6 Find the value of x from the following figures.
1)

The answer choice which is correct regarding the two functions is; For any value of x, g(x) will always be greater than h(x).

It follows from the task content that the functions given are; g(x) = x² and h(x) = –x².

On this note, since all values of x return a positive value for g(x) due to the square, it follows that the corresponding value of h(x) is always lesser.

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The angle between the two extreme vectors of Sofia bats is 74.60 degrees.

In this question,

The angle between two vectors will be deferred by a single point, which is called as the shortest angle at which we have to turn around one of the vectors to the position of co-directional with another vector.

The extreme vectors of Sofia bats are  [tex]\vec u = < -8, 12 >[/tex] and [tex]\vec v = < -8, 12 >[/tex]

The angle between the vectors is

[tex]\theta = cos^{-1} \frac{\vec u.\vec v}{||\vec u|| ||\vec v||}[/tex]

The dot product is calculated as

[tex]\vec u. \vec v = (-8)(13)+(12)(15)[/tex]

⇒ [tex]-104+180[/tex]

⇒ 76

The magnitude can be calculated as

[tex]||\vec u|| = \sqrt{(-8 )^{2} +(12)^{2} }[/tex]

⇒ [tex]\sqrt{64+144}[/tex]

⇒ [tex]\sqrt{208}[/tex]

[tex]||\vec v|| = \sqrt{(13 )^{2} +(15)^{2} }[/tex]

⇒ [tex]\sqrt{169+225}[/tex]

⇒ [tex]\sqrt{394}[/tex]

Thus the angle between the vectors is

[tex]\theta = cos^{-1} \frac{76}{(\sqrt{208} )(\sqrt{394} )}[/tex]

⇒ [tex]\theta = cos^{-1} \frac{76}{\sqrt{81952} }[/tex]

⇒ [tex]\theta = cos^{-1} \frac{76}{286.27 }[/tex]

⇒ [tex]\theta = cos^{-1} (0.2654)[/tex]

⇒ [tex]\theta=74.60[/tex]

Hence we can conclude that the angle between the two extreme vectors of Sofia bats is 74.60 degrees.

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Answer:

x=2 and y=-2

Step-by-step explanation:

Solution Given:

6x+2y=8....................................................[1]

12x+y=22....................................................[2]

Multiplying equation in 1 by 2 and subtracting equation 1 by 2 we get

equation 1 becomes 12x+4y=16

and subtracting by equation 2 we get

12x+4y=16

-12x-y=-22[Note: while subtracting we must change sigh)

__________________

0x+3y= -6 [note: while subtracting we must keep the sigh which have greater value]

3y=-6

dividing both side by 3, we get

3y/3=-6/3

we get y=-2

Again similarly

Multiplying equation in 2 by 2 and subtracting equation 2 by 1 we get

equation 2 becomes 24x+2y=44

and subtracting by equation 1 we get

24x+2y=44

-6x-2y=-8

_____________________

18x-0y=36

18x=36

dividing both side by 18, we get

18x/18=36/18

x=2

Answer:2.36

Step-by-step explanation:

The surface area of the sphere is 108.16π in². So, option b is correct.

The surface area of the sphere is calculated by the formula,

A = 4πr²

In terms of diameter - d;

A = 4π × (d/2)²

  = 4π × d²/4

  = πd² sq. inches

The given sphere has a diameter d = 10.4 inches

So, the surface area of the sphere is calculated by

A = πd²

  = π × (10.4)²

  = 108.16 π sq. inches

So, option b is correct.

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Disclaimer: The given question on the portal is incomplete. Here is the complete question.

Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?

a. 432.64π in²

b. 108.16π in²

c. 54.08π in²

d. 216.32π in²

Answer:

Step-by-step explanation:

The surface area of the sphere is 108.16π in². So, option b is correct.

What is the surface area of a sphere?

The surface area of the sphere is calculated by the formula,

A = 4πr²

In terms of diameter - d;

A = 4π × (d/2)²

 = 4π × d²/4

 = πd² sq. inches

Calculation:

The given sphere has a diameter d = 10.4 inches

So, the surface area of the sphere is calculated by

A = πd²

 = π × (10.4)²

 = 108.16 π sq. inches

So, option b is correct.

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Disclaimer: The given question on the portal is incomplete. Here is the complete question.

Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?

a. 432.64π in²

b. 108.16π in²

c. 54.08π in²

d. 216.32π in²

Answer:

y=3x-5

Step-by-step explanation:

they are parallel meaning that only the constant is changing

-2 = 3(1) - (something)

-2 = 3 - (something)

something = 5.   - > that was 3+2

so y=3x+(-5)

Based on the samples that the scientists picked, and the weight of these samples, the various sample means are:

The range of the sample means is 0.4 pounds.

The true statements on the mean weights to be used by the scientists are:

First, find the sample means of each sample.

