Solve each system by substitution. Check your answers.
y = 2x - 1 , 3x - y = -1

[tex]\displaystyle\\Answer:\ y=\frac{x}{3}-3[/tex]

Step-by-step explanation:

      [tex](0,-3)\ \ \ \ \ (6,-1)[/tex]

     [tex]\displaystyle\\ Equation\ of\ the\ line\\\\\boxed {\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1} }[/tex]

 [tex]\displaystyle\\x_1=0\ \ \ \ x_2=6\ \ \ \ \ y_1=-3\ \ \ \ \ y_2=-1\\\\\frac{x-0}{6-0}=\frac{y-(-3)}{-1-(-3)}\\\\\frac{x}{6}=\frac{y+3}{-1+3} \\\\\frac{x}{6} =\frac{y+3}{2} \\\\Multiply\ both\ parts\ of \ the\ equation \ by \ 2:\\\\\frac{x}{3}=y+3\\\\\frac{x}{3}-3=y+3-3\\\\ \frac{x}{3} -3=y \\\\Thus,\\\\y=\frac{x}{3}-3[/tex]              

Answer:

118

Step-by-step explanation:

[tex]10^{2} + 2(6-3)^{2}[/tex]   To start off, we work in the Parenthesis; 6-3 = 3

[tex]10^{2} + 2(3)^{2}[/tex]  Now, we must do the exponents; 10^2 = 100; 3^2 = 9

[tex]100 + 2(9)[/tex]   Next, we have to distribute the 2 to the 9; 2 x 9 = 18

[tex]100 + 18[/tex]  Lastly, we have to add 100 and 18; 100 + 18 = 118

So! Our final answer is 118!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

118

Step-by-step explanation:

m)  [tex]10^{2} + 2(6-3)^{2} = 10^{2} + 2(3)^{2} = 10^{2} + 2(9)= 100 + 18 = 118[/tex]

The number of ounces gained by the Kitten before it went home with its new owner is; 3 1/8 ounces.

It follows from the task content that the it is required that the weight gained by the kitten in ounces is to be determined.

Since the kitten weighed 5 1/2 ounces on the day it was sold and weighed; 3 3/8 ounces at birth, the number of ounces gained is;

= 5 1/2 - 3 3/8

= 11/2 - 27/8

= (44 - 27)/8

= 17/8

= 2 1/8 ounces.

Ultimately, the weight gained by the kitten, in ounces following evaluation from the task content is; 2 1/8 ounces.

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The simplified form of expression is  (2y + 3).

Rewriting the provided mathematical expression first -

5/(y + 3) + 15/(y - 3)

Shifting the second expression on other side of equation -

5/(y + 3) = - 15/(y - 3)

Performing cross multiplication

5 (y - 3) = -15 (y + 3)

5y - 15 = -15y - 45

Rearranging the equation

5y - (-15y) = -45 - (-15)

Performing addition and subtraction

5y + 15y = -45 + 15

20y = -30

Dividing both sides of equation by 10

2y = - 3

Rearranging the equation -

2y + 3

Hence, the simplified form of expression is (2y + 3).

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The quadratic equation which has solutions x = 8 and x = -1 is [tex]\bold{x^2-7x-8}[/tex] = 0.

An equation of degree 2 is called a quadratic equation. That is, the highest power of x in the equation will be two. It has at most two solutions.

Given the solutions are x = 8 and x = -1.

If x = a is a solution, then (x-a) is a factor for the equation.

So here, x-8 and x+1 are factors of the required quadratic equation.

Thus, the quadratic equation will be, (x-8)(x+1) = [tex]\bold{x^2-7x-8}[/tex] = 0.

We can check if x = 8 and x = -1 are the solutions. Put x = 8 in [tex]\bold{x^2-7x-8}[/tex]

Then, 8 x 8 - 7 x 8 - 8 = 0 and -1 x -1 - 7 x -1 - 8 = 0.

So [tex]\bold{x^2-7x-8}[/tex] = 0 is the quadratic equation with solutions x = 8 and x = -1.

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Answer: 37°  53°  90°

Step-by-step explanation:

Given:

ΔABC    m∠C=90°    

Solution:

m∠A+m∠B+m∠C=180°

m∠A+m∠B+90°=180°

m∠A+m∠B+90°-90°=180°-90°

m∠A+m∠B=90°

Let m∠A=x°

Hence,

m∠B=(x+16)°

Thus,

x°+(x+16)°=90°

(2x)°+16°=90°

(2x)°+16°-16°=90°-16°

(2)(x)°=74°

Divide both parts of the equation by 2:

x°=m∠A=37°

m∠B=37°+16°

m∠B=53°

The circumference of one tire is 75.36 inches.

