A cake has 77 slices. Harry ate 48 slices; Jack ate 17 slices; Dave ate 3 & Mary ate 6 slices. What fraction of the cake is remaining?

Both the planes of the given equations,

2x+3y-z=12 (1)

2x-4y+z=8 (2)

They have been drawn in a three-dimensional plane, and the images are attached below.

Answer:

Step-by-step explanation:

need bigger image cant see

The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.

Given: y = -0.8x + 0.4

As we know that the slop-intercept form of the equation of a line is given by: y = mx + c, where

On comparing the given equation of line with the above form of equation of line, we get: m = -0.8 and c = 0.4.

Hence, The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.

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Answer:

Yes, 2² = -2².

Step-by-step explanation:

Given that,

→ prove that 2² equals to -2².

Let's prove the equation,

→ 2² = -2²

→ 4 = 4

→ [ LHS = RHS ]

Hence, it is proved to be equal.

y-3=4 x is in point-slope form, it is neither in slope-intercept form nor standard form.

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We know that  point-slope form = y₂ - y₁ = m(x₂ - x₁)

the equation looks like this in point-slope form ⇒ y-2= 4(x-0)

Here, the points are (x, y) and the points the line is passing through is

(0, 2)

y-2= 4(x-0) is in point-slope form, it is neither in slope-intercept form nor  standard form.

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   Evaluating each series of 8 terms, the result is

∑ = 42

We solve this problem by defining, succession:

  A sequence is defined by an order of values and/or elements that have a relationship of variation as a ratio or proportion that makes them predictable.

As we can see the variation between each of the terms is:

   The initial number is -13

a1 = -13

  The final number is -23.5

an = -23.5

 Let's determine the sum of this sequence of numbers

∑ = n(a1 + an)/2

 Our values are:

-13,-14.5,-16, .......,-23.5

∑ = 8(-13 - (-23.5))/2

∑ = 42

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Answer:

A=45

Step-by-step explanation:

Area of a rectangle equation: A=L*W

A=9*5=45

Step-by-step explanation: I hope this helps.

Answer: the correct answer is 1, 2, and 5

f (9) =  15  is the output for the given input .

How can you tell whether a function is linear or not?

f(x)= 2 x   - 33

Put x = 9    ⇒   2 × 9  - 33

                ⇒     18 - 33

                ⇒       15

Therefore f (9) =  15

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The two legs of the right isosceles triangle are both [tex]\frac{11\sqrt{2} }{2}[/tex]

Since two of the angles in this triangle are 45 degrees and it has a 90 degree angle. It is a right isosceles triangle. An isosceles triangle has two sides the same, which have to be the two legs in this triangle because a triangle can not have two hypotenuses.

According to the Pythagorean Theorem:

[tex]a^{2}+b^{2} =c^{2}[/tex]

where a and b are the legs and c is the hypotenuse.

Since two legs in this right triangle are the same , the formula can be altered to be:

[tex]a^{2}+a^{2} =c^{2}[/tex]

[tex]2a^{2} =c^{2}[/tex]

Putting the value of c is 11

[tex]2a^{2} =11^{2}\\ \\ 2a^{2} = 121\\ \\a^{2} = \frac{121}{2\\}\\ a =\sqrt{\frac{121}{2} }[/tex]

[tex]a =\frac{121}{\sqrt{2} }\\ \\a =\frac{11\sqrt{2} }{2}[/tex] ~ [tex]7.78[/tex]

Hence, The two legs of the right isosceles triangle are both [tex]\frac{11\sqrt{2} }{2}[/tex]

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The corresponding sides have the same measure and are congruent. So,  ΔABC ≅ ΔXYZ by SSS.

What in mathematics is the Pythagoras Theorem?

Observe the graph, the triangles are right triangles. In triangle ABC, AC = 2 and BC = 4. Use the Pythagorean

Theorem to find AB.

