination

$\displaystyle C(21,4)=\frac{21!}{4!(17)!}=\frac{21\cdot 20\cdot 19\cdot 18\cdot 17!}{4\cdot 3\cdot 2\cdot 1(17)!}$

$\displaystyle C(21,4)=\frac{143,640}{24}=5,985$

I can make almost 6,000 sets of 4 songs

5 0

3 years ago

What fraction strips could you make if you started with a fourths strip?

Tju [1.3M]

Anything that with a denominator that is a multiple of 4, for example: $\frac{2}{8}$ , $\frac{3}{12}$ , $\frac{4}{16}$ , $\frac{5}{20}$ , and so on.

Hope this helps you =)

4 0

4 years ago

If right answer good review

enot [183]

Answer:

The slope line will change from negative to positive.

5 0

3 years ago