Using the identity. (a - b) ²= (a² - 2ab + b²), evaluate 699²​

Answer:

The third option.

Step-by-step explanation:

Mathematical induction is a 2 step mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number.

Step 1 (Base step) - It proves that a statement is true for the initial value.

Step 2 (Inductive step) - It proves that if the statement is true for the nth iteration (or number n), then it is also true for (n + 1)th iteration (or number n + 1)

Hope this helps.

Please mark Brainliest.

Answer:

A method of improving statments

Step-by-step explanation:

"Mathematical Induction is a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number."

Answer:

  17 by 21 inches

Step-by-step explanation:

The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...

  L + W = 38

  LW = 357

__

Solution:

  W(38 -W) = 357 . . . . . substitute for L

  -(W^2 -76W) = 357 . . expand on the left

  -(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square

  (W -19)^2 = 4 . . . . . . . write as a square

  W -19 = ±√4 = ±2 . . . take the square root; next, add 19

  W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other

The dimensions are 17 by 21 inches.

We have 26 letters and 3 slots to fill. We can reuse a letter if it has been picked, so we have 26^3 = 26*26*26 = 17,576 different three letter "words". I put that in quotes because a lot of the words aren't actual words, but more just a sequence of letters.

Answer:

Step-by-step explanation:

a) First differences of the f(x) values in the table are ...

  19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162

The second differences are not constant:

  18 -6 = 12, 54 -18 = 36, 162 -54 = 108

But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.

__

b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...

  9, 15, 33, 87, 249

__

c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...

  (x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)

Answer: I think this is it:

The parent function of the function represented in the table is exponential. If function f was translated down 4 units, the f(x)-values would be decreased by 4. A point in the table for the transformed function would be (4,87)

Step-by-step explanation: I got it right on Edmentum!

Answer:

25

Step-by-step explanation:

Let x represent the number of $50 jackets that were sold, and let y represent how many $30 jackets were sold.

50x + 30y = 2360

y = x + 12

Solve by substitution by substituting the second equation into the first one. Then, solve for x:

50x + 30y = 2360

50x + 30(x + 12) = 2360

50x + 30x + 360 = 2360

80x + 360 = 2360

80x = 2000

x = 25

So, 25 $50 jackets were sold.

Answer:

1/2

Step-by-step explanation:

The probailty of an event A is:

● P(A) = ( outcomes that give A) / (total number of possible outcomes)

Let A be the event in wich we get an even number.

● The sample space is {2,4,6}

So there are 3 possible outcomes that give A .

The six-sided dice has 6 outcomes

● { 1,2,3,4,5,6}

■■■■■■■■■■■■■■■■■■■■■■■■■■

● P(A) = 3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

i took the test

9514 1404 393

Answer:

Step-by-step explanation:

Put the numbers in place of the corresponding variables and do the arithmetic.

  √(2a) -b = √(2·8) -(-5) = 4 +5 = 9

  -3ac +2b = -3(8)(1/4) +2(-5) = -6 -10 = -16

  b² -8c = (-5)² -8(1/4) = 25 -2 = 23

Answer:

The answer is 20

Step-by-step explanation:

3 times 2 is 6, and 120 divided by six is 20%.

Answer:

[tex] {x}^{4} = 2880[/tex]

Step-by-step explanation:

[tex] {y}^{2} = 20 \: (eq . \: 1)[/tex]

[tex] {x}^{2} = {(2 \sqrt{3y)} }^{2} = 12y [/tex]

Putting value of eq. 1 in the following:

[tex] {x}^{4 } = {(12y)}^{2} = 144{y}^{2} = 144 \times 20 = 2880[/tex]

Answer:

x = 66.74715005725

Step-by-step explanation:

First you bring over the added variable. 0.194185, and subtract it from 66. Then you divide your difference by 0.985897. This gives you 66.74715005725

Answer:

1526.04

Step-by-step explanation:

the formula for calculating the volume of cone is

V=πr^2(h/3)

Thus,

V = (3.14)(9)^2(18/3)

V = (3.14)(81)(6)

V = 1536.04 yd^3

Rounding off to the nearest tenth, we get

V = 1536 yd^3

$2x+7$

according to the flow chart,

1. multiply [tex] x[/tex] by $2$, so $2x$

and then add seven to it so $2x+7$

note, if the order was reverse, i.e. first add seven ($x+7$). then multiply by two ($2(x+7)$)

the answer would be $2x+14$

The perimeter of a triangle is the summation of the three sides of the triangle. Base on the assumed values, the length of side BD is 2.

