Nagi has 8 red marbles
and 12 yellow marbles.
His mom doubled his red
and yellow marbles for
his birthday. Use the
distributive property to
show how many marbles
Nagi has now.

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)

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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Congruent radii are found in congruent circles. Concentric circles share a common center.

Congruent circles contain congruent radii. Concentric circles all have the same center. A central angle has a center vertex and circle endpoints.

The distances OA and OB are both equal to the radius of the circle because all points on the circle are equidistant from O. OA = OB, to put it another way.

According to the definition of line segment congruence, segments OA and OB are congruent. This is known as the "wheel theorem," because it is responsible for the operation of wheels.

Because all points on a circle are the same distance from the center, and circle radii have one endpoint on the circle and one at the center, all circle radii are congruent by definition. Every circle has an outer diameter.

Congruent circles contain congruent radii (the plural of radius). Concentric circles all have the same center.

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The probability of spinner pointer landing on blue color region is equal to 1/3 .

As given in the question,

Total colors in the spinner is equal to 6

Each color is 2 times

Total number of colored region =6

Number of blue region = 2

Probability of pointer landing on blue color region denoted by P(B)

Probability is

= ( Total number of favourable outcomes) /  (Total number of outcomes )

⇒ P(B) = 2 / 6

⇒ P(B) = 1 /3

Therefore, the probability of spinner pointer landing on blue color region is equal to 1/3.

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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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Answer:

A=45

Step-by-step explanation:

Area of a rectangle equation: A=L*W

A=9*5=45

Step-by-step explanation:

so, f(x) = 3x

now, this is reflected around the x-axis.

points that were n units above the x-axis are now n units below the x-axis and vice versa.

so, the functional values start the same in their size, but their sign flips. for every point.

that means,

g(x) = -f(x) = -3x

   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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28.1 amu is the atomic weight of x.

What is atomic weight defined as?

The term "atomic weight" refers to an atom's overall weight. With the addition of a small amount from the electrons, it is roughly equal to the sum of the protons and neutrons.

What does atomic weight vs. atomic mass mean?

The atomic weight of the element will be a weighted average of the isotopes based on the relative abundance:

(27.977 x 0.9221) + (28.976 x 0.0470) + (29.974 x 0.0309

) = 25.798 + 1.362 + 0.926

= 28.08 = 28.1 amu

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By elimination, the solution of the system of equations, 2w + 5y = -24 and 3w - 5y = 14, is (w, y) = (-2 , -4).

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 w and y, a variable should be eliminated by adding/subtracting the two equations.

Adding the two equations will eliminate the variable y.

2w + 5y = -24     (equation 1)

3w  - 5y = 14     (equation 2)

5w + 0y = -10

w = -2

Substitute the value of w to any of the two equations and solve for y.

2w + 5y = -24     (equation 1)

2(-2) + 5y = -24

5y = -24 + 4

5y = -20

y = -4

Hence, the solution of the system of equations is (w, y) = (-2 , -4).

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Using proportions, it is found that Chris made the most money in the week.

The rates for Michelle's works are missing, as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Chris's salary is given by the sum of the base plus commissions, hence:

C = 250 + 0.015 x 1500 = $272.5.

Michelle's salary is given as follows, considering she is paid double the hourly rate for the holiday:

M = 12 x 2 x 6.50 + 10 x 5 = $206.

Alex salary's is found as follows, considering the rate and the hour and a half for the weekend:

A = 5 x 1.5 x 7 + 7 x (6 + 5.75 + 4.5 + 6.75 + 5.5) = $252.

Hence Chris made the most money in the week.

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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

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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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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The given sequence is geometric, with a common ratio of -5.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 2, -10, 50, -250, ....

We can observe here: [tex]\frac{-10}{2}=\frac{50}{-10}=\frac{-250}{50} = -5[/tex], hence following the condition required for a sequence to be geometric.

Hence, The given sequence is geometric, with a common ratio of -5.

