The area of a rectangular piece of metal is 1,984 square centimeters. The perimeter is 188 centimeters. What are the dimensions of the piece?

Answers

Answer 1

Answer:

There are 2 options:

x = 32 cm and y = 62 cmx = 62 cm and y = 32 cm

Step-by-step explanation:

That's a rectangular piece, therefore let's consider the width to be x and the length to be y.

A = width * length

1) A = x * y = 1,984 cm^2

P = 2 * (width) + 2 * (length)

2) P = 2x + 2y = 188 cm

Isolate x or y in one of the equations.

xy = 1,984 cm^2

y = 1,984 cm^2 / x

Now plug it in the second equation.

2x + 2y = 188 cm

2x + 2 * (1,984 / x) = 188

Now we have only one variable. Now just solve it alegebraically.

2x + (3,968 / x) = 188

Multiply both sides by x in order to get rid of the fraction.

[tex]2x^{2}[/tex] + 3968 = 188 x

Substract both sides by 188 x

2x^2 + 3968 - 188x = 0

Now divide by 2 to make the equation simpler.

x^2 - 94x + 1984 = 0

use the quadratic formula:

[tex]\frac{94 + \sqrt{(-94)^2 - 4(1)(1984)} }{2(1)} = 62\\\frac{94 - \sqrt{(-94)^2 - 4(1)(1984)} }{2(1)} = 32[/tex]    

  [tex]x1 = \frac{-b + \sqrt{b^2 - 4ac} }{2a} \\x2 = \frac{-b - \sqrt{b^2 - 4ac} }{2a}[/tex]

x is either 62 or 32.

let's find y:

y = 1,984 / x

y = 1,984 / 62 = 32

y = 1,984 / 32 = 62

There are 2 options:

x = 32 cm and y = 62 cmx = 62 cm and y = 32 cm


Related Questions

juan rolls a fair number cube twice what is the probability that he will roll an odd number on the first roll and an even number in second

Answers

Answer:

1/4

Step-by-step explanation:

[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]

Assuming the number cube has faces number 1 through 6, the probability of rolling any of the number is 1/6.

Therefore,

P(odd number) = P(1) or P(3) or P(5)

                         = 1/6 + 1/6 + 1/6

                         = 3/6

                         = 1/2

Similarly,

P(even number) = P(2) or P(4) or P(6)

                           = 1/6 + 1/6 + 1/6

                           = 3/6

                           = 1/2

⇒ P(odd) AND P(even) = 1/2 × 1/2 = 1/4

Gabrielle’s age is two time Mikhaïl’s age. The sum of their ages is 27. What is Mikhail’s age?

Answers

Mikhail is 9

Step-by-step explanation:

Divide 27 by 3 because G is 2 times than Mik. So G=2 Mik=1. and 27 divided 3 is 9

(WILL MARK BRAINLIEST) Keisha is playing a game using a wheel divided into 8 equal sectors, as shown in the diagram below. Each time the spinner lands on blue, she will win a prize.

If Keisha spins this wheel twice, what is the probability that she will win a prize on both spins?

Answers

Answer:

6/11

Each time you spin the pointer there is a 3/8 for each of the two spins. That means there is a 6/11 chance of the pointer landing on blue for both times the pointer is spun.


Step-by-step explanation:

Each spin there are 8 possible sections the spinner can land on. The circle has 3 blue sections. The question asks what is the probability of the spinner landing on blue for BOTH spins. This means that you would have to show the denominator as 16. Each time you spin the pointer there is a 3/8 chance it will touch blue. When you spin it two times there is a 6/16 probability that the spinner will land on blue for each of the times the pointer is spun.



Have a great rest of your day
#TheWizzer

Which ratio is less than 7/15?
9/15
2/5
3/5
24/45

Answers

Answer:

2/5 :)

Step-by-step explanation:

A T.V. se was bought for Rs. 13950, when 10% discount is given. , calculate the marked price of the T.V.

Answers

Answer:

15500

Step-by-step explanation:

Solution

here

price of tv after discount: 13950

discount : 10%

now,

price of tv without discount= 13950÷90×100price of tv without discount= Rs15500

All exponential functions can be written in many forms. Write the function
f(t) = 2800(0.95)' in the form f(t) = abro. Round all coefficients to four
decimal places.

Answers

[tex]2800(0.95)^t~~ = ~~2800(b)^{\frac{t}{10}}\implies \cfrac{2800(0.95)^t}{2800}=b^{\frac{t}{10}}\implies 0.95^t=b^{\frac{t}{10}} \\\\\\ (0.95)^{\frac{10t}{10}}=b^{\frac{t}{10}}\implies (0.95^{10})^{\frac{t}{10}}=b^{\frac{t}{10}}\implies (0.5987)^{\frac{t}{10}}\approx b^{\frac{t}{10}}\implies 0.5987 \approx b \\\\[-0.35em] ~\dotfill\\\\ ~\hfill f(t)\approx 2800(0.5987)^{\frac{t}{10}}~\hfill[/tex]

Consider the diagram.

