The area of a rectangle is 56 cm. The length is 2cm more than x and the width is 5 cm less than twice x.Solve for x

Answers

Answer 1

Area of a rectangle is A = L*W.

Here, A = 56 cm^2 (not 56 cm).

= (56 cm^2)=( L )( W ) = (x+2)*(2x-5) = 2x^2 - 5x + 4x - 10

Simplifying, 2x^2 - 5x + 4x - 10 = 56, or 2x^2 - x - 66 = 0.

Solve this using the quadratic formula:

-(-1) plus or minus sqrt ( (-1)^2 - 4(2)(-66) )
x = -------------------------------------------------------------
2(2)

Finish the work: find x. Most likely you will need to check both of the roots. Keep in mind that x will likely be a positive number.

Related Questions

The length of a rectangle is 4 inches less than twice its width. If the area of the rectangle is 70 square inches, what are its demensions

Answers

By definition, the area of a rectangle is given by:
A = w * l
Where,
w: width
l: long
Substituting values we have:
70 = w * (2w-4)
Rewriting we have:
70 = 2w ^ 2-4w
2w ^ 2 - 4w - 70 = 0
Solving the polynomial we have:
w1 = -5
w2 = 7
We take the positive root because it is a dimension.
w = 7 inches
Then, the length will be:
l = 2w-4
l = 2 (7) -4
l = 14-4
l = 10 inches
Answer:
its demensions are:
w = 7 inches
l = 10 inches

let
x-----------> the length side of rectangle
y----------> the width side of rectangle

we know that
70=x*y--------> x=70/y-----------> equation 1
x-4=2y--------> equation 2
substitute equation 1 in equation 2

[70/y]-4=2y--------> multiply by y------> 70-4y=2y²----> 2y²+4y-70=0

using a graph tool ----> to resolve the second order equation
see the attached figure

the solution is
y=5
x=70/y--------> x=70/5=14

the answer is
the dimensions are
length=14 in
width=5 in

please help!!!

Write an expression for the volume of a cylinder with a height 7in. greater than the radius.

Answers

Answer: 7 π r² + π r³

Explanation:

1) The general formula for the volumen, V, of a cylinder with radius r and height h is:

V = π r² h

2) Now you have the condition that the height is 7 inches greater than the radius, that is:

h = 7 + r

3) Replace h with its expression

V = π r² (7 + r)

4) Expand the product (use distributive property):

V = π (7r²) + π r³ = 7 π r² + π r³

Answer: 7 π r² + π r³

Carlos swam the perimeter of a rectangular pool seven times. If the length of the pool is 21 ft and the width of the pool is 9 ft, how many feet did Carlos swim?

Answers

21+9+21+9=Perimeter of the pool = 60
And Carlos did this 7 times (x)...60 x 7 = 420

The total length did Carlos swim is 420 feet.

To find the perimeter.

What is rectangle?

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that:

Let the perimeter of rectangular swimming pool be x metres.

Then, its length =21 feet.

The width of the pool = 9 feet

The Perimeter of a rectangle =2(Length+Breadth)

According to the given condition, we have

Perimeter of a rectangle =2(Length+Breadth)

Perimeter of a rectangle=2(21+9)

Perimeter of a rectangle=2*30

Perimeter of a rectangle=60 feet

But, carlos swam the perimeter of a rectangular pool seven times.

Old perimeter=7*60=420 feet

Thus ,the total length did Carlos swim is 420 feet.

Learn more about rectangle here:

https://brainly.com/question/10064327

#SPJ2

2/3 - 4x + 7/2 = -9x + 5/6

Answers

The answer is:
x=-2/3

You can convert the equation to 4/6+21/6-5/6=-9x+4x, which equals 0.666 repeating.

. Stephen deposited $1800 into a savings account for which interest is compounded weekly at a rate of 3.2%. How much interest will he earn after 10 years?
58.81
678.59
2478.59
im just putting this up to see if my answer was write. i did the math and unless i messed up writing i got the second answer

Answers

A = P(1+i/n)^nt

A = Total amount paid
P = Principal amount
i = Annual interest
n = number of payments per year
t = time in years

Substituting the values given,
A = 1800(1+0.032/52)^52*10 = $2,478.59

Interest paid = A - P = 2478.59-1800 = $678.59

Second answer is correct.

What is the length of the unknown side of the right triangle? (1 point) A right triangle with hypotenuse x and legs 5 and 12 13 17 25 60

Answers

If the legs are...

5,12 --> 13

Why? Pythagorean theorem.

5 squared plus 12 squared equals 169. The square root of that is 13.

