The Jones family is having lasagna for dinner. Before dinner, 15/15 of the lasagna was in the pan. The family ate 10/15 of the lasagna.

What fraction of the lasagna was left in the pan after dinner? (PROVIDE SCREENSHOT TO SHOW HOW TO DO IT)

The numerical values of a in the points Q(-1, a) and P(3, -2) with a distance of 4√5 are  6 and -10.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point Q( -1, a )

Point P( 3, -2 )

To find the numerical value of a, plug the given coordinates into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

Square both sides

( 4√5 )² = ( 3 - (-1) )² + ( -2 - a )²

( 4√5 )² = ( 3 + 1 )² + ( -2 - a )²

( 4√5 )² = ( 4 )² + ( -2 - a )²

80 = 16 + ( -2 - a )²

80 - 16 = ( -2 - a )²

64 = ( -2 - a )²

( -2 - a )² = 64

Expand the parenthesis

( -2 - a )( -2 - a ) = 64

a² + 4a + 4 = 64

a² + 4a + 4 - 64 = 0

a² + 4a - 60 = 0

solve for a

( a - 6 )( a + 10 ) = 0

a - 6 = 0, a + 10 = 0

a = 6, a = -10

Therefore, the values of a are 6 and -10.

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Answer:

15

Step-by-step explanation:

16c+4(-5)=220

16c-20=220

16c=240

C=15

The most appropriate choice for matrix and multiplicative inverse of matrix will be given by

B is the multiplicative inverse of A

What is a matrix and multiplicative inverse of matrix?

Matrix is a rectangular representation of numbers or symbols arranged in the form of rows and column. Matrix is a very important tool in mathematics.

To learn about multiplicative inverse, it is important to know about identity matrix

[tex]\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}[/tex] is a 2 x 2 identity matrix denoted by I.

Let A and B be two matrices

A is said to be a multiplicative inverse of B if AB = BA = I

Here,

A=   [tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex] B = [tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]

AB =

[tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]

[tex]\begin{bmatrix} 2\times 1 + 1 \times -1& 2 \times -1 + 1\times 2\\1 \times 1+1\times-1 & 1 \times -1 + 1 \times 2\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

BA =

[tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex]

[tex]\begin{bmatrix} 1\times 2 + -1 \times 1& 1 \times 1 + -1\times 1\\-1 \times 2+2\times 1 & -1 \times 1+ 2 \times 1\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

AB = BA = [tex]\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

So B is the multiplicative inverse of A

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Answer: x^2-9x+20

Step-by-step explanation: you have to distribute (x-5) (x-4)

which would be x^2-4x -5x +20 when you simplify that you get x^2-9x+20

Each person will get a 5/24 portion of the available cake with Paige

Cake available with Paige = 5/6

Number of people = 4 people

Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Fraction of cake each person gets:

Cake available with Paige/Number of people with whom the cake is to share equally

= (5/6)/(4)

= (5/6)*(1/4)

= 5/24

The fraction of cake each person will get is 5/24

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The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7

Given,

The binomials; (2x² + 4x - 7) (3x - 1)

We can use FOIL method to solve this;

FOIL method;

Binomials are multiplied using the FOIL Method. An acronym is FOIL FOIL. First, Outside, Inside, and Last are the letters that stand for the order of multiplying terms. To get your answer, multiply the first term, then the outside term, then the inside term, then the last term, and then combine terms that are similar.

Here,

(2x² + 4x - 7) (3x - 1)

= (3x × 2x²) + (3x × 4x) - (3x × 7) - 2x² + 4x - 7

= 6x³ + 12x² - 21x - 2x² + 4x - 7

= 6x³ + 10x² - 17x - 7

That is,

The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7

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Answer:

2000 pounds is 1 ton

6 tons is 12,000

7 tons is 14,000

16,000 pounds is 8 tons

a)I WILL USE THE THEOREM OF PYTHAGORAS IN TRIANGLE BCD

[tex] {y}^{2} = {(5.3)}^{2} - {(4.4)}^{2} \\ {y}^{2} = 28.9 - 19.36 \\ {y}^{2} = 9.54 \\ y = \sqrt{9.54} \\ y = 3.09[/tex]

y=3.90cm

b)

[tex] \sin(x) = \frac{cb}{ac} \\ \sin(x) = \frac{5.3}{8.2} \\ x = sin^{ - 1} ( \frac{5.3}{8.2} ) \\ x =40.27[/tex]

x=40,27 cm

GOODLUCK.

