x-4[x-2(x+6)]=5x+3
[tex]x - 4 [ x - 2(x + 6)] = 5x + 3[/tex]


​

See below for the missing terms of the sequences

The given parameters are:

T4 = 30

T5 = 49

Calculate the third term as follows:

T3 = T5 - T4

T3 = 49 - 30

T3 = 19

Calculate the second term as follows:

T2 = T4 - T3

T2 = 30 - 19

T2 = 11

Calculate the first term as follows:

T1 = T3 - T2

T1 = 19 - 11

T1 = 8

Hence, the first term of the sequence is 8

The given parameters are:

T2 = x

T3 = y

Calculate the first term as follows:

T1 = T3 - T2

T1 = y - x

Calculate the fourth term as follows:

T4 = T2 + T3

T4 = x + y

Calculate the fifth term as follows:

T5 = T3 + T4

T5 = y + x + y

T5 = x + 2y

Hence, the missing terms of the sequence are y - x, x + y and x + 2y

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[tex]f(x) = \sqrt{1 - 4{ x}^{2} } [/tex]

[tex]1 - 4x {}^{2} \geqslant 0[/tex]

[tex] - \infty \: \: \: \: \: \: \: \: - 0.5 \: \: \: \: \: \: \: \: \: 0.5 \: \: \: \: \: \: \: \: \infty \\ - \: \: \: \: \: \: \: \: \: \: \: \: \: \:0 \: \: \: \: \: + \: \: \: \:0 \: \: \: \: \: - [/tex]

[tex]domain \\ [ \: -0.5 \: , \: 0.5 \: ][/tex]

[tex]g(x) = 1 - 4x {}^{2} \\ g'(x) = - 8x \\ g'(x) = 0 \\ x = 0 \\ g(0) = 1 - 4(0) = 1 \\ maximum \: = 1[/tex]

[tex]range \\ [ \: 0 \: , \: 1 \: ][/tex]

Answer:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

[tex]\textsf{Range}: \quad [0, 1][/tex]

Step-by-step explanation:

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

Given function:

[tex]f(x)=\sqrt{1-4x^2}[/tex]

As negative numbers don't have real square roots:

[tex]\implies 1-4x^2\geq 0[/tex]

Therefore, to find the domain, solve the inequality.

Subtract 1 from both sides:

[tex]\implies -4x^2\geq -1[/tex]

Divide both sides by -1 (reverse the inequality):

[tex]\implies 4x^2 \leq 1[/tex]

Divide both sides by 4:

[tex]\implies x^2\leq \dfrac{1}{4}[/tex]

[tex]\textsf{For }\:a^n \leq b,\:\:\textsf{if }n\textsf{ is even then }-\sqrt[n]{b} \leq a \leq \sqrt[n]{b}:[/tex]

[tex]\implies -\sqrt[2]{\dfrac{1}{4}} \leq x \leq \sqrt[2]{\dfrac{1}{4}}[/tex]

[tex]\implies -\sqrt{\dfrac{1}{4}} \leq x \leq \sqrt{\dfrac{1}{4}}[/tex]

[tex]\implies -\dfrac{1}{2} \leq x \leq \dfrac{1}{2}[/tex]

Therefore:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

To find the range, input the endpoints of the domain into the function:

[tex]\implies f\left(-\dfrac{1}{2}\right)=\sqrt{1-4\left(-\dfrac{1}{2}\right)^2}=0[/tex]

[tex]\implies f\left(\dfrac{1}{2}\right)=\sqrt{1-4\left(\dfrac{1}{2}\right)^2}=0[/tex]

To find the limit of the range, find the extreme point(s) of the function by differentiating the function and setting it to zero.

