Find the value of x

The point-slope form of the equations of the line are listed below:

Case 1: y - 4 = 2 · (x + 2)

Case 2: y - 1 = - 3 · (x - 2)

Case 3: y + 1 = - (x + 4)

Case 4: y + 2 = 5 · (x - 4)

In this problem we must derive the point-slope form of the equation of the line for each of four cases described in statement. This form is introduced below:

y - k = m · (x - h)

Where:

Now we proceed to determine the resulting expression for each case:

Case 1

y - 4 = 2 · (x + 2)

Case 2

y - 1 = - 3 · (x - 2)

Case 3

y + 1 = - (x + 4)

Case 4

y + 2 = 5 · (x - 4)

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Answer:

[tex]\frac{6}{x+1}[/tex]

Step-by-step explanation:

I learned this like a month ago so I have notes abt it if you don't understand how it works. Just lmk if you need them

The equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

We can use the point-slope version of the equation, which is: to determine the equation of a line passing through two specified points.

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

Use the points (1,6) and (2,7) to find the equation of the line:

Using (x₁, y₁) = (1,6):

y - 6 = m(x - 1)

Now, substitute the coordinates (2,7) into the equation:

7 - 6 = m(2 - 1)

1 = m

So, the slope of the line is m = 1.

Substitute this value into the equation:

y - 6 = 1(x - 1)

y - 6 = x - 1

y = x + 5

Therefore, the equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

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The volume of the cylinder with the same radius and double the height is 2πx²h in³.

To find the volume of a cylinder, we use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, we are given a cylinder with a certain radius and height, and we need to find the volume of another cylinder with the same radius but double the height.

Let's assume the radius of the cylinder is x, and the original height is h.

The volume of the original cylinder is V = πx²h.

Now, we need to find the volume of the cylinder with the same radius (x) but double the height (2h).

The volume of this cylinder is V' = πx²(2h) = 2πx²h.

So, the volume of the second cylinder is twice the volume of the first cylinder.

Therefore, the volume of the second cylinder is 2 times the volume of the first cylinder, which can be expressed as 2V = 2πx²h.

Therefore, the volume of the cylinder with the same radius and double the height is 2πx²h in³.

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To estimate the total distance traveled by the car in those 36 seconds, we can use the trapezium rule to approximate the area under the curve.

From the graph, we can see that the car's speed is constant between 0 and 30 seconds, and then it starts to decrease. Therefore, we can use a single trapezium to estimate the area under the curve for the first part.

The base of the trapezium is 30 seconds, and the height is the average of the speeds at 0 and 30 seconds. Let's denote the speed at 0 seconds as v0 and the speed at 30 seconds as v30.

The distance traveled in the first part can be estimated as:

Distance = 30 * (v0 + v30) / 2

To get a more accurate estimate, we need the specific values of v0 and v30 from the graph. Please provide the corresponding speed values for 0 and 30 seconds, and I can help you calculate the estimated distance.

Answer: 7.8

Step-by-step explanation: Identify the triangle as a 45-45-90 triangle.

Recognize that the sides of a 45-45-90 triangle are in a ratio of 1:1:√2.

Find the length of the hypotenuse of the triangle. In this case, the hypotenuse is 11 units.

Divide the length of the hypotenuse by √2 to find the length of the side opposite the 45-degree angle. In this case, the length of side x is 11/√2 = 7.77 units.

Round the length of side x to the nearest tenth. In this case, the length of side x is 7.8 units.

Answer:

= 10.4

Step-by-step explanation:

Here given is the right-angled triangle

For angle: = 60º

Perpendicular: = 9

Hypotenuse: =

Now using the trigonometry formula:

  = /

sin 60º = 9/

3√2 = 9/

= 18/3√

= 10.4(rounded to the nearest tenth)

Therefore required length is = 10.4

Answer:

True, True, False

Step-by-step explanation:

1. 8 ≥ 5-1 Is correct

2. 8 ≥ 5-4 is correct

3. 8 ≥ 5-(-4) is not correct

Answer:

x = 1 makes the inequality true

x = 4 makes the inequality true

x = -4 makes the inequality false

Step-by-step explanation:

We can determine whether x = 1, x = 4, and x = -4 makes the inequality by plugging in 1, 4, and -4 for x and seeing whether the inequality still holds true:

Step 1:  Plugging in 1 for x:

8 ≥ 5 - 1

8 ≥ 4

Because 8 is greater than 4, x = 1 makes the inequality true.

Step 2:  Plugging in 4 for x:

8 ≥ 5 - 4

8 ≥ 1

Because 8 is also greater than 4, x = 4 also makes the inequality true.

