Pedro solves the quadratic equation x^2+6x –14 using the quadratic formula. In which step did Pedro make an error?

Answer:

(8, 11π/6)

Step-by-step explanation:

r= √(4√3)²+(-4)² = √48+16=√64=8

0 = tan~¹ -4/(4√3)

= tan~¹ -⅓√3 = 330° = 11π/6

the polar coord. => (8, 11π/6)

9514 1404 393

Answer:

  8∠11π/6

Step-by-step explanation:

To simplify the way we talk of this number, we will refer to it as a vector. We'll assume its head is at the given coordinates, and its tail is at the origin. The magnitude of the vector is the root of the sum of the squares of its components:

  [tex]\displaystyle r=\sqrt{x^2+y^2}=\sqrt{(4\sqrt{3})^2+(-4)^2}=\sqrt{48+16}=\sqrt{64}\\\\r=8[/tex]

The angle of the vector with respect to the +x axis is ...

  [tex]\theta=\arctan{\dfrac{y}{x}}\qquad\text{a 4-quadrant arctangent}\\\\\theta=\arctan{\dfrac{-4}{4\sqrt{3}}}=-\arctan{\dfrac{1}{\sqrt{3}}}\qquad\text{a 4th-quadrant angle}\\\\\theta=\dfrac{11\pi}{6}[/tex]

In magnitude∠angle notation, the polar coordinates are ...

  (4√3, -4)  ⇔  8∠(11π/6) . . . . . θ in radians

_____

Additional comment

Spreadsheets generally have an ATAN2(x, y) function that will return a 4-quadrant version of the angle. The usual ATAN( ) function will give the angle only in quadrants I or IV.

Some graphing calculators may also have the ATAN2 function. Some will simply do the entire conversion for you, without any need to deal separately with magnitude and angle. (You may need to write the number as a complex number, x +iy.)

Answer:

Plot B

Step-by-step explanation:

Plot B has a negative slope.

Answer:

This is decay. The exponent has a negative sign. The reciprocal of 2 is 0.5. So N(t) can be rewritten as 0.5^(t/8). The base is fraction less than 1, which is decay.

Step-by-step explanation:

sample response on edgen 2022

Answer:

The correct approach will be "0.612580".

Step-by-step explanation:

Given:

Randomly selected customers,

n = 10

Probability of recognition,

p = 90%

or,

  = 0.9

q = 1 - p

  = 1 - 0.9

  = 0.1

Now,

The probability that 9 out of 10 clients are likely to be familiar with the brand will be:

⇒ [tex]P(X=r)=nCr\times (p)^r\times (q)^{(n-r)}[/tex]

⇒ [tex]P(X=9)=10C_9\times (0.9)^9\times (0.1)^{(10-9)}[/tex]

                    [tex]=10C_9\times (0.9)^9\times (0.1)^1[/tex]

                    [tex]=10\times (0.9)^9\times 0.1[/tex]

                    [tex]=0.387420[/tex]

hence,

The probability that not nine seem to be the numbers recognizing her brand name will be:

⇒ [tex]P(X=not \ 9)=1-P(X=9)[/tex]

                          [tex]=1-0.387420[/tex]

                          [tex]=0.612580[/tex]

Answer:

(a) [tex]Area = 14.7824cm^2[/tex]

(b) [tex]Area = 118.2592cm^2[/tex]

(c) [tex]Area = 4nh[/tex]

Step-by-step explanation:

Given

[tex]\theta = 67.5[/tex]

[tex]b= 8cm[/tex] --- base

[tex]n = 8[/tex] --- triangles

Solving (a) The area of each triangle

First, calculate the height (h) of each triangle using:

[tex]\sin(67.5) = \frac{h}{b/2}[/tex] --- i.e. we consider half of the triangle

[tex]\sin(67.5) = \frac{h}{8/2}[/tex]

[tex]\sin(67.5) = \frac{h}{4}[/tex]

Solve for h

[tex]h =4*\sin(67.5)[/tex]

[tex]h =4*0.9239[/tex]

[tex]h =3.6956[/tex]

The area of each triangle is:

[tex]Area = \frac{1}{2} *b * h[/tex]

[tex]Area = \frac{1}{2} *3.6956 * 8[/tex]

[tex]Area = 14.7824cm^2[/tex]

Solving (b): Area of the octagon

This is calculated as:

Area = 8 * area of 1 triangle

[tex]Area = 8 * 14.7824cm^2[/tex]