[tex]\implies f(x)=(1-4x^2)^{\frac{1}{2}}[/tex]

[tex]\implies f'(x)=\dfrac{1}{2}(1-4x^2)^{-\frac{1}{2}} \cdot -8x[/tex]

[tex]\implies f'(x)=-\dfrac{4x}{\sqrt{1-4x^2}}[/tex]

Setting it to zero and solving for x:

[tex]\implies -\dfrac{4x}{\sqrt{1-4x^2}}=0[/tex]

[tex]\implies -4x=0[/tex]

[tex]\implies x=0[/tex]

Substitute x = 0 into the function:

[tex]\implies f(0)=\sqrt{1-4(0)^2}=1[/tex]

Therefore, the range is [0, 1]

Answer:

B. ABCD is a trapezoid because it has at least

one pair of parallel sides.  

Step-by-step explanation:

the two points A(-3,-1) and D(5,-1) have the same y-coordinates

Then

The line AD is parallel to the x-axis

On the other hand,

the two points B(1,5) and C(5,5) have the same y-coordinates

Then

The line BC is parallel to the x-axis.

We obtain :

• AD is parallel to the x-axis

• BC is parallel to the x-axis.

Therefore

AD // BC

Conclusion:

ABCD is a trapezoid because it has at least

one pair of parallel sides. 

Answer:

b

Step-by-step explanation:

plato

The proof that the diagram is a square is that; D: slopes are perpendicular where the sides meet

We know that a square is a quadrilateral that has 4 sides. Now, the 4 sides of a square are all equal and at right angles.

Since all sides of the square are equal, then it means that 2 consecutive sides must be perpendicular to each other. Thus, this means that the slope of 2 consecutive sides must be perpendicular to each other.

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Considering the given equations for revenue and cost, the company will break-even when 356 widgets are sold.

The break-even point is the value of x for which:

R(x) = C(x).

In this problem, the functions are:

Hence:

R(x) = C(x)

16x = 12x + 1424

4x = 1424

x = 1424/4

x = 356

The company will break-even when 356 widgets are sold.

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The value of the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex] after substituting y = 7 is 108

The given expression is:

[tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex]

Simplifying the expression, we have:

[tex]2+4+y^2+4+y^2\\\\2y^2+10[/tex]

Substitute y = 7 into the simplified expression

[tex]2(7)^2+10\\\\=2(49)+10\\\\=98+10\\\\=108[/tex]

Therefore, after substituting y = 7, into the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex], the resulting value is 108

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Answer: -1

Step-by-step explanation: khan academy

The area of the rectangular field is 468cm².

Step-by-step explanation:

If, length is 18cm; width is unknown( let x represent width). Then,

Perimeter of a rectangle= Length + Width+ Length + Width

88= 18 + x + 18 + x

88= 36 + 2x

88-36 =2x

52= 2x

52/2=2x/2

26=x

•x=26cm

The width of the rectangle is 26cm.

Area of a rectangle= Length × Width

=18cm×26cm

= 468cm².

Answer:  [tex]\frac{\sqrt{7}}{7}[/tex]

========================================================

Explanation:

The reciprocal of x is 1/x where x is nonzero. Multiplying x with 1/x leads to 1. For example, the numbers 9 and 1/9 are multiplicative inverses of each other.

We'll stick 1 over the given square root expression. Then follow these steps to rationalize the denominator.

[tex]\frac{1}{\sqrt{7}}\\\\\\\frac{1*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\\\frac{\sqrt{7}}{(\sqrt{7})^2}\\\\\\\frac{\sqrt{7}}{7}\\\\[/tex]

In short, [tex]\frac{1}{\sqrt{7}}=\frac{\sqrt{7}}{7}[/tex]

The sweatshirt size which the vendor should bring more of by virtue of that which is most likely to be sold is; Choice A; Extra-large.

If follows from the task content that the

ratio of extralarge shirts sold relative to the quantity he had to sell is

= 99/108

= 11/12,

This is a ratio which is larger than any other shirt.

Consequently, the vendor must bring more of the X-large shirts to avoid running out of them.

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The graph of function f is shifted right 3 units and up 4 units.