Answer is 13;
[tex] \sqrt{{(12)}^{2} + {(5)}^{2}} = 13[/tex]

What is the measure of BAC

50
80
100
130

Answers

80 because 50 + 50 = 100 & 180 - 100 equals 80

isosceles triangle

so <BAC = 180 - 2(50) = 180 - 100 = 80
answer
80

Someone please help

Answers

D is the right answer!

ANSWER TRUTHFULLY WILL NAME YOU BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!
The ordered pairs (1,5) (2,25) (3,125) (4,625) and (5,3125) represent the function y=5^x. How does this rule represent the function?

A) y=x5
B) y=5x
C) y=5^5=x
D) y=x+5

Answers

For each answer, we can plug in the given points:

A) is technically the same as B), but B) expresses correct function notation.

B) 5 = 5(1) ⇒ 5 = 5
25 = 5(2) ⇒ 25 ≠ 10
B) is incorrect.

C) I'm not sure what you mean y=5^5=x, but I'm going to use [tex]y=5^{x} [/tex] because it's close to what you wrote:
[tex]5=5^{1} =\ \textgreater \ 5=5 \\ 25=5^{2} =\ \textgreater \ 25=25 \\ 125=5^{3} =\ \textgreater \ 125 = 125 \\ 625=5^{4}=\ \textgreater \ 625=625 \\ 3125=5^{5}=\ \textgreater \ 3125=3125[/tex]
The function [tex]y=5^{x} [/tex] works for the points given.

D) 5 = 1 + 5 ⇒ 5 ≠ 6
D) is not correct.

Please check your functions; I'm not sure that C) is a function. In any case, the answer is C) because all the other answers are wrong.

Roger goose had a 500-yard head start on willa. if willa's speed was 40 yards per second and roger's speed was only 20 yards per second, how long did it take willa to catch up

Answers

For this case what we should do is write the equation of movement for each person.
We have then:
For Roger:
r = 20 * t + 500
For Willa:
r = 40 * t
Equating the equations:
20 * t + 500 = 40 * t
We cleared t:
40 * t - 20 * t = 500
20 * t = 500
t = 500/20
t = 25 s
Answer:
it did take willa 25 s to catch up Roger.

What is the distance between point (3, 2) and line y = 1/4x-9

Answers

Hello!

You can put 3 in for x

y = 1/4(3) - 9

y = 0.75 - 9

y = -8.25

A point on the line is (3, -8.25)

Find the difference in y values

-8.25 - 2 = -10.25

The answer is 10.25 units

Hope this helps!

for the function f(x)= -(x + 1)^2 + 4 identify the vertex, domain, and range

Answers

Vertex (-1, 4)

Domain = All real numbers

Range = All y values such that y ≤ 4

Answer:

Vertex = (-1, 4)

Domain = All real numbers i.e. R

Range = (-∞, 4)

Step-by-step explanation:

The vertex of the quadratic equation:

f(x) = a(x - h)² + k

Here, Vertex = (h,k)

Thus, Vertex = (-1, 4)

Domain = All real numbers i.e. R

Range = All real numbers less than or equal to 4 i.e. (-∞, 4) or f = ≤ 4.

Further, the possible values of x are called Domain.

And, the possible output we get as y is called Range.

Which expression is equivalent to mc003-1.jpg?

Answers

Given two functions f(x) and g(x), when you multiply the two functions, according to algebra:
f(x)*g(x)
=(fg)(x)
hence when x=5
then
f(5)*g(5)
=(fg)(5)
therefore, the answer to
(fg)(5)
=f(5)*g(5)

Answer:

Option A is correct

The expression which is equivalent to [tex](f\cdot g)(5)[/tex] is [tex] f(5) \cdot g(5)[/tex]

Step-by-step explanation:

Using the formula:

[tex](f \cdot g)(x) = f(x) \cdot g(x)[/tex] .....[1]

Given the expression:

[tex](f\cdot g)(5)[/tex]

Substitute the value of x = 5 in [1]

we get;

[tex](f \cdot g)(5) = f(5) \cdot g(5)[/tex]

Therefore, the expression which is equivalent to [tex](f\cdot g)(5)[/tex] is [tex] f(5) \cdot g(5)[/tex]

Give an exact answer in simplified form. 5y+3 > -7y + 13 5y+3>−7y+13 (see pic

Answers

Th answer to the inequality will be evaluated as follows:
5y+3>-7y+3
putting like terms together we obtain:
5y+7y>3-3
2y>0
dividing both sides by 2 we get:
(2y)/2>0/2
thus
y>0

Answer: y>0

Th answer to the inequality will be evaluated as follows:

5y+3>-7y+3

putting like terms together we obtain:

5y+7y>3-3

2y>0

dividing both sides by 2 we get:

(2y)/2>0/2

thus

y>0

Melissa pulls the pep club to see which sport they like. She finds that 45 students like soccer only, 35 students like football only, and 15 students like soccer and football. There is no one who doesn't like at least one of the two sports mentioned. Which venn diagram would be an appropriate model for the data melissa collected

Answers

The one that looks like this.

