Deduce the polynomial with the given roots: 5; 3 + 2i; 1 - 3i​

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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43 Beacuse mee smart Beacuse mee smart

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:

[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:

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 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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Step-by-step explanation:

Steps for Solving Linear Equation

3x+14y=x

Subtract x from both sides.

3x+14y−x=0

Combine 3x and −x to get 2x.

2x+14y=0

Subtract 14y from both sides. Anything subtracted from zero gives its negation.

2x=−14y

Divide both sides by 2.

2x/2=-14y/2

Dividing by 2 undoes the multiplication by 2.

x=-14y/2

​Divide −14y by 2.

x=−7y

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 number of cubes with an edge of 1/5 inches will be 2040.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

Given that the sides of the prism are,

2²/₅ = 2.40 inches

3¹/₅ = 3.20 inches

2 inches

The volume of the cube is,

2.40 × 3.20 = 8.16

8.16 × 2 = 16.32

The volume of a small cube is,

V = 0.2 x 0.2 x 0.2 = 0.008 cubic inches

Now we need to divide the volume by 2 since each cube is an inch as shown below.

16.32 ÷ 0.008 = 2040

The number of cubes will be 2040.

The complete question is given below.

A rectangular prism measures 2 & 2/5 inches by 3 & 1/5 inches by 2 inches. How many cubes with an edge length 1/5 inch fit in the prism? Show your reasoning.

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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 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: x=5

Step-by-step explanation:

5

x

+

10

=

35

Subtract

10

from both sides.

5

x

=

35

−

10

Simplify.

5

x

=

25

Divide both sides by

5

.

x

=

25

5

Simplify.

x

=

5

Answer:

X=5

Step-by-step explanation:

The classifications of the densities of these objects are given as follows:

The density of an object is calculated as the division of the object's mass by the object's volume, according to the equation presented as follows:

Density = mass/volume.

The standard unit of the mass of an object is in grams per cubic centimeters, that is, g/cm³.

Most of the known substances on earth also have known densities, and two examples are cooking oil and water, for which the densities are given as follows:

1 > 0.6, hence we have that:

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Answer:

1) y=-2/3x+5

Step-by-step explanation:

Now I know that I didn't actually do the math for this one. I did see though that it needs to have the point (3,3) on the graph. So then I went to desmos graphing calculator, and I put all of them on the graph. The only one with a (3,3) point was number 1. I put it in the image below so you could see. I know that the rest aren't on there, that's because I removed them because they were in the way.

I hope this helps!!!

Answer:

90 units²

Step-by-step explanation:

The scale factor of the lengths of the sides of a solid must be squared to to find the ratio of the areas and cubed to find the ratio of the volumes.

For example, if you are given two solids with a scale factor of the lengths of the sides of 2, meaning that the sides of the second solid are twice the length of the sides of the first solid, then the surface area of the second solid is 2² (= 4) times the surface area of the original solid, and the volume of the second solid is 2² (= 8) times the volume of the original solid.

Let's say you have a cube with edge of 1 cm. The volume is (1 cm)³ = 1 cm³.

The surface area is the sum of the areas of the 6 faces which are squares 1 cm by 1 cm. 6 × (1 cm)² = 6 × 1 cm² = 6 cm².

The original cube with edge of 1 cm has a volume of 1 cm³ and total surface  area of 6 cm².

Now double the size of the edge of the cube. The new cube has an edge of 2 cm. The volume is (2 cm)³ = 8 cm³. Each face of the cube is a square 2 cm by 2 cm. The total surface area of the new cube is 6 × (2 cm)² = 24 cm².

The new cube has volume 8 cm³ and total surface area 26 cm².

Compare the edges, surface areas and volumes of the two cubes:

                             Original Cube     Dilated Cube    Ratio new/dilated

Edge                              1 cm                    2 cm                    1:2

Surface area                 6 cm²                 24 cm²                 1:4

Volume                          1 cm³                  8 cm³                   1:8

Now here is your problem.

We start with the ratio of the volumes.