Answer

The polynomial is

P(x) = 2x⁴ - 5x³ + 3x²

Explanation

We are told to write a polynomial of degree 4 with zeros (roots)

x = 1

x = (3/2) = 1.5

x = 0

x = 0 (multiplicity of 2 means it appears twice)

So, we can piece together the polynomial

P(x) = (x - 1) (x - 1.5) (x) (x)

We can write this as

P(x) = x² (x - 1) (x - 1.5)

= (x³ - x²) (x - 1.5)

We can multiply through by 2 to turn the 1.5 into a whole number

P(x) = (x³ - x²) (2x - 3)

= x³ (2x - 3) - x² (2x - 3)

= 2x⁴ - 3³ - 2³ + 3x²

= 2x⁴ - 5x³ + 3x²

Hope this Helps!!!

Answer:

QPR SAS

Step-by-step explanation:

As you can see. Hope it can help

The new length of the building will be 110 feet.

Volume of Cuboid:

                              Volume of cuboid is

                        V =  length x breadth x height cubic unit

Given,

The building was going to be 100 feet long, 75 feet deep, and 30 feet high.

Therefore, the volume will be:

               = 75 × 100 × 30 ft³

               = 225000 ft³

Now owner decided increase the volume of the building by 10% without changing the dimensions of the depth and the height.

There was an increase by 10%,

New volume will be,

V' = 225000 + (10% × 225000)

  = 247500 ft³

Therefore, the new length will be:

as,

        Volume =  length x breadth x height

        length  =  Volume/ (breadth x height)

New length will be

                      = 247500/(30 × 75)

= 110 feet

Thus the new length of the building will be 110 feet.

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The union of two sets contains all the elements contained in either set (or both sets). The intersection of two sets contains only the elements that are in both sets

Therefore the answer is B.

7/3 in notation one can be written as 7 : 3 and 7/3 in notation two can be written as 0.7 and 0.3.

The ratio is a comparison between two similar quantities in the simplest fraction form. We can write ratios in fractions and in decimals also.

We know we can write a : b as a/b in fraction form and a/(a+b) and b/(a+b) in decimal form.

∴ 7/3 in decimal form can be written as 7 : 3 and 7/3 can also be written as 7/(7+3) = 7/10 = 0.7 and 3/(7+3) = 3/10 = 0.3.

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Step-by-step explanation:

(f○g)(x) means f(g(x))

(g○f)(x) means g(f(x))

f(g(x)) means to use the expression of g(x) as input to f(x). so, we replace all simple x in f(x) by g(x) = x².

f(g(x)) = x²/(x² + 2)

using the same principle we get for

g(f(x)) = (x/(x + 2))² = x²/(x + 2)²

now we need to solve

x²/(x² + 2) = x²/(x + 2)²

let's multiply both sides with both denominators :

x²(x + 2)² = x²(x² + 2)

x²(x² + 4x + 4) = x²(x² + 2)

so, one solution is clear : x = 0.

because then we have 0 = 0.

for x <> 0 we can divide both sides by x² and get

x² + 4x + 4 = x² + 2

4x + 4 = 2

4x = -2

x = -2/4 = -1/2

both expressions are equal for x = 0 and x = -1/2

Answer:

119º and 61º

Step-by-step explanation:

2x-15 and 3x+5 are supplementary because the angles corresponding to 2x-15 is supplementary with 3x+5

2x-15+3x+5=180

5x-10=180

5x=190

x=38

fill in x

2(38)-15

=76-15

=61

angle is 61

fill in x for angle 2

3(38)+5

=114+5

=119

angle 2 is 119

Answer: x = 22

Step-by-step explanation:

       We will use the exterior angle theorem to solve. First, we will write an equation, then we will solve by combing like terms are using inverse operations.

(6x - 7) = (2x) + (103 - x)

6x - 7 = 2x + 103 - x

6x - 7 = x + 103

5x = 110

x = 22

Answer:

  (a)  y < 3(x +2)² +2

Step-by-step explanation:

You want to know the inequality representing the region less than the quadratic with vertex (-2, 2) and containing the point (-4, 14).

The vertex form equation for a quadratic with vertex (h, k) and some scale factor 'a' is ...

  y = a(x -h)² +k

For the given vertex (-2, 2), the boundary line equation is ...

  y = a(x -(-2))² +2 = a(x +2)² +2

The value of 'a' is positive when the curve opens upward.