Which of the following best describes the following set of numbers? 6 + 8 + 10 + 12 + ... + (4 + 2n) + ...

answers:
Arithmetic SequenceGeometric SeriesGeometric SequenceArithmetic Series

Answers

From the series given:
6+8+10+12+.....+(4+2n)+
the common difference is:
8-6=10-8=12-10=2
since the series has a common difference then it is known as:
Arithmetic series.

Answer:

The term that best describes the given set of numbers is:

Arithmetic Series.

Step-by-step explanation:

We are given a series of numbers as:

6 + 8 + 10 + 12 + ... + (4 + 2n) + ...

Clearly as wee could see that each term in the given expression is separated by a plus sign, Hence, the given expression is a series and not a sequence.

Also as we could see that each in the series is more than the preceding term by 2 i.e. the common difference of the term is 2.

( Since, the set of numbers is given as:

[tex]a_0+a_1+a_2+a_3+....[/tex]

where,

[tex]a_n=2n+4[/tex]

[tex]when,n=0\\\\a_1=4\\\\when,n=1\\\\a_1=6\\\\and\ so\ on[/tex]

Also,

[tex]a_0-a_1=2\\\\Simialrly\\a_2-a_1=2\\\\and\ so\ on[/tex]

Hence, the common difference is 2. )

Hence, the given series is an Arithmetic series.

Easy math problem, please help.

O is the center of the circle. Assume that lines appear to be tangent are tangent. What is the value of x?

A. 34
B. 36.5
C. 73
D. 107

Answers

tangent lines are perpendicular to their intersection point so add 17 and 90 then subtract 107 to 180 to get {[(73)]}

Answer:

Option C. 73

Step-by-step explanation:

In the given figure Δ OPQ is the right angle triangle because radius is always perpendicular to the tangent drawn on the circle from an external point.

Here OQ is radius and PO is tangent.

So ∠OQP = 90°

Now sum of all angles of a triangle is 180°

Therefore, ∠OPQ + ∠OQP + ∠POQ = 180°

17° + 90° + x° = 180°

107 + x = 180

x = 180 - 107

x = 73°

Option C. 73

Which equation represents a parabola with a focus at (0,-2) and a directrix of y=6?

Answers

Hey there!!

First, let's learn the parabola formula when the focus and the directrix is given.

Formula :

[tex]y = \frac{( x - a ) ^{2} }{ 2 ( b - k ) } + \frac{( b + k ) }{2}[/tex]

We have ,

Focus : ( 0 , -2 )

Hence, a = 0 and b = -2

And k = 6

Now, we will just have to plug in the values and find out the equation.

[tex]y = \frac{( x - 0 )^{2} }{2 ( - 2 - 6 )} + \frac{( - 2 + 6 ) }{2}[/tex]

[tex]y = \frac{x^{2} }{-16}+ 2[/tex]

The final equation would be :

[tex]y = \frac{-x^{2} }{16} + 2[/tex]

Hope my answer helps!!

Solve a(x - b) - 2k = l for k

Answers

a(x - b) - 2k = l
ax - ab - 2k = l

Subtract ax, add ab to both sides

- 2k = l - ax + ab

Divide by - 2 to isolate variable K

k = (l - ax + ab) / - 2 or [tex]k = \frac{l - ax + ab}{-2} [/tex]

Claudia is on a motorcycle trip. She checked the odometer at the beginning of the trip, and it showed 16,789 miles. After 15 days it showed 22,189 miles. If Claudia rode the same number of miles each day how many miles did she ride in a day?
A.360 miles
B 540 miles.
C.771 miles
D.1,479 miles
please help me

Answers

22,189 - 16,789 = 5,400

Total miles = 5,400
Days = 15

Divide total by how many days:

5,400 ÷ 15 = 360

Answer = A.360

Hope this helped :)

22,189 - 16,789 = 5,400

5,400 / 15 = 360

360 miles a day

Greg wants to move out of his dormitory and into an apartment near his college. His parents agreed, on the condition that the rent is no more than 25% of the cost of dorm living. To get an idea of rent amounts for one-bedroom apartments, Greg looks at listings in a local newspaper and on an Internet site.

Which answer best describes the sample and population?

