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4 years ago

Long division 8 divided by 1,613 show your work all your work

Mathematics

1 answer:

SOVA2 [1]4 years ago

3 0

8 goes in to 16 2 times so put 2 on the top. 8 x 2 is 16 so do 16 - 16 which is 0. 8 cant go into 0 so put a 0 on top. Bring down the 1; 8 cant go into 1 so bring down the 3. 8 can go into 13 1 time so put a 1 on top. 13 - 8 is 5 so the remainder is 5

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100 Points<br><br> Solve for X

bixtya [17]

A) By the rules of secants,
5(x +5) = 6(6 +4)
x + 5 = 12
x = 7

b) 3(3 +5) = 4(x +4)
6 = x +4
2 = x

5 0

3 years ago

Read 2 more answers

Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.

Makovka662 [10]

Given:

The geometric sequence is:

$n$ $a_n$

1 -4

2 20

3 -100

To find:

The explicit formula and list any restrictions to the domain.

Solution:

The explicit formula of a geometric sequence is:

$a_n=ar^{n-1}$ ...(i)

Where, a is the first term, r is the common ratio and $n\geq 1$ .

In the given sequence the first term is -4 and the second term is 20, so the common ratio is:

$r=\dfrac{a_2}{a_1}$

$r=\dfrac{20}{-4}$

$r=-5$

Putting $a=-4,r=-5$ in (i), we get

$a_n=-4(-5)^{n-1}$ where $n\geq 1$

Therefore, the correct option is B.

5 0

3 years ago

Relations and Functions, please help with these 3 questions asap. I will give brainliest! Only answer if you know how to do this

gladu [14]

<h2> Question # 1</h2>

Part A) Is the relation a function? Explain.

A function relates each element of a set with exactly one element of another set.

Important things for a relationship to be a function:

Every element in X is related to some element in Y.

A function cannot have one-to-many relationship.

A function must contain single valued, means it is not having one-to-many relation

Considering the points on coordinate plane

(-4, 2), (-3, 0), (-2, -1), (0, 2), (2, -3), (3, 3)

If we carefully observe, we determine that relation

relates each element of a set with exactly one element of another set

is single-valued, means It is not giving back 2 or more results for the same input. In other words, it is not having one-to-many relation.

It is in fact, having many to one. For example, the pairs (0, 2) and (-4, 2) is having many- to-one relationship.

So, from the above observation, it is clear that the relationship is a function.

Part B) What is the domain of the relation?

Considering the points on coordinate plane

(-4, 2)

(-3, 0)

(-2, -1)

(0, 2)

(2, -3)

(3, 3)

Also we know that domain of the relation is the set of all the x-values of an ordered pairs.

So, the domain of the relation: {-4, -3, -2, 0, 2, 3}

Part C) What is the range of the relation?

Considering the points on coordinate plane

(-4, 2)

(-3, 0)

(-2, -1)

(0, 2)

(2, -3)

(3, 3)

As we know that the range of a relationship is the set of all the y-values of an ordered pair.

So, the range of the relationship will be: { -3, -1, 0, 2, 3}

<em>Note:</em>

The duplicated entries in the domain and range are written only once.
Also, the domain and range can be written in ascending order.

Part D) What is the value of y when x = 2? Explain

Considering the points on coordinate plane

(-4, 2)

(-3, 0)

(-2, -1)

(0, 2)

(2, -3)

(3, 3)

From the given points on the coordinate plane, it is clear that when the value of x = 2, then the value of y = -3

Therefore, the value of y is -2 when x = 2

<h2> Question # 2</h2>

Considering the points on coordinate plane

(-4, -1), (-2, 1), (0, -3), (2, 3), (4, -2)

If we bring a point, let say (2, 4), and graphed on the coordinate system, then the relation will no longer be function.

The reason is that the induction of the point (2, 4) would violate the definition of a relation to be a function.

Observe that (2, 4) and (2, 3) will make the relation having one-to-many relationship as (2, 4) and (2, 3) is giving 2 outputs i.e. y = 4, and y = 3 for a single input i.e. x = 2.

Therefore, the induction of the point (2, 4), when graphed, makes the relation not a function.