Line l is a perpendicular bisector of line segment R Q. It intersects line segment R Q at point T. Line l also contains point S. Line segment R S is 3 x + 2. Line segment S Q is 5 x minus 8.

What is QS?

2 units.
5 units.
17 units.
33 units.

Answers

Answer:

A on edge

Step-by-step explanation:

:)

A triangle is a three-edged polygon with three vertices. The length of QS is equal to 17 units.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Given that the Line l is a perpendicular bisector of line segment RQ and bisects it at point T. Therefore, the length of the two lines is,

RT = QT

Now, in ΔRST and ΔQST,

RT ≅ QT

ST ≅ ST {Common side}

Now, since the two triangles are the right-angled triangle, therefore, the two triangles are congruent. Thus, we can write,

RS = SQ

Given that the Line segment, RS is 3x+2. Line segment SQ is 5x-8.

RS = SQ

3x + 2 = 5x - 8

2 + 8 = 5x - 3x

10 = 2x

x = 5

QS = 5x - 8

     = 5(5) - 8

     = 25 - 8

     = 17 units

Hence, the length of QS is equal to 17 units.

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Do basketball players hit a higher proportion of free throws when they're playing at home or when they're playing away this best is assessed by using

Answers

Answer:

home

Step-by-step explanation:

I'm not sure I'm just guessing honestly

.............help me

Answers

Answer:

A Translation 2 units left and 1 unit down

Step-by-step explanation:

Help please anybody?

Answers

Answer:

.................

216cm^2

Step-by-step explanation:

brainliest please

A square is inscribed in a circle. How much larger is the area of the circle than the area of the square?
ratio form

Answers

Answer:

π/2 : 1 or π : 2

Step-by-step explanation:

In the attachments I have a picture of a square inscribed in a circle.

Call the side of the square a. Therefore, the area of the square is a^2.

We can also see that the diagonal of the square is the circle's diameter.

Using the Pythagorean Theorem we find that the diagonal/diameter of the circle is a√2. Thus the radius is that divided by 2, which is (a√2)/2.

We also know that the formula for a circle's area is πr^2, so the area of the circle is π((a√2)/2)^2 --> π(a^2)(2)/4 --> π(a^2)/2.

Hence the ratio of the circle to the square is π(a^2)/2 to a^2 which is π/2 to 1 or π to 2.

What is the solution to this system of
equations?
6x - 2y = 8
1-3x + y = -4
A. No Solution
B. (0, -4)
C. Infinite Solutions

Answers

Answer:

No solution

Step-by-step explanation:

System of Linear Equations given :

[1]           6x-2y=8

 [2]           1-3x+y=-4

Equations Simplified or Rearranged :

  [1]    6x - 2y = 8

  [2]    -3x + y = -5

Solve by Substitution :

// Solve equation [2] for the variable  y

 [2]    y = 3x - 5

// Plug this in for variable  y  in equation [1]

  [1]    6x - 2•(3x-5) = 8

  [1]    0 = -2 =>  NO solution

Complete the net worth statement. What is the net worth of the individual?
A) $171,645
B) $19,950
C) $21,000
D) $26,595

Answers

Considering it's concept, it is found that the net worth of the individual is given by:

D) $26,595.

What is the net worth of an individual?

It is given by the sum of the individual assets subtracted by the sum of it's liabilities.

Researching the problem on the internet, we have that:

The sum of the assets, in dollars, is of 545 + 165000 + 6100 = 171645.The sum of the liabilities, in dollars, is of 144000 + 1050 = 145050.

Hence, his net worth is given by:

N = 171645 - 145050 = $26,595.

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The net worth of the individual with assets worth $171,645 and liabilities of $145,050 is D) $26,595.

What is the net worth?

The net worth is the value of assets less the value of liabilities.

The net worth shows the amount by which the assets have increased or decreased in value versus the liabilities.

Data and Calculations:

Assets = $171,645

Liabilities = $145,050
Net worth = $26,595 ($171,645 - $145,050)

Thus, the net worth of the individual with assets worth $171,645 and liabilities of $145,050 is D) $26,595.

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What fraction is equivalent to six tenths and has a denominator of 100?

Answers

Answer:

6 = 6/10

Step-by-step explanation:

.6 = 6/10 , by definition. = 3/5 (reduced -- divide numerator and denominator by 2.

Answer:

[tex]\dfrac{60}{100}[/tex]

Step-by-step explanation:

Six tenths:

[tex]\dfrac{6}{10}[/tex]

where 6 is the numerator and 10 is the denominator

We want the denominator to be 100, so how do we convert 10 into 100?