[tex]Area = 118.2592cm^2[/tex]

Solving (c): Area of octagon of side length n

In (a), we have:

[tex]Area = \frac{1}{2} *b * h[/tex]

Replace b with n

[tex]Area = \frac{1}{2} *n * h[/tex]

Multiply by 8 (the sides) to get the area of the octagon

[tex]Area = 8 * \frac{1}{2} *n * h[/tex]

[tex]Area = 4nh[/tex]

Answer: 7

Step-by-step explanation: 7+7=14

Answer:

B. 500

Hope this helps!! :D

Answer:

The answer is B

explanation:

78.8 is nearly 80 and 6.8 is nearly 7

so an estimate would be 80 × 7

= 560

Answer:

Number of biscuit needs = 28 packets

Number of Pemmican needs = 18 packets

Number of Butter cocoa needs = 4 packets

Step-by-step explanation:

GIven:

Total calorie required = 5,600 calories

Biscuits 80 (Calorie per packet) 40% of total diet

Pemmican 140 (Calorie per packet) 45% of total diet

Butter cocoa 210 (Calorie per packet) 15% of total diet

Find:

Number of biscuit, Pemmican and butter cocoa need

Computation:

Number of biscuit needs = [5,600(40%)]/80

Number of biscuit needs = [2,240]/80

Number of biscuit needs = 28 packets

Number of Pemmican needs = [5,600(45%)]/140

Number of Pemmican needs = [2,520]/140

Number of Pemmican needs = 18 packets

Number of Butter cocoa needs = [5,600(15%)]/210

Number of Butter cocoa needs = [840]/210

Number of Butter cocoa needs = 4 packets

Answer:-5

Step-by-step explanation:

Hello!

-6-4/2 = -10/2=-5

Hope this helps, have a great day!

Answer:

1/4

Step-by-step explanation:

Total number of plants,

= 13 + 2 = 15

Number of plants in a row = 3

Hence, Total Number of rows,

Therefore, he will have five rows.

Answer:

1/2

Step-by-step explanation:

According to pythagoras theorem;

(sinx)²+(cosx)² = 1

Given that sinФ = √3/2

Substitute into the formula

(√3/2)²+(cosx)² = 1

3/4+(cosx)² = 1

(cosx)² = 1 - 3/4

(cosx)²  = 1/4

cos x = √1/4

cos x = 1/2

Hence the value of cosФ is 1/2

Answer:

<5, <1

Step-by-step explanation:

.............

........

Answer:

5

Step-by-step explanation:

Given :

Observed values = 5, 10, 15

Expected freqencies = 10

χ² = Σ(observed - Expected)² / Expected

χ² = (5-10)²/10 + (10-10)²/10 + (15-10)²/10

χ² = 25/10 + 0/10 + 25/10

χ² = 2.5 + 0 + 2.5

χ² = 5

Answer:

-5+(-7)+9+(-3) = -6

Step-by-step explanation:

We need to add the following i.e.

-5+(-7)+9+(-3)

We know that, +(-) = - (minus)

So,

-5-7+9-3 = -12+6

= -6

So, the value of the given expression is equal to -6.

Answer:

x-6+6(6+6+6)X I am a pro boiiiiii

Step-by-step explanation:

We can set up the ration of the radian angle θ in your problem in terms of degrees given as the ratio: (Θ/2·pi) = (72/360), solving for Θ we get Θ = 1.26 radians. Then for the arc length s = Θ·r using this value gives s = 1.26·4 = 5.04

Answer:

The equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is [tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex].

Step-by-step explanation:

A sphere is described by its radius and center, the radius of the largest sphere contained in the first octant are determined by the least distance of the center with respect to an orthogonal axis, that is:

Distance regarding x-axis:

[tex]d_{x} = 10 - 0[/tex]

[tex]d_{x} = 10[/tex]

Distance regarding y-axis:

[tex]d_{y} = 8 - 0[/tex]

[tex]d_{y} = 8[/tex]

Distance regarding z-axis:

[tex]d_{z} = 7 - 0[/tex]

[tex]d_{z} = 7[/tex]

Hence, the radius of the sphere must have a measure of 7. The equation of the sphere is represented by the following geometric locus:

[tex](x-h)^{2} + (y-k)^{2} + (z - j)^{2} = r^{2}[/tex] (1)

Where:

[tex]h, k, j[/tex] - Coordinates of the center.