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

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

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:

r = 3

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]\large\boxed{y=mx+b}[/tex]

where:

Given:

Substitute the given slope and point into the formula and solve for b:

[tex]\begin{aligned}y & = mx+b\\\implies -3 & = \dfrac{6}{5}(-2)+b\\-3 & = -\dfrac{12}{5}+b\\-3 +\dfrac{12}{5} & = b\\\implies b & = -\dfrac{3}{5}\end{aligned}[/tex]

Substitute the given slope and found value of b into the formula to create an equation for the line:

[tex]\boxed{y=\dfrac{6}{5}x-\dfrac{3}{5}}[/tex]

Substitute the point (r, 3) into the equation and solve for r:

[tex]\begin{aligned}y & = \dfrac{6}{5}x-\dfrac{3}{5}\\\implies 3 & = \dfrac{6}{5}r-\dfrac{3}{5}\\5 \cdot 3& = 5 \cdot \left(\dfrac{6}{5}r-\dfrac{3}{5}\right)\\15 & = 6r-3\\15+3&=6r-3+3\\ 18 & = 6r\\\dfrac{18}{6} & = \dfrac{6r}{6}\\3 & = r\\ \implies r & =3\end{aligned}[/tex]

Solution

Therefore, the value of r is 3.

Answer:

102.9 m

Step-by-step explanation:

The shortest distance from A to C would be diagonally from A to C.

This comprises:

The length of the diagonal between A and C can be calculated using Pythagoras Theorem:

[tex]\begin{aligned}c^2&=a^2+b^2\\\implies \sf AC^2 & = \sf AB^2+AD^2\\\sf AC^2 & = \sf 50^2+80^2\\\sf AC^2 & = \sf 2500+6400^2\\\sf AC^2 & = \sf 8900\\\sf AC & = \sqrt{\sf 8900}\\\sf AC & = \sf 94.33981132\;m\end{aligned}[/tex]

Subtract the diameter of the circular path from this to calculate the sum of the lengths of the straight paths.

[tex]\implies \sf 94.33981132-15=79.33981132\;m[/tex]

To calculate the length of the circular part of the path, find half the circumference of the central circle:

[tex]\begin{aligned}\implies \textsf{Half the circumference} & = \sf \dfrac{1}{2} \pi d\\& =\sf \dfrac{1}{2} \pi (15)\\& =\sf 23.5619449\;m\end{aligned}[/tex]

Therefore, the shortest distance from A to C across the park is:

[tex]\begin{aligned} \implies \textsf{Shortest distance} & = \sf 79.33981132+23.5619449\\& = \sf 102.9017562\\& = \sf 102.9\;m\;(nearest\:tenth)\end{aligned}[/tex]

Answer: times 3 each time or 3

Step-by-step explanation:

1 is the first value

1x3=3

3x3=9

18x3=54

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

 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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Answer: $110

Step-by-step explanation: 50+10*6=50+60=110

Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so a function's mirroring is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.

The function's reflection should be similar in size and shape to the original position.

f(x)=3x; y-axis

(consult the pictures attached below)

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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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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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Computing the sum of the first term in the arithmetic series is relatively straightforward. Just add these values ​​together. However, adding, say, the first 100 words creates more problems. Instead of manually summing all these terms, mathematicians devised an arithmetic progression formula that efficiently computes the sum of the arithmetic progression.

a1 =-6

S50 = -5150

an=?

Sn=n(a1+an)/2

So, to find an

((2*sn) /n)-a1=an

((2*-5150) /50) -(-6)=an

An=200

D=-194/49

Here the first term a=-6,

Common difference d=-3.96

We know that,

f(n)=a+(n-1)d

f(50)=-6+(50-1)(-3.96)

=-6+(-193.99)

=-199.99

We know that,

Sn=n2[2a+(n-1)d]

∴S50=502⋅[2(-6)+(50-1)(-3.96)]

=25⋅[-12+(-193.99)]

=25⋅[-205.99]

=-5149.78

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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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Answer:

The last one.

Step-by-step explanation:

2(x + 3)

= 2*x + 2*3

= 2x + 6.