Write the equation of the line that passes through (1, 3) and has a slope of 2 in point-slope form. (2 points)

Lucas read 30% of his book containing 480 pages. What page is he going to read next?

mihalych1998 [28]

The page he will read next is 145

8 0

2 years ago

Find the fifth term in the sequence that is defined as follows a1=1. An=3an-1+2

faltersainse [42]

The fifth term in the sequence would be 161.

Step-by-step explanation:

We have to find the fifth term in the sequence $an=3a(n-1)+2$

Given that

a1 = 1 (that is the first term)

If we follow the formula, the value of every term depends on the value of immediate lower term. Therefore, the a2 can be calculated by putting 2 in place of n in above equation

$a2=3a(2-1)+2$

$a2=3a1+2$

$a2=3(1)+2$ as a1 = 1

$a2=5$

Similarly,

$a3=3a(3-1)+2$

$a3=3a2+2$

$a3=3(5)+2$ as a2 = 5

$a3=17$

and

$a4=3a(4-1)+2$

$a4=3a3+2$

$a4=3(17)+2$ as a3= 17

$a4=53$

and

$a5=3a(5-1)+2$

$a5=3a4+2$

$a5=3(53)+2$ as a4 = 53

$a5=161$

Therefore, the fifth term in the sequence would be 161.

Learn more:

The following links have more information about sequencing

brainly.com/question/7221312

Keywords: sequence, arithmetic series

#learnwithBrainly

6 0

2 years ago

Plz...solve this question.... If n(A) = 37, n(B) = 50, and A is subsets of B, find n(AUB).

valentina_108 [34]

Answer:

n(B)=21.

Step-by-step explanation:

n(AUB) means the the number of elements in both A & B. And that includes the ones in common too.

n(A∩B) means the ones that in common.

n(A-B) refers to the elements that belong to A alone. That means the elements in A excluding the common elements.

n(B) is the number of elements that belong to B and that includes the common ones too.

Now coming to your question.

The total number of elements that can fit in both the sets is 36.

While the number of common elements is 16.

And also given that n(A-B)=15.

Now according to the definitions above....n(A) should include the ones that belong exclusively to A alone and also the ones in common.

So,

n(A)=n(A-B)+n(A∩B)

=15+16

=31

Therefore, n(A) is 31.

Now when n(AUB) is 36 and n(A) is 31, it is clear that the elements exclusive to B alone is 5, i.e.36-31.

Now n(B)=n(A∩B)+n(B-A)

Therefore, n(B) is 16+5 = 21.

n(B)=21.

6 0

2 years ago

a rectangle has an area of 54 square inches the width of the rectangle is 9 inches what is the langth

STatiana [176]

Answer:

As per Provided Information

Area of rectangle is 54 square inches
Width of the rectangle is 9 inches.

We have to calculate the length of rectangle .

As we know the formula to find the Area of rectangle .

$\boxed{\bf \: Area_{(Rectangle)} = length \: \times width}$

On substituting the value we obtain

$\sf \qquad \: \longrightarrow 54 = length \times 9 \\ \\ \\ \sf \qquad \: \longrightarrow \cfrac{54}{9} = length \\ \\ \\ \sf \qquad \: \longrightarrow \: length \: = \cfrac{54}{9} \\ \\ \\ \sf \qquad \: \longrightarrow \: length \: = \cancel \cfrac{54}{9} \\ \\ \\ \sf \qquad \: \longrightarrow \: length \: = 6 \: inches$

Therefore,

Length of the rectangle is 6 inches .

8 0

1 year ago

The algebraic expression for "the quotient of 77 and x" is

Illusion [34]

The correct answer is:

_______________________
" 77 / x " ; or; "x ÷ 77" .

_________________________
In algebra, the former is preferred; that is: " 77 / x " .

7 0

3 years ago