Let f(x) be the parent function

Now use the Rule : f(x)→f(x-b) to find the shifting of graph

The graph shifts right by b units

So, shift the graph by 3 unit

So, f(x)→f(x-3)

So, the graph shifted right by 3 units

2nd rule used is Rule : f(x)→f(x)+b to find the another shifting of graph

The graph shifts up by b units

Now shift the obtained graph up by 4 units

So,  f(x-3)→f(x-3)+4

So, the graph shifts up by 4 units

Thus, The graph of function f is shifted right 3 units and up 4 units.

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Answer:  True

Explanation:  Parallel lines are two lines that lie on the same plane and they never intersect.  

Answer: 36

Step-by-step explanation:

As this is a two-digit number, it will have a digit in its 10's place and a digit in its 1's place. We can represent the 10's digit using x and the 1's digit using y.

Since the ones is twice the number of tens, this means that y is equal to 2*x. Let's put this into an equation.

[tex]y=2x[/tex]

If the 10's digit is x and the 1's digit is y, the original number would be [tex]10x + y[/tex], as x must be multiplied by 10 to get it to the 10's place. Similarly, the reversed number would be [tex]10y + x[/tex], as y must be multiplied by 10 to get it to the 10's place.

Twice the original number (10x+y) is equal to 9 more than (i.e. 9 plus) the reversed number. We can put this into an equation to help us answer the question.

[tex]2(10x+y)=9+10y+x\\20x+2y=9+10y+x\\19x+2y=9+10y\\19x=9+8y[/tex]

Now we have a system of two equations.

[tex]y=2x\\19x=9+8y[/tex]

We can solve this system by substituting y for 2x in the second equation. Then, we can isolate and get the value of x.

[tex]19x=9+8(2x)\\19x=9+16x\\3x=9\\x=3[/tex]

Now that we have the value of x, let's put it back into the first equation and solve for y.

[tex]y=2(3)\\y=6[/tex]

Remember that x is the 10's digit and y is the one's digit of our answer. Since x is 3 and y is 6, our answer is 36.

We can quickly check if our answer is right by making sure both conditions in the question are met.

6 (the one's digit) is twice the value of 3 (the ten's digit), making the first condition true. Twice of 36 is 72, which is 9 more than the reversed number, which is 63.

The fraction computed shows that the total inches the infant grew over the three months is 3 3/4 inches.

First month = 2/4 inches

Second month = 1 inch

Third month = 7/4 inches.

The total inches the infant grew over the three months will be;

= 2/4 + 1 + 7/4

= 3 1/4 inches.

The difference in the infants from the second month to the third month will be:

= 7/4 - 1

= 3/4 inches.

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The list price of the house is $260,869.57

What is a list price?

This is the price the property is valued to sell at in an arm's length transaction in a transaction that occurs between independent parties.

In this case, the property was sold for 92% of its list price, which means the sales price is 92% multiplied by the list price.

sales price=92%* list price

sales price=$240,000

list price=unknown(assume it is X)

$240,000=92%*X

X=$240,000/92%

X=$260,869.57

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a)

b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights

c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on

d) sample size [tex]n \approx 27[/tex].

Generally,
Here n = 17

T= 3.15

[tex]\sigma=0.40[/tex]

confidence level =c = 0.80

Here we will usethe  z critical value.

z critical value for (1+c) /2 = (1+0.80)/2

z critical value for (1+c) /2= 0.9

Zc = 1.28

Critical value = 1.28

a) Margin of error (E) :

[tex]E = Zc*\frac{\sigma}{\sqrt{n}}\\\\\E = 1.28*\frac{0.40}{\sqrt{17}}[/tex]

E =0.124

Margin of error = E =0.124

Lower limit = x-E

L= 3.15 - 0.124

L= 3.026

Lower limit =3.026

Upper limit = x + E

U= 3.15 + 0.124

U= 3.274

Upper limit =  3.274

The following is a confidence interval with a value of 80 percent for the mean weights of Allen's hummingbirds in the area under study: (3.02,3.28)

b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights

c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on.

d) When is already known, the following equation may be used to determine the appropriate number of samples, n:

[tex]n=(\frac{z_c*\sigma }{E})^2[/tex]

Margin of error = 0.13

Sample size (n):

[tex]n= (\frac{z_c*\sigma }{E})^2[/tex]

[tex]n=(\frac{ 1.28*0.36}{0.09})^2[/tex]

n = 26.21

[tex]n \approx 27[/tex]

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Based on the width of the aluminum sheets and the angle of the edges, the depth that allows maximum cross-sectional area is 4 inches.

