he area of a rectangular piece of metal is 20 square centimeters. The perimeter is 18 centimeters. What are the dimensions of the piece?

Answer:

c) x = 1 ± i √29 / 5​

Step-by-step explanation:

assuming we are solving for x we can use the quadratic formula

quadratic formula : [tex]\frac{-b+or-\sqrt{b^2-4(a)(c)} }{2(a)}[/tex]

where the values of a,b and c are derived from the equation

the equation is put in quadratic form : ax² + bx + c

so in 5x² -2x + 6 a = 5 , b = - 2 and c = 6

we then plug these values of a, b and c into the quadratic formula

recall quadratic formula [tex]\frac{-b+or-\sqrt{b^2-4(a)(c)} }{2(a)}[/tex]

a = 5 , b = - 2 , c = 6

[tex]\frac{-(-2)+or-\sqrt{(-2)^2-4(5)(6)} }{2(5)}[/tex]

remove parenthesis at -(-2) to get positive 2 because the negative signs cancel out

[tex]\frac{2+or-\sqrt{(-2)^2-4(5)(6)} }{2(5)}[/tex]

evaluate exponent

[tex]\frac{2+or-\sqrt{4-4(5)(6)} }{2(5)}[/tex]

multiply -4(5)(6)

[tex]\frac{2+or-\sqrt{4-120} }{2(5)}[/tex]

subtract 120 from 4

[tex]\frac{2+or-\sqrt{-116} }{2(5)}[/tex]

multiply 2 and 5

[tex]\frac{2+or-\sqrt{-116} }{10}[/tex]

because we cant have a negative square root we replace the negative sign with i (which equals -1 )  and add it to the outside of the square root

[tex]\frac{2+or-i\sqrt{116} }{10}[/tex]

we then simplify  the radical

[tex]\frac{2+or-2i\sqrt{29} }{10}[/tex]

we then simplify the fraction

2/10 = 1/5 so both 2's cancel out

[tex]\frac{1+or-i\sqrt{29} }{10}[/tex]

the answer is C

Answer:

the probability is 3/5

Step-by-step explanation:

you have the numbers 2, 4, 6

and the numbers 3, 5

the 1 doesn't count, the question says numbers greater than or equal to 2

so, the remaining numbers add up to 3/5

Answer:

[tex]y=-0.667x+-10[/tex]

Step-by-step explanation:

Given the following question:

Point A = (-9, -4), (x1, y1)
Point B = (-6, -6), (x2, y2)

[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{-6--4}{-6--9} =\frac{-2}{3}[/tex]
[tex]m=\frac{-2}{3}[/tex]

Write in slope intercept form:

[tex]y=mx+b[/tex]
[tex]m=\frac{-2}{3}=-2\div3=-0.667[/tex]
[tex]y=-4[/tex]
[tex]x=-9[/tex]
[tex]-4=-0.667\times-9+b[/tex]
[tex]-0.667\times-9=6[/tex]
[tex]b=-10[/tex]
[tex]y=-0.667x+-10[/tex]

Hope this helps.

Answer:

Step-by-step explanation:

Domain of a function represents the set of x-values (input values) and y-values (output values) of the function represent the Range of the function.

Given function is,

If Domain (input values) of this function is,

{-12, -6, 3, 15}

Table for the input-output values of this function,

x        -6         3        15       -12

y        11         5         -3        15

Answer:

r = 3.95 mm (nearest hundredth)

Step-by-step explanation:

[tex]\textsf{volume of a cylinder} = \pi r^2h[/tex]

(where r = radius and h = height)

Given, volume = 686 mm² and height = 14 mm:

[tex]686=\pi r^2\times14[/tex]

[tex]\implies\pi r^2=686 \div14=49[/tex]

[tex]\implies r^2=49 \div \pi[/tex]

[tex]\implies r=\sqrt{49 \div \pi }=3.949327085...[/tex]

[tex]\implies r=3.95 \ \textsf{mm}[/tex]

Answer:

21.15 hrs

Step-by-step explanation:

I divided 55 by 2.6 to get the 21.15.

Have a good day!

Answer:

x = [tex]\frac{25}{4}[/tex] so the answer is B

Step-by-step explanation:

Answer: To test whether the given trinomial is a perfect square, we should try to write the trinomial in the form of a² + 2ab + b² (or) a² - 2ab + b² If we are able to write the given trinomial in the above form, then it is perfect square. Otherwise the given trinomial is not a perfect square.

