Question 2
A square room of side length x is made 5 m longer (its width stays the same). What is the new area
of the room?​

Answer: the real solution: x = - 2

Find the attached file for the remaining solution

Step-by-step explanation:

The equation given is:

x3 - 5x2 + 28 = 0 

Let assume that -2 is one of the root of the equation. Substitute -2 for x

(-2)^3 - 5(-2)^2 + 28

-8 - 20 + 28 = 0

Therefore, -2 is one of the root of the equation since the equation tend to zero.

If x = -2, then x+2 is one of the factors of the equation. Therefore, the real solution is x = -2

Please find the attached file for the remaining solution.

Looks like your function is

[tex]f(x)=\dfrac x{6x^2+1}[/tex]

Rewrite it as

[tex]f(x)=\dfrac x{1-(-6x^2)}[/tex]

Recall that for [tex]|x|<1[/tex], we have

[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]

If we replace [tex]x[/tex] with [tex]-6x^2[/tex], we get

[tex]f(x)=\displaystyle x\sum_{n=0}^\infty\frac(-6x^2)^n=\sum_{n=0}^\infty (-6)^n x^{2n+1}[/tex]

By the ratio test, the series converges if

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(-6)^{n+1} x^{2(n+1)+1}}{(-6)^n x^{2n+1}}\right|=6|x^2|\lim_{n\to\infty}1=6|x|^2<1[/tex]

Solving for [tex]x[/tex] gives the interval of convergence,

[tex]|x|^2<\dfrac16\implies|x|<\dfrac1{\sqrt6}\implies -\dfrac1{\sqrt 6}<x<\dfrac1{\sqrt 6}[/tex]

We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.

The interval of the convergence is (-1/√6 < x < 1/√6). We can confirm that the interval is open by checking for convergence at the endpoints.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The given function is

[tex]\rm f(x) = \dfrac{x}{6x^2 + 1} \\\\or \\\\f(x) = \dfrac{x}{1 - (-6x^2)}[/tex]

For |x| < 1, we have

[tex]\rm \dfrac{1}{1-x} = \Sigma_{n=0}^{\infty} \ x^n[/tex]

If x is replaced with -6x², then we have

[tex]\rm f(x)= \Sigma_{n=0}^{\infty} (-6x^2 )^n = \Sigma_{n=0}^{\infty} (-6)^n x^{2n+1}[/tex]

Then by the ratio test, the series converges if

[tex]\displaystyle \lim_{n \to \infty} \left| \dfrac{(-6)^{n+1}x^{2(n+1)+1}}{(-6)^{n}x^{2n+1}} \right|=6|x^{2}| \displaystyle \lim_{n \to \infty }1=6|x^{2}| < 1[/tex]

Solving for x, the interval of convergence will be

[tex]|x^2| < \dfrac{1}{6} \\\\|x| < \dfrac{1}{\sqrt6} \\\\-\dfrac{1}{\sqrt6} < x < \dfrac{1}{\sqrt6}[/tex]

We can confirm that the interval is open by checking for convergence at the endpoints.

More about the function link is given below.

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Answer:

-2°F

Step-by-step explanation:

So on Sunday night, the temperature was -10°F.

And by Monday morning, the temperature has increased by 8°F.

In other words, to find the temperature on Monday morning, we just have to add 8 to -10. Therefore:

[tex](-10)+(8)=-2[/tex]

The temperature on Monday morning is -2°F

Answer:

-2 degrees F.

If you have -10, you have to add positive 10 just to get to 0.

Answer: 3

Step-by-step explanation: you add 7+3 which is 10 - 7 =3

Answer:

The solution of the equation f(x) = g(x) is the set of all x for which the graphs of f and g intersect. The solution of the inequality f(x) < g(x) is the set of all x for which the graph of f lies below the graph of g.

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

;)

Answer:

y = -7x + 2

Step-by-step explanation:

Use the slope-intercept form y = mx + b.

Substitute -7 for m, 0 for x and 2 for y.  Then

2 = (-7)(0) + b, so b must be 2.

The desired equation is y = -7x + 2.