Sample 1:

= (3 + 2 + 6 + 4 + 2) / 5

= 3.4 pounds

Sample 2:

= (2 + 2 + 3 + 7 + 3) / 5

= 3.4 pounds

Sample 3:

= (6 + 4 + 2 + 2 + 4) / 5

= 3.6 pounds

Sample 4:

= (5 + 3 + 2 + 5 + 4) / 5

= 3.8 pounds

The range is;

= 3.8 - 3.4

= 0.4

The closer the range of the mean is to 0, the better the sample because it shows that in general, the sample means are the same. This is good for the research because it points to the uniformity of fish weights.

Using all the sample means as an average captures the data better than if a single sample mean is used.

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Check the picture below.

well, let's take a peek at the distances of each side.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{[ 4- 0]^2 + [ 3- 0]^2} \\\\\\ ~\hfill AB=\sqrt{25}\implies \boxed{AB=5} \\\\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-3}) ~\hfill BC=\sqrt{[ 4- 4]^2 + [ -3- 3]^2} \\\\\\ ~\hfill BC=\sqrt{36}\implies \boxed{BC=6}[/tex]

[tex]C(\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) ~\hfill CA=\sqrt{[ 0- 4]^2 + [ 0- (-3)]^2} \\\\\\ ~\hfill CA=\sqrt{25}\implies \boxed{CA=5} \\\\\\ \textit{so it's an \underline{isosceles triangle}}[/tex]

Answer:

  50 miles/1 hour = 50 miles/hour

Step-by-step explanation:

The fraction is reduced by dividing numerator and denominator by their common factor of 2.

  100 miles / (2 hours) = 50 miles/ (1 hour) = 50 miles/hour

[tex]\boldsymbol{\sf{3(x-4) > 5x +2 }}[/tex]

Use the distributive property to multiply 3 by x−4.

[tex]\boldsymbol{\sf{3x-12 > 5x+2 }}[/tex]

Subtract 5x on both sides.

[tex]\boldsymbol{\sf{3x-12-5x > 2 } }[/tex]

Combine 3x and −5x to get −2x.

[tex]\boldsymbol{\sf{-2x-12 > 2 }}[/tex]

Add 12 to both sides.

[tex]\boldsymbol{\sf{-2x > 2+12 \ \longmapsto \ \ [Add \ 2 +12]}}[/tex]

[tex]\boldsymbol{\sf{-2x > 14}}[/tex]

Divide both sides by −2. Since −2 is < 0, the inequality direction is changed.

[tex]\boldsymbol{\sf{x < \dfrac{14}{-2} \ \ \longmapsto \ \ \ [Split]}}[/tex]

[tex]\boxed{\boldsymbol{\sf{x < -7 }}}[/tex]

So in the inequality 3(x-4)>5x +2, the value of x is -7.

ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.

According to the statement

we have given some data in the form of graph according to the velocity per time and we have to find the relationship between the velocity and time.

So, for this purpose,

we know that the best method show the relationship is a slope intercept form.

So,

The slope intercept form is a the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

And

Using the coordinate points on the plane (0, 6) and (10, 28)

now we Determine the slope

Slope = 28-6/10-0

Slope = 22/10

Slope = 2.2

And then Determine the y-intercept

6 = 2.2(0) + b

b = 6

And now we have to put in the general form of the slope intercept form which is y = mx + b

Then the equation become

y = 2.2x + 6

So, The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.

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C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.

What is linear regression?

Linear regression analysis is used to predict the value of a variable based on the value of another variable.

The variable you want to predict is called the dependent variable.

The variable you are using to predict the other variable's value is called the independent variable.

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Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.

Therefore, Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.

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The complete question is given below:

If Amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? explain your answer.

A) Company A: Using linear regression models from both data sets, she determines that it pays about $14 more.

B) Company A: Using quadratic regression models from both data sets, she determines that it pays about $5 more.

C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.

D) Company B: Using exponential regression models from both data sets, she determines that it pays about $8 more.

Answer: [tex]\Large\boxed{z=57}[/tex]

Concept:

Here, we need to know how to expand expressions like (a - b)(a + b).

For expressions like (a - b)(a + b), the expanded form must be:

                                                  a² - b²

For checking whether it is true:

 (a - b)(a + b)

= a² - ab + ba - b²

= a² - b²

Solve:

Given equation

[tex](\sqrt{z}+\sqrt{22})(\sqrt{z}-\sqrt22)}=35[/tex]

Expand the parenthesis by the concept

[tex](\sqrt{z})^2-\sqrt{22}^2=35[/tex]

Simplify the exponents

[tex]z-22=35[/tex]

Add 22 on both sides

[tex]z-22+22=35+22[/tex]

[tex]\Large\boxed{z=57}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

A.

alternate exterior

exterior means outside

like a front entrance to a home

1. o & t

2. n & u

B.

alternate interior

interior means inside

like as if its inside a house

1. p & s

2. q & r

( p & s ) AND ( q & r ) both look like the letter Z

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The graph (C) Y represents the function g(x) = (x 1`)2.

To find which of the graphs below represents the function g(x) = (x 1)2:

Parabola: It's a conic section formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements.

Therefore, the graph (C) Y represents the function g(x) = (x 1)2.