A. Sample: listings in a local newspaper and on an Internet site
Population: all available apartments near the college

B. Sample: all available apartments near the college
Population: all available dormitories near the college

C. Sample: all available dormitories near the college
Population: all available apartments near the college

D. Sample: all available apartments near the college
Population: listings in a local newspaper and on an Internet site

Answers

the sample would be where Greg searched so the sample is the local newspaper and the internet site
the population would be all available apartments
the answer would be

A. Sample: listings in a local newspaper and on an Internet site
Population: all available apartments near the college

I am posting my work for an application of integrals problem. I would love to know if anyone else agrees with my work!

Answers

Your work appears to be correct.

The results from a graphing calculator are in agreement.

The equation of a parabola is given. y=−16x2+7x−80 What is the equation of the directrix of the parabola?

Answers

we have that
y=−16x²+7x−80

see the answer in the attached figure

y=-1/6x^2+7x-80
the answer is y=-5

I don't understand this question. Could anyone excplain to me what it wants me to do and what the answer is?

What is the diameter of a sphere that has a surface area of 1041 square inches?

A) 9.1

B) 22.5

C) 40.3

D) 18.2

Answers

The answer is 18.2
I got the answer by solving it

1st you need equation for the surface area of a sphere which is:
A=4*π*r^2
Where r=radius
r = diameter/2 or d/2

So
area of a sphere = 4*π*(d/2)^2

Plug in the area given
1041 = 4*π*(d/2)^2

Solve for d
1041/(4* π)=82.84

82.84 = (d/2)^2

Sqrt(82.84)=d/2

9.10=d/2

9.10*2= d

18.2=d
So the answer is 18.2 in

URGENT PLEASE HELP

Suppose 20% of all widgets produced at a factory are defective.

A simulation is used to model widgets randomly selected and then recorded as defective or working.

Which simulation best models the scenario?

Place 50 equally sized pieces of paper in a hat. Of the 50, 5 read “defective” and the rest read “working”.

Place 25 equally sized pieces of paper in a hat. Of the 25, 5 read “defective” and the rest read “working”.

Place 20 equally sized pieces of paper in a hat. Of the 20, 5 read “defective” and the rest read “working”.

Place 100 equally sized pieces of paper in a hat. Of the 100, 5 read “defective” and the rest read “working”.

Answers

Place 25 equally sized pieces of paper in a hat. Of the 25, 5 read “defective” and the rest read “working”.

What is the surface area of a sphere with the given dimension? Express your answer to nearest hundredth. Use 3.14 for pi. Radius = 5cm.

Answers

Okay. The equation for a sphere's surface area is A = 4 * pi * r^2. Let's plug 5 in for r.
[tex]4 \pi (5^2) = 4(3.14)*25 = 100 * 3.14 = 314[/tex]
I got 314 cm^2 is the surface area, but it always helps to double check work! Hope this helps!

Surface area of a sphere can be calculated as:

Surface Area = 4πr²

r = 5cm
π = 3.14

Using the values we get:

Surface Area = 4(3.14)(5²) = 314 cm²

Thus, the surface area of the sphere is 314 cm²

find the volume of the specificed cone. Use 3.14 for pie, and round your answer to the nearest whole number.
Radius=9 in., Height=8 in.
a. 1017 cu. in.
b. 151 cu. in.
c. 678 cu. in.
d. 1356 cu. in.

Answers

The answer is C.678 cu. in. :D

Pete is purchasing an mp3 player for 199.90 he gives the sales clerk 2 fifty dollar bills, 4 twenty dollar bills and 4 five dollar bills how much should he receive back

Answers

Amount of money Peter gave the sales clerk is:
2(50)+4(20)+4(5)
=100+80+20
=$200
Thus the balance he received was :
200-199.90
=$0.1
=10 cents

The length of a rectangle is 7 cm less than twice its width. if the area of the rectangle is 39 cm2, find the dimensions of the rectangle.

Answers

Use the equation 2n+2(n-7)=39 to find the answer :)

(08.05 HC) The work of a student to solve a set of equations is shown: Equation A: y = 15 − 2z Equation B: 3y = 3 − 4z Step 1: −3(y) = −3(15 − 2z) [Equation A is multiplied by −3.] 3y = 3 − 4z [Equation B] Step 2: −3y = 15 − 2z [Equation A in Step 1 is simplified.] 3y = 3 − 4z [Equation B] Step 3: 0 = 18 − 6z [Equations in Step 2 are added.] Step 4: 6z = 18 Step 5: z = 3 In which step did the student first make an error?

Answers

The error appears to be in Step 2.

Simplifying
-3(y) = -3(15 -2z)
should yield
-3y = -45 +6z
not
-3y = 15 -2z

Answer:

STEP 2

Step-by-step explanation:Simplifying

-3(y) = -3(15 -2z)

should yield

-3y = -45 +6z

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