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2 years ago

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if a rug was 5 times as long as thia record sheet, how long would it be? measure the length of this record sheet in centimeters.

1 answer:

vlada-n [284]2 years ago

4 0

<u>Answer: </u>

If a rug was 5 times as long as this record sheet. The length of this record sheet in centimeters is 100x centimeter

<u>Solution: </u>

Given that a rug was 5 times than the record sheet.

Let assume the length of the record sheet = x units

Then from given information,

Length of the rug = 5x units

Conversion of measure of record sheet in centimeter completely depends upon in which unit the length is given.

Suppose the given length is in meters, than need to multiply the given length by 100 to get the length in centimeter that is

x meter = $x \times 100$ = 100x cm

Conversion factor will change accordingly to the unit of given length which needs to be convert into centimeter.

You might be interested in

If the function f (x) has a domain of (a,b] and a range of [c,d), then what is the domain and range of g (x) = m × f (x) + n?

xz_007 [3.2K]

<h3>Answer: Choice A</h3>

Domain = (a,b]

Range = [mc + n,md + n)

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

Explanation:

The domain stays the same because we still have to go through f(x) as our first hurdle in order to get g(x).

Think of it like having 2 doors. The first door is f(x) and the second is g(x). The fact g(x) is dependent on f(x) means that whatever input restrictions are on f, also apply on g as well. So going back to the "2 doors" example, we could have a problem like trying to move a piece of furniture through them and we'd have to be concerned about the f(x) door.

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

The range will be different however. The smallest value in the range of f(x) is y = c as it is the left endpoint. So the smallest f(x) can be is c. This means the smallest g(x) can be is...

g(x) = m*f(x) + n

g(x) = m*c + n

All we're doing is replacing f with c.

So that means mc+n is the starting point of the range for g(x).

The ending point of the range is md+n for similar reasons. Instead of 'c', we're dealing with 'd' this time. The curved parenthesis says we don't actually include this value in the range. A square bracket means include that value.

6 0

2 years ago

Jane has a pre-paid cell phone with Splint. She can't remember the exact costs, but her plan has a monthly fee and a charge for

yan [13]

Answer:

The costs of the plan are $0.15 per minute and a monthly fee of $39

Step-by-step explanation:

Let

x ----> the number of minutes used

y ----> is the total cost

step 1

Find the slope of the linear equation

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the ordered pairs

(100,54) and (660, 138)

substitute

$m=\frac{138-54}{660-100}$

$m=\frac{84}{560}=\$0.15\ per\ minute$

step 2

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=0.15\\point\ (100,54)$

substitute

$y-54=0.15(x-100)$

step 3

Convert to slope intercept form

Isolate the variable y

$y-54=0.15x-15\\y=0.15x-15+54\\y=0.15x+39$

therefore

The costs of the plan are $0.15 per minute and a monthly fee of $39

6 0

2 years ago

A new neighborhood activity complex is being built in erie. The perimeter of the rectangular playing field is 256 yards. The len

maw [93]

Answer:

The length of the rectangular playing field is 84 yards and the width is 44 yards

Step-by-step explanation:

Let

x ------> the length of the rectangular playing field

y -----> the width of the rectangular playing field

we know that

The perimeter of the rectangular playing field is equal to

$P=2(x+y)$

$P=256\ yd$

so

$256=2(x+y)$ ------> equation A

we have that

$x=2y-4$ -----> equation B

Solve the system by substitution

Substitute equation B in equation A and solve for y

$256=2(2y-4+y)$

$128=3y-4$

$3y=128+4$

$3y=132$

$y=44$

Find the value of x

$x=2(44)-4=84$

therefore

The length of the rectangular playing field is 84 yards and the width is 44 yards

4 0

3 years ago

Let f(x) = 6x^2 + 5 and g(x) = 3x - 5. Find f(g(7)).

Vedmedyk [2.9K]

Answer:

D) 1541

Step-by-step explanation:

I like to answer it w without deriving the formula of f(g(x)). So, we go this way, you firstly have to find g(7) which will be equal to 3 * 7 - 5 = 16.

And then you find f(16) = 6*16*16+5 = 1541. That's all.

8 0

2 years ago

3. Complete the proof below.<br><br><br> Help please!!!

baherus [9]

Answer:

The completed proof is presented as follows;

The two column proof is presented as follows;

Statements ${}$ Reason

1. $\overline {HI}$ ║ $\overline {KL}$ , J is the midpoint of $\overline {HL}$ ${}$ 1. Given

2. ∠IHJ ≅ ∠JLK ${}$ 2. Alternate angles are congruent

3. ∠IJH ≅ ∠KJL ${}$ 3. Vertically opposite angles

4. $\overline {HJ}$ ≅ $\overline {JL}$ ${}$ 4. Definition of midpoint

5. ΔHIJ ≅ ΔLKJ ${}$ 5. By ASA rule of congruency

Step-by-step explanation:

Alternate angles formed by the crossing of the two parallel lines $\overline {HI}$ and $\overline {KL}$ , by the transversal $\overline {HL}$ are equal

Vertically opposite angles formed by the crossing of two straight lines $\overline {IK}$ and $\overline {HL}$ are always equal

A midpoint divides a line into two equal halves

Angle-Side-Angle, ASA rule of congruency states that two triangles ΔHIJ and ΔLKJ, that have two congruent angles, ∠IHJ in ΔHIJ ≅ ∠JLK ${}$ in ΔLKJ and ∠IJH in ΔHIJ ≅ ∠KJL in ΔLKJ, and that the included sides between the two congruent angles is also congruent $\overline {HJ}$ ≅ $\overline {JL}$ , then the two triangles are congruent, ΔHIJ ≅ ΔLKJ.

5 0

2 years ago