Step-by-step explanation:

Answer:

D. 2144.6

Step-by-step explanation:

volume of a sphere is 4/3 * pi * r^3

we've been given the value of our radius as 8 and also the value for pi is 3.142 so in you solve using the formula you get 2144

[tex]\\ \rm\Rrightarrow V=4/3\pi r^3[/tex]

[tex]\\ \rm\Rrightarrow V=4/3\pi (8)^3[/tex]

[tex]\\ \rm\Rrightarrow V=4/3\pi 512[/tex]

[tex]\\ \rm\Rrightarrow V=170.6(4)\pi[/tex]

[tex]\\ \rm\Rrightarrow V=682.4cm^3[/tex]

Rhombus has all sides equal. The total amount of paper that will be needed to cover the wall is 396 in².

Given to us

Each rhombus will be 6 inches tall and 4 inches wide.

A.)

The area of each rhombus can be found using the formula,

[tex]Area = \dfrac{1}{2} \times d_1 \times d_2[/tex]

We know that diagonals of the rhombus are of length 6 in and 4 in. therefore,

[tex]Area = \dfrac{1}{2} \times 6 \times 4\\\\Area = 12\ in^2[/tex]

Hence, the area of the single rhombus is 12 in².

We know that the wall is 11 feet long, also, 1 foot = 12 inches, therefore,

11 feet = 132 in.

Now, since the wall is 132 in long and the width of the rhombus is 4 in, therefore, the number of rhombi that will be needed,

[tex]\dfrac{132}{4} =33[/tex]

Hence, the number of rhombi that will be needed is 33.

We know the area of each paper rhombus, also, we know the number of rhombi that will be needed. Therefore,

[tex]33 \times 12 = 396\ in^2[/tex]

Hence, the total amount of paper that will be needed to cover the wall is 396 in².

Learn more about Rhombus:

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Answer:

3 rhombi are connected at a point, side by side. All sides are congruent.

Juan is making a model out of rhombi. Each rhombus will be connected to the one before it. Each rhombus will be 6 inches tall and 4 inches wide.

How much paper does he need for each rhombus?

✔ 12

square inches

If his wall is 11 feet long, how much paper does he use?

✔ 396

square inches

Step-by-step explanation:

egd

Answer:

2 mm

Step-by-step explanation:

Let x be the sides of the original square,

then the area of the original square is x^2

The sides of the new square is x + 6

The area is (x + 6)^2

Then (x + 6)^2 = 16*x^2

Take square root on both sides and get

x + 6 = 4x,

3x = 6

so x = 2 mm

Answer:it’s 10x + 12

Step-by-step explanation:

your welcome

The sum of ten times a number and 12 can be written as 10x + 12.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The expression "ten times a number" can be represented as 10x, where x is the number.

So, "the sum of ten times a number and 12" can be written as:

10x + 12

This expression represents a mathematical operation where 10 times the number is added to 12.

Thus,

The sum of ten times a number and 12 can be written as 10x + 12.

Learn more about expressions here:

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#SPJ2

Answer:

Yes, they're the same.

Step-by-step explanation:

-3-2c can be re-written as -1(2c+3) and -3 can be re-written as -1(3). So you can rewrite the fraction as -1(2c+3)/-1(3). The -1's go away and the new fraction is (2c+3)/3.

Answer:

104 m²

Step-by-step explanation:

From inspection of the diagram, we can see that the composite figure is made up of a triangle and a rectangle.

Triangle

If you turn the figure 90° clockwise, you will see that the base of the triangle = 8m and the height of the triangle = 6m.

Area of a triangle = 1/2 x base x height

⇒ area of the triangle = 1/2 x 8 x 6 = 24 m²

Rectangle

From inspection, the length of the rectangle = 10m and the width = 8m

Area of a rectangle = length x width

⇒ area of the rectangle = 10 x 8 = 80 m²

Composite figure area

Therefore the total area of the figure = area of triangle + area of rectangle

⇒ total area = 24 + 80 = 104 m²

Answer:

104 m^2

Step-by-step explanation:

See attached image.

Answer:

0

Step-by-step explanation:

Since displacement is the distance between the journey starting point and the final point if they both are the same the difference becomes zero and hence the displacement.

Displacement = final point - initial point

(both are same)

= same - same

= 0

Answer:

  B. 15 m^3

Step-by-step explanation:

The volume of a rectangular prism is the product ...

  V = lwh

For the given values of l, w, h, the volume is ...