Answer:

D

Step-by-step explanation:

So we have the expression:

[tex](6m+3)(m-2)[/tex]

Use the distributive property and distribute:

[tex]=(6m+3)(m)+(6m+3)(-2)[/tex]

Distribute:

[tex]=(6m^2+3m)+(-12m-6)[/tex]

Combine like terms:

[tex]=6m^2+3m-12m-6\\=6m^2-9m-6[/tex]

The correct answer is D

Edit: Typo

Answer:

found this on the web. hopefully it helps

Answer:

x = 16

Step-by-step explanation:

Step 1: We know DF - DE = EF

9x - 39 - 47 = EF

Step 2: Simplify

9x - 86 = EF

Step 3: Set the equation equal to 3x + 10

9x - 86 = 3x + 10

6x = 96

x = 16

Therefore x is equal to 16

Answer:

58

Step-by-step explanation:

DE + EF = DF

47+ 3x+10 = 9x-39

Combine like terms

57 +3x = 9x-39

Subtract 3x from each side

57+3x-3x = 9x-3x-39

57 = 6x-39

Add 39 to each side

57+39 = 6x-39+39

96 = 6x

Divide by 6

96/6 = 6x/6

16 =x

We want the length of EF

EF = 3x+10

     = 3*16 +10

    = 48+10

   = 58

Answer:

soln,

y=37/100×x

or, 100y=37x.....is the answer

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The equation of y is 37% of x is

y = 0.37x

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example:

2 + 3x + 4y = 7 is an expression.

2 + 3 - 4 is an expression.

2x4 + 4x = 4 is an expression.

We have,

y is 37% of x.

This can be written as,

y = 37/100 of x

y = 0.37x

Thus,

The equation of y is 37% of x is

y = 0.37x

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Answer:

  [tex]1-\dfrac{2}{3}\sqrt{3}[/tex]

Step-by-step explanation:

Maybe you want to simplify ...

  [tex](1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}[/tex]

Multiply numerator and denominator by the 'conjugate' of the denominator:

  [tex](1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}\cdot\dfrac{3-\sqrt{3}}{3-\sqrt{3}}=\dfrac{(1-\sqrt{3})(3-\sqrt{3})}{9-3}=\dfrac{3-4\sqrt{3}+3}{6}\\\\\boxed{1-\dfrac{2}{3}\sqrt{3}}[/tex]

Answer:

Reflexive property

Step-by-step explanation:

The statement says that some number is equal to itself.

That's the reflexive property.

Answer:

Step-by-step explanation:

The solutions to the answers are given below :

1) option c

2) option f

3) option b

4) option d

[tex]a)\frac{5x -7}{7(x+1)} \\\\\\b) 7(5x-7) (x+ 1 )\\\\\[/tex]

  [tex]c)\frac{5x^3 + 7x +1}{5}[/tex]

  [tex]d) \frac{5x-1 }{7(x+1)}[/tex]

An Expression is a mathematical term consisting of variables, connected using some operators.

Example :  2x + 3

where x is the coefficient of 2 and both the terms are joined using the addition operator.

The verbal description of the corresponding expression is:

 1) The cube of the difference of 5 times  x and divided by the sum of 7 times x  and 1

 ans.[tex]\frac{5x - 7}{7(x+1)}[/tex]

2) 7 times the difference of 5 times 6 and 7 and the sum of x and 1.

ans. [tex]7( 5x - 7 )( x+1)[/tex]

3) The sum of 5 times the cube of x , 1 and 7 times x , divided by 5 .

ans. [tex]\frac{5x^3 = 7x +1}{5}[/tex]

4) The difference of 5 times the cube of x and 7 divided by 7 times the sum of x and 1.

ans  [tex]\frac{5x -7}{7(x+ 1)}[/tex].

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Answer:What if you were asking this question? How would you explain it to yourself?

Step-by-step explanation:

Answer:

  C.  47°

Step-by-step explanation:

The angle between the terminal ray of 227° and the nearest x-axis (the negative x-axis) is ...

  227° -180° = 47°

The reference angle is 47°.

_____

In mathematical terms the reference angle is the minimum of the angle modulo 180° and the supplement of that angle.