[tex]r[/tex] - Radius of the sphere.

If we know that [tex](h,k,j) = (10, 8, 7)[/tex] and [tex]r = 7[/tex], then the equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is:

[tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex]

Answer: b= - -log10(7)+3/2

Step-by-step explanation: log 10 (7) -2b-9=-6 : b= - -log10(7)+3/2 (Decimal : b = -1.07745...)

so these are the steps how I got it I did log 10 (7)-2b-9=-6 subtract log 10 (7) -9 from both sides log 10 (7)-2b-9-(log10(7)-9)=-6-(log 10 (7) -9)

Simplify -2b= -log10(7)+3

Divide both sides by -2  -2b/2= - log 10(7)/-2+ 3/-2 if you simplify it should give you b= - -log10(7)+3/2 that should be your answer but i'm not sure those I think that's how you do it let me know if you got it right bye!

Answer:

72ft^3

Step-by-step explanation:

I first took a single slice off the box and counted how many cubes there were. By looking at the blue side, I counted 12 cubes in that slice. I then counted how many slices were in the box, which were 6.

12* 6 = 72ft^3

Answer:

[tex]\frac{37}{28}[/tex] miles

Step-by-step explanation:

Use the area formula, A = lw, where l is the length and w is the width.

Plug in the area and length into the formula, and solve for w:

A = lw

37 = 28w

37/28 = w

So, as a fraction, the width of the garden is [tex]\frac{37}{28}[/tex] miles

Answer:

37/28 =w

Step-by-step explanation:

Area for a rectangle is given by

A = l*w

Substitute in what we know

37 = 28*w

Divide each side by 28

37/28 = 28w/28

37/28 =w

Answer: [tex]\dfrac{2}{65}[/tex]

Step-by-step explanation:

Given

There is a six letter word with no repeated letters

Number of ways of arranging 6 letters out of 26 letters is [tex]^{26}P_6[/tex]

For the 6 letter word with vowels in the beginning and the end can be formed by selecting 2 vowels out of 5 available.

First place has 5 choices to fill and the last place left with 4 choices to fill

Remaining 4 places can be filled by [tex]^{24}P_4[/tex] ways

So, the required probability is given by

[tex]\Rightarrow \dfrac{5\times ^{24}P_4\times 4}{^{26}P_6}=\dfrac{2}{65}[/tex]

Answer:

18x^3sqrt(7)

Step-by-step explanation:

14x^3sqrt(7)+4x^3sqrt(7); factor our 4 in the first radical and factor out x^6 in both radicals

Add like terms;

18x^3sqrt(7).

9514 1404 393

Answer:

  equation: y = 4x

  graph is attached

Step-by-step explanation:

Let y represent the cost of the peaches in dollars. Let x represent their weight in pounds. Then the relation between the two variables is ...

  cost = (cost per pound) × (pounds)

  y = 4x

__

This graphs as a line through the origin with a slope of 4. In the attached, the x- and y-axes have different scales so more of the graph can be seen.

Answer:

11/20 cups left

Step-by-step explanation:

first, we need to convert 3/4 and 1/5 into fractions with common denominators

so we would have:

15/20 and 4/20

now we need to subtract the fractions to get the difference

so we would do:

15/20 - 4/20 = 11/20

and that's the answer

hope that helped

Answer:

11/20 cup

Step-by-step explanation:

3/4 - 1/5

use common denominator of 20

15/20 - 4/20

11/20 cup

Answer:

(c) No; There is an exponent on a variable x that is not a whole number

Step-by-step explanation:

Given

[tex]f(x) = x^2 - \sqrt[5]{x}[/tex]

Required

Determine if the function is a polynomial function of not

A polynomial function is represented as:

[tex]f(x) =ax^n + bx^{n-1} + cx^{n-2}+........+z[/tex]

Where n is an integer and the least power is 0

So, we have:

[tex]f(x) = x^2 - \sqrt[5]{x}[/tex]

The degree of x is [tex]\frac{1}{5}[/tex] ----- i.e. not an integer

Hence, the function is not a polynomial

Answer:

9 ft by 9 ft

Step-by-step explanation:

Answer:

length of 9 ft; width of 9 ft

Step-by-step explanation:

It is because you see it says it is square storage, which means its length and width have to be the same, and when you do 607.5 divided by 7.5, you get 81 which you can guess is a length of 9 ft; width of 9 ft because 9 x 9 equals to 81. I hope it helps! :)