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AlladinOne [14]
3 years ago
7

The length of a rectangle is seven units more than it's width if the width is doubled and the length is increased by two the are

a is increased by 42 square Units find the dimensiones of the original rectangle
Mathematics
2 answers:
My name is Ann [436]3 years ago
7 0

Answer:

length = 10 units; width = 3 units

Step-by-step explanation:

Let the width = w

Then the length is w + 7

Original area: w(w + 7)

Double the width: 2w

Increase the length by 2: w + 9

Area of new rectangle: 2w(w + 9)

Area of new rectangle = w(w + 7) + 42

2w(w + 9) = w(w + 7) + 42

2w^2 + 18w = w^2 + 7w + 42

w^2 + 11w - 42 = 0

(w + 14)(w - 3) = 0

w + 14 = 0 or w - 3 = 0

w = -14 or w = 3

A width cannot be negative, so we discard w = -14.

The original width is 3 units.

The length is 7 more than the width, so the length is 10 units.

Anit [1.1K]3 years ago
5 0

yup the guy below me Is right

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Jacques wants to make up packs of $0.45 comic books mixed with $0.75 ones to sell at $9.00 per pack. The number of $0.45 comic b
Anna007 [38]

Answer:

The number of each type in the pack is 5 of $0.45 comic books and 9 of $0.75 comic books

Step-by-step explanation:

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, the unknowns or unknown variables are:

x: number of $ 0.45 comic books

y: number of $ 0.75 comic books

Jacques wants to make up packs of $0.45 comic books mixed with $0.75 ones to sell at $9.00 per pack.  Then the equation that represents this situation is:

x*0.45 + y*0.75= 9

On the other side, the number of $0.45 comic books is 4 more than the number of $0.75 comic books.  Then the equation that represents this situation is:

x+4=y

The system of equations to solve is:

\left \{ {{x*0.45+y*0.75=9} \atop {x+4=y}} \right.

One way to solve a system of equations is the substitution method, which consists of solving one of the unknowns in one of the equations and substituting its value in the next.

In this case we directly replace the expression of the variable and of the second equation in the first:

x*0.45 + (x+4)*0.75= 9

Solving:

x*0.45 + 0.75*x + 4*0.75= 9

1.2*x + 3=9

1.2*x= 9-3

1.2*x= 6

x= 6÷ 1.2

x=5

Replacing this value in the expression x+4=y you get:

5 +4=y

9=y

<u><em>The number of each type in the pack is 5 of $0.45 comic books and 9 of $0.75 comic books</em></u>

8 0
3 years ago
Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms
guapka [62]

an aritmetic sequence increases by the same amount each time (if it decreases, then it increases by a negative number)


the common difference is the number that must be added to a term to get the next term


let's see if it increases by the same amount

-5 to -11 is increase of -6

-11 to -17 is increase of -6

-17 to -23 is increase of -6

-23 to -29 is increase of -6


so it appears to be aritmetic

common difference is -6

-29-6=-35

-35-6=-41

-41-6=-47

the next 3 terms are -35, -41, -47

4 0
3 years ago
Find the circumference of the circle to the nearest hundredth. Use 3.14 for π. Radius 21 cm.
Ierofanga [76]

Answer:

131.95 cm

Step-by-step explanation:

C=2 \pi r

C=2 \pi \times 21

C=42\pi

C \approx 131.946891451

3 0
3 years ago
What does translation means in math? I am taking a quiz on this right now, I need an answer ASAP!!!!!!
Morgarella [4.7K]

Answer:

Translation is moving an object to one place to another.

Step-by-step explanation:


8 0
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What is the value of x?<br><br> 6(−3−x)−2x=14<br><br> Enter your answer in the box.
olchik [2.2K]
For this we would first simplify using order of operations.
6(-3-x) - 2x = 14 ------> Distribute
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-8x - 18 = 14 Now we want to isolate x!
-8x - 18 = 14 ------> Add 18 to both sides.
-8x = 32 ------> Divide both sides by -8.
x = -4
Hope this helps!
8 0
3 years ago
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