We are given the diameter of tire of bicycle. The formula of circumference is as follows -  

Circumference = 2× π × r, where r is representative of radius of circle.  As we are given the diameter, we will use the formula of circumference with diameter. The formula to be used is as follows -

Circumference = π × d, where d is representative of diameter of circle.

Keep the values in formula to find the value of circumference of one tire. We will be taking the value of π as 3.14.

Circumference = 3.14 × 24

Performing multiplication to find the circumference of one tire.

Circumference = 75.36 inches

Hence, the circumference of one tire of bicycle is 75.36 inches.

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The 4th, 5th, 6th,and 7th terms of the sequence an = n²/{n+1} are 16/5, 25/6, 36/7, and 49/8 respectively.

According to the given question.

We have,

A formual for finding the gereral term of the sequence i.e.

an = n²/{n+1}.

Since, we have to find the 4th, 5th, 6th, and 7th term of the sequence.

Therefore,

4th term of the sequence is given by

[tex]a_{4}[/tex]  = (4)^2/{4 + 1) = 16/5

5th term of the sequence is given by

[tex]a_{5}[/tex]  = (5)^2/{5 + 1}  = 25/6

6th term of the sequence is given by

[tex]a_{6}[/tex]  = 6^2/{6 + 1} = 36/7

7th term of the sequence is given by

[tex]a_{7}[/tex] = 7^2/{7 + 1} = 49/8

Hence, the 4th, 5th, 6th,and 7th terms of the sequence an = n²/{n+1} are 16/5, 25/6, 36/7, and 49/8 respectively.

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The decimal number with repeating digits can be written as:

0.344... = 31/90

Here we have the number:

0.3444....

Where the 4 keeps repeating.

First, we need to multiply this by 10, so we get:

10*0.344... = 3.444...

Now if we subtract the original number we get:

10*0.344... - 0.344... = 3.444... - 0.344...

9*(0.344...) = 3.1

Now, isolating the original number:

0.344... = 3.1/9

Finally, we multiply and divide the fraction by 10 so we get two whole numbers:

0.344... = (10/10)*(3.1/9) = 31/90

0.344... = 31/90

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Two angles that form a linear pair are supplementary:  Always TRUE

Therefore, the statement "two angles that form a linear pair are supplementary" is Always TRUE.

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Based on the definition of supplementary angles:

Algebraic equation: A. x + (1/2x + 3) = 180

The measure of the smaller angle is: 62°

The measure of the larger angle is: 118°.

The sum of the two angles that are supplement of each other is equal to 180 degrees, hence they are called supplementary angles.

One of the angles = x

The second angle = 1/2x + 3

Since they are supplementary angles, we will have the following algebraic equation:

x + (1/2x + 3) = 180

Solve for x

x + 1/2x + 3 = 180

3/2x = 180 - 3

3/2x = 177

2/3(3/2x) = 2/3(177)

x = 118°

The second angle = 180 - 118 = 62°

Therefore, based on the definition of supplementary angles, we have the following:

Algebraic equation: A. x + (1/2x + 3) = 180

The measure of the smaller angle is: 62°

The measure of the larger angle is: 118°.

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The possible value of angle ∠K, to the nearest degree is 31 degrees

The given parameters are

Triangle = ΔKLM,

Length k = 56 inches,

Length m = 51 inches

Angle ∠M =28

To calculate the possible value of angle K, we make use of the following sine rule

k/sin(K) = m/sin(M)

Substitute the known values in the above equation

So, we have

56/sin(K) = 51/sin(28)

Cross multiply in the above equation

So, we have

51 x sin(K) = 56 x sin(28)

Evaluate the product in the above equation

So, we have

51 x sin(K) = 26.29

Divide both sides of the above equation by 51

So, we have

sin(K) = 0.52

Take the arc sin of both sides

So, we have

K = 31

Hence, the possible value of angle ∠K, to the nearest degree is 31 degrees

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Answer:

[tex]\textsf{1.} \quad 5x+3-\dfrac{3}{x-4}[/tex]

[tex]\textsf{2.} \quad 2x^2-4x+3[/tex]

[tex]\textsf{3.} \quad x^3+3x^2-2x+4+\dfrac{25}{2x-5}[/tex]

Step-by-step explanation:

Long Division Method of dividing polynomials

Divide the first term of the dividend by the first term of the divisor and put that in the answer.

Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.

Repeat until no more division is possible.

Write the solution as the quotient plus the remainder divided by the divisor.