Original solid: 128 u³

Dilated solid: 54 u³

ratio of volumes: 54/128 = 27/64 = 3³/4³

The ratio of volumes is the cube of the ratio of the lengths.

ratio of lengths: 3/4

ratio of area: 3²/4² = 9/16

Surface area of original solid: 160 u² × 9/16 = 90 u²

Answer: 90 units²

Answer:

[tex]18x+27y-45z[/tex]

Step-by-step explanation:

[tex]9(2x+3y-5z)[/tex]

[tex]= 9(2x)+9(3y)+9(-5z)[/tex]

[tex]=18x+27y-45z[/tex]

I would appreciate it if you mark my answer as brainliest.

Answer:  18x + 27y -45z

Step-by-step explanation:

9(2x + 3y - 5z)

= 18x + 27y -45z

Answer:

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

You have completed 100% - 25% = 75% of the assignment and have a 72% score.

It gives:

With getting zero it doesn't add anything to overall score of 54% and you lose:

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)

The Rileys will pay a total of $37500 in $250000 cost for the closing costs and down payment on their mortgage.

Given that,

The Rileys are spending $250,000 on a house. They are making a down payment of 12% and paying 3% in closing expenses.

We have to fill the blanks.

We know that,

$250000 Rileys are spending on a house.

The down payment for 12% and closing cost for 3%

So,

$250000×(12+3)%

$250000×15%

$37500

Therefore, The Rileys will pay a total of $37500 in $250000 cost for the closing costs and down payment on their mortgage.

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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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From the given graphs the values of 'c' and 'd' are c = -0.84,

d = 0.84.

What is sinusoidal wave?

A mathematical curve defined in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.

Let the graphs of y = cos(x) and y = cos(x/2) are given.

From this graphs we have to find the value of c and d.

First from y = cos(x) to find the value of 'a'.

Consider, the point  [tex](a, \frac{1}{8})[/tex]

⇒

[tex]cos(a) = \frac{1}{8} \\a = cos^-^1(\frac{1}{8})\\ a = 82.82[/tex]

Now to find the value of 'c'.

Plug a = 82.82 in y = cos(x/2).

[tex]cos(\frac{82.82}{2}) = c \\c = -0.84[/tex]

Hence, the value of 'c' is 'c = -0.84'.

Now to find the value of 'd'.

Consider, the point [tex](b, \frac{1}{8})[/tex]

⇒

[tex]cosb = \frac{1}{8} \\b = cos^-^1(\frac{1}{8})\\b = 82.82[/tex]

Now, plug b = 82.82 in y = cos(x/2)

[tex]cos(\frac{82.82}{2}) = d\\ d = 0.84[/tex]

Hence, from the given graphs the values of 'c' and 'd' are c = -0.84,

d = 0.84.

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Answer:

corresponding

Step-by-step explanation:

Answer:

x1 =1.317

x2=-5.317

Step-by-step explanation:

Answer:

The circumference is 56.55

Answer: C≈56.55in

Step-by-step explanation

Using the formulas

C=2πr

d=2r

Solving forC

C=πd=π·18≈56.54867inC=2πr

d=2r

Solving forC

C=πd=π·18≈56.54867in

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

The number of chickens in the farm = 12 chickens

The number of cows in the farm = 32 cows

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of chickens in the farm be = x

Let the number of cows in the farm be = y

Now , the total number of animal heads in the farm = 43

So , the equation will be

x + y = 43   be equation (1)

Now ,

The total number of cow legs = 124

The number of legs for cows = 4

So , the equation will be

4y = 124

Divide by 4 on both sides of the equation , we get

y = 31   be equation (2)

Now , the value of y is 31 , substitute the value of y in equation (1) , we get

x + y = 43

x + 31 = 43

Subtracting 31 on both sides of the equation , we get

x = 12

And , the value of x is 12

Therefore , the number of chickens is 12 and number of cows is 32

Hence , The number of chickens in the farm = 12 chickens

The number of cows in the farm = 32 cows

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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:

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

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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From the calculations triangle DEF ≠ triangle PQR

The side lengths of each triangle are

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

Triangle DEF

D(-7,-3), E(- 4, - 1)

D(-7,-3), F(- 2, - 5)

E(- 4, - 1)), F(- 2, - 5)

Triangle PQR

P(2,- 2) Q(5, - 4)

P(2,- 2) R(0, - 5)

Q(5, - 4) R(0, - 5)

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