Assuming that the depth is x, the area would be:

= x (16 - 2x)

= 16x - 2x²

The maximum of the parabola is:

x = -b / 2a

= - 16 / (2 x -2)

= -16 / -4

= 4 inches

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The volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.

To find the volume of the solid generated, we use the shell method since the cross-sections are parallel to the axis of rotation.

So, [tex]V = 2\pi\int\limits^a_b {xy} \, dx[/tex]

Now given that  the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis.

So, we integrate from x = 0 to x = 2.

[tex]V = 2\pi\int\limits^a_b {xy} \, dx\\= 2\pi\int\limits^2_0 {x(x^{2} + x)} \, dx\\= 2\pi\int\limits^2_0 {(x^{3} + x^{2} )} \, dx\\= 2\pi\int\limits^2_0 {x^{3} + 2\pi\int\limits^2_0 x^{2} } \, dx\\= 2\pi[\frac{x^{4} }{4}]_{0}^{2} + 2\pi[\frac{x^{3} }{3}]_{0}^{2} \\= 2\pi[\frac{2^{4} - 0^{4} }{4}}]+ 2\pi[\frac{2^{3} - 0^{3} }{3}]\\= 2\pi[\frac{16 - 0}{4}}]+ 2\pi[\frac{8 - 0}{3}]\\= 2\pi[\frac{16}{4}}]+ 2\pi[\frac{8}{3}]\\= 2\pi (4)+ [\frac{16\pi}{3}]\\= 8\pi + [\frac{16\pi}{3}]\\[/tex]

[tex]= \frac{24\pi + 16\pi}{3} \\= \frac{40\pi}{3}[/tex]

So, the volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.

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The attached image shows the image of A"B"C" after the transformation

The transformation rule states:

A"B"C" = Ro90° (T(-4,3)(ABC))

This implies that one need to rotate the triangle in a 90⁰ clockwise direction, and then one need to translate the triangle.

Using the image shown, the coordinates of ABC are;

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The 90⁰ rule clockwise rotation  will be:

(x,y) -- (y,-x)

So, when translated, it will be:

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

Then the translation of the triangle using T(-4,3):

(x, y) -  (x - 4, y + 3)

So, there is:

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

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The following expressions set up as an equation to solve for the unknown numbers in the cases given below:

let

5x + 6 = 46

5x = 46 - 6

5x = 40

x = 40/5

x = 8

2/3x - 5 = 11

2/3x = 11 + 5

2/3x = 16

x = 16 ÷ 2/3

x = 16 × 3/2

x = 48/2

x = 24

1/3x + 4 = 45

1/3x = 45 - 4

1/3x = 41

x = 41 ÷ 1/3

x = 41 × 3/1

x = 123

3x - 12 = 18

3x = 18 + 12

3x = 30

x = 30/3

x = 10

40 - 2x = 16

-2x = 16 - 40

-2x = -24

x = -24/-2

x = 12

(x + 18) / 6 = 7

(x + 18) = 7 × 6

x + 18 = 42

x = 42 - 18

x = 24

2/3x - 8 = 6

2/3x = 6 + 8

2/3x = 14

x = 14 ÷ 2/3

x = 14 × 3/2

= 42/2

x = 21

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The probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.

When a random variable X is normally distributed, with the mean as μ, and standard deviation as σ, then the probability P(X < x) is calculated using the Z-score table, as the probability P(Z < z), where z is calculated using the formula, z = (x - μ)/σ.