AB² = AC² + BC²

AB = √ AC² + BC²

AB = √ 2² + 4²

AB = √4 + 16

AB = √20

Similarly In triangle XYZ, ZX = 2 and ZY = 4. Use the Pythagorean Theorem to find XY

XY² = XZ² +  ZY²

XY = √ XZ² + ZY²

XY = √ 2² + 4²

XY = √4 + 16

XY =  √20

The corresponding sides have the same measure and are congruent. So,  ΔABC ≅ ΔXYZ by SSS.

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When Kayla rode her bike home from college one weekend, her biking speed is 15 miles per hour

Speed is defined as the ratio between the distance and the amount of time an object traveled.

speed = distance/time

If the average speed of the bus was 10 miles per hour faster than Kayla’s biking speed, we have:

average speed of the bus = 10 mph + biking speed

let x = biking speed

y = average speed of the bus

y = 10 + x

Covering the same distance of 75 miles, calculate the time it took her riding the bus and the bike.

time = distance/speed

time riding the bus = 75 miles/(10 + x)

time riding the bike = 75 miles/x

If it took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike

time riding the bus = time riding the bike - 2

75 miles/(10 + x) = (75 miles/x) - 2

75/(10 + x) = (75 - 2x)/x

Multiplying both sides by x(10 + x),

x(10 + x)[75/(10 + x)] = x(10 + x)[(75 - 2x)/x]

75x = 750 - 20x + 75x - 2x^2

2x^2 + 20x - 750 = 0

x^2 + 10x - 375 = 0

(x - 15)(x + 25) = 0

x = 15   ;   x = -25

Since we cannot have negative amount of time, choose x = 15.

Hence, Kayla's biking speed is 15 miles per hour.

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The equation of the line in point-slope form, which passes through the pair of points located at (0 , -1) and (3 , -5), is y + 5 = -4/3(x - 3).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (0 , -1) and (3 , -5).

m = (y2 - y1)/(x2 - x1)

m = (-5 - -1)/(3 - 0)

m = -4/3

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = -4/3 and (x1 , y1) =  (3 , -5)

(y - -5) = -4/3(x - 3)

y + 5 = -4/3(x - 3)

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The solution for w in the equation is w = 2. therefore, the correct option is A; w = 2

An equation represents equality of two or more mathematical expression.

The solution of an equation refers to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

WE have been given the equation: w + 1/2 = 1/4w + 2

Then to solve, Subtract 1/2 from both sides of the equation.

w=1/4w+1 1/2

Then Multiply both sides by 4

4w=w+6

Now Subtract w from both sides

3w=6

Now Divide both sides by 3

w=2

Therefore,  the solution for w in the equation is w = 2 , the correct option is A; w = 2

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By elimination, the system of equations, 6x - 2y = 11 and -9x + 3y = 16, has no solutions.

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Multiply first equation 1 by 3 and equation 2 by -2.

6x - 2y = 11 ⇒ 18x -6y = 33     (equation 1)

-9x + 3y = 16 ⇒ 18x - 6y = -32     (equation 2)

Since the new equation of the two equations have the same coefficients, but different constants, then the two lines are in parallel.

Hence, the system of equations has no solutions.

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She will share 513 candies, each students will receive 27 candies and the amount remaining is 13.

She has 526 pieces of candy that she wants to share with the 19 students in her class.

She makes sure that each classmate gets the same amount of candy.

This means each person or student gets the same or equal amount of candy.

let

x = amount of candy each student gets.

Therefore, the total amount of candy she shared is 526 pieces and the total number of students is 19.

Hence,

x =  amount of candy each student gets = 526 / 19

x =  amount of candy each student gets = 27.6842105263

x =  amount of candy each student gets = 27

Therefore, she will share 513 candies, each students will receive 27 candies and the amount remaining is 13.

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The given pattern forms an Arithmetic progression.

Complete pattern is 144,132,120,108,96,84,72,....

As the given series is in A.P.