We multiply by 10, since 10 x 10 = 100

When working out equivalent fractions, we must remember to do the same operation to both the numerator and denominator.  Therefore, we should multiply both by 10:

[tex]\dfrac{6 \times 10}{10 \times 10}=\dfrac{60}{100}[/tex]

Therefore, the fraction that is equivalent to six tenths and has a denominator of 100 is:

[tex]\dfrac{60}{100}[/tex]

(sixty hundredths)

The circumference of the base of a cone is 24 inches. The slant height of the cone is 20 inches.

What is the surface area of the cone? Express the answer in terms of .

240 square inches
384 square inches
480 square inches
624 square inches

Answers

The surface area of a cone with circumference base of 24π inches and slant height of 20 inches is 384π inches² in terms of π.

Surface area of a cone

surface area = πr(r + l)

where

r = radiusl = slant height

Therefore,

l = 20 inches

24π = 2πr

r = 12

Therefore,

surface area  = π(12)(12 + 20)

surface area = 12π(12 + 20)

surface area = 12π × 32

surface area = 384π inches²

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Answer:

B)  384 π square inches

Step-by-step explanation:

E2020

what ratio is equivilant to 4 : 5

Answers

Answer:

Any ratio where the original sides are both multiplied by the same number.

For example,

4 : 5  (your ratio)

4 x 2 : 5 x 2  (multiply both sides by a number)

8 : 10   (equivalent ration)

For which values of c does the quadratic equation x^2−2x+c=0 have two roots of one sign?

Answers

The equation x^2−2x+c=0 is an illustration of a quadratic equation

The value of c is 1

How to determine the value of c?

The equation is given as:

x^2 -2x + c = 0

A quadratic equation is represented as:

ax^2 + bx+ c = 0

When the quadratic equation  has two roots of one sign, the following equation is true

b^2 =4ac

So, we have:

(-2)^2 =4 * 1 * c

Evaluate the exponent and the product

4 = 4c

Divide both sides by 4

c= 1

Hence, the value of c is 1

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The answer to this problem is:

0<c<1

41. Henry stands on a platform and shoots a rocket in his 10th
grade science class. He found that the motion of the rocket can be
described by the equation y = 60 + 28x – x2, where y is the
vertical distance and x is the horizontal distance traveled. If this
trajectory equation were to be graphed, find the x-intercepts of the
equation. (Fun fact: The positive x-intercept is how far away from
the platform the rocket hits the ground!)

Answers

The x-intercepts of the quadratic equation are given by x = -2 and x = 30.

What are the x-intercepts of a quadratic equation?

A quadratic equation is modeled by:

y = ax² + bx + c.

The x-intercepts are the values of x when y = 0, given by:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

In this problem, the equation is:

y = 60 + 28x - x².

Hence the coefficients are a = -1, b = 28, c = 60.

Then:

[tex]\Delta = 28^2 - 4(-1)(60) = 1024[/tex]

[tex]x_1 = \frac{-28 + \sqrt{1028}}{-2} = -2[/tex]

[tex]x_2 = \frac{-28 - \sqrt{1028}}{-2} = 30[/tex]

The x-intercepts of the quadratic equation are given by x = -2 and x = 30.

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Determine which of the triangles below are unique. Share your reasoning.
Triangle A: All angle measure 60 degrees
Triangle B: All sides have length 6 cm.
Triangle C: Two sides have length 6 cm, and the included angle measures 55
degrees
Triangle D: Base has length of 6 cm, and the base angles are 50 degrees.

Answers

Answer:

Triangle A and Triangle B

Step-by-step explanation:

I think this is the answer because Triangle A, has a unique that all sides have a measure of 60 degrees. And I also think that Triangle B is unique because It's an Equilateral triangle, which means that all sides have the same length.

So hence, I think the answer is A and B

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

Always keep more than 2 smiles! You have to share them with people who don't have one too, right??

Thanks!

:D

PLEASE HELP WILL MARK BRAINLIEST THANK YOU

Answers

Here is the answer: x=4

please help me solve for m<C and m<D​

Answers

Answer:

Step-by-step explanation:

Use law of cosine to calculate the other side.

c² = a² + b² -2ab Cos C

Here, c  is the length of the side which is  opposite side to ∠E

a = 29   ; b = 25  and C = 109

c² = 29² + 25² - 2*29*25*Cos 107

    = 841 + 625 - 1450* (-0.2923)