[tex]\large \begin{array}{r}5x+3\phantom{)}\\x-4{\overline{\smash{\big)}\,5x^2-17x-15\phantom{)}}}\\{-~\phantom{(}\underline{(5x^2-20x)\phantom{-b)..}}\\3x-15\phantom{)}\\-~\phantom{()}\underline{(3x-12)\phantom{}}\\-3\phantom{)}\\\end{array}[/tex]

Solution

[tex](5x^2-17x-15) \div (x-4)=\dfrac{5x^2-17x-15}{x-4}=5x+3-\dfrac{3}{x-4}[/tex]

[tex]\large \begin{array}{r}2x^2-4x+3\phantom{)}\\3x-2{\overline{\smash{\big)}\,6x^3-16x^2+17x-6\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-4x^2)\phantom{-bbbbbbbb.)}}\\-12x^2+17x-6\phantom{)}\\-~\phantom{()}\underline{(-12x^2+8x)\phantom{))))).}}\\9x-6\phantom{)}\\-~\phantom{()}\underline{(9x-6)\phantom{}}\\0\phantom{)}\end{array}[/tex]

Solution

[tex](6x^3-16x^2+17x-6) \div (3x-2)=\dfrac{6x^3-16x^2+17x-6}{3x-2}=2x^2-4x+3[/tex]

[tex]\large \begin{array}{r}x^3+3x^2-2x+4\phantom{)}\\2x-5{\overline{\smash{\big)}\,2x^4+x^3-19x^2+18x+5\phantom{)}}}\\{-~\phantom{(}\underline{(2x^4-5x^3)\phantom{-bbbbbbbbbbb.bb.)}}\\6x^3-19x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(6x^3-15x^2)\phantom{))))bbbb..).}}\\-4x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(-4x^2+10x)\phantom{)))..}}\\8x+5\phantom{)}\\-~\phantom{()}\underline{(8x-20)}\\25\phantom{)}\end{array}[/tex]

Solution

[tex]\begin{aligned}(2x^4+x^3-19x^2+18x+5) \div (2x-5) & =\dfrac{2x^4+x^3-19x^2+18x+5}{2x-5}\\ & =x^3+3x^2-2x+4+\dfrac{25}{2x-5}\end{aligned}[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{x}{5} +1=\frac{1}{15}[/tex]

[tex]\frac{x}{5} = \frac{1}{15} -1[/tex]

[tex]\frac{x}{5} = \frac{1-15}{15}[/tex]

[tex]\frac{x}{5} = \frac{-14}{15}[/tex]

multiply both sides by 5

[tex]5*\frac{x}{5} = \frac{-14}{15} *5[/tex]

[tex]x=-\frac{14}{3}[/tex]

Answer:

470,006,962

hope this helped :)

Answer:

407,006,962

you can check it on the internet ;)

The percent of 16, which is equal to the 80 percent of 42 is 210.

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.

Let x be the percent of 16, which is equal to the 80 percent of 42.

80% of 42 = x % of 16

80/100 [tex]*[/tex] 42 = x/100 [tex]*[/tex] 16

80(42)/100 = 16/100 [tex]*[/tex] x

Multiplying both sides of the equation by 16/100, then we get

80(42)/100 [tex]*[/tex] (16/100) = 16/100 [tex]*[/tex] x [tex]*[/tex] (16/100)

simplifying the above equation, we get

80(42)/100 [tex]*[/tex] (16/100) =  x

80(42)/16 =  x

210 = x

The value of x = 210.

Therefore, the correct answer is option b. 210.

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Answer:

210

Step-by-step explanation:

We can start by finding 80% of 42:

80% of 42 = (80/100) x 42 = 33.6

So, the question now becomes: what percent of 16 is 33.6?

Let's call the unknown percentage "x".

We can set up the following equation:

x/100 x 16 = 33.6

Multiplying both sides by 100/16, we get:

x = (33.6 x 100)/16

x = 210

Hence, the number of people are in the Smith family is [tex]23[/tex].

What is the division?

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.

Here given that,

A hotel charges $[tex]80[/tex] for a basic room for one person per night. It charges $[tex]15[/tex] for each additional person per night. The Smith family takes three rooms for three nights. The bill comes to $[tex]1035[/tex].

So,

Rent for the one day is

[tex]\frac{1035}{3}=345[/tex]

Number of people are in the Smith family is

[tex]\frac{345}{15}=23[/tex]

Hence, the number of people are in the Smith family is [tex]23[/tex].