Step 3:  Plugging in -4 for x:

8 ≥ 5 - (-4)

8 ≥ 5 + 4

8 ≥ 9

Because 8 is not less than 9, x = -4 makes the inequality false

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2496\\ P=\textit{original amount deposited}\dotfill & \pounds1600\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2496 = 1600[1+(0.08)(t)]\implies \cfrac{2496}{1600}=1+0.08t\implies \cfrac{39}{25}=1+0.08t \\\\\\ \cfrac{39}{25}-1=0.08t \implies \cfrac{14}{25}=0.08t\implies \cfrac{14}{25(0.08)}=t\implies 7=t[/tex]

Answer:

  (b)  $2109.85

Step-by-step explanation:

You want the monthly loan payment on a 15-year loan for a home with a $284,500 purchase price if 20% is put down, and the borrower's credit score is 700.

The table tells you that a 15-year loan for a borrower with a 700 credit score will have a monthly payment of $9.27 per thousand dollars of loan value.

The loan will be for the 80% of the home value that is not already paid by the down payment. In thousands of dollars, that is 284.5 × 0.80.

The monthly payment is the product of the loan value (in thousands) and the payment multiplier:

  $284.5 × 0.80 × 9.27 = $2109.85

The monthly payment is $2109.85.

__

Additional comment

The higher loan cost for a borrower with a low credit score is effectively saying the lender is presuming about 12% of loans to such borrowers will be in default.

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answer Each person will get 1/8 of a cake.

Step-by-step explanation: 1/2 Divided by 4= 4 = 1 = 1 x 1 = 1 4 2 x 4 = 8

The binary predicate refers to the membership relation denoted by the symbol "€" (read as "belongs to" or "is an element of").

We have,

The binary predicate is a binary relation because it takes two arguments: an element and a set.

The predicate evaluates to true if the element is a member of the set, and false otherwise.

The binary predicate € is used to establish the membership relationship between elements and sets in set theory.

For example, if we have a set A and an element x, we can write "x € A" to indicate that x is an element of A.

The use of a binary predicate in set theory allows for the formulation of statements and properties involving membership.

It enables us to define sets, make assertions about their elements, and perform operations such as union, intersection, and complement.

Thus,

The binary predicate € forms an essential part of the language and logic of set theory.

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The Probability of rolling a number less than 3 on a regular 6-sided die is 1/3 or approximately 0.333.

The probability of rolling a number less than 3 on a regular 6-sided die, we need to determine the number of favorable outcomes and the total number of possible outcomes.

The favorable outcomes are the numbers that meet the condition of being less than 3. In this case, the favorable outcomes are the numbers 1 and 2.

The total number of possible outcomes is the total number of sides on the die, which is 6.

Therefore, the probability of rolling a number less than 3 can be calculated as:

Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)

Probability = 2 / 6

Simplifying the fraction, we have:

Probability = 1 / 3

So, the probability of rolling a number less than 3 on a regular 6-sided die is 1/3 or approximately 0.333.

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Step-by-step explanation:

Well, this includes subtraction.

11-1 1/2=11-3/2=22/2-3/2=19/2

So it was 19/2 Inches longer

The scale statement for the photograph is :

"The photograph is magnified by a factor of 200."

A scale statement is described as  a ratio of the length of the drawing or model to the length of the actual object which can be represented in these three way.

If the photograph of a strand of human hair shows the hair magnified by a factor of 200, we can write the statement as  photograph is magnified by a factor of 200.

In order to solve a scale factor, we do the following:

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Answer:

6 inches

Step-by-step explanation:

Volume= Length*Width*Height

720=15*8*H

720=120H

H=6

Answer:

8[tex]\sqrt[3]{2}[/tex]

Step-by-step explanation:

The cube root of -2 to the power of 10 is;

(-2)^10=2^10

2^10=(2^3)*(2^3)*(2^3)*2

You can factor out 2^3=8 of the cube root

So you get 8 times the cube root of 2

The coordinates of the focus obtained from the vertex form of the equation of the parabola is; (h, v) = (2, -7/4)

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

The points on the parabola are;

(3, -1), and (2, -2)

The vertex of the parabola is; (2, -2)

Therefore, we get;

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex, therefore;

y = a·(x - 2)² - 2

y + 2 = a·(x - 2)²

The point (3, -1), indicates that we get;

-1 + 2 = a·(3 - 2)²

(-1 + 2)/((3 - 2)²) = 1 = a

The equation of the parabola in focus form is; (x - h)² = 4·p·(y - k)

Therefore; (x - 2)² = 4·p·(y + k)

We get; (x - 2)² = (y + k)

(x - 2)²/(4·p) = y + k

(4·p) = a = 1

p = 1/4

The y-coordinates of the focus, v = -2 + 1/4 = -1 3/4 = -7/4

The coordinates of the focus, (h, v) is therefore;

(h, v) = (2, -7/4)

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Turn me into a superhero

The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.