In the question, we are asked to find the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12.

We calculate as follows:

P(X < 105)

= P(Z < (105-90)/12)

= P(Z < 1.25)

Now we check the z-score table for the value of z as 1.25.

On the left column we choose the value 1.2.

On the top row, we choose the value .05.

The intersection of these, gives us the value,

P(Z < 1.25) = 0.8944.

Thus, the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.

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Answer:

Step-by-step explanation:

3 things of triangle are given.

2 sides + 1 angle

so, possible triangles = 1 ans

The total value of the investment is $107,032.16.

The total interest earned is $53,032.16

The inheritance would last the tenure of the university.

The formula that can be used to determine the future value of the 18-year annuity is: annuity factor x amount deposited yearly

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$3000 x [(1.075^18 - 1) / 0.075] = $107,032.16

Amount deposited in the course of 18 years = (3000 x 18) = 54,000

Interest earned = 107,032.16 - 54,000 = $53,032.16

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The height of the ramp above the ground is 1.55 meters.

The difference between the height of the tree is 33.20 meters

The situation forms a right angle triangle.

Therefore, the height the ramp above the ground can be calculated as follows:

Using Pythagoras theorem,

sin 15  = opposite / hypotenuse

sin 15 = x / 6

cross multiply

x = 6 sin 15

x = 6 × 0.2588190451

x = 1.55291427062

x = 1.55

Therefore, the height of the ramp above the ground is 1.55 meters

tan 36  = opposite / adjacent

tan 36 = x / 60

x = 60 tan 36

x = 43.5925516803

x = 43.60 meters

tan 52 = y / 60

60 tan 52 = y

y = 76.7964979316

y = 76.79 meters

The difference between the height of the tree = 76.79 - 43.60 = 33.20 meters

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The equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

[tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex]

Evaluate the product

[tex]7 * 6x^2 \sqrt{2x^4*2x^{12 }[/tex]

This gives

[tex]42x^2 \sqrt{4x^{16}[/tex]

Take the square root of 4

[tex]2*42x^2 \sqrt{x^{16}[/tex]

Take the square root of x^16

[tex]2*42x^2 *x^8[/tex]

So, we have:

[tex]84x^{10[/tex]

Hence, the equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

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Answer:

Step-by-step explanation:

The equivalent expression of  is

How to determine the equivalent expression?

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

Evaluate the product

This gives

Take the square root of 4

Take the square root of x^16

So, we have:

Hence, the equivalent expression of is

Answer:

f(x)⁻¹ = (x - 11)²

Step-by-step explanation:

To find the inverse of the function, you need to (1) swap the places of the "x" and "y" variables and then (2) solve for "y". Remember, f(x) is another way of writing "y".

y = √x + 11                                        <----- Original equation

x = √y + 11                                        <----- Swap variables

x - 11 = √y                                         <----- Subtract 11 from both sides

(x - 11)² = (√y)²                                  <----- Square both sides

(x - 11)² = y                                        <----- Simplify

Another way of writing the output of an inverse function is with f(x)⁻¹.

The probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.9

Standard deviation = 0.2

Calculate the z-score at x = 0.92 using

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

z = (0.92 - 0.9)/0.02

Evaluate the numerator; subtract 0.9 from 0.92

z = 0.02/0.02

Divide 0.02 by 0.02. This gives

z = 1

The probability is then represented as:

P(x > 0.92) = P(z > 1)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.92) = 0.841

Hence, the probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

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All the angles required to complete each sentence are:

In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:

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Answer:

Six Serving Men is a team exercise that examines an issue from twelve different viewpoints. It is based on the words of the poem by Rudyard Kipling: I keep six honest serving men, they taught me all I knew. Their names are What and Why and When and How and Where and Who. To use this technique in a meeting, provide 12 areas for answering questions related to the central topic

Step-by-step explanation: