Lillian has a rectangular garden with an area of 10x2 +33x – 7 square feet. Find the expressions that would represent the length and width of the garden. Make sure you show all your work for full credit.
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The cube has a side that is 6 cm long.

Volume of cuboid:-

Height × width × depth

⇒9 cm × 6 cm × 4 cm

⇒ 216 cm³

when the cuboid is melted and a cube is made using just metal.

So, the cube's volume is 216 cm³.

side³ = volume of cube

⇒ Side³ = 216

⇒ Side = ∛216

⇒ Side = ∛6×6×6

⇒Side = 6 cm

As a result, the cube's side measures 6 cm.

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Answer:

[tex]\dfrac{17}{8}[/tex]

Step-by-step explanation:

Given statement:

[tex]\implies \dfrac{\frac{8}{5}}{\frac{8}{10}}+\left(\dfrac{8}{14} \times \dfrac{7}{12} \times \dfrac{3}{8}\right)[/tex]

To divide two fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:

[tex]\implies \left(\dfrac{8}{5} \times \dfrac{10}{8}\right)+\left(\dfrac{8}{14} \times \dfrac{7}{12} \times \dfrac{3}{8}\right)[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{ab}{cd}:[/tex]

[tex]\implies \left(\dfrac{8 \times 10}{5\times 8}\right)+\left(\dfrac{8 \times 7 \times 3}{14 \times 12 \times 8}\right)[/tex]

Carry out the multiplications:

[tex]\implies \dfrac{80}{40}+\dfrac{168}{1344}[/tex]

Simplify the fractions by dividing the numerator and denominator by the GCF:

[tex]\implies \dfrac{80 \div 40}{40\div 40}+\dfrac{168 \div 168}{1344 \div 168}[/tex]

[tex]\implies \dfrac{2}{1}+\dfrac{1}{8}[/tex]

Make the denominators of both fractions the same:

[tex]\implies \dfrac{2 \times 8}{1\times 8}+\dfrac{1}{8}[/tex]

[tex]\implies \dfrac{16}{8}+\dfrac{1}{8}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{16+1}{8}[/tex]

[tex]\implies \dfrac{17}{8}[/tex]

Answer:

[tex] {x + 2x}^{2} [/tex]

The length of the given rectangle is 7 units.

The area of the rectangle is the product of its length and width.

I.e., A = l × w sq. units

It is given that, the width of a rectangle is the length minus 6 units.

I.e., W = L - 6 units

Then, the area of the rectangle is

A = L × (L - 6)

But we have given that, the area of the rectangle is 7 sq. units.

So, we can write

7 = L² - 6L

⇒ L² - 6L - 7 = 0

⇒ L² - 7L + L - 7 = 0

⇒ L(L - 7) + 1(L - 7) = 0

⇒ (L + 1)(L - 7) = 0

∴ L = -1 or L = 7

The length should not be a negative value. So, the length of the given rectangle is 7 units.

Then, the width of the rectangle is

W = L - 6 = 7 - 6 = 1 unit.

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The perimeter of the rhombus is 34.40 units. The length of diagonal is 7.21 units. The perimeter of the rectangle is 44.98 units. The perimeter of the square is 42.44 units

1.  Given: a rhombus with diagonals 10 and 14

Half-length of the diagonals are 10/2 = 5 and 14/2 =7

Length of side = √(5²+7²) = √74 = 8.6 units

Perimeter, P = 4 × length of side

P = 4 × 8.60 = 34.40 units

2. Given: m<ADC = 60⁰

Missing...

3. Given: a rectangle with side length of 6 and 4. The length of one of its diagonal can be found using Pythagoras' theorem:

length of diagonal = √(4²+6²) = √52 = 7.21 units

4. Given: a rectangle with a diagonal length of 16 and side length of 10

other side length = √(16²-10²) = √156 = 12.49 units

Perimeter, P = 2(L+W)

P = 2(10+12.49) = 44.98 units

5. Given: a square with diagonal length of 15

Let represent the side length of the square

x² + x² = 15²

2x² = 15²

x² = 225/2

x² = 112.5

x = √112.5 = 10.61 units

Perimeter, P = 4 × side length

P = 4×10.61 = 42.44 units

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Answer:

y + 4 = 5(x + 8)

Step-by-step explanation:

Slope: 5 => m = 5

Point: (-8, -4) => x = -8 and y = -4

y - y1 = m(x - x1)

y - (-4) = 5(x - (-8))

y + 4 = 5(x +8)

Answer: 261 cm²

Step-by-step explanation: 87 x 3 = 261

Answer:

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

The area is the function of two dimensions.

The scale factor is 3. It means each dimension is 3 times greater.

Therefore the surface area is 3*3 = 9 times greater:

Answer in image

Step-by-step explanation:

Simplify both sides of the inequality.