The set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.

The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.

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Answer:

  D.  62 points

Step-by-step explanation:

You want to know the improvement in credit score needed so that Josua can borrow $150,000 with payments less than $14000 per year.

Josua can afford 12 monthly payments of $14,000/12 = $1166.67. According to the rate table, the monthly payment will be less than this amount if Josua has a credit score of 560 or better. With a score of 560, his payment would be $1157.

To get his score up to 560, he needs to improve it by ...

  560 -498 = 62 . . . . points

He would need to improve his credit by 62 points.

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Based on the information provided, we have an angle labeled as (4x-10)° and another angle labeled as K. It seems like we need to determine the relationship between these angles and find the value of x.

To determine the relationship between the angles, we need more context or information about the specific geometric configuration or properties mentioned in the task card. Without additional information, it is not possible to determine the relationship between (4x-10)° and K.

If you can provide further details or a description of the geometric setup or any additional instructions related to the angle relationship, I'll be glad to help you further.

The domain of the function graphed in this problem is given as follows:

a) [-3,0].

The values of x from the graph are given as follows:

Hence the domain of the function is given as follows:

[-3, 0].

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Based on the paired difference test conducted at a significance level of α = 0.05, there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the two sets of paired data.

In this paired difference experiment, we have the following data: D₁ = 6, D₂ = 10, D₃ = -3, D₄ = 5, D₅ = 7.

Our objective is to determine if there is a significant difference between the two sets of paired data.

To begin the paired difference test, we state the null hypothesis (H₀) and the alternative hypothesis (H₁).

The null hypothesis assumes that the mean difference between the paired data is equal to zero (µd = 0), while the alternative hypothesis suggests that the mean difference is not equal to zero (µd ≠ 0).

Next, we calculate the mean difference (¯d) by summing the differences and dividing by the number of pairs.

In this case, ¯d = (6 + 10 - 3 + 5 + 7) / 5 = 5.

To assess the variability in the data, we calculate the standard deviation of the differences (sᵈ).

This involves computing the sum of squared differences (SSᵈ) by squaring each difference and summing them.

Dividing SSᵈ by the number of pairs minus 1 (n-1), we then take the square root to obtain sᵈ.

With the mean difference (¯d) and standard deviation (sᵈ) calculated, we can determine the test statistic (t) using the formula t = ¯d / (sᵈ / √n), where n is the number of pairs.

Substituting the values, we compute the test statistic.

Next, we identify the degrees of freedom (df) for the test, which is equal to the number of pairs minus 1 (n-1).

Using the significance level α = 0.05, we consult a t-table or use statistical software to find the critical value for the rejection region.

By comparing the absolute value of the test statistic (t) to the critical value, we make a decision to either reject the null hypothesis if t falls within the rejection region or fail to reject the null hypothesis if it does not.

Finally, we state the final conclusion based on our decision.

If we reject the null hypothesis, we conclude that there is a significant difference between the two sets of paired data.

On the other hand, if we fail to reject the null hypothesis, we conclude that there is insufficient evidence to suggest a significant difference.

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The complete question may be like:

A paired difference experiment produced the following results: D₁ = 6, D₂ = 10, D₃ = -3, D₄ = 5, D₅ = 7. Conduct a paired difference test to determine if there is a significant difference between the two sets of paired data. Use a significance level of α = 0.05.

Context: The paired difference experiment involves measuring a variable of interest on two related subjects or under two different conditions. The goal is to determine if there is a significant difference between the two sets of measurements.

The graph of the function 25x² + 9y² - 108x - 54y - 44  is added as an attachment

From the question, we have the following parameters that can be used in our computation:

25x² + 9y² - 108x - 54y - 44

The above function is the equation of an ellipse that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

[tex]\huge\boxed{\sf (4q - 1)\²}[/tex]

Step-by-step explanation:

= 16q² - 8q + 1

We can also write it as:

= (4q)² - 2(4q)(1) + (1)²

a² - 2ab + b² = (a - b)²

So, the above expression becomes:

[tex]\rule[225]{225}{2}[/tex]

The vector shown in component form is (-4, -3)

We have to find the vector which is shown in the component form

To find this vector we have to find the difference of tail and head

Tail has coordinates (1, 2)

Head has coordinates (-3, -1)

We have to subtract  (-3, -1) from (1, 2)

(-3, -1)-(1,2)

We have to do this by subtracting x coordinates and y coordinates

(-3-1, -1-2)

(-4, -3)

Hence, (-4, -3) is the vector shown in component form

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Answer:  it would take the cyclist 8.5 hours to travel 153 miles.

