Geometry Homework Question

The linear equation y = 5 · x - 14 is a possible equation that intercepts the line 2 · x + y = 0 at point (x, y) = (2, - 4),

To generate a system of linear equations, we need to derive an additional that intercepts the line 2 · x + y = 0 at point (x, y) = (2, - 4). We need to find an equation of the form:

y = m · x + b

Where:

Please notice that there are more than a single choice. First, choose the slope of the line:

m = 5

Second, substitute the slope and the independent and dependent variables:

b = y - m · x

b = - 4 - 5 · 2

b = - 14

Third, write the resulting linear equation:

y = 5 · x - 14

The linear equation y = 5 · x - 14 is a possible equation of the system of equations.

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a) The hypothesis are given as follows:

b) The significance level is of α = 0.1.

c) The test statistic is of: t = 4.86.

d) The p-value is of: 0.

At the null hypothesis, it is tested if there is not enough evidence that the mean level is greater at the bottom of the surface, that is, if the mean is not positive, hence:

[tex]H_0: \mu_d \leq 0[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean level is greater at the bottom of the surface, that is, if the mean is positive, hence:

[tex]H_1: \mu_d > 0[/tex]

As stated in the problem, the significance level is of:

α = 0.1.

The test statistic is calculated by the formula presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The variables of this formula are listed as follows:

From the table, the sample is composed by the differences and given as follows:

0.015, 0.028, 0.177, 0.121, 0.102, 0.107, 0.019, 0.066, 0.058, 0.121.

The above sample is inserted into a calculator, to obtain the parameter values given as follows:

[tex]\overline{x} = 0.0814, \mu = 0, s = 0.053, n = 10[/tex]

Hence the numeric value of the test statistic is given as follows:

t = (0.0814 - 0)/(0.053/sqrt(10))

t = 4.86.

Using a t-distribution calculator, considering a right-tailed test, as we are testing if the mean is greater than a value, with 10 - 1 = 9 df and t = 4.86, the p-value is of 0.

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10 is the geometric mean between 23 and 4.35.

The geometric mean is a type of average,  generally used for growth rates. Let c is the geometric mean of a and b, then c=[tex]\sqrt{ab}[/tex].

Given that,

The geometric mean of 23 and other value is 10.

Let the other value is x.

Use the geometric mean property,

G.M.=[tex]\sqrt{ab}[/tex]        (1)

Substitute the given values in equation (1)

10=[tex]\sqrt{23x}[/tex]

⇒x=100/23

⇒x=4.347

The geometric mean of 23 and 4.35 is 10.

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The compound inequality is 12 ≤ 6x + 3 ≤ 36. and the solution is 1.5  ≤ x ≤ 5.5

The compound inequality is represented as

12 ≤ A ≤ 36.

Such that

The area of the rectangle is calculated as

A = Product of the sides

So, we have the following representation

A = (2x + 1) * 3

Evaluate

A = 6x + 3

Substitute A = 6x + 3 in 12 ≤ A ≤ 36.

So, we have

12 ≤ 6x + 3 ≤ 36.

In (a), we have

12 ≤ 6x + 3 ≤ 36

This gives

9 ≤ 6x ≤ 33

Divide by 6

1.5  ≤ x ≤ 5.5

So, the result is 1.5  ≤ x ≤ 5.5

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Answer:

7.5 feet

Step-by-step explanation:

We can use the Pythagorean therom

x=square root of 15^2-13^2

x= square root of 225-169

x=square root of 56

x=7.5

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The equation that can be use to find the total cost y in dollars for x sheets of sticker is y = 2.55x.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, it should be noted that a proportional relationship exist between the figures that are given.

Therefore, the constant will be:

= Cost / Number of sheet

= 12.75 / 5

= 2.55

Therefore, the equation is y = 2.55x

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Vertical asymptotes is x = -4 and horizontal asymptote is y = 1

What is an Asymptote?

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote.

There are 3 types of asymptotes.

The given expression,

f(x) = (x² - 3x) / (x² + x - 12)

First, find Horizontal asymptote

so,

Horizontal asymptote (y) = (leading coefficient of numerator) / (leading coefficient of denominator)

leading coefficient of numerator = 1

leading coefficient of denominator = 1

y = 1/1

y =1 (Horizontal asymptote)

Now, find Vertical asymptote

so, let's simplify the expression f(x) = (x² - 3x) / (x + x - 12)

f(x) = (x(x - 3) ) / (x² + 4x - 3x - 12)

f(x) = (x(x - 3) ) / (x(x + 4) - 3 (x + 4) )

f(x) = (x(x - 3) ) / ( (x -3) (x + 4) )

f(x) = x / (x + 4)

Now, put the denominator = 0

x + 4 = 0

x = -4 ( Vertical asymptote )

Hence, Vertical asymptotes is x = -4 and horizontal asymptote is y = 1

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Answer:

x+4x=25

A: 0<x<=25 0<y<=75

Step-by-step explanation:

The equation of straight line plotted on the graph are all attached below

The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry. The equation of a straight line can be written in different forms such as point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a two-dimensional geometrical entity that extends on both its ends till infinity.