<h2> Question # 3</h2>

Part A)

$f\left(x\right)\:=\:|x\:-\:3|\:-\:2$ ; $x = -5$

The attached figure a shows the graph for the function

$f\left(x\right)\:=\:|x\:-\:3|\:-\:2$

In the attached figure a, the graph represents an absolute value relationship as the absolute value of a number is never negative.

Evaluate the function for x = -5

$f\left(x\right)\:=\:|x\:-\:3|\:-\:2$

$|\left-5\right\:-\:3|\:-\:2....[A]$

Solving

$\left|-5-3\right|$

$\mathrm{Subtract\:the\:numbers:}\:-5-3=-8$

$=\left|-8\right|$

$\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a$

$\left|-8\right|=8$

So,

$\left|-5-3\right|=8$

Equation [A] becomes

$\:|-5\:-\:3|\:-\:2\:=8\:-\:2\:$ ∵ $\left|-5-3\right|=8$

$=6$

Therefore,

the value of $f\left(x\right)\:=\:|x\:-\:3|\:-\:2$ at $x = -5$ will be 6.

i.e. $f(x)=6$

<h2 />

Part B)

$g\left(x\right)=1.5x;\:x=0.2$

The attached figure b shows the graph for the function

$g\left(x\right)=1.5x$

In the attached figure b, the graph shows that the function represents a linear relationship as the graph is a straight line.

Evaluate the function for x = 0.2

$g\left(x\right)=1.5x$

Putting x = 0.2

$g\left(x\right)=1.5\left(0.2\right)$

$1.5\left(0.2\right)=0.3$

$g\left(x\right)=0.3$

So,

the value of $g\left(x\right)=1.5x$ at $x = 0.2$ will be 0.3.

i.e. $g\left(x\right)=0.3$

Part C)

$p\left(x\right)\:=\:|7\:-\:2x|;\:x\:=\:-3$

As the absolute value of a number will be never negative.

The attached figure c shows the graph for the function

$p\left(x\right)\:=\:|7\:-\:2x|$

In the attached figure c, the graph represents an absolute value relationship as the absolute value of a number is never negative.

Evaluate the function for x = -3

$p\left(x\right)\:=\:|7\:-\:2x|$

Solving

$\left|7-2x\right|$

$\left|7-2\left(-3\right)\right|$

$=\left|7+6\right|$

$=\left|13\right|$

$\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0$

$=13$

So,

$\left|7-2x\right|=13$

So,

the value of $p\left(x\right)\:=\:|7\:-\:2x|$ at $x = -3$ will be 13.

i.e $p\left(x\right)\:=13$

Keywords: function, relation

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3 0

4 years ago

Through (1,-6) parallel to the line x + 2y = 6

MakcuM [25]

Hello!

To find the line parallel to the line x + 2y = 6 and passing through the point (1, -6), we will need to know that if two lines are parallel, then their slopes are equivalent to each other.

Since the given equation is written in standard form, we will need to change it to slope-intercept form to get the slope. Slope-intercept form is: y = mx + b.

x + 2y = 6 (subtract x from both sides)

2y = 6 - x (divide both sides by 2)

y = 6/2 - x/2

y = -1/2x + 3 | The slope of parallel lines are -1/2.

Since we are given the slope, we need to find the y-intercept of the line that goes through the point (1, -6) by substituting that point into a new equation with a slope of m equalling to -1/2.

y = -1/2x + b (substitute the given point)

-6 = -1/2(1) + b (simplify - multiply)

-6 = -1/2 + b (add 1/2 to both sides)

b = -11/2 | The y-intercept of the parallel line is -13/2.

Therefore, the line parallel to x + 2y = 6 and goes through the ordered pair (1, -6) is y = -1/2x + -11/2.

8 0

3 years ago

Desiree drove north for 30 minutes at 50 miles per hour. Then, she drove south for 60 minutes at 20 miles per hours. How far and

mylen [45]

Answer:

Step-by-step explanation:

The scenario is illustrated in the attached photo.

Desiree drove north for 30 minutes at 50 miles per hour.

Distance = speed × time

Distance travelled by Desiree to the north is 50 × 30 = 1500 miles

Distance travelled by Desiree back from the north and to the south is

60 × 20 = 1500 miles

She started from south and drove 1500 miles towards the north. She returned by driving 1200 miles again towards south . Distance of Desiree from where she started will be 1500 - 1200 = 300 miles.

She is 300 miles from her starting position and she is in the southern direction.

5 0

4 years ago