⇒ a5 = a + (n - 1)d

⇒ a5 = 144 + (4)d

⇒ a5 = 144 +4 (-12)

⇒ a5 = 144 - 48

⇒ a5 = 96

⇒ a6 = 144 + (6 - 1)d

a6 = 84

⇒ a7 = 144 + (7 - 1)d

a7 = 144 + 6d

a7 = 72

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Answer:

15.6

Step-by-step explanation:

Find the difference between coordinates:

(x2-x1) = (4 - -7) = 11

(y2-y1) = (3 - -8) = 11

Square the results and sum them up:

(11)2 + (11)2 = 121 + 121 = 242

Now Find the square root and that's your result:

Exact solution: √242 = 11√2

Aprox solution: 15.5563

Rounded to nearest tenth: 15.6

Evaluating the expression b(2b - a) for a = 3 and b = -5 is equal to 65.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.

Given the expression b(2b - a), substitute the value of the variable a and the value of variable b.

b(2b - a)

-5[2(-5) - (3)]

Performing the arithmetic operations, we can have the value of the expression.

-5[2(-5) - (3)]

= -5(-10 - 3)

= -5(-13)

= 65

Hence, the expression b(2b - a) when a = 3 and b = -5 is equal to 65.

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Answer: times 3 each time or 3

Step-by-step explanation:

1 is the first value

1x3=3

3x3=9

18x3=54

 The result of the evaluation of the series described by:

∑ = 3755.5

The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.

A series is the summation of a set of numbers or sequences.

The equation for this type of problem is:

∑ = n(a1 + an)/2

 Our values are:

1765,1414,1063, ........ ,-692

1765 - 351X = -692

351X = 1765 + 692

X = 7

∑ = 7(1765 - 692)/2

∑ = 3755.5

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power of 3 is zero

Solution:

87499

Prime Number :

A prime number is a whole number greater than 1 whose only factors are 1 and itself. An element is a real number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Numbers that have more than two factors are called composite numbers.

Factorization:

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler things of the same kind

Factorization may also refer to more general decompositions of a mathematical object into the product of smaller or simpler objects. For example, every function may be factored into the composition of a surjective function with an injective function. Matrices possess many kinds of matrix factorizations. For example, every matrix has a unique LUP factorization as a product of a lower triangular matrix L with all diagonal entries equal to one, an upper triangular matrix U, and a permutation matrix P; this is a matrix formulation of Gaussian elimination.

Factorization of the number = 87499

= 87499

= 5147*17

=5147*7*1

power of 3 is zero

5147 is the prime number  

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10 miles in 30 minutes would mean Julia was riding at 20mph.

5 miles in 12 minutes would mean Alex was riding at 25mph which means Alex would've had the greater average speed.

miles per hour is a good measure for this scenario because a hour is 60 minutes and the numbers 12 and 30 go into 60 cleanly.

12*5=60

30*2=60

60 minutes=1 hour

The words that complete the drop down menus are

This is further explained below.

In geometry, a translation is a transformation that involves moving every point in a figure, shape, or space by the same distance in a specific direction.

A translation may either be seen as the addition of a constant vector to each point or as the movement of the origin of the coordinate system. Both of these interpretations are valid.

Generally,  You need to turn the ship such that all of the sides are aligned parallel to one another.

Move the vertices around in the shape until they are aligned properly.

The rotation should be somewhere about ninety degrees, and the translation should move the form up in a diagonal direction.

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Answer:

12.44 repeated

Step-by-step explanation:

Answer:

112/9

12.4

12 4/9

The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

A triangular is a geometry with 3 sides and three angles. The triangle has angles that sum up to 180 °.

In a triangle, if the angle is small then the opposite side will be short, and if the angle increases then the side also increases.

The sides of the triangle are in ascending order, then we have

WY < YZ < WX < XY < XZ

Then the sequence of the angles is given as,

∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ

The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

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Answer:

(4x+3iy)(4x−3iy)

Step-by-step explanation:

We have a^2 + b^2

Over  the complex number, this is equal to

(a-bi) (a+bi)

(4x -3yi) (4x+3yi)

Answer:

The last one.

Step-by-step explanation:

2(x + 3)

= 2*x + 2*3

= 2x + 6.

Answer: 10

Step-by-step explanation:

its 10 x

may 27, 28, 29, 30, 31, june 1, 2, 3, 4, 5,

         1.    2.   3.    4.   5.          6. 7  8  9. 10

Answer:

Step-by-step explanation:

4 + 4 = 4 so 9 is equal to 6