  227° modulo 180° = 47°

  180° -47° = 133° . . . . supplement of 47°

  min(47°, 133°) = 47° . . . the reference angle

Answer:

125 10/14

Step-by-step explanation:

1,760/14 = 125 r10

- 125 x 14 + 10 = 1,760

You turn the remainder into a fraction using whatever number you divided the main number by. In this case that would be 14.

201 bars

Let the number of bars bought be x.

Cost of three bars is 20 cents.

Therefore, 1 bar will cost [tex]\frac{20}{3}[/tex] cents.

He ate one of the bars...

Therefore, remaining bars will be x - 1

... He sold the remainder at 10 cents each i.e

1 bar = 10 cents

(x - 1) bars = 10( x - 1) cents

...He made $200.00 from selling the remaining bars.

10( x - 1) cents = $200.00             ---------------(i)

Convert from dollars to cents

$1 = 10 cents

$200 = 200 x 10 cents = 2000 cents

From equation (i)

10(x - 1)cents = 2000 cents

=> 10( x - 1) = 2000            [divide both sides by 10]

=> x - 1 = 200

=> x = 200 + 1

=> x = 201

Therefore, he bought 201 bars of ice cream.

Answer:

False

Step-by-step explanation:

In an essay, you have to cite every source you use because

a) the teacher needs to KNOW you didn't copy

b) the teacher needs to know if you got your info from a reliable source

c) the teacher needs to see your ability to use info from a source to put into your essay

This may be different for books, but citation is always a rule of thumb for essays in school, so don't forget unless you want points to be taken off of your score.

Answer:

20

Step-by-step explanation:

Given:

As per the picture:

Comparing the two equations above:

x = 20 is the correct answer for this question

Otherwise something is wrong with the question.

Answer: The answers are in the steps I numbered it as a question from 1 to 12 hopes it helps.Read it carefully.

Step-by-step explanation:

(1)  Answer is RATIONAL NUMBERS.

(2) Answer is  Fraction  

(3) Answer is Terminating decimal

(4) Answer  is  Decimal

(5)  Answer is Integer  

(6) Answer  is Repeating Decimal

(7)  Answer is  Perfect Square  

(8) Answer   is CLASSIFY

(9) Answer is Real Numbers  

(10) Answer is Percent

(11) Answer   Whole numbers

(12) Answer is Irrational numbers

Answer:

Yes, the table represents quadratic function.

[tex]Y = 3X^2+10[/tex]

Step-by-step explanation:

Given that table of values:

[tex]\begin{center}\begin{tabular}{ c c}X & Y \\ 1 & 13 \\ 2 & 22 \\ 3 & 37 \\ 4 & 58 \\ 5 & 85 \\\end{tabular}\end{center}[/tex]

To find:

Whether the given table represents a quadratic?

Solution:

First of all, let us plot the given values on the coordinate xy plane.

Kindly refer to the attached image for the graph of given values.

The graph seems parabolic in nature which is the graph of a quadratic equation.

Now, let us try to find the equation from the given set of values from hit and trial.

Let Quadratic equation be:

[tex]y=ax^{2} +b[/tex]

If the coefficient a = 1

[tex]f(1) = 13 = 1^2+12[/tex]

[tex]f(2) = 22 = 2^2+18[/tex]

[tex]f(3) = 37= 3^2+28[/tex]

[tex]f(4) = 58 = 4^2+42[/tex]

[tex]f(5) = 85 = 5^2+60[/tex]

value of b is not same in each case.