  V = (5 m)(1 m)(3 m) = 15 m^3

Answer:

x = 24

PS = 45

Step-by-step explanation:

Perimeter of P Q R S is :

( 4x + 1 ) + ( 2x - 3 ) + ( 2x - 3 ) + 4 + ( 4x + 1 )

4x + 1 +  2x - 3  +  2x - 3 + 4 +  4x + 1

And in the question , given that the perimeter of this figure is 288.

Now let us find the value of x.

4x + 1 +  2x - 3  +  2x - 3 + 4 +  4x + 1  = 288

4x + 2x + 2x + 4x + 1 - 3 - 3 + 4  + 1 = 288

12x + 0 = 288

12x = 288

Divide both sides by 12

x =  24

And now let us find the value of PS

PS = 2x - 3

PS = 2× 24 - 3

PS = 48 - 3

PS = 45

Hope this helps you :-)

Answer:

9x +24y = -8

Step-by-step explanation:

2y + 3/4 x = -2/3 ( multiple by 4)

24y + 9 x = -8 (move x to the front)

9x + 24y = -8

Answer:

53 i think

Step-by-step explanation:

Answer:

x^2y−7xy+10xy^2

Step-by-step explanation:

(the first y isn't up but I tried)

anyways, hope this helped! :)

Answer:

[tex]4x^2y-7xy+10xy^2[/tex]

Step-by-step explanation:

We have [tex]\left(6x^2y-8xy+7xy^2\right)+\left(3xy^2-2x^2y+xy\right)[/tex] and need to add them together.

Though complicated at first, we can simplify by taking out the parenthesis and making this whole question into one equation.

[tex]\left6x^2y-8xy+7xy^2\right+\left3xy^2-2x^2y+xy\right[/tex]

Now combine like terms, meaning you can only add the terms that have the same ending, in math, you cannot add numbers that have different exponents or variables.

Therefore:

[tex]\left6x^2y-8xy+7xy^2\right+\left3xy^2-2x^2y+xy\right[/tex]

[tex]6x^2y-2x^2y-8xy+xy+7xy^2+3xy^2[/tex]

[tex]4x^2y-7xy+10xy^2[/tex]

The average daily balance after 20 days is; $1750

The initial balance after grace period is; $25,000

Afterwards, A payment of $5,000 each is made on the 10th and 20th day.

Hence, the total balance after 20 days is;

The average daily balance is therefore the quotient of $35,000 and 20 days

Read more on average;

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Answer:

it would be 23/2

Step-by-step explanation:

Answer:

11.5

Step-by-step explanation:

A rational number is one that does not repeat.

Answer:

see below

Step-by-step explanation:

1) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex].

[tex]3.4x*\frac{1}{10^{15} } +8.1*x*10^{-14}[/tex]

2) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex].

[tex]3.4x*\frac{1}{10^{15} } +8.1*x*\frac{1}{10^{14} }[/tex]

3) Use this rule: [tex]\frac{a}{b} *\frac{c}{d} =\frac{ac}{bd} .[/tex]

[tex]\frac{3.4x*1}{10^{15} }+8.1*x*\frac{1}{10^{14} }[/tex]

4) Simplify [tex]3.4x*1[/tex] to [tex](3.4)x[/tex].

[tex]\frac{3.4x}{10^{15} } +8.1*x*\frac{1}{10^{14} } }[/tex]

5) Use this rule: [tex]\frac{a}{b} *\frac{c}{d} =\frac{ac}{bd} .[/tex]

[tex]\frac{3.4x}{10^{15} } +\frac{8.1*x*1}{10^{14} }[/tex]

6) Simplify [tex]8.1*x*1[/tex] to [tex]8.1(x)[/tex].

[tex]\frac{3.4x}{10^{15} } *\frac{8.1*x}{10^{14} }[/tex]

Answer:

7v+70

1v x 7=7v

10 x 7=70

Step-by-step explanation:

Sorry if wrong!

Answer:

the answer is

7v + 70

Answer:  1/11

Step-by-step explanation:

The probability that the selected piece will be red velvet is equal to the amount of red velvet cake divided by the total amount of cake.

Therefore, it would be 3/(25+1+2+3+2)

= 3/33

= 1/11 when simplified

Answer:

Yes.

Step-by-step explanation:

Replace x with -2 and y with -3.

-3 = 2(-2) + 1

-3 = -4 + 1

Is -3 = -4 + 1?

Yes, so the answer is yes.

Answer:

I believe it's the 1st one.

HOPE IT HELPS! BE SAFE :3

Answer:

A

Step-by-step explanation: