7. x – a is the factor of a polynomial P(x) if P(a) is equal to

options:
A) 2
B) 1
C) 3
D) 0

Answer:

The domain of f is equal to x = log8 x.

Step-by-step explanation:

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:

  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:

yes

Step-by-step explanation:

2 = (3)(18) + (6)(7)

54 + 42 = (9)(10) + 6

54 + 42 = 90 + 6

O 54 + 42 = 6(9 + 7)

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:

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

Step-by-step explanation:

2 cups of sugar =5 cups of flour

1 cup of sugar =x cups of flour

2x=5

x=5/2

Answer:

(B) Between 6 and 9 minutes, Sameen's distance from work is decreasing

Step-by-step explanation:

Looking at the graph, we want to make sure we are looking at the right axis.

The x-axis, the horizontal one, is minutes.

The y-axis, the vertical one, is distance from work.

We can see that while x is between 6 and 9 minutes, the graph slopes downwards. This signifies a decrease in distance from work.

So between 6 and 9 minutes, Sameen's distance from work is decreasing.

Hope this helped!

Answer:

Between 6 and 9 minutes, Sameen's distance from work is decreasing

Step-by-step

Hey there! I'm happy to help!

Let's represent the number of days with x.

WAREHOUSE A

200-15x

WAREHOUSE B

80+25x

We want to find how many days it will take for the two warehouses to have the same amount of coal. Let's put these expressions into an equation to show that they are equal and see what x is.

200-15x=80+25x

We subtract 25x from both sides.

200-40x=80

We subtract 200 from both sides.

-40x=-120

We divide both sides by -40

x=3

Therefore, warehouse A and warehouse B will have the same amount of coal after 3 days.

Have a wonderful day! :D

Answer:

Y=1.25M

Step-by-step explanation:

Y represents the total amount of money being earn

1.25 is how much 1 lemonade drink cost

M represents the number of lemonade that was sold

The amount of lemonade sold time's How much each lemonade drink cost shall give you the total amount of money earn.

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:259,200 seconds

Step-by-step explanation:

24 hours in one day

1 hour= 60 minutes

1 minute =60seconds

60x60=3,600

3,600x24=86,400 seconds

86,400x3(days)=259,200 seconds

Answer:

Reflexive property

Step-by-step explanation:

The statement says that some number is equal to itself.

That's the reflexive property.

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:

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:

[tex]\huge \boxed{\mathrm{47\° C}}[/tex]

Step-by-step explanation:

The velocity is given as 358 meters per second.

358 = 20√(273 + t)

Solve for t.

Divide both sides by 20.

17.9 = √(273 + t)

Square both sides.

320.41 = 273 + t

Subtract 273 from both sides.

47.41 = t

Round to nearest degree.

t = 47°C

Answer:

A 95% confidence interval for the population mean is [3315.13, 22480.87] .

Step-by-step explanation:

We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~  [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample proportion of defective items = 12,898

             s = sample standard deviation = 7,719

            n = sample size = 5

             [tex]\mu[/tex] = population mean

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.776 < [tex]t_4[/tex] < 2.776) = 0.95  {As the critical value of t at 4 degrees of

                                               freedom are -2.776 & 2.776 with P = 2.5%}  

P(-2.776 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.776) = 0.95

P( [tex]-2.776 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.776 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.776 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.776 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.776 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.776 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                = [ [tex]12,898-2.776 \times {\frac{7,719}{\sqrt{5} } }[/tex] , [tex]12,898+2.776 \times {\frac{7,719}{\sqrt{5} } }[/tex] ]

                               = [3315.13, 22480.87]

Therefore, a 95% confidence interval for the population mean is [3315.13, 22480.87] .

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:

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.

Answer:

Step-by-step explanation:

Since we have the legs of the right angled triangle we can use Pythagoras theorem to find the hypotenuse

That's

where

h is the hypotenuse

From the question

The legs of the right angled triangle are 89cm and 38 cm

So the hypotenuse is

h = 96.7729

We have the final answer as

96.8 cm to the nearest tenth

Hope this helps you

Answer:

5

Step-by-step explanation:

Since, Left Hand Limit and Right Hand Limit at x = 2 are approximately equal to 5 at the point of discontinuity (x = 2), the limit of f(x) as x approaches 2 is 5.

Supplementary angles = 180

X = 180 - 37

X = 143

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.

Hi!

To find this, multiply 42, 21 and 360 first:

317520

Now, multiply 21 and 270:

5670

Now, divide 317520 by 5670:

56 days

(I've had problems like these before, this is how my teacher taught me to solve them. If you have any more trouble, try to use these steps!)

Hope this helps!

Step-by-step explanation:

-3(3)(2).

-3(6).

=-18.

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: 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:

67

Step-by-step explanation:

Evaluate 7 - 3 x where x = -20:

7 - 3 x = -3 (-20) + 7

Hint: | Multiply -3 and -20 together.

-3 (-20) = 60:

60 + 7

Hint: | Evaluate 60 + 7.

60 + 7 = 67:

Answer: 67

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!

;)