Add 60 to both sides.

Divide both sides by 14.

r = 67/14 or 4.78571...

Answer:

corresponding

Step-by-step explanation:

Answer:

a worker can plant 2/5 acres in 7/8 days

or a worker can plant 2/5 acres in 7/8 hrs=21hrs

in one hrs he can plant 2/5×21 acres

in 24 hrs he can plant 2/105 ×24 acres

Therefore in one day he can plant 16/35 Acres

After the dilation, the new volume of the cube is 125 times the original volume of the cube.

Remember that for a cube of sidelength S, the volume is written as:

V = S^3

If we apply a dilation of scale factor 5 to the cube, then the new sidelength of the cube is 5*S

Replacing that in the volume formula we will get the volume of the dilated cube, it is:

V' = (5*S)^3

V' = 5^3*S^3

V' = 125*S^3

Where S^3 is the original volume, so we can write:

V' = 125*V

So the new volume is 125 times the original volume.

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Answer:

Regular pizzas are $8 and Deluxe pizzas are $20

Step-by-step explanation:

if you go to Desmos graphing calculator you can use it to solve this problem

We are going to make to line graphs to represent each situation.

We'll let x equal the price for regular pizzas and y be equal to the price for deluxe pizzas.

For Ruth:

4x + 4x = 112 <--- type this in the first line on the graphing calculator then hit enter to make another line

For Gabrielle:

4x + 1y = 52<---- type this in the second line you made

The two lines should intercept at the point (8,20) this interception represents the price of the pizzas. The x value (8) is the price of your regular pizzas and the y value (20) is the price for your deluxe pizzas

The graph of your equation: [See in attachment]

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

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Answer:

biology = 255 ; sociology = 192

Step-by-step explanation:

b + s = 447

s = b - 63

b + b - 63 = 447

2b = 447 + 63

2b = 510

2/2 b = 510/2

b = 255

s = 255 - 63

s = 192

Answer: 192 sociology textbooks,  255 biology textbooks

Step-by-step explanation:

Let the number of biology be x, and the number of sociology be x

The number of the sociology textbook is x+63

So the equation is

x + x + 63 = 447

2x = 384

x= 192 sociology textbooks

To find the number of biology textbooks, just take 447- 192 = 255 biology textbooks

The value of [x] in the triangle is 36.25°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a right angled triangle.

We can write -

tan(x°) = (22/30)

x° = tan⁻¹(22/30)

x° = 36.25°

Therefore, the value of [x] in the triangle is 36.25°.

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Answer:

First, you need to add 15x to both sides in order to get y by itself. Then, you need to divide all the numbers by 12. Your answer should be Y=1.25x+7. I hope this helps!

Step-by-step explanation:

The complete table of function is,

   x        h(x)

  -4        -11

   0         -3

   2          1

   4          5

   5          7

What is function?

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.

Let, the function h is defined by the rule,

h(x) = 2x - 3

We have to complete the function table.

x = -4  ⇒  h(-4) = 2(-4) - 3 = -8 - 3 = -11

x = 0  ⇒  h(0) = 2(0) - 3 = -3

x = 2  ⇒  h(2) = 2(2) - 3 = 4 - 3 = 1

x = 4  ⇒  h(4) = 2(4) - 3 = 8 - 3 = 5

x = 5  ⇒  h(5) = 2(5) - 3 = 10 - 3 = 7

Hence, the table becomes,

   x        h(x)

  -4        -11

   0         -3

   2          1

   4          5

   5          7

This is the complete table of function.

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a) The area of Helen's circular garden is 314 m².

b) The estimation for the number of boxes of grass seed Helen needs, is 5 boxes.

c) B. The estimation we did in (b) is an underestimation.

The area of a circle is calculated by the formula,

A = πr² sq. units; r - radius

When we have the diameter, we can find the radius by

r = d/2 units

Given that Helen has a garden in the shape of a circle of diameter 20 m.

She is going to cover the garden with grass seed to make a lawn.

Grass seed is sold in boxes. Each box of grass seed will cover 58 m² of the garden.

a) The area of the circular garden is

A =  πr² = 3.14 × (d/2)²

⇒ A = 3.14 × (20/2)²

⇒ A = 3.14 × 100

∴ A = 314 m²

Thus, the area of Helen's garden is 314 m².

b) The number of boxes of grass seed to cover the area of 314 m² is

= area of the garden/area covered by each box of seeds

= 314 m²/58 m²

= 5.4179

So, on an estimation, there are 5 boxes of grass seed that Helen needs.

c) Here, in the above estimation, we rounded the decimal number 5.4179 to 5. Since the number is rounded to the nearest value (smallest value), the estimation is an underestimate.

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Answer: 3

Step-by-step explanation:  (x-2)(2x+1)=2x^2-3x-2 = 3

please put brainiest, please.

Answer:

C

Step-by-step explanation:

-2x + 10  Means that the line crosses the y axis at 10.  The slope is -2 that means that as the y changes by -2, the x changes by 1.  

The second equations means that we have a horizontal line with no slope that goes through -28 1/2

5(x2 + 4x + 4) = 7 + 20 quadratic equation by completing the square The correct statement  is 5(x2 + 4x + 4) = 7 + 20.

A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape.

Quadratic equations are the degree two, one-variable polynomial equations of the form f(x) = ax2 + bx + c = 0, where a, b, c, and an are all divisible by R and an is equal to zero. It is the quadratic equation's general form, with 'a' standing for the leading coefficient and 'c' standing for the absolute term of f. (x).

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The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.

The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines.

Now, we are given the exponential function as;  ƒ(x) = e^(2x + 1)

Now, as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, we can see that the exponent we are given increases as seen in the exponent attached to it.

Thus, we can conclude that The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.

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The expression 2 1/2 (x - 8) = 4 1/2 is solved to get the value of x to be

The expression, 2 1/2 (x - 8) = 4 1/2 is solved be converting to decimal

2 1/2 (x - 8) = 4 1/2

2.5 (x - 8) = 4.5

expanding to remove the parenthesis

2.5x - 20 = 4.5

collecting like terms, being mindful of change of negative to positive when crossing the equality sign

2.5x = 4.5 + 20

applying addition property

2.5x = 24.5

dividing through by coefficient of  x which is 2.5

x = 24.5 / 2.5

x = 9.8

x = 9 4/5 as a mixed number

Therefore the value of x = 9 4/5

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Answer:

68266==874624./4

Step-by-step explanation:

77353877473=287365-2874662kkh=2875

Answer:

Total APROBADOS = 41 estudiantes

Step-by-step explanation:

Total personas que tomaron el examen = 100 % = 48

Porcentaje personas reprobadas = 15 %

Luego,

Total personas reprobadas = (15%)*48

Total personas reprobadas =  (0.15)*48 = 7.2 aprox 7

Luego restando del total de estudiantes, los reprobados, tendrás los APROBADOS:

Total APROBADOS = 48 - total reprobados

Total APROBADOS = 48 - 7

Total APROBADOS = 41

Answer:

B. False

Step-by-step explanation:

5x² - 6x + 4 | 5 × 4 = 20

Can't factor it normally

           √b² - 4ac

 -b  ±   ---------------

                2a

           √(-6)² - 4(5)(4)

 -(-6)  ±   ---------------

                   2(5)

           √36 - 80

 6  ±   ---------------

                 10

    6 ± √-44

  ---------------

         10

    6 ± √-4 × 11

  ---------------

         10

    6 ± 2i√11

  ---------------

         10

The answer is actually

    3 ± i√11

  ---------------

         5

I hope this helps!

Answer:

  B.  False

Step-by-step explanation:

You want to know if (x -2) is a factor of 5x² -6x +4.

There are a couple of ways you can determine whether (x -2) is a factor. One is to look at the polynomial value at x=2:

  5x² -6x +4 = (5x -6)x +4 = (5(2) -6)(2) +4 = 4(2) +4 = 12

The value is not 0, so (x -2) is not a factor.

Another way to tell is to determine what the other factor would be.

The product of roots is the ratio c/a = 4/5 in the polynomial. If 2 is a root, then (4/5)/2 = 2/5 is the other root. That would mean the factorization of the polynomial is ...

  (5x -2)(x -2) = 5x² -12x +4 . . . . . . not the same polynomial

The polynomial 5x² -6x +4 does not have a factor (x -2).

The graph of the polynomial has no x-intercepts, so (x -2) cannot be a factor.

23.4 is  8.125 percentage of 288.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.

1. Since 288 is the output value of the task, we assume that it is 100%.

2. We make the assumption that the value we are looking for is x.

3. If 100% = 288 then we can express that as 100% = 288.

4. Since we already know that the output result of x% equals 23.4, we can write it down as x%=23.4.

5. We now have two straightforward equations:

1) 100%=288

2) x%=23.4 where both of their right sides and left sides have the same units, allowing us to write something like this: 100%/x%=288/23.4

6. All that is left for us to do is solve the straightforward equation, and we will have our answer.

7. Calculate 23.4 as a percentage of 288.

100%/x%=288/23.4

We multiply both sides of the equation by x 100=12.307692307692 to get *x=(288/23.4)*x.

*x - we get x 100/12.307692307692=x 8.125=x by dividing both sides of the equation by (12.307692307692) to get x=8.125.

23.4 is  8.125 percentage of 288.

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