For straight line graphs there is a linear relationship between the x and y values and so the line is straight and must be drawn with a ruler. The gradient determines how steep the line is and the y-intercept tells us the location where the straight line intersects the y-axis.

Linear means straight and a graph is a diagram which shows a connection or relation between two or more quantity. So, the linear graph is nothing but a straight line or straight graph which is drawn on a plane connecting the points on x and y coordinates.

Question 1;

The point is (-2, 5) and it has a slope of 2/3

We can find the y-intercept of the graph and then plot it's coordinate.

y = mx + c

5 = 2/3(-2) + c

c =19/3

The equation of the line is y = 2/3x + 19/3 or 3y = 2x + 19

We can proceed to use a graphing calculator to plot this.

Question 2;

The two given which the line pass across are (-2, -1) and (-3, 3)

Using a graphing calculator, the graph is attached below.

Question 3;

The equation 4x - 5y = 20 can be plotted as a straight line graph which is attached below.

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The set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers is given as below as

Cars, Are cars up to date, Select the car to check, Stopped cars, Convenience sampling ,The cars that are not stopped might be having more problems

Given that,

The Population

The Population parameter of interest

The Sampling frame

The Sample

The Sampling Method, Including whether or not randomization was employed.

Any potential source of bias you can detect any problems you see in generalizing to the population of interest.

To find : The set up a roadblock

A. Cars

B. Are cars up to date

C. Select the car to check

D. Stopped cars

E. Convenience sampling

F. The cars that are not stopped might be having more problems

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The statistics z is -1.878 and the p value is 0.0302

Given,

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Estimated proportion of return rate;

p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

That is,

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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Answer:

-1

Step-by-step explanation:

Jada = 12 books

Han = 13 less books than Jada

12-13= -1

Han would have negative 1 books but in this situation it would not be possible.

The length of the wallpaper of 27 inches wide required is  35.56 feet

The problem requires conversion of the dimensions to have similar unit

To convert 80 square feet to square inches. we multiply by 144

80 * 144 = 11520 square inches

area = length * wide

11520 = length * 27

length = 11520 / 27

length = 426.667 feet

to get the length in inches we divide the unit in feet by 12

length = 426.667 inches / 12

length = 35.56 feet

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For the given measurement of the congruent triangles RWS and TUV, the value of x = 4° and y = 10 units.

As given in the question,

For the given congruent triangles,

ΔRWS ≅ ΔTUV

⇒ RWS ↔ TUV

⇒RW ≅TU , RS ≅TV , WS ≅ UV

And ∠W ≅ ∠U , ∠R ≅ ∠T , ∠S ≅ ∠V

Given measurements are :

m ∠W = 90°

m ∠R = ( 8x + 26)°

m ∠V = 32°

∠S ≅ ∠V

⇒ m ∠S = 32°

m ( ∠R + ∠W + ∠S ) = 180°

⇒ 8x° + 26° + 90° + 32° = 180°

⇒8x° = 180° -148°

⇒ x° = 32°/8

⇒ x= 4°

RS ≅TV

⇒30 = 2y + 10

⇒2y = 20

⇒y= 10 units

Therefore, for the given measurement of the congruent triangles RWS and TUV, the value of x = 4° and y = 10 units.

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Answer:

The answer to this question is undefined or c

Step-by-step explanation:

A horizontal line has a slope of 0 because it does not go vertically and a vertical line has a slope of undefined because it does not go horizontally

The trigonometric function use to solve the angle x in the right triangles are as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The side and angles of a right angle triangle can be found using trigonometric ratios.

Therefore, the trigonometric function that can be use to find the angle x in the triangles are as follows:

Triangle PNM

sin x = opposite / hypotenuse

sin x = 6 / 10

sin x = 3 / 5

Triangle ABC

cos x = adjacent / hypotenuse

cos x = 5 / 10

cos x = 1 / 2

Triangle DEF

tan x = opposite / adjacent

tan x = 4 / 6

tan x = 2 / 3

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For given inequality 2y-x>1 point (-7,-3) is not the solution set of given inequality.