For [tex]\triangle ACD[/tex], the sides are: AC, AD and CD

So, the perimeter is:

[tex]P_{\triangle ACD} = AC + AD + CD[/tex]

For [tex]\triangle ABD[/tex], the sides are: AB, AD and BD

So, the perimeter is:

[tex]P_{\triangle ABD} = AB + AD + BD[/tex]

The difference in the perimeters is:

[tex]P_{\triangle ACD} - P_{\triangle ABD} =1 + \sqrt 3[/tex]

So, we have:

[tex](AC + AD + CD) - ( AB + AD + BD) =1 + \sqrt 3[/tex]

Open brackets

[tex]AC + AD + CD - AB - AD - BD =1 + \sqrt 3[/tex]

Evaluate like terms

[tex]AC + CD - AB - BD =1 + \sqrt 3[/tex]

Make BD the subject

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex]

The solution cannot be completed because the side lengths of [tex]\triangle ACD[/tex] and [tex]\triangle ABD[/tex] are not given; so, I will assume the following values.

[tex]AC =2; CD = 1; AB = \sqrt 3[/tex]

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex] becomes

[tex]BD = 2 + 1 + \sqrt 3 - (1 + \sqrt 3)[/tex]

Open bracket

[tex]BD = 2 + 1 + \sqrt 3 - 1 - \sqrt 3[/tex]

Evaluate like terms

[tex]BD = 2[/tex]

Base on the assumed values, the length of side BD is 2.

Read more about perimeters at:

https://brainly.com/question/6465134

Answer:

the probability will be 0.

Step-by-step explanation:

0.12%= 0.0012= 3/2500.

Answer:

A

Step-by-step explanation:

In the second step, they added 5 to both sides to get rid of the -5 on the left side. Since the same thing was done to both sides (addition), the answer is the addition property of equality.

Answer:

Addition property of equality

Step-by-step explanation:

The equation is like:

=> x - 5 = -14

=> x - 5 + 5 = -14 + 5

=> x = -9

Since, we add 5 to both sides to solve for "x", the answer is "Addition Property of Equality".

Hope this helps.

Answer:

simplest fraction: 2 1/3         the tick marks split the number into 7 regions

Step-by-step explanation:

The red heart is on the 2 tick mark of the 6 ticks between 2 and 3. The answer is 2 2/6 which after simplifying if equal to 2 1/3.

Answer:

16/7

Step-by-step explanation:

2-3 is devided into 7 segments if you make 2  14/7 and 3 21/7 then you have 16/7 with no common devisor other than 1

Answer: Midline equation: y = -7

Step-by-step explanation: This function is a sinusoidal function of the form:

y = a.cos(b(x+c))+d

Midline is a horizontal line where the function oscillates above and below.

In the sinusoidal function d represents its vertical shift. Midline is not influenced by any other value except vertical shift. For that reason,

Midline, for the function: [tex]h(x) = -4cos(5x-9) - 7[/tex] is y=d, i.e., [tex]y=-7[/tex]

Answer:

y=-7

Step-by-step explanation:

Answer:

the standard deviation of the sample is less than  0.1

Step-by-step explanation:

Given that :

The sample size n = 100 units

The average proportion of non-conforming windshield wipers is found to be 0.042 which is the defective rate P-bar

The standard deviation of the machine([tex]S_p[/tex]) can be calculated  by using the formula:

[tex]S_p =\dfrac{ \sqrt{ \overline P \times (1 - \overline P)} }{n}[/tex]

[tex]S_p =\dfrac{ \sqrt{0.042 \times (1 -0.042)} }{100}[/tex]

[tex]S_p =\dfrac{ \sqrt{0.042 \times (0.958)} }{100}[/tex]

[tex]S_p =\dfrac{ \sqrt{0.040236} }{100}[/tex]

[tex]S_p =\dfrac{ 0.2005891323 }{100}[/tex]

[tex]S_p =0.002[/tex]

Thus , the standard deviation of the sample is less than  0.1

Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P [tex](x_0,y_0,z_0)[/tex] is

[tex]z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\[/tex]

Now the partial derivatives of f are

[tex]f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}[/tex]

[tex]\\\\=\frac{1}{9-8}[/tex]

= 1

Now

[tex]f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}[/tex]

= -8

So, the tangent equation is

[tex]z - 0 = 1\times (x - 9) -8\times (y - 1)[/tex]

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

The equation of the tangent plane is [tex]x-8y-z=1[/tex]

An equation of the tangent plane to the given surface at the point [tex]P(x_0,y_0,z_0)[/tex] is,

[tex]z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)[/tex]

The function is,

[tex]z = ln(x-8y)[/tex]

And the point is (9,1,0)

Now, calculating [tex]f_x,f_y[/tex]

[tex]f_x(x,y)=\frac{1}{x-8y}\\ f_y(x,y)=\frac{x-8}{x-8y}[/tex]

Now, substituting the given points into the above functions we get,

[tex]f_x(9,1)=\frac{1}{9-8(1)}=1\\ f_y(x,y)=\frac{-8}{9-8(1)}=-8[/tex]

So, the equation of the tangent plane is,

[tex]z-0=1(x-9)-8(y-1)\\z=x-8y-1\\x-8y-z=1[/tex]

Learn more about the topic tangent plane:

https://brainly.com/question/14850585

Answer:

The value of x= 20

Step-by-step explanation:

I believe the question is ,"60% of x is us, find x"

So , if the percentage of x to 60 is 12.

