Find the area of the shape shown below.

The equation to determine the length and the width of the rug is

21 = W² - 4W.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

A quadrilateral is a rectangle.

A rectangle's opposing sides are equal and parallel to one another.

Each vertex of a rectangle has a 90° internal angle.

360° is the total of all interior angles.

The diagonals cut each other in half.

The diagonals are all the same length.

The Pythagorean theorem may be used to determine the length of the diagonals.

A rectangle is also referred to as a parallelogram since its sides are parallel.

While all parallelograms are rectangles, not all rectangles are parallelograms.

The length of the rug is l ft

Then the width of the rug will be l-4 ft

So the are will be l*(l-4) = [tex]l\x^{2} - 4l[/tex]

We know area is 21

so the equation is 21 = [tex]l\x^{2} - 4l[/tex]  (Option a)

And after solving the equation the lenght is7m and breadth is 3 m.

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the value of log2 log32 is 0.5899 and  the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.J

The logarithmic equation that has the same solution as x-4=2^3 is log2(x-4)=3.

Logarithm

The logarithm of a number can be calculated from the following relationship:

Thus, the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.

So, we have that the third expression

Therefore, this expression is the one corresponding to x-4=2^3.

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Answer:

20 i think i forgot but, hopefully u get it right

Step-by-step explanation:

Answer:

12

Step-by-step explanation: i think

Answer:

15% of 60 is equal to 9

Step-by-step explanation:

If this helps please mark as brainliest

Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.

Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k

y = a(x-h)^2 + k

Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get

7 = a(-2 - h)^2 + k

It passing through (1, 10), we can substitute the values of x and y in the equation and get

10 = a(1 - h)^2 + k

It passing through (2,27), we can substitute the values of x and y in the equation and get

27 = a(2 - h)^2 + k

Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k

Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.

Step-by-step explanation:

The total amount for Elizabeth's purchase after 10 percent discount on her total bill is 33 dollars and 84 cents which is equivalent to 34 dollars.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Elizabeth bought the grocery for a total of 37 dollars and 60 cents.

She has a coupon of 10% discount.

Which means, she can get 10% discount on her total bill.

The amount of her total bill is $37.60.

So, calculate using percentage, the value of 10% of $37.60.

=(10 × 37.60/100)

= 376/100

= 3.76

So, Elizabeth would get a discount of $3.76 on her total bill -

= 37.60 - 3.76

= 33.84

Therefore, after the discount Elizabeth's total bill is $33.84 ≈ $34.

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Answer:

HAH DUM

Step-by-step explanation:

Step-by-step explanation:

To prove that two triangles are congruent by SAS, two sides and the INCLUDED angle in the first triangle must be congruent to the corresponding two sides and INCLUDED angle in the second one.

Answer:

x = 81

Step-by-step explanation:

180 (62 + 37) = x

81 = x

Hope this helps!

Answer:

81

Step-by-step explanation:

x + 37 + 62 = 180

x + 99 = 180

x = 180 - 99

x = 81

The scale model door of 2.4 inches is 9.3 ft tall in the actual building.

By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape.

By multiplying the numerator of one fraction by the denominator of another and the first term's denominator by the numerator of another, we can do cross multiplication.

Given that:

16 inches = 62 ft

2.4 inches = x ft

To calculate the actual value cross multiply the values:

[tex]x= \frac{(62)(2.4)}{16} \\\\x= 9.3 ft[/tex]

Hence, the actual door is 9.3 ft tall.

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Answer:  

a = 1.5  

VW = 9 ft  

Step-by-step explanation:  

Since the tangent lines connect both circles, we know that the line VU and VX are congruent (equal). Thus, we can set them equal to each other and solve for a:

a + 4 = a² + 0.25                            Set equal  

a² - a = 3.75                                    Isolate a values  

a² - a + 0.25 = 3.75 + 0.25            Complete the square  

(a + 0.5)² = 4                                  Factor  

a + 0.5 = 2                                     Simplify  

a = 1.5

Now we need to calculate VW, but thats easy because its equal to TV, and since we know a, we can just plug it in:

((1.5) + 7.5) ft  

9 ft

Respuesta:

4 1/5 bombones

3 1/3 bombones

Explicación paso a paso:

Distribuir 21 bombones entre 5 niños;

21/5 = 4 resto 1

Por lo tanto, se le da 4 chocolates a cada niño y el 1 chocolate restante se divide en 5 partes iguales y se le da 1/5 a cada niño. Por lo tanto, cada niño recibe 4 1/5 chocolates.

Distribuir 10 bombones entre 3 niños;

10/3 = 3 resto 1

Por lo tanto, se le da 3 chocolates a cada niño y el 1 chocolate restante se divide en 3 partes iguales y se le da 1/3 a cada niño. Por lo tanto, cada niño recibe 3 1/3 chocolates.

Answer:

12 miles

Step-by-step explanation:

Kyle's speed = 2 mph

Steve's speed = 2 mph

Time traveled = 3 hours

Distance apart after 3 hours

Distance moved by Kyle + Distance moved by Steve

Distance = Speed * time

Distance moved by Kyle = 2 * 3 = 6 miles

Distance moved by Steve = 2 * 3 = 6 miles

Total distance apart = 6 + 6 = 12 miles

The object will hit the ground after 5.01 seconds.

When an object is propelled upward from ground level with an initial velocity of 80.1 feet per second then its height h in feet t seconds later is giving by the equation,

h= -16t^2+ (80.1)t

When the object hit the ground, the height of the object h would be zero.