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In the given arithmetic series, the first term is a(1) = 3x and the sum of the first 15 terms is S(15) = 45x - 210y

The given series is:

    3x + (3 x-2 y) + (3x-4y) + ......

Notice that this is an arithmetic series with:

the first term, a(1) = 3x

the second term, a(2) = 3x - 2y

the 3rd term, a(3) = 3x - 4y

Hence, the common difference is:

     d = (3x - 2y) - 3x = -2y

Recall that the nth term of an arithmetic series is given by:

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

Substitute n = 15, a(1) = 3x, and d = -2y:

a(15) = 3x + (15 - 1) . (-2y)

a(15) = 3x - 28y

The sum of the first n terms in an arithmetic series is given by:

S(n) = n/2 [a(1) + a(n)]

Substitute n = 15

S(15) = 15/2 [a(1) + a(15)]

S(15) = 15/2 . (3x + 3x - 28y)

S(15) = 15 . (3x - 14y) = 45x - 210y

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The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.

The given arithmetic series is 6+7.4+8.8+ . . .

The summation notion of given series is ∑6+1.4n , here n starts from 0.

The sum of arithmetic series can be written as,

[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]

n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.

We have, n=11, [tex]a_{1}[/tex] = 6

To calculate sum of arithmetic series, we need to find [tex]a_{11}[/tex] .

[tex]a_{11} = a_{1} + (n-1)d[/tex]

d = 1.4 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get

[tex]a_{11}[/tex] = 6 + (11-1)(1.4)

[tex]a_{11}[/tex] = 6 + 14 = 20

On substituting values in sum of arithmetic series formula, we get

[tex]S_{7}[/tex] = (11(6 + 20))/2 = 143

The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.

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Answer:

Step-by-step explanation:

-y = -4x +6

y = 4x -6

Any line with a slope of 4 and y-int other than -6 is parallel to y = 4x-6

Answer:24939.5 i think

Step-by-step explanation:

Answer:

81 feet & 19 feet

Step-by-step explanation:

The sum of the infinite geometric series 6+5+ 25/6 + . .  is S = 36

The given geometric series is:

  1 - 1/2 + 1/4 - . . ..

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 1

a(2) = -1/2

a(3) = 1/4

Hence, the common ratio is

   r = a(2) / a(1) = -1/2

Since 0 < | r | < 1, the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 1 and r = -1/2 into the formula:

S = 1 / (1 - (-1/2))

   = 1 / (3/2)

   = 2/3

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When written as a radical, the index of a expression x²/³ is 2.

To rewrite the expression x²/³ as a radical expression, we must first understand what such a radical expression is.

A radical expression is a form expression:  ⁿ√x.

As,  ⁿ√x = x¹/ⁿ

Thus the given expression x²/³ can be written in the above form as;

x²/³ = (³√x)²

Now, the obtained result (³√x)² is written in the radical form where (³√x) is a radical.

As, the expression (³√x) is raised to the 2 power, the index of the expression when the expression is written as x²/³ have a radical is 2.

As a result, the index of the expression x²/³ when rewritten as a radical is 2.

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The complete question is-

What is the index when the expression x^2/3

is rewritten as a radical expression?

There are 190 more birds than expected at the refuge.

The information provided in the question indicates that there are 3 percent more birds than there were previously. The sanctuary houses 175 birds, which may be pictured as follows:

There are 175 birds in all.

According to the inquiry, it is rising by 3%.

Number of birds = (175)(3%) = 5.25 at this point.

As a result, given the data, the anticipated enhanced data is as follows:

Added birds is 175 + 5 + 5 + 5 = 190.

190 more birds are therefore expected in the refuge.

The final computed numbers should be divided by the total value and then multiplied by 100 to obtain the percentage.

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Answer 825

Step-by-step explanation:

275/2=137.5

137.5x6=825

There are 5040 different ways can the runners finish first, second, third, and fourth place if ten runners are racing.

The permutation is defined as considered an ordered combination.

The general formula for this is:

P(n, r) = n! (n-r)!

Ten runners are racing

There are ten runners who can win first place, hence there are ten ways.

Any of the remaining 9 runners may get up to the second position in nine different ways.

Any of the remaining 8 runners may get up to the third position in eight different ways

Any of the remaining 7 runners may get up to the fourth position in seven different ways

So total number of ways = 10 × 9 × 8 × 7 = 5040

Another way 4 Out of 10 need to select where order matters

= ¹⁰P₄

= 10!/6!

= 10 × 9 × 8 × 7

= 5040

Hence, there are 5040 different ways can the runners finish first, second, third, and fourth place if ten runners are racing.

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