60/100 * x = 12

0.6 *x = 12

Dividing both sides by 0.6

X= 12/0.6

X= (12/6) *(10)

X= 2*10

.x= 20

The value of x= 20

Answer:

[tex]x = \frac{1}{3} [/tex]

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒([tex]\frac{1}{3x}[/tex])

*rewrite to solve for x :

10⁰ = [tex]\frac{1}{3x}[/tex]

1 = [tex]\frac{1}{3x}[/tex]

1 · x = [tex]\frac{1}{3x}[/tex] · x

1x = [tex]\frac{1}{3}[/tex]

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x = [tex]\frac{1}{3}[/tex]

Answer:

-2x + 22

Step-by-step explanation:

We have the function f(x) = -1/2x + 11 and are asked to find the inverse of it.

To find the inverse, we will follow the according steps :

Let's do as followed:

Replacing x with y :

Since f(x) can be also written as y, we can do y = -1/2x + 11, thus making the switch alot easier.

y = -1/2x + 11

x = -1/2y + 11

Solve for y :

We have to get y alone to find the inverse, to do so, get rid of the outlier by subtracting 11 from both sides :

x - 11 = -1/2y

Now divide both sides by -1/2 to get y alone and retrieve our inverse :

-2(x - 11)

Distribute to get the inverse :

-2x + 22

Answer:

Step-by-step explanation:

The first one is true. There can't be any other choice.

a = 5959599949 b = 0 then a*b = 0 because b = 0

The Second one is also true, although you may stall trying to figure out what is meant.

Suppose the angle to start with is 30 degrees

There are two angles that are supplementary to this angle. They can only be 180 - 30 = 150 each. Therefore they are equal to each other. This happens because supplementary angles must add to 180 and nothing else.

The third one is false. You can think of states like Montana which has 3 syllables and Wyoming which also has 3. Texas has two. But guess what? Maine only has 1.

The last one is also false. If you square an even number, you get an even number. Add 1 and you get an odd number. 4^2 = 16 Add 1 you get 17. Seventeen is odd.

Without knowing what Juan's exact steps were, it's hard to say what he did wrong. The least you could say is that his solution is simply not correct.

4 sin²(θ) - 1 = 0

==>   sin²(θ) = 1/4

==>   sin(θ) = ±1/√2

==>   θ = π/4, 3π/4, 5π/4, 7π/4

Answer:

4 · 1/4 (I-0) = (A-0)∧2

see details in the graph

Step-by-step explanation:

Matrix A is expressed in the form A∧2=I

To proof that Matrix A is both orthogonal and involutory, if and only if A is symmetric is shown by re-expressing that

A∧2=I in the standard form

4 · 1/4 (I-0) = (A-0)∧2

Re-expressing

A∧2 = I as a graphical element plotted on the graph

X∧2=I

The orthogonality is shown in the graphical plot displayed in the picture. Orthogonality expresses the mutually independent form of two vectors expressed in their perpendicularity.

Answer:

Step-by-step explanation:

if we shift 13 units right and 6 units down we get the reqd. graph.

Answer:

see explanation

Step-by-step explanation:

Given the graph of f(x) then f(x + k) is a horizontal translation of f(x)

• If k > 0 then shift left by k units

• If k < 0 then shift right by k units

Thus y = (x - 13)² represents a shift to the right of 13 units

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Thus

y = (x - 13)² + 6 is the graph of y = x² translated 13 units right and 6 units up

Answer:

Step-by-step explanation:

102-8= 94

94/2= 47

Jiri is 47 years old.

Answer:

49

Step-by-step explanation:

sin(theta) = P/H

sin(28)=23/x, x=23/sin(28)=49

Answer:

12,18, and 72 respectively

Step-by-step explanation:

102=A+H+D

A+6=H

D=4H=4(A+6)=4A+24

102=A+H+D=A+A+6+4A+24

102=6A+30

6A=72

A=12

H=18

D=72

Answer:

The 99% confidence interval is  [tex]71.67 < \mu < 78.33[/tex]

Step-by-step explanation:

From the question we are told that

     The sample  size  is  [tex]n = 15[/tex]

      The  sample  mean is  [tex]\= x = 75[/tex]

        The  standard deviation is  [tex]s = 5[/tex]

 Given that confidence is  99%  then the level of significance is mathematically represented as

              [tex]\alpha = 100 - 99[/tex]

             [tex]\alpha = 1\%[/tex]

             [tex]\alpha = 0.01[/tex]

Next we obtain the critical values of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table

   The  value is

                  [tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]

Generally the margin for error is mathematically represented as

            [tex]E = Z_{\frac{ \alpha }{2} } * \frac{ s}{ \sqrt{n} }[/tex]

=>         [tex]E = 2.58 * \frac{ 5}{ \sqrt{15} }[/tex]

=>         [tex]E = 3.3307[/tex]

   The  99% confidence interval is mathematically represented as

             [tex]\= x -E < \mu < \= x +E[/tex]

=>          [tex]75 - 3.3307 < \mu <75 + 3.3307[/tex]

=>          [tex]71.67 < \mu < 78.33[/tex]