To find: time (t) when h = 0

Substitute h = 0 in given equation.

h = -16t^2+ (80.1)t

0 = -16t^2+ (80.1)t

16t^2 -  (80.1)t = 0

t (16t - 80.1) = 0

t = 0  or  16t - 80.1 = 0

t = 0   OR   t = (80.1)/16

t = 0 OR t = 5.01

Therefore, it will hit the ground after 5.01 seconds.

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Answer: The tree is 27 feet tall.

Step-by-step explanation:

Here's what we know:

6/10 = x/45 (a 6 foot object creating a 10 shadow is equivalent to something else making a 45 shadow)

We need to isolate x. Multiply both sides by 45:

6*45/10 = x

We can factor out a 2:

3*45/5 = x

We can also factor out a 5:

3*9/1 = x

27 = x

The tree is 27 feet tall.

Answer:

  Manuel can make 5 batches of muffins using Recipe 1

Step-by-step explanation:

You want to know the value of b in the equation 2b = 10, where b is the number of batches of muffins Manuel can make using recipe 1.

Divide both sides of the given equation by 2 so solve for the value of b.

  (2b)/2 = (10)/2

  b = 5

Manuel can make 5 batches of muffins using Recipe 1.

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Answer:

x = 24

. So, first number = 7 * 24 = 168. and second number = 4 * 24 = 96. Therefore the numbers are 168 and 96.

Answer:

42 and 24

Step-by-step explanation:

The numbers in ratio 7 : 4 = 7x : 4x ( x is a multiplier ) , then

7x - 4x = 18 ( difference of 2 numbers is 18 )

3x = 18 ( divide both sides by 3 )

x = 6

Then

7x = 7 × 6 = 42

4x = 4 × 6 = 24

The numbers are 42 and 24

Answer:

x^-8.x^3

x^-8+3

x^-5

1/x^5

Step-by-step explanation:

If Ojemba is sitting on a sled on the side of a hill inclined at 60° and  weight of Ojemba and sled is 160 pounds , then magnitude of force needed for Mandisa to keep sled from sliding down the hill is 355.59 N   .

the inclination angle of the the side of the hill is = 60° ;

the compound mass of Ojemba and Sled is = 160 pounds ,

On conversion we get the mass in Kg is = 72.57 Kg .

the acceleration due to gravity is , [tex]g = 9.8 m/s^{2}[/tex] ;

The force required for Mandisa to keep sled from sliding down the hill can be calculated by the formula ;

[tex]F = mgSin\theta[/tex] , Substituting the values ,

we get ;

[tex]F = 72.57\times 9.8\times Sin(30\textdegree)[/tex]

[tex]F = 72.57\times 9.8\times \frac{1}{2}[/tex] ;

So , [tex]F = 355.59 N[/tex] .

The required magnitude of the force is 355.59 N .

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The value of x using Pythagorean theorem is 14.05 units

An equation shows how two or more numbers and variables are related to each other.

Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:

hypotenuse² = adjacent² + opposite²

In the diagram, using Pythagoras theorem:

22² = (x + 1)² + (x + 2)²

484 = x² + 2x + 1 + (x² + 4x + 4)

2x² + 6x + 5 = 484

2x² + 6x - 479 = 0

x = 14.05

The value of x is 14.05 units

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Answer:

Step-by-step explanation:

[tex]y=x^2+2x-2\\\\y=x^2+2x+1-1-2\\\\\bold{y=(x+1)^2-3}[/tex]

a = 1 > 0  ← it means the parabla opens up, so, the vertex is minimum

The vertex form is  y = a(x - h)² + k, where (h, k) is the vertex

So, from  y = (x + 1)² - 3   the vertex is:  (-1, -3)

Answer:

2 units up

Step-by-step explanation:

You have no stretch because no number in front and nothing is done to x do no movement to the sides

Answer:

27

Step-by-step explanation:

Area of Triangle x 2 = 3 * 3

The reason I did not divide it by 2 is because of how the other triangle is bound to have the same area. Just leave it as it is because later you're going to reach the same answer.

3 * 3 = 9

Rectangle Area = 6 * 3 = 18

18 + 9 = 27

When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Solving the given trinomial 3x² - x - 10.

=>3x² - 6x+5x - 10

=>3x(x-2)+5(x-2)

=>(3x+5)(x-2)

The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.

Thus, When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Complete question: 3x² - x - 10

When this trinomial is factored completely, one of its factors is

A) x + 2

B) x - 5

C) 3x + 5

D) 3x - 2

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Answer:

25

Step-by-step explanation:

they are alternative exterior angles meaning they are equal.so you can solve by doing

7x-40=5x+10

isolate the terms by adding like terms. ( add 40 from the left side of the equation to the right.)

so it would look like this.

7x=5x+10+40. (the 40 was negative on the left side so you have to do the inverse to move it) do the same with the 5x.

now you have

2x=50. divide 50 by 2 to get your final answer .

Answer:

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

D)

hope this helped

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

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Answer:

50 inches

Step-by-step explanation:

Hi there!

[tex]P=2l+2w[/tex] where l is the length of the rectangle and w is the width of the rectangle

Plug in the length (15 inches) and width (10 inches)

[tex]P=2(15)+2(10)\\P=30+20\\P=50[/tex]

Therefore, the perimeter of the frame is 50 inches.

I hope this helps!