Step-by-step explanation: We can use proportions to solve this problem.

Let's define:

x = the time it would take for the cyclist to travel 153 miles.

Using proportions, we can set up the following equation:

45 miles / 2.5 hours = 153 miles / x

We can then cross-multiply and solve for x:

45 * x = 2.5 * 153

45x = 382.5

x = 382.5 / 45

x = 8.5

Answer:

                                                                      250

                                                                     /       \

                                                   126            124

                                                           \        /     \

                 102                      24                87       57

                /     \                 /     \       /     \

             100     6          22     2          40     17

            /     /   \       /     /   \       /     /   \

         95     0     5      22     0      20     0      37

The frequency tree shows that 126 people arrived late, and 102 of them travelled by train. This means that 24 people arrived late and travelled by bus. There were a total of 250 people who attended the conference, so 124 people arrived on time. Of the people who arrived on time, 87 travelled by bus and 57 travelled by train.

Answer:

Step-by-step explanation:

Answer:

906.89 in²

Step-by-step explanation:

A regular dodecagon is a specific type of 12-sided polygon where all sides and angles are equal.

The formula for the area of a regular polygon is:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

We know that the number of sides is 12 and that the length of one side is 9 inches, so in order to calculate the area, we first need to find the apothem.

The formula for the apothem of a regular polygon is:

[tex]\boxed{\begin{minipage}{6cm}\underline{Length of apothem}\\\\$a=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $a$ is the apothem.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Substitute s = 9 and n = 12 into the apothem formula, and solve for a:

[tex]a=\dfrac{9}{2 \tan\left(\frac{180^{\circ}}{12}\right)}[/tex]

[tex]a=\dfrac{9}{2 \tan\left(15^{\circ}\right)}[/tex]

[tex]a=\dfrac{9}{2 \left(2-\sqrt{3}\right)}[/tex]

[tex]a=\dfrac{9}{4-2\sqrt{3}}[/tex]

[tex]a=\dfrac{9}{4-2\sqrt{3}}\cdot \dfrac{4+2\sqrt{3}}{4+2\sqrt{3}}[/tex]

[tex]a=\dfrac{36+18\sqrt{3}}{4}[/tex]

[tex]a=\dfrac{18+9\sqrt{3}}{2}[/tex]

Now we have calculated the apothem, substitute this along with n = 12 and s = 9 into the area of a polygon formula

[tex]A=\dfrac{n \cdot s \cdot a}{2}[/tex]

[tex]A=\dfrac{12 \cdot 9 \cdot \frac{18+9\sqrt{3}}{2}}{2}[/tex]

[tex]A=\dfrac{108 \cdot \frac{18+9\sqrt{3}}{2}}{2}[/tex]

[tex]A=54 \cdot \dfrac{18+9\sqrt{3}}{2}}[/tex]

[tex]A=27\cdot (18+9\sqrt{3}})[/tex]

[tex]A=486+243\sqrt{3}[/tex]

[tex]A=906.89\; \sf in^2\;(nearest\;hundredth)[/tex]

Therefore, the area of a regular dodecagon with a side length of 9 inches is 906.89 in² (nearest hundredth).

Note: Please see the attached image for confirmation of the area using a graphic calculator.

The weight of the liquid can be found by multiplying its volume by its density. The volume will be that of a hemisphere, which can be found using the appropriate formula.

The volume of a hemisphere with radius r is given by ...

 [tex]\sf V = \huge \text(\dfrac{2\pi}{3}\huge \text)r^3[/tex]

When the radius is 4 ft, the volume is ...

 [tex]\sf V = \huge \text(\dfrac{2\pi}{3}\huge \text)(4 \ ft)^3 = \dfrac{128\pi }{3} \ ft^3[/tex]

The weight of the liquid in the tank is found using the density.

 [tex]\sf W = \rho V[/tex]

 [tex]\sf W = (75 \ lb/ft^3)\huge \text(\dfrac{128\pi}{3} \ ft^3\huge \text) = 3200\pi \ lb \thickapprox 10,053 \ lb[/tex]

The total weight of the liquid in the tank is about 10,053 pounds.