Now, let us try coefficient a = 3

[tex]f(1) = 13 = 3 \times 1^2+10[/tex]

[tex]f(2) = 22 = 3\times 2^2+10[/tex]

[tex]f(3) = 37= 3\times 3^2+10[/tex]

[tex]f(4) = 58 = 3\times 4^2+10[/tex]

[tex]f(5) = 85 =3\times 5^2+10[/tex]

Value of b = 10

So, we can clearly say that the given table represents a quadratic equation.

and the quadratic equation is:

[tex]Y = 3X^2+10[/tex]

Answer:

Once we got

[tex]x=-1[/tex]

[tex]y=3[/tex]

[tex]z=2[/tex]

[tex]\boxed{\text{The sum is 4}}[/tex]

Step-by-step explanation:

Given the linear system:

[tex]\begin{cases} 2x + 3y-z = 5 \\ x- 3y + 2z = -6 \\ 3x + y - 4z = -8 \end{cases}[/tex]

Let's solve it using matrices. I will use Cramer's rule

[tex]M=\left[\begin{array}{ccc}2&3&-1\\1&-3&2\\3&1&-4\end{array}\right][/tex]

Considering determinant as D.

[tex]D=\begin{vmatrix}2&3&-1\\1&-3&2\\3&1&-4\\\end{vmatrix}=40[/tex]

[tex]M_x = \left[\begin{array}{ccc}5&3&-1\\-6&-3&2\\-8&1&-4\end{array}\right] \implies D_x = \begin{vmatrix}5&3&-1\\-6&-3&2\\-8&1&-4\\\end{vmatrix}=-40[/tex]

[tex]M_y = \left[\begin{array}{ccc}2&5&-1\\1&-6&2\\3&-8&-4\end{array}\right] \implies D_y = \begin{vmatrix}2&5&-1\\1&-6&2\\3&-8&-4\\\end{vmatrix}=120[/tex]

[tex]M_z = \left[\begin{array}{ccc}2&3&5\\1&-3&-6\\3&1&-8\end{array}\right] \implies D_z= \begin{vmatrix}2&3&5\\1&-3&-6\\3&1&-8\\\end{vmatrix}=80[/tex]

So, we have

[tex]$x=\frac{D_x}{D} =\frac{-40}{40}=-1 $[/tex]

[tex]$y=\frac{D_y}{D} =\frac{120}{40}=3$[/tex]

[tex]$z=\frac{D_z}{D} =\frac{80}{40}=2 $[/tex]

Answer:

D.  The line is dashed with a y-intercept at (0,-3) and slope of -.

Step-by-step explanation:

If you rearrange the inequality -3x-2y<6 to y=mx+b form you should get y>-3/2x-3

The slope would be mx or -3/2

The Y intercept would be b or -3

I hope this helps :)

The line with an inequality equation -3x - 2y < 6 when plotted on the graph, occupies a region with a dashed boundary line with the attributes, the slope m = -3/2, and the y-intercept c = -3.

An inequality equation for a line is the equation that is true for certain values of its variables. The inequality symbols are ' <, >, ≤, ≥ '.

When inequality is graphed,

The inequality equation is re-arranged in the slope-intercept form to know the attributes of the line such as the slope of the line and the y-intercept of the line.

The given inequality is -3x - 2y < 6

Step 1: Rewriting the equation into the slope-intercept form:

-3x - 2y < 6

To change the sign,  change the inequality symbol also.

⇒ 3x + 2y > 6

⇒ 2y > 6 - 3x

⇒ y > -3/2x - 3

Therefore, the obtained equation is in the slope-intercept form.

So, m = -3/2 and c = -3

Step 2: Graphing the inequality:

To graph the line, we need coordinates.

So, consider x = 0  inorder to get y-coordinate

On substituting,

-3(0) -2y = 6

y = -3

∴ (0, -3) is one of the coordinates of the line

Then, consider y = 0 inorder to get x-coordinate

On substituting,

-3x - 2(0) = 6

x = -2

∴ (-2, 0) is one of the coordinates of the line

These points are plotted in the graph and a line is drawn from these points.

Step 3: Observations from the graph:

Therefore, the attributes of the boundary line (dashed line) are slope -3/2 and y-intercept -3.

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Answer:

1.33

Step-by-step explanation:

Given that:

Upper specification limit ( USL ) = 10

Lower specification limit ( LSL ) =  2

the standard deviation σ =  1

What is the Cp"

The Cp is the process capability ratio which can be expressed by the formula:

[tex]C_P = \dfrac{USL -LSL}{6 \times \sigma}[/tex]

[tex]C_P = \dfrac{10 -2}{6 \times 1}[/tex]

[tex]C_P = \dfrac{8}{6}[/tex]

[tex]C_P = \dfrac{4}{3}[/tex]

[tex]C_P =1.33[/tex]

Answer:

true

Step-by-step explanation:

Answer:

0.1875

Step-by-step explanation:

The well formatted expression for the series has been attached to this response.