Here, the point (-4, 14) has a y-value greater than that of the vertex, so we know the curve opens upward (a > 0).

The only reasonable answer choice is ...

  y < 3(x +2)² +2

Using a linear function, it is found that her taxi ride was of 5 miles.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

For the cost function, we have that:

Thus the cost for a ride of x miles is of:

C(x) = 3.75x + 1.10.

Her total fee was of $19.85, hence the mileage is found as follows:

19.85 = 3.75x + 1.10

x = (19.85 - 1.10)/3.75

x = 5 miles.

Which was the length of her taxi ride.

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Answer:

y-21 = 4(x+9)

For the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.

As given in the question,

On a tour of a gold mine,

Ounce of gold contained by nuggets found in the mine = 0.82 ounce

Worth of gold per ounce = $1323.80 per ounce

Worth of nuggets containing 0.82 ounce of gold

Worth of 1 ounce of gold = $1323.80

⇒ Worth of nuggets containing 0.82 ounce of gold =$( 1323.80 ×0.82 )

                                                                                      = $1085.516

Therefore, for the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.

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89 squares will be present.

Given that the rectangle has the following dimensions: length = 96 cm, breadth = 84 cm, and

its total area is 8064 square centimeters, we may deduce that the maximum square area

[tex]\sqrt[2]{8064}[/tex]

that can be removed from the rectangle with its total area of 8064 square centimeters is equal to 89.8 square centimeters.

In order to determine the total number of squares, divide 8064 by 89.8 to arrive at 89.

Taking an integer's square root is the opposite of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root value is obtained by finding a number that, when squared, produces the original value of the number.

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Answer:

x=65

Step-by-step explanation:

47+68+x=180

x=65

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Answer: 65 = x

Step-by-step explanation:

1) First find the mini triangles, left and right angles

We will be calling the left one A and the right one B.

2) Next use triangle sum to find B.

62 + 50 + b = 180

b=68

3) Use triangle sum again to find A.

53 + 80 + a = 180

a = 47

4) Use triangle sum to find the top mini angle.

47 + 68 + c = 180

c = 65

5) Since x is in the vertical angle of c, they are equal

c = x

65 = x

If the university invest in a one year CD at 5.12% interest compounded continuously, the interest it will earn is determined by calculating as: Interest = Future value – Present value which would be $2.54 million

Continuously compounded interest means that a principal amount is constantly earning interest with infinite compounding periods for a certain time period. There are no increment compounding periods as with monthly or annually compounding.

The continuously compounding formula:

FV = PV* e^rt

Where FV is the future amount, PV is the initial amount, e is a mathematical constant (2.7183), r is the rate and t is the time period.

Hence,

FV = 49* 2.7183^(0.0512*1) =51.57

Interest earned= 51.57-49=2.54

Hence, the university will earn an interest of $2.54 million.

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Answer:

h = 6.36619772 cm

Step-by-step explanation:

h = (3 * v) / (πr2)

Answer:

h = 20 cm

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( where r is the radius )

given r = 9 and V = 540π , then

[tex]\frac{1}{3}[/tex] π × 9² × h = 540π

[tex]\frac{1}{3}[/tex] × π × 81h = 540π

27πh = 540π ( divide both sides by 27π )

h = [tex]\frac{540\pi }{27\pi }[/tex] = 20 cm

The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.

Given,

The equation; [tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]

We have to solve this equation to get the value of x.

That is,

[tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]

Square both sides to remove square root.

[tex]\sqrt{3x-4} ^{2} = (2\sqrt{x-5} )^{2}[/tex]

We get,

3x - 4 = 4 (x - 5)

That is,

3x - 4 = 4x - 20

Here,

20 - 4 = 4x - 3x

Then,

x = 16

That is,

The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.

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area of triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is

(x1 (y2 - y3 ) + x2 ( y3 - y1 )+ x3 ( y1 - y2))/2

hence, substituting the points (x1, y1)= (-2, 1);

( x2, y2)= (0,3) ; and (x3, y3)= (4,-4) in the area formula ,we get

area of triangle =

( -2(3-(-4)) + 0( -4 - 1) + 4(1-3))/2

(-14+0-8)\2

22\2

11 sq unit

Answer:

B and c

Step-by-step explanation:

182/7=26

168/6=28