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Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm

Perimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)

150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4

150 = 6x + 24

150 - 24 = 6x

126 = 6x

x = 126/6

x = 21

The longest side of the polygon is (x + 8)

= 21 + 8

= 29 cm

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Answer:

Yes

Step-by-step explanation:

The missing angle in triangle DER is 42 (as angles in a triangle add up to 180) and the missing angle in TVA (LOKI lol ) is 110 (as angles in a triangle add up to 180) .

Since all angles are equal the triangles must be similar .

Hope this helped and have a good day

Answer:

7 to 22.96

Step-by-step explanation:

Hello!

We can represent each ratio as a fraction:

To find equivalent values, we can convert each fraction into a decimal by dividing them.

The ratio of 7 to 22.96 is equivalent to the ratio of 15 to 49.2.

Answer:

y = -3x + 1

Step-by-step explanation:

First, we can find the slope of the line.

The slope is (change in y)/(change in x).

We can use the points that are marked in orange: (0,1) and (1,-2)

The change in y is 1 to -2, which is -3.

The change in x is 0 to 2, which is 1.

The slope will be -3/1, which is also: -3.

We have y = -3x + b currently.

The b is the y-intercept, meaning (the point that touches the y axis, the vertical line).

The point (0,1) touches the y-intercept, so b will be 1.

We can finish our equation as: y = -3x + 1

The trigonometric values we require :

[tex]\begin{tabular}{c | l}trigonometric value & numerical value \\\cline{1-2}tan 45^{o}& 1 \\cos 60^{o} & 0.5 \\sin 45^{o} & 1 \div \sqrt{2}\end{tabular}[/tex]

Now, let's solve for x.

tan 45° - cos 60° = x (sin 45°)

[tex]\mathrm {1 - \frac{1}{2} = x (\frac{1}{\sqrt{2}})}[/tex]

[tex]\mathrm {\frac{1}{2} = \frac{x}{\sqrt{2}}}[/tex]

[tex]\mathrm {x = \frac{\sqrt{2}}{2}}[/tex]

[tex]\mathrm {x = \frac{1}{\sqrt{2}}}[/tex]

The value of x is 1/√2.

I hope it helped you solve the problem

Good luck on your studies!

The correct equation says to find R = 32 - 11 (X+2y). This gives us the value of -78.

We have this

R = 32 - 11 (X+2y)

we have the following values for x and y as 2 and 4 respectively.

What we have to do would be to find the value of R after we have put in these values in the equation.

To do this, we would then have:

R = 32 - 11(2 + 2*4)

R = 32 -11(2+8)

R = 32 - 11 * 10

R = 32 - 110

This would give us the value that says

R = -78

Hence the value of R is given as -78

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Answer:

15:7

Step-by-step explanation:

you put the numbers in order first the number of on time trains to off time trains

Answer:

its log 5 7/8

Step-by-step explanation:

Answer:  108 square feet

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

Work Shown:

L = 4 = length

W = 3 = width

H = 6 = height

SA = surface area of the box

SA = 2*(LW + LH + WH)

SA = 2*(4*3 + 4*6 + 3*6)

SA = 108

The differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.

For given question,

we have been given  a differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex]

We have to determine given differential equation is exact or not.

Compare it with M dx + N dy = 0

⇒ M = cos(x) and N = y/x

Find the derivative of M with respect to y.

[tex]\Rightarrow M_y=-sin(x)[/tex]

Now, find the derivative of N with respect to x.

[tex]\Rightarrow N_x=\frac{-y}{x^{2} }[/tex]

Since [tex]M_y \neq N_x[/tex], given differential equation is not exact.

Therefore, the differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.

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Answer:

0.6kg

Step-by-step explanation:

first roses share becomes 2:5

then you change the kilograms into grams for an easier working

then you multiply 2:5 by 1500g to get roses share

Answer:

he will earn 32$ worth of commision

Step-by-step explanation:

so if the commission is 9$ and 9 is 5% of 180$ then commission percentage is 5% so to find how much commission he got selling 640$ worth of phones we just have to find 5% of 640$  which is 32$

Answer:

A 90°

B 90°

C 62°

D 118°

Hopefully this helps u

- 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5. This can be obtained by finding sum separately and then subtracting them.

Here in the question it is given that,

subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5

By separating them as two parts

⇒ sum of -5/6 and -1 3/5  

- 5/6 + - 1 3/5 = - 5/6 + - 8/5  (∵ a b/c = (ac+b)/c(5+3)/5 = 8/5)

                      = (- 25 - 48)/30  (LCM = 30)

                      = - 73/30

⇒ sum of 2 2/3 and -6 2/5

2 2/3 + -6 2/5 = 8/3 + -32/5

                       = (40 - 96)/15  (LCM = 15)

                       = - 56/15

subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5

= (sum of 2 2/3 and -6 2/5) - (sum of -5/6 and -1 3/5)

= (- 56/15) - (- 73/30 )  

= - 56/15 + 73/30

= - 112/30 + 73/30   (LCM = 30)

= - 39/30

= - 13/10

= - 1.3

Hence - 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5.

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Answer:

-20

Step-by-step explanation:

He went back 20 and not forward 20.  Everyone would want a penalty if you got to go forward.