Each term in the series is govern by the rule, Tₙ

Where

n = term position

Tₙ = [tex]\frac{(-1)^{n+1}n}{2^n}[/tex]

To get the first six terms, we substitute n = 1 through 6 into Tₙ as follows:

When n = 1, we have;

T₁ = [tex]\frac{(-1)^{1+1}(1)}{2^1} = \frac{1}{2}[/tex] = 0.50000

When n = 2, we have;

T₂ = [tex]\frac{(-1)^{2+1}(2)}{2^2} = \frac{-2}{4} = \frac{-1}{2}[/tex] = -0.50000

When n = 3, we have;

T₃ = [tex]\frac{(-1)^{3+1}(3)}{2^3} = \frac{3}{8}[/tex] = 0.37500

When n = 4, we have;

T₄ = [tex]\frac{(-1)^{4+1}(4)}{2^4} = \frac{-1}{4}[/tex] = -0.25000

When n = 5, we have;

T₅ = [tex]\frac{(-1)^{5+1}(5)}{2^5} = \frac{5}{32}[/tex] = 0.15625

When n = 6, we have;

T₆ = [tex]\frac{(-1)^{6+1}(6)}{2^6} = \frac{-6}{64} = \frac{-3}{32}[/tex] = -0.09375

Therefore, the approximate sum of the series using the sum of the first six terms is

=> T₁ + T₂ + T₃ + T₄ + T₅ + T₆

=> 0.50000 + -0.50000 + 0.37500 + -0.25000 + 0.15625 + -0.09375

=> 0.1875

Answer:

D.  She added the wrong value to both sides of the equation to complete the square.

Step-by-step explanation:

Got it right on plato

The first error in Carly's work is instead adding 2² on both the side of an equation, she added 4².

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given equation is x(x+4)=117.

Here, x²+4x=117

Now, b/2 =4/2 =2

So, add 2² to both the sides of an equation, we get

x²+4x+2²=117+2²

⇒ x²+4x+4=117+4

⇒ (x+2)²=121

⇒ x+2=±√121

⇒ x+2=±11

⇒ x=±11-2

⇒ x=11-2=9 and x=-11-2=-13

The solution for the given a quadratic equation is x=9 and x=-13. Therefore, the first error in Carly's work is instead adding 2² on both the side of an equation, she added 4².

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Answer:    140°

Step-by-step explanation:

Heptagon is a seven-sided polygon. So heptagon has 7 angles.

As known the sum of the angles in poligon is

N=180°*(n-2)

So N(7)=180°*(7-2)=900°

if the sum of 2 angles are 200° then  the sum of residual 5 angles is

900°-200°=700°

The remaining 5 angles are equal so each of them is

∠α=700°:5=140°

Answer:

3.2 units

Step-by-step explanation:

Given that:

WY bisects UV at Y.

[tex]UV=x-7[/tex] and

[tex]YV = 3x-29[/tex],

To find: UV = ?

Solution:

First of all, let us draw the diagram of the given dimensions and bisector line WY of UV.

As UV is bisected i.e. divided in two equal parts at Y by the line WY

Therefore, UY = YV

UV = UY+YV

OR

UV = 2 YV

Now, let us put the given values to solve for [tex]x[/tex]:

[tex]x-7=2 \times (3x-29)\\\Rightarrow x-7=2 \times 3x-2 \times 29\\\Rightarrow x-7=6x-58\\\Rightarrow 6x-x=58-7\\\Rightarrow 5x=51\\\Rightarrow \bold{x =10.2 }[/tex]

Now, we are given that:

[tex]UV=x-7[/tex]

Putting value of [tex]x[/tex] as solved in above step to get the value of UV:

[tex]UV=10.2-7\\\Rightarrow \bold{UV=3.2}[/tex]

So, answer is UV = 3.2 units