     = 1466 + 423.835

     = 1889.835

c =√1889.835

c = 43.47 ≈ 43

No, find ∠D using again use law of cosine

[tex]Cos \ \beta = \dfra{a^{2}+c^{2}}-b^{2}{2ac}\\\\\\ = \dfrac{29^{2}+43^{2}-25^{2}}{2*29*43}\\\\\\Cos \ \beta =\dfrac{841+1849-625}{2494}=\dfrac{2065}{2494}\\\\Cos \ \beta = 0.828\\\\\beta =Cos^{-1} \ 0.828\\\\[/tex]

β = ∠C = 34°

α = 180 - (34 +107)

α = ∠D = 39

Other angles are

∠C = 34°     and  ∠D°39

Help Please Quick! Pleasee

Answers

Answer:

you can search them up! Just search up fractions calculator

Step-by-step explanation:

PLEASE HELP PLEASE PLEASE HELP

Answers

Answer:

Light

Step-by-step explanation:

Light can travel approximately 186,000 miles per second so the answer we are looking for in here is light.

A wall is 3600 sq ft.
A gallon of paint covers 600 sq ft.
Complete the conversion factor: 1 gallon / ? sq ft

Answers

Answer:

1 gallon / 600 sq ft

Step-by-step explanation:

As we can see, we are given that 600 sq ft uses one gallon to cover, therefore one gallon covers 600 sq ft (just vice versa of what's given).

Maria rolls a regular number cube with sides labeled 1 through 6. How many possible outcomes are there?

Answers

The answer would be 6. One for each side

Use synthetic division to divide:

(2x^4+5x^3-3x^2-x+1) / (x+2)

Answers

Answer:

[tex]2x^3 +x^2 -5x+9 -\frac{17}{x+2}[/tex]

Step-by-step explanation:

See picture for explanation

This recipe makes three portions of soup.
Navina follows this recipe but only wants to make enough for one portion of soup.
How much of each ingredient does she need?

Recipe: Serves 3
180 g onions
120 g carrots
3 tablespoons of oil
600 g tomatoes
1.2 litres vegetable stock

Answers

Answer:

Step-by-step explanation:

To get one portion of soup, each ingredient should be divided by 3

Quantity of onion required=  180 ÷ 3 = 60 g

Quantity of carrots required = 120 ÷ 3 = 60 g

Oil = 3 ÷ 3 = 1 table spoon

Quantity of tomatoes required = 600 ÷ 3 = 300 g

Vegetable stock = 1.2 ÷ 3 = 0.4 litres

In the diagram, mZXYZ (Exterior Angle Y)=115º and
mZWXY (Angle X) = 45°.

What is m

Answers

Answer: 70 degrees

Step-by-step explanation:

Find the equation of the line through the points (0, –3) and (4, 5)

Answers

Answer:

y=2x-3

Step-by-step explanation:

Hi there!

We are given the points  (0, –3) and (4, 5)

We want to find the equation of the line between these points

There are 3 ways to write the equation of the line, yet the most common way is slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

To write the equation of the line in this way, we need to first find the slope of the line
The slope can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We already have 2 points, but let's label their values to avoid confusion and mistakes when calculating.

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{5--3}{4-0}[/tex]

Simplify

m=[tex]\frac{5+3}{4-0}[/tex]

m=[tex]\frac{8}{4}[/tex]

Divide

m=2

We found the slope of the line.

Here is the equation of the line so far:

y=2x+b

Now let's find b

As stated before, b is the y intercept of the line, which is the point where the line passes through the y axis; the value of x at the y intercept is 0

One of the points we were given (0, -3) is actually the y intercept of the line!

The value of b is the value of y at the y intercept; in this case, b is equal to -3

Now substitute -3 as b in the equation.

y=2x-3

Hope this helps!

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Consider the function f(x)=8x3−2. If f(g(x))=x and g(f(x))=x, find g(x)

Answers

I can give you a hint. So when we do the composition of functions, if we plug 2 functions into each other and get x by itself, that means the functions are inversely related.

For this problem, simply find the inverse of f(x).

If you are stuck, I could provide you with a solution below...

f(x) = 8x³ - 2

y = 8x³ - 2

y + 2 = 8x³

(y + 2)/8 = x³

cube root((y + 2)/8) = x

g(x) = cube root((x + 2)/8)

The value of function g(x) after solving will be ∛(x + 2) / 2.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The value of function,

f(x) = 8x³ − 2

And, f(g(x)) = x and g(f(x)) = x

Now,

Since, f(g(x)) = x

And, f(x) = 8x³ − 2

The substitute x = g (x) in above equation we get;

f (g(x)) = 8 (g(x))³ - 2

x = 8 (g(x))³ - 2

Add 2 both side;

x + 2 = 8 (g(x))³  

Divide by 8;

(x + 2)/8 = (g(x))³

Take cube root both side;

∛(x + 2)/8 = g(x)

g(x) = ∛(x + 2) / 2

So, The value of function g(x) after solving will be ∛(x + 2) / 2.

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