Inequality:

               Inequalities are mathematical sentences formed by relating two expressions to each other.

Different inequality sign are:

            x>y ,

                  x is greater than y

           x≥y

                x is greater than or equal to y

           x<y

                 x is less than y

          x≤y

                 x is less than or equal to y

Given inequality is,

             2y - x > 1

In the given inequality

       L.H.S (Left hand Side) = 2y - x

       R.H.S (Right Hand Side) = 1

and the given point is (-7,-3)

Left hand Side at point (-7,-3)

L.H.S  = 2y - x

          = 2 (-3) - (-7)

          = -6 + 7

          = 1

and

       Right Hand Side = 1

Here we can see both L.H.S and R.H.S are equal,but in the given inequality there is no equality,so the point (-7,-3) is not the solution set.

Thus we conclude,

                            (-7,-3) is not the solution set of given inequality.

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Answer: In one serving of Sarah's dish 0.05 more cheese than in one serving of Amyn's dish.

Given: Sarah used cups of cheese in a dish that serves people and  Amyn used cups of cheese in a dish that serves people.

Now, the amount of cheese served by Sarah for a people is.

And the amount of cheese served by Amyn for a people is

Therefore, the difference between the amount of cheese served by Sarah and Amyn is calculated as

Cheese served by Sarah's in one serving  cheese served by Amyn's in one serving              

Hence, 0.05 more cheese is in one serving of Sarah's dish.

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Step-by-step explanation:

There will be 0.84% chances that resulting sequence in cat to occur.

Total number of nucleotides floating around = 10

Let the event of picking cat be "A"

Number of cat in group = 3

Probability of picking cat is picked at first position = P(A1) = 3 / 10

= 0.3

Probability of picking cat is picked at second position = P(A2) =  2 / 9

= 0.223

Probability of picking cat is picked at third position = P(A3) = 1 / 8

= 0.125

so , probability of picking cat in first position and again in second position and again in third position will be = P(A1) . P(A2) . P(A3)

= 0.3 × 0.223 × 0.125

= 0.0084 required probability

There will be 0.84% chances that resulting sequence in cat

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There are 2940 no votes.

From the question, we have

there were 8085 total votes

ratio= 7 :4

No votes = 4/11*8085

=2940

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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Answer: (9t + 10)(t - 2)

Step-by-step explanation:

9t (t − 2) + 10(t − 2)

9t^2 − 8t − 20

= (9t + 10)(t − 2)

Answer:

It is C

Step-by-step explanation:

Answer:

a x=10

b x=7

Step-by-step explanation:

(a) 2(x+3) = x  -  4

    2x+6 = x - 4

    2x+6-6= x-4-6

    2x=x-10

     2x-x=x-10-x

    x=10

(b) 4(5x-2) = 2(9x+3)

     20x-8  =18x+6

     20x-8+8=18x+6+8

     20x=18x+14

     20x-18x =18x+14-18x
     2x=14

      /2  /2

     x = 7.

The coordinates of figure and the coordinates of the image after rotation is as below

preimage        image

J(-4,1)               J' (1, 4)

K(-2,1)              K' (1, 2)

L(-4,-3)             L' (-3, 4)

Rotation is one the movements involve in transformation

In rotation, the objects moves about an axis in a circular direction

The transformation rule for 90 degrees clockwise rotation is

(x, y) → (y -x)

applying the rule gives the new coordinates of the image as

Image

J' (1, 4)

K' (1, 2)

L' (-3, 4)

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There are a couple ways to solve this but I will show you the way I think is easiest:

You should make the fraction parts of the numbers have an equivalent denominator. Right now, the denominators are 10 and 5. It would be best to make both denominators equal 10.

In - 2 [tex]\frac{3}{5}[/tex],  3/5 x 2 = 6/10

So now the fractions are [tex]-10\frac{7}{10} - 2[/tex][tex]\frac{6}{10}[/tex]

Remember the sign rules!

The answer is - 13[tex]\frac{3}{10}[/tex]

I hope this helps!

Answer:

     [tex]-\frac{133}{10}[/tex]

Step-by-step explanation:

[tex]-10\frac{7}{10}[/tex] = [tex]-\frac{107}{10}[/tex]               (10x(-10)+7)

[tex]-2\frac{3}{5}[/tex] = [tex]-\frac{13}{5}[/tex]                   (5x(-2)+3)

lcm of 10 and 5 is 10:

[tex]-\frac{107}{10} -\frac{13}{5}[/tex]

[tex]\frac{-107-26}{10}[/tex]

[tex]-